Finite Group Databasebeta

← #21438397

Subgroups — #21438397

Order 7552.

1160 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838149C211yesmaximal, characteristic, complemented
2#16838148C211yesmaximal, characteristic, complemented
3#16838141C211yesmaximal, characteristic, complemented
4#16838140C211yesmaximal, characteristic, complemented
5#16838114C211yesmaximal, characteristic, complemented
6#16838101C211yesmaximal, characteristic, complemented
7#16838089C211yesmaximal, characteristic, complemented
8#16838081C211yesmaximal, characteristic, complemented
9#16838078C211yesmaximal, characteristic, complemented
10#16838070C211yesmaximal, characteristic, complemented
11#16838051C211yesmaximal, characteristic, complemented
12#16838042C211yesmaximal, characteristic, complemented
13#16838041C211yesmaximal, characteristic, complemented
14#16838039C211yesmaximal, characteristic, complemented
15D4×C22⋊D59C211yesmaximal, characteristic, complemented
16#16838022C211yesmaximal, characteristic, complemented
17#16838004C211yesmaximal, characteristic, complemented
18#16838003C211yesmaximal, characteristic, complemented
19#16838002C211yesmaximal, characteristic, complemented
20#16837990C211yesmaximal, characteristic, complemented
21#16837986C211yesmaximal, characteristic, complemented
22#16837979C211yesmaximal, characteristic, complemented
23#16837967C211yesmaximal, characteristic, complemented
24#16837967C211yesmaximal, characteristic, complemented
25#16837966C211yesmaximal, characteristic, complemented
26#16837963C211yesmaximal, characteristic, complemented
27#16837961C211yesmaximal, characteristic, complemented
28#16837912C211yesmaximal, characteristic, complemented
29#16837911C211yesmaximal, characteristic, complemented
30C2×#14273700C211yesmaximal, characteristic, complemented
31C59×#546C211yesmaximal, characteristic, complemented
32C2×#11745685C2211yescharacteristic, complemented
33C2×#11745687C2211yescharacteristic, complemented
34C2×#11745687C2211yescharacteristic, complemented
35C2×#11745687C2211yescharacteristic, complemented
36C22×D236C2211yescharacteristic, complemented
37C22×C22⋊D59C2211yescharacteristic
38C22×C22⋊D59C2211yescharacteristic, complemented
39C22×C22⋊D59C2211yescharacteristic, complemented
40C2×D4×D59C2211yescharacteristic
41C22×C4×D59C2211yescharacteristic, complemented
42#14273725C2211yescharacteristic, complemented
43#14273723C2211yescharacteristic, complemented
44#14273723C2211yescharacteristic, complemented
45#14273723C2211yescharacteristic, complemented
46#14273723C2211yescharacteristic, complemented
47#14273723C2211yescharacteristic, complemented
48#14273722C2211yescharacteristic, complemented
49#14273721C2211yescharacteristic, complemented
50#14273720C2211yescharacteristic, complemented
51#14273720C2211yescharacteristic, complemented
52#14273720C2211yescharacteristic, complemented
53#14273720C2211yescharacteristic, complemented
54#14273718C2211yescharacteristic, complemented
55#14273717C2211yescharacteristic, complemented
56#14273717C2211yescharacteristic, complemented
57#14273716C2211yescharacteristic, complemented
58#14273716C2211yescharacteristic, complemented
59#14273713C2211yescharacteristic, complemented
60#14273713C2211yescharacteristic, complemented
61#14273713C2211yescharacteristic, complemented
62#14273713C2211yescharacteristic, complemented
63#14273713C2211yescharacteristic, complemented
64#14273713C2211yescharacteristic, complemented
65#14273712C2211yescharacteristic, complemented
66#14273712C2211yescharacteristic, complemented
67#14273712C2211yescharacteristic, complemented
68#14273712C2211yescharacteristic, complemented
69#14273711C2211yescharacteristic, complemented
70#14273711C2211yescharacteristic, complemented
71#14273710C2211yescharacteristic, complemented
72#14273710C2211yescharacteristic, complemented
73#14273710C2211yescharacteristic, complemented
74#14273710C2211yescharacteristic, complemented
75#14273710C2211yescharacteristic, complemented
76#14273709C2211yescharacteristic, complemented
77#14273709C2211yescharacteristic, complemented
78#14273709C2211yescharacteristic, complemented
79#14273709C2211yescharacteristic, complemented
80#14273709C2211yescharacteristic, complemented
81#14273709C2211yescharacteristic, complemented
82#14273708C2211yescharacteristic
83#14273708C2211yescharacteristic, complemented
84#14273708C2211yescharacteristic, complemented
85#14273707C2211yescharacteristic, complemented
86#14273706C2211yescharacteristic, complemented
87#14273706C2211yescharacteristic, complemented
88#14273705C2211yescharacteristic, complemented
89#14273705C2211yescharacteristic, complemented
90#14273705C2211yescharacteristic, complemented
91#14273704C2211yescharacteristic, complemented
92#14273704C2211yescharacteristic, complemented
93#14273704C2211yescharacteristic, complemented
94#14273703C2211yescharacteristic, complemented
95#14273702C2211yescharacteristic, complemented
96#14273702C2211yescharacteristic, complemented
97#14273701C2211yescharacteristic, complemented
98#14273701C2211yescharacteristic, complemented
99#14273701C2211yescharacteristic, complemented
100#14273701C2211yescharacteristic, complemented
101#14273701C2211yescharacteristic, complemented
102#14273700C2211yescharacteristic
103#14273700C2211yescharacteristic
104#14273700C2211yescharacteristic, complemented
105#14273700C2211yescharacteristic, complemented
106#14273700C2211yescharacteristic, complemented
107#14273700C2211yescharacteristic, complemented
108#14273700C2211yescharacteristic, complemented
109#14273700C2211yescharacteristic, complemented
110#14273700C2211yescharacteristic, complemented
111#14273700C2211yescharacteristic, complemented
112#14273700C2211yescharacteristic, complemented
113#14273700C2211yescharacteristic, complemented
114#14273700C2211yescharacteristic, complemented
115#14273700C2211yescharacteristic, complemented
116#14273699C2211yescharacteristic
117#14273699C2211yescharacteristic, complemented
118#14273699C2211yescharacteristic, complemented
119#14273699C2211yescharacteristic, complemented
120#14273699C2211yescharacteristic, complemented
121#14273699C2211yescharacteristic, complemented
122#14273699C2211yescharacteristic, complemented
123#14273699C2211yescharacteristic, complemented
124#14273699C2211yescharacteristic, complemented
125#14273699C2211yescharacteristic, complemented
126#14273699C2211yescharacteristic, complemented
127#14273699C2211yescharacteristic, complemented
128#14273698C2211yescharacteristic, complemented
129#14273698C2211yescharacteristic, complemented
130#14273698C2211yescharacteristic, complemented
131#14273697C2211yescharacteristic, complemented
132#14273697C2211yescharacteristic, complemented
133#14273697C2211yescharacteristic, complemented
134#14273696C2211yescharacteristic
135#14273696C2211yescharacteristic, complemented
136#14273696C2211yescharacteristic, complemented
137#14273696C2211yescharacteristic, complemented
138#14273695C2211yescharacteristic
139#14273695C2211yescharacteristic
140#14273695C2211yescharacteristic, complemented
141#14273695C2211yescharacteristic, complemented
142#14273695C2211yescharacteristic, complemented
143#14273695C2211yescharacteristic, complemented
144#14273695C2211yescharacteristic, complemented
145#14273692C2211yescharacteristic, complemented
146C4×D236C2211yescharacteristic, complemented
147D4×Dic59C2211yescharacteristic
148D4×Dic59C2211yescharacteristic, complemented
149C4×C22⋊D59C2211yescharacteristic, complemented
150C4×C22⋊D59C2211yescharacteristic, complemented
151C4×C22⋊D59C2211yescharacteristic, complemented
152C4×C22⋊D59C2211yescharacteristic, complemented
153C4×C22⋊D59C2211yescharacteristic, complemented
154(C22⋊D59)⋊C4C2211yescharacteristic, complemented
155(C22⋊D59)⋊C4C2211yescharacteristic, complemented
156(C22⋊D59)⋊C4C2211yescharacteristic, complemented
157(C22⋊D59)⋊C4C2211yescharacteristic, complemented
158(C22⋊D59)⋊C4C2211yescharacteristic, complemented
159#14273686C2211yescharacteristic, complemented
160#14273685C2211yescharacteristic, complemented
161#14273684C2211yescharacteristic, complemented
162#14273684C2211yescharacteristic, complemented
163#14273683C2211yescharacteristic, complemented
164#14273683C2211yescharacteristic, complemented
165#14273683C2211yescharacteristic, complemented
166C2×Dic59⋊C4C2211yescharacteristic, complemented
167C2×Dic59⋊C4C2211yescharacteristic, complemented
168C2×C22⋊Dic59C2211yescharacteristic, complemented
169C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
170C22⋊C4×D59C2211yescharacteristic, complemented
171C22⋊C4×D59C2211yescharacteristic, complemented
172C2×#41×C59C2211yescharacteristic, complemented
173C22×D4×C59C2211yescharacteristic
174#124×C59C2211yescharacteristic, complemented
175#123×C59C2211yescharacteristic
176#123×C59C2211yescharacteristic, complemented
177C22⋊Q8×C59C2211yescharacteristic, complemented
178#121×C59C2211yescharacteristic
179#121×C59C2211yescharacteristic, complemented
180#121×C59C2211yescharacteristic, complemented
181#120×C59C2211yescharacteristic, complemented
182#120×C59C2211yescharacteristic, complemented
183C4×D4×C59C2211yescharacteristic, complemented
184C4×D4×C59C2211yescharacteristic, complemented
185C2×C22⋊C4×C59C2211yescharacteristic, complemented
186C2×C22⋊C4×C59C2211yescharacteristic, complemented
187C24×C59C2311yescharacteristic
188C24×C59C2311yescharacteristic
189C23×D59C2311yescharacteristic
190C23×D59C2311yescharacteristic
191C23×D59C2311yescharacteristic
192#41×C59—42no—
193C2×Q8×C59C2311yescharacteristic
194C2×D4×C59—42no—
195C2×D4×C59C2311yescharacteristic
196C2×D4×C59C2311yescharacteristic
197C2×D4×C59C2311yescharacteristic
198C2×D4×C59C2311yescharacteristic
199C2×D4×C59C2311yescharacteristic
200C2×D4×C59C2311yescharacteristic
201C2×D4×C59C2311yescharacteristic
202C2×D4×C59C2311yescharacteristic
203C2×D4×C59C2311yescharacteristic
204C22×C4×C59C2311yescharacteristic
205C22×C4×C59C2311yescharacteristic
206C22×C4×C59C2311yescharacteristic
207C22×C4×C59C2311yescharacteristic
208C22×C4×C59C2311yescharacteristic
209C22×C4×C59C2311yescharacteristic
210C2×C22⋊D59—42no—
211C2×C22⋊D59—42no—
212C2×C22⋊D59—42no—
213C2×C22⋊D59C2311yescharacteristic
214C2×C22⋊D59C2311yescharacteristic
215C2×C22⋊D59C2311yescharacteristic
216C2×C22⋊D59C2311yescharacteristic
217C2×C22⋊D59C2311yescharacteristic
218C2×C22⋊D59C2311yescharacteristic
219C2×C22⋊D59C2311yescharacteristic
220C2×C22⋊D59C2311yescharacteristic
221C2×C22⋊D59C2311yescharacteristic
222C2×C22⋊D59C2311yescharacteristic
223C2×C22⋊D59C2311yescharacteristic
224C2×C22⋊D59C2311yescharacteristic
225C2×C22⋊D59C2311yescharacteristic
226C2×C22⋊D59C2311yescharacteristic
227C2×C22⋊D59C2311yescharacteristic
228C2×C22⋊D59C2311yescharacteristic
229C2×C22⋊D59C2311yescharacteristic
230C2×C22⋊D59C2311yescharacteristic
231C2×C22⋊D59C2311yescharacteristic
232C2×C22⋊D59C2311yescharacteristic
233C2×C22⋊D59C2311yescharacteristic
234C2×C22⋊D59C2311yescharacteristic
235C2×C22⋊D59C2311yescharacteristic
236C2×C22⋊D59C2311yescharacteristic
237C22×Dic59C2311yescharacteristic
238C22×Dic59C2311yescharacteristic
239C22×Dic59C2311yescharacteristic
240C22×Dic59C2311yescharacteristic
241C22×Dic59C2311yescharacteristic
242C22×Dic59C2311yescharacteristic
243C22×Dic59C2311yescharacteristic
244#11745687—42no—
245#11745687—42no—
246#11745687—42no—
247D4×D59—42no—
248#11745685—42no—
249C2×D236—42no—
250C2×D236C2311yescharacteristic
251C2×D236C2311yescharacteristic
252C2×D236C2311yescharacteristic
253C2×D236C2311yescharacteristic
254C2×D236C2311yescharacteristic
255C2×D236C2311yescharacteristic
256C2×D236C2311yescharacteristic
257C2×C4×D59—42no—
258C2×C4×D59C2311yescharacteristic
259C2×C4×D59C2311yescharacteristic
260C2×C4×D59C2311yescharacteristic
261C2×C4×D59C2311yescharacteristic
262C2×C4×D59C2311yescharacteristic
263C2×C4×D59C2311yescharacteristic
264C2×C4×D59C2311yescharacteristic
265C2×C4×D59C2311yescharacteristic
266C2×C4×D59C2311yescharacteristic
267C2×Dic118C2311yescharacteristic
268C2×Dic118C2311yescharacteristic
269C2×Dic118C2311yescharacteristic
270C4⋊C4×C59C2311yescharacteristic
271C4⋊C4×C59C2311yescharacteristic
272C4⋊C4×C59C2311yescharacteristic
273C4⋊C4×C59C2311yescharacteristic
274C22⋊C4×C59C2311yescharacteristic
275C22⋊C4×C59C2311yescharacteristic
276C22⋊C4×C59C2311yescharacteristic
277C22⋊C4×C59C2311yescharacteristic
278C22⋊C4×C59C2311yescharacteristic
279C22⋊C4×C59C2311yescharacteristic
280C22⋊C4×C59C2311yescharacteristic
281C22⋊C4×C59C2311yescharacteristic
282C22⋊C4×C59C2311yescharacteristic
283C22⋊C4×C59C2311yescharacteristic
284C22⋊C4×C59C2311yescharacteristic
285C22⋊C4×C59C2311yescharacteristic
286C42×C59C2311yescharacteristic
287C22⋊Dic59C2311yescharacteristic
288C22⋊Dic59C2311yescharacteristic
289C22⋊Dic59C2311yescharacteristic
290C22⋊Dic59C2311yescharacteristic
291C22⋊Dic59C2311yescharacteristic
292C22⋊Dic59C2311yescharacteristic
293C22⋊Dic59C2311yescharacteristic
294C22⋊Dic59C2311yescharacteristic
295C22⋊Dic59C2311yescharacteristic
296C22⋊Dic59C2311yescharacteristic
297C22⋊Dic59C2311yescharacteristic
298C22⋊Dic59C2311yescharacteristic
299C22⋊Dic59C2311yescharacteristic
300C22⋊Dic59C2311yescharacteristic
301(C2×D59)⋊C4C2311yescharacteristic
302(C2×D59)⋊C4C2311yescharacteristic
303(C2×D59)⋊C4C2311yescharacteristic
304(C2×D59)⋊C4C2311yescharacteristic
305(C2×D59)⋊C4C2311yescharacteristic
306(C2×D59)⋊C4C2311yescharacteristic
307(C2×D59)⋊C4C2311yescharacteristic
308(C2×D59)⋊C4C2311yescharacteristic
309(C2×D59)⋊C4C2311yescharacteristic
310(C2×D59)⋊C4C2311yescharacteristic
311(C2×D59)⋊C4C2311yescharacteristic
312(C2×D59)⋊C4C2311yescharacteristic
313(C2×D59)⋊C4C2311yescharacteristic
314(C2×D59)⋊C4C2311yescharacteristic
315(C2×D59)⋊C4C2311yescharacteristic
316(C2×D59)⋊C4C2311yescharacteristic
317(C2×D59)⋊C4C2311yescharacteristic
318(C2×D59)⋊C4C2311yescharacteristic
319(C2×D59)⋊C4C2311yescharacteristic
320(C2×D59)⋊C4C2311yescharacteristic
321(C2×D59)⋊C4C2311yescharacteristic
322(C2×D59)⋊C4C2311yescharacteristic
323C4⋊Dic59C2311yescharacteristic
324C4⋊Dic59C2311yescharacteristic
325C4⋊Dic59C2311yescharacteristic
326C4⋊Dic59C2311yescharacteristic
327C4⋊Dic59C2311yescharacteristic
328C4⋊Dic59C2311yescharacteristic
329Dic59⋊C4C2311yescharacteristic
330Dic59⋊C4C2311yescharacteristic
331Dic59⋊C4C2311yescharacteristic
332Dic59⋊C4C2311yescharacteristic
333Dic59⋊C4C2311yescharacteristic
334Dic59⋊C4C2311yescharacteristic
335Dic59⋊C4C2311yescharacteristic
336Dic59⋊C4C2311yescharacteristic
337Dic59⋊C4C2311yescharacteristic
338Dic59⋊C4C2311yescharacteristic
339Dic59⋊C4C2311yescharacteristic
340Dic59⋊C4C2311yescharacteristic
341Dic59⋊C4C2311yescharacteristic
342Dic59⋊C4C2311yescharacteristic
343Dic59⋊C4C2311yescharacteristic
344Dic59⋊C4C2311yescharacteristic
345Dic59⋊C4C2311yescharacteristic
346Dic59⋊C4C2311yescharacteristic
347C4×Dic59C2311yescharacteristic
348C4×Dic59C2311yescharacteristic
349C4×Dic59C2311yescharacteristic
350C4×Dic59C2311yescharacteristic
351C4×Dic59C2311yescharacteristic
352C4×Dic59C2311yescharacteristic
353C4×Dic59C2311yescharacteristic
354C23×C59—22no—
355C23×C59—41no—
356C23×C59—41no—
357C23×C59—41no—
358C23×C59—41no—
359C23×C59—41no—
360C23×C59C2411yescharacteristic
361C23×C59C2411yescharacteristic
362C23×C59C2411yescharacteristic
363C23×C59C2411yescharacteristic
364C23×C59C2411yescharacteristic
365C23×C59C2411yescharacteristic
366C22×D59—22no—
367C22×D59—22no—
368C22×D59—41no—
369C22×D59—41no—
370C22×D59—41no—
371C22×D59—41no—
372C22×D59—41no—
373C22×D59—41no—
374C22×D59—41no—
375C22×D59C2411yescharacteristic
376C22×D59C2411yescharacteristic
377C22×D59C2411yescharacteristic
378C22×D59C2411yescharacteristic
379C22×D59C2411yescharacteristic
380Q8×C59—41no—
381D4×C59—22no—
382D4×C59—22no—
383D4×C59—22no—
384D4×C59—41no—
385D4×C59—41no—
386D4×C59—41no—
387D4×C59—41no—
388D4×C59—41no—
389D4×C59—41no—
390C2×C4×C59—22no—
391C2×C4×C59—41no—
392C2×C4×C59—41no—
393C2×C4×C59—41no—
394C2×C4×C59—41no—
395C2×C4×C59—41no—
396C2×C4×C59C2411yescharacteristic
397C2×C4×C59C2411yescharacteristic
398C2×C4×C59C2411yescharacteristic
399C2×C4×C59C2411yescharacteristic
400C2×C4×C59C2411yescharacteristic
401C2×C4×C59C2411yescharacteristic
402C2×C4×C59C2411yescharacteristic
403C2×C4×C59C2411yescharacteristic
404C2×C4×C59C2411yescharacteristic
405C22⋊D59—22no—
406C22⋊D59—22no—
407C22⋊D59—22no—
408C22⋊D59—22no—
409C22⋊D59—41no—
410C22⋊D59—41no—
411C22⋊D59—41no—
412C22⋊D59—41no—
413C22⋊D59—41no—
414C22⋊D59—41no—
415C22⋊D59—41no—
416C22⋊D59—41no—
417C22⋊D59—41no—
418C22⋊D59—41no—
419C22⋊D59—41no—
420C22⋊D59—41no—
421C22⋊D59—41no—
422C22⋊D59—41no—
423C22⋊D59—41no—
424C22⋊D59—41no—
425C22⋊D59—41no—
426C22⋊D59—41no—
427C22⋊D59—41no—
428C22⋊D59—41no—
429C2×Dic59—22no—
430C2×Dic59—22no—
431C2×Dic59—22no—
432C2×Dic59—22no—
433C2×Dic59—41no—
434C2×Dic59—41no—
435C2×Dic59—41no—
436C2×Dic59C2411yescharacteristic
437C2×Dic59C2411yescharacteristic
438C2×Dic59C2411yescharacteristic
439C2×Dic59C2411yescharacteristic
440C2×Dic59C2411yescharacteristic
441C2×Dic59C2411yescharacteristic
442C2×Dic59C2411yescharacteristic
443C2×Dic59C2411yescharacteristic
444C2×Dic59C2411yescharacteristic
445C2×Dic59C2411yescharacteristic
446C2×Dic59C2411yescharacteristic
447D236—41no—
448D236—41no—
449D236—41no—
450D236—41no—
451D236—41no—
452D236—41no—
453D236—41no—
454C4×D59—22no—
455C4×D59—22no—
456C4×D59—41no—
457C4×D59—41no—
458C4×D59—41no—
459C4×D59—41no—
460C4×D59—41no—
461C4×D59—41no—
462C4×D59—41no—
463Dic118—22no—
464Dic118—41no—
465Dic118—41no—
466C22×C59—21no—
467C22×C59—21no—
468C22×C59—21no—
469C22×C59—21no—
470C22×C59—21no—
471C22×C59—21no—
472C22×C59—21no—
473C22×C59—21no—
474C22×C59—21no—
475C22×C59—21no—
476C22×C59—21no—
477C22×C59—21no—
478C22×C59—21no—
479C22×C59—21no—
480C22×C59—21no—
481C22×C59—21no—
482C22×C59—21no—
483C22×C59—82no—
484C22×C59—82no—
485C22×C59H(5,𝔽2)12yes—
486C22×C59C2511yescharacteristic
487C2×D59—21no—
488C2×D59—21no—
489C2×D59—21no—
490C2×D59—21no—
491C2×D59—21no—
492C2×D59—21no—
493C2×D59—21no—
494C2×D59—21no—
495C2×D59—21no—
496C2×D59—21no—
497C2×D59—21no—
498C2×D59—21no—
499C2×D59—21no—
500C2×D59—21no—
501C2×D59—21no—
502C2×D59—44no—
503C2×D59—82no—
504C2×D59—82no—
505C4×C59—21no—
506C4×C59—21no—
507C4×C59—21no—
508C4×C59—21no—
509C4×C59—21no—
510C4×C59—21no—
511C4×C59—21no—
512C4×C59—21no—
513C4×C59—21no—
514Dic59—21no—
515Dic59—21no—
516Dic59—21no—
517Dic59—21no—
518Dic59—21no—
519Dic59—21no—
520Dic59—21no—
521Dic59—21no—
522Dic59—21no—
523Dic59—21no—
524Dic59H(5,𝔽2)12yes—
525#3542—591nomaximal, Sylow
526C2×C59—22no—
527C2×C59—41no—
528C2×C59—41no—
529C2×C59—41no—
530C2×C59—41no—
531C2×C59—41no—
532C2×C59C2×H(5,𝔽2)11yescharacteristic
533C2×C59C2×H(5,𝔽2)11yescharacteristic
534C2×C59#58511yescharacteristic
535D59—41no—
536D59—41no—
537D59—41no—
538D59—41no—
539D59—41no—
540#562—591no—
541#562—591no—
542#560—591no—
543#560—591no—
544#555—591no—
545#553—591no—
546#552—591no—
547#551—591no—
548#551—591no—
549#550—591no—
550#547—591no—
551#546—591no—
552#546—591no—
553#546—591no—
554#546D5911yescharacteristic, complemented
555D42—591no—
556#542—591no—
557#540—591no—
558#540—591no—
559#540—591no—
560#538—591no—
561#538—591no—
562#537—591no—
563#535—591no—
564#535—591no—
565#535—591no—
566#534—591no—
567#534—591no—
568#525—591no—
569#525—591no—
570C2×#121—591no—
571C59#354211yescharacteristic, complemented, Sylow
572C2×#41—591no—
573C2×#41—591no—
574C2×#41—591no—
575C2×#41—591no—
576C2×#41C2×D5911yescharacteristic, complemented
577C22×D4—591no—
578C22×D4—591no—
579C22×D4—591no—
580C22×D4—591no—
581C22×D4—591no—
582C22×D4C2×D5911yescharacteristic
583C23×C4—591no—
584C4⋊Q8—591no—
585#127—591no—
586#127—591no—
587#127—591no—
588#127—591no—
589#127—591no—
590#126—591no—
591#126—591no—
592#126—591no—
593#126—591no—
594#126—591no—
595#126—591no—
596#125—591no—
597#125—591no—
598#125—591no—
599#124—591no—
600#124—591no—
601#124—591no—
602#124—591no—
603#124—591no—
604#124—591no—
605#124—591no—
606#124—591no—
607#124C2×D5911yescharacteristic, complemented
608#123—591no—
609#123—591no—
610#123—591no—
611#123—591no—
612#123—591no—
613#123—591no—
614#123—591no—
615#123—591no—
616#123—591no—
617#123—591no—
618#123—591no—
619#123—591no—
620#123—591no—
621#123—591no—
622#123—591no—
623#123—591no—
624#123—591no—
625#123—591no—
626#123—591no—
627#123—591no—
628#123C2×D5911yescharacteristic
629#123C2×D5911yescharacteristic, complemented
630C22⋊Q8—591no—
631C22⋊Q8—591no—
632C22⋊Q8—591no—
633C22⋊Q8—591no—
634C22⋊Q8—591no—
635C22⋊Q8—591no—
636C22⋊Q8—591no—
637C22⋊Q8—591no—
638C22⋊Q8—591no—
639C22⋊Q8—591no—
640C22⋊Q8C2×D5911yescharacteristic, complemented
641#121—591no—
642#121—591no—
643#121—591no—
644#121—591no—
645#121—591no—
646#121—591no—
647#121—591no—
648#121—591no—
649#121—591no—
650#121—591no—
651#121—591no—
652#121—591no—
653#121—591no—
654#121—591no—
655#121—591no—
656#121—591no—
657#121—591no—
658#121—591no—
659#121—591no—
660#121—591no—
661#121—591no—
662#121—591no—
663#121—591no—
664#121—591no—
665#121—591no—
666#121—591no—
667#121—591no—
668#121—591no—
669#121—591no—
670#121—591no—
671#121—591no—
672#121—591no—
673#121—591no—
674#121—591no—
675#121—591no—
676#121—591no—
677#121C2×D5911yescharacteristic
678#121C2×D5911yescharacteristic, complemented
679#121C2×D5911yescharacteristic, complemented
680#120—591no—
681#120—591no—
682#120—591no—
683#120—591no—
684#120—591no—
685#120—591no—
686#120—591no—
687#120—591no—
688#120—591no—
689#120—591no—
690#120—591no—
691#120—591no—
692#120—591no—
693#120—591no—
694#120C2×D5911yescharacteristic, complemented
695#120C2×D5911yescharacteristic, complemented
696C4×Q8—591no—
697C4×D4—591no—
698C4×D4—591no—
699C4×D4—591no—
700C4×D4—591no—
701C4×D4—591no—
702C4×D4—591no—
703C4×D4—591no—
704C4×D4—591no—
705C4×D4—591no—
706C4×D4—591no—
707C4×D4—591no—
708C4×D4—591no—
709C4×D4—591no—
710C4×D4C2×D5911yescharacteristic, complemented
711C4×D4C2×D5911yescharacteristic, complemented
712#117—591no—
713#117—591no—
714#117—591no—
715#117—591no—
716#117—591no—
717#117—591no—
718#117—591no—
719C2×C4⋊C4—591no—
720C2×C4⋊C4—591no—
721C2×C22⋊C4—591no—
722C2×C22⋊C4—591no—
723C2×C22⋊C4—591no—
724C2×C22⋊C4—591no—
725C2×C22⋊C4C2×D5911yescharacteristic, complemented
726C2×C22⋊C4C2×D5911yescharacteristic, complemented
727C24—591no—
728C24—591no—
729C24—591no—
730C24C22×D5911yescharacteristic
731C24C22×D5911yescharacteristic
732#41—42no—
733#41—2362no—
734#41—2362no—
735#41—2362no—
736#41—2362no—
737C2×Q8—591no—
738C2×Q8—591no—
739C2×Q8—591no—
740C2×Q8C22×D5911yescharacteristic
741C2×D4—42no—
742C2×D4—591no—
743C2×D4—591no—
744C2×D4—591no—
745C2×D4—591no—
746C2×D4—591no—
747C2×D4—591no—
748C2×D4—591no—
749C2×D4—591no—
750C2×D4—591no—
751C2×D4—591no—
752C2×D4—591no—
753C2×D4—591no—
754C2×D4—591no—
755C2×D4—591no—
756C2×D4—591no—
757C2×D4—591no—
758C2×D4—591no—
759C2×D4—591no—
760C2×D4—591no—
761C2×D4—591no—
762C2×D4—591no—
763C2×D4—591no—
764C2×D4—591no—
765C2×D4—591no—
766C2×D4—591no—
767C2×D4—591no—
768C2×D4—591no—
769C2×D4—591no—
770C2×D4—591no—
771C2×D4—591no—
772C2×D4—591no—
773C2×D4—2362no—
774C2×D4—2362no—
775C2×D4—2362no—
776C2×D4—2362no—
777C2×D4—2362no—
778C2×D4C22×D5911yescharacteristic
779C2×D4C22×D5911yescharacteristic
780C2×D4C22×D5911yescharacteristic
781C2×D4C22×D5911yescharacteristic
782C2×D4C22×D5911yescharacteristic
783C2×D4C22×D5911yescharacteristic
784C2×D4C22×D5911yescharacteristic
785C2×D4C22×D5911yescharacteristic
786C2×D4C22×D5911yescharacteristic
787C22×C4—591no—
788C22×C4—591no—
789C22×C4—591no—
790C22×C4—591no—
791C22×C4—591no—
792C22×C4—591no—
793C22×C4—591no—
794C22×C4—591no—
795C22×C4—591no—
796C22×C4—591no—
797C22×C4—591no—
798C22×C4—591no—
799C22×C4—591no—
800C22×C4—591no—
801C22×C4—591no—
802C22×C4—591no—
803C22×C4—2362no—
804C22×C4C22×D5911yescharacteristic
805C22×C4C22×D5911yescharacteristic
806C22×C4C22×D5911yescharacteristic
807C22×C4C22×D5911yescharacteristic
808C22×C4C22×D5911yescharacteristic
809C22×C4C22×D5911yescharacteristic
810C4⋊C4—591no—
811C4⋊C4—591no—
812C4⋊C4—591no—
813C4⋊C4—591no—
814C4⋊C4—591no—
815C4⋊C4—591no—
816C4⋊C4—591no—
817C4⋊C4—591no—
818C4⋊C4—591no—
819C4⋊C4—591no—
820C4⋊C4—591no—
821C4⋊C4—591no—
822C4⋊C4—591no—
823C4⋊C4—591no—
824C4⋊C4—591no—
825C4⋊C4—591no—
826C4⋊C4—591no—
827C4⋊C4—591no—
828C4⋊C4—591no—
829C4⋊C4—591no—
830C4⋊C4—591no—
831C4⋊C4—591no—
832C4⋊C4—591no—
833C4⋊C4—591no—
834C4⋊C4C22×D5911yescharacteristic
835C4⋊C4C22×D5911yescharacteristic
836C4⋊C4C22×D5911yescharacteristic
837C4⋊C4C22×D5911yescharacteristic
838C22⋊C4—591no—
839C22⋊C4—591no—
840C22⋊C4—591no—
841C22⋊C4—591no—
842C22⋊C4—591no—
843C22⋊C4—591no—
844C22⋊C4—591no—
845C22⋊C4—591no—
846C22⋊C4—591no—
847C22⋊C4—591no—
848C22⋊C4—591no—
849C22⋊C4—591no—
850C22⋊C4—591no—
851C22⋊C4—591no—
852C22⋊C4—591no—
853C22⋊C4—591no—
854C22⋊C4—591no—
855C22⋊C4—591no—
856C22⋊C4—591no—
857C22⋊C4—591no—
858C22⋊C4—591no—
859C22⋊C4—591no—
860C22⋊C4—591no—
861C22⋊C4—591no—
862C22⋊C4—591no—
863C22⋊C4—591no—
864C22⋊C4—591no—
865C22⋊C4—591no—
866C22⋊C4—591no—
867C22⋊C4—591no—
868C22⋊C4—591no—
869C22⋊C4—591no—
870C22⋊C4—591no—
871C22⋊C4—591no—
872C22⋊C4—591no—
873C22⋊C4—591no—
874C22⋊C4C22×D5911yescharacteristic
875C22⋊C4C22×D5911yescharacteristic
876C22⋊C4C22×D5911yescharacteristic
877C22⋊C4C22×D5911yescharacteristic
878C22⋊C4C22×D5911yescharacteristic
879C22⋊C4C22×D5911yescharacteristic
880C22⋊C4C22×D5911yescharacteristic
881C22⋊C4C22×D5911yescharacteristic
882C22⋊C4C22×D5911yescharacteristic
883C22⋊C4C22×D5911yescharacteristic
884C22⋊C4C22×D5911yescharacteristic
885C22⋊C4C22×D5911yescharacteristic
886C42—591no—
887C42—591no—
888C42—591no—
889C42—591no—
890C42—591no—
891C42—591no—
892C42—591no—
893C42C22×D5911yescharacteristic
894C23—22no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—591no—
901C23—591no—
902C23—591no—
903C23—591no—
904C23—591no—
905C23—1182no—
906C23—1182no—
907C23—2361no—
908C23—2361no—
909C23—2361no—
910C23—2361no—
911C23—2361no—
912C23—2361no—
913C23—2361no—
914C23C23×D5911yescharacteristic
915C23C23×D5911yescharacteristic
916C23C23×D5911yescharacteristic
917C23C23×D5911yescharacteristic
918C23C23×D5911yescharacteristic
919C23C23×D5911yescharacteristic
920Q8—41no—
921Q8—1182no—
922Q8—2361no—
923Q8—2361no—
924D4—22no—
925D4—22no—
926D4—22no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—1182no—
934D4—1182no—
935D4—1182no—
936D4—1182no—
937D4—2361no—
938D4—2361no—
939D4—2361no—
940D4—2361no—
941D4—2361no—
942D4—2361no—
943D4—2361no—
944D4—2361no—
945D4—2361no—
946D4—2361no—
947D4—2361no—
948D4—2361no—
949D4—2361no—
950D4—2361no—
951D4—2361no—
952D4—2361no—
953D4—2361no—
954D4—2361no—
955D4—2361no—
956D4—2361no—
957D4—2361no—
958D4—2361no—
959D4—2361no—
960D4—2361no—
961D4—2361no—
962D4—2361no—
963D4—2361no—
964C2×C4—22no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—591no—
971C2×C4—591no—
972C2×C4—591no—
973C2×C4—591no—
974C2×C4—591no—
975C2×C4—591no—
976C2×C4—591no—
977C2×C4—591no—
978C2×C4—591no—
979C2×C4—591no—
980C2×C4—591no—
981C2×C4—1182no—
982C2×C4—1182no—
983C2×C4—1182no—
984C2×C4—1182no—
985C2×C4—1182no—
986C2×C4—1182no—
987C2×C4—2361no—
988C2×C4—2361no—
989C2×C4—2361no—
990C2×C4—2361no—
991C2×C4—2361no—
992C2×C4—2361no—
993C2×C4—2361no—
994C2×C4—2361no—
995C2×C4—2361no—
996C2×C4—2361no—
997C2×C4C23×D5911yescharacteristic
998C2×C4C23×D5911yescharacteristic
999C2×C4C23×D5911yescharacteristic
1000C2×C4C23×D5911yescharacteristic
1001C2×C4C23×D5911yescharacteristic
1002C2×C4C23×D5911yescharacteristic
1003C2×C4C23×D5911yescharacteristic
1004C2×C4C23×D5911yescharacteristic
1005C2×C4C23×D5911yescharacteristic
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—21no—
1018C22—21no—
1019C22—21no—
1020C22—21no—
1021C22—21no—
1022C22—21no—
1023C22—82no—
1024C22—82no—
1025C22—1181no—
1026C22—1181no—
1027C22—1181no—
1028C22—1181no—
1029C22—1181no—
1030C22—1181no—
1031C22—1181no—
1032C22—1181no—
1033C22—1181no—
1034C22—1181no—
1035C22—1181no—
1036C22—1181no—
1037C22—1181no—
1038C22—1181no—
1039C22—1181no—
1040C22—4722no—
1041C22—4722no—
1042C22—2364no—
1043C22#1427377212yes—
1044C22C24×D5911yescharacteristic
1045C4—21no—
1046C4—21no—
1047C4—21no—
1048C4—21no—
1049C4—21no—
1050C4—21no—
1051C4—21no—
1052C4—21no—
1053C4—21no—
1054C4—592no—
1055C4—1181no—
1056C4—1181no—
1057C4—1181no—
1058C4—1181no—
1059C4—1181no—
1060C4—1181no—
1061C4—1181no—
1062C4—1181no—
1063C4—1181no—
1064C4—1181no—
1065C2—22no—
1066C2—41no—
1067C2—41no—
1068C2—41no—
1069C2—41no—
1070C2—41no—
1071C2—2361no—
1072C2—2361no—
1073C2—2361no—
1074C2—2361no—
1075C2—2361no—
1076C2H(5,𝔽2)×D5911yescharacteristic
1077C2C2×#1427377211yescharacteristic
1078C2#1683823811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D59
commutator, socleC22×C59C25
FittingC59×#546C2
hypercenter#546D59
hypocenterC59#3542
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ #546

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #16838149C2semidirect
2. #16838148C2semidirect
3. #16838141C2semidirect
4. #16838140C2semidirect
5. #16838114C2semidirect
6. #16838101C2semidirect
7. #16838089C2semidirect
8. #16838081C2semidirect
9. #16838078C2semidirect
10. #16838070C2semidirect
11. #16838051C2semidirect
12. #16838042C2semidirect
13. #16838041C2semidirect
14. #16838039C2semidirect
15. D4×C22⋊D59C2semidirect
16. #16838022C2semidirect
17. #16838004C2semidirect
18. #16838003C2semidirect
19. #16838002C2semidirect
20. #16837990C2semidirect
21. #16837986C2semidirect
22. #16837979C2semidirect
23. #16837967C2semidirect
24. #16837967C2semidirect
25. #16837966C2semidirect
26. #16837963C2semidirect
27. #16837961C2semidirect
28. #16837912C2semidirect
29. #16837911C2semidirect
30. C2×#14273700C2semidirect
31. C59×#546C2semidirect
32. C2×#11745685C22semidirect
33. C2×#11745687C22semidirect
34. C2×#11745687C22semidirect
35. C2×#11745687C22semidirect
36. C22×D236C22semidirect
38. C22×C22⋊D59C22semidirect
39. C22×C22⋊D59C22semidirect
41. C22×C4×D59C22semidirect
42. #14273725C22semidirect
43. #14273723C22semidirect
44. #14273723C22semidirect
45. #14273723C22semidirect
46. #14273723C22semidirect
47. #14273723C22semidirect
48. #14273722C22semidirect
49. #14273721C22semidirect
50. #14273720C22semidirect
51. #14273720C22semidirect
52. #14273720C22semidirect
53. #14273720C22semidirect
54. #14273718C22semidirect
55. #14273717C22semidirect
56. #14273717C22semidirect
57. #14273716C22semidirect
58. #14273716C22semidirect
59. #14273713C22semidirect
60. #14273713C22semidirect
61. #14273713C22semidirect
62. #14273713C22semidirect
63. #14273713C22semidirect
64. #14273713C22semidirect
65. #14273712C22semidirect
66. #14273712C22semidirect
67. #14273712C22semidirect
68. #14273712C22semidirect
69. #14273711C22semidirect
70. #14273711C22semidirect
71. #14273710C22semidirect
72. #14273710C22semidirect
73. #14273710C22semidirect
74. #14273710C22semidirect
75. #14273710C22semidirect
76. #14273709C22semidirect
77. #14273709C22semidirect
78. #14273709C22semidirect
79. #14273709C22semidirect
80. #14273709C22semidirect
81. #14273709C22semidirect
83. #14273708C22semidirect
84. #14273708C22semidirect
85. #14273707C22semidirect
86. #14273706C22semidirect
87. #14273706C22semidirect
88. #14273705C22semidirect
89. #14273705C22semidirect
90. #14273705C22semidirect
91. #14273704C22semidirect
92. #14273704C22semidirect
93. #14273704C22semidirect
94. #14273703C22semidirect
95. #14273702C22semidirect
96. #14273702C22semidirect
97. #14273701C22semidirect
98. #14273701C22semidirect
99. #14273701C22semidirect
100. #14273701C22semidirect
101. #14273701C22semidirect
104. #14273700C22semidirect
105. #14273700C22semidirect
106. #14273700C22semidirect
107. #14273700C22semidirect
108. #14273700C22semidirect
109. #14273700C22semidirect
110. #14273700C22semidirect
111. #14273700C22semidirect
112. #14273700C22semidirect
113. #14273700C22semidirect
114. #14273700C22semidirect
115. #14273700C22semidirect
117. #14273699C22semidirect
118. #14273699C22semidirect
119. #14273699C22semidirect
120. #14273699C22semidirect
121. #14273699C22semidirect
122. #14273699C22semidirect
123. #14273699C22semidirect
124. #14273699C22semidirect
125. #14273699C22semidirect
126. #14273699C22semidirect
127. #14273699C22semidirect
128. #14273698C22semidirect
129. #14273698C22semidirect
130. #14273698C22semidirect
131. #14273697C22semidirect
132. #14273697C22semidirect
133. #14273697C22semidirect
135. #14273696C22semidirect
136. #14273696C22semidirect
137. #14273696C22semidirect
140. #14273695C22semidirect
141. #14273695C22semidirect
142. #14273695C22semidirect
143. #14273695C22semidirect
144. #14273695C22semidirect
145. #14273692C22semidirect
146. C4×D236C22semidirect
148. D4×Dic59C22semidirect
149. C4×C22⋊D59C22semidirect
150. C4×C22⋊D59C22semidirect
151. C4×C22⋊D59C22semidirect
152. C4×C22⋊D59C22semidirect
153. C4×C22⋊D59C22semidirect
154. (C22⋊D59)⋊C4C22semidirect
155. (C22⋊D59)⋊C4C22semidirect
156. (C22⋊D59)⋊C4C22semidirect
157. (C22⋊D59)⋊C4C22semidirect
158. (C22⋊D59)⋊C4C22semidirect
159. #14273686C22semidirect
160. #14273685C22semidirect
161. #14273684C22semidirect
162. #14273684C22semidirect
163. #14273683C22semidirect
164. #14273683C22semidirect
165. #14273683C22semidirect
166. C2×Dic59⋊C4C22semidirect
167. C2×Dic59⋊C4C22semidirect
168. C2×C22⋊Dic59C22semidirect
169. C2×(C2×D59)⋊C4C22semidirect
170. C22⋊C4×D59C22semidirect
171. C22⋊C4×D59C22semidirect
172. C2×#41×C59C22semidirect
174. #124×C59C22semidirect
176. #123×C59C22semidirect
177. C22⋊Q8×C59C22semidirect
179. #121×C59C22semidirect
180. #121×C59C22semidirect
181. #120×C59C22semidirect
182. #120×C59C22semidirect
183. C4×D4×C59C22semidirect
184. C4×D4×C59C22semidirect
185. C2×C22⋊C4×C59C22semidirect
186. C2×C22⋊C4×C59C22semidirect
554. #546D59semidirect
571. C59#3542semidirect
576. C2×#41C2×D59semidirect
607. #124C2×D59semidirect
629. #123C2×D59semidirect
640. C22⋊Q8C2×D59semidirect
678. #121C2×D59semidirect
679. #121C2×D59semidirect
694. #120C2×D59semidirect
695. #120C2×D59semidirect
710. C4×D4C2×D59semidirect
711. C4×D4C2×D59semidirect
725. C2×C22⋊C4C2×D59semidirect
726. C2×C22⋊C4C2×D59semidirect