Finite Group Databasebeta

← #20257554

Subgroups — #20257554

Order 6016.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689877C211yesmaximal, characteristic, complemented
2#15689871C211yesmaximal, characteristic, complemented
3#15689869C211yesmaximal, characteristic, complemented
4#15689864C211yesmaximal, characteristic, complemented
5#15689858C211yesmaximal, characteristic, complemented
6#15689826C211yesmaximal, characteristic, complemented
7#15689824C211yesmaximal, characteristic, complemented
8#15689806C211yesmaximal, characteristic, complemented
9#15689800C211yesmaximal, characteristic, complemented
10#15689797C211yesmaximal, characteristic, complemented
11#15689797C211yesmaximal, characteristic, complemented
12#15689774C211yesmaximal, characteristic, complemented
13#15689771C211yesmaximal, characteristic, complemented
14#15689768C211yesmaximal, characteristic, complemented
15#15689765C211yesmaximal, characteristic, complemented
16#15689745C211yesmaximal, characteristic, complemented
17#15689739C211yesmaximal, characteristic, complemented
18#15689729C211yesmaximal, characteristic, complemented
19#15689728C211yesmaximal, characteristic, complemented
20#15689721C211yesmaximal, characteristic, complemented
21#15689721C211yesmaximal, characteristic, complemented
22#15689713C211yesmaximal, characteristic, complemented
23#15689713C211yesmaximal, characteristic, complemented
24#15689712C211yesmaximal, characteristic, complemented
25#15689706C211yesmaximal, characteristic, complemented
26#15689692C211yesmaximal, characteristic, complemented
27#15689684C211yesmaximal, characteristic, complemented
28#15689635C211yesmaximal, characteristic, complemented
29#15689631C211yesmaximal, characteristic, complemented
30C2×#13094009C211yesmaximal, characteristic, complemented
31C47×#552C211yesmaximal, characteristic, complemented
32C2×#10625350C2211yescharacteristic
33C2×#10625350C2211yescharacteristic, complemented
34C2×#10625352C2211yescharacteristic
35C22×D188C2211yescharacteristic
36C2×D4×D47C2211yescharacteristic
37C22×C4×D47C2211yescharacteristic, complemented
38#13094023C2211yescharacteristic, complemented
39#13094023C2211yescharacteristic, complemented
40#13094021C2211yescharacteristic
41#13094021C2211yescharacteristic, complemented
42#13094019C2211yescharacteristic, complemented
43#13094019C2211yescharacteristic, complemented
44#13094019C2211yescharacteristic, complemented
45#13094019C2211yescharacteristic, complemented
46#13094019C2211yescharacteristic, complemented
47#13094019C2211yescharacteristic, complemented
48#13094019C2211yescharacteristic, complemented
49#13094018C2211yescharacteristic, complemented
50#13094018C2211yescharacteristic, complemented
51#13094018C2211yescharacteristic, complemented
52#13094016C2211yescharacteristic, complemented
53#13094014C2211yescharacteristic, complemented
54#13094014C2211yescharacteristic, complemented
55#13094013C2211yescharacteristic, complemented
56#13094013C2211yescharacteristic, complemented
57#13094013C2211yescharacteristic, complemented
58#13094012C2211yescharacteristic
59#13094012C2211yescharacteristic, complemented
60#13094012C2211yescharacteristic, complemented
61#13094012C2211yescharacteristic, complemented
62#13094012C2211yescharacteristic, complemented
63#13094010C2211yescharacteristic, complemented
64#13094010C2211yescharacteristic, complemented
65#13094009C2211yescharacteristic
66#13094009C2211yescharacteristic
67#13094009C2211yescharacteristic
68#13094009C2211yescharacteristic
69#13094009C2211yescharacteristic
70#13094009C2211yescharacteristic
71#13094009C2211yescharacteristic, complemented
72#13094009C2211yescharacteristic, complemented
73#13094009C2211yescharacteristic, complemented
74#13094009C2211yescharacteristic, complemented
75#13094009C2211yescharacteristic, complemented
76#13094009C2211yescharacteristic, complemented
77#13094009C2211yescharacteristic, complemented
78#13094009C2211yescharacteristic, complemented
79#13094009C2211yescharacteristic, complemented
80#13094009C2211yescharacteristic, complemented
81#13094009C2211yescharacteristic, complemented
82#13094009C2211yescharacteristic, complemented
83#13094009C2211yescharacteristic, complemented
84#13094009C2211yescharacteristic, complemented
85#13094009C2211yescharacteristic, complemented
86#13094008C2211yescharacteristic
87#13094008C2211yescharacteristic, complemented
88#13094008C2211yescharacteristic, complemented
89#13094007C2211yescharacteristic
90#13094007C2211yescharacteristic, complemented
91#13094007C2211yescharacteristic, complemented
92#13094006C2211yescharacteristic, complemented
93#13094004C2211yescharacteristic, complemented
94#13094004C2211yescharacteristic, complemented
95#13094004C2211yescharacteristic, complemented
96#13094002C2211yescharacteristic, complemented
97#13094002C2211yescharacteristic, complemented
98#13094002C2211yescharacteristic, complemented
99#13094002C2211yescharacteristic, complemented
100#13094002C2211yescharacteristic, complemented
101#13094002C2211yescharacteristic, complemented
102#13094002C2211yescharacteristic, complemented
103#13094002C2211yescharacteristic, complemented
104#13094001C2211yescharacteristic, complemented
105#13094001C2211yescharacteristic, complemented
106#13094000C2211yescharacteristic, complemented
107#13093999C2211yescharacteristic
108#13093999C2211yescharacteristic
109#13093999C2211yescharacteristic
110#13093999C2211yescharacteristic
111#13093999C2211yescharacteristic, complemented
112#13093999C2211yescharacteristic, complemented
113#13093999C2211yescharacteristic, complemented
114#13093999C2211yescharacteristic, complemented
115#13093999C2211yescharacteristic, complemented
116#13093999C2211yescharacteristic, complemented
117#13093999C2211yescharacteristic, complemented
118#13093999C2211yescharacteristic, complemented
119#13093999C2211yescharacteristic, complemented
120#13093998C2211yescharacteristic
121#13093998C2211yescharacteristic, complemented
122#13093998C2211yescharacteristic, complemented
123#13093997C2211yescharacteristic
124#13093997C2211yescharacteristic
125#13093997C2211yescharacteristic, complemented
126#13093997C2211yescharacteristic, complemented
127#13093997C2211yescharacteristic, complemented
128#13093997C2211yescharacteristic, complemented
129#13093997C2211yescharacteristic, complemented
130#13093996C2211yescharacteristic
131#13093994C2211yescharacteristic
132#13093994C2211yescharacteristic
133#13093994C2211yescharacteristic
134#13093994C2211yescharacteristic
135#13093994C2211yescharacteristic
136#13093994C2211yescharacteristic, complemented
137#13093994C2211yescharacteristic, complemented
138#13093994C2211yescharacteristic, complemented
139#13093994C2211yescharacteristic, complemented
140#13093992C2211yescharacteristic
141C4×Dic94C2211yescharacteristic, complemented
142C4×D188C2211yescharacteristic, complemented
143C4×D188C2211yescharacteristic, complemented
144C4×D188C2211yescharacteristic, complemented
145C4×D188C2211yescharacteristic, complemented
146C4×D188C2211yescharacteristic, complemented
147C4×D188C2211yescharacteristic, complemented
148#13093986C2211yescharacteristic, complemented
149#13093986C2211yescharacteristic, complemented
150#13093986C2211yescharacteristic, complemented
151#13093986C2211yescharacteristic, complemented
152#13093986C2211yescharacteristic, complemented
153C4×C22⋊D47C2211yescharacteristic, complemented
154(C22⋊D47)⋊C4C2211yescharacteristic
155(C22⋊D47)⋊C4C2211yescharacteristic, complemented
156(C22⋊D47)⋊C4C2211yescharacteristic, complemented
157(C22⋊D47)⋊C4C2211yescharacteristic, complemented
158(C22⋊D47)⋊C4C2211yescharacteristic, complemented
159#13093982C2211yescharacteristic, complemented
160#13093981C2211yescharacteristic, complemented
161#13093981C2211yescharacteristic, complemented
162#13093980C2211yescharacteristic, complemented
163C2×Dic47⋊C4C2211yescharacteristic, complemented
164C4⋊C4×D47C2211yescharacteristic, complemented
165C4⋊C4×D47C2211yescharacteristic, complemented
166C2×(C2×D47)⋊C4C2211yescharacteristic
167C2×(C2×D47)⋊C4C2211yescharacteristic
168C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
169C2×(C2×D47)⋊C4C2211yescharacteristic, complemented
170C22⋊C4×D47C2211yescharacteristic
171C22⋊C4×D47C2211yescharacteristic, complemented
172#126×C47C2211yescharacteristic, complemented
173#126×C47C2211yescharacteristic, complemented
174#125×C47C2211yescharacteristic, complemented
175#125×C47C2211yescharacteristic, complemented
176#125×C47C2211yescharacteristic, complemented
177#123×C47C2211yescharacteristic
178#123×C47C2211yescharacteristic
179C22⋊Q8×C47C2211yescharacteristic, complemented
180C22⋊Q8×C47C2211yescharacteristic, complemented
181C4×Q8×C47C2211yescharacteristic, complemented
182C4×D4×C47C2211yescharacteristic
183#117×C47C2211yescharacteristic, complemented
184#117×C47C2211yescharacteristic, complemented
185#117×C47C2211yescharacteristic, complemented
186C2×C4⋊C4×C47C2211yescharacteristic, complemented
187C23×D47C2311yescharacteristic
188C23×D47C2311yescharacteristic
189C23×D47C2311yescharacteristic
190C2×Q8×C47C2311yescharacteristic
191C2×D4×C47C2311yescharacteristic
192C22×C4×C47C2311yescharacteristic
193C22×C4×C47C2311yescharacteristic
194C22×C4×C47C2311yescharacteristic
195C22×C4×C47C2311yescharacteristic
196C2×C22⋊D47C2311yescharacteristic
197C2×C22⋊D47C2311yescharacteristic
198C2×C22⋊D47C2311yescharacteristic
199C2×C22⋊D47C2311yescharacteristic
200C2×C22⋊D47C2311yescharacteristic
201C2×C22⋊D47C2311yescharacteristic
202C2×C22⋊D47C2311yescharacteristic
203C2×C22⋊D47C2311yescharacteristic
204C22×Dic47C2311yescharacteristic
205C22×Dic47C2311yescharacteristic
206C22×Dic47C2311yescharacteristic
207#10625352—42no—
208D4×D47—42no—
209#10625350—42no—
210#10625350—42no—
211C2×D188—42no—
212C2×D188C2311yescharacteristic
213C2×D188C2311yescharacteristic
214C2×D188C2311yescharacteristic
215C2×D188C2311yescharacteristic
216C2×D188C2311yescharacteristic
217C2×D188C2311yescharacteristic
218C2×D188C2311yescharacteristic
219C2×D188C2311yescharacteristic
220C2×D188C2311yescharacteristic
221C2×D188C2311yescharacteristic
222C2×D188C2311yescharacteristic
223C2×D188C2311yescharacteristic
224C2×D188C2311yescharacteristic
225C2×D188C2311yescharacteristic
226C2×D188C2311yescharacteristic
227C2×D188C2311yescharacteristic
228C2×D188C2311yescharacteristic
229C2×D188C2311yescharacteristic
230C2×C4×D47—42no—
231C2×C4×D47C2311yescharacteristic
232C2×C4×D47C2311yescharacteristic
233C2×C4×D47C2311yescharacteristic
234C2×C4×D47C2311yescharacteristic
235C2×C4×D47C2311yescharacteristic
236C2×C4×D47C2311yescharacteristic
237C2×C4×D47C2311yescharacteristic
238C2×C4×D47C2311yescharacteristic
239C2×C4×D47C2311yescharacteristic
240C2×C4×D47C2311yescharacteristic
241C2×C4×D47C2311yescharacteristic
242C2×C4×D47C2311yescharacteristic
243C2×C4×D47C2311yescharacteristic
244C2×C4×D47C2311yescharacteristic
245C2×C4×D47C2311yescharacteristic
246C2×Dic94C2311yescharacteristic
247C2×Dic94C2311yescharacteristic
248C2×Dic94C2311yescharacteristic
249C2×Dic94C2311yescharacteristic
250C4⋊C4×C47C2311yescharacteristic
251C4⋊C4×C47C2311yescharacteristic
252C4⋊C4×C47C2311yescharacteristic
253C4⋊C4×C47C2311yescharacteristic
254C4⋊C4×C47C2311yescharacteristic
255C4⋊C4×C47C2311yescharacteristic
256C4⋊C4×C47C2311yescharacteristic
257C4⋊C4×C47C2311yescharacteristic
258C4⋊C4×C47C2311yescharacteristic
259C4⋊C4×C47C2311yescharacteristic
260C4⋊C4×C47C2311yescharacteristic
261C4⋊C4×C47C2311yescharacteristic
262C4⋊C4×C47C2311yescharacteristic
263C4⋊C4×C47C2311yescharacteristic
264C4⋊C4×C47C2311yescharacteristic
265C4⋊C4×C47C2311yescharacteristic
266C22⋊C4×C47C2311yescharacteristic
267C22⋊C4×C47C2311yescharacteristic
268C22⋊C4×C47C2311yescharacteristic
269C22⋊C4×C47C2311yescharacteristic
270C22⋊C4×C47C2311yescharacteristic
271C22⋊C4×C47C2311yescharacteristic
272C22⋊C4×C47C2311yescharacteristic
273C22⋊C4×C47C2311yescharacteristic
274C42×C47C2311yescharacteristic
275C42×C47C2311yescharacteristic
276C42×C47C2311yescharacteristic
277C42×C47C2311yescharacteristic
278C42×C47C2311yescharacteristic
279C22⋊Dic47C2311yescharacteristic
280C22⋊Dic47C2311yescharacteristic
281(C2×D47)⋊C4C2311yescharacteristic
282(C2×D47)⋊C4C2311yescharacteristic
283(C2×D47)⋊C4C2311yescharacteristic
284(C2×D47)⋊C4C2311yescharacteristic
285(C2×D47)⋊C4C2311yescharacteristic
286(C2×D47)⋊C4C2311yescharacteristic
287(C2×D47)⋊C4C2311yescharacteristic
288(C2×D47)⋊C4C2311yescharacteristic
289(C2×D47)⋊C4C2311yescharacteristic
290(C2×D47)⋊C4C2311yescharacteristic
291(C2×D47)⋊C4C2311yescharacteristic
292(C2×D47)⋊C4C2311yescharacteristic
293(C2×D47)⋊C4C2311yescharacteristic
294(C2×D47)⋊C4C2311yescharacteristic
295(C2×D47)⋊C4C2311yescharacteristic
296(C2×D47)⋊C4C2311yescharacteristic
297(C2×D47)⋊C4C2311yescharacteristic
298(C2×D47)⋊C4C2311yescharacteristic
299(C2×D47)⋊C4C2311yescharacteristic
300(C2×D47)⋊C4C2311yescharacteristic
301(C2×D47)⋊C4C2311yescharacteristic
302(C2×D47)⋊C4C2311yescharacteristic
303(C2×D47)⋊C4C2311yescharacteristic
304(C2×D47)⋊C4C2311yescharacteristic
305(C2×D47)⋊C4C2311yescharacteristic
306(C2×D47)⋊C4C2311yescharacteristic
307(C2×D47)⋊C4C2311yescharacteristic
308(C2×D47)⋊C4C2311yescharacteristic
309(C2×D47)⋊C4C2311yescharacteristic
310(C2×D47)⋊C4C2311yescharacteristic
311(C2×D47)⋊C4C2311yescharacteristic
312(C2×D47)⋊C4C2311yescharacteristic
313(C2×D47)⋊C4C2311yescharacteristic
314(C2×D47)⋊C4C2311yescharacteristic
315(C2×D47)⋊C4C2311yescharacteristic
316(C2×D47)⋊C4C2311yescharacteristic
317(C2×D47)⋊C4C2311yescharacteristic
318(C2×D47)⋊C4C2311yescharacteristic
319(C2×D47)⋊C4C2311yescharacteristic
320(C2×D47)⋊C4C2311yescharacteristic
321C4⋊Dic47C2311yescharacteristic
322C4⋊Dic47C2311yescharacteristic
323C4⋊Dic47C2311yescharacteristic
324C4⋊Dic47C2311yescharacteristic
325C4⋊Dic47C2311yescharacteristic
326C4⋊Dic47C2311yescharacteristic
327Dic47⋊C4C2311yescharacteristic
328Dic47⋊C4C2311yescharacteristic
329Dic47⋊C4C2311yescharacteristic
330Dic47⋊C4C2311yescharacteristic
331Dic47⋊C4C2311yescharacteristic
332Dic47⋊C4C2311yescharacteristic
333Dic47⋊C4C2311yescharacteristic
334Dic47⋊C4C2311yescharacteristic
335Dic47⋊C4C2311yescharacteristic
336Dic47⋊C4C2311yescharacteristic
337Dic47⋊C4C2311yescharacteristic
338Dic47⋊C4C2311yescharacteristic
339Dic47⋊C4C2311yescharacteristic
340Dic47⋊C4C2311yescharacteristic
341Dic47⋊C4C2311yescharacteristic
342Dic47⋊C4C2311yescharacteristic
343C4×Dic47C2311yescharacteristic
344C4×Dic47C2311yescharacteristic
345C4×Dic47C2311yescharacteristic
346C4×Dic47C2311yescharacteristic
347C4×Dic47C2311yescharacteristic
348C23×C47C2411yescharacteristic
349C23×C47C2411yescharacteristic
350C22×D47—22no—
351C22×D47—22no—
352C22×D47—41no—
353C22×D47—41no—
354C22×D47—41no—
355C22×D47—41no—
356C22×D47—41no—
357C22×D47—41no—
358C22×D47—41no—
359C22×D47C2411yescharacteristic
360C22×D47C2411yescharacteristic
361C22×D47C2411yescharacteristic
362C22×D47C2411yescharacteristic
363C22×D47C2411yescharacteristic
364C22×D47C2411yescharacteristic
365C22×D47C2411yescharacteristic
366Q8×C47—41no—
367D4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—22no—
370C2×C4×C47—41no—
371C2×C4×C47—41no—
372C2×C4×C47C2411yescharacteristic
373C2×C4×C47C2411yescharacteristic
374C2×C4×C47C2411yescharacteristic
375C2×C4×C47C2411yescharacteristic
376C2×C4×C47C2411yescharacteristic
377C2×C4×C47C2411yescharacteristic
378C2×C4×C47C2411yescharacteristic
379C2×C4×C47C2411yescharacteristic
380C2×C4×C47C2411yescharacteristic
381C2×C4×C47C2411yescharacteristic
382C2×C4×C47C2411yescharacteristic
383C2×C4×C47C2411yescharacteristic
384C2×C4×C47C2411yescharacteristic
385C22⋊D47—22no—
386C22⋊D47—22no—
387C22⋊D47—22no—
388C22⋊D47—41no—
389C22⋊D47—41no—
390C22⋊D47—41no—
391C22⋊D47—41no—
392C22⋊D47—41no—
393C2×Dic47—22no—
394C2×Dic47—41no—
395C2×Dic47—41no—
396C2×Dic47C2411yescharacteristic
397C2×Dic47C2411yescharacteristic
398C2×Dic47C2411yescharacteristic
399C2×Dic47C2411yescharacteristic
400C2×Dic47C2411yescharacteristic
401C2×Dic47C2411yescharacteristic
402C2×Dic47C2411yescharacteristic
403C2×Dic47C2411yescharacteristic
404C2×Dic47C2411yescharacteristic
405D188—41no—
406D188—41no—
407D188—41no—
408D188—41no—
409D188—41no—
410D188—41no—
411D188—41no—
412D188—41no—
413D188—41no—
414D188—41no—
415D188—41no—
416D188—41no—
417D188—41no—
418D188—41no—
419D188—41no—
420D188—41no—
421D188—41no—
422D188—41no—
423C4×D47—41no—
424C4×D47—41no—
425C4×D47—41no—
426C4×D47—41no—
427C4×D47—41no—
428C4×D47—41no—
429C4×D47—41no—
430C4×D47—41no—
431C4×D47—41no—
432C4×D47—41no—
433C4×D47—41no—
434C4×D47—41no—
435C4×D47—41no—
436C4×D47—41no—
437C4×D47—41no—
438Dic94—41no—
439Dic94—41no—
440Dic94—41no—
441Dic94—41no—
442C22×C47—21no—
443C22×C47—21no—
444C22×C47—21no—
445C22×C47—21no—
446C22×C47—21no—
447C22×C47H(5,𝔽2)12yes—
448C22×C47C2511yescharacteristic
449C2×D47—21no—
450C2×D47—21no—
451C2×D47—21no—
452C2×D47—21no—
453C2×D47—21no—
454C2×D47—21no—
455C2×D47—21no—
456C2×D47—21no—
457C2×D47—21no—
458C2×D47—21no—
459C2×D47—21no—
460C2×D47—21no—
461C2×D47—21no—
462C2×D47—21no—
463C2×D47—21no—
464C2×D47—21no—
465C2×D47—21no—
466C2×D47—21no—
467C2×D47—21no—
468C2×D47—21no—
469C2×D47—21no—
470C2×D47—44no—
471C2×D47—82no—
472C2×D47—82no—
473C4×C47—21no—
474C4×C47—21no—
475C4×C47—21no—
476C4×C47—21no—
477C4×C47—21no—
478C4×C47—21no—
479C4×C47—21no—
480C4×C47—21no—
481C4×C47—21no—
482C4×C47—21no—
483C4×C47—21no—
484C4×C47—21no—
485C4×C47—21no—
486Dic47—21no—
487Dic47—21no—
488Dic47—21no—
489Dic47—21no—
490Dic47—21no—
491Dic47—21no—
492Dic47—21no—
493Dic47—21no—
494Dic47—21no—
495#3533—471nomaximal, Sylow
496C2×C47—22no—
497C2×C47—41no—
498C2×C47C2×H(5,𝔽2)11yescharacteristic
499C2×C47#58511yescharacteristic
500C2×C47#58511yescharacteristic
501D47—41no—
502D47—41no—
503D47—41no—
504D47—41no—
505D47—41no—
506D47—41no—
507D47—41no—
508#563—471no—
509#562—471no—
510#562—471no—
511#560—471no—
512#559—471no—
513#553—471no—
514#553—471no—
515#552—471no—
516#552D4711yescharacteristic, complemented
517#551—471no—
518#551—471no—
519#551—471no—
520#547—471no—
521#547—471no—
522#546—471no—
523#546—471no—
524#542—471no—
525#542—471no—
526#540—471no—
527#540—471no—
528#539—471no—
529#539—471no—
530#538—471no—
531#538—471no—
532#538—471no—
533#538—471no—
534#535—471no—
535#534—471no—
536#525—471no—
537#525—471no—
538C2×#123—471no—
539C47#353311yescharacteristic, complemented, Sylow
540C2×#41—471no—
541C2×#41—471no—
542C2×#41—471no—
543C22×D4—471no—
544C22×D4—471no—
545C23×C4—471no—
546C4⋊Q8—471no—
547C4⋊Q8—471no—
548#127—471no—
549#127—471no—
550#126—471no—
551#126—471no—
552#126—471no—
553#126—471no—
554#126—471no—
555#126—471no—
556#126—471no—
557#126—471no—
558#126—471no—
559#126—471no—
560#126C2×D4711yescharacteristic, complemented
561#126C2×D4711yescharacteristic, complemented
562#125—471no—
563#125—471no—
564#125—471no—
565#125C2×D4711yescharacteristic, complemented
566#125C2×D4711yescharacteristic, complemented
567#125C2×D4711yescharacteristic, complemented
568#124—471no—
569#124—471no—
570#124—471no—
571#124—471no—
572#124—471no—
573#124—471no—
574#124—471no—
575#124—471no—
576#124—471no—
577#124—471no—
578#123—471no—
579#123—471no—
580#123—471no—
581#123—471no—
582#123—471no—
583#123—471no—
584#123—471no—
585#123—471no—
586#123—471no—
587#123—471no—
588#123—471no—
589#123—471no—
590#123—471no—
591#123—471no—
592#123—471no—
593#123—471no—
594#123—471no—
595#123—471no—
596#123—471no—
597#123—471no—
598#123—471no—
599#123—471no—
600#123—471no—
601#123—471no—
602#123—471no—
603#123—471no—
604#123—471no—
605#123—471no—
606#123C2×D4711yescharacteristic
607#123C2×D4711yescharacteristic
608C22⋊Q8—471no—
609C22⋊Q8—471no—
610C22⋊Q8—471no—
611C22⋊Q8—471no—
612C22⋊Q8—471no—
613C22⋊Q8—471no—
614C22⋊Q8—471no—
615C22⋊Q8—471no—
616C22⋊Q8—471no—
617C22⋊Q8—471no—
618C22⋊Q8—471no—
619C22⋊Q8—471no—
620C22⋊Q8—471no—
621C22⋊Q8—471no—
622C22⋊Q8C2×D4711yescharacteristic, complemented
623C22⋊Q8C2×D4711yescharacteristic, complemented
624#121—471no—
625#121—471no—
626#121—471no—
627#121—471no—
628#121—471no—
629#121—471no—
630#121—471no—
631#121—471no—
632#121—471no—
633#121—471no—
634#121—471no—
635#121—471no—
636#121—471no—
637#121—471no—
638#121—471no—
639#121—471no—
640#121—471no—
641#121—471no—
642#121—471no—
643#121—471no—
644#121—471no—
645#121—471no—
646#121—471no—
647#121—471no—
648#120—471no—
649#120—471no—
650#120—471no—
651#120—471no—
652#120—471no—
653#120—471no—
654#120—471no—
655#120—471no—
656#120—471no—
657#120—471no—
658C4×Q8—471no—
659C4×Q8C2×D4711yescharacteristic, complemented
660C4×D4—471no—
661C4×D4—471no—
662C4×D4—471no—
663C4×D4—471no—
664C4×D4—471no—
665C4×D4—471no—
666C4×D4—471no—
667C4×D4—471no—
668C4×D4—471no—
669C4×D4—471no—
670C4×D4—471no—
671C4×D4—471no—
672C4×D4—471no—
673C4×D4—471no—
674C4×D4—471no—
675C4×D4—471no—
676C4×D4—471no—
677C4×D4C2×D4711yescharacteristic
678#117—471no—
679#117—471no—
680#117—471no—
681#117—471no—
682#117C2×D4711yescharacteristic, complemented
683#117C2×D4711yescharacteristic, complemented
684#117C2×D4711yescharacteristic, complemented
685C2×C4⋊C4—471no—
686C2×C4⋊C4—471no—
687C2×C4⋊C4—471no—
688C2×C4⋊C4C2×D4711yescharacteristic, complemented
689C2×C22⋊C4—471no—
690C2×C22⋊C4—471no—
691C2×C22⋊C4—471no—
692C2×C22⋊C4—471no—
693C2×C22⋊C4—471no—
694C2×C22⋊C4—471no—
695C24—471no—
696C24—471no—
697C24—471no—
698#41—1882no—
699#41—1882no—
700#41—1882no—
701C2×Q8—471no—
702C2×Q8—471no—
703C2×Q8—471no—
704C2×Q8—471no—
705C2×Q8C22×D4711yescharacteristic
706C2×D4—471no—
707C2×D4—471no—
708C2×D4—471no—
709C2×D4—471no—
710C2×D4—471no—
711C2×D4—471no—
712C2×D4—471no—
713C2×D4—471no—
714C2×D4—471no—
715C2×D4—471no—
716C2×D4—471no—
717C2×D4—471no—
718C2×D4—471no—
719C2×D4—471no—
720C2×D4—471no—
721C2×D4—471no—
722C2×D4—471no—
723C2×D4—471no—
724C2×D4—471no—
725C2×D4—471no—
726C2×D4—471no—
727C2×D4—471no—
728C2×D4—471no—
729C2×D4—471no—
730C2×D4—471no—
731C2×D4—471no—
732C2×D4—1882no—
733C2×D4—1882no—
734C2×D4C22×D4711yescharacteristic
735C22×C4—471no—
736C22×C4—471no—
737C22×C4—471no—
738C22×C4—471no—
739C22×C4—471no—
740C22×C4—471no—
741C22×C4—471no—
742C22×C4—471no—
743C22×C4—471no—
744C22×C4—471no—
745C22×C4—471no—
746C22×C4—471no—
747C22×C4—471no—
748C22×C4—471no—
749C22×C4—471no—
750C22×C4—471no—
751C22×C4—471no—
752C22×C4—471no—
753C22×C4—1882no—
754C22×C4C22×D4711yescharacteristic
755C22×C4C22×D4711yescharacteristic
756C22×C4C22×D4711yescharacteristic
757C22×C4C22×D4711yescharacteristic
758C4⋊C4—471no—
759C4⋊C4—471no—
760C4⋊C4—471no—
761C4⋊C4—471no—
762C4⋊C4—471no—
763C4⋊C4—471no—
764C4⋊C4—471no—
765C4⋊C4—471no—
766C4⋊C4—471no—
767C4⋊C4—471no—
768C4⋊C4—471no—
769C4⋊C4—471no—
770C4⋊C4—471no—
771C4⋊C4—471no—
772C4⋊C4—471no—
773C4⋊C4—471no—
774C4⋊C4—471no—
775C4⋊C4—471no—
776C4⋊C4—471no—
777C4⋊C4—471no—
778C4⋊C4—471no—
779C4⋊C4—471no—
780C4⋊C4C22×D4711yescharacteristic
781C4⋊C4C22×D4711yescharacteristic
782C4⋊C4C22×D4711yescharacteristic
783C4⋊C4C22×D4711yescharacteristic
784C4⋊C4C22×D4711yescharacteristic
785C4⋊C4C22×D4711yescharacteristic
786C4⋊C4C22×D4711yescharacteristic
787C4⋊C4C22×D4711yescharacteristic
788C4⋊C4C22×D4711yescharacteristic
789C4⋊C4C22×D4711yescharacteristic
790C4⋊C4C22×D4711yescharacteristic
791C4⋊C4C22×D4711yescharacteristic
792C4⋊C4C22×D4711yescharacteristic
793C4⋊C4C22×D4711yescharacteristic
794C4⋊C4C22×D4711yescharacteristic
795C4⋊C4C22×D4711yescharacteristic
796C22⋊C4—471no—
797C22⋊C4—471no—
798C22⋊C4—471no—
799C22⋊C4—471no—
800C22⋊C4—471no—
801C22⋊C4—471no—
802C22⋊C4—471no—
803C22⋊C4—471no—
804C22⋊C4—471no—
805C22⋊C4—471no—
806C22⋊C4—471no—
807C22⋊C4—471no—
808C22⋊C4—471no—
809C22⋊C4—471no—
810C22⋊C4—471no—
811C22⋊C4—471no—
812C22⋊C4—471no—
813C22⋊C4—471no—
814C22⋊C4—471no—
815C22⋊C4—471no—
816C22⋊C4—471no—
817C22⋊C4—471no—
818C22⋊C4—471no—
819C22⋊C4—471no—
820C22⋊C4—471no—
821C22⋊C4—471no—
822C22⋊C4—471no—
823C22⋊C4—471no—
824C22⋊C4—471no—
825C22⋊C4—471no—
826C22⋊C4—471no—
827C22⋊C4—471no—
828C22⋊C4—471no—
829C22⋊C4—471no—
830C22⋊C4—471no—
831C22⋊C4—471no—
832C22⋊C4—471no—
833C22⋊C4—471no—
834C22⋊C4—471no—
835C22⋊C4—471no—
836C22⋊C4—471no—
837C22⋊C4—471no—
838C22⋊C4C22×D4711yescharacteristic
839C22⋊C4C22×D4711yescharacteristic
840C22⋊C4C22×D4711yescharacteristic
841C22⋊C4C22×D4711yescharacteristic
842C22⋊C4C22×D4711yescharacteristic
843C22⋊C4C22×D4711yescharacteristic
844C22⋊C4C22×D4711yescharacteristic
845C22⋊C4C22×D4711yescharacteristic
846C42—471no—
847C42—471no—
848C42—471no—
849C42—471no—
850C42—471no—
851C42C22×D4711yescharacteristic
852C42C22×D4711yescharacteristic
853C42C22×D4711yescharacteristic
854C42C22×D4711yescharacteristic
855C42C22×D4711yescharacteristic
856C23—471no—
857C23—471no—
858C23—471no—
859C23—471no—
860C23—471no—
861C23—471no—
862C23—471no—
863C23—942no—
864C23—942no—
865C23—1881no—
866C23—1881no—
867C23—1881no—
868C23—1881no—
869C23—1881no—
870C23—1881no—
871C23—1881no—
872C23C23×D4711yescharacteristic
873C23C23×D4711yescharacteristic
874Q8—41no—
875Q8—1881no—
876Q8—1881no—
877Q8—1881no—
878Q8—1881no—
879D4—22no—
880D4—942no—
881D4—942no—
882D4—942no—
883D4—1881no—
884D4—1881no—
885D4—1881no—
886D4—1881no—
887D4—1881no—
888D4—1881no—
889D4—1881no—
890D4—1881no—
891D4—1881no—
892D4—1881no—
893D4—1881no—
894D4—1881no—
895D4—1881no—
896D4—1881no—
897D4—1881no—
898D4—1881no—
899D4—1881no—
900D4—1881no—
901D4—1881no—
902D4—1881no—
903D4—1881no—
904D4—1881no—
905D4—1881no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—471no—
911C2×C4—471no—
912C2×C4—471no—
913C2×C4—471no—
914C2×C4—471no—
915C2×C4—471no—
916C2×C4—471no—
917C2×C4—471no—
918C2×C4—471no—
919C2×C4—942no—
920C2×C4—1881no—
921C2×C4—1881no—
922C2×C4—1881no—
923C2×C4—1881no—
924C2×C4—1881no—
925C2×C4—1881no—
926C2×C4—1881no—
927C2×C4—1881no—
928C2×C4—1881no—
929C2×C4—1881no—
930C2×C4—1881no—
931C2×C4—1881no—
932C2×C4—1881no—
933C2×C4—1881no—
934C2×C4—1881no—
935C2×C4—1881no—
936C2×C4—1881no—
937C2×C4C23×D4711yescharacteristic
938C2×C4C23×D4711yescharacteristic
939C2×C4C23×D4711yescharacteristic
940C2×C4C23×D4711yescharacteristic
941C2×C4C23×D4711yescharacteristic
942C2×C4C23×D4711yescharacteristic
943C2×C4C23×D4711yescharacteristic
944C2×C4C23×D4711yescharacteristic
945C2×C4C23×D4711yescharacteristic
946C2×C4C23×D4711yescharacteristic
947C2×C4C23×D4711yescharacteristic
948C2×C4C23×D4711yescharacteristic
949C2×C4C23×D4711yescharacteristic
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—941no—
956C22—941no—
957C22—941no—
958C22—941no—
959C22—941no—
960C22—941no—
961C22—941no—
962C22—941no—
963C22—941no—
964C22—941no—
965C22—941no—
966C22—941no—
967C22—941no—
968C22—941no—
969C22—941no—
970C22—941no—
971C22—941no—
972C22—941no—
973C22—941no—
974C22—941no—
975C22—941no—
976C22—3762no—
977C22—3762no—
978C22—1884no—
979C22#1309407012yes—
980C22C24×D4711yescharacteristic
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—21no—
991C4—21no—
992C4—21no—
993C4—21no—
994C4—941no—
995C4—941no—
996C4—941no—
997C4—941no—
998C4—941no—
999C4—941no—
1000C4—941no—
1001C4—941no—
1002C4—941no—
1003C2—22no—
1004C2—41no—
1005C2—1881no—
1006C2—1881no—
1007C2—1881no—
1008C2—1881no—
1009C2—1881no—
1010C2—1881no—
1011C2—1881no—
1012C2C2×#1309407011yescharacteristic
1013C2#1568995911yescharacteristic
1014C2#1568996011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#552C2
hypercenter#552D47
hypocenterC47#3533
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #552

Complements

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

NH ≅ G/Ntype
1. #15689877C2semidirect
2. #15689871C2semidirect
3. #15689869C2semidirect
4. #15689864C2semidirect
5. #15689858C2semidirect
6. #15689826C2semidirect
7. #15689824C2semidirect
8. #15689806C2semidirect
9. #15689800C2semidirect
10. #15689797C2semidirect
11. #15689797C2semidirect
12. #15689774C2semidirect
13. #15689771C2semidirect
14. #15689768C2semidirect
15. #15689765C2semidirect
16. #15689745C2semidirect
17. #15689739C2semidirect
18. #15689729C2semidirect
19. #15689728C2semidirect
20. #15689721C2semidirect
21. #15689721C2semidirect
22. #15689713C2semidirect
23. #15689713C2semidirect
24. #15689712C2semidirect
25. #15689706C2semidirect
26. #15689692C2semidirect
27. #15689684C2semidirect
28. #15689635C2semidirect
29. #15689631C2semidirect
30. C2×#13094009C2semidirect
31. C47×#552C2semidirect
33. C2×#10625350C22semidirect
37. C22×C4×D47C22semidirect
38. #13094023C22semidirect
39. #13094023C22semidirect
41. #13094021C22semidirect
42. #13094019C22semidirect
43. #13094019C22semidirect
44. #13094019C22semidirect
45. #13094019C22semidirect
46. #13094019C22semidirect
47. #13094019C22semidirect
48. #13094019C22semidirect
49. #13094018C22semidirect
50. #13094018C22semidirect
51. #13094018C22semidirect
52. #13094016C22semidirect
53. #13094014C22semidirect
54. #13094014C22semidirect
55. #13094013C22semidirect
56. #13094013C22semidirect
57. #13094013C22semidirect
59. #13094012C22semidirect
60. #13094012C22semidirect
61. #13094012C22semidirect
62. #13094012C22semidirect
63. #13094010C22semidirect
64. #13094010C22semidirect
71. #13094009C22semidirect
72. #13094009C22semidirect
73. #13094009C22semidirect
74. #13094009C22semidirect
75. #13094009C22semidirect
76. #13094009C22semidirect
77. #13094009C22semidirect
78. #13094009C22semidirect
79. #13094009C22semidirect
80. #13094009C22semidirect
81. #13094009C22semidirect
82. #13094009C22semidirect
83. #13094009C22semidirect
84. #13094009C22semidirect
85. #13094009C22semidirect
87. #13094008C22semidirect
88. #13094008C22semidirect
90. #13094007C22semidirect
91. #13094007C22semidirect
92. #13094006C22semidirect
93. #13094004C22semidirect
94. #13094004C22semidirect
95. #13094004C22semidirect
96. #13094002C22semidirect
97. #13094002C22semidirect
98. #13094002C22semidirect
99. #13094002C22semidirect
100. #13094002C22semidirect
101. #13094002C22semidirect
102. #13094002C22semidirect
103. #13094002C22semidirect
104. #13094001C22semidirect
105. #13094001C22semidirect
106. #13094000C22semidirect
111. #13093999C22semidirect
112. #13093999C22semidirect
113. #13093999C22semidirect
114. #13093999C22semidirect
115. #13093999C22semidirect
116. #13093999C22semidirect
117. #13093999C22semidirect
118. #13093999C22semidirect
119. #13093999C22semidirect
121. #13093998C22semidirect
122. #13093998C22semidirect
125. #13093997C22semidirect
126. #13093997C22semidirect
127. #13093997C22semidirect
128. #13093997C22semidirect
129. #13093997C22semidirect
136. #13093994C22semidirect
137. #13093994C22semidirect
138. #13093994C22semidirect
139. #13093994C22semidirect
141. C4×Dic94C22semidirect
142. C4×D188C22semidirect
143. C4×D188C22semidirect
144. C4×D188C22semidirect
145. C4×D188C22semidirect
146. C4×D188C22semidirect
147. C4×D188C22semidirect
148. #13093986C22semidirect
149. #13093986C22semidirect
150. #13093986C22semidirect
151. #13093986C22semidirect
152. #13093986C22semidirect
153. C4×C22⋊D47C22semidirect
155. (C22⋊D47)⋊C4C22semidirect
156. (C22⋊D47)⋊C4C22semidirect
157. (C22⋊D47)⋊C4C22semidirect
158. (C22⋊D47)⋊C4C22semidirect
159. #13093982C22semidirect
160. #13093981C22semidirect
161. #13093981C22semidirect
162. #13093980C22semidirect
163. C2×Dic47⋊C4C22semidirect
164. C4⋊C4×D47C22semidirect
165. C4⋊C4×D47C22semidirect
168. C2×(C2×D47)⋊C4C22semidirect
169. C2×(C2×D47)⋊C4C22semidirect
171. C22⋊C4×D47C22semidirect
172. #126×C47C22semidirect
173. #126×C47C22semidirect
174. #125×C47C22semidirect
175. #125×C47C22semidirect
176. #125×C47C22semidirect
179. C22⋊Q8×C47C22semidirect
180. C22⋊Q8×C47C22semidirect
181. C4×Q8×C47C22semidirect
183. #117×C47C22semidirect
184. #117×C47C22semidirect
185. #117×C47C22semidirect
186. C2×C4⋊C4×C47C22semidirect
516. #552D47semidirect
539. C47#3533semidirect
560. #126C2×D47semidirect
561. #126C2×D47semidirect
565. #125C2×D47semidirect
566. #125C2×D47semidirect
567. #125C2×D47semidirect
622. C22⋊Q8C2×D47semidirect
623. C22⋊Q8C2×D47semidirect
659. C4×Q8C2×D47semidirect
682. #117C2×D47semidirect
683. #117C2×D47semidirect
684. #117C2×D47semidirect
688. C2×C4⋊C4C2×D47semidirect