Finite Group Databasebeta

← C2×#21433169 #29453469

Subgroups — C2×#21433169 #29453469

Order 15104.

2230 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837948C211yesmaximal, characteristic
2#21433169C2116yesmaximal, direct product factor
3C2×#16837478C211yesmaximal, characteristic, complemented
4C2×#16837477C211yesmaximal, characteristic, complemented
5C2×#16837476C211yesmaximal, characteristic, complemented
6C2×#16837473C211yesmaximal, characteristic, complemented
7C2×#16837471C211yesmaximal, characteristic, complemented
8C2×#16837470C211yesmaximal, characteristic, complemented
9C2×C8×C22⋊D59C211yesmaximal, characteristic, complemented
10C2×(C22⋊D59)⋊C8C211yesmaximal, characteristic, complemented
11C2×#16837456C211yesmaximal, characteristic, complemented
12C2×#16837452C211yesmaximal, characteristic, complemented
13C2×#16837369C211yesmaximal, characteristic, complemented
14C2×#16837367C211yesmaximal, characteristic, complemented
15C2×#16837367C211yesmaximal, characteristic, complemented
16C2×C59×#408C211yesmaximal, characteristic, complemented
17C22×#11745685C2211yescharacteristic
18C22×#11745664C2211yescharacteristic
19C22×#11745659C2211yescharacteristic
20C22×#11745659C2211yescharacteristic
21C23×C59⋊C8C2211yescharacteristic
22C22×C8×D59C2211yescharacteristic
23C22×C8×D59C2211yescharacteristic
24#16837948C418yes—
25#16837948C2218yes—
26C2×#14273725C411yescharacteristic
27C2×#14273723C411yescharacteristic
28C2×#14273716C411yescharacteristic
29C2×#14273714C411yescharacteristic
30C2×#14273699C411yescharacteristic
31C2×#14273699C411yescharacteristic
32C2×#14273699C411yescharacteristic
33C2×#14273699C411yescharacteristic
34C2×C4×C22⋊D59C2211yescharacteristic
35C2×C4×C22⋊D59C2211yescharacteristic
36C2×C4×C22⋊D59C2211yescharacteristic
37C2×C4×C22⋊D59C2211yescharacteristic
38C22×C4×Dic59C2211yescharacteristic
39#16837478C2218yescomplemented
40#16837477C2218yescomplemented
41#16837476C2218yescomplemented
42#16837473C2218yescomplemented
43#16837471C2218yescomplemented
44#16837470C2218yescomplemented
45C8×C22⋊D59C2218yescomplemented
46(C22⋊D59)⋊C8C2218yescomplemented
47#16837456C2218yescomplemented
48#16837452C2218yescomplemented
49C2×Dic59⋊C8C2211yescharacteristic
50C2×Dic59⋊C8C2211yescharacteristic
51C2×Dic59⋊C8C2211yescharacteristic
52C2×Dic59⋊C8C2211yescharacteristic
53#16837369C2218yescomplemented
54#16837367C2218yescomplemented
55#16837367C2218yescomplemented
56C2×C22⋊(C59⋊C8)C2211yescharacteristic
57C2×C22⋊(C59⋊C8)C2211yescharacteristic
58C2×C22⋊(C59⋊C8)C2211yescharacteristic
59C2×C22⋊(C59⋊C8)C2211yescharacteristic
60C2×(C2×D59)⋊C8C2211yescharacteristic
61C2×(C2×D59)⋊C8C2211yescharacteristic
62C2×(C2×D59)⋊C8C2211yescharacteristic
63C2×(C2×D59)⋊C8C2211yescharacteristic
64C2×#14273637C2211yescharacteristic
65C2×#14273637C2211yescharacteristic
66C2×C8×Dic59C2211yescharacteristic
67C2×C8×Dic59C2211yescharacteristic
68C22×#41×C59C2211yescharacteristic
69C22×M16×C59C2211yescharacteristic
70C23×C8×C59C2211yescharacteristic
71C59×#408C2218yescomplemented
72C2×C22⋊C8×C59C2211yescharacteristic
73C2×C22⋊C8×C59C2211yescharacteristic
74C2×C22⋊C8×C59C2211yescharacteristic
75C2×C22⋊C8×C59C2211yescharacteristic
76C2×#11745685—42no—
77C2×#11745685—42no—
78C2×#11745685C2×C414yes—
79C2×#11745685C2314yes—
80C22×Dic118C2×C411yescharacteristic
81C22×D236C2×C411yescharacteristic
82C22×C22⋊D59C2×C411yescharacteristic
83C22×C22⋊D59C2×C411yescharacteristic
84C22×C22⋊D59C2×C411yescharacteristic
85C22×C22⋊D59C2×C411yescharacteristic
86C22×C22⋊D59C2×C411yescharacteristic
87C22×C22⋊D59C2×C411yescharacteristic
88C23×Dic59C2×C411yescharacteristic
89C23×Dic59C2×C411yescharacteristic
90C22×C4×D59C2311yescharacteristic
91C22×C4×D59C2311yescharacteristic
92C2×#11745664—42no—
93C2×#11745664C2314yes—
94C2×#11745659—42no—
95C2×#11745659—42no—
96C2×#11745659C2314yes—
97C2×#11745659C2314yes—
98C22×C59⋊C8—42no—
99C22×C59⋊C8C2311yescharacteristic
100C22×C59⋊C8C2311yescharacteristic
101C22×C59⋊C8C2311yescharacteristic
102C22×C59⋊C8C2311yescharacteristic
103C22×C59⋊C8C2314yes—
104C2×C8×D59—42no—
105C2×C8×D59—42no—
106C2×C8×D59C2314yes—
107C2×C8×D59C2314yes—
108#14273725C2×C418yes—
109#14273723C2×C418yes—
110#14273716C2×C418yes—
111#14273714C2×C418yes—
112#14273699C2×C418yes—
113#14273699C2×C418yes—
114#14273699C2×C418yes—
115#14273699C2×C418yes—
116C4×C22⋊D59C2×C414yes—
117C4×C22⋊D59C2×C414yes—
118C4×C22⋊D59C2×C414yes—
119C4×C22⋊D59C2×C414yes—
120C4×C22⋊D59C2314yes—
121C4×C22⋊D59C2314yes—
122C4×C22⋊D59C2314yes—
123C4×C22⋊D59C2314yes—
124C2×Dic59⋊C4C2×C411yescharacteristic
125C2×Dic59⋊C4C2×C411yescharacteristic
126C2×Dic59⋊C4C2×C411yescharacteristic
127C2×Dic59⋊C4C2×C411yescharacteristic
128C2×C22⋊Dic59C2×C411yescharacteristic
129C2×C22⋊Dic59C2×C411yescharacteristic
130C2×C22⋊Dic59C2×C411yescharacteristic
131C2×C22⋊Dic59C2×C411yescharacteristic
132C2×(C2×D59)⋊C4C2×C411yescharacteristic
133C2×(C2×D59)⋊C4C2×C411yescharacteristic
134C2×(C2×D59)⋊C4C2×C411yescharacteristic
135C2×(C2×D59)⋊C4C2×C411yescharacteristic
136C2×C4×Dic59C2×C411yescharacteristic
137C2×C4×Dic59C2×C411yescharacteristic
138C2×C4×Dic59C2×C414yes—
139C2×C4×Dic59C2311yescharacteristic
140C2×C4×Dic59C2311yescharacteristic
141C2×C4×Dic59C2314yes—
142Dic59⋊C8C2314yes—
143Dic59⋊C8C2314yes—
144Dic59⋊C8C2314yes—
145Dic59⋊C8C2314yes—
146C22⋊(C59⋊C8)C2314yes—
147C22⋊(C59⋊C8)C2314yes—
148C22⋊(C59⋊C8)C2314yes—
149C22⋊(C59⋊C8)C2314yes—
150(C2×D59)⋊C8C2314yes—
151(C2×D59)⋊C8C2314yes—
152(C2×D59)⋊C8C2314yes—
153(C2×D59)⋊C8C2314yes—
154#14273637C2314yes—
155#14273637C2314yes—
156C8×Dic59C2314yes—
157C8×Dic59C2314yes—
158C2×#41×C59—42no—
159C2×#41×C59—42no—
160C2×#41×C59C2×C414yes—
161C2×#41×C59C2314yes—
162C22×Q8×C59C2×C411yescharacteristic
163C22×D4×C59C2×C411yescharacteristic
164C22×D4×C59C2×C411yescharacteristic
165C22×D4×C59C2×C411yescharacteristic
166C23×C4×C59C2311yescharacteristic
167C23×C4×C59C2311yescharacteristic
168C23×C4×C59C2311yescharacteristic
169C2×M16×C59—42no—
170C2×M16×C59C2314yes—
171C22×C8×C59—42no—
172C22×C8×C59C2311yescharacteristic
173C22×C8×C59C2311yescharacteristic
174C22×C8×C59C2311yescharacteristic
175C22×C8×C59C2311yescharacteristic
176C22×C8×C59C2314yes—
177C22⋊C8×C59C2314yes—
178C22⋊C8×C59C2314yes—
179C22⋊C8×C59C2314yes—
180C22⋊C8×C59C2314yes—
181C24×C59C22×C411yescharacteristic
182C24×C59C22×C411yescharacteristic
183C24×C59C22×C411yescharacteristic
184C23×D59C22×C411yescharacteristic
185C23×D59C22×C411yescharacteristic
186#41×C59—48no—
187#41×C59—44no—
188#41×C59—44no—
189C2×Q8×C59—42no—
190C2×Q8×C59C22×C414yes—
191C2×D4×C59—42no—
192C2×D4×C59—42no—
193C2×D4×C59—42no—
194C2×D4×C59C22×C414yes—
195C2×D4×C59C22×C414yes—
196C2×D4×C59C22×C414yes—
197C22×C4×C59—22no—
198C22×C4×C59—22no—
199C22×C4×C59—22no—
200C22×C4×C59—22no—
201C22×C4×C59—22no—
202C22×C4×C59—22no—
203C22×C4×C59C22×C411yescharacteristic
204C22×C4×C59C22×C411yescharacteristic
205C22×C4×C59C22×C411yescharacteristic
206C22×C4×C59C22×C412yes—
207C22×C4×C59C22×C412yes—
208C22×C4×C59C22×C412yes—
209C22×C4×C59C2412yes—
210C22×C4×C59C2412yes—
211C22×C4×C59C2412yes—
212C22×C4×C59C2411yescharacteristic
213C2×C22⋊D59—24no—
214C2×C22⋊D59—24no—
215C2×C22⋊D59—42no—
216C2×C22⋊D59—42no—
217C2×C22⋊D59—42no—
218C2×C22⋊D59—42no—
219C2×C22⋊D59C22×C414yes—
220C2×C22⋊D59C22×C414yes—
221C2×C22⋊D59C22×C414yes—
222C2×C22⋊D59C22×C414yes—
223C2×C22⋊D59C22×C414yes—
224C2×C22⋊D59C22×C414yes—
225C22×Dic59—24no—
226C22×Dic59—42no—
227C22×Dic59C22×C411yescharacteristic
228C22×Dic59C22×C411yescharacteristic
229C22×Dic59C22×C411yescharacteristic
230C22×Dic59C22×C414yes—
231C22×Dic59C22×C411yescharacteristic
232C22×Dic59C22×C411yescharacteristic
233C22×Dic59C22×C414yes—
234C22×Dic59C22×C411yescharacteristic
235#11745685—48no—
236#11745685—44no—
237#11745685—44no—
238C2×D236—42no—
239C2×D236C22×C414yes—
240C2×C4×D59—22no—
241C2×C4×D59—22no—
242C2×C4×D59—22no—
243C2×C4×D59—22no—
244C2×C4×D59C22×C412yes—
245C2×C4×D59C22×C412yes—
246C2×C4×D59C2412yes—
247C2×C4×D59C2412yes—
248C2×Dic118—42no—
249C2×Dic118C22×C414yes—
250M16×C59—44no—
251C2×C8×C59—22no—
252C2×C8×C59—22no—
253C2×C8×C59—22no—
254C2×C8×C59—22no—
255C2×C8×C59—44no—
256C2×C8×C59C2412yes—
257C2×C8×C59C2412yes—
258C2×C8×C59C2412yes—
259C2×C8×C59C2412yes—
260C22⋊Dic59C22×C414yes—
261C22⋊Dic59C22×C414yes—
262C22⋊Dic59C22×C414yes—
263C22⋊Dic59C22×C414yes—
264(C2×D59)⋊C4C22×C414yes—
265(C2×D59)⋊C4C22×C414yes—
266(C2×D59)⋊C4C22×C414yes—
267(C2×D59)⋊C4C22×C414yes—
268Dic59⋊C4C22×C414yes—
269Dic59⋊C4C22×C414yes—
270Dic59⋊C4C22×C414yes—
271Dic59⋊C4C22×C414yes—
272C4×Dic59C22×C412yes—
273C4×Dic59C22×C412yes—
274C4×Dic59C22×C414yes—
275C4×Dic59C22×C414yes—
276C4×Dic59C2412yes—
277C4×Dic59C2412yes—
278#11745664—44no—
279C2×C59⋊C8—22no—
280C2×C59⋊C8—22no—
281C2×C59⋊C8—22no—
282C2×C59⋊C8—22no—
283C2×C59⋊C8—44no—
284C2×C59⋊C8C2412yes—
285C2×C59⋊C8C2412yes—
286C2×C59⋊C8C2412yes—
287C2×C59⋊C8C2412yes—
288#11745659—44no—
289#11745659—44no—
290C8×D59—44no—
291C8×D59—44no—
292C23×C59—22no—
293C23×C59—22no—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59—22no—
297C23×C59—22no—
298C23×C59—22no—
299C23×C59—22no—
300C23×C59—22no—
301C23×C59C23×C412yes—
302C23×C59C23×C412yes—
303C23×C59C23×C412yes—
304C23×C59C23×C411yescharacteristic
305C22×D59—22no—
306C22×D59—22no—
307C22×D59—22no—
308C22×D59—22no—
309C22×D59—22no—
310C22×D59—22no—
311C22×D59C23×C412yes—
312C22×D59C23×C412yes—
313Q8×C59—44no—
314D4×C59—44no—
315D4×C59—44no—
316D4×C59—44no—
317C2×C4×C59—22no—
318C2×C4×C59—22no—
319C2×C4×C59—22no—
320C2×C4×C59—24no—
321C2×C4×C59—24no—
322C2×C4×C59—24no—
323C2×C4×C59—22no—
324C2×C4×C59—22no—
325C2×C4×C59—22no—
326C2×C4×C59—22no—
327C2×C4×C59—22no—
328C2×C4×C59—22no—
329C2×C4×C59C23×C412yes—
330C2×C4×C59C23×C412yes—
331C2×C4×C59C23×C412yes—
332C2×C4×C59C23×C411yescharacteristic
333C2×C4×C59H(5,𝔽2)12yes—
334C2×C4×C59H(5,𝔽2)12yes—
335C2×C4×C59C2511yescharacteristic
336C22⋊D59—28no—
337C22⋊D59—28no—
338C22⋊D59—44no—
339C22⋊D59—44no—
340C22⋊D59—44no—
341C22⋊D59—44no—
342C2×Dic59—22no—
343C2×Dic59—22no—
344C2×Dic59—22no—
345C2×Dic59—22no—
346C2×Dic59—22no—
347C2×Dic59—28no—
348C2×Dic59—44no—
349C2×Dic59#13114yes—
350C2×Dic59C23×C412yes—
351C2×Dic59C23×C412yes—
352C2×Dic59C23×C412yes—
353C2×Dic59C23×C412yes—
354C2×Dic59C23×C412yes—
355C2×Dic59C23×C412yes—
356D236—44no—
357C4×D59—24no—
358C4×D59—24no—
359C4×D59—22no—
360C4×D59—22no—
361C4×D59—22no—
362C4×D59—22no—
363Dic118—44no—
364C8×C59—22no—
365C8×C59—22no—
366C8×C59—22no—
367C8×C59—22no—
368C59⋊C8—22no—
369C59⋊C8—22no—
370C59⋊C8—22no—
371C59⋊C8—22no—
372C2×#2981—591nomaximal, Sylow
373C22×C59—22no—
374C22×C59—22no—
375C22×C59—22no—
376C22×C59—22no—
377C22×C59—22no—
378C22×C59—22no—
379C22×C59—22no—
380C22×C59—22no—
381C22×C59—22no—
382C22×C59—44no—
383C22×C59—44no—
384C22×C59—44no—
385C22×C59#51812yes—
386C22×C59C2×#13112yes—
387C22×C59#56812yes—
388C22×C59C24×C411yescharacteristic
389C2×D59—22no—
390C2×D59—22no—
391C2×D59—22no—
392C2×D59—22no—
393C2×D59—22no—
394C2×D59—22no—
395C2×D59—44no—
396C2×D59—44no—
397C4×C59—22no—
398C4×C59—22no—
399C4×C59—22no—
400C4×C59#51812yes—
401C4×C59C2×H(5,𝔽2)11yescharacteristic
402C4×C59C2×H(5,𝔽2)11yescharacteristic
403Dic59—22no—
404Dic59—22no—
405Dic59—22no—
406Dic59—22no—
407Dic59—22no—
408Dic59C2×#13114yes—
409C2×#532—591no—
410#2981—5916no—
411C2×#436—591no—
412C2×#436—591no—
413C2×#435—591no—
414C2×#435—591no—
415C2×#435—591no—
416C2×#435—591no—
417C2×C8×D4—591no—
418C2×C8×D4—591no—
419C2×#432—591no—
420C2×#431—591no—
421C2×#408—591no—
422C2×#408—591no—
423C2×#408—591no—
424C2×#408D5911yescharacteristic, complemented
425C2×C59—42no—
426C2×C59—42no—
427C2×C59—42no—
428C2×C59#298114yescomplemented
429C2×C59C2×#51811yescharacteristic
430C2×C59C22×#13111yescharacteristic
431C2×C59C2×#56811yescharacteristic
432D59—42no—
433D59—42no—
434C22×#41—591no—
435C22×#41C2×D5911yescharacteristic
436C22×M16—591no—
437C22×M16—591no—
438C22×M16—591no—
439C22×M16C2×D5911yescharacteristic
440C23×C8—591no—
441C23×C8—591no—
442C23×C8—591no—
443C23×C8C2×D5911yescharacteristic
444#532—598no—
445#532—598no—
446C2×C4⋊Q8—591no—
447C2×#127—591no—
448C2×#124—591no—
449C2×#124—591no—
450C2×#121—591no—
451C2×#121—591no—
452C2×#121—591no—
453C2×#121—591no—
454C2×C4×D4—591no—
455C2×C4×D4—591no—
456C2×C4×D4—591no—
457C2×C4×D4—591no—
458C22×C42—591no—
459#436—598no—
460#436—598no—
461#435—598no—
462#435—598no—
463#435—598no—
464#435—598no—
465C8×D4—598no—
466C8×D4—598no—
467#432—598no—
468#431—598no—
469C2×C4⋊C8—591no—
470C2×C4⋊C8—591no—
471C2×C4⋊C8—591no—
472C2×C4⋊C8—591no—
473#408—598no—
474#408—598no—
475#408—598no—
476#408C2×D5918yescomplemented
477C2×C22⋊C8—591no—
478C2×C22⋊C8—591no—
479C2×C22⋊C8—591no—
480C2×C22⋊C8—591no—
481C2×C22⋊C8—591no—
482C2×C22⋊C8—591no—
483C2×C22⋊C8—591no—
484C2×C22⋊C8—591no—
485C2×C22⋊C8C2×D5911yescharacteristic
486C2×C22⋊C8C2×D5911yescharacteristic
487C2×C22⋊C8C2×D5911yescharacteristic
488C2×C22⋊C8C2×D5911yescharacteristic
489C2×#97—591no—
490C2×#97—591no—
491C2×C4×C8—591no—
492C2×C4×C8—591no—
493C59C2×#298111yescharacteristic, complemented, Sylow
494C2×#41—42no—
495C2×#41—42no—
496C2×#41—594no—
497C2×#41—594no—
498C2×#41—2362no—
499C2×#41—2362no—
500C2×#41C4×D5914yes—
501C2×#41C22×D5914yes—
502C22×Q8—591no—
503C22×Q8C4×D5911yescharacteristic
504C22×D4—591no—
505C22×D4—591no—
506C22×D4—591no—
507C22×D4—591no—
508C22×D4—591no—
509C22×D4—591no—
510C22×D4—591no—
511C22×D4C4×D5911yescharacteristic
512C22×D4C4×D5911yescharacteristic
513C22×D4C4×D5911yescharacteristic
514C23×C4—591no—
515C23×C4—591no—
516C23×C4—591no—
517C23×C4—591no—
518C23×C4C22×D5911yescharacteristic
519C23×C4C22×D5911yescharacteristic
520C23×C4C22×D5911yescharacteristic
521C2×M16—42no—
522C2×M16—594no—
523C2×M16—594no—
524C2×M16—594no—
525C2×M16—2362no—
526C2×M16—2362no—
527C2×M16—2362no—
528C2×M16C22×D5914yes—
529C22×C8—42no—
530C22×C8—591no—
531C22×C8—591no—
532C22×C8—591no—
533C22×C8—591no—
534C22×C8—594no—
535C22×C8—594no—
536C22×C8—594no—
537C22×C8—2362no—
538C22×C8—2362no—
539C22×C8—2362no—
540C22×C8C22×D5911yescharacteristic
541C22×C8C22×D5911yescharacteristic
542C22×C8C22×D5911yescharacteristic
543C22×C8C22×D5911yescharacteristic
544C22×C8C22×D5914yes—
545C4⋊Q8—598no—
546#127—598no—
547#124—598no—
548#124—598no—
549#121—598no—
550#121—598no—
551#121—598no—
552#121—598no—
553C4×D4—594no—
554C4×D4—594no—
555C4×D4—594no—
556C4×D4—594no—
557C4×D4—594no—
558C4×D4—594no—
559C4×D4—594no—
560C4×D4—594no—
561C2×C4⋊C4—591no—
562C2×C4⋊C4—591no—
563C2×C4⋊C4—591no—
564C2×C4⋊C4—591no—
565C2×C22⋊C4—591no—
566C2×C22⋊C4—591no—
567C2×C22⋊C4—591no—
568C2×C22⋊C4—591no—
569C2×C22⋊C4—591no—
570C2×C22⋊C4—591no—
571C2×C22⋊C4—591no—
572C2×C22⋊C4—591no—
573C2×C42—591no—
574C2×C42—591no—
575C2×C42—594no—
576C2×C42—594no—
577C2×C42—591no—
578C2×C42—591no—
579C4⋊C8—594no—
580C4⋊C8—594no—
581C4⋊C8—594no—
582C4⋊C8—594no—
583C22⋊C8—594no—
584C22⋊C8—594no—
585C22⋊C8—594no—
586C22⋊C8—594no—
587C22⋊C8—594no—
588C22⋊C8—594no—
589C22⋊C8—594no—
590C22⋊C8—594no—
591C22⋊C8C22×D5914yes—
592C22⋊C8C22×D5914yes—
593C22⋊C8C22×D5914yes—
594C22⋊C8C22×D5914yes—
595#97—594no—
596#97—594no—
597C4×C8—594no—
598C4×C8—594no—
599C24—591no—
600C24—591no—
601C24C2×C4×D5911yescharacteristic
602C24C2×C4×D5911yescharacteristic
603C24C2×C4×D5911yescharacteristic
604#41—48no—
605#41—44no—
606#41—44no—
607#41—2364no—
608#41—2364no—
609#41—2368no—
610C2×Q8—42no—
611C2×Q8—594no—
612C2×Q8—2362no—
613C2×Q8C2×C4×D5914yes—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—594no—
618C2×D4—594no—
619C2×D4—594no—
620C2×D4—594no—
621C2×D4—594no—
622C2×D4—594no—
623C2×D4—594no—
624C2×D4—1184no—
625C2×D4—1184no—
626C2×D4—2362no—
627C2×D4—2362no—
628C2×D4—2362no—
629C2×D4—2362no—
630C2×D4—2362no—
631C2×D4C2×C4×D5914yes—
632C2×D4C2×C4×D5914yes—
633C2×D4C2×C4×D5914yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—591no—
641C22×C4—591no—
642C22×C4—591no—
643C22×C4—591no—
644C22×C4—594no—
645C22×C4—591no—
646C22×C4—591no—
647C22×C4—594no—
648C22×C4—592no—
649C22×C4—592no—
650C22×C4—592no—
651C22×C4—592no—
652C22×C4—1184no—
653C22×C4—1182no—
654C22×C4—1182no—
655C22×C4—1182no—
656C22×C4—1182no—
657C22×C4—2362no—
658C22×C4C2×C4×D5911yescharacteristic
659C22×C4C2×C4×D5912yes—
660C22×C4C2×C4×D5911yescharacteristic
661C22×C4C2×C4×D5911yescharacteristic
662C22×C4C2×C4×D5912yes—
663C22×C4C2×C4×D5912yes—
664C22×C4C23×D5912yes—
665C22×C4C23×D5912yes—
666C22×C4C23×D5912yes—
667C22×C4C23×D5911yescharacteristic
668M16—44no—
669M16—2364no—
670M16—2364no—
671M16—2364no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—44no—
677C2×C8—592no—
678C2×C8—592no—
679C2×C8—592no—
680C2×C8—592no—
681C2×C8—1182no—
682C2×C8—1182no—
683C2×C8—1182no—
684C2×C8—1182no—
685C2×C8—2364no—
686C2×C8—2364no—
687C2×C8—2364no—
688C2×C8C23×D5912yes—
689C2×C8C23×D5912yes—
690C2×C8C23×D5912yes—
691C2×C8C23×D5912yes—
692C4⋊C4—594no—
693C4⋊C4—594no—
694C4⋊C4—594no—
695C4⋊C4—594no—
696C22⋊C4—594no—
697C22⋊C4—594no—
698C22⋊C4—594no—
699C22⋊C4—594no—
700C22⋊C4—594no—
701C22⋊C4—594no—
702C22⋊C4—594no—
703C22⋊C4—594no—
704C42—592no—
705C42—592no—
706C42—594no—
707C42—594no—
708C42—592no—
709C42—592no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—592no—
720C23—592no—
721C23—1182no—
722C23—1182no—
723C23—1182no—
724C23—1182no—
725C23—1182no—
726C23—1182no—
727C23C22×C4×D5912yes—
728C23C22×C4×D5912yes—
729C23C22×C4×D5912yes—
730C23C22×C4×D5911yescharacteristic
731Q8—44no—
732Q8—2364no—
733D4—44no—
734D4—44no—
735D4—44no—
736D4—1188no—
737D4—1188no—
738D4—2364no—
739D4—2364no—
740D4—2364no—
741D4—2364no—
742D4—2364no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—594no—
756C2×C4—592no—
757C2×C4—592no—
758C2×C4—592no—
759C2×C4—592no—
760C2×C4—592no—
761C2×C4—592no—
762C2×C4—1188no—
763C2×C4—1182no—
764C2×C4—1182no—
765C2×C4—1182no—
766C2×C4—1182no—
767C2×C4—1182no—
768C2×C4—1182no—
769C2×C4—1182no—
770C2×C4—1182no—
771C2×C4—1182no—
772C2×C4—1184no—
773C2×C4—1184no—
774C2×C4—2364no—
775C2×C4C22×C4×D5912yes—
776C2×C4C22×C4×D5912yes—
777C2×C4C22×C4×D5912yes—
778C2×C4C22×C4×D5911yescharacteristic
779C2×C4#1427377212yes—
780C2×C4#1427377212yes—
781C2×C4C24×D5911yescharacteristic
782C8—22no—
783C8—22no—
784C8—22no—
785C8—22no—
786C8—1182no—
787C8—1182no—
788C8—1182no—
789C8—1182no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—1182no—
803C22—1182no—
804C22—1182no—
805C22—1182no—
806C22—1182no—
807C22—1182no—
808C22—2364no—
809C22—2364no—
810C22#1683787512yes—
811C22#131×D5912yes—
812C22#1683816712yes—
813C22C23×C4×D5911yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—594no—
818C4—1182no—
819C4—1182no—
820C4—1182no—
821C4—1182no—
822C4—1182no—
823C4#1683787512yes—
824C4C2×#1427377211yescharacteristic
825C4C2×#1427377211yescharacteristic
826C2—42no—
827C2—42no—
828C2—42no—
829C2—2362no—
830C2—2362no—
831C2#2143316914yesdirect product factor
832C2C2×#1683787511yescharacteristic
833C2C2×#131×D5911yescharacteristic
834C2C2×#1683816711yescharacteristic
subgroupG/H
centerC22×C4C23×D59
commutatorC22×C59C24×C4
FrattiniC2×C4C24×D59
FittingC2×C59×#408C2
socleC23×C59C23×C4
prime radicalC2×#16837948C2
cosocleC2×C4×C59C25
hypercenterC2×#408D59
hypocenterC59C2×#2981
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. #21433169C2direct (N × H)
3. C2×#16837478C2semidirect
4. C2×#16837477C2semidirect
5. C2×#16837476C2semidirect
6. C2×#16837473C2semidirect
7. C2×#16837471C2semidirect
8. C2×#16837470C2semidirect
9. C2×C8×C22⋊D59C2semidirect
10. C2×(C22⋊D59)⋊C8C2semidirect
11. C2×#16837456C2semidirect
12. C2×#16837452C2semidirect
13. C2×#16837369C2semidirect
14. C2×#16837367C2semidirect
15. C2×#16837367C2semidirect
16. C2×C59×#408C2semidirect
39. #16837478C22semidirect
40. #16837477C22semidirect
41. #16837476C22semidirect
42. #16837473C22semidirect
43. #16837471C22semidirect
44. #16837470C22semidirect
45. C8×C22⋊D59C22semidirect
46. (C22⋊D59)⋊C8C22semidirect
47. #16837456C22semidirect
48. #16837452C22semidirect
53. #16837369C22semidirect
54. #16837367C22semidirect
55. #16837367C22semidirect
71. C59×#408C22semidirect
424. C2×#408D59semidirect
428. C2×C59#2981semidirect
476. #408C2×D59semidirect
493. C59C2×#2981semidirect
831. C2#21433169direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168379482
#214331692
C2×#168374782
C2×#168374772
C2×#168374762
C2×#168374732
C2×#168374712
C2×#168374702
C2×C8×C22⋊D592
C2×(C22⋊D59)⋊C82
C2×#168374562
C2×#168374522
C2×#168373692
C2×#168373672
C2×C59×#4082
C2×#298159