Finite Group Databasebeta

← #27400254

Subgroups — #27400254

Order 13568.

1068 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811313C211yesmaximal, characteristic
2D4×#11719917C211yesmaximal, characteristic
3#20275708C211yesmaximal, characteristic, complemented
4#20275707C211yesmaximal, characteristic, complemented
5#20275183C211yesmaximal, characteristic, complemented
6#20275183C211yesmaximal, characteristic, complemented
7#20275181C211yesmaximal, characteristic, complemented
8#20275181C211yesmaximal, characteristic, complemented
9#20274796C211yesmaximal, characteristic, complemented
10#20274793C211yesmaximal, characteristic, complemented
11#20274708C211yesmaximal, characteristic, complemented
12C4×#13133135C211yesmaximal, characteristic, complemented
13#20274453C211yesmaximal, characteristic, complemented
14C2×#16810391C211yesmaximal, characteristic, complemented
15D4×M16×C53C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic
17C22×#11719917C2211yescharacteristic
18#16811313—21no—
19#16811313—21no—
20#16811313—21no—
21#16811313—21no—
22#16811313—21no—
23#16811313—21no—
24#16811313—21no—
25#16811313—21no—
26C2×#13133210C412yes—
27C2×#13133209C2211yescharacteristic
28C2×#13133207C412yes—
29C2×#13133198C412yes—
30C2×#13133196C2211yescharacteristic
31C2×#13133196C2211yescharacteristic
32C2×C4×Dic106C2211yescharacteristic
33C2×#13133176C2211yescharacteristic
34C2×#13133173C412yes—
35C22×C4⋊Dic53C2211yescharacteristic
36#16810701—21no—
37#16810695—21no—
38#16810695—21no—
39D4×#88322—21no—
40#16810647C2211yescharacteristic
41C2×#13133135C2211yescharacteristic
42C2×#13133135C2211yescharacteristic
43C2×#13133135C2211yescharacteristic
44C2×#13133135C2211yescharacteristic
45#16810587C2211yescharacteristic
46#16810587C2211yescharacteristic
47C4×#11719917C2211yescharacteristic
48#16810391C2211yescharacteristic
49#16810391C2211yescharacteristic
50#16810391C2211yescharacteristic
51#16810391C2211yescharacteristic
52#16810391C2211yescharacteristic
53#16810391C2211yescharacteristic
54#16810391C2211yescharacteristic
55#16810391C2211yescharacteristic
56#16810391C2211yescharacteristic
57#16810391C2211yescharacteristic
58#16810391C2211yescharacteristic
59#16810391C2211yescharacteristic
60C22×M16×C53C2211yescharacteristic
61C22×M16×C53C2211yescharacteristic
62C2×C4×D4×C53C2211yescharacteristic
63C53×#436—21no—
64C53×#435—21no—
65C53×#435—21no—
66C8×D4×C53—21no—
67C53×#423C2211yescharacteristic
68C53×#407C2211yescharacteristic
69C53×#407C2211yescharacteristic
70C4×M16×C53C2211yescharacteristic
71C22×Dic106C2311yescharacteristic
72C23×Dic53C2×C412yes—
73C2×#11719917—22no—
74C2×#11719917—22no—
75C2×#11719917—21no—
76C2×#11719917—21no—
77C2×#11719917—41no—
78C2×#11719917—41no—
79C2×#11719917C2311yescharacteristic
80C2×#11719917C2311yescharacteristic
81C2×#11719917C2311yescharacteristic
82C2×#11719917C2311yescharacteristic
83C22×#88322—21no—
84C22×#88322—21no—
85#13133210—22no—
86#13133210—22no—
87#13133210—22no—
88#13133210—22no—
89#13133209—21no—
90#13133209—21no—
91#13133209—21no—
92#13133209—21no—
93#13133207—22no—
94#13133207—22no—
95#13133207—22no—
96#13133207—22no—
97#13133198—22no—
98#13133198—22no—
99#13133198—22no—
100#13133198—22no—
101#13133196—21no—
102#13133196—21no—
103#13133196—21no—
104#13133196—21no—
105#13133196—21no—
106#13133196—21no—
107#13133196—21no—
108#13133196—21no—
109C4×Dic106—21no—
110C4×Dic106—21no—
111C4×Dic106—21no—
112C4×Dic106—21no—
113#13133176—21no—
114#13133176—21no—
115#13133176—21no—
116#13133176—21no—
117#13133173—22no—
118#13133173—22no—
119#13133173—22no—
120#13133173—22no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53C2×C412yes—
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×#11719919C2×C412yes—
130C2×#11719919C2×C412yes—
131C2×#11719919C2×C412yes—
132C2×#11719919C2×C412yes—
133C2×#11719919C2×C412yes—
134C2×C22⋊Dic53C2×C412yes—
135C2×C22⋊Dic53C2×C412yes—
136C2×C22⋊Dic53C2×C412yes—
137C2×C4×Dic53C2×C412yes—
138C2×C4×Dic53C2×C412yes—
139C4⋊#88322—21no—
140C4⋊#88322—21no—
141#13133135—22no—
142#13133135—22no—
143#13133135—41no—
144#13133135—41no—
145C22⋊#88322—21no—
146C22⋊#88322—21no—
147C22⋊#88322—21no—
148C22⋊#88322—21no—
149#13133128—21no—
150C4×#88322—21no—
151C22×D4×C53C2×C411yescharacteristic
152C23×C4×C53C2311yescharacteristic
153C23×C4×C53C2311yescharacteristic
154C2×M16×C53—22no—
155C2×M16×C53—22no—
156C2×M16×C53—21no—
157C2×M16×C53—21no—
158C2×M16×C53—41no—
159C2×M16×C53—41no—
160C2×M16×C53C2311yescharacteristic
161C2×M16×C53C2311yescharacteristic
162C2×M16×C53C2311yescharacteristic
163C2×M16×C53C2311yescharacteristic
164C22×C8×C53—21no—
165C22×C8×C53—21no—
166C4×D4×C53D411yescharacteristic
167C4×D4×C53D411yescharacteristic
168C4×D4×C53D411yescharacteristic
169C4×D4×C53D411yescharacteristic
170C4×D4×C53D411yescharacteristic
171C4×D4×C53D411yescharacteristic
172C4×D4×C53D411yescharacteristic
173C4×D4×C53D411yescharacteristic
174C2×C4⋊C4×C53C2×C411yescharacteristic
175C2×C22⋊C4×C53C2×C411yescharacteristic
176C2×C22⋊C4×C53C2×C411yescharacteristic
177C2×C42×C53C2311yescharacteristic
178C4⋊C8×C53—21no—
179C4⋊C8×C53—21no—
180C22⋊C8×C53—21no—
181C22⋊C8×C53—21no—
182C22⋊C8×C53—21no—
183C22⋊C8×C53—21no—
184#97×C53—21no—
185C4×C8×C53—21no—
186C24×C53C22×C411yescharacteristic
187C24×C53C22×C411yescharacteristic
188C2×D4×C53—42no—
189C2×D4×C53C22⋊C411yescharacteristic
190C2×D4×C53C22⋊C411yescharacteristic
191C2×D4×C53C22⋊C411yescharacteristic
192C2×D4×C53C22⋊C411yescharacteristic
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53C22×C411yescharacteristic
202C22×C4×C53C22×C411yescharacteristic
203C22×C4×C53C22×C411yescharacteristic
204C22×C4×C53C22×C411yescharacteristic
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53C2×D411yescharacteristic
210C22×C4×C53C2×D411yescharacteristic
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2411yescharacteristic
214C22×Dic53—22no—
215C22×Dic53—22no—
216C22×Dic53—44no—
217C22×Dic53C22×C412yes—
218C22×Dic53C22×C412yes—
219C22×Dic53C22×C412yes—
220C22×Dic53C22×C412yes—
221C2×Dic106—21no—
222C2×Dic106—21no—
223C2×Dic106—21no—
224C2×Dic106—21no—
225C2×Dic106—21no—
226C2×Dic106—21no—
227M16×C53—21no—
228M16×C53—21no—
229M16×C53—21no—
230M16×C53—21no—
231M16×C53—21no—
232M16×C53—21no—
233M16×C53—21no—
234M16×C53—42no—
235M16×C53—42no—
236M16×C53#4112yes—
237C2×C8×C53—21no—
238C2×C8×C53—21no—
239C2×C8×C53—21no—
240C2×C8×C53—21no—
241C2×C8×C53—42no—
242C2×C8×C53—42no—
243C4⋊C4×C53C22⋊C411yescharacteristic
244C4⋊C4×C53C22⋊C411yescharacteristic
245C4⋊C4×C53C22⋊C411yescharacteristic
246C4⋊C4×C53C22⋊C411yescharacteristic
247C22⋊C4×C53C22⋊C411yescharacteristic
248C22⋊C4×C53C22⋊C411yescharacteristic
249C22⋊C4×C53C22⋊C411yescharacteristic
250C22⋊C4×C53C22⋊C411yescharacteristic
251C22⋊C4×C53C22⋊C411yescharacteristic
252C22⋊C4×C53C22⋊C411yescharacteristic
253C22⋊C4×C53C22⋊C411yescharacteristic
254C22⋊C4×C53C22⋊C411yescharacteristic
255C42×C53C2×D411yescharacteristic
256C42×C53C2×D411yescharacteristic
257C42×C53C2×D411yescharacteristic
258C42×C53C2×D411yescharacteristic
259C22⋊Dic53—22no—
260C22⋊Dic53—22no—
261C22⋊Dic53—22no—
262C22⋊Dic53—22no—
263C22⋊Dic53—22no—
264C22⋊Dic53—22no—
265C4⋊Dic53—22no—
266C4⋊Dic53—22no—
267C4⋊Dic53—21no—
268C4⋊Dic53—21no—
269C4⋊Dic53—21no—
270C4⋊Dic53—21no—
271C4⋊Dic53—21no—
272C4⋊Dic53—21no—
273#11719919—22no—
274#11719919—22no—
275#11719919—22no—
276#11719919—22no—
277#11719919—22no—
278#11719919—22no—
279#11719919—22no—
280#11719919—22no—
281#11719919—22no—
282#11719919—22no—
283C4×Dic53—22no—
284C4×Dic53—22no—
285C4×Dic53—22no—
286C4×Dic53—22no—
287#11719917—21no—
288#11719917—21no—
289#11719917—21no—
290#11719917—21no—
291#11719917—21no—
292#11719917—21no—
293#11719917—21no—
294#11719917—42no—
295#11719917—42no—
296#11719917#4112yes—
297C2×#88322—21no—
298C2×#88322—21no—
299C2×#88322—21no—
300C2×#88322—21no—
301C2×#88322—42no—
302C2×#88322—42no—
303C23×C53—21no—
304C23×C53—21no—
305C23×C53—22no—
306C23×C53—21no—
307C23×C53—21no—
308C23×C53—41no—
309C23×C53—41no—
310C23×C53—41no—
311C23×C53C2×C22⋊C411yescharacteristic
312C23×C53C2×C22⋊C411yescharacteristic
313C23×C53C2×C22⋊C411yescharacteristic
314C23×C53C2×C22⋊C411yescharacteristic
315C23×C53C23×C411yescharacteristic
316D4×C53—22no—
317D4×C53—22no—
318D4×C53—41no—
319D4×C53—41no—
320C2×C4×C53—21no—
321C2×C4×C53—21no—
322C2×C4×C53—21no—
323C2×C4×C53—21no—
324C2×C4×C53—21no—
325C2×C4×C53—21no—
326C2×C4×C53—21no—
327C2×C4×C53—21no—
328C2×C4×C53—21no—
329C2×C4×C53—21no—
330C2×C4×C53—21no—
331C2×C4×C53—21no—
332C2×C4×C53—21no—
333C2×C4×C53—21no—
334C2×C4×C53—21no—
335C2×C4×C53—21no—
336C2×C4×C53—21no—
337C2×C4×C53—21no—
338C2×C4×C53—21no—
339C2×C4×C53—21no—
340C2×C4×C53—41no—
341C2×C4×C53—41no—
342C2×C4×C53C2×C22⋊C411yescharacteristic
343C2×C4×C53C2×C22⋊C411yescharacteristic
344C2×C4×C53C2×C22⋊C411yescharacteristic
345C2×C4×C53C2×C22⋊C411yescharacteristic
346C2×C4×C53C2×C22⋊C411yescharacteristic
347C2×C4×C53C2×C22⋊C411yescharacteristic
348C2×C4×C53C2×C22⋊C411yescharacteristic
349C2×C4×C53C2×C22⋊C411yescharacteristic
350C2×C4×C53C22×D411yescharacteristic
351C2×C4×C53C22×D411yescharacteristic
352C2×C4×C53C2×#4111yescharacteristic
353C2×C4×C53C2×#4111yescharacteristic
354C2×C4×C53H(5,𝔽2)11yescharacteristic
355C2×C4×C532−1+411yescharacteristic
356C2×Dic53—22no—
357C2×Dic53—22no—
358C2×Dic53—22no—
359C2×Dic53—22no—
360C2×Dic53—22no—
361C2×Dic53—22no—
362C2×Dic53—44no—
363C2×Dic53—44no—
364C2×Dic53—42no—
365C2×Dic53—42no—
366C2×Dic53—42no—
367Dic106—41no—
368Dic106—41no—
369Dic106—41no—
370Dic106—41no—
371C8×C53—22no—
372C8×C53—41no—
373C8×C53—41no—
374C8×C53—41no—
375#88322—22no—
376#88322—41no—
377#88322—41no—
378#88322—41no—
379#22480—531nomaximal, Sylow
380C22×C53—21no—
381C22×C53—21no—
382C22×C53—21no—
383C22×C53—21no—
384C22×C53—21no—
385C22×C53—21no—
386C22×C53—21no—
387C22×C53—21no—
388C22×C53—21no—
389C22×C53—21no—
390C22×C53—21no—
391C22×C53—21no—
392C22×C53—21no—
393C22×C53—42no—
394C22×C53—42no—
395C22×C53—81no—
396C22×C53—81no—
397C22×C53#41312yes—
398C22×C53C22×C22⋊C411yescharacteristic
399C22×C53C4×#4111yescharacteristic
400C22×C53#52011yescharacteristic
401C4×C53—21no—
402C4×C53—21no—
403C4×C53—21no—
404C4×C53—21no—
405C4×C53—21no—
406C4×C53—21no—
407C4×C53—21no—
408C4×C53—21no—
409C4×C53#54611yescharacteristic
410C4×C53#54611yescharacteristic
411C4×C53#54711yescharacteristic
412C4×C53#54711yescharacteristic
413Dic53—42no—
414Dic53—42no—
415Dic53—42no—
416Dic53—42no—
417C2×#552—531no—
418D4×M16—531no—
419D4×M16D5311yescharacteristic
420#1998—531no—
421#1998—531no—
422#1901—531no—
423#1901—531no—
424#1901—531no—
425#1901—531no—
426#1822—531no—
427#1821—531no—
428#1801—531no—
429C4×#101—531no—
430#1742—531no—
431C2×#343—531no—
432C2×C53—21no—
433C2×C53—21no—
434C2×C53—22no—
435C2×C53—41no—
436C2×C53—41no—
437C2×C53—41no—
438C2×C53#233911yescharacteristic
439C2×C53C2×#41311yescharacteristic
440C2×C53#288911yescharacteristic
441C22×M16—531no—
442C22×M16—531no—
443C22×M16C2×D5311yescharacteristic
444C22×M16C2×D5311yescharacteristic
445#552—1061no—
446#552—1061no—
447#552—1061no—
448#552—1061no—
449#552—1061no—
450#552—1061no—
451#552—1061no—
452#552—1061no—
453C2×#126—532no—
454C2×#125—532no—
455C2×#125—531no—
456C2×#123—532no—
457C2×C22⋊Q8—531no—
458C2×C22⋊Q8—531no—
459C2×C4×Q8—531no—
460C2×C4×D4C2×D5311yescharacteristic
461C2×#117—531no—
462C2×#117—532no—
463C22×C4⋊C4—531no—
464#436—21no—
465#436—1061no—
466#435—21no—
467#435—21no—
468#435—1061no—
469#435—1061no—
470C8×D4—21no—
471C8×D4—1061no—
472#423—531no—
473#423C2×D5311yescharacteristic
474C2×#101—531no—
475C2×#101—531no—
476C2×#101—531no—
477C2×#101—531no—
478#407—531no—
479#407—531no—
480#407C2×D5311yescharacteristic
481#407C2×D5311yescharacteristic
482C4×M16—531no—
483C4×M16C2×D5311yescharacteristic
484#343—531no—
485#343—531no—
486#343—531no—
487#343—531no—
488#343—531no—
489#343—531no—
490#343—531no—
491#343—531no—
492#343—531no—
493#343—531no—
494#343—531no—
495#343—531no—
496C53#2248011yescharacteristic, complemented, Sylow
497C22×Q8—531no—
498C22×D4C4×D5311yescharacteristic
499C23×C4—532no—
500C23×C4C22×D5311yescharacteristic
501C23×C4C22×D5311yescharacteristic
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—22no—
505C2×M16—22no—
506C2×M16—41no—
507C2×M16—41no—
508C2×M16—531no—
509C2×M16—531no—
510C2×M16—531no—
511C2×M16—531no—
512C2×M16—1061no—
513C2×M16—1061no—
514C2×M16—1062no—
515C2×M16—1062no—
516C2×M16—2121no—
517C2×M16—2121no—
518C2×M16C22×D5311yescharacteristic
519C2×M16C22×D5311yescharacteristic
520C2×M16C22×D5311yescharacteristic
521C2×M16C22×D5311yescharacteristic
522C22×C8—21no—
523C22×C8—21no—
524C22×C8—1061no—
525C22×C8—1061no—
526#126—1062no—
527#126—1062no—
528#126—1062no—
529#126—1062no—
530#125—1062no—
531#125—1062no—
532#125—1062no—
533#125—1062no—
534#125—1061no—
535#125—1061no—
536#125—1061no—
537#125—1061no—
538#123—1062no—
539#123—1062no—
540#123—1062no—
541#123—1062no—
542C22⋊Q8—1061no—
543C22⋊Q8—1061no—
544C22⋊Q8—1061no—
545C22⋊Q8—1061no—
546C22⋊Q8—1061no—
547C22⋊Q8—1061no—
548C22⋊Q8—1061no—
549C22⋊Q8—1061no—
550C4×Q8—1061no—
551C4×Q8—1061no—
552C4×Q8—1061no—
553C4×Q8—1061no—
554C4×D4D21211yescharacteristic
555C4×D4D21211yescharacteristic
556C4×D4D21211yescharacteristic
557C4×D4D21211yescharacteristic
558C4×D4C22⋊D5311yescharacteristic
559C4×D4C22⋊D5311yescharacteristic
560C4×D4C22⋊D5311yescharacteristic
561C4×D4C22⋊D5311yescharacteristic
562#117—1061no—
563#117—1061no—
564#117—1061no—
565#117—1061no—
566#117—1062no—
567#117—1062no—
568#117—1062no—
569#117—1062no—
570C2×C4⋊C4—532no—
571C2×C4⋊C4—532no—
572C2×C4⋊C4—532no—
573C2×C4⋊C4—532no—
574C2×C4⋊C4—532no—
575C2×C4⋊C4—532no—
576C2×C4⋊C4—531no—
577C2×C4⋊C4—531no—
578C2×C4⋊C4—531no—
579C2×C4⋊C4—1061no—
580C2×C4⋊C4—1061no—
581C2×C4⋊C4—1061no—
582C2×C4⋊C4—1061no—
583C2×C4⋊C4C4×D5311yescharacteristic
584C2×C22⋊C4—532no—
585C2×C22⋊C4—532no—
586C2×C22⋊C4—532no—
587C2×C22⋊C4C4×D5311yescharacteristic
588C2×C22⋊C4C4×D5311yescharacteristic
589C2×C42—532no—
590C2×C42—532no—
591C2×C42C22×D5311yescharacteristic
592C4⋊C8—21no—
593C4⋊C8—21no—
594C4⋊C8—1061no—
595C4⋊C8—1061no—
596#101—1062no—
597#101—1062no—
598#101—2121no—
599#101—2121no—
600C22⋊C8—21no—
601C22⋊C8—21no—
602C22⋊C8—21no—
603C22⋊C8—21no—
604C22⋊C8—1061no—
605C22⋊C8—1061no—
606C22⋊C8—1061no—
607C22⋊C8—1061no—
608#97—21no—
609#97—1061no—
610C4×C8—21no—
611C4×C8—1061no—
612C24C2×C4×D5311yescharacteristic
613C24C2×C4×D5311yescharacteristic
614C2×Q8—1061no—
615C2×Q8—1061no—
616C2×Q8—1061no—
617C2×Q8—1061no—
618C2×Q8—1061no—
619C2×Q8—1061no—
620C2×D4—42no—
621C2×D4#1171992111yescharacteristic
622C2×D4#1171992111yescharacteristic
623C2×D4#1171992111yescharacteristic
624C2×D4#1171992111yescharacteristic
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—532no—
634C22×C4—532no—
635C22×C4—532no—
636C22×C4—532no—
637C22×C4—1062no—
638C22×C4—1062no—
639C22×C4—2124no—
640C22×C4C2×C4×D5311yescharacteristic
641C22×C4C2×C4×D5311yescharacteristic
642C22×C4C2×C4×D5311yescharacteristic
643C22×C4C2×C4×D5311yescharacteristic
644C22×C4C2×D21211yescharacteristic
645C22×C4C2×D21211yescharacteristic
646C22×C4C2×D21211yescharacteristic
647C22×C4C2×D21211yescharacteristic
648C22×C4C2×C22⋊D5311yescharacteristic
649C22×C4C2×C22⋊D5311yescharacteristic
650C22×C4C2×C22⋊D5311yescharacteristic
651C22×C4C2×C22⋊D5311yescharacteristic
652C22×C4C23×D5311yescharacteristic
653M16—21no—
654M16—21no—
655M16—21no—
656M16—21no—
657M16—21no—
658M16—21no—
659M16—21no—
660M16—42no—
661M16—42no—
662M16—532no—
663M16—1061no—
664M16—1061no—
665M16—1061no—
666M16—1061no—
667M16—1061no—
668M16—1061no—
669M16—1061no—
670M16—2122no—
671M16—2122no—
672M16#1171994712yes—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—42no—
678C2×C8—42no—
679C2×C8—1061no—
680C2×C8—1061no—
681C2×C8—1061no—
682C2×C8—1061no—
683C2×C8—2122no—
684C2×C8—2122no—
685C4⋊C4—1062no—
686C4⋊C4—1062no—
687C4⋊C4—1062no—
688C4⋊C4—1062no—
689C4⋊C4—1062no—
690C4⋊C4—1062no—
691C4⋊C4—1062no—
692C4⋊C4—1062no—
693C4⋊C4—1062no—
694C4⋊C4—1062no—
695C4⋊C4—1062no—
696C4⋊C4—1062no—
697C4⋊C4—1061no—
698C4⋊C4—1061no—
699C4⋊C4—1061no—
700C4⋊C4—1061no—
701C4⋊C4—1061no—
702C4⋊C4—1061no—
703C4⋊C4#1171992111yescharacteristic
704C4⋊C4#1171992111yescharacteristic
705C4⋊C4#1171992111yescharacteristic
706C4⋊C4#1171992111yescharacteristic
707C22⋊C4—1062no—
708C22⋊C4—1062no—
709C22⋊C4—1062no—
710C22⋊C4—1062no—
711C22⋊C4—1062no—
712C22⋊C4—1062no—
713C22⋊C4#1171992111yescharacteristic
714C22⋊C4#1171992111yescharacteristic
715C22⋊C4#1171992111yescharacteristic
716C22⋊C4#1171992111yescharacteristic
717C22⋊C4#1171992111yescharacteristic
718C22⋊C4#1171992111yescharacteristic
719C22⋊C4#1171992111yescharacteristic
720C22⋊C4#1171992111yescharacteristic
721C42—1062no—
722C42—1062no—
723C42—1062no—
724C42—1062no—
725C42C2×D21211yescharacteristic
726C42C2×D21211yescharacteristic
727C42C2×C22⋊D5311yescharacteristic
728C42C2×C22⋊D5311yescharacteristic
729C23—21no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—21no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23C2×#1171992111yescharacteristic
738C23C2×#1171992111yescharacteristic
739C23C2×#1171992111yescharacteristic
740C23C2×#1171992111yescharacteristic
741C23C22×C4×D5311yescharacteristic
742Q8—2121no—
743Q8—2121no—
744Q8—2121no—
745Q8—2121no—
746D4—22no—
747D4—22no—
748D4—41no—
749D4—41no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—1062no—
773C2×C4—1062no—
774C2×C4—1062no—
775C2×C4—1062no—
776C2×C4—1062no—
777C2×C4—1062no—
778C2×C4—2124no—
779C2×C4—2124no—
780C2×C4—2122no—
781C2×C4—2122no—
782C2×C4—2122no—
783C2×C4C2×#1171992111yescharacteristic
784C2×C4C2×#1171992111yescharacteristic
785C2×C4C2×#1171992111yescharacteristic
786C2×C4C2×#1171992111yescharacteristic
787C2×C4C2×#1171992111yescharacteristic
788C2×C4C2×#1171992111yescharacteristic
789C2×C4C2×#1171992111yescharacteristic
790C2×C4C2×#1171992111yescharacteristic
791C2×C4C22×C22⋊D5311yescharacteristic
792C2×C4C22×D21211yescharacteristic
793C2×C4#41×D5311yescharacteristic
794C2×C4C2×#1171994711yescharacteristic
795C2×C4#1313326211yescharacteristic
796C2×C4#1313326411yescharacteristic
797C8—22no—
798C8—41no—
799C8—41no—
800C8—41no—
801C8—1062no—
802C8—2121no—
803C8—2121no—
804C8—2121no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—42no—
819C22—42no—
820C22—81no—
821C22—81no—
822C22#1681060512yes—
823C22C22×#1171992111yescharacteristic
824C22C4×#1171994711yescharacteristic
825C22#1681110211yescharacteristic
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—2122no—
835C4—2122no—
836C4—2122no—
837C4—2122no—
838C4#1681126711yescharacteristic
839C4#1681126811yescharacteristic
840C4#1681127211yescharacteristic
841C4#1681127711yescharacteristic
842C2—21no—
843C2—21no—
844C2—22no—
845C2—41no—
846C2—41no—
847C2—41no—
848C2#2027754011yescharacteristic
849C2C2×#1681060511yescharacteristic
850C2#2028319711yescharacteristic
subgroupG/H
centerC22C22×#11719921
commutatorC23×C53C23×C4
FrattiniC22×C4C23×D53
FittingD4×M16×C53C2
socleC22×C53C22×C22⋊C4
prime radicalC22×D4×C53C2×C4
cosocleC22×C4×C53C24
hypercenterD4×M16D53
hypocenterC53#22480
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
3. #20275708C2semidirect
4. #20275707C2semidirect
5. #20275183C2semidirect
6. #20275183C2semidirect
7. #20275181C2semidirect
8. #20275181C2semidirect
9. #20274796C2semidirect
10. #20274793C2semidirect
11. #20274708C2semidirect
12. C4×#13133135C2semidirect
13. #20274453C2semidirect
14. C2×#16810391C2semidirect
496. C53#22480semidirect

Maximal subgroups

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

subgroupindex
C2×#168113132
D4×#117199172
#202757082
#202757072
#202751832
#202751812
#202747962
#202747932
#202747082
C4×#131331352
#202744532
C2×#168103912
D4×M16×C532
#2248053