Finite Group Databasebeta

← #14682282

Subgroups — #14682282

Order 2816.

1614 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic
2C2×#10622542C211yesmaximal, characteristic
3C2×#10622259C211yesmaximal, characteristic
4#13066886C211yesmaximal, characteristic
5#13066886C211yesmaximal, characteristic
6#13066870C211yesmaximal, characteristic
7#13066869C211yesmaximal, characteristic
8#13066868C211yesmaximal, characteristic
9#13066867C211yesmaximal, characteristic
10#13066850C211yesmaximal, characteristic
11#13066849C211yesmaximal, characteristic
12#13066847C211yesmaximal, characteristic
13#13066842C211yesmaximal, characteristic
14#13066841C211yesmaximal, characteristic
15C11×#1436C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C2×#66941—24no—
28C2×#66941—24no—
29C2×#66941C418yescomplemented
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2211yescharacteristic
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54#10622542—24no—
55#10622259—24no—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C22×Dic22—22no—
72C22×Dic22—22no—
73C22×Dic22—41no—
74C22×Dic22—41no—
75C22×Dic22—41no—
76C22×Dic22—41no—
77C22×Dic22—41no—
78C22×Dic22—41no—
79C22×Dic22—41no—
80C22×Dic22—41no—
81C22×Dic22C2×C414yes—
82C22×Dic22C2×C414yes—
83C22×Dic22D414yes—
84C22×Dic22D414yes—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4C2×C414yes—
88C2×C42×C11—22no—
89C2×C42×C11—41no—
90C2×C42×C11—41no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—41no—
95C2×C4⋊Dic11—41no—
96C2×C4⋊Dic11C2×C414yes—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—41no—
103C2×Dic11⋊C4—41no—
104C2×Dic11⋊C4C2×C414yes—
105C2×Dic11⋊C4C2×C414yes—
106C2×C4×Dic11—22no—
107C2×C4×Dic11—22no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—41no—
110C2×C4×Dic11—41no—
111C2×C4×Dic11C2×C414yes—
112#66941—232no—
113C11×#95—22no—
114C11×#95—22no—
115C11×#95—41no—
116C11×#95—41no—
117C11×#95Q814yescomplemented
118C11⋊#95—22no—
119C11⋊#95—22no—
120C11⋊#95—22no—
121C11⋊#95—22no—
122C11⋊#95—22no—
123C11⋊#95—22no—
124C11⋊#95—22no—
125C11⋊#95—22no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95—22no—
129C11⋊#95—22no—
130C11⋊#95—41no—
131C11⋊#95—41no—
132C11⋊#95—41no—
133C11⋊#95—41no—
134C11⋊#95—41no—
135C11⋊#95—41no—
136C11⋊#95Q814yescomplemented
137#14450—111nomaximal, Sylow
138C24×C11C2411yescharacteristic
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11C22×C412yes—
179C22×C4×C11C22×C412yes—
180C22×C4×C11C22×C412yes—
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2×D412yes—
183C22×C4×C11C2×Q812yes—
184C22×C4×C11C2×Q812yes—
185C22×C4×C11C2×Q812yes—
186C22×C4×C11C2×Q812yes—
187C22×C4×C11#4112yes—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11C22×C412yes—
234C22×Dic11C22×C412yes—
235C22×Dic11C22×C412yes—
236C22×Dic11C22×C412yes—
237C22×Dic11C2×D412yes—
238C22×Dic11C2×D412yes—
239C22×Dic11C2×D412yes—
240C22×Dic11C2×D412yes—
241C22×Dic11C2×Q812yes—
242C22×Dic11C2×Q812yes—
243C22×Dic11#4112yes—
244C2×Dic22—28no—
245C2×Dic22—44no—
246C2×Dic22—44no—
247C2×Dic22—44no—
248C2×Dic22—44no—
249C2×Dic22—44no—
250C2×Dic22—44no—
251C2×Dic22—44no—
252C2×Dic22—44no—
253C2×Dic22—44no—
254C2×Dic22—44no—
255C2×Dic22—44no—
256C2×Dic22—44no—
257C2×Dic22C22⋊C4116yes—
258C11×C4⋊C4—28no—
259C42×C11—44no—
260C4⋊Dic11—28no—
261C4⋊Dic11—44no—
262Dic11⋊C4—28no—
263Dic11⋊C4—28no—
264Dic11⋊C4—44no—
265C4×Dic11—28no—
266C4×Dic11—44no—
267C22×C4⋊Q8—111no—
268C2×#391—111no—
269C2×#391—111no—
270#1446—111no—
271#1446—111no—
272#1441—111no—
273#1441—111no—
274#1441—111no—
275#1441—111no—
276#1436—111no—
277#1436—111no—
278#1436—111no—
279#1436D1111yescharacteristic
280#1434—111no—
281#1434—111no—
282C23×C11C23×C411yescharacteristic
283C23×C11C22×D411yescharacteristic
284C23×C11C22×D411yescharacteristic
285C23×C11C22×Q811yescharacteristic
286C23×C11C22×Q811yescharacteristic
287C23×C11C2×#4111yescharacteristic
288C23×C11C2×#4111yescharacteristic
289C23×C11H(5,𝔽2)11yescharacteristic
290C23×C11H(5,𝔽2)11yescharacteristic
291C23×C11H(5,𝔽2)11yescharacteristic
292C23×C11H(5,𝔽2)11yescharacteristic
293C23×C112−1+411yescharacteristic
294C23×C112−1+411yescharacteristic
295C23×C112−1+411yescharacteristic
296C23×C112−1+411yescharacteristic
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—41no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11C2×C22⋊C414yes—
345C2×C4×C11C4×Q814yes—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384C2×Dic11—41no—
385C2×Dic11—41no—
386C2×Dic11—41no—
387C2×Dic11—41no—
388C2×Dic11—41no—
389C2×Dic11—41no—
390C2×Dic11—41no—
391C2×Dic11—41no—
392C2×Dic11—41no—
393C2×Dic11—41no—
394C2×Dic11—41no—
395C2×Dic11—41no—
396C2×Dic11—41no—
397C2×Dic11—41no—
398C2×Dic11—41no—
399C2×Dic11C2×C22⋊C414yes—
400C2×Dic11C2×C22⋊C414yes—
401C2×Dic11C4×Q814yes—
402Dic22—416no—
403Dic22—416no—
404C23×Q8—111no—
405C23×Q8—111no—
406C2×C4⋊Q8—118no—
407C2×C4⋊Q8—224no—
408C2×C4⋊Q8—224no—
409C22×C4⋊C4—111no—
410C22×C4⋊C4—111no—
411C22×C4⋊C4—111no—
412C22×C4⋊C4—111no—
413C22×C4⋊C4—111no—
414C22×C4⋊C4C2×D1111yescharacteristic
415C22×C42—111no—
416C22×C42—111no—
417C22×C42C2×D1111yescharacteristic
418#391—224no—
419#391—224no—
420C2×#95—111no—
421C2×#95—111no—
422C2×#95—111no—
423C2×#95—111no—
424C2×#95—111no—
425C2×#95—111no—
426C2×#95—111no—
427C2×#95—111no—
428C2×#95—111no—
429C2×#95—111no—
430C2×#95—111no—
431C2×#95—111no—
432C2×#95—111no—
433C2×#95—111no—
434C2×#95—111no—
435C2×#95—111no—
436C2×#95—111no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95C2×D1111yescharacteristic
440C2×#95C2×D1111yescharacteristic
441C2×#95C2×D1111yescharacteristic
442C2×#95C2×D1111yescharacteristic
443C2×#95C2×D1111yescharacteristic
444C22×C11C22×C22⋊C411yescharacteristic
445C22×C11C2×C4×Q811yescharacteristic
446C22×C11C2×C4×Q811yescharacteristic
447C22×C11#51811yescharacteristic
448C22×C11#51811yescharacteristic
449C22×C11#51911yescharacteristic
450C22×C11#51911yescharacteristic
451C22×C11#53411yescharacteristic
452C22×C11#53411yescharacteristic
453C22×C11#53411yescharacteristic
454C22×C11#53411yescharacteristic
455C22×C11#54211yescharacteristic
456C22×C11#54211yescharacteristic
457C22×C11#54211yescharacteristic
458C22×C11#54211yescharacteristic
459C22×C11#54411yescharacteristic
460C22×C11#54411yescharacteristic
461C22×C11#54411yescharacteristic
462C22×C11#54411yescharacteristic
463C22×C11#54811yescharacteristic
464C22×C11#54811yescharacteristic
465C22×C11#54811yescharacteristic
466C22×C11#54811yescharacteristic
467C22×C11D4×Q811yescharacteristic
468C22×C11D4×Q811yescharacteristic
469C22×C11D4×Q811yescharacteristic
470C22×C11D4×Q811yescharacteristic
471C22×C11#55411yescharacteristic
472C22×C11#55411yescharacteristic
473C22×C11#55511yescharacteristic
474C22×C11Q8211yescharacteristic
475C22×C11#56311yescharacteristic
476C22×C11#56311yescharacteristic
477C22×C11#56311yescharacteristic
478C22×C11#56311yescharacteristic
479C4×C11—24no—
480C4×C11—24no—
481C4×C11—42no—
482C4×C11—42no—
483C4×C11—42no—
484C4×C11—42no—
485C4×C11—81no—
486Dic11—24no—
487Dic11—24no—
488Dic11—24no—
489Dic11—42no—
490Dic11—42no—
491Dic11—81no—
492Dic11—81no—
493Dic11—81no—
494C22×Q8—114no—
495C22×Q8—114no—
496C22×Q8—114no—
497C22×Q8—114no—
498C22×Q8—222no—
499C22×Q8—222no—
500C22×Q8—441no—
501C22×Q8—441no—
502C22×Q8—441no—
503C22×Q8—441no—
504C22×Q8—441no—
505C22×Q8—441no—
506C22×Q8—441no—
507C22×Q8—441no—
508C23×C4—111no—
509C23×C4—111no—
510C23×C4—111no—
511C23×C4—111no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4C22×D1111yescharacteristic
517C23×C4C22×D1111yescharacteristic
518C23×C4C22×D1111yescharacteristic
519C23×C4C22×D1111yescharacteristic
520C23×C4C22×D1111yescharacteristic
521C23×C4C22×D1111yescharacteristic
522C23×C4C22×D1111yescharacteristic
523C4⋊Q8—2232no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—114no—
527C2×C4⋊C4—114no—
528C2×C4⋊C4—114no—
529C2×C4⋊C4—222no—
530C2×C4⋊C4—222no—
531C2×C4⋊C4—222no—
532C2×C4⋊C4—222no—
533C2×C4⋊C4—222no—
534C2×C4⋊C4—222no—
535C2×C4⋊C4—222no—
536C2×C4⋊C4—222no—
537C2×C4⋊C4—441no—
538C2×C4⋊C4—441no—
539C2×C4⋊C4—441no—
540C2×C4⋊C4—441no—
541C2×C4⋊C4C4×D1114yes—
542C2×C42—22no—
543C2×C42—41no—
544C2×C42—41no—
545C2×C42—114no—
546C2×C42—222no—
547C2×C42—222no—
548C2×C42—222no—
549C2×C42—441no—
550C2×C42—441no—
551#95—22no—
552#95—22no—
553#95—41no—
554#95—41no—
555#95—114no—
556#95—222no—
557#95—222no—
558#95—222no—
559#95—222no—
560#95—222no—
561#95—222no—
562#95—222no—
563#95—222no—
564#95—222no—
565#95—222no—
566#95—222no—
567#95—222no—
568#95—441no—
569#95—441no—
570#95—441no—
571#95—441no—
572#95—441no—
573#95—441no—
574#95Dic2214yescomplemented
575C2×C11#230811yescharacteristic
576C2×C11#233111yescharacteristic
577C2×C11#233111yescharacteristic
578C2×C11Q8×C22⋊C411yescharacteristic
579C2×C11Q8×C22⋊C411yescharacteristic
580C2×C11#236911yescharacteristic
581C2×C11#238111yescharacteristic
582C2×C11#272911yescharacteristic
583C2×C11#272911yescharacteristic
584C2×C11#272911yescharacteristic
585C2×C11#272911yescharacteristic
586C2×C11#273111yescharacteristic
587C2×C11#273111yescharacteristic
588C2×C11#273411yescharacteristic
589C2×C11#273411yescharacteristic
590C24C23×D1111yescharacteristic
591C2×Q8—1116no—
592C2×Q8—228no—
593C2×Q8—444no—
594C2×Q8—444no—
595C2×Q8—444no—
596C2×Q8—444no—
597C2×Q8—444no—
598C2×Q8—444no—
599C2×Q8—444no—
600C2×Q8—444no—
601C2×Q8—444no—
602C2×Q8—444no—
603C2×Q8—444no—
604C2×Q8—444no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
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—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—112no—
645C22×C4—112no—
646C22×C4—112no—
647C22×C4—112no—
648C22×C4—112no—
649C22×C4—112no—
650C22×C4—112no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—221no—
656C22×C4—221no—
657C22×C4—221no—
658C22×C4—221no—
659C22×C4—221no—
660C22×C4—221no—
661C22×C4—221no—
662C22×C4—221no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4—221no—
679C22×C4—221no—
680C22×C4—221no—
681C22×C4—221no—
682C22×C4—221no—
683C22×C4—221no—
684C22×C4—221no—
685C22×C4—221no—
686C22×C4—221no—
687C22×C4—221no—
688C22×C4—221no—
689C22×C4—221no—
690C22×C4—221no—
691C22×C4—221no—
692C22×C4—221no—
693C22×C4—221no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—221no—
698C22×C4—221no—
699C22×C4—221no—
700C22×C4C2×Dic2212yes—
701C22×C4C2×Dic2212yes—
702C22×C4C2×Dic2212yes—
703C22×C4C2×C4×D1112yes—
704C22×C4C2×C4×D1112yes—
705C22×C4C2×C4×D1112yes—
706C22×C4#433912yes—
707C22×C4D4×D1112yes—
708C22×C4D4×D1112yes—
709C22×C4Q8×D1112yes—
710C4⋊C4—28no—
711C4⋊C4—228no—
712C4⋊C4—228no—
713C4⋊C4—228no—
714C4⋊C4—444no—
715C4⋊C4—444no—
716C42—44no—
717C42—228no—
718C42—444no—
719C11#1445011yescharacteristic, complemented, Sylow
720C23C22×Dic2211yescharacteristic
721C23C22×C4×D1111yescharacteristic
722C23C2×#433911yescharacteristic
723C23C2×D4×D1111yescharacteristic
724C23C2×D4×D1111yescharacteristic
725C23#6703711yescharacteristic
726C23#6703711yescharacteristic
727C23C2×Q8×D1111yescharacteristic
728C23#6704011yescharacteristic
729C23#41×D1111yescharacteristic
730C23#6704211yescharacteristic
731C23#6704211yescharacteristic
732C23#6704311yescharacteristic
733C23#6704311yescharacteristic
734C23#6704311yescharacteristic
735Q8—4416no—
736Q8—4416no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
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—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—114no—
785C2×C4—114no—
786C2×C4—114no—
787C2×C4—222no—
788C2×C4—222no—
789C2×C4—222no—
790C2×C4—222no—
791C2×C4—222no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—222no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—441no—
815C2×C4—441no—
816C2×C4—441no—
817C2×C4—441no—
818C2×C4—441no—
819C2×C4—441no—
820C2×C4—441no—
821C2×C4—441no—
822C2×C4—441no—
823C2×C4—441no—
824C2×C4—441no—
825C2×C4—441no—
826C2×C4—441no—
827C2×C4—441no—
828C2×C4—441no—
829C2×C4—441no—
830C2×C4—441no—
831C2×C4—441no—
832C2×C4—441no—
833C2×C4—441no—
834C2×C4—441no—
835C2×C4—441no—
836C2×C4—441no—
837C2×C4—441no—
838C2×C4—441no—
839C2×C4—441no—
840C2×C4C4×Dic2214yes—
841C2×C4C22⋊C4×D1114yes—
842C22C2×C4×Dic2211yescharacteristic
843C22C2×C22⋊C4×D1111yescharacteristic
844C22#1062303111yescharacteristic
845C22#1062304211yescharacteristic
846C22#1062304711yescharacteristic
847C22#1062305011yescharacteristic
848C22#1062306311yescharacteristic
849C22D4×Dic2211yescharacteristic
850C22D4×Dic2211yescharacteristic
851C22#1062307011yescharacteristic
852C22#1062307611yescharacteristic
853C22#1062307611yescharacteristic
854C22#1062308311yescharacteristic
855C22#1062308311yescharacteristic
856C22#1062309211yescharacteristic
857C22Q8×Dic2211yescharacteristic
858C22C4×Q8×D1111yescharacteristic
859C22#1062310311yescharacteristic
860C22#1062311311yescharacteristic
861C22#1062312011yescharacteristic
862C22#1062313611yescharacteristic
863C22#1062313611yescharacteristic
864C22#1062315411yescharacteristic
865C22#1062316311yescharacteristic
866C22#1062316411yescharacteristic
867C22#1062317711yescharacteristic
868C22#1062318211yescharacteristic
869C22#1062318411yescharacteristic
870C22#1062319311yescharacteristic
871C22#1062320811yescharacteristic
872C22#1062322011yescharacteristic
873C22#1062323011yescharacteristic
874C22#1062324111yescharacteristic
875C22#1062324311yescharacteristic
876C22#1062325811yescharacteristic
877C4—24no—
878C4—24no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—81no—
884C4—224no—
885C4—224no—
886C4—224no—
887C4—442no—
888C4—442no—
889C4—881no—
890C4—881no—
891C4—881no—
892C2#1307119011yescharacteristic
893C2#1307136011yescharacteristic
894C2#1307136111yescharacteristic
895C2#1307145011yescharacteristic
896C2C22⋊C4×Dic2211yescharacteristic
897C2#1307170311yescharacteristic
898C2#1307179411yescharacteristic
899C2#1307559311yescharacteristic
900C2#1307559511yescharacteristic
901C2#1307559811yescharacteristic
902C2#1307560211yescharacteristic
903C2#1307562311yescharacteristic
904C2#1307562611yescharacteristic
905C2#1307564711yescharacteristic
906C2#1307564911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1436D11
hypocenterC11#14450
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
29. C2×#66941C4semidirect
117. C11×#95Q8semidirect
136. C11⋊#95Q8semidirect
574. #95Dic22semidirect
719. C11#14450semidirect

Maximal subgroups

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

subgroupindex
C22×#669412
C2×#106225422
C2×#106222592
#130668862
#130668702
#130668692
#130668682
#130668672
#130668502
#130668492
#130668472
#130668422
#130668412
C11×#14362
#1445011