Finite Group Databasebeta

← #14685071

Subgroups — #14685071

Order 2816.

1630 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622259C211yesmaximal, characteristic
2C2×#10622259C211yesmaximal, characteristic
3C2×#10622259C211yesmaximal, characteristic
4C2×#10622585C211yesmaximal, characteristic
5C2×C42×Dic11C211yesmaximal, characteristic
6#13066851C211yesmaximal, characteristic
7#13066849C211yesmaximal, characteristic
8#13066848C211yesmaximal, characteristic
9Dic11⋊#95C211yesmaximal, characteristic
10Dic11⋊#95C211yesmaximal, characteristic
11#13066841C211yesmaximal, characteristic
12#13066841C211yesmaximal, characteristic
13#13066840C211yesmaximal, characteristic
14#13066840C211yesmaximal, characteristic
15C11×#1436C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×Dic11⋊C4C2211yescharacteristic
20C22×Dic11⋊C4C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
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
51#10622585—24no—
52C42×Dic11—24no—
53#10622259—24no—
54#10622259—24no—
55#10622259C418yescomplemented
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—22no—
74C22×Dic22—22no—
75C22×Dic22—22no—
76C22×Dic22—22no—
77C22×Dic22C2×C414yes—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C42×C11—22no—
82C2×C42×C11—22no—
83C2×C42×C11—22no—
84C2×Dic11⋊C4—22no—
85C2×Dic11⋊C4—22no—
86C2×Dic11⋊C4—22no—
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—22no—
92C2×Dic11⋊C4—22no—
93C2×Dic11⋊C4—22no—
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4C2×C414yes—
96C2×C4×Dic11—22no—
97C2×C4×Dic11—22no—
98C2×C4×Dic11—22no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—22no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—22no—
104C2×C4×Dic11—22no—
105C2×C4×Dic11—22no—
106C2×C4×Dic11—22no—
107C2×C4×Dic11—22no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11C2×C414yes—
110C2×C4×Dic11D414yes—
111C2×C4×Dic11D414yes—
112C2×C4×Dic11Q814yescomplemented
113C2×C4×Dic11Q814yescomplemented
114C11×#95—22no—
115C11×#95—22no—
116C11×#95—22no—
117C11×#95—22no—
118C11×#95C2×C414yes—
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—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95C2×C414yes—
134C11⋊#95C2×C414yes—
135C11⋊#95C2×C414yes—
136#14703—111nomaximal, Sylow
137C24×C11C2411yescharacteristic
138C22×C4×C11—21no—
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×C11C22×C412yes—
177C22×C4×C11C22×C412yes—
178C22×C4×C11C22×C412yes—
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2×D412yes—
181C22×C4×C11C2×Q812yes—
182C22×C4×C11C2×Q812yes—
183C22×C4×C11#4112yes—
184C22×C4×C11#4112yes—
185C22×C4×C11#4112yes—
186C22×C4×C11#4112yes—
187C22×Dic11—21no—
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×Dic11C22×C412yes—
226C22×Dic11C22×C412yes—
227C22×Dic11C22×C412yes—
228C22×Dic11C22×C412yes—
229C22×Dic11C2×D412yes—
230C22×Dic11C2×D412yes—
231C22×Dic11C2×D412yes—
232C22×Dic11C2×D412yes—
233C22×Dic11C2×Q812yes—
234C22×Dic11C2×Q812yes—
235C22×Dic11C2×Q812yes—
236C22×Dic11C2×Q812yes—
237C22×Dic11#4112yes—
238C22×Dic11#4112yes—
239C22×Dic11#4112yes—
240C22×Dic11#4112yes—
241C22×Dic11#4112yes—
242C22×Dic11#4112yes—
243C2×Dic22—28no—
244C2×Dic22—28no—
245C2×Dic22—28no—
246C2×Dic22—44no—
247C2×Dic22—44no—
248C2×Dic22—44no—
249C2×Dic22—44no—
250C11×C4⋊C4—44no—
251C42×C11—28no—
252Dic11⋊C4—28no—
253Dic11⋊C4—44no—
254Dic11⋊C4—44no—
255Dic11⋊C4—44no—
256C4×Dic11—28no—
257C4×Dic11—28no—
258C4×Dic11—28no—
259C4×Dic11—28no—
260C4×Dic11—28no—
261C4×Dic11—28no—
262C2×#391—111no—
263C2×#391—111no—
264C2×#391—111no—
265C2×#389—111no—
266C2×C43—111no—
267#1436—111no—
268#1436—111no—
269#1436—111no—
270#1436D1111yescharacteristic
271C4⋊#95—111no—
272C4⋊#95—111no—
273#1434—111no—
274#1434—111no—
275#1434—111no—
276#1434—111no—
277C23×C11C23×C411yescharacteristic
278C23×C11C22×D411yescharacteristic
279C23×C11C22×D411yescharacteristic
280C23×C11C22×Q811yescharacteristic
281C23×C11C22×Q811yescharacteristic
282C23×C11C2×#4111yescharacteristic
283C23×C11C2×#4111yescharacteristic
284C23×C11C2×#4111yescharacteristic
285C23×C11C2×#4111yescharacteristic
286C23×C11C2×#4111yescharacteristic
287C23×C11C2×#4111yescharacteristic
288C23×C11C2×#4111yescharacteristic
289C23×C11C2×#4111yescharacteristic
290C23×C11C2×#4111yescharacteristic
291C23×C11C2×#4111yescharacteristic
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
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—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
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×C11C4×Q814yes—
339C2×C4×C11C22⋊Q814yes—
340C2×C4×C11#12414yes—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
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—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C2×Dic11—41no—
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#11714yes—
388C2×Dic11C4×D414yes—
389C2×Dic11C4×D414yes—
390C2×Dic11C4×Q814yes—
391C2×Dic11#12114yes—
392C2×Dic11C22⋊Q814yes—
393C2×Dic11#12314yes—
394C2×Dic11#12414yes—
395C2×Dic11#12614yes—
396C2×Dic11C4⋊Q814yes—
397Dic22—416no—
398C23×Q8—111no—
399C22×C4⋊C4—111no—
400C22×C4⋊C4—111no—
401C22×C4⋊C4—111no—
402C22×C4⋊C4—111no—
403C22×C4⋊C4C2×D1111yescharacteristic
404C22×C42—111no—
405C22×C42—111no—
406C22×C42—111no—
407C22×C42—111no—
408C22×C42—111no—
409C22×C42—111no—
410C22×C42C2×D1111yescharacteristic
411#391—118no—
412#391—224no—
413#391—224no—
414#389—224no—
415C2×#95—111no—
416C2×#95—111no—
417C2×#95—111no—
418C2×#95—111no—
419C2×#95—111no—
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×#95C2×D1111yescharacteristic
433C2×#95C2×D1111yescharacteristic
434C2×#95C2×D1111yescharacteristic
435C2×#95C2×D1111yescharacteristic
436C2×#95C2×D1111yescharacteristic
437C43—224no—
438C22×C11C2×#11711yescharacteristic
439C22×C11C2×C4×D411yescharacteristic
440C22×C11C2×C4×D411yescharacteristic
441C22×C11C2×C4×Q811yescharacteristic
442C22×C11C2×C4×Q811yescharacteristic
443C22×C11C4×#4111yescharacteristic
444C22×C11C4×#4111yescharacteristic
445C22×C11C2×#12111yescharacteristic
446C22×C11C2×C22⋊Q811yescharacteristic
447C22×C11C2×C22⋊Q811yescharacteristic
448C22×C11C2×#12311yescharacteristic
449C22×C11#52511yescharacteristic
450C22×C11#52511yescharacteristic
451C22×C11C2×#12411yescharacteristic
452C22×C11C2×#12411yescharacteristic
453C22×C11C2×#12611yescharacteristic
454C22×C11#52911yescharacteristic
455C22×C11#52911yescharacteristic
456C22×C11#52911yescharacteristic
457C22×C11#52911yescharacteristic
458C22×C11#52911yescharacteristic
459C22×C11#52911yescharacteristic
460C22×C11#52911yescharacteristic
461C22×C11#52911yescharacteristic
462C22×C11C2×C4⋊Q811yescharacteristic
463C22×C11#53211yescharacteristic
464C22×C11#53211yescharacteristic
465C22×C11#53311yescharacteristic
466C22×C11#53311yescharacteristic
467C22×C11#53311yescharacteristic
468C22×C11#53311yescharacteristic
469C22×C11#53311yescharacteristic
470C22×C11#53311yescharacteristic
471C22×C11#53311yescharacteristic
472C22×C11#53311yescharacteristic
473C4×C11—24no—
474C4×C11—24no—
475C4×C11—24no—
476C4×C11—42no—
477C4×C11—42no—
478C4×C11—81no—
479C4×C11—81no—
480Dic11—24no—
481Dic11—24no—
482Dic11—24no—
483Dic11—42no—
484Dic11—42no—
485Dic11—81no—
486Dic11—81no—
487Dic11#38818yes—
488C22×Q8—114no—
489C22×Q8—222no—
490C22×Q8—222no—
491C22×Q8—222no—
492C22×Q8—222no—
493C22×Q8—222no—
494C22×Q8—222no—
495C23×C4—111no—
496C23×C4—111no—
497C23×C4—111no—
498C23×C4—111no—
499C23×C4—111no—
500C23×C4—111no—
501C23×C4—111no—
502C23×C4—111no—
503C23×C4C22×D1111yescharacteristic
504C23×C4C22×D1111yescharacteristic
505C23×C4C22×D1111yescharacteristic
506C23×C4C22×D1111yescharacteristic
507C23×C4C22×D1111yescharacteristic
508C23×C4C22×D1111yescharacteristic
509C23×C4C22×D1111yescharacteristic
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—114no—
514C2×C4⋊C4—222no—
515C2×C4⋊C4—222no—
516C2×C4⋊C4—222no—
517C2×C4⋊C4—222no—
518C2×C4⋊C4—222no—
519C2×C4⋊C4—222no—
520C2×C4⋊C4—222no—
521C2×C4⋊C4—222no—
522C2×C4⋊C4—222no—
523C2×C4⋊C4—222no—
524C2×C4⋊C4—222no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—114no—
529C2×C42—114no—
530C2×C42—114no—
531C2×C42—114no—
532C2×C42—114no—
533C2×C42—222no—
534C2×C42—222no—
535C2×C42—222no—
536C2×C42—222no—
537C2×C42—222no—
538C2×C42—222no—
539C2×C42—222no—
540C2×C42—222no—
541C2×C42—222no—
542C2×C42—222no—
543C2×C42—222no—
544C2×C42—222no—
545C2×C42—222no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—114no—
551#95—114no—
552#95—114no—
553#95—222no—
554#95—222no—
555#95—222no—
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#95C4×D1114yes—
568C2×C11C2×#38811yescharacteristic
569C2×C11#229511yescharacteristic
570C2×C11#229511yescharacteristic
571C2×C11C4×C22⋊Q811yescharacteristic
572C2×C11C4×C22⋊Q811yescharacteristic
573C2×C11C4×#12411yescharacteristic
574C2×C11C4×C4⋊Q811yescharacteristic
575C2×C11#285011yescharacteristic
576C2×C11#285511yescharacteristic
577C2×C11#285511yescharacteristic
578C2×C11#285711yescharacteristic
579C2×C11#286111yescharacteristic
580C2×C11#286211yescharacteristic
581C2×C11#286311yescharacteristic
582C2×C11#286311yescharacteristic
583C24C23×D1111yescharacteristic
584C2×Q8—228no—
585C2×Q8—228no—
586C2×Q8—228no—
587C2×Q8—444no—
588C2×Q8—444no—
589C2×Q8—444no—
590C2×Q8—444no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
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—112no—
630C22×C4—112no—
631C22×C4—112no—
632C22×C4—112no—
633C22×C4—112no—
634C22×C4—112no—
635C22×C4—112no—
636C22×C4—112no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—112no—
640C22×C4—112no—
641C22×C4—112no—
642C22×C4—112no—
643C22×C4—112no—
644C22×C4—112no—
645C22×C4—112no—
646C22×C4—112no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—221no—
650C22×C4—221no—
651C22×C4—221no—
652C22×C4—221no—
653C22×C4—221no—
654C22×C4—221no—
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×C4C2×C4×D1112yes—
686C22×C4C2×C4×D1112yes—
687C22×C4C2×C4×D1112yes—
688C22×C4#433912yes—
689C22×C4#433912yes—
690C22×C4D4×D1112yes—
691C22×C4D4×D1112yes—
692C22×C4#434112yes—
693C22×C4#434112yes—
694C22×C4Q8×D1112yes—
695C22×C4Q8×D1112yes—
696C4⋊C4—44no—
697C4⋊C4—228no—
698C4⋊C4—444no—
699C4⋊C4—444no—
700C4⋊C4—444no—
701C42—28no—
702C42—228no—
703C42—228no—
704C42—228no—
705C42—228no—
706C42—228no—
707C42—228no—
708C11#1470311yescharacteristic, complemented, Sylow
709C23C22×C4×D1111yescharacteristic
710C23C2×#433911yescharacteristic
711C23C2×#433911yescharacteristic
712C23C2×D4×D1111yescharacteristic
713C23C2×D4×D1111yescharacteristic
714C23C2×#434111yescharacteristic
715C23C2×#434111yescharacteristic
716C23C2×Q8×D1111yescharacteristic
717C23C2×Q8×D1111yescharacteristic
718C23#41×D1111yescharacteristic
719C23#41×D1111yescharacteristic
720C23#41×D1111yescharacteristic
721C23#41×D1111yescharacteristic
722C23#41×D1111yescharacteristic
723C23#41×D1111yescharacteristic
724Q8—4416no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
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—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
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—114no—
772C2×C4—114no—
773C2×C4—114no—
774C2×C4—114no—
775C2×C4—114no—
776C2×C4—114no—
777C2×C4—114no—
778C2×C4—114no—
779C2×C4—114no—
780C2×C4—114no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—222no—
784C2×C4—222no—
785C2×C4—222no—
786C2×C4—222no—
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—441no—
806C2×C4—441no—
807C2×C4—441no—
808C2×C4—441no—
809C2×C4—441no—
810C2×C4—441no—
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#6693814yes—
828C2×C4#6694014yes—
829C2×C4#6694914yes—
830C22C4×#433911yescharacteristic
831C22C2×#6693811yescharacteristic
832C22C2×#6694011yescharacteristic
833C22C2×#6694911yescharacteristic
834C22D11×#11711yescharacteristic
835C22#1062305911yescharacteristic
836C22#1062305911yescharacteristic
837C22C4×#434111yescharacteristic
838C22#1062306911yescharacteristic
839C22#1062306911yescharacteristic
840C22#1062306911yescharacteristic
841C22C4×D4×D1111yescharacteristic
842C22C4×D4×D1111yescharacteristic
843C22#1062307811yescharacteristic
844C22#1062307911yescharacteristic
845C22C4×Q8×D1111yescharacteristic
846C22#1062310911yescharacteristic
847C22#1062310911yescharacteristic
848C22#1062310911yescharacteristic
849C22#1062311711yescharacteristic
850C22#1062312711yescharacteristic
851C22D11×#12111yescharacteristic
852C22#1062315311yescharacteristic
853C22#1062315311yescharacteristic
854C22#1062315311yescharacteristic
855C22D11×C22⋊Q811yescharacteristic
856C22#1062318011yescharacteristic
857C22#1062318011yescharacteristic
858C22D11×#12311yescharacteristic
859C22D11×#12411yescharacteristic
860C22#1062321911yescharacteristic
861C22#1062321911yescharacteristic
862C22D11×#12611yescharacteristic
863C22#1062323711yescharacteristic
864C22D11×C4⋊Q811yescharacteristic
865C4—24no—
866C4—24no—
867C4—24no—
868C4—42no—
869C4—42no—
870C4—81no—
871C4—81no—
872C4—118no—
873C4—224no—
874C4—224no—
875C4—224no—
876C4—442no—
877C4—442no—
878C4—881no—
879C4—881no—
880C2D11×#38811yescharacteristic
881C2#1307108911yescharacteristic
882C2#1307109211yescharacteristic
883C2#1307114811yescharacteristic
884C2C4×#6694911yescharacteristic
885C2C4×#6693811yescharacteristic
886C2#1307118711yescharacteristic
887C2#1307691311yescharacteristic
888C2#1307695111yescharacteristic
889C2#1307695211yescharacteristic
890C2#1307696711yescharacteristic
891C2#1307698511yescharacteristic
892C2#1307699111yescharacteristic
893C2#1307699711yescharacteristic
894C2#1307699711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1436D11
hypocenterC11#14703
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
55. #10622259C4semidirect
112. C2×C4×Dic11Q8semidirect
113. C2×C4×Dic11Q8semidirect
708. C11#14703semidirect

Maximal subgroups

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

subgroupindex
C2×#106222592
C2×#106225852
C2×C42×Dic112
#130668512
#130668492
#130668482
Dic11⋊#952
#130668412
#130668402
C11×#14362
#1470311