Finite Group Databasebeta

← #14682276

Subgroups — #14682276

Order 2816.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic
2C2×#10622542C211yesmaximal, characteristic, complemented
3C2×#10622259C211yesmaximal, characteristic, complemented
4#13066882C211yesmaximal, characteristic, complemented
5#13066882C211yesmaximal, characteristic, complemented
6#13066869C211yesmaximal, characteristic, complemented
7#13066867C211yesmaximal, characteristic, complemented
8#13066862C211yesmaximal, characteristic
9#13066860C211yesmaximal, characteristic
10#13066854C211yesmaximal, characteristic
11#13066852C211yesmaximal, characteristic
12#13066847C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×#66949—24no—
32C2×#66949—24no—
33C2×#66949C418yescomplemented
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—
56C24×D11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C22×C4×D11—22no—
72C22×C4×D11—22no—
73C22×C4×D11—41no—
74C22×C4×D11—41no—
75C22×C4×D11—41no—
76C22×C4×D11—41no—
77C22×C4×D11C2×C414yes—
78C22×Dic22—41no—
79C22×Dic22—41no—
80C22×Dic22—41no—
81C22×Dic22—41no—
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×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—22no—
100C2×(C2×D11)⋊C4—41no—
101C2×(C2×D11)⋊C4—41no—
102C2×(C2×D11)⋊C4—41no—
103C2×(C2×D11)⋊C4—41no—
104C2×(C2×D11)⋊C4—41no—
105C2×(C2×D11)⋊C4—41no—
106C2×(C2×D11)⋊C4C2×C414yes—
107C2×(C2×D11)⋊C4C2×C414yes—
108C2×(C2×D11)⋊C4Q814yescomplemented
109C2×C4⋊Dic11—22no—
110C2×C4⋊Dic11—41no—
111C2×C4⋊Dic11—41no—
112C2×Dic11⋊C4—22no—
113C2×Dic11⋊C4—22no—
114C2×Dic11⋊C4—22no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—41no—
118C2×Dic11⋊C4—41no—
119C2×Dic11⋊C4C2×C414yes—
120C2×Dic11⋊C4C2×C414yes—
121C2×C4×Dic11—22no—
122C2×C4×Dic11—41no—
123C2×C4×Dic11—41no—
124#66949—232no—
125C11×#95—22no—
126C11×#95—22no—
127C11×#95—22no—
128C11×#95—41no—
129C11×#95—41no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—41no—
140C11⋊#95—41no—
141C11⋊#95—41no—
142C11⋊#95—41no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145#14449—111nomaximal, Sylow
146C24×C11C2411yescharacteristic
147C23×D11—21no—
148C23×D11—21no—
149C23×D11—21no—
150C23×D11—21no—
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—21no—
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—21no—
157C23×D11—21no—
158C23×D11—21no—
159C23×D11C22×C412yes—
160C23×D11C2×Q812yes—
161C23×D11#4112yes—
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×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11C22×C412yes—
204C22×C4×C11C22×C412yes—
205C22×C4×C11C22×C412yes—
206C22×C4×C11C2×D412yes—
207C22×C4×C11C2×D412yes—
208C22×C4×C11C2×Q812yes—
209C22×C4×C11#4112yes—
210C22×C4×C11#4112yes—
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×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11C22×C412yes—
253C22×Dic11C22×C412yes—
254C22×Dic11C22×C412yes—
255C22×Dic11C2×D412yes—
256C22×Dic11C2×D412yes—
257C22×Dic11C2×D412yes—
258C22×Dic11C2×D412yes—
259C22×Dic11C2×Q812yes—
260C2×C4×D11—28no—
261C2×C4×D11—44no—
262C2×C4×D11—44no—
263C2×C4×D11—44no—
264C2×C4×D11—44no—
265C2×C4×D11—44no—
266C2×C4×D11—44no—
267C2×Dic22—44no—
268C2×Dic22—44no—
269C2×Dic22—44no—
270C2×Dic22—44no—
271C2×Dic22—44no—
272C2×Dic22—44no—
273C2×Dic22C22⋊C4116yescomplemented
274C11×C4⋊C4—28no—
275C42×C11—44no—
276(C2×D11)⋊C4—28no—
277(C2×D11)⋊C4—28no—
278(C2×D11)⋊C4—44no—
279(C2×D11)⋊C4—44no—
280(C2×D11)⋊C4—44no—
281(C2×D11)⋊C4—44no—
282C4⋊Dic11—44no—
283Dic11⋊C4—28no—
284Dic11⋊C4—28no—
285Dic11⋊C4—44no—
286C4×Dic11—44no—
287C22×C22⋊Q8—111no—
288C2×#391—111no—
289C2×#391—111no—
290#1445—111no—
291#1445—111no—
292#1441—111no—
293#1441—111no—
294#1439—111no—
295#1439—111no—
296#1437—111no—
297#1437—111no—
298#1436—111no—
299#1436D1111yescharacteristic, complemented
300C22⋊#95—111no—
301C22⋊#95—111no—
302C23×C11C23×C411yescharacteristic
303C23×C11C22×D411yescharacteristic
304C23×C11C22×D411yescharacteristic
305C23×C11C22×Q811yescharacteristic
306C23×C11C2×#4111yescharacteristic
307C23×C11C2×#4111yescharacteristic
308C23×C11C2×#4111yescharacteristic
309C23×C11H(5,𝔽2)11yescharacteristic
310C23×C11H(5,𝔽2)11yescharacteristic
311C23×C11H(5,𝔽2)11yescharacteristic
312C23×C11H(5,𝔽2)11yescharacteristic
313C23×C11H(5,𝔽2)11yescharacteristic
314C23×C112−1+411yescharacteristic
315C23×C112−1+411yescharacteristic
316C23×C112−1+411yescharacteristic
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—41no—
336C22×D11—41no—
337C22×D11—41no—
338C22×D11—41no—
339C22×D11—41no—
340C22×D11—41no—
341C22×D11—41no—
342C22×D11—41no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11—41no—
347C22×D11—41no—
348C22×D11—41no—
349C22×D11—41no—
350C22×D11—41no—
351C22×D11C4×Q814yes—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11C2×C22⋊C414yes—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—41no—
420C2×Dic11—41no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—41no—
426C2×Dic11—41no—
427C2×Dic11—41no—
428C2×Dic11—41no—
429C2×Dic11—41no—
430C2×Dic11—41no—
431C2×Dic11—41no—
432C2×Dic11—41no—
433C2×Dic11—41no—
434C2×Dic11—41no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11—41no—
438C2×Dic11—41no—
439C2×Dic11—41no—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—41no—
444C2×Dic11—41no—
445C2×Dic11—41no—
446C2×Dic11—41no—
447C2×Dic11—41no—
448C2×Dic11C2×C22⋊C414yes—
449C2×Dic11C2×C22⋊C414yes—
450C4×D11—416no—
451Dic22—416no—
452C23×Q8—111no—
453C24×C4—111no—
454C2×C22⋊Q8—118no—
455C2×C22⋊Q8—224no—
456C2×C22⋊Q8—224no—
457C22×C4⋊C4—111no—
458C22×C4⋊C4—111no—
459C22×C4⋊C4—111no—
460C22×C4⋊C4—111no—
461C22×C4⋊C4C2×D1111yescharacteristic
462C22×C22⋊C4—111no—
463C22×C22⋊C4—111no—
464C22×C22⋊C4—111no—
465C22×C22⋊C4—111no—
466C22×C22⋊C4—111no—
467C22×C22⋊C4—111no—
468C22×C42—111no—
469C22×C42C2×D1111yescharacteristic
470#391—224no—
471#391—224no—
472C2×#95—111no—
473C2×#95—111no—
474C2×#95—111no—
475C2×#95—111no—
476C2×#95—111no—
477C2×#95—111no—
478C2×#95—111no—
479C2×#95—111no—
480C2×#95—111no—
481C2×#95—111no—
482C2×#95—111no—
483C2×#95—111no—
484C2×#95—111no—
485C2×#95—111no—
486C2×#95—111no—
487C2×#95C2×D1111yescharacteristic
488C2×#95C2×D1111yescharacteristic
489C2×#95C2×D1111yescharacteristic
490C2×#95C2×D1111yescharacteristic
491C2×#95C2×D1111yescharacteristic
492C22×C11C22×C22⋊C411yescharacteristic
493C22×C11C2×C4×Q811yescharacteristic
494C22×C11C4×#4111yescharacteristic
495C22×C11#51811yescharacteristic
496C22×C11#51811yescharacteristic
497C22×C11#51911yescharacteristic
498C22×C11#52011yescharacteristic
499C22×C11#53411yescharacteristic
500C22×C11#53411yescharacteristic
501C22×C11#53411yescharacteristic
502C22×C11#53411yescharacteristic
503C22×C11#53811yescharacteristic
504C22×C11#53911yescharacteristic
505C22×C11#53911yescharacteristic
506C22×C11#53911yescharacteristic
507C22×C11#54211yescharacteristic
508C22×C11#54211yescharacteristic
509C22×C11#54311yescharacteristic
510C22×C11#54411yescharacteristic
511C22×C11#54811yescharacteristic
512C22×C11#54811yescharacteristic
513C22×C11#54811yescharacteristic
514C22×C11#54811yescharacteristic
515C22×C11D4×Q811yescharacteristic
516C22×C11D4×Q811yescharacteristic
517C22×C11#55011yescharacteristic
518C22×C11#55011yescharacteristic
519C22×C11#55111yescharacteristic
520C22×C11#55111yescharacteristic
521C22×C11#55411yescharacteristic
522C22×C11#55411yescharacteristic
523C22×C11#56211yescharacteristic
524C22×C11#56211yescharacteristic
525C22×C11#56311yescharacteristic
526C22×C11#56311yescharacteristic
527C2×D11—24no—
528C2×D11—24no—
529C2×D11—24no—
530C2×D11—42no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—42no—
540C2×D11—42no—
541C2×D11—42no—
542C4×C11—24no—
543C4×C11—42no—
544C4×C11—42no—
545C4×C11—42no—
546C4×C11—42no—
547C4×C11—42no—
548C4×C11—81no—
549Dic11—24no—
550Dic11—24no—
551Dic11—42no—
552Dic11—42no—
553Dic11—81no—
554Dic11—81no—
555Dic11—81no—
556C25—111no—
557C22×Q8—114no—
558C22×Q8—114no—
559C22×Q8—114no—
560C22×Q8—441no—
561C22×Q8—441no—
562C22×Q8—441no—
563C22×Q8—441no—
564C23×C4—111no—
565C23×C4—111no—
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—114no—
569C23×C4—111no—
570C23×C4—111no—
571C23×C4—111no—
572C23×C4—222no—
573C23×C4—222no—
574C23×C4—441no—
575C23×C4—441no—
576C23×C4—441no—
577C23×C4—441no—
578C23×C4C22×D1111yescharacteristic
579C23×C4C22×D1111yescharacteristic
580C23×C4C22×D1111yescharacteristic
581C23×C4C22×D1111yescharacteristic
582C23×C4C22×D1111yescharacteristic
583C23×C4C22×D1111yescharacteristic
584C23×C4C22×D1111yescharacteristic
585C22⋊Q8—2232no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—114no—
589C2×C4⋊C4—114no—
590C2×C4⋊C4—222no—
591C2×C4⋊C4—222no—
592C2×C4⋊C4—222no—
593C2×C4⋊C4—222no—
594C2×C4⋊C4—222no—
595C2×C4⋊C4—222no—
596C2×C4⋊C4—441no—
597C2×C4⋊C4—441no—
598C2×C4⋊C4—441no—
599C2×C4⋊C4—441no—
600C2×C4⋊C4C4×D1114yes—
601C2×C22⋊C4—114no—
602C2×C22⋊C4—114no—
603C2×C22⋊C4—114no—
604C2×C22⋊C4—222no—
605C2×C22⋊C4—222no—
606C2×C22⋊C4—222no—
607C2×C22⋊C4—222no—
608C2×C22⋊C4—222no—
609C2×C22⋊C4—222no—
610C2×C22⋊C4—222no—
611C2×C22⋊C4—222no—
612C2×C22⋊C4—222no—
613C2×C22⋊C4—441no—
614C2×C22⋊C4—441no—
615C2×C22⋊C4—441no—
616C2×C22⋊C4—441no—
617C2×C22⋊C4—441no—
618C2×C22⋊C4—441no—
619C2×C42—22no—
620C2×C42—41no—
621C2×C42—41no—
622C2×C42—222no—
623C2×C42—441no—
624C2×C42—441no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—41no—
629#95—41no—
630#95—222no—
631#95—222no—
632#95—222no—
633#95—222no—
634#95—222no—
635#95—222no—
636#95—222no—
637#95—222no—
638#95—222no—
639#95—441no—
640#95—441no—
641#95—441no—
642#95—441no—
643#95—441no—
644#95—441no—
645C2×C11#230811yescharacteristic
646C2×C11#232911yescharacteristic
647C2×C11#233211yescharacteristic
648C2×C11Q8×C22⋊C411yescharacteristic
649C2×C11#234111yescharacteristic
650C2×C11#236811yescharacteristic
651C2×C11#237811yescharacteristic
652C2×C11#272811yescharacteristic
653C2×C11#272811yescharacteristic
654C2×C11#272911yescharacteristic
655C2×C11#272911yescharacteristic
656C2×C11#273011yescharacteristic
657C2×C11#273011yescharacteristic
658C2×C11#273211yescharacteristic
659C2×C11#273211yescharacteristic
660D11—44no—
661C24—112no—
662C24—112no—
663C24—112no—
664C24—221no—
665C24—221no—
666C24—221no—
667C24—221no—
668C24—221no—
669C24—221no—
670C24—221no—
671C24—221no—
672C24—221no—
673C24—221no—
674C24—221no—
675C24—221no—
676C24C23×D1111yescharacteristic
677C2×Q8—1116no—
678C2×Q8—444no—
679C2×Q8—444no—
680C2×Q8—444no—
681C2×Q8—444no—
682C2×Q8—444no—
683C2×Q8—444no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—112no—
726C22×C4—112no—
727C22×C4—112no—
728C22×C4—112no—
729C22×C4—112no—
730C22×C4—112no—
731C22×C4—112no—
732C22×C4—112no—
733C22×C4—228no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—221no—
756C22×C4—221no—
757C22×C4—221no—
758C22×C4—221no—
759C22×C4—221no—
760C22×C4—221no—
761C22×C4—221no—
762C22×C4—221no—
763C22×C4—221no—
764C22×C4—221no—
765C22×C4—221no—
766C22×C4—221no—
767C22×C4—221no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4—444no—
776C22×C4—444no—
777C22×C4—444no—
778C22×C4—444no—
779C22×C4—444no—
780C22×C4—444no—
781C22×C4C2×C4×D1112yes—
782C22×C4C2×C4×D1112yes—
783C22×C4C2×C4×D1112yes—
784C22×C4#433912yes—
785C22×C4#433912yes—
786C22×C4D4×D1112yes—
787C22×C4D4×D1112yes—
788C22×C4Q8×D1112yes—
789C4⋊C4—28no—
790C4⋊C4—228no—
791C4⋊C4—228no—
792C4⋊C4—444no—
793C4⋊C4—444no—
794C22⋊C4—228no—
795C22⋊C4—228no—
796C22⋊C4—444no—
797C22⋊C4—444no—
798C22⋊C4—444no—
799C22⋊C4—444no—
800C42—44no—
801C42—444no—
802C11#1444911yescharacteristic, complemented, Sylow
803C23—114no—
804C23—222no—
805C23—222no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—222no—
810C23—222no—
811C23—222no—
812C23—222no—
813C23—222no—
814C23—222no—
815C23—222no—
816C23—222no—
817C23—222no—
818C23—222no—
819C23—222no—
820C23—222no—
821C23—222no—
822C23—441no—
823C23—441no—
824C23—441no—
825C23—441no—
826C23—441no—
827C23—441no—
828C23—441no—
829C23—441no—
830C23—441no—
831C23—441no—
832C23—441no—
833C23—441no—
834C23—441no—
835C23—441no—
836C23—441no—
837C23—441no—
838C23C22×C4×D1111yescharacteristic
839C23C2×#433911yescharacteristic
840C23C2×#433911yescharacteristic
841C23C2×D4×D1111yescharacteristic
842C23C2×D4×D1111yescharacteristic
843C23#6703711yescharacteristic
844C23#6703711yescharacteristic
845C23C2×Q8×D1111yescharacteristic
846C23#6704011yescharacteristic
847C23#41×D1111yescharacteristic
848C23#6704211yescharacteristic
849C23#6704211yescharacteristic
850C23#6704211yescharacteristic
851C23#6704311yescharacteristic
852C23#6704311yescharacteristic
853Q8—4416no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—114no—
903C2×C4—114no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—222no—
913C2×C4—222no—
914C2×C4—222no—
915C2×C4—222no—
916C2×C4—222no—
917C2×C4—222no—
918C2×C4—222no—
919C2×C4—222no—
920C2×C4—222no—
921C2×C4—222no—
922C2×C4—4416no—
923C2×C4—441no—
924C2×C4—441no—
925C2×C4—441no—
926C2×C4—441no—
927C2×C4—441no—
928C2×C4—441no—
929C2×C4—441no—
930C2×C4—441no—
931C2×C4—441no—
932C2×C4—441no—
933C2×C4—441no—
934C2×C4—441no—
935C2×C4—441no—
936C2×C4—441no—
937C2×C4—441no—
938C2×C4—441no—
939C2×C4—441no—
940C2×C4—441no—
941C2×C4—441no—
942C2×C4—441no—
943C2×C4—441no—
944C2×C4—441no—
945C2×C4—441no—
946C2×C4—441no—
947C2×C4—441no—
948C2×C4—441no—
949C2×C4—441no—
950C2×C4—441no—
951C2×C4—441no—
952C2×C4C22⋊C4×D1114yes—
953C22—224no—
954C22—224no—
955C22—224no—
956C22—442no—
957C22—442no—
958C22—442no—
959C22—442no—
960C22—442no—
961C22—442no—
962C22—442no—
963C22—442no—
964C22—442no—
965C22—442no—
966C22—442no—
967C22—442no—
968C22C4×#433911yescharacteristic
969C22C2×C22⋊C4×D1111yescharacteristic
970C22#1062304211yescharacteristic
971C22#1062304611yescharacteristic
972C22#1062305411yescharacteristic
973C22#1062305811yescharacteristic
974C22#1062306511yescharacteristic
975C22#1062307611yescharacteristic
976C22#1062307611yescharacteristic
977C22#1062308311yescharacteristic
978C22#1062308311yescharacteristic
979C22#1062308411yescharacteristic
980C22#1062308411yescharacteristic
981C22#1062308711yescharacteristic
982C22#1062309511yescharacteristic
983C22C4×Q8×D1111yescharacteristic
984C22#1062310311yescharacteristic
985C22#1062311011yescharacteristic
986C22#1062311311yescharacteristic
987C22#1062312011yescharacteristic
988C22#1062313611yescharacteristic
989C22#1062313611yescharacteristic
990C22#1062316311yescharacteristic
991C22#1062316411yescharacteristic
992C22#1062316511yescharacteristic
993C22#1062317711yescharacteristic
994C22#1062318411yescharacteristic
995C22#1062319111yescharacteristic
996C22#1062319811yescharacteristic
997C22#1062320811yescharacteristic
998C22#1062322011yescharacteristic
999C22#1062323111yescharacteristic
1000C22#1062323511yescharacteristic
1001C22#1062324311yescharacteristic
1002C22#1062325811yescharacteristic
1003C4—24no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—42no—
1008C4—42no—
1009C4—81no—
1010C4—224no—
1011C4—224no—
1012C4—442no—
1013C4—442no—
1014C4—881no—
1015C4—881no—
1016C4—881no—
1017C2—444no—
1018C2#1307119011yescharacteristic
1019C2#1307134311yescharacteristic
1020C2#1307136711yescharacteristic
1021C2#1307145011yescharacteristic
1022C2#1307145611yescharacteristic
1023C2#1307170011yescharacteristic
1024C2#1307178111yescharacteristic
1025C2#1307558411yescharacteristic
1026C2#1307558911yescharacteristic
1027C2#1307559311yescharacteristic
1028C2#1307560111yescharacteristic
1029C2#1307561011yescharacteristic
1030C2#1307561711yescharacteristic
1031C2#1307563211yescharacteristic
1032C2#1307563511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#14449
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#10622542C2semidirect
3. C2×#10622259C2semidirect
4. #13066882C2semidirect
5. #13066882C2semidirect
6. #13066869C2semidirect
7. #13066867C2semidirect
12. #13066847C2semidirect
15. C11×#1436C2semidirect
33. C2×#66949C4semidirect
108. C2×(C2×D11)⋊C4Q8semidirect
273. C2×Dic22C22⋊C4semidirect
299. #1436D11semidirect
802. C11#14449semidirect

Maximal subgroups

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

subgroupindex
C22×#669492
C2×#106225422
C2×#106222592
#130668822
#130668692
#130668672
#130668622
#130668602
#130668542
#130668522
#130668472
(C2×D11)⋊#952
C11×#14362
#1444911