Finite Group Databasebeta

← #14685225

Subgroups — #14685225

Order 2816.

2558 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D11C211yesmaximal, characteristic
3C2×#10622592C211yesmaximal, characteristic, complemented
4C2×#10622560C211yesmaximal, characteristic, complemented
5C2×#10622823C211yesmaximal, characteristic, complemented
6#13066867C211yesmaximal, characteristic, complemented
7#13066860C211yesmaximal, characteristic, complemented
8#13066859C211yesmaximal, characteristic, complemented
9#13066858C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic
11#13066855C211yesmaximal, characteristic
12#13066851C211yesmaximal, characteristic, complemented
13#13066848C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#385C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×Dic22C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C2×C4×C22⋊D11—24no—
28C2×C4×C22⋊D11—24no—
29C2×C4×C22⋊D11—24no—
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C2×#66949—24no—
41C2×#66949—24no—
42C2×#66949—24no—
43C11×#385—24no—
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2211yescharacteristic
46#10622823—24no—
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59#10622592—24no—
60#10622560—24no—
61C25×C11C2311yescharacteristic
62C24×D11C2311yescharacteristic
63C23×C4×C11—22no—
64C23×C4×C11—22no—
65C23×C4×C11—22no—
66C23×C4×C11—22no—
67C23×C4×C11—22no—
68C23×C4×C11—41no—
69C23×C4×C11—41no—
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C22×C22⋊D11—22no—
77C22×C22⋊D11—22no—
78C22×C22⋊D11—22no—
79C22×C22⋊D11—22no—
80C22×C22⋊D11—22no—
81C22×C22⋊D11—22no—
82C22×C22⋊D11Q814yescomplemented
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C22×C4×D11—22no—
91C22×C4×D11—22no—
92C22×C4×D11—22no—
93C22×C4×D11—22no—
94C22×C4×D11—41no—
95C22×C4×D11—41no—
96C22×C4×D11D414yes—
97C22×Dic22—22no—
98C22×Dic22—22no—
99C22×Dic22—22no—
100C22×Dic22—22no—
101C22×Dic22—22no—
102C22×Dic22—41no—
103C22×Dic22—41no—
104C2×C11×C4⋊C4—22no—
105C2×C11×C4⋊C4—22no—
106C2×C11×C4⋊C4—22no—
107C2×C11×C4⋊C4—22no—
108C2×C11×C4⋊C4—41no—
109C2×C11×C4⋊C4D414yescomplemented
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4—22no—
114C2×C11×C22⋊C4—22no—
115C2×C11×C22⋊C4—41no—
116C2×C22⋊Dic11—22no—
117C2×C22⋊Dic11—22no—
118C2×C22⋊Dic11—22no—
119C2×C22⋊Dic11—22no—
120C2×C22⋊Dic11—22no—
121C2×C22⋊Dic11—22no—
122C2×C22⋊Dic11—22no—
123C2×C22⋊Dic11—41no—
124C2×C22⋊Dic11D414yes—
125C4×C22⋊D11—232no—
126C2×(C2×D11)⋊C4—22no—
127C2×(C2×D11)⋊C4—22no—
128C2×(C2×D11)⋊C4—22no—
129C2×(C2×D11)⋊C4—22no—
130C2×(C2×D11)⋊C4—22no—
131C2×(C2×D11)⋊C4—22no—
132C2×(C2×D11)⋊C4—22no—
133C2×(C2×D11)⋊C4—22no—
134C2×(C2×D11)⋊C4—22no—
135C2×(C2×D11)⋊C4—22no—
136C2×(C2×D11)⋊C4—22no—
137C2×(C2×D11)⋊C4—22no—
138C2×(C2×D11)⋊C4—22no—
139C2×(C2×D11)⋊C4—41no—
140C2×(C2×D11)⋊C4—41no—
141C2×Dic11⋊C4—22no—
142C2×Dic11⋊C4—22no—
143C2×Dic11⋊C4—22no—
144C2×Dic11⋊C4—22no—
145C2×Dic11⋊C4—22no—
146C2×Dic11⋊C4—22no—
147C2×Dic11⋊C4—22no—
148C2×Dic11⋊C4—22no—
149C2×Dic11⋊C4—22no—
150C2×Dic11⋊C4—41no—
151C2×Dic11⋊C4D414yes—
152C2×Dic11⋊C4D414yescomplemented
153C2×C4×Dic11—22no—
154C2×C4×Dic11—22no—
155C2×C4×Dic11—22no—
156#66949—232no—
157C11×#95—22no—
158C11×#95—22no—
159C11⋊#95—22no—
160C11⋊#95—22no—
161C11⋊#95—22no—
162C11⋊#95—22no—
163C11⋊#95—22no—
164C11⋊#95—22no—
165C11⋊#95—22no—
166C11⋊#95—22no—
167C11⋊#95—22no—
168C11⋊#95—22no—
169C11⋊#95—22no—
170C11⋊#95—22no—
171#14723—111nomaximal, Sylow
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11—21no—
184C24×C11C2×D412yes—
185C24×C11C2×Q812yes—
186C24×C11#4112yes—
187C24×C11C2411yescharacteristic
188C23×D11—21no—
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—21no—
194C23×D11—21no—
195C23×D11—21no—
196C23×D11—21no—
197C23×D11—21no—
198C23×D11—21no—
199C23×D11—21no—
200C23×D11C2×D412yes—
201C23×D11C2×Q812yes—
202C23×D11#4112yes—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—28no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—44no—
240C22×C4×C11—44no—
241C22×C4×C11—44no—
242C22×C4×C11—44no—
243C22×C4×C11—44no—
244C22×C4×C11—44no—
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2×D412yes—
248C22×C4×C11C2×D412yes—
249C22×C4×C11C2×D412yes—
250C22×C4×C11C2×D412yes—
251C22×C4×C11#4112yes—
252C2×C22⋊D11—28no—
253C2×C22⋊D11—28no—
254C2×C22⋊D11—28no—
255C2×C22⋊D11—28no—
256C2×C22⋊D11—28no—
257C2×C22⋊D11—28no—
258C2×C22⋊D11—28no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—21no—
279C22×Dic11—21no—
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11—21no—
283C22×Dic11—21no—
284C22×Dic11—21no—
285C22×Dic11—21no—
286C22×Dic11—21no—
287C22×Dic11—21no—
288C22×Dic11—21no—
289C22×Dic11—21no—
290C22×Dic11—21no—
291C22×Dic11—21no—
292C22×Dic11—21no—
293C22×Dic11—21no—
294C22×Dic11—21no—
295C22×Dic11—21no—
296C22×Dic11—21no—
297C22×Dic11—21no—
298C22×Dic11C2×D412yes—
299C22×Dic11C2×D412yes—
300C22×Dic11C2×D412yes—
301C22×Dic11C2×D412yes—
302C22×Dic11C2×D412yes—
303C22×Dic11C2×D412yes—
304C22×Dic11C2×D412yes—
305C22×Dic11C2×Q812yes—
306C22×Dic11#4112yes—
307C22×Dic11#4112yes—
308C2×C4×D11—28no—
309C2×C4×D11—28no—
310C2×C4×D11—44no—
311C2×C4×D11—44no—
312C2×C4×D11—44no—
313C2×C4×D11—44no—
314C2×C4×D11—44no—
315C2×Dic22—28no—
316C2×Dic22—44no—
317C2×Dic22—44no—
318C2×Dic22—44no—
319C2×Dic22—44no—
320C2×Dic22—44no—
321C2×Dic22—44no—
322C11×C4⋊C4—28no—
323C11×C4⋊C4—44no—
324C11×C22⋊C4—28no—
325C11×C22⋊C4—44no—
326C22⋊Dic11—28no—
327C22⋊Dic11—28no—
328C22⋊Dic11—44no—
329(C2×D11)⋊C4—28no—
330(C2×D11)⋊C4—28no—
331(C2×D11)⋊C4—28no—
332(C2×D11)⋊C4—44no—
333(C2×D11)⋊C4—44no—
334Dic11⋊C4—28no—
335Dic11⋊C4—28no—
336Dic11⋊C4—28no—
337Dic11⋊C4—44no—
338C4×Dic11—28no—
339C22×C22⋊Q8—111no—
340C22×C4×D4—111no—
341C2×#395—111no—
342C2×#393—111no—
343C2×#385—111no—
344C2×#385D1111yescharacteristic, complemented
345#1441—111no—
346#1439—111no—
347#1439—111no—
348#1439—111no—
349#1438—111no—
350#1438—111no—
351#1436—111no—
352#1436—111no—
353C22⋊#95—111no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11—41no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11—41no—
386C23×C11—41no—
387C23×C11—41no—
388C23×C11C22⋊Q814yescomplemented
389C23×C11C22×D411yescharacteristic
390C23×C11C22×D411yescharacteristic
391C23×C11C22×D411yescharacteristic
392C23×C11C22×D411yescharacteristic
393C23×C11C22×D411yescharacteristic
394C23×C11C22×Q811yescharacteristic
395C23×C11C2×#4111yescharacteristic
396C23×C11C2×#4111yescharacteristic
397C23×C11C2×#4111yescharacteristic
398C23×C11C2×#4111yescharacteristic
399C23×C11C2×#4111yescharacteristic
400C23×C11H(5,𝔽2)11yescharacteristic
401C23×C11H(5,𝔽2)11yescharacteristic
402C23×C112−1+411yescharacteristic
403C23×C112−1+411yescharacteristic
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—22no—
411C22×D11—22no—
412C22×D11—22no—
413C22×D11—22no—
414C22×D11—22no—
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—22no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—22no—
421C22×D11—22no—
422C22×D11—41no—
423C22×D11—41no—
424C22×D11—41no—
425C22×D11—41no—
426C22×D11—41no—
427C22×D11—41no—
428C22×D11—41no—
429C22×D11—41no—
430C22×D11—41no—
431C22×D11—41no—
432C22×D11—41no—
433C22×D11—41no—
434C22×D11—41no—
435C22×D11—41no—
436C22×D11—41no—
437C22×D11—41no—
438C22×D11C22⋊Q814yes—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—416no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11—41no—
470C2×C4×C11—41no—
471C2×C4×C11—41no—
472C2×C4×C11—41no—
473C2×C4×C11—41no—
474C2×C4×C11—41no—
475C2×C4×C11—41no—
476C2×C4×C11—41no—
477C2×C4×C11—41no—
478C2×C4×C11—41no—
479C2×C4×C11—41no—
480C2×C4×C11—41no—
481C2×C4×C11#12014yes—
482C22⋊D11—232no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—22no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—22no—
494C2×Dic11—22no—
495C2×Dic11—22no—
496C2×Dic11—22no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—22no—
501C2×Dic11—22no—
502C2×Dic11—22no—
503C2×Dic11—22no—
504C2×Dic11—22no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—41no—
508C2×Dic11—41no—
509C2×Dic11—41no—
510C2×Dic11—41no—
511C2×Dic11—41no—
512C2×Dic11—41no—
513C2×Dic11—41no—
514C2×Dic11—41no—
515C2×Dic11—41no—
516C2×Dic11—41no—
517C2×Dic11—41no—
518C2×Dic11—41no—
519C2×Dic11—41no—
520C2×Dic11—41no—
521C2×Dic11—41no—
522C2×Dic11—41no—
523C2×Dic11—41no—
524C2×Dic11—41no—
525C2×Dic11—41no—
526C2×Dic11—41no—
527C2×Dic11—41no—
528C2×Dic11—41no—
529C2×Dic11—41no—
530C2×Dic11#12014yes—
531C2×Dic11C22⋊Q814yescomplemented
532C4×D11—416no—
533Dic22—416no—
534C23×Q8—111no—
535C23×D4—111no—
536C24×C4—111no—
537C24×C4C2×D1111yescharacteristic
538C2×C22⋊Q8—224no—
539C2×C22⋊Q8—224no—
540C2×C22⋊Q8—224no—
541C2×C4×D4—224no—
542C2×C4×D4—224no—
543C2×C4×D4—224no—
544C22×C4⋊C4—111no—
545C22×C4⋊C4—111no—
546C22×C4⋊C4—111no—
547C22×C4⋊C4—111no—
548C22×C4⋊C4C2×D1111yescharacteristic
549C22×C4⋊C4C2×D1111yescharacteristic
550C22×C22⋊C4—111no—
551C22×C22⋊C4—111no—
552C22×C22⋊C4—111no—
553C22×C22⋊C4—111no—
554C22×C22⋊C4—111no—
555C22×C22⋊C4—111no—
556C22×C22⋊C4—111no—
557C22×C22⋊C4—111no—
558C22×C22⋊C4C2×D1111yescharacteristic
559C22×C22⋊C4C2×D1111yescharacteristic
560C22×C42—111no—
561#395—224no—
562#393—224no—
563#385—24no—
564#385—224no—
565C2×#95—111no—
566C2×#95—111no—
567C2×#95—111no—
568C2×#95—111no—
569C2×#95—111no—
570C2×#95—111no—
571C2×#95—111no—
572C2×#95—111no—
573C2×#95—111no—
574C2×#95—111no—
575C2×#95—111no—
576C2×#95—111no—
577C2×#95C2×D1111yescharacteristic
578C2×#95C2×D1111yescharacteristic
579C22×C11—24no—
580C22×C11—24no—
581C22×C11—24no—
582C22×C11—42no—
583C22×C11—42no—
584C22×C11—42no—
585C22×C11—42no—
586C22×C11—42no—
587C22×C11—42no—
588C22×C11—42no—
589C22×C11—42no—
590C22×C11—42no—
591C22×C11—42no—
592C22×C11—42no—
593C22×C11—42no—
594C22×C11C2×#12011yescharacteristic
595C22×C11C2×#12011yescharacteristic
596C22×C11C2×C22⋊Q811yescharacteristic
597C22×C11C2×C22⋊Q811yescharacteristic
598C22×C11C2×C22⋊Q811yescharacteristic
599C22×C11#52511yescharacteristic
600C22×C11#52511yescharacteristic
601C22×C11#52511yescharacteristic
602C22×C11#52511yescharacteristic
603C22×C11#52511yescharacteristic
604C22×C11#53211yescharacteristic
605C22×C11#53211yescharacteristic
606C22×C11#53211yescharacteristic
607C22×C11#53411yescharacteristic
608C22×C11#53611yescharacteristic
609C22×C11#53911yescharacteristic
610C22×C11#53911yescharacteristic
611C22×C11#54211yescharacteristic
612C22×C11#54211yescharacteristic
613C22×C11D4211yescharacteristic
614C22×C11D4211yescharacteristic
615C22×C11D4211yescharacteristic
616C22×C11D4211yescharacteristic
617C22×C11#54711yescharacteristic
618C22×C11#54711yescharacteristic
619C22×C11#54811yescharacteristic
620C22×C11#54811yescharacteristic
621C22×C11#54811yescharacteristic
622C22×C11#54811yescharacteristic
623C22×C11D4×Q811yescharacteristic
624C22×C11D4×Q811yescharacteristic
625C22×C11#55111yescharacteristic
626C22×C11#55111yescharacteristic
627C22×C11#55411yescharacteristic
628C22×C11#55411yescharacteristic
629C2×D11—24no—
630C2×D11—24no—
631C2×D11—24no—
632C2×D11—42no—
633C2×D11—42no—
634C2×D11—42no—
635C2×D11—42no—
636C2×D11—42no—
637C2×D11—42no—
638C2×D11—42no—
639C2×D11—42no—
640C2×D11—42no—
641C2×D11—42no—
642C2×D11—42no—
643C2×D11—42no—
644C4×C11—24no—
645C4×C11—42no—
646C4×C11—42no—
647C4×C11—42no—
648C4×C11—42no—
649C4×C11—81no—
650Dic11—24no—
651Dic11—24no—
652Dic11—42no—
653Dic11—42no—
654Dic11—42no—
655Dic11—42no—
656Dic11—81no—
657C25—111no—
658C25C22×D1111yescharacteristic
659C22×Q8—222no—
660C22×Q8—222no—
661C22×Q8—222no—
662C22×Q8—222no—
663C22×Q8—222no—
664C22×Q8—441no—
665C22×Q8—441no—
666C22×D4—114no—
667C22×D4—222no—
668C22×D4—222no—
669C22×D4—222no—
670C22×D4—222no—
671C22×D4—222no—
672C22×D4—222no—
673C23×C4—22no—
674C23×C4—22no—
675C23×C4—22no—
676C23×C4—22no—
677C23×C4—22no—
678C23×C4—41no—
679C23×C4—41no—
680C23×C4—111no—
681C23×C4—111no—
682C23×C4—111no—
683C23×C4—111no—
684C23×C4—111no—
685C23×C4—111no—
686C23×C4—114no—
687C23×C4—111no—
688C23×C4—222no—
689C23×C4—222no—
690C23×C4—222no—
691C23×C4—222no—
692C23×C4—441no—
693C23×C4—441no—
694C23×C4C22×D1111yescharacteristic
695C23×C4C22×D1111yescharacteristic
696C23×C4C22×D1111yescharacteristic
697C23×C4C22×D1111yescharacteristic
698C23×C4C22×D1111yescharacteristic
699C23×C4C22×D1111yescharacteristic
700C22⋊Q8—2232no—
701C4×D4—2232no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4—22no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4—41no—
707C2×C4⋊C4—114no—
708C2×C4⋊C4—114no—
709C2×C4⋊C4—222no—
710C2×C4⋊C4—222no—
711C2×C4⋊C4—222no—
712C2×C4⋊C4—222no—
713C2×C4⋊C4—222no—
714C2×C4⋊C4—222no—
715C2×C4⋊C4—222no—
716C2×C4⋊C4—222no—
717C2×C4⋊C4—222no—
718C2×C4⋊C4—441no—
719C2×C4⋊C4C22⋊D1114yescomplemented
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—41no—
726C2×C22⋊C4—114no—
727C2×C22⋊C4—222no—
728C2×C22⋊C4—222no—
729C2×C22⋊C4—222no—
730C2×C22⋊C4—222no—
731C2×C22⋊C4—222no—
732C2×C22⋊C4—222no—
733C2×C22⋊C4—222no—
734C2×C22⋊C4—222no—
735C2×C22⋊C4—222no—
736C2×C22⋊C4—222no—
737C2×C22⋊C4—222no—
738C2×C22⋊C4—222no—
739C2×C22⋊C4—222no—
740C2×C22⋊C4—222no—
741C2×C22⋊C4—222no—
742C2×C22⋊C4—222no—
743C2×C22⋊C4—222no—
744C2×C22⋊C4—222no—
745C2×C22⋊C4—222no—
746C2×C22⋊C4—222no—
747C2×C22⋊C4—441no—
748C2×C22⋊C4—441no—
749C2×C22⋊C4—441no—
750C2×C42—222no—
751C2×C42—222no—
752C2×C42—222no—
753#95—22no—
754#95—22no—
755#95—222no—
756#95—222no—
757#95—222no—
758#95—222no—
759#95—222no—
760#95—222no—
761#95—222no—
762#95—222no—
763#95—222no—
764#95—222no—
765#95—222no—
766#95—222no—
767C2×C11—44no—
768C2×C11#238811yescharacteristic
769C2×C11#240311yescharacteristic
770C2×C11#240911yescharacteristic
771C2×C11#243211yescharacteristic
772C2×C11#244911yescharacteristic
773C2×C11#244911yescharacteristic
774C2×C11#245211yescharacteristic
775C2×C11#245211yescharacteristic
776C2×C11#246111yescharacteristic
777C2×C11#246111yescharacteristic
778C2×C11#246311yescharacteristic
779C2×C11#246311yescharacteristic
780C2×C11#256411yescharacteristic
781C2×C11#263811yescharacteristic
782C2×C11#284811yescharacteristic
783D11—44no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—112no—
797C24—112no—
798C24—112no—
799C24—221no—
800C24—221no—
801C24—221no—
802C24—221no—
803C24—221no—
804C24—221no—
805C24—221no—
806C24—221no—
807C24—221no—
808C24—221no—
809C24—221no—
810C24—221no—
811C24#433912yes—
812C24D4×D1112yes—
813C24Q8×D1112yes—
814C24C23×D1111yescharacteristic
815C2×Q8—228no—
816C2×Q8—444no—
817C2×Q8—444no—
818C2×Q8—444no—
819C2×Q8—444no—
820C2×Q8—444no—
821C2×Q8—444no—
822C2×D4—228no—
823C2×D4—228no—
824C2×D4—228no—
825C2×D4—228no—
826C2×D4—228no—
827C2×D4—228no—
828C2×D4—228no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—28no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—112no—
872C22×C4—112no—
873C22×C4—112no—
874C22×C4—112no—
875C22×C4—112no—
876C22×C4—112no—
877C22×C4—112no—
878C22×C4—112no—
879C22×C4—112no—
880C22×C4—112no—
881C22×C4—228no—
882C22×C4—221no—
883C22×C4—221no—
884C22×C4—221no—
885C22×C4—221no—
886C22×C4—221no—
887C22×C4—221no—
888C22×C4—221no—
889C22×C4—221no—
890C22×C4—221no—
891C22×C4—221no—
892C22×C4—221no—
893C22×C4—221no—
894C22×C4—221no—
895C22×C4—221no—
896C22×C4—221no—
897C22×C4—221no—
898C22×C4—221no—
899C22×C4—221no—
900C22×C4—221no—
901C22×C4—221no—
902C22×C4—221no—
903C22×C4—221no—
904C22×C4—221no—
905C22×C4—221no—
906C22×C4—221no—
907C22×C4—221no—
908C22×C4—221no—
909C22×C4—221no—
910C22×C4—221no—
911C22×C4—221no—
912C22×C4—221no—
913C22×C4—221no—
914C22×C4—228no—
915C22×C4—221no—
916C22×C4—221no—
917C22×C4—221no—
918C22×C4—221no—
919C22×C4—221no—
920C22×C4—221no—
921C22×C4—221no—
922C22×C4—444no—
923C22×C4—444no—
924C22×C4—444no—
925C22×C4—444no—
926C22×C4—444no—
927C22×C4#433912yes—
928C22×C4D4×D1112yes—
929C22×C4D4×D1112yes—
930C22×C4D4×D1112yes—
931C22×C4C2×C22⋊D1112yes—
932C22×C4C2×C22⋊D1112yes—
933C22×C4C2×C22⋊D1112yes—
934C4⋊C4—28no—
935C4⋊C4—44no—
936C4⋊C4—228no—
937C4⋊C4—228no—
938C4⋊C4—228no—
939C4⋊C4—444no—
940C22⋊C4—28no—
941C22⋊C4—44no—
942C22⋊C4—228no—
943C22⋊C4—228no—
944C22⋊C4—228no—
945C22⋊C4—228no—
946C22⋊C4—228no—
947C22⋊C4—444no—
948C22⋊C4—444no—
949C22⋊C4—444no—
950C42—228no—
951C11#1472311yescharacteristic, complemented, Sylow
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—114no—
987C23—222no—
988C23—222no—
989C23—222no—
990C23—222no—
991C23—222no—
992C23—222no—
993C23—222no—
994C23—222no—
995C23—222no—
996C23—222no—
997C23—222no—
998C23—222no—
999C23—222no—
1000C23—222no—
1001C23—222no—
1002C23—222no—
1003C23—222no—
1004C23—222no—
1005C23—441no—
1006C23—441no—
1007C23—441no—
1008C23—441no—
1009C23—441no—
1010C23—441no—
1011C23—441no—
1012C23—441no—
1013C23—441no—
1014C23—441no—
1015C23—441no—
1016C23—441no—
1017C23—441no—
1018C23—441no—
1019C23—441no—
1020C23—441no—
1021C23#6694914yescomplemented
1022C23C2×#433911yescharacteristic
1023C23C2×#433911yescharacteristic
1024C23C2×D4×D1111yescharacteristic
1025C23C2×D4×D1111yescharacteristic
1026C23C2×D4×D1111yescharacteristic
1027C23C2×D4×D1111yescharacteristic
1028C23#6703711yescharacteristic
1029C23#6703711yescharacteristic
1030C23C2×Q8×D1111yescharacteristic
1031C23#6704011yescharacteristic
1032C23#41×D1111yescharacteristic
1033C23#41×D1111yescharacteristic
1034C23#41×D1111yescharacteristic
1035C23#6704311yescharacteristic
1036C23C22×C22⋊D1111yescharacteristic
1037Q8—4416no—
1038D4—2232no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—416no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—114no—
1082C2×C4—114no—
1083C2×C4—222no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—222no—
1099C2×C4—222no—
1100C2×C4—222no—
1101C2×C4—222no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—222no—
1106C2×C4—222no—
1107C2×C4—4416no—
1108C2×C4—441no—
1109C2×C4—441no—
1110C2×C4—441no—
1111C2×C4—441no—
1112C2×C4—441no—
1113C2×C4—441no—
1114C2×C4—441no—
1115C2×C4—441no—
1116C2×C4—441no—
1117C2×C4—441no—
1118C2×C4—441no—
1119C2×C4—441no—
1120C2×C4—441no—
1121C2×C4—441no—
1122C2×C4—441no—
1123C2×C4—441no—
1124C2×C4—441no—
1125C2×C4—441no—
1126C2×C4—441no—
1127C2×C4—441no—
1128C2×C4—441no—
1129C2×C4—441no—
1130C2×C4—441no—
1131C2×C4#6699014yes—
1132C22—24no—
1133C22—24no—
1134C22—24no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—224no—
1148C22—224no—
1149C22—224no—
1150C22—442no—
1151C22—442no—
1152C22—442no—
1153C22—442no—
1154C22—442no—
1155C22—442no—
1156C22—442no—
1157C22—442no—
1158C22—442no—
1159C22—442no—
1160C22—442no—
1161C22—442no—
1162C22#1062303811yescharacteristic
1163C22C2×#6694911yescharacteristic
1164C22#1062304211yescharacteristic
1165C22#1062304611yescharacteristic
1166C22#1062307811yescharacteristic
1167C22#1062307811yescharacteristic
1168C22#1062307811yescharacteristic
1169C22#1062307911yescharacteristic
1170C22#1062307911yescharacteristic
1171C22#1062308311yescharacteristic
1172C22#1062308711yescharacteristic
1173C22#1062309511yescharacteristic
1174C22D11×#12011yescharacteristic
1175C22#1062312011yescharacteristic
1176C22#1062312111yescharacteristic
1177C22#1062312111yescharacteristic
1178C22D11×C22⋊Q811yescharacteristic
1179C22D11×C22⋊Q811yescharacteristic
1180C22#1062315911yescharacteristic
1181C22#1062316311yescharacteristic
1182C22#1062316411yescharacteristic
1183C22#1062316411yescharacteristic
1184C22#1062316711yescharacteristic
1185C22#1062317111yescharacteristic
1186C22#1062318611yescharacteristic
1187C22#1062318711yescharacteristic
1188C22#1062319011yescharacteristic
1189C22#1062319311yescharacteristic
1190C22#1062332211yescharacteristic
1191C22C2×#6699011yescharacteristic
1192C22D4×C22⋊D1111yescharacteristic
1193C22D4×C22⋊D1111yescharacteristic
1194C22Q8×C22⋊D1111yescharacteristic
1195C22#1062336211yescharacteristic
1196C22#1062336311yescharacteristic
1197C4—24no—
1198C4—42no—
1199C4—42no—
1200C4—42no—
1201C4—42no—
1202C4—81no—
1203C4—224no—
1204C4—224no—
1205C4—442no—
1206C4—442no—
1207C4—442no—
1208C4—442no—
1209C4—881no—
1210C2—44no—
1211C2—444no—
1212C2#1307183111yescharacteristic
1213C2#1307192711yescharacteristic
1214C2#1307197711yescharacteristic
1215C2#1307224211yescharacteristic
1216C2#1307242511yescharacteristic
1217C2#1307242711yescharacteristic
1218C2#1307246311yescharacteristic
1219C2#1307246511yescharacteristic
1220C2#1307258011yescharacteristic
1221C2#1307258211yescharacteristic
1222C2#1307260711yescharacteristic
1223C2#1307261211yescharacteristic
1224C2#1307380111yescharacteristic
1225C2#1307453711yescharacteristic
1226C2#1307690211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC2×C11×#385C2
prime radicalC23×C22⋊D11C22
hypercenterC2×#385D11
hypocenterC11#14723
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#66949C2semidirect
3. C2×#10622592C2semidirect
4. C2×#10622560C2semidirect
5. C2×#10622823C2semidirect
6. #13066867C2semidirect
7. #13066860C2semidirect
8. #13066859C2semidirect
9. #13066858C2semidirect
12. #13066851C2semidirect
13. #13066848C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C2×C11×#385C2semidirect
82. C22×C22⋊D11Q8semidirect
109. C2×C11×C4⋊C4D4semidirect
152. C2×Dic11⋊C4D4semidirect
344. C2×#385D11semidirect
388. C23×C11C22⋊Q8semidirect
531. C2×Dic11C22⋊Q8semidirect
719. C2×C4⋊C4C22⋊D11semidirect
951. C11#14723semidirect
1021. C23#66949semidirect

Maximal subgroups

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

subgroupindex
C22×#669492
C22×C4×C22⋊D112
C2×#106225922
C2×#106225602
C2×#106228232
#130668672
#130668602
#130668592
#130668582
#130668552
#130668512
#130668482
(C2×D11)⋊#952
C2×C11×#3852
#1472311