Finite Group Databasebeta

← #14685227

Subgroups — #14685227

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×D44C211yesmaximal, characteristic
3C2×#10622269C211yesmaximal, characteristic, complemented
4C2×#10622286C211yesmaximal, characteristic, complemented
5C2×#10622281C211yesmaximal, characteristic, complemented
6C2×#10622602C211yesmaximal, characteristic, complemented
7#13066868C211yesmaximal, characteristic, complemented
8#13066862C211yesmaximal, characteristic, complemented
9#13066860C211yesmaximal, characteristic, complemented
10#13066860C211yesmaximal, characteristic, complemented
11#13066856C211yesmaximal, characteristic
12#13066856C211yesmaximal, characteristic
13#13066849C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×Dic22C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C2×#66949—24no—
38C2×#66949—24no—
39C2×#66949—24no—
40C2×C4×D44—24no—
41C2×C4×D44—24no—
42C2×C4×D44—24no—
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
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622602—24no—
58#10622286—24no—
59#10622281—24no—
60#10622269—24no—
61C24×D11C2311yescharacteristic
62C24×D11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C22×D44—22no—
77C22×D44—22no—
78C22×D44—22no—
79C22×D44—22no—
80C22×D44—22no—
81C22×D44—22no—
82C22×D44Q814yescomplemented
83C22×C4×D11—22no—
84C22×C4×D11—22no—
85C22×C4×D11—22no—
86C22×C4×D11—22no—
87C22×C4×D11—22no—
88C22×C4×D11—22no—
89C22×C4×D11—22no—
90C22×C4×D11—22no—
91C22×C4×D11—22no—
92C22×C4×D11—41no—
93C22×C4×D11—41no—
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⋊C4D414yescomplemented
107C2×C42×C11—22no—
108C2×C42×C11—22no—
109C2×C42×C11—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4—22no—
116C2×(C2×D11)⋊C4—22no—
117C2×(C2×D11)⋊C4—22no—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4—22no—
121C2×(C2×D11)⋊C4—22no—
122C2×(C2×D11)⋊C4—22no—
123C2×(C2×D11)⋊C4—22no—
124C2×(C2×D11)⋊C4—22no—
125C2×(C2×D11)⋊C4—22no—
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—41no—
136C2×(C2×D11)⋊C4—41no—
137C2×(C2×D11)⋊C4—41no—
138C2×(C2×D11)⋊C4—41no—
139C2×(C2×D11)⋊C4D414yes—
140C2×C4⋊Dic11—22no—
141C2×C4⋊Dic11—22no—
142C2×C4⋊Dic11—22no—
143C2×C4⋊Dic11—22no—
144C2×C4⋊Dic11—41no—
145C2×C4⋊Dic11D414yes—
146C2×Dic11⋊C4—22no—
147C2×Dic11⋊C4—22no—
148C2×Dic11⋊C4—22no—
149C2×Dic11⋊C4—22no—
150C2×Dic11⋊C4—22no—
151C2×Dic11⋊C4—22no—
152C2×Dic11⋊C4—22no—
153C2×Dic11⋊C4—41no—
154C2×Dic11⋊C4D414yescomplemented
155#66949—232no—
156C4×D44—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×C11C2411yescharacteristic
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11—21no—
177C23×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11—21no—
181C23×D11—21no—
182C23×D11—21no—
183C23×D11—21no—
184C23×D11—21no—
185C23×D11—21no—
186C23×D11—21no—
187C23×D11—21no—
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×D11C2×D412yes—
198C23×D11C2×D412yes—
199C23×D11C2×Q812yes—
200C23×D11C2×Q812yes—
201C23×D11#4112yes—
202C23×D11#4112yes—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
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—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11C2×D412yes—
243C22×C4×C11C2×D412yes—
244C22×C4×C11C2×D412yes—
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2×D412yes—
248C22×C4×C11C2×D412yes—
249C22×C4×C11C2×Q812yes—
250C22×C4×C11#4112yes—
251C22×C4×C11#4112yes—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
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×Dic11C2×D412yes—
288C22×Dic11C2×D412yes—
289C22×Dic11C2×D412yes—
290C22×Dic11C2×D412yes—
291C22×Dic11C2×D412yes—
292C22×Dic11C2×D412yes—
293C22×Dic11#4112yes—
294C2×D44—28no—
295C2×D44—28no—
296C2×D44—28no—
297C2×D44—28no—
298C2×D44—28no—
299C2×D44—28no—
300C2×D44—28no—
301C2×C4×D11—28no—
302C2×C4×D11—28no—
303C2×C4×D11—28no—
304C2×C4×D11—44no—
305C2×C4×D11—44no—
306C2×C4×D11—44no—
307C2×C4×D11—44no—
308C2×C4×D11—44no—
309C2×C4×D11—44no—
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—
323C42×C11—28no—
324(C2×D11)⋊C4—28no—
325(C2×D11)⋊C4—28no—
326(C2×D11)⋊C4—28no—
327(C2×D11)⋊C4—28no—
328(C2×D11)⋊C4—28no—
329(C2×D11)⋊C4—28no—
330(C2×D11)⋊C4—44no—
331(C2×D11)⋊C4—44no—
332(C2×D11)⋊C4—44no—
333(C2×D11)⋊C4—44no—
334C4⋊Dic11—28no—
335C4⋊Dic11—44no—
336Dic11⋊C4—28no—
337Dic11⋊C4—28no—
338Dic11⋊C4—44no—
339C22×C22⋊Q8—111no—
340C22×C4×D4—111no—
341C2×#395—111no—
342C2×#393—111no—
343C2×#385—111no—
344C2×#385—111no—
345#1441—111no—
346#1439—111no—
347#1439—111no—
348#1439—111no—
349#1438—111no—
350#1438—111no—
351#1436—111no—
352#1436D1111yescharacteristic, complemented
353C22⋊#95—111no—
354C23×C11C22×D411yescharacteristic
355C23×C11C22×D411yescharacteristic
356C23×C11C22×D411yescharacteristic
357C23×C11C22×D411yescharacteristic
358C23×C11C22×D411yescharacteristic
359C23×C11C22×Q811yescharacteristic
360C23×C11C2×#4111yescharacteristic
361C23×C11C2×#4111yescharacteristic
362C23×C11C2×#4111yescharacteristic
363C23×C11C2×#4111yescharacteristic
364C23×C11C2×#4111yescharacteristic
365C23×C11H(5,𝔽2)11yescharacteristic
366C23×C11H(5,𝔽2)11yescharacteristic
367C23×C112−1+411yescharacteristic
368C23×C112−1+411yescharacteristic
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
383C22×D11—22no—
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—22no—
404C22×D11—22no—
405C22×D11—41no—
406C22×D11—41no—
407C22×D11—41no—
408C22×D11—41no—
409C22×D11—41no—
410C22×D11—41no—
411C22×D11—41no—
412C22×D11—41no—
413C22×D11—41no—
414C22×D11—41no—
415C22×D11—41no—
416C22×D11—41no—
417C22×D11—41no—
418C22×D11—41no—
419C22×D11—41no—
420C22×D11—41no—
421C22×D11—41no—
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×D11C22⋊Q814yes—
438C22×D11C22⋊Q814yescomplemented
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—22no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
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—41no—
482C2×C4×C11—41no—
483C2×C4×C11—41no—
484C2×C4×C11—41no—
485C2×C4×C11—41no—
486C2×C4×C11#12014yes—
487C2×C4×C11C22⋊Q814yescomplemented
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—41no—
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#12014yes—
530D44—232no—
531C4×D11—416no—
532C4×D11—416no—
533Dic22—416no—
534C23×Q8—111no—
535C23×D4—111no—
536C24×C4—111no—
537C24×C4—111no—
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⋊C4—111no—
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⋊C4—111no—
559C22×C22⋊C4—111no—
560C22×C42C2×D1111yescharacteristic
561#395—224no—
562#393—224no—
563#385—224no—
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×#95C2×D1111yescharacteristic
575C2×#95C2×D1111yescharacteristic
576C2×#95C2×D1111yescharacteristic
577C2×#95C2×D1111yescharacteristic
578C2×#95C2×D1111yescharacteristic
579C22×C11C2×#12011yescharacteristic
580C22×C11C2×#12011yescharacteristic
581C22×C11C2×C22⋊Q811yescharacteristic
582C22×C11C2×C22⋊Q811yescharacteristic
583C22×C11C2×C22⋊Q811yescharacteristic
584C22×C11#52511yescharacteristic
585C22×C11#52511yescharacteristic
586C22×C11#52511yescharacteristic
587C22×C11#52511yescharacteristic
588C22×C11#52511yescharacteristic
589C22×C11#53211yescharacteristic
590C22×C11#53211yescharacteristic
591C22×C11#53211yescharacteristic
592C22×C11#53411yescharacteristic
593C22×C11#53611yescharacteristic
594C22×C11#53911yescharacteristic
595C22×C11#53911yescharacteristic
596C22×C11#54211yescharacteristic
597C22×C11#54211yescharacteristic
598C22×C11D4211yescharacteristic
599C22×C11D4211yescharacteristic
600C22×C11D4211yescharacteristic
601C22×C11D4211yescharacteristic
602C22×C11#54711yescharacteristic
603C22×C11#54711yescharacteristic
604C22×C11#54811yescharacteristic
605C22×C11#54811yescharacteristic
606C22×C11#54811yescharacteristic
607C22×C11#54811yescharacteristic
608C22×C11D4×Q811yescharacteristic
609C22×C11D4×Q811yescharacteristic
610C22×C11#55111yescharacteristic
611C22×C11#55111yescharacteristic
612C22×C11#55411yescharacteristic
613C22×C11#55411yescharacteristic
614C2×D11—24no—
615C2×D11—24no—
616C2×D11—24no—
617C2×D11—24no—
618C2×D11—24no—
619C2×D11—24no—
620C2×D11—42no—
621C2×D11—42no—
622C2×D11—42no—
623C2×D11—42no—
624C2×D11—42no—
625C2×D11—42no—
626C2×D11—42no—
627C2×D11—42no—
628C2×D11—42no—
629C2×D11—42no—
630C2×D11—42no—
631C2×D11—42no—
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—24no—
646C4×C11—42no—
647C4×C11—42no—
648C4×C11—42no—
649C4×C11—42no—
650C4×C11—81no—
651Dic11—24no—
652Dic11—42no—
653Dic11—42no—
654Dic11—42no—
655Dic11—42no—
656Dic11—81no—
657C25—111no—
658C25—111no—
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—111no—
674C23×C4—111no—
675C23×C4—111no—
676C23×C4—111no—
677C23×C4—111no—
678C23×C4—114no—
679C23×C4—111no—
680C23×C4—222no—
681C23×C4—222no—
682C23×C4—222no—
683C23×C4—222no—
684C23×C4—222no—
685C23×C4—222no—
686C23×C4—222no—
687C23×C4—222no—
688C23×C4—222no—
689C23×C4—441no—
690C23×C4—441no—
691C23×C4—441no—
692C23×C4—441no—
693C23×C4C22×D1111yescharacteristic
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—114no—
705C2×C4⋊C4—114no—
706C2×C4⋊C4—222no—
707C2×C4⋊C4—222no—
708C2×C4⋊C4—222no—
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—441no—
718C2×C4⋊C4—441no—
719C2×C4⋊C4D4414yescomplemented
720C2×C22⋊C4—114no—
721C2×C22⋊C4—222no—
722C2×C22⋊C4—222no—
723C2×C22⋊C4—222no—
724C2×C22⋊C4—222no—
725C2×C22⋊C4—222no—
726C2×C22⋊C4—222no—
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—441no—
747C2×C22⋊C4—441no—
748C2×C22⋊C4—441no—
749C2×C22⋊C4—441no—
750C2×C42—22no—
751C2×C42—22no—
752C2×C42—22no—
753#95—22no—
754#95—22no—
755#95—22no—
756#95—22no—
757#95—22no—
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#238811yescharacteristic
768C2×C11#240311yescharacteristic
769C2×C11#240911yescharacteristic
770C2×C11#243211yescharacteristic
771C2×C11#244911yescharacteristic
772C2×C11#244911yescharacteristic
773C2×C11#245211yescharacteristic
774C2×C11#245211yescharacteristic
775C2×C11#246111yescharacteristic
776C2×C11#246111yescharacteristic
777C2×C11#246311yescharacteristic
778C2×C11#246311yescharacteristic
779C2×C11#256411yescharacteristic
780C2×C11#263811yescharacteristic
781C2×C11#284811yescharacteristic
782D11—44no—
783D11—44no—
784C24—112no—
785C24—112no—
786C24—112no—
787C24—112no—
788C24—112no—
789C24—112no—
790C24—221no—
791C24—221no—
792C24—221no—
793C24—221no—
794C24—221no—
795C24—221no—
796C24—221no—
797C24—221no—
798C24—221no—
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—221no—
812C24—221no—
813C24—221no—
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—21no—
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—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—112no—
869C22×C4—112no—
870C22×C4—112no—
871C22×C4—112no—
872C22×C4—112no—
873C22×C4—112no—
874C22×C4—112no—
875C22×C4—228no—
876C22×C4—228no—
877C22×C4—221no—
878C22×C4—221no—
879C22×C4—221no—
880C22×C4—221no—
881C22×C4—221no—
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—228no—
906C22×C4—221no—
907C22×C4—221no—
908C22×C4—221no—
909C22×C4—221no—
910C22×C4—221no—
911C22×C4—221no—
912C22×C4—221no—
913C22×C4—444no—
914C22×C4—444no—
915C22×C4—444no—
916C22×C4—444no—
917C22×C4—444no—
918C22×C4—444no—
919C22×C4—444no—
920C22×C4—444no—
921C22×C4—444no—
922C22×C4—444no—
923C22×C4—444no—
924C22×C4C2×D4412yes—
925C22×C4C2×D4412yes—
926C22×C4C2×D4412yes—
927C22×C4#433912yes—
928C22×C4#433912yes—
929C22×C4D4×D1112yes—
930C22×C4D4×D1112yes—
931C22×C4D4×D1112yes—
932C22×C4D4×D1112yes—
933C22×C4Q8×D1112yes—
934C4⋊C4—28no—
935C4⋊C4—228no—
936C4⋊C4—228no—
937C4⋊C4—228no—
938C4⋊C4—444no—
939C4⋊C4—444no—
940C22⋊C4—228no—
941C22⋊C4—228no—
942C22⋊C4—228no—
943C22⋊C4—228no—
944C22⋊C4—228no—
945C22⋊C4—228no—
946C22⋊C4—444no—
947C22⋊C4—444no—
948C22⋊C4—444no—
949C22⋊C4—444no—
950C42—28no—
951C11#1472311yescharacteristic, complemented, Sylow
952C23—114no—
953C23—114no—
954C23—222no—
955C23—222no—
956C23—222no—
957C23—222no—
958C23—222no—
959C23—222no—
960C23—222no—
961C23—222no—
962C23—222no—
963C23—222no—
964C23—222no—
965C23—222no—
966C23—222no—
967C23—222no—
968C23—222no—
969C23—222no—
970C23—222no—
971C23—222no—
972C23—222no—
973C23—222no—
974C23—222no—
975C23—222no—
976C23—222no—
977C23—222no—
978C23—222no—
979C23—222no—
980C23—222no—
981C23—222no—
982C23—222no—
983C23—222no—
984C23—222no—
985C23—222no—
986C23—222no—
987C23—222no—
988C23—222no—
989C23—222no—
990C23—441no—
991C23—441no—
992C23—441no—
993C23—441no—
994C23—441no—
995C23—441no—
996C23—441no—
997C23—441no—
998C23—441no—
999C23—441no—
1000C23—441no—
1001C23—441no—
1002C23—441no—
1003C23—441no—
1004C23—441no—
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—441no—
1022C23C22×D4411yescharacteristic
1023C23C2×#433911yescharacteristic
1024C23C2×#433911yescharacteristic
1025C23C2×D4×D1111yescharacteristic
1026C23C2×D4×D1111yescharacteristic
1027C23C2×D4×D1111yescharacteristic
1028C23C2×D4×D1111yescharacteristic
1029C23C2×Q8×D1111yescharacteristic
1030C23#6704011yescharacteristic
1031C23#41×D1111yescharacteristic
1032C23#41×D1111yescharacteristic
1033C23#41×D1111yescharacteristic
1034C23#6704211yescharacteristic
1035C23#6704211yescharacteristic
1036C23#6704311yescharacteristic
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—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
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—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—114no—
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—4416no—
1106C2×C4—4416no—
1107C2×C4—441no—
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#6693514yes—
1131C2×C4#6694914yescomplemented
1132C22—224no—
1133C22—224no—
1134C22—224no—
1135C22—224no—
1136C22—224no—
1137C22—224no—
1138C22—442no—
1139C22—442no—
1140C22—442no—
1141C22—442no—
1142C22—442no—
1143C22—442no—
1144C22—442no—
1145C22—442no—
1146C22—442no—
1147C22—442no—
1148C22—442no—
1149C22—442no—
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#1062300811yescharacteristic
1163C22C2×#6693511yescharacteristic
1164C22#1062303811yescharacteristic
1165C22C2×#6694911yescharacteristic
1166C22#1062305511yescharacteristic
1167C22#1062305811yescharacteristic
1168C22#1062306511yescharacteristic
1169C22#1062307811yescharacteristic
1170C22#1062307811yescharacteristic
1171C22#1062307811yescharacteristic
1172C22#1062307911yescharacteristic
1173C22#1062307911yescharacteristic
1174C22D4×D4411yescharacteristic
1175C22D4×D4411yescharacteristic
1176C22#1062308311yescharacteristic
1177C22Q8×D4411yescharacteristic
1178C22#1062310711yescharacteristic
1179C22#1062311011yescharacteristic
1180C22#1062311311yescharacteristic
1181C22D11×#12011yescharacteristic
1182C22#1062314011yescharacteristic
1183C22#1062314011yescharacteristic
1184C22D11×C22⋊Q811yescharacteristic
1185C22D11×C22⋊Q811yescharacteristic
1186C22#1062315911yescharacteristic
1187C22#1062316411yescharacteristic
1188C22#1062318411yescharacteristic
1189C22#1062318611yescharacteristic
1190C22#1062318711yescharacteristic
1191C22#1062320811yescharacteristic
1192C22#1062322111yescharacteristic
1193C22#1062322311yescharacteristic
1194C22#1062323611yescharacteristic
1195C22#1062323811yescharacteristic
1196C22#1062325811yescharacteristic
1197C4—24no—
1198C4—24no—
1199C4—42no—
1200C4—42no—
1201C4—42no—
1202C4—42no—
1203C4—81no—
1204C4—224no—
1205C4—442no—
1206C4—442no—
1207C4—442no—
1208C4—442no—
1209C4—881no—
1210C2—444no—
1211C2—444no—
1212C2#1307183211yescharacteristic
1213C2#1307192811yescharacteristic
1214C2#1307197911yescharacteristic
1215C2#1307224211yescharacteristic
1216C2#1307243011yescharacteristic
1217C2#1307243211yescharacteristic
1218C2#1307246611yescharacteristic
1219C2#1307246711yescharacteristic
1220C2#1307258311yescharacteristic
1221C2#1307258511yescharacteristic
1222C2#1307261011yescharacteristic
1223C2#1307261111yescharacteristic
1224C2#1307379511yescharacteristic
1225C2#1307454011yescharacteristic
1226C2#1307690211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×#1436C2
prime radicalC23×D44C22
hypercenter#1436D11
hypocenterC11#14723
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
1. C22×#66949C2semidirect
3. C2×#10622269C2semidirect
4. C2×#10622286C2semidirect
5. C2×#10622281C2semidirect
6. C2×#10622602C2semidirect
7. #13066868C2semidirect
8. #13066862C2semidirect
9. #13066860C2semidirect
10. #13066860C2semidirect
13. #13066849C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1436C2semidirect
82. C22×D44Q8semidirect
106. C2×C11×C4⋊C4D4semidirect
154. C2×Dic11⋊C4D4semidirect
352. #1436D11semidirect
438. C22×D11C22⋊Q8semidirect
487. C2×C4×C11C22⋊Q8semidirect
719. C2×C4⋊C4D44semidirect
951. C11#14723semidirect
1131. C2×C4#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×D442
C2×#106222692
C2×#106222862
C2×#106222812
C2×#106226022
#130668682
#130668622
#130668602
#130668562
#130668492
(C2×D11)⋊#952
C11×#14362
#1472311