Finite Group Databasebeta

← C2×#13071949 #14922460

Subgroups — C2×#13071949 #14922460

Order 2816.

5718 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4339C211yesmaximal, characteristic
2C22×#66947C211yesmaximal, characteristic, complemented
3C22×#66936C211yesmaximal, characteristic, complemented
4C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
5#13071949C2116yesmaximal, direct product factor
6C2×#10622269C211yesmaximal, characteristic, complemented
7C2×#10622592C211yesmaximal, characteristic, complemented
8C2×#10622574C211yesmaximal, characteristic, complemented
9C2×#10622572C211yesmaximal, characteristic, complemented
10C2×#10622278C211yesmaximal, characteristic, complemented
11C2×#10622569C211yesmaximal, characteristic, complemented
12C2×#10622281C211yesmaximal, characteristic, complemented
13C2×#10622823C211yesmaximal, characteristic, complemented
14C2×#10622602C211yesmaximal, characteristic, complemented
15C2×#10622277C211yesmaximal, characteristic, complemented
16C2×C11×#385C211yesmaximal, characteristic, complemented
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C22×#4339—28no—
21C22×#4339—28no—
22C22×#4339—28no—
23C22×#4339C2218yes—
24C23×D44C2211yescharacteristic
25C23×C4×D11C2211yescharacteristic
26C23×C4×D11C2211yescharacteristic
27C23×C4×D11C2211yescharacteristic
28C23×C4×D11C2211yescharacteristic
29C23×Dic22C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic
31C22×C11×C4⋊C4C2211yescharacteristic
32C22×C11×C22⋊C4C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×C4⋊Dic11C2211yescharacteristic
43C22×C4⋊Dic11C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C2×#66947—28no—
49C2×#66947C2218yescomplemented
50C2×C4⋊C4×D11—28no—
51C2×C4⋊C4×D11C2218yescomplemented
52C2×#66936—28no—
53C2×#66936C2218yescomplemented
54C11×#385C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57#10622823C2218yescomplemented
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64#10622602C2218yescomplemented
65#10622592C2218yescomplemented
66#10622574C2218yescomplemented
67#10622572C2218yescomplemented
68#10622569C2218yescomplemented
69#10622281C2218yescomplemented
70#10622278C2218yescomplemented
71#10622277C2218yescomplemented
72#10622269C2218yescomplemented
73C25×C11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C24×D11C2311yescharacteristic
76C23×C4×C11—24no—
77C23×C4×C11—24no—
78C23×C4×C11—24no—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2314yes—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11D418yes—
92C22×C22⋊D11C2314yes—
93C22×C22⋊D11C2314yes—
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C2×#4339—2128no—
101C2×#4339—232no—
102C2×#4339—232no—
103C2×#4339—232no—
104C22×D44—24no—
105C22×D44—24no—
106C22×D44D418yes—
107C22×D44C2314yes—
108C22×C4×D11—24no—
109C22×C4×D11—24no—
110C22×C4×D11—24no—
111C22×C4×D11—24no—
112C22×C4×D11—24no—
113C22×C4×D11—24no—
114C22×C4×D11—24no—
115C22×C4×D11—24no—
116C22×C4×D11—24no—
117C22×C4×D11—24no—
118C22×C4×D11—24no—
119C22×C4×D11D418yes—
120C22×C4×D11C2314yes—
121C22×C4×D11C2314yes—
122C22×C4×D11C2314yes—
123C22×C4×D11C2314yes—
124C22×Dic22—24no—
125C22×Dic22—24no—
126C22×Dic22—24no—
127C22×Dic22C2314yes—
128C2×C11×C4⋊C4—24no—
129C2×C11×C4⋊C4—24no—
130C2×C11×C4⋊C4C2314yes—
131C2×C11×C4⋊C4C2314yes—
132C2×C11×C22⋊C4—24no—
133C2×C11×C22⋊C4—24no—
134C2×C11×C22⋊C4C2314yes—
135C2×C11×C22⋊C4C2314yes—
136C2×C22⋊Dic11—24no—
137C2×C22⋊Dic11—24no—
138C2×C22⋊Dic11C2314yes—
139C2×C22⋊Dic11C2314yes—
140C2×(C2×D11)⋊C4—24no—
141C2×(C2×D11)⋊C4—24no—
142C2×(C2×D11)⋊C4—24no—
143C2×(C2×D11)⋊C4—24no—
144C2×(C2×D11)⋊C4—24no—
145C2×(C2×D11)⋊C4—24no—
146C2×(C2×D11)⋊C4C2314yes—
147C2×(C2×D11)⋊C4C2314yes—
148C2×(C2×D11)⋊C4C2314yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2314yes—
151C2×(C2×D11)⋊C4C2314yes—
152C2×C4⋊Dic11—24no—
153C2×C4⋊Dic11—24no—
154C2×C4⋊Dic11C2314yes—
155C2×C4⋊Dic11C2314yes—
156C2×Dic11⋊C4—24no—
157C2×Dic11⋊C4—24no—
158C2×Dic11⋊C4—24no—
159C2×Dic11⋊C4—24no—
160C2×Dic11⋊C4C2314yes—
161C2×Dic11⋊C4C2314yes—
162C2×Dic11⋊C4C2314yes—
163C2×Dic11⋊C4C2314yes—
164#66947—232no—
165C4⋊C4×D11—232no—
166#66936—232no—
167C11×#95C2314yes—
168C11×#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2314yes—
171C11⋊#95C2314yes—
172C11⋊#95C2314yes—
173C11⋊#95C2314yes—
174C11⋊#95C2314yes—
175C2×#2406—111nomaximal, Sylow
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11C2×D414yes—
183C24×C11C2412yes—
184C24×C11C2411yescharacteristic
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11—22no—
189C23×D11—22no—
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—22no—
195C23×D11C2×D414yes—
196C23×D11C2×D414yes—
197C23×D11C2×D414yes—
198C23×D11C2×D414yes—
199C23×D11C2412yes—
200C23×D11C2412yes—
201C22×C4×C11—232no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—28no—
208C22×C4×C11—22no—
209C22×C4×C11—28no—
210C22×C4×C11—28no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11C2×D414yes—
221C22×C4×C11C2×D414yes—
222C22×C4×C11#4114yescomplemented
223C22×C4×C11C2412yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2412yes—
226C22×C4×C11C2412yes—
227C22×C4×C11C2412yes—
228C22×C4×C11C2412yes—
229C2×C22⋊D11—232no—
230C2×C22⋊D11—28no—
231C2×C22⋊D11—28no—
232C2×C22⋊D11—232no—
233C2×C22⋊D11—28no—
234C2×C22⋊D11—28no—
235C2×C22⋊D11—28no—
236C2×C22⋊D11C2×D4116yes—
237C22×Dic11—22no—
238C22×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11—22no—
241C22×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11—22no—
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11C2×D414yes—
253C22×Dic11C2×D414yes—
254C22×Dic11#4114yescomplemented
255C22×Dic11C2412yes—
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C22×Dic11C2412yes—
259C22×Dic11C2412yes—
260C22×Dic11C2412yes—
261#4339—2256no—
262C2×D44—232no—
263C2×D44—28no—
264C2×D44—28no—
265C2×D44C2×D4116yes—
266C2×C4×D11—232no—
267C2×C4×D11—232no—
268C2×C4×D11—28no—
269C2×C4×D11—28no—
270C2×C4×D11—232no—
271C2×C4×D11—28no—
272C2×C4×D11—28no—
273C2×C4×D11—28no—
274C2×C4×D11—28no—
275C2×C4×D11—28no—
276C2×C4×D11—28no—
277C2×C4×D11—28no—
278C2×C4×D11—28no—
279C2×C4×D11—28no—
280C2×C4×D11—416no—
281C2×C4×D11C2×D4116yes—
282C2×Dic22—232no—
283C2×Dic22—28no—
284C2×Dic22—28no—
285C2×Dic22—28no—
286C11×C4⋊C4—28no—
287C11×C4⋊C4—28no—
288C11×C22⋊C4—28no—
289C11×C22⋊C4—28no—
290C22⋊Dic11—28no—
291C22⋊Dic11—28no—
292(C2×D11)⋊C4—28no—
293(C2×D11)⋊C4—28no—
294(C2×D11)⋊C4—28no—
295(C2×D11)⋊C4—28no—
296(C2×D11)⋊C4—28no—
297(C2×D11)⋊C4—28no—
298C4⋊Dic11—28no—
299C4⋊Dic11—28no—
300Dic11⋊C4—28no—
301Dic11⋊C4—28no—
302Dic11⋊C4—28no—
303Dic11⋊C4—28no—
304C23×#41—111no—
305C22×#123—111no—
306C22×#123—111no—
307C23×C4⋊C4—111no—
308#2406—1116no—
309C2×#395—111no—
310C2×#395—111no—
311C2×#394—111no—
312C2×#394—111no—
313C2×#386—111no—
314C2×#386—111no—
315C2×#385—111no—
316C2×#385—111no—
317C2×#385—111no—
318C2×#385D1111yescharacteristic, complemented
319C2×#381—111no—
320C23×C11—28no—
321C23×C11—28no—
322C23×C11—28no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—44no—
330C23×C11—44no—
331C23×C11—44no—
332C23×C11—44no—
333C23×C11C22×D414yes—
334C23×C11C22×D412yes—
335C23×C11C22×D412yes—
336C23×C11C22×D412yes—
337C23×C11C2×#4112yes—
338C23×C11C2×#4112yes—
339C23×C112−1+412yes—
340C23×C112−1+412yes—
341C23×C11C2511yescharacteristic
342C22×D11—28no—
343C22×D11—28no—
344C22×D11—28no—
345C22×D11—28no—
346C22×D11—28no—
347C22×D11—28no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—28no—
353C22×D11—28no—
354C22×D11—28no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—44no—
362C22×D11—44no—
363C22×D11—44no—
364C22×D11—44no—
365C22×D11#120116yes—
366C22×D11C22×D414yes—
367C22×D11C22×D414yes—
368C22×D11C22×D414yes—
369C22×D11C22×D414yes—
370C2×C4×C11—232no—
371C2×C4×C11—28no—
372C2×C4×C11—28no—
373C2×C4×C11—28no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—44no—
390C2×C4×C11—44no—
391C2×C4×C11—44no—
392C2×C4×C11C22×D414yes—
393C2×C4×C11C22×D414yes—
394C2×C4×C11C2×#4114yescomplemented
395C22⋊D11—232no—
396C22⋊D11—232no—
397C2×Dic11—28no—
398C2×Dic11—28no—
399C2×Dic11—28no—
400C2×Dic11—22no—
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—44no—
416C2×Dic11—44no—
417C2×Dic11—44no—
418C2×Dic11C22×D414yes—
419C2×Dic11C22×D414yes—
420C2×Dic11C2×#4114yescomplemented
421D44—232no—
422C4×D11—232no—
423C4×D11—232no—
424C4×D11—232no—
425C4×D11—416no—
426Dic22—232no—
427C22×#41—118no—
428C22×#41—228no—
429C22×#41—228no—
430C22×#41—228no—
431C23×Q8—111no—
432C23×D4—111no—
433C23×D4—111no—
434C23×D4—111no—
435C24×C4—111no—
436C24×C4—111no—
437C24×C4—111no—
438C24×C4—111no—
439C24×C4C2×D1111yescharacteristic
440C2×#123—118no—
441C2×#123—118no—
442C2×#123—228no—
443C2×#123—228no—
444C22×C4⋊C4—111no—
445C22×C4⋊C4—111no—
446C22×C4⋊C4—111no—
447C22×C4⋊C4—111no—
448C22×C4⋊C4—111no—
449C22×C4⋊C4—111no—
450C22×C4⋊C4—118no—
451C22×C4⋊C4—228no—
452C22×C4⋊C4C2×D1111yescharacteristic
453C22×C4⋊C4C2×D1111yescharacteristic
454C22×C22⋊C4—111no—
455C22×C22⋊C4—111no—
456C22×C22⋊C4—111no—
457C22×C22⋊C4—111no—
458C22×C22⋊C4—111no—
459C22×C22⋊C4—111no—
460C22×C22⋊C4—111no—
461C22×C22⋊C4—111no—
462C22×C22⋊C4C2×D1111yescharacteristic
463C22×C22⋊C4C2×D1111yescharacteristic
464#395—118no—
465#395—118no—
466#394—118no—
467#394—118no—
468#386—118no—
469#386—118no—
470#385—118no—
471#385—118no—
472#385—118no—
473#385C2×D1118yescomplemented
474#381—118no—
475C2×#95—111no—
476C2×#95—111no—
477C2×#95—111no—
478C2×#95—111no—
479C2×#95—111no—
480C2×#95—111no—
481C2×#95C2×D1111yescharacteristic
482C2×#95C2×D1111yescharacteristic
483C22×C11—24no—
484C22×C11—24no—
485C22×C11—24no—
486C22×C11—416no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11C2×#12014yes—
492C22×C11#52514yes—
493C22×C11#53614yes—
494C22×C11#54714yes—
495C22×C11#54714yes—
496C22×C11#54714yes—
497C22×C11#54714yes—
498C22×C11C23×D411yescharacteristic
499C22×C11C23×D411yescharacteristic
500C22×C11C23×D411yescharacteristic
501C22×C11C22×#4111yescharacteristic
502C22×C11C22×#4111yescharacteristic
503C22×C11C2×2−1+411yescharacteristic
504C22×C11C2×2−1+411yescharacteristic
505C2×D11—232no—
506C2×D11—24no—
507C2×D11—24no—
508C2×D11—24no—
509C2×D11—24no—
510C2×D11—24no—
511C2×D11—24no—
512C2×D11—24no—
513C2×D11—24no—
514C2×D11—24no—
515C2×D11—416no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11C2×#12018yes—
521C4×C11—24no—
522C4×C11—24no—
523C4×C11—24no—
524C4×C11—42no—
525C4×C11—42no—
526C4×C11—42no—
527Dic11—24no—
528Dic11—24no—
529Dic11—24no—
530Dic11—42no—
531Dic11—42no—
532Dic11—42no—
533C25—111no—
534C25—111no—
535C25C22×D1111yescharacteristic
536C2×#41—2232no—
537C2×#41—2232no—
538C2×#41—2232no—
539C2×#41—22128no—
540C22×Q8—114no—
541C22×Q8—224no—
542C22×Q8—224no—
543C22×Q8—224no—
544C22×D4—118no—
545C22×D4—114no—
546C22×D4—114no—
547C22×D4—118no—
548C22×D4—114no—
549C22×D4—224no—
550C22×D4—224no—
551C22×D4—224no—
552C22×D4—224no—
553C22×D4—224no—
554C22×D4—224no—
555C22×D4—224no—
556C23×C4—24no—
557C23×C4—24no—
558C23×C4—24no—
559C23×C4—111no—
560C23×C4—111no—
561C23×C4—111no—
562C23×C4—118no—
563C23×C4—114no—
564C23×C4—111no—
565C23×C4—111no—
566C23×C4—111no—
567C23×C4—114no—
568C23×C4—114no—
569C23×C4—114no—
570C23×C4—224no—
571C23×C4—224no—
572C23×C4—224no—
573C23×C4—224no—
574C23×C4—224no—
575C23×C4—224no—
576C23×C4—224no—
577C23×C4—224no—
578C23×C4—224no—
579C23×C4—224no—
580C23×C4—224no—
581C23×C4C22×D1114yes—
582C23×C4C22×D1111yescharacteristic
583C23×C4C22×D1111yescharacteristic
584C23×C4C22×D1111yescharacteristic
585C23×C4C22×D1111yescharacteristic
586C23×C4C22×D1111yescharacteristic
587C23×C4C22×D1111yescharacteristic
588#123—2232no—
589#123—2232no—
590C2×C4⋊C4—24no—
591C2×C4⋊C4—24no—
592C2×C4⋊C4—114no—
593C2×C4⋊C4—114no—
594C2×C4⋊C4—114no—
595C2×C4⋊C4—114no—
596C2×C4⋊C4—114no—
597C2×C4⋊C4—114no—
598C2×C4⋊C4—2232no—
599C2×C4⋊C4—224no—
600C2×C4⋊C4—224no—
601C2×C4⋊C4—224no—
602C2×C4⋊C4—224no—
603C2×C4⋊C4—224no—
604C2×C4⋊C4—224no—
605C2×C4⋊C4C22×D1114yes—
606C2×C4⋊C4C22×D1114yes—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—24no—
609C2×C22⋊C4—114no—
610C2×C22⋊C4—114no—
611C2×C22⋊C4—114no—
612C2×C22⋊C4—114no—
613C2×C22⋊C4—114no—
614C2×C22⋊C4—114no—
615C2×C22⋊C4—114no—
616C2×C22⋊C4—114no—
617C2×C22⋊C4—224no—
618C2×C22⋊C4—224no—
619C2×C22⋊C4—224no—
620C2×C22⋊C4—224no—
621C2×C22⋊C4—224no—
622C2×C22⋊C4—224no—
623C2×C22⋊C4—224no—
624C2×C22⋊C4—224no—
625C2×C22⋊C4C22×D1114yes—
626C2×C22⋊C4C22×D1114yes—
627#95—114no—
628#95—114no—
629#95—114no—
630#95—114no—
631#95—114no—
632#95—114no—
633#95C22×D1114yes—
634#95C22×D1114yes—
635C2×C11—44no—
636C2×C11#240618yescomplemented
637C2×C11C22×#12011yescharacteristic
638C2×C11C2×#52511yescharacteristic
639C2×C11C2×#53611yescharacteristic
640C2×C11C2×#54711yescharacteristic
641C2×C11C2×#54711yescharacteristic
642C2×C11C2×#54711yescharacteristic
643C2×C11C2×#54711yescharacteristic
644D11—28no—
645D11—44no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—114no—
653C24—114no—
654C24—114no—
655C24—112no—
656C24—114no—
657C24—112no—
658C24—222no—
659C24—222no—
660C24—222no—
661C24—222no—
662C24—222no—
663C24—222no—
664C24—222no—
665C24—222no—
666C24—222no—
667C24—222no—
668C24D4×D1114yes—
669C24C23×D1112yes—
670C24C23×D1111yescharacteristic
671#41—22256no—
672C2×Q8—228no—
673C2×Q8—228no—
674C2×Q8—2232no—
675C2×Q8—228no—
676C2×D4—1116no—
677C2×D4—1116no—
678C2×D4—2232no—
679C2×D4—228no—
680C2×D4—228no—
681C2×D4—228no—
682C2×D4—2232no—
683C2×D4—228no—
684C2×D4—228no—
685C2×D4—228no—
686C2×D4—2232no—
687C2×D4—228no—
688C22×C4—232no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—28no—
695C22×C4—22no—
696C22×C4—28no—
697C22×C4—28no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—114no—
708C22×C4—114no—
709C22×C4—114no—
710C22×C4—112no—
711C22×C4—112no—
712C22×C4—112no—
713C22×C4—1116no—
714C22×C4—112no—
715C22×C4—112no—
716C22×C4—112no—
717C22×C4—228no—
718C22×C4—228no—
719C22×C4—228no—
720C22×C4—2232no—
721C22×C4—228no—
722C22×C4—228no—
723C22×C4—228no—
724C22×C4—2232no—
725C22×C4—2232no—
726C22×C4—228no—
727C22×C4—228no—
728C22×C4—228no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—222no—
732C22×C4—222no—
733C22×C4—222no—
734C22×C4—222no—
735C22×C4—228no—
736C22×C4—228no—
737C22×C4—222no—
738C22×C4—222no—
739C22×C4—222no—
740C22×C4—222no—
741C22×C4—222no—
742C22×C4—222no—
743C22×C4—222no—
744C22×C4—222no—
745C22×C4—222no—
746C22×C4—4416no—
747C22×C4#433914yescomplemented
748C22×C4D4×D1114yes—
749C22×C4D4×D1114yes—
750C22×C4C23×D1112yes—
751C22×C4C23×D1112yes—
752C22×C4C23×D1112yes—
753C22×C4C23×D1112yes—
754C22×C4C23×D1112yes—
755C22×C4C23×D1112yes—
756C4⋊C4—28no—
757C4⋊C4—28no—
758C4⋊C4—228no—
759C4⋊C4—228no—
760C4⋊C4—228no—
761C4⋊C4—228no—
762C4⋊C4—228no—
763C4⋊C4—228no—
764C22⋊C4—28no—
765C22⋊C4—28no—
766C22⋊C4—228no—
767C22⋊C4—228no—
768C22⋊C4—228no—
769C22⋊C4—228no—
770C22⋊C4—228no—
771C22⋊C4—228no—
772C22⋊C4—228no—
773C22⋊C4—228no—
774C11C2×#240611yescharacteristic, complemented, Sylow
775C23—28no—
776C23—28no—
777C23—28no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—1116no—
789C23—114no—
790C23—114no—
791C23—114no—
792C23—114no—
793C23—228no—
794C23—228no—
795C23—228no—
796C23—228no—
797C23—228no—
798C23—228no—
799C23—222no—
800C23—222no—
801C23—222no—
802C23—222no—
803C23—228no—
804C23—228no—
805C23—228no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—222no—
810C23—222no—
811C23—222no—
812C23—444no—
813C23—444no—
814C23—444no—
815C23—444no—
816C23C2×#433912yes—
817C23C2×D4×D1114yes—
818C23C2×D4×D1112yes—
819C23C2×D4×D1112yes—
820C23C2×D4×D1112yes—
821C23#6704012yes—
822C23#41×D1112yes—
823C23#6704312yes—
824C23C24×D1111yescharacteristic
825Q8—2232no—
826D4—2232no—
827D4—2232no—
828D4—2232no—
829C2×C4—232no—
830C2×C4—28no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—114no—
852C2×C4—114no—
853C2×C4—114no—
854C2×C4—2232no—
855C2×C4—2232no—
856C2×C4—2232no—
857C2×C4—228no—
858C2×C4—228no—
859C2×C4—228no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—4416no—
876C2×C4—444no—
877C2×C4—444no—
878C2×C4—444no—
879C2×C4C2×#433914yescomplemented
880C2×C4C2×D4×D1114yes—
881C2×C4C2×D4×D1114yes—
882C22—24no—
883C22—24no—
884C22—24no—
885C22—42no—
886C22—42no—
887C22—416no—
888C22—42no—
889C22—42no—
890C22—118no—
891C22—224no—
892C22—224no—
893C22—2232no—
894C22—224no—
895C22—224no—
896C22—224no—
897C22—224no—
898C22—224no—
899C22—224no—
900C22—224no—
901C22—442no—
902C22—442no—
903C22—4416no—
904C22—442no—
905C22—442no—
906C22#1062303814yes—
907C22#1062307814yes—
908C22#1062308214yes—
909C22D11×#12014yes—
910C22#1062315914yes—
911C22#1062316214yes—
912C22#1062318614yes—
913C22C22×#433911yescharacteristic
914C22C22×D4×D1111yescharacteristic
915C22C22×D4×D1111yescharacteristic
916C22C22×D4×D1111yescharacteristic
917C22C2×#6704011yescharacteristic
918C22C2×#41×D1111yescharacteristic
919C22C2×#6704311yescharacteristic
920C4—24no—
921C4—24no—
922C4—24no—
923C4—42no—
924C4—42no—
925C4—42no—
926C4—224no—
927C4—224no—
928C4—224no—
929C4—442no—
930C4—442no—
931C4—442no—
932C2—44no—
933C2—228no—
934C2—444no—
935C2#1307194918yesdirect product factor
936C2C2×D11×#12011yescharacteristic
937C2C2×#1062307811yescharacteristic
938C2C2×#1062315911yescharacteristic
939C2C2×#1062318611yescharacteristic
940C2C2×#1062303811yescharacteristic
941C2C2×#1062316211yescharacteristic
942C2C2×#1062308211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#385C2
socleC24×C11C24
prime radicalC23×#4339C2
hypercenterC2×#385D11
hypocenterC11C2×#2406
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#66947C2semidirect
3. C22×#66936C2semidirect
4. C22×C4⋊C4×D11C2semidirect
5. #13071949C2direct (N × H)
6. C2×#10622269C2semidirect
7. C2×#10622592C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622572C2semidirect
10. C2×#10622278C2semidirect
11. C2×#10622569C2semidirect
12. C2×#10622281C2semidirect
13. C2×#10622823C2semidirect
14. C2×#10622602C2semidirect
15. C2×#10622277C2semidirect
16. C2×C11×#385C2semidirect
49. C2×#66947C22semidirect
51. C2×C4⋊C4×D11C22semidirect
53. C2×#66936C22semidirect
54. C11×#385C22semidirect
57. #10622823C22semidirect
64. #10622602C22semidirect
65. #10622592C22semidirect
66. #10622574C22semidirect
67. #10622572C22semidirect
68. #10622569C22semidirect
69. #10622281C22semidirect
70. #10622278C22semidirect
71. #10622277C22semidirect
72. #10622269C22semidirect
222. C22×C4×C11#41semidirect
254. C22×Dic11#41semidirect
318. C2×#385D11semidirect
394. C2×C4×C11C2×#41semidirect
420. C2×Dic11C2×#41semidirect
473. #385C2×D11semidirect
636. C2×C11#2406semidirect
747. C22×C4#4339semidirect
774. C11C2×#2406semidirect
879. C2×C4C2×#4339semidirect
935. C2#13071949direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43392
C22×#669472
C22×#669362
C22×C4⋊C4×D112
#130719492
C2×#106222692
C2×#106225922
C2×#106225742
C2×#106225722
C2×#106222782
C2×#106225692
C2×#106222812
C2×#106228232
C2×#106226022
C2×#106222772
C2×C11×#3852
C2×#240611