Finite Group Databasebeta

← C2×#13072224 #14922406

Subgroups — C2×#13072224 #14922406

Order 2816.

6042 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4341C211yesmaximal, characteristic, complemented
2C22×#66939C211yesmaximal, characteristic, complemented
3C22×#66983C211yesmaximal, characteristic, complemented
4C22×#66992C211yesmaximal, characteristic, complemented
5#13072224C2116yesmaximal, direct product factor
6C2×#10622269C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622286C211yesmaximal, characteristic, complemented
9C2×#10622573C211yesmaximal, characteristic, complemented
10C2×#10622278C211yesmaximal, characteristic, complemented
11C2×#10622571C211yesmaximal, characteristic, complemented
12C2×#10622571C211yesmaximal, characteristic, complemented
13C2×#10622563C211yesmaximal, characteristic, complemented
14C2×#10622281C211yesmaximal, characteristic, complemented
15C22×C11⋊#95C211yesmaximal, characteristic, complemented
16C2×C11×#386C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C24×Dic11C2211yescharacteristic
24C24×Dic11C2211yescharacteristic
25C24×Dic11C2211yescharacteristic
26C22×#4341—28no—
27C22×#4341—28no—
28C22×#4341—28no—
29C22×#4341C2218yescomplemented
30C23×D44C2211yescharacteristic
31C23×C4×D11C2211yescharacteristic
32C23×Dic22C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic
34C22×C11×C22⋊C4C2211yescharacteristic
35C22×C11×C22⋊C4C2211yescharacteristic
36C22×C22⋊Dic11C2211yescharacteristic
37C2×#66992—28no—
38C2×#66992C2218yescomplemented
39C2×#66983—28no—
40C2×#66983C2218yescomplemented
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C22×(C2×D11)⋊C4C2211yescharacteristic
47C22×(C2×D11)⋊C4C2211yescharacteristic
48C22×C4⋊Dic11C2211yescharacteristic
49C22×C4⋊Dic11C2211yescharacteristic
50C22×C4⋊Dic11C2211yescharacteristic
51C22×Dic11⋊C4C2211yescharacteristic
52C2×#66939—28no—
53C2×#66939C2218yescomplemented
54C11×#386C2218yescomplemented
55C2×C11×#95C2211yescharacteristic
56C2×C11×#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2218yescomplemented
64#10622574C2218yescomplemented
65#10622573C2218yescomplemented
66#10622571C2218yescomplemented
67#10622571C2218yescomplemented
68#10622563C2218yescomplemented
69#10622286C2218yescomplemented
70#10622281C2218yescomplemented
71#10622278C2218yescomplemented
72#10622269C2218yescomplemented
73C25×C11C2311yescharacteristic
74C25×C11C2311yescharacteristic
75C24×D11C2311yescharacteristic
76C24×D11C2311yescharacteristic
77C22×D4×C11—24no—
78C22×D4×C11—24no—
79C22×D4×C11D418yescomplemented
80C22×D4×C11C2314yes—
81C23×C4×C11—24no—
82C23×C4×C11—24no—
83C23×C4×C11—42no—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2314yes—
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—24no—
93C22×C22⋊D11—24no—
94C22×C22⋊D11—24no—
95C22×C22⋊D11—24no—
96C22×C22⋊D11—24no—
97C22×C22⋊D11—24no—
98C22×C22⋊D11—24no—
99C22×C22⋊D11—24no—
100C22×C22⋊D11—42no—
101C22×C22⋊D11D418yescomplemented
102C22×C22⋊D11C2314yes—
103C22×C22⋊D11C2314yes—
104C22×C22⋊D11C2314yes—
105C22×C22⋊D11C2314yes—
106C23×Dic11—24no—
107C23×Dic11—24no—
108C23×Dic11—24no—
109C23×Dic11—24no—
110C23×Dic11—24no—
111C23×Dic11—24no—
112C23×Dic11—24no—
113C23×Dic11—42no—
114C23×Dic11D418yescomplemented
115C23×Dic11C2311yescharacteristic
116C23×Dic11C2311yescharacteristic
117C23×Dic11C2314yes—
118C23×Dic11C2314yes—
119C23×Dic11C2311yescharacteristic
120C23×Dic11C2311yescharacteristic
121C23×Dic11C2311yescharacteristic
122C23×Dic11C2314yes—
123C23×Dic11C2311yescharacteristic
124C2×#4341—2128no—
125C2×#4341—232no—
126C2×#4341—232no—
127C2×#4341—232no—
128C22×D44—24no—
129C22×D44—24no—
130C22×D44—42no—
131C22×D44C2314yes—
132C22×C4×D11—24no—
133C22×C4×D11—24no—
134C22×C4×D11—24no—
135C22×C4×D11C2314yes—
136C22×Dic22—24no—
137C22×Dic22—24no—
138C22×Dic22—24no—
139C22×Dic22C2314yes—
140C2×C11×C22⋊C4—24no—
141C2×C11×C22⋊C4—24no—
142C2×C11×C22⋊C4—42no—
143C2×C11×C22⋊C4C2314yes—
144C2×C11×C22⋊C4C2314yes—
145C2×C11×C22⋊C4C2314yes—
146C2×C22⋊Dic11—24no—
147C2×C22⋊Dic11C2314yes—
148#66992—232no—
149#66983—232no—
150C2×(C2×D11)⋊C4—24no—
151C2×(C2×D11)⋊C4—24no—
152C2×(C2×D11)⋊C4—24no—
153C2×(C2×D11)⋊C4—24no—
154C2×(C2×D11)⋊C4—24no—
155C2×(C2×D11)⋊C4—24no—
156C2×(C2×D11)⋊C4—42no—
157C2×(C2×D11)⋊C4C2314yes—
158C2×(C2×D11)⋊C4C2314yes—
159C2×(C2×D11)⋊C4C2314yes—
160C2×(C2×D11)⋊C4C2314yes—
161C2×(C2×D11)⋊C4C2314yes—
162C2×(C2×D11)⋊C4C2314yes—
163C2×(C2×D11)⋊C4C2314yes—
164C2×C4⋊Dic11—24no—
165C2×C4⋊Dic11—24no—
166C2×C4⋊Dic11—24no—
167C2×C4⋊Dic11C2314yes—
168C2×C4⋊Dic11C2314yes—
169C2×C4⋊Dic11C2314yes—
170C2×Dic11⋊C4—24no—
171C2×Dic11⋊C4C2314yes—
172#66939—232no—
173C11×#95C2314yes—
174C11×#95C2314yes—
175C11⋊#95C2314yes—
176C11⋊#95C2314yes—
177C11⋊#95C2314yes—
178C11⋊#95C2314yes—
179C11⋊#95C2314yes—
180C11⋊#95C2314yes—
181C2×#2430—111nomaximal, Sylow
182C24×C11—22no—
183C24×C11—22no—
184C24×C11—22no—
185C24×C11—22no—
186C24×C11—22no—
187C24×C11—22no—
188C24×C11—22no—
189C24×C11—22no—
190C24×C11—22no—
191C24×C11—22no—
192C24×C11C2×D414yes—
193C24×C11C2×D414yes—
194C24×C11C2×D414yes—
195C24×C11C2×D414yes—
196C24×C11C2412yes—
197C24×C11C2412yes—
198C24×C11C2411yescharacteristic
199C23×D11—22no—
200C23×D11—22no—
201C23×D11—22no—
202C23×D11—22no—
203C23×D11—22no—
204C23×D11—22no—
205C23×D11—22no—
206C23×D11—22no—
207C23×D11—22no—
208C23×D11—22no—
209C23×D11—22no—
210C23×D11—22no—
211C23×D11—22no—
212C23×D11C2×D414yes—
213C23×D11C2412yes—
214C23×D11C2412yes—
215C2×D4×C11—232no—
216C2×D4×C11—28no—
217C2×D4×C11—28no—
218C2×D4×C11C2×D4116yescomplemented
219C22×C4×C11—22no—
220C22×C4×C11—22no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—28no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11—28no—
234C22×C4×C11—44no—
235C22×C4×C11—416no—
236C22×C4×C11C2×D414yes—
237C22×C4×C11#4114yescomplemented
238C22×C4×C11C2412yes—
239C22×C4×C11C2412yes—
240C22×C4×C11C2412yes—
241C22×C4×C11C2412yes—
242C22×C4×C11C2412yes—
243C2×C22⋊D11—232no—
244C2×C22⋊D11—28no—
245C2×C22⋊D11—28no—
246C2×C22⋊D11—232no—
247C2×C22⋊D11—28no—
248C2×C22⋊D11—28no—
249C2×C22⋊D11—28no—
250C2×C22⋊D11—28no—
251C2×C22⋊D11—28no—
252C2×C22⋊D11—28no—
253C2×C22⋊D11—28no—
254C2×C22⋊D11—28no—
255C2×C22⋊D11—44no—
256C2×C22⋊D11—416no—
257C2×C22⋊D11—416no—
258C2×C22⋊D11C2×D4116yescomplemented
259C22×Dic11—232no—
260C22×Dic11—28no—
261C22×Dic11—28no—
262C22×Dic11—28no—
263C22×Dic11—232no—
264C22×Dic11—22no—
265C22×Dic11—22no—
266C22×Dic11—22no—
267C22×Dic11—22no—
268C22×Dic11—22no—
269C22×Dic11—22no—
270C22×Dic11—22no—
271C22×Dic11—28no—
272C22×Dic11—28no—
273C22×Dic11—28no—
274C22×Dic11—22no—
275C22×Dic11—22no—
276C22×Dic11—22no—
277C22×Dic11—22no—
278C22×Dic11—28no—
279C22×Dic11—22no—
280C22×Dic11—22no—
281C22×Dic11—22no—
282C22×Dic11—44no—
283C22×Dic11—416no—
284C22×Dic11C2×D414yes—
285C22×Dic11C2×D414yes—
286C22×Dic11C2×D414yes—
287C22×Dic11C2×D4116yescomplemented
288C22×Dic11#4114yescomplemented
289C22×Dic11C2412yes—
290C22×Dic11C2412yes—
291C22×Dic11C2412yes—
292C22×Dic11C2412yes—
293C22×Dic11C2412yes—
294C22×Dic11C2412yes—
295#4341—2256no—
296C2×D44—28no—
297C2×D44—28no—
298C2×D44—44no—
299C2×D44—416no—
300C2×C4×D11—232no—
301C2×C4×D11—28no—
302C2×C4×D11—28no—
303C2×C4×D11—28no—
304C2×Dic22—232no—
305C2×Dic22—28no—
306C2×Dic22—28no—
307C2×Dic22—28no—
308C11×C22⋊C4—28no—
309C11×C22⋊C4—28no—
310C11×C22⋊C4—44no—
311C22⋊Dic11—28no—
312(C2×D11)⋊C4—28no—
313(C2×D11)⋊C4—28no—
314(C2×D11)⋊C4—28no—
315(C2×D11)⋊C4—28no—
316(C2×D11)⋊C4—28no—
317(C2×D11)⋊C4—28no—
318(C2×D11)⋊C4—44no—
319C4⋊Dic11—28no—
320C4⋊Dic11—28no—
321C4⋊Dic11—28no—
322Dic11⋊C4—28no—
323C23×#41—111no—
324C22×#123—111no—
325C22×#121—111no—
326C22×#121—111no—
327#2430—1116no—
328C2×#395—111no—
329C2×#394—111no—
330C2×#393—111no—
331C2×#392—111no—
332C2×#386—111no—
333C2×#386—111no—
334C2×#386—111no—
335C2×#386D1111yescharacteristic, complemented
336C2×#385—111no—
337C2×#385—111no—
338C22×#95—111no—
339C23×C11—28no—
340C23×C11—28no—
341C23×C11—28no—
342C23×C11—28no—
343C23×C11—28no—
344C23×C11—28no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—28no—
350C23×C11—28no—
351C23×C11—28no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—44no—
359C23×C11—44no—
360C23×C11—44no—
361C23×C11—44no—
362C23×C11#120116yes—
363C23×C11C22×D414yes—
364C23×C11C22×D414yes—
365C23×C11C22×D412yes—
366C23×C11C22×D414yes—
367C23×C11C22×D414yes—
368C23×C11C22×D412yes—
369C23×C11C22×D412yes—
370C23×C11C2×#4112yes—
371C23×C11C2×#4112yes—
372C23×C11H(5,𝔽2)12yes—
373C23×C112−1+412yes—
374C23×C11C2511yescharacteristic
375C22×D11—28no—
376C22×D11—28no—
377C22×D11—28no—
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—44no—
392C22×D11—44no—
393C22×D11—44no—
394C22×D11—44no—
395C22×D11—44no—
396C22×D11—44no—
397C22×D11—44no—
398C22×D11—44no—
399C22×D11—44no—
400C22×D11—44no—
401C22×D11—44no—
402C22×D11C22×D414yes—
403D4×C11—232no—
404C2×C4×C11—28no—
405C2×C4×C11—28no—
406C2×C4×C11—22no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—22no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
418C2×C4×C11—22no—
419C2×C4×C11—416no—
420C2×C4×C11—44no—
421C2×C4×C11—44no—
422C2×C4×C11—44no—
423C2×C4×C11C22×D414yes—
424C2×C4×C11C2×#4114yescomplemented
425C22⋊D11—232no—
426C22⋊D11—232no—
427C22⋊D11—416no—
428C22⋊D11—416no—
429C2×Dic11—232no—
430C2×Dic11—28no—
431C2×Dic11—28no—
432C2×Dic11—28no—
433C2×Dic11—232no—
434C2×Dic11—28no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—22no—
439C2×Dic11—22no—
440C2×Dic11—22no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—22no—
448C2×Dic11—22no—
449C2×Dic11—416no—
450C2×Dic11—44no—
451C2×Dic11—44no—
452C2×Dic11C22×D414yes—
453C2×Dic11C22×D414yes—
454C2×Dic11C22×D414yes—
455C2×Dic11C2×#4114yescomplemented
456D44—416no—
457C4×D11—232no—
458Dic22—232no—
459C22×#41—118no—
460C22×#41—228no—
461C22×#41—228no—
462C22×#41—228no—
463C23×Q8—111no—
464C23×D4—111no—
465C23×D4—111no—
466C23×D4—111no—
467C23×D4—111no—
468C23×D4—111no—
469C23×D4C2×D1111yescharacteristic
470C24×C4—111no—
471C24×C4—111no—
472C24×C4—111no—
473C24×C4—111no—
474C24×C4C2×D1111yescharacteristic
475C2×#123—118no—
476C2×#123—228no—
477C2×#121—118no—
478C2×#121—118no—
479C2×#121—228no—
480C2×#121—228no—
481C22×C4⋊C4—111no—
482C22×C4⋊C4—111no—
483C22×C4⋊C4—111no—
484C22×C4⋊C4—111no—
485C22×C22⋊C4—111no—
486C22×C22⋊C4—111no—
487C22×C22⋊C4—111no—
488C22×C22⋊C4—111no—
489C22×C22⋊C4—111no—
490C22×C22⋊C4—111no—
491C22×C22⋊C4—111no—
492C22×C22⋊C4—111no—
493C22×C22⋊C4C2×D1111yescharacteristic
494C22×C22⋊C4C2×D1111yescharacteristic
495C22×C22⋊C4C2×D1111yescharacteristic
496#395—118no—
497#394—118no—
498#393—118no—
499#392—118no—
500#386—118no—
501#386—118no—
502#386—118no—
503#386C2×D1118yescomplemented
504#385—118no—
505#385—118no—
506C2×#95—111no—
507C2×#95—111no—
508C2×#95—111no—
509C2×#95—111no—
510C2×#95—111no—
511C2×#95—111no—
512C2×#95—118no—
513C2×#95C2×D1111yescharacteristic
514C2×#95C2×D1111yescharacteristic
515C22×C11—24no—
516C22×C11—24no—
517C22×C11—232no—
518C22×C11—24no—
519C22×C11—24no—
520C22×C11—24no—
521C22×C11—24no—
522C22×C11—24no—
523C22×C11—24no—
524C22×C11—24no—
525C22×C11—42no—
526C22×C11—42no—
527C22×C11—416no—
528C22×C11—42no—
529C22×C11—42no—
530C22×C11C2×#12018yes—
531C22×C11C2×#12014yes—
532C22×C11#53214yes—
533C22×C11#53714yes—
534C22×C11#54614yes—
535C22×C11#54614yes—
536C22×C11#54714yes—
537C22×C11#54714yes—
538C22×C11C23×D411yescharacteristic
539C22×C11C23×D411yescharacteristic
540C22×C11C23×D411yescharacteristic
541C22×C11C22×#4111yescharacteristic
542C22×C11C22×#4111yescharacteristic
543C22×C11C2×H(5,𝔽2)11yescharacteristic
544C22×C11C2×2−1+411yescharacteristic
545C2×D11—24no—
546C2×D11—24no—
547C2×D11—24no—
548C2×D11—42no—
549C2×D11—42no—
550C2×D11—416no—
551C2×D11—42no—
552C2×D11—42no—
553C2×D11—42no—
554C2×D11—42no—
555C2×D11—42no—
556C2×D11—42no—
557C2×D11—42no—
558C2×D11—42no—
559C2×D11—42no—
560C2×D11—88no—
561C4×C11—24no—
562C4×C11—24no—
563C4×C11—42no—
564C4×C11—42no—
565C4×C11—42no—
566Dic11—24no—
567Dic11—24no—
568Dic11—24no—
569Dic11—24no—
570Dic11—42no—
571Dic11—42no—
572C25—111no—
573C25—111no—
574C25C22×D1111yescharacteristic
575C25C22×D1111yescharacteristic
576C2×#41—2232no—
577C2×#41—2232no—
578C2×#41—22128no—
579C2×#41—2232no—
580C22×Q8—114no—
581C22×Q8—224no—
582C22×Q8—224no—
583C22×Q8—224no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—118no—
587C22×D4—114no—
588C22×D4—114no—
589C22×D4—114no—
590C22×D4—114no—
591C22×D4—114no—
592C22×D4—224no—
593C22×D4—224no—
594C22×D4—224no—
595C22×D4—224no—
596C22×D4—224no—
597C22×D4—224no—
598C22×D4—224no—
599C22×D4—224no—
600C22×D4—224no—
601C22×D4—224no—
602C22×D4—224no—
603C22×D4—224no—
604C22×D4—442no—
605C22×D4—442no—
606C22×D4D4418yescomplemented
607C22×D4C22×D1114yes—
608C23×C4—24no—
609C23×C4—24no—
610C23×C4—42no—
611C23×C4—118no—
612C23×C4—114no—
613C23×C4—111no—
614C23×C4—111no—
615C23×C4—111no—
616C23×C4—111no—
617C23×C4—114no—
618C23×C4—111no—
619C23×C4—111no—
620C23×C4—114no—
621C23×C4—114no—
622C23×C4—224no—
623C23×C4—224no—
624C23×C4—224no—
625C23×C4—224no—
626C23×C4—224no—
627C23×C4—224no—
628C23×C4—224no—
629C23×C4—224no—
630C23×C4—224no—
631C23×C4—224no—
632C23×C4—442no—
633C23×C4C22×D1111yescharacteristic
634C23×C4C22×D1111yescharacteristic
635C23×C4C22×D1111yescharacteristic
636C23×C4C22×D1114yes—
637C23×C4C22×D1111yescharacteristic
638C23×C4C22×D1111yescharacteristic
639#123—2232no—
640#121—2232no—
641#121—2232no—
642C2×C4⋊C4—114no—
643C2×C4⋊C4—114no—
644C2×C4⋊C4—114no—
645C2×C4⋊C4—114no—
646C2×C4⋊C4—224no—
647C2×C4⋊C4—224no—
648C2×C4⋊C4—224no—
649C2×C4⋊C4—224no—
650C2×C22⋊C4—24no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—42no—
653C2×C22⋊C4—114no—
654C2×C22⋊C4—114no—
655C2×C22⋊C4—114no—
656C2×C22⋊C4—114no—
657C2×C22⋊C4—114no—
658C2×C22⋊C4—114no—
659C2×C22⋊C4—114no—
660C2×C22⋊C4—114no—
661C2×C22⋊C4—224no—
662C2×C22⋊C4—224no—
663C2×C22⋊C4—224no—
664C2×C22⋊C4—224no—
665C2×C22⋊C4—224no—
666C2×C22⋊C4—224no—
667C2×C22⋊C4—224no—
668C2×C22⋊C4—442no—
669C2×C22⋊C4C22×D1114yes—
670C2×C22⋊C4C22×D1114yes—
671C2×C22⋊C4C22×D1114yes—
672#95—114no—
673#95—114no—
674#95—114no—
675#95—114no—
676#95—114no—
677#95—114no—
678#95C22×D1114yes—
679#95C22×D1114yes—
680C2×C11—28no—
681C2×C11—44no—
682C2×C11#243018yescomplemented
683C2×C11C22×#12011yescharacteristic
684C2×C11C2×#53211yescharacteristic
685C2×C11C2×#53711yescharacteristic
686C2×C11C2×#54611yescharacteristic
687C2×C11C2×#54611yescharacteristic
688C2×C11C2×#54711yescharacteristic
689C2×C11C2×#54711yescharacteristic
690D11—44no—
691D11—82no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—22no—
702C24—114no—
703C24—112no—
704C24—112no—
705C24—222no—
706C24—222no—
707C24—222no—
708C24—222no—
709C24—222no—
710C24—222no—
711C24—222no—
712C24—222no—
713C24—222no—
714C24—222no—
715C24—222no—
716C24—222no—
717C24—222no—
718C24C2×D4414yes—
719C24C2×D4414yes—
720C24D4×D1114yes—
721C24D4×D1114yes—
722C24C23×D1112yes—
723C24C23×D1112yes—
724C24C23×D1111yescharacteristic
725#41—22256no—
726C2×Q8—228no—
727C2×Q8—228no—
728C2×Q8—2232no—
729C2×Q8—228no—
730C2×D4—232no—
731C2×D4—28no—
732C2×D4—28no—
733C2×D4—1116no—
734C2×D4—228no—
735C2×D4—228no—
736C2×D4—228no—
737C2×D4—228no—
738C2×D4—2232no—
739C2×D4—2232no—
740C2×D4—228no—
741C2×D4—228no—
742C2×D4—228no—
743C2×D4—228no—
744C2×D4—228no—
745C2×D4—228no—
746C2×D4—228no—
747C2×D4—228no—
748C2×D4—444no—
749C2×D4—4416no—
750C2×D4—444no—
751C2×D4—4416no—
752C2×D4—4416no—
753C2×D4C2×D44116yescomplemented
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—28no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—28no—
769C22×C4—44no—
770C22×C4—416no—
771C22×C4—114no—
772C22×C4—114no—
773C22×C4—114no—
774C22×C4—1116no—
775C22×C4—114no—
776C22×C4—112no—
777C22×C4—112no—
778C22×C4—112no—
779C22×C4—112no—
780C22×C4—112no—
781C22×C4—112no—
782C22×C4—228no—
783C22×C4—228no—
784C22×C4—2232no—
785C22×C4—228no—
786C22×C4—228no—
787C22×C4—228no—
788C22×C4—2232no—
789C22×C4—2232no—
790C22×C4—222no—
791C22×C4—222no—
792C22×C4—222no—
793C22×C4—222no—
794C22×C4—228no—
795C22×C4—228no—
796C22×C4—222no—
797C22×C4—222no—
798C22×C4—222no—
799C22×C4—228no—
800C22×C4—222no—
801C22×C4—228no—
802C22×C4—222no—
803C22×C4—222no—
804C22×C4—228no—
805C22×C4—222no—
806C22×C4—222no—
807C22×C4—222no—
808C22×C4—222no—
809C22×C4—444no—
810C22×C4—4416no—
811C22×C4C2×D4414yes—
812C22×C4#434114yescomplemented
813C22×C4C23×D1112yes—
814C22×C4C23×D1112yes—
815C22×C4C23×D1112yes—
816C22×C4C23×D1112yes—
817C22×C4C23×D1112yes—
818C4⋊C4—228no—
819C4⋊C4—228no—
820C4⋊C4—228no—
821C4⋊C4—228no—
822C22⋊C4—28no—
823C22⋊C4—28no—
824C22⋊C4—44no—
825C22⋊C4—228no—
826C22⋊C4—228no—
827C22⋊C4—228no—
828C22⋊C4—228no—
829C22⋊C4—228no—
830C22⋊C4—228no—
831C22⋊C4—228no—
832C22⋊C4—444no—
833C11C2×#243011yescharacteristic, complemented, Sylow
834C23—28no—
835C23—28no—
836C23—28no—
837C23—28no—
838C23—28no—
839C23—28no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—28no—
845C23—28no—
846C23—28no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—44no—
854C23—44no—
855C23—44no—
856C23—44no—
857C23—114no—
858C23—228no—
859C23—228no—
860C23—228no—
861C23—222no—
862C23—222no—
863C23—222no—
864C23—222no—
865C23—222no—
866C23—222no—
867C23—222no—
868C23—222no—
869C23—222no—
870C23—222no—
871C23—222no—
872C23—222no—
873C23—222no—
874C23—444no—
875C23—444no—
876C23—444no—
877C23—444no—
878C23—444no—
879C23—444no—
880C23—444no—
881C23—444no—
882C23—444no—
883C23—444no—
884C23—444no—
885C23#66935116yes—
886C23C22×D4414yes—
887C23C22×D4414yes—
888C23C22×D4412yes—
889C23C2×D4×D1114yes—
890C23C2×D4×D1114yes—
891C23C2×D4×D1112yes—
892C23C2×D4×D1112yes—
893C23C2×#434112yes—
894C23#6703712yes—
895C23#41×D1112yes—
896C23#6704312yes—
897C23C24×D1111yescharacteristic
898Q8—2232no—
899D4—232no—
900D4—2232no—
901D4—2232no—
902D4—4416no—
903D4—4416no—
904D4—4416no—
905C2×C4—28no—
906C2×C4—28no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—416no—
921C2×C4—44no—
922C2×C4—44no—
923C2×C4—44no—
924C2×C4—114no—
925C2×C4—114no—
926C2×C4—114no—
927C2×C4—114no—
928C2×C4—2232no—
929C2×C4—2232no—
930C2×C4—228no—
931C2×C4—228no—
932C2×C4—228no—
933C2×C4—2232no—
934C2×C4—228no—
935C2×C4—222no—
936C2×C4—222no—
937C2×C4—222no—
938C2×C4—222no—
939C2×C4—222no—
940C2×C4—222no—
941C2×C4—222no—
942C2×C4—222no—
943C2×C4—222no—
944C2×C4—222no—
945C2×C4—222no—
946C2×C4—222no—
947C2×C4—222no—
948C2×C4—222no—
949C2×C4—4416no—
950C2×C4—444no—
951C2×C4—444no—
952C2×C4C22×D4414yes—
953C2×C4C2×#434114yescomplemented
954C22—24no—
955C22—24no—
956C22—232no—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—24no—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—42no—
965C22—42no—
966C22—416no—
967C22—42no—
968C22—42no—
969C22—224no—
970C22—224no—
971C22—224no—
972C22—442no—
973C22—442no—
974C22—4416no—
975C22—442no—
976C22—442no—
977C22—442no—
978C22—442no—
979C22—442no—
980C22—442no—
981C22—442no—
982C22—442no—
983C22—442no—
984C22—888no—
985C22C2×#6693518yes—
986C22C2×#6693514yes—
987C22#1062308514yes—
988C22#1062308614yes—
989C22#1062312214yes—
990C22#1062312714yes—
991C22#1062312814yes—
992C22#1062318614yes—
993C22C23×D4411yescharacteristic
994C22C22×D4×D1111yescharacteristic
995C22C22×D4×D1111yescharacteristic
996C22C22×#434111yescharacteristic
997C22C2×#6703711yescharacteristic
998C22C2×#41×D1111yescharacteristic
999C22C2×#6704311yescharacteristic
1000C4—24no—
1001C4—24no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—224no—
1006C4—224no—
1007C4—224no—
1008C4—224no—
1009C4—442no—
1010C4—442no—
1011C2—28no—
1012C2—44no—
1013C2—444no—
1014C2—882no—
1015C2#1307222418yesdirect product factor
1016C2C22×#6693511yescharacteristic
1017C2C2×#1062312711yescharacteristic
1018C2C2×#1062312811yescharacteristic
1019C2C2×#1062312211yescharacteristic
1020C2C2×#1062308511yescharacteristic
1021C2C2×#1062318611yescharacteristic
1022C2C2×#1062308611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
hypercenterC2×#386D11
hypocenterC11C2×#2430
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C23×#4341C2semidirect
2. C22×#66939C2semidirect
3. C22×#66983C2semidirect
4. C22×#66992C2semidirect
5. #13072224C2direct (N × H)
6. C2×#10622269C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622286C2semidirect
9. C2×#10622573C2semidirect
10. C2×#10622278C2semidirect
11. C2×#10622571C2semidirect
12. C2×#10622571C2semidirect
13. C2×#10622563C2semidirect
14. C2×#10622281C2semidirect
15. C22×C11⋊#95C2semidirect
16. C2×C11×#386C2semidirect
29. C22×#4341C22semidirect
38. C2×#66992C22semidirect
40. C2×#66983C22semidirect
53. C2×#66939C22semidirect
54. C11×#386C22semidirect
63. C2×C11⋊#95C22semidirect
64. #10622574C22semidirect
65. #10622573C22semidirect
66. #10622571C22semidirect
67. #10622571C22semidirect
68. #10622563C22semidirect
69. #10622286C22semidirect
70. #10622281C22semidirect
71. #10622278C22semidirect
72. #10622269C22semidirect
79. C22×D4×C11D4semidirect
101. C22×C22⋊D11D4semidirect
114. C23×Dic11D4semidirect
218. C2×D4×C11C2×D4semidirect
237. C22×C4×C11#41semidirect
258. C2×C22⋊D11C2×D4semidirect
287. C22×Dic11C2×D4semidirect
288. C22×Dic11#41semidirect
335. C2×#386D11semidirect
424. C2×C4×C11C2×#41semidirect
455. C2×Dic11C2×#41semidirect
503. #386C2×D11semidirect
606. C22×D4D44semidirect
682. C2×C11#2430semidirect
753. C2×D4C2×D44semidirect
812. C22×C4#4341semidirect
833. C11C2×#2430semidirect
953. C2×C4C2×#4341semidirect
1015. C2#13072224direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43412
C22×#669392
C22×#669832
C22×#669922
#130722242
C2×#106222692
C2×#106225742
C2×#106222862
C2×#106225732
C2×#106222782
C2×#106225712
C2×#106225632
C2×#106222812
C22×C11⋊#952
C2×C11×#3862
C2×#243011