Finite Group Databasebeta

← C2×#13074499 #14920169

Subgroups — C2×#13074499 #14920169

Order 2816.

3606 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C211yesmaximal, characteristic, complemented
2C22×D4×Dic11C211yesmaximal, characteristic, complemented
3#13074499C2116yesmaximal, direct product factor
4C2×#10622273C211yesmaximal, characteristic, complemented
5C2×#10622562C211yesmaximal, characteristic, complemented
6C2×#10622574C211yesmaximal, characteristic, complemented
7C2×#10622574C211yesmaximal, characteristic, complemented
8C2×#10622835C211yesmaximal, characteristic, complemented
9C2×#10622836C211yesmaximal, characteristic, complemented
10C2×#10622836C211yesmaximal, characteristic, complemented
11C2×#10622564C211yesmaximal, characteristic, complemented
12C2×#10622282C211yesmaximal, characteristic, complemented
13C2×#10622833C211yesmaximal, characteristic, complemented
14C2×#10622571C211yesmaximal, characteristic, complemented
15C2×#10622556C211yesmaximal, characteristic, complemented
16C2×C11×#392C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C24×Dic11C2211yescharacteristic
24C24×Dic11C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C2×#66992—28no—
36C2×#66992C2218yescomplemented
37C2×D4×Dic11—28no—
38C2×D4×Dic11C2218yescomplemented
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×(C2×D11)⋊C4C2211yescharacteristic
41C22×(C2×D11)⋊C4C2211yescharacteristic
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×C4⋊Dic11C2211yescharacteristic
44C22×C4⋊Dic11C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C11×#392C2218yescomplemented
49C2×C11×#95C2211yescharacteristic
50#10622836C2218yescomplemented
51#10622836C2218yescomplemented
52#10622835C2218yescomplemented
53#10622833C2218yescomplemented
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622574C2218yescomplemented
62#10622574C2218yescomplemented
63#10622571C2218yescomplemented
64#10622564C2218yescomplemented
65#10622562C2218yescomplemented
66#10622556C2218yescomplemented
67#10622282C2218yescomplemented
68#10622273C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C25×C11C2311yescharacteristic
72C24×D11C2311yescharacteristic
73C22×D4×C11—24no—
74C22×D4×C11—24no—
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—24no—
78C22×D4×C11—42no—
79C22×D4×C11—42no—
80C22×D4×C11—42no—
81C22×D4×C11—42no—
82C22×D4×C11C2314yes—
83C22×D4×C11C2314yes—
84C22×D4×C11C2314yes—
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—42no—
93C22×C22⋊D11—42no—
94C22×C22⋊D11—42no—
95C22×C22⋊D11—42no—
96C22×C22⋊D11—42no—
97C22×C22⋊D11—42no—
98C22×C22⋊D11C2314yes—
99C22×C22⋊D11C2314yes—
100C22×C22⋊D11C2314yes—
101C23×Dic11—24no—
102C23×Dic11—42no—
103C23×Dic11—42no—
104C23×Dic11—42no—
105C23×Dic11—42no—
106C23×Dic11D418yescomplemented
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2311yescharacteristic
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2311yescharacteristic
114C23×Dic11C2314yes—
115C23×Dic11C2314yes—
116C2×C11×C22⋊C4—24no—
117C2×C11×C22⋊C4—42no—
118C2×C11×C22⋊C4—42no—
119C2×C11×C22⋊C4C2314yes—
120C2×C11×C22⋊C4C2314yes—
121C2×C11×C22⋊C4C2314yes—
122C2×C22⋊Dic11—24no—
123C2×C22⋊Dic11—24no—
124C2×C22⋊Dic11—24no—
125C2×C22⋊Dic11—42no—
126C2×C22⋊Dic11—42no—
127C2×C22⋊Dic11—42no—
128C2×C22⋊Dic11—42no—
129C2×C22⋊Dic11C2314yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134C2×C22⋊Dic11C2314yes—
135C2×C22⋊Dic11C2314yes—
136#66992—232no—
137D4×Dic11—232no—
138C2×(C2×D11)⋊C4—24no—
139C2×(C2×D11)⋊C4—24no—
140C2×(C2×D11)⋊C4—42no—
141C2×(C2×D11)⋊C4—42no—
142C2×(C2×D11)⋊C4C2314yes—
143C2×(C2×D11)⋊C4C2314yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×C4⋊Dic11—24no—
147C2×C4⋊Dic11—42no—
148C2×C4⋊Dic11C2314yes—
149C2×C4⋊Dic11C2314yes—
150C2×Dic11⋊C4—24no—
151C2×Dic11⋊C4—42no—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×C4×Dic11—24no—
155C2×C4×Dic11C2314yes—
156C11×#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C2×#2635—111nomaximal, Sylow
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—22no—
169C24×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—22no—
183C24×C11—22no—
184C24×C11C2×D414yes—
185C24×C11#4114yes—
186C24×C11C2412yes—
187C24×C11C2412yes—
188C24×C11C2412yes—
189C24×C11C2411yescharacteristic
190C23×D11—22no—
191C23×D11—22no—
192C23×D11—22no—
193C23×D11—22no—
194C23×D11—22no—
195C23×D11—22no—
196C23×D11—22no—
197C23×D11C2412yes—
198C2×D4×C11—232no—
199C2×D4×C11—28no—
200C2×D4×C11—28no—
201C2×D4×C11—28no—
202C2×D4×C11—28no—
203C2×D4×C11—28no—
204C2×D4×C11—44no—
205C2×D4×C11—44no—
206C2×D4×C11—44no—
207C2×D4×C11—44no—
208C2×D4×C11—416no—
209C2×D4×C11—416no—
210C22×C4×C11—22no—
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×C11—22no—
221C22×C4×C11#4114yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2412yes—
226C2×C22⋊D11—28no—
227C2×C22⋊D11—28no—
228C2×C22⋊D11—28no—
229C2×C22⋊D11—44no—
230C2×C22⋊D11—44no—
231C2×C22⋊D11—44no—
232C2×C22⋊D11—44no—
233C2×C22⋊D11—44no—
234C2×C22⋊D11—44no—
235C2×C22⋊D11—416no—
236C2×C22⋊D11—416no—
237C2×C22⋊D11—416no—
238C22×Dic11—28no—
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×Dic11—22no—
253C22×Dic11—22no—
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—22no—
258C22×Dic11—416no—
259C22×Dic11—44no—
260C22×Dic11—44no—
261C22×Dic11—44no—
262C22×Dic11—44no—
263C22×Dic11—416no—
264C22×Dic11C2×D414yes—
265C22×Dic11C2×D414yes—
266C22×Dic11C2×D4116yescomplemented
267C22×Dic11C2412yes—
268C22×Dic11C2412yes—
269C22×Dic11C2412yes—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C11×C22⋊C4—28no—
275C11×C22⋊C4—44no—
276C11×C22⋊C4—44no—
277C22⋊Dic11—28no—
278C22⋊Dic11—28no—
279C22⋊Dic11—28no—
280C22⋊Dic11—44no—
281C22⋊Dic11—44no—
282C22⋊Dic11—44no—
283C22⋊Dic11—44no—
284(C2×D11)⋊C4—28no—
285(C2×D11)⋊C4—28no—
286(C2×D11)⋊C4—44no—
287(C2×D11)⋊C4—44no—
288C4⋊Dic11—28no—
289C4⋊Dic11—44no—
290Dic11⋊C4—28no—
291Dic11⋊C4—44no—
292C4×Dic11—28no—
293C22×#121—111no—
294C22×C4×D4—111no—
295#2635—1116no—
296C2×#400—111no—
297C2×#399—111no—
298C2×#394—111no—
299C2×#394—111no—
300C2×#394—111no—
301C2×#392—111no—
302C2×#392—111no—
303C2×#392D1111yescharacteristic, complemented
304C2×#388—111no—
305C2×#388—111no—
306C2×#386—111no—
307C2×#386—111no—
308C2×#381—111no—
309C23×C11—28no—
310C23×C11—28no—
311C23×C11—28no—
312C23×C11—28no—
313C23×C11—28no—
314C23×C11—28no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—44no—
335C23×C11—44no—
336C23×C11—44no—
337C23×C11—44no—
338C23×C11—44no—
339C23×C11—44no—
340C23×C11—44no—
341C23×C11—44no—
342C23×C11—44no—
343C23×C11—44no—
344C23×C11—44no—
345C23×C11—44no—
346C23×C11—44no—
347C23×C11—44no—
348C23×C11—44no—
349C23×C11C22×D414yes—
350C23×C11C22×D412yes—
351C23×C11C2×#4114yes—
352C23×C11C2×#4112yes—
353C23×C11C2×#4112yes—
354C23×C11H(5,𝔽2)12yes—
355C23×C11H(5,𝔽2)12yes—
356C23×C11H(5,𝔽2)12yes—
357C23×C11H(5,𝔽2)12yes—
358C23×C11C2511yescharacteristic
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—44no—
367C22×D11—44no—
368C22×D11—44no—
369C22×D11—44no—
370C22×D11—44no—
371C22×D11—44no—
372C22×D11—44no—
373D4×C11—232no—
374D4×C11—416no—
375D4×C11—416no—
376C2×C4×C11—28no—
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—44no—
389C2×C4×C11—44no—
390C2×C4×C11—44no—
391C2×C4×C11C2×#4114yes—
392C22⋊D11—416no—
393C22⋊D11—416no—
394C22⋊D11—416no—
395C2×Dic11—28no—
396C2×Dic11—28no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
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—22no—
416C2×Dic11—416no—
417C2×Dic11—416no—
418C2×Dic11—44no—
419C2×Dic11—44no—
420C2×Dic11—44no—
421C2×Dic11—44no—
422C2×Dic11—44no—
423C2×Dic11C22×D414yes—
424C2×Dic11C22×D414yes—
425C23×D4—111no—
426C23×D4—111no—
427C23×D4—111no—
428C23×D4C2×D1111yescharacteristic
429C23×D4C2×D1111yescharacteristic
430C23×D4C2×D1111yescharacteristic
431C24×C4—111no—
432C24×C4—111no—
433C2×#121—118no—
434C2×#121—228no—
435C2×C4×D4—118no—
436C2×C4×D4—228no—
437C22×C4⋊C4—111no—
438C22×C4⋊C4—111no—
439C22×C4⋊C4—111no—
440C22×C4⋊C4—111no—
441C22×C22⋊C4—111no—
442C22×C22⋊C4—111no—
443C22×C22⋊C4—111no—
444C22×C22⋊C4—111no—
445C22×C22⋊C4—111no—
446C22×C22⋊C4—111no—
447C22×C22⋊C4—111no—
448C22×C22⋊C4—111no—
449C22×C22⋊C4—111no—
450C22×C22⋊C4—111no—
451C22×C22⋊C4—111no—
452C22×C22⋊C4C2×D1111yescharacteristic
453C22×C22⋊C4C2×D1111yescharacteristic
454C22×C22⋊C4C2×D1111yescharacteristic
455C22×C42—111no—
456#400—118no—
457#399—118no—
458#394—118no—
459#394—118no—
460#394—118no—
461#392—118no—
462#392—118no—
463#392C2×D1118yescomplemented
464#388—118no—
465#388—118no—
466#386—118no—
467#386—118no—
468#381—118no—
469C2×#95—111no—
470C2×#95—111no—
471C2×#95—111no—
472C2×#95—111no—
473C2×#95—111no—
474C2×#95—111no—
475C2×#95—111no—
476C2×#95C2×D1111yescharacteristic
477C22×C11—24no—
478C22×C11—24no—
479C22×C11—24no—
480C22×C11—24no—
481C22×C11—24no—
482C22×C11—24no—
483C22×C11—416no—
484C22×C11—416no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—42no—
500C22×C11—88no—
501C22×C11#52514yes—
502C22×C11#53414yes—
503C22×C11#53514yes—
504C22×C11#53814yes—
505C22×C11#53814yes—
506C22×C11#54014yes—
507C22×C11#54014yes—
508C22×C11C23×D411yescharacteristic
509C22×C11C22×#4111yescharacteristic
510C22×C11C22×#4111yescharacteristic
511C22×C11C2×H(5,𝔽2)11yescharacteristic
512C22×C11C2×H(5,𝔽2)11yescharacteristic
513C22×C11C2×H(5,𝔽2)11yescharacteristic
514C22×C11C2×H(5,𝔽2)11yescharacteristic
515C2×D11—42no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—88no—
523C4×C11—24no—
524C4×C11—42no—
525C4×C11—42no—
526C4×C11—42no—
527Dic11—24no—
528Dic11—24no—
529Dic11—42no—
530Dic11—42no—
531Dic11—42no—
532Dic11—42no—
533Dic11—42no—
534C25—111no—
535C25C22×D1111yescharacteristic
536C25C22×D1111yescharacteristic
537C25C22×D1111yescharacteristic
538C22×D4—24no—
539C22×D4—24no—
540C22×D4—24no—
541C22×D4—24no—
542C22×D4—24no—
543C22×D4—42no—
544C22×D4—42no—
545C22×D4—42no—
546C22×D4—42no—
547C22×D4—114no—
548C22×D4—114no—
549C22×D4—114no—
550C22×D4—224no—
551C22×D4—224no—
552C22×D4—224no—
553C22×D4—442no—
554C22×D4—442no—
555C22×D4—442no—
556C22×D4—442no—
557C22×D4—442no—
558C22×D4—442no—
559C22×D4C22×D1114yes—
560C22×D4C22×D1114yes—
561C22×D4C22×D1114yes—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—118no—
565C23×C4—114no—
566C23×C4—111no—
567C23×C4—111no—
568C23×C4—111no—
569C23×C4—111no—
570C23×C4—111no—
571C23×C4—114no—
572C23×C4—224no—
573C23×C4—442no—
574C23×C4—442no—
575C23×C4—442no—
576C23×C4—442no—
577C23×C4C22×D1111yescharacteristic
578C23×C4C22×D1111yescharacteristic
579C23×C4C22×D1111yescharacteristic
580C23×C4C22×D1111yescharacteristic
581#121—2232no—
582C4×D4—2232no—
583C2×C4⋊C4—114no—
584C2×C4⋊C4—114no—
585C2×C4⋊C4—114no—
586C2×C4⋊C4—114no—
587C2×C4⋊C4—224no—
588C2×C4⋊C4—224no—
589C2×C4⋊C4—442no—
590C2×C4⋊C4—442no—
591C2×C22⋊C4—24no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—114no—
595C2×C22⋊C4—114no—
596C2×C22⋊C4—114no—
597C2×C22⋊C4—114no—
598C2×C22⋊C4—114no—
599C2×C22⋊C4—114no—
600C2×C22⋊C4—114no—
601C2×C22⋊C4—114no—
602C2×C22⋊C4—114no—
603C2×C22⋊C4—114no—
604C2×C22⋊C4—114no—
605C2×C22⋊C4—224no—
606C2×C22⋊C4—224no—
607C2×C22⋊C4—224no—
608C2×C22⋊C4—224no—
609C2×C22⋊C4—224no—
610C2×C22⋊C4—442no—
611C2×C22⋊C4—442no—
612C2×C22⋊C4—442no—
613C2×C22⋊C4—442no—
614C2×C22⋊C4—442no—
615C2×C22⋊C4—442no—
616C2×C22⋊C4C22×D1114yes—
617C2×C22⋊C4C22×D1114yes—
618C2×C22⋊C4C22×D1114yes—
619C2×C42—114no—
620C2×C42—224no—
621#95—114no—
622#95—114no—
623#95—114no—
624#95—114no—
625#95—114no—
626#95—114no—
627#95—114no—
628#95C22×D1114yes—
629C2×C11—44no—
630C2×C11—44no—
631C2×C11—82no—
632C2×C11#263518yescomplemented
633C2×C11C2×#52511yescharacteristic
634C2×C11C2×#53411yescharacteristic
635C2×C11C2×#53511yescharacteristic
636C2×C11C2×#53811yescharacteristic
637C2×C11C2×#53811yescharacteristic
638C2×C11C2×#54011yescharacteristic
639C2×C11C2×#54011yescharacteristic
640D11—82no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—112no—
661C24—222no—
662C24—222no—
663C24—222no—
664C24—222no—
665C24—222no—
666C24—222no—
667C24—222no—
668C24D4×D1114yes—
669C24#434114yes—
670C24C23×D1112yes—
671C24C23×D1112yes—
672C24C23×D1112yes—
673C24C23×D1111yescharacteristic
674C2×D4—232no—
675C2×D4—28no—
676C2×D4—28no—
677C2×D4—28no—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—416no—
685C2×D4—416no—
686C2×D4—228no—
687C2×D4—228no—
688C2×D4—228no—
689C2×D4—444no—
690C2×D4—444no—
691C2×D4—444no—
692C2×D4—444no—
693C2×D4—444no—
694C2×D4—444no—
695C2×D4—4416no—
696C2×D4—4416no—
697C2×D4—4416no—
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—22no—
708C22×C4—22no—
709C22×C4—114no—
710C22×C4—114no—
711C22×C4—112no—
712C22×C4—112no—
713C22×C4—1116no—
714C22×C4—112no—
715C22×C4—112no—
716C22×C4—112no—
717C22×C4—112no—
718C22×C4—112no—
719C22×C4—228no—
720C22×C4—222no—
721C22×C4—222no—
722C22×C4—222no—
723C22×C4—222no—
724C22×C4—222no—
725C22×C4—222no—
726C22×C4—222no—
727C22×C4—222no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—222no—
732C22×C4—222no—
733C22×C4—222no—
734C22×C4—222no—
735C22×C4—222no—
736C22×C4—222no—
737C22×C4—222no—
738C22×C4—222no—
739C22×C4—4416no—
740C22×C4—444no—
741C22×C4—444no—
742C22×C4—444no—
743C22×C4—444no—
744C22×C4—4416no—
745C22×C4#434114yes—
746C22×C4C23×D1112yes—
747C22×C4C23×D1112yes—
748C22×C4C23×D1112yes—
749C22×C4C23×D1112yes—
750C4⋊C4—228no—
751C4⋊C4—228no—
752C4⋊C4—444no—
753C4⋊C4—444no—
754C22⋊C4—28no—
755C22⋊C4—44no—
756C22⋊C4—44no—
757C22⋊C4—228no—
758C22⋊C4—228no—
759C22⋊C4—228no—
760C22⋊C4—228no—
761C22⋊C4—228no—
762C22⋊C4—444no—
763C22⋊C4—444no—
764C22⋊C4—444no—
765C22⋊C4—444no—
766C22⋊C4—444no—
767C22⋊C4—444no—
768C42—228no—
769C11C2×#263511yescharacteristic, complemented, Sylow
770C23—28no—
771C23—28no—
772C23—28no—
773C23—28no—
774C23—28no—
775C23—28no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23—44no—
799C23—44no—
800C23—44no—
801C23—44no—
802C23—44no—
803C23—44no—
804C23—44no—
805C23—44no—
806C23—44no—
807C23—44no—
808C23—44no—
809C23—44no—
810C23—222no—
811C23—222no—
812C23—222no—
813C23—222no—
814C23—222no—
815C23—222no—
816C23—222no—
817C23—444no—
818C23—444no—
819C23—444no—
820C23—444no—
821C23—444no—
822C23—444no—
823C23—444no—
824C23C2×D4×D1114yes—
825C23C2×D4×D1112yes—
826C23C2×#434114yes—
827C23C2×#434112yes—
828C23C2×#434112yes—
829C23#6703712yes—
830C23#6703712yes—
831C23#6703712yes—
832C23#6704212yes—
833C23C24×D1111yescharacteristic
834D4—232no—
835D4—416no—
836D4—416no—
837D4—4416no—
838D4—4416no—
839D4—4416no—
840C2×C4—28no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—114no—
856C2×C4—114no—
857C2×C4—228no—
858C2×C4—228no—
859C2×C4—222no—
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—222no—
876C2×C4—222no—
877C2×C4—222no—
878C2×C4—4416no—
879C2×C4—4416no—
880C2×C4—444no—
881C2×C4—444no—
882C2×C4—444no—
883C2×C4—444no—
884C2×C4—444no—
885C2×C4C2×#434114yes—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—24no—
892C22—42no—
893C22—416no—
894C22—416no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—88no—
910C22—442no—
911C22—442no—
912C22—442no—
913C22—442no—
914C22—442no—
915C22—442no—
916C22—442no—
917C22—888no—
918C22#1062311714yes—
919C22#1062312314yes—
920C22#1062312414yes—
921C22#1062313614yes—
922C22#1062314814yes—
923C22#1062315014yes—
924C22#1062325014yes—
925C22C22×D4×D1111yescharacteristic
926C22C22×#434111yescharacteristic
927C22C22×#434111yescharacteristic
928C22C2×#6703711yescharacteristic
929C22C2×#6703711yescharacteristic
930C22C2×#6703711yescharacteristic
931C22C2×#6704211yescharacteristic
932C4—24no—
933C4—42no—
934C4—42no—
935C4—42no—
936C4—224no—
937C4—224no—
938C4—442no—
939C4—442no—
940C4—442no—
941C4—442no—
942C4—442no—
943C2—44no—
944C2—44no—
945C2—82no—
946C2—882no—
947C2#1307449918yesdirect product factor
948C2C2×#1062311711yescharacteristic
949C2C2×#1062313611yescharacteristic
950C2C2×#1062312311yescharacteristic
951C2C2×#1062312411yescharacteristic
952C2C2×#1062314811yescharacteristic
953C2C2×#1062315011yescharacteristic
954C2C2×#1062325011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2635
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#66992C2semidirect
2. C22×D4×Dic11C2semidirect
3. #13074499C2direct (N × H)
4. C2×#10622273C2semidirect
5. C2×#10622562C2semidirect
6. C2×#10622574C2semidirect
7. C2×#10622574C2semidirect
8. C2×#10622835C2semidirect
9. C2×#10622836C2semidirect
10. C2×#10622836C2semidirect
11. C2×#10622564C2semidirect
12. C2×#10622282C2semidirect
13. C2×#10622833C2semidirect
14. C2×#10622571C2semidirect
15. C2×#10622556C2semidirect
16. C2×C11×#392C2semidirect
36. C2×#66992C22semidirect
38. C2×D4×Dic11C22semidirect
48. C11×#392C22semidirect
50. #10622836C22semidirect
51. #10622836C22semidirect
52. #10622835C22semidirect
53. #10622833C22semidirect
61. #10622574C22semidirect
62. #10622574C22semidirect
63. #10622571C22semidirect
64. #10622564C22semidirect
65. #10622562C22semidirect
66. #10622556C22semidirect
67. #10622282C22semidirect
68. #10622273C22semidirect
106. C23×Dic11D4semidirect
266. C22×Dic11C2×D4semidirect
303. C2×#392D11semidirect
463. #392C2×D11semidirect
632. C2×C11#2635semidirect
769. C11C2×#2635semidirect
947. C2#13074499direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669922
C22×D4×Dic112
#130744992
C2×#106222732
C2×#106225622
C2×#106225742
C2×#106228352
C2×#106228362
C2×#106225642
C2×#106222822
C2×#106228332
C2×#106225712
C2×#106225562
C2×C11×#3922
C2×#263511