Finite Group Databasebeta

← C2×#13076738 #14960118

Subgroups — C2×#13076738 #14960118

Order 2816.

2822 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076738C2116yesmaximal, direct product factor
2C2×#10622273C211yesmaximal, characteristic, complemented
3C2×#10622565C211yesmaximal, characteristic, complemented
4C2×#10622566C211yesmaximal, characteristic, complemented
5C2×#10622574C211yesmaximal, characteristic, complemented
6C2×#10622574C211yesmaximal, characteristic, complemented
7C2×#10622572C211yesmaximal, characteristic, complemented
8C2×#10622835C211yesmaximal, characteristic, complemented
9C2×#10622835C211yesmaximal, characteristic, complemented
10C2×#10622836C211yesmaximal, characteristic, complemented
11C2×#10622836C211yesmaximal, characteristic, complemented
12C2×#10622836C211yesmaximal, characteristic, complemented
13C2×#10622834C211yesmaximal, characteristic, complemented
14C2×#10622564C211yesmaximal, characteristic, complemented
15C2×#10622282C211yesmaximal, 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
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×C4⋊Dic11C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C11×#392C2218yescomplemented
45C2×C11×#95C2211yescharacteristic
46#10622836C2218yescomplemented
47#10622836C2218yescomplemented
48#10622836C2218yescomplemented
49#10622835C2218yescomplemented
50#10622835C2218yescomplemented
51#10622834C2218yescomplemented
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59#10622574C2218yescomplemented
60#10622574C2218yescomplemented
61#10622572C2218yescomplemented
62#10622566C2218yescomplemented
63#10622565C2218yescomplemented
64#10622564C2218yescomplemented
65#10622282C2218yescomplemented
66#10622273C2218yescomplemented
67C25×C11C2311yescharacteristic
68C25×C11C2311yescharacteristic
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C22×D4×C11—24no—
72C22×D4×C11—42no—
73C22×D4×C11—42no—
74C22×D4×C11—42no—
75C22×D4×C11—42no—
76C22×D4×C11—42no—
77C22×D4×C11—42no—
78C22×D4×C11—42no—
79C22×D4×C11—42no—
80C22×D4×C11C2314yes—
81C22×D4×C11C2314yes—
82C22×D4×C11C2314yes—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—42no—
88C22×C22⋊D11—42no—
89C22×C22⋊D11—42no—
90C22×C22⋊D11—42no—
91C22×C22⋊D11—42no—
92C22×C22⋊D11—42no—
93C22×C22⋊D11—42no—
94C22×C22⋊D11—42no—
95C22×C22⋊D11—42no—
96C22×C22⋊D11C2314yes—
97C22×C22⋊D11C2314yes—
98C22×C22⋊D11C2314yes—
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C2×C11×C22⋊C4—24no—
107C2×C11×C22⋊C4—42no—
108C2×C11×C22⋊C4—42no—
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2314yes—
111C2×C11×C22⋊C4C2314yes—
112C2×C22⋊Dic11—42no—
113C2×C22⋊Dic11—42no—
114C2×C22⋊Dic11—42no—
115C2×C22⋊Dic11—42no—
116C2×C22⋊Dic11—42no—
117C2×C22⋊Dic11—42no—
118C2×C22⋊Dic11—42no—
119C2×C22⋊Dic11—42no—
120C2×C22⋊Dic11—42no—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129C2×C22⋊Dic11C2314yes—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4—42no—
132C2×(C2×D11)⋊C4—42no—
133C2×(C2×D11)⋊C4—42no—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×C4⋊Dic11—42no—
139C2×C4⋊Dic11—42no—
140C2×C4⋊Dic11C2314yes—
141C2×C4⋊Dic11C2314yes—
142C2×Dic11⋊C4—42no—
143C2×Dic11⋊C4—42no—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×C4×Dic11—42no—
147C2×C4×Dic11C2314yes—
148C11×#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C2×#2828—111nomaximal, Sylow
157C24×C11—22no—
158C24×C11—22no—
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
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×C11C2412yes—
179C24×C11C2412yes—
180C24×C11C2412yes—
181C24×C11C2411yescharacteristic
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11—22no—
189C23×D11C2412yes—
190C2×D4×C11—28no—
191C2×D4×C11—44no—
192C2×D4×C11—44no—
193C2×D4×C11—44no—
194C2×D4×C11—44no—
195C2×D4×C11—44no—
196C2×D4×C11—44no—
197C2×D4×C11—44no—
198C2×D4×C11—44no—
199C2×D4×C11—416no—
200C2×D4×C11—416no—
201C2×D4×C11—416no—
202C22×C4×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11#4114yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C2×C22⋊D11—44no—
219C2×C22⋊D11—44no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—44no—
223C2×C22⋊D11—44no—
224C2×C22⋊D11—44no—
225C2×C22⋊D11—44no—
226C2×C22⋊D11—44no—
227C2×C22⋊D11—416no—
228C2×C22⋊D11—416no—
229C2×C22⋊D11—416no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—22no—
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×Dic11C2412yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C22×Dic11C2412yes—
255C22×Dic11C2412yes—
256C22×Dic11C2412yes—
257C22×Dic11C2412yes—
258C11×C22⋊C4—28no—
259C11×C22⋊C4—44no—
260C11×C22⋊C4—44no—
261C22⋊Dic11—44no—
262C22⋊Dic11—44no—
263C22⋊Dic11—44no—
264C22⋊Dic11—44no—
265C22⋊Dic11—44no—
266C22⋊Dic11—44no—
267C22⋊Dic11—44no—
268C22⋊Dic11—44no—
269C22⋊Dic11—44no—
270(C2×D11)⋊C4—28no—
271(C2×D11)⋊C4—44no—
272(C2×D11)⋊C4—44no—
273(C2×D11)⋊C4—44no—
274C4⋊Dic11—44no—
275C4⋊Dic11—44no—
276Dic11⋊C4—44no—
277Dic11⋊C4—44no—
278C4×Dic11—44no—
279#2828—1116no—
280C2×#400—111no—
281C2×#397—111no—
282C2×#397—111no—
283C2×#394—111no—
284C2×#394—111no—
285C2×#394—111no—
286C2×#394—111no—
287C2×#394—111no—
288C2×#392—111no—
289C2×#392—111no—
290C2×#392—111no—
291C2×#392D1111yescharacteristic, complemented
292C2×#390—111no—
293C2×#388—111no—
294C2×#388—111no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—44no—
317C23×C11—44no—
318C23×C11—44no—
319C23×C11—44no—
320C23×C11—44no—
321C23×C11—44no—
322C23×C11—44no—
323C23×C11—44no—
324C23×C11—44no—
325C23×C11—44no—
326C23×C11—44no—
327C23×C11—44no—
328C23×C11—44no—
329C23×C11—44no—
330C23×C11—44no—
331C23×C11—44no—
332C23×C11—44no—
333C23×C11—44no—
334C23×C11—44no—
335C23×C11—44no—
336C23×C11—44no—
337C23×C11C2×#4112yes—
338C23×C11H(5,𝔽2)12yes—
339C23×C11H(5,𝔽2)12yes—
340C23×C11H(5,𝔽2)12yes—
341C23×C11H(5,𝔽2)12yes—
342C23×C11H(5,𝔽2)12yes—
343C23×C11H(5,𝔽2)12yes—
344C23×C11C2511yescharacteristic
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—44no—
353C22×D11—44no—
354C22×D11—44no—
355C22×D11—44no—
356C22×D11—44no—
357C22×D11—44no—
358C22×D11—44no—
359D4×C11—416no—
360D4×C11—416no—
361D4×C11—416no—
362C2×C4×C11—28no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—44no—
375C2×C4×C11—44no—
376C2×C4×C11—44no—
377C2×C4×C11C2×#4114yes—
378C22⋊D11—416no—
379C22⋊D11—416no—
380C22⋊D11—416no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—44no—
403C2×Dic11—44no—
404C2×Dic11—44no—
405C2×Dic11—44no—
406C2×Dic11—44no—
407C2×Dic11—44no—
408C2×Dic11—44no—
409C23×D4—111no—
410C23×D4—111no—
411C23×D4—111no—
412C23×D4C2×D1111yescharacteristic
413C23×D4C2×D1111yescharacteristic
414C23×D4C2×D1111yescharacteristic
415C22×C4⋊C4—111no—
416C22×C4⋊C4—111no—
417C22×C4⋊C4—111no—
418C22×C4⋊C4—111no—
419C22×C22⋊C4—111no—
420C22×C22⋊C4—111no—
421C22×C22⋊C4—111no—
422C22×C22⋊C4—111no—
423C22×C22⋊C4—111no—
424C22×C22⋊C4—111no—
425C22×C22⋊C4—111no—
426C22×C22⋊C4—111no—
427C22×C22⋊C4—111no—
428C22×C22⋊C4—111no—
429C22×C22⋊C4—111no—
430C22×C22⋊C4—111no—
431C22×C22⋊C4—111no—
432C22×C22⋊C4C2×D1111yescharacteristic
433C22×C22⋊C4C2×D1111yescharacteristic
434C22×C22⋊C4C2×D1111yescharacteristic
435C22×C42—111no—
436#400—118no—
437#397—118no—
438#397—118no—
439#394—118no—
440#394—118no—
441#394—118no—
442#394—118no—
443#394—118no—
444#392—118no—
445#392—118no—
446#392—118no—
447#392C2×D1118yescomplemented
448#390—118no—
449#388—118no—
450#388—118no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95—111no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95C2×D1111yescharacteristic
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—88no—
481C22×C11—88no—
482C22×C11—88no—
483C22×C11#53814yes—
484C22×C11#54014yes—
485C22×C11#54014yes—
486C22×C11#56014yes—
487C22×C11#56014yes—
488C22×C11#56014yes—
489C22×C11H(3,𝔽4)14yes—
490C22×C11C22×#4111yescharacteristic
491C22×C11C2×H(5,𝔽2)11yescharacteristic
492C22×C11C2×H(5,𝔽2)11yescharacteristic
493C22×C11C2×H(5,𝔽2)11yescharacteristic
494C22×C11C2×H(5,𝔽2)11yescharacteristic
495C22×C11C2×H(5,𝔽2)11yescharacteristic
496C22×C11C2×H(5,𝔽2)11yescharacteristic
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—42no—
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—88no—
505C4×C11—24no—
506C4×C11—42no—
507C4×C11—42no—
508C4×C11—42no—
509Dic11—42no—
510Dic11—42no—
511Dic11—42no—
512Dic11—42no—
513Dic11—42no—
514Dic11—42no—
515Dic11—42no—
516C25—111no—
517C25C22×D1111yescharacteristic
518C25C22×D1111yescharacteristic
519C25C22×D1111yescharacteristic
520C22×D4—24no—
521C22×D4—42no—
522C22×D4—42no—
523C22×D4—42no—
524C22×D4—42no—
525C22×D4—42no—
526C22×D4—42no—
527C22×D4—42no—
528C22×D4—42no—
529C22×D4—114no—
530C22×D4—114no—
531C22×D4—114no—
532C22×D4—442no—
533C22×D4—442no—
534C22×D4—442no—
535C22×D4—442no—
536C22×D4—442no—
537C22×D4—442no—
538C22×D4—442no—
539C22×D4—442no—
540C22×D4—442no—
541C22×D4C22×D1114yes—
542C22×D4C22×D1114yes—
543C22×D4C22×D1114yes—
544C23×C4—111no—
545C23×C4—111no—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—111no—
550C23×C4—111no—
551C23×C4C22×D1111yescharacteristic
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1111yescharacteristic
554C23×C4C22×D1111yescharacteristic
555C2×C4⋊C4—114no—
556C2×C4⋊C4—114no—
557C2×C4⋊C4—114no—
558C2×C4⋊C4—114no—
559C2×C4⋊C4—442no—
560C2×C4⋊C4—442no—
561C2×C4⋊C4—442no—
562C2×C4⋊C4—442no—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—114no—
567C2×C22⋊C4—114no—
568C2×C22⋊C4—114no—
569C2×C22⋊C4—114no—
570C2×C22⋊C4—114no—
571C2×C22⋊C4—114no—
572C2×C22⋊C4—114no—
573C2×C22⋊C4—114no—
574C2×C22⋊C4—114no—
575C2×C22⋊C4—114no—
576C2×C22⋊C4—114no—
577C2×C22⋊C4—114no—
578C2×C22⋊C4—114no—
579C2×C22⋊C4—224no—
580C2×C22⋊C4—442no—
581C2×C22⋊C4—442no—
582C2×C22⋊C4—442no—
583C2×C22⋊C4—442no—
584C2×C22⋊C4—442no—
585C2×C22⋊C4—442no—
586C2×C22⋊C4—442no—
587C2×C22⋊C4—442no—
588C2×C22⋊C4—442no—
589C2×C22⋊C4—442no—
590C2×C22⋊C4—442no—
591C2×C22⋊C4—442no—
592C2×C22⋊C4C22×D1114yes—
593C2×C22⋊C4C22×D1114yes—
594C2×C22⋊C4C22×D1114yes—
595C2×C42—114no—
596C2×C42—442no—
597#95—114no—
598#95—114no—
599#95—114no—
600#95—114no—
601#95—114no—
602#95—114no—
603#95—114no—
604#95C22×D1114yes—
605C2×C11—82no—
606C2×C11—82no—
607C2×C11—82no—
608C2×C11#282818yescomplemented
609C2×C11C2×#53811yescharacteristic
610C2×C11C2×#54011yescharacteristic
611C2×C11C2×#54011yescharacteristic
612C2×C11C2×#56011yescharacteristic
613C2×C11C2×#56011yescharacteristic
614C2×C11C2×#56011yescharacteristic
615C2×C11C2×H(3,𝔽4)11yescharacteristic
616D11—82no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—112no—
639C24—222no—
640C24—222no—
641C24—222no—
642C24—222no—
643C24—222no—
644C24—222no—
645C24—222no—
646C24C23×D1112yes—
647C24C23×D1112yes—
648C24C23×D1112yes—
649C24C23×D1111yescharacteristic
650C2×D4—28no—
651C2×D4—44no—
652C2×D4—44no—
653C2×D4—44no—
654C2×D4—44no—
655C2×D4—44no—
656C2×D4—44no—
657C2×D4—44no—
658C2×D4—44no—
659C2×D4—416no—
660C2×D4—416no—
661C2×D4—416no—
662C2×D4—444no—
663C2×D4—444no—
664C2×D4—444no—
665C2×D4—444no—
666C2×D4—444no—
667C2×D4—444no—
668C2×D4—444no—
669C2×D4—444no—
670C2×D4—444no—
671C2×D4—4416no—
672C2×D4—4416no—
673C2×D4—4416no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—112no—
686C22×C4—112no—
687C22×C4—112no—
688C22×C4—112no—
689C22×C4—112no—
690C22×C4—112no—
691C22×C4—112no—
692C22×C4—222no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—222no—
697C22×C4—222no—
698C22×C4—222no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—222no—
702C22×C4—222no—
703C22×C4—222no—
704C22×C4—222no—
705C22×C4—222no—
706C22×C4—222no—
707C22×C4—222no—
708C22×C4—222no—
709C22×C4—222no—
710C22×C4—222no—
711C22×C4—222no—
712C22×C4—222no—
713C22×C4#434114yes—
714C22×C4C23×D1112yes—
715C22×C4C23×D1112yes—
716C22×C4C23×D1112yes—
717C22×C4C23×D1112yes—
718C4⋊C4—444no—
719C4⋊C4—444no—
720C4⋊C4—444no—
721C4⋊C4—444no—
722C22⋊C4—28no—
723C22⋊C4—44no—
724C22⋊C4—44no—
725C22⋊C4—228no—
726C22⋊C4—444no—
727C22⋊C4—444no—
728C22⋊C4—444no—
729C22⋊C4—444no—
730C22⋊C4—444no—
731C22⋊C4—444no—
732C22⋊C4—444no—
733C22⋊C4—444no—
734C22⋊C4—444no—
735C22⋊C4—444no—
736C22⋊C4—444no—
737C22⋊C4—444no—
738C42—444no—
739C11C2×#282811yescharacteristic, complemented, Sylow
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23—44no—
779C23—44no—
780C23—44no—
781C23—44no—
782C23—222no—
783C23—222no—
784C23—222no—
785C23—222no—
786C23—222no—
787C23—222no—
788C23—222no—
789C23—444no—
790C23—444no—
791C23—444no—
792C23—444no—
793C23—444no—
794C23—444no—
795C23—444no—
796C23C2×#434112yes—
797C23#6703712yes—
798C23#6703712yes—
799C23#6703712yes—
800C23#6703712yes—
801C23#6703712yes—
802C23#6704212yes—
803C23C24×D1111yescharacteristic
804D4—416no—
805D4—416no—
806D4—416no—
807D4—4416no—
808D4—4416no—
809D4—4416no—
810C2×C4—28no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—222no—
835C2×C4—222no—
836C2×C4—222no—
837C2×C4—222no—
838C2×C4—222no—
839C2×C4—222no—
840C2×C4—222no—
841C2×C4—222no—
842C2×C4—222no—
843C2×C4—222no—
844C2×C4—222no—
845C2×C4—222no—
846C2×C4—444no—
847C2×C4—444no—
848C2×C4—444no—
849C2×C4—444no—
850C2×C4—444no—
851C2×C4—444no—
852C2×C4—444no—
853C2×C4C2×#434114yes—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—88no—
876C22—88no—
877C22—88no—
878C22—442no—
879C22—442no—
880C22—442no—
881C22—442no—
882C22—442no—
883C22—442no—
884C22—442no—
885C22—888no—
886C22#1062312414yes—
887C22#1062312514yes—
888C22#1062312614yes—
889C22#1062315014yes—
890C22#1062315114yes—
891C22#1062315114yes—
892C22#1062325014yes—
893C22C22×#434111yescharacteristic
894C22C2×#6703711yescharacteristic
895C22C2×#6703711yescharacteristic
896C22C2×#6703711yescharacteristic
897C22C2×#6703711yescharacteristic
898C22C2×#6703711yescharacteristic
899C22C2×#6704211yescharacteristic
900C4—24no—
901C4—42no—
902C4—42no—
903C4—42no—
904C4—442no—
905C4—442no—
906C4—442no—
907C4—442no—
908C4—442no—
909C4—442no—
910C4—442no—
911C2—82no—
912C2—82no—
913C2—82no—
914C2—882no—
915C2#1307673818yesdirect product factor
916C2C2×#1062312411yescharacteristic
917C2C2×#1062315011yescharacteristic
918C2C2×#1062325011yescharacteristic
919C2C2×#1062315111yescharacteristic
920C2C2×#1062315111yescharacteristic
921C2C2×#1062312611yescharacteristic
922C2C2×#1062312511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2828
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. #13076738C2direct (N × H)
2. C2×#10622273C2semidirect
3. C2×#10622565C2semidirect
4. C2×#10622566C2semidirect
5. C2×#10622574C2semidirect
6. C2×#10622574C2semidirect
7. C2×#10622572C2semidirect
8. C2×#10622835C2semidirect
9. C2×#10622835C2semidirect
10. C2×#10622836C2semidirect
11. C2×#10622836C2semidirect
12. C2×#10622836C2semidirect
13. C2×#10622834C2semidirect
14. C2×#10622564C2semidirect
15. C2×#10622282C2semidirect
16. C2×C11×#392C2semidirect
44. C11×#392C22semidirect
46. #10622836C22semidirect
47. #10622836C22semidirect
48. #10622836C22semidirect
49. #10622835C22semidirect
50. #10622835C22semidirect
51. #10622834C22semidirect
59. #10622574C22semidirect
60. #10622574C22semidirect
61. #10622572C22semidirect
62. #10622566C22semidirect
63. #10622565C22semidirect
64. #10622564C22semidirect
65. #10622282C22semidirect
66. #10622273C22semidirect
291. C2×#392D11semidirect
447. #392C2×D11semidirect
608. C2×C11#2828semidirect
739. C11C2×#2828semidirect
915. C2#13076738direct (N × H)

Maximal subgroups

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

subgroupindex
#130767382
C2×#106222732
C2×#106225652
C2×#106225662
C2×#106225742
C2×#106225722
C2×#106228352
C2×#106228362
C2×#106228342
C2×#106225642
C2×#106222822
C2×C11×#3922
C2×#282811