Finite Group Databasebeta

← C2×#13076736 #14960121

Subgroups — C2×#13076736 #14960121

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#13076736C2116yesmaximal, direct product factor
2C2×#10622595C211yesmaximal, characteristic, complemented
3C2×#10622288C211yesmaximal, characteristic, complemented
4C2×#10622566C211yesmaximal, characteristic, complemented
5C2×#10622604C211yesmaximal, characteristic, complemented
6C2×#10622574C211yesmaximal, characteristic, complemented
7C2×#10622572C211yesmaximal, characteristic, complemented
8C2×#10622572C211yesmaximal, characteristic, complemented
9C2×#10622573C211yesmaximal, characteristic, complemented
10C2×#10622573C211yesmaximal, characteristic, complemented
11C2×#10622836C211yesmaximal, characteristic, complemented
12C2×#10622836C211yesmaximal, characteristic, complemented
13C2×#10622570C211yesmaximal, characteristic, complemented
14C2×#10622558C211yesmaximal, characteristic, complemented
15C2×#10622283C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×D44C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×(C2×D11)⋊C4C2211yescharacteristic
40C22×C4⋊Dic11C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C11×#394C2218yescomplemented
45C2×C11×#95C2211yescharacteristic
46#10622836C2218yescomplemented
47#10622836C2218yescomplemented
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55#10622604C2218yescomplemented
56#10622595C2218yescomplemented
57#10622574C2218yescomplemented
58#10622573C2218yescomplemented
59#10622573C2218yescomplemented
60#10622572C2218yescomplemented
61#10622572C2218yescomplemented
62#10622570C2218yescomplemented
63#10622566C2218yescomplemented
64#10622558C2218yescomplemented
65#10622288C2218yescomplemented
66#10622283C2218yescomplemented
67C25×C11C2311yescharacteristic
68C25×C11C2311yescharacteristic
69C24×D11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C22×D4×C11—42no—
72C22×D4×C11—42no—
73C22×D4×C11—42no—
74C22×D4×C11C2314yes—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—24no—
81C22×C22⋊D11—42no—
82C22×C22⋊D11—42no—
83C22×C22⋊D11—42no—
84C22×C22⋊D11—42no—
85C22×C22⋊D11—42no—
86C22×C22⋊D11—42no—
87C22×C22⋊D11—42no—
88C22×C22⋊D11—42no—
89C22×C22⋊D11—42no—
90C22×C22⋊D11—42no—
91C22×C22⋊D11—42no—
92C22×C22⋊D11C2314yes—
93C22×C22⋊D11C2314yes—
94C22×C22⋊D11C2314yes—
95C22×C22⋊D11C2314yes—
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C22×D44—42no—
103C22×D44—42no—
104C22×D44—42no—
105C22×D44C2314yes—
106C2×C11×C4⋊C4—42no—
107C2×C11×C4⋊C4C2314yes—
108C2×C11×C22⋊C4—42no—
109C2×C11×C22⋊C4—42no—
110C2×C11×C22⋊C4—42no—
111C2×C11×C22⋊C4—42no—
112C2×C11×C22⋊C4C2314yes—
113C2×C11×C22⋊C4C2314yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C22⋊Dic11—24no—
117C2×C22⋊Dic11—42no—
118C2×C22⋊Dic11—42no—
119C2×C22⋊Dic11—42no—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×(C2×D11)⋊C4—24no—
125C2×(C2×D11)⋊C4—42no—
126C2×(C2×D11)⋊C4—42no—
127C2×(C2×D11)⋊C4—42no—
128C2×(C2×D11)⋊C4—42no—
129C2×(C2×D11)⋊C4—42no—
130C2×(C2×D11)⋊C4—42no—
131C2×(C2×D11)⋊C4—42no—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×(C2×D11)⋊C4C2314yes—
140C2×C4⋊Dic11—42no—
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×C11C2412yes—
172C24×C11C2412yes—
173C24×C11C2411yescharacteristic
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11—22no—
181C23×D11—22no—
182C23×D11—22no—
183C23×D11—22no—
184C23×D11—22no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11C2412yes—
189C23×D11C2412yes—
190C2×D4×C11—44no—
191C2×D4×C11—44no—
192C2×D4×C11—44no—
193C2×D4×C11—416no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
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×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C2×C22⋊D11—28no—
215C2×C22⋊D11—44no—
216C2×C22⋊D11—44no—
217C2×C22⋊D11—44no—
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—416no—
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#4114yes—
248C22×Dic11C2412yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C22×Dic11C2412yes—
253C22×Dic11C2412yes—
254C2×D44—44no—
255C2×D44—44no—
256C2×D44—44no—
257C2×D44—416no—
258C11×C4⋊C4—44no—
259C11×C22⋊C4—44no—
260C11×C22⋊C4—44no—
261C11×C22⋊C4—44no—
262C11×C22⋊C4—44no—
263C22⋊Dic11—28no—
264C22⋊Dic11—44no—
265C22⋊Dic11—44no—
266C22⋊Dic11—44no—
267(C2×D11)⋊C4—28no—
268(C2×D11)⋊C4—44no—
269(C2×D11)⋊C4—44no—
270(C2×D11)⋊C4—44no—
271(C2×D11)⋊C4—44no—
272(C2×D11)⋊C4—44no—
273(C2×D11)⋊C4—44no—
274(C2×D11)⋊C4—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×#394D1111yescharacteristic, complemented
288C2×#392—111no—
289C2×#392—111no—
290C2×#392—111no—
291C2×#392—111no—
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—44no—
310C23×C11—44no—
311C23×C11—44no—
312C23×C11—44no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11—44no—
317C23×C11—44no—
318C23×C11—44no—
319C23×C11—44no—
320C23×C11—44no—
321C23×C11—44no—
322C23×C11—44no—
323C23×C11C2×#4112yes—
324C23×C11H(5,𝔽2)12yes—
325C23×C11H(5,𝔽2)12yes—
326C23×C11H(5,𝔽2)12yes—
327C23×C11H(5,𝔽2)12yes—
328C23×C11H(5,𝔽2)12yes—
329C23×C11H(5,𝔽2)12yes—
330C23×C11C2511yescharacteristic
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—44no—
346C22×D11—44no—
347C22×D11—44no—
348C22×D11—44no—
349C22×D11—44no—
350C22×D11—44no—
351C22×D11—44no—
352C22×D11—44no—
353C22×D11—44no—
354C22×D11—44no—
355C22×D11—44no—
356C22×D11—44no—
357C22×D11—44no—
358C22×D11—44no—
359D4×C11—416no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
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—22no—
375C2×C4×C11—44no—
376C2×C4×C11—44no—
377C2×C4×C11—44no—
378C2×C4×C11—44no—
379C2×C4×C11—44no—
380C22⋊D11—416no—
381C22⋊D11—416no—
382C22⋊D11—416no—
383C22⋊D11—416no—
384C2×Dic11—28no—
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×Dic11C2×#4114yes—
408D44—416no—
409C23×D4—111no—
410C23×D4—111no—
411C23×D4—111no—
412C23×D4—111no—
413C23×D4—111no—
414C23×D4C2×D1111yescharacteristic
415C22×C4⋊C4—111no—
416C22×C4⋊C4—111no—
417C22×C4⋊C4—111no—
418C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic
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#394C2×D1118yescomplemented
444#392—118no—
445#392—118no—
446#392—118no—
447#392—118no—
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—88no—
474C22×C11—88no—
475C22×C11#53814yes—
476C22×C11#54014yes—
477C22×C11#54014yes—
478C22×C11#56014yes—
479C22×C11#56014yes—
480C22×C11#56014yes—
481C22×C11H(3,𝔽4)14yes—
482C22×C11C22×#4111yescharacteristic
483C22×C11C2×H(5,𝔽2)11yescharacteristic
484C22×C11C2×H(5,𝔽2)11yescharacteristic
485C22×C11C2×H(5,𝔽2)11yescharacteristic
486C22×C11C2×H(5,𝔽2)11yescharacteristic
487C22×C11C2×H(5,𝔽2)11yescharacteristic
488C22×C11C2×H(5,𝔽2)11yescharacteristic
489C2×D11—42no—
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—42no—
502C2×D11—42no—
503C2×D11—88no—
504C2×D11—88no—
505C4×C11—42no—
506C4×C11—42no—
507C4×C11—42no—
508C4×C11—42no—
509C4×C11—42no—
510Dic11—24no—
511Dic11—42no—
512Dic11—42no—
513Dic11—42no—
514Dic11—42no—
515Dic11—42no—
516C25—111no—
517C25—111no—
518C25C22×D1111yescharacteristic
519C25C22×D1111yescharacteristic
520C22×D4—42no—
521C22×D4—42no—
522C22×D4—42no—
523C22×D4—114no—
524C22×D4—114no—
525C22×D4—114no—
526C22×D4—114no—
527C22×D4—114no—
528C22×D4—224no—
529C22×D4—442no—
530C22×D4—442no—
531C22×D4—442no—
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×D4—442no—
542C22×D4—442no—
543C22×D4C22×D1114yes—
544C23×C4—111no—
545C23×C4—111no—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—111no—
550C23×C4C22×D1111yescharacteristic
551C23×C4C22×D1111yescharacteristic
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1111yescharacteristic
554C23×C4C22×D1111yescharacteristic
555C2×C4⋊C4—42no—
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⋊C4C22×D1114yes—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
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—224no—
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⋊C4C22×D1114yes—
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#282818yescomplemented
608C2×C11C2×#53811yescharacteristic
609C2×C11C2×#54011yescharacteristic
610C2×C11C2×#54011yescharacteristic
611C2×C11C2×#56011yescharacteristic
612C2×C11C2×#56011yescharacteristic
613C2×C11C2×#56011yescharacteristic
614C2×C11C2×H(3,𝔽4)11yescharacteristic
615D11—82no—
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—112no—
632C24—112no—
633C24—222no—
634C24—222no—
635C24—222no—
636C24—222no—
637C24—222no—
638C24—222no—
639C24—222no—
640C24—222no—
641C24—222no—
642C24—222no—
643C24—222no—
644C24—222no—
645C24—222no—
646C24—222no—
647C24C23×D1112yes—
648C24C23×D1112yes—
649C24C23×D1111yescharacteristic
650C2×D4—44no—
651C2×D4—44no—
652C2×D4—44no—
653C2×D4—416no—
654C2×D4—228no—
655C2×D4—444no—
656C2×D4—444no—
657C2×D4—444no—
658C2×D4—4416no—
659C2×D4—444no—
660C2×D4—444no—
661C2×D4—444no—
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—4416no—
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—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—114no—
690C22×C4—112no—
691C22×C4—112no—
692C22×C4—112no—
693C22×C4—112no—
694C22×C4—112no—
695C22×C4—112no—
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×C4C23×D1112yes—
714C22×C4C23×D1112yes—
715C22×C4C23×D1112yes—
716C22×C4C23×D1112yes—
717C22×C4C23×D1112yes—
718C4⋊C4—44no—
719C4⋊C4—444no—
720C4⋊C4—444no—
721C4⋊C4—444no—
722C22⋊C4—44no—
723C22⋊C4—44no—
724C22⋊C4—44no—
725C22⋊C4—44no—
726C22⋊C4—228no—
727C22⋊C4—228no—
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—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—222no—
769C23—222no—
770C23—222no—
771C23—222no—
772C23—222no—
773C23—222no—
774C23—222no—
775C23—222no—
776C23—222no—
777C23—222no—
778C23—222no—
779C23—222no—
780C23—222no—
781C23—222no—
782C23—444no—
783C23—444no—
784C23—444no—
785C23—444no—
786C23—444no—
787C23—444no—
788C23—444no—
789C23—444no—
790C23—444no—
791C23—444no—
792C23—444no—
793C23—444no—
794C23—444no—
795C23—444no—
796C23#6703712yes—
797C23#6703712yes—
798C23#6703712yes—
799C23#6703712yes—
800C23#41×D1112yes—
801C23#6704212yes—
802C23#6704212yes—
803C23C24×D1111yescharacteristic
804D4—416no—
805D4—4416no—
806D4—4416no—
807D4—4416no—
808D4—4416no—
809D4—4416no—
810C2×C4—22no—
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—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—114no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—228no—
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—222no—
847C2×C4—222no—
848C2×C4—222no—
849C2×C4—444no—
850C2×C4—444no—
851C2×C4—444no—
852C2×C4—444no—
853C2×C4—444no—
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—88no—
869C22—88no—
870C22—442no—
871C22—442no—
872C22—442no—
873C22—442no—
874C22—442no—
875C22—442no—
876C22—442no—
877C22—442no—
878C22—442no—
879C22—442no—
880C22—442no—
881C22—442no—
882C22—442no—
883C22—442no—
884C22—888no—
885C22—888no—
886C22#1062312514yes—
887C22#1062314614yes—
888C22#1062315114yes—
889C22#1062315114yes—
890C22#1062319414yes—
891C22#1062319714yes—
892C22#1062320914yes—
893C22C2×#6703711yescharacteristic
894C22C2×#6703711yescharacteristic
895C22C2×#6703711yescharacteristic
896C22C2×#6703711yescharacteristic
897C22C2×#41×D1111yescharacteristic
898C22C2×#6704211yescharacteristic
899C22C2×#6704211yescharacteristic
900C4—42no—
901C4—42no—
902C4—42no—
903C4—42no—
904C4—42no—
905C4—224no—
906C4—442no—
907C4—442no—
908C4—442no—
909C4—442no—
910C4—442no—
911C2—82no—
912C2—82no—
913C2—882no—
914C2—882no—
915C2#1307673618yesdirect product factor
916C2C2×#1062320911yescharacteristic
917C2C2×#1062314611yescharacteristic
918C2C2×#1062319411yescharacteristic
919C2C2×#1062315111yescharacteristic
920C2C2×#1062315111yescharacteristic
921C2C2×#1062319711yescharacteristic
922C2C2×#1062312511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
hypercenterC2×#394D11
hypocenterC11C2×#2828
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. #13076736C2direct (N × H)
2. C2×#10622595C2semidirect
3. C2×#10622288C2semidirect
4. C2×#10622566C2semidirect
5. C2×#10622604C2semidirect
6. C2×#10622574C2semidirect
7. C2×#10622572C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622573C2semidirect
10. C2×#10622573C2semidirect
11. C2×#10622836C2semidirect
12. C2×#10622836C2semidirect
13. C2×#10622570C2semidirect
14. C2×#10622558C2semidirect
15. C2×#10622283C2semidirect
16. C2×C11×#394C2semidirect
44. C11×#394C22semidirect
46. #10622836C22semidirect
47. #10622836C22semidirect
55. #10622604C22semidirect
56. #10622595C22semidirect
57. #10622574C22semidirect
58. #10622573C22semidirect
59. #10622573C22semidirect
60. #10622572C22semidirect
61. #10622572C22semidirect
62. #10622570C22semidirect
63. #10622566C22semidirect
64. #10622558C22semidirect
65. #10622288C22semidirect
66. #10622283C22semidirect
287. C2×#394D11semidirect
443. #394C2×D11semidirect
607. C2×C11#2828semidirect
739. C11C2×#2828semidirect
915. C2#13076736direct (N × H)

Maximal subgroups

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

subgroupindex
#130767362
C2×#106225952
C2×#106222882
C2×#106225662
C2×#106226042
C2×#106225742
C2×#106225722
C2×#106225732
C2×#106228362
C2×#106225702
C2×#106225582
C2×#106222832
C2×C11×#3942
C2×#282811