Finite Group Databasebeta

← C2×#13072517 #14921884

Subgroups — C2×#13072517 #14921884

Order 2816.

3438 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66936C211yesmaximal, characteristic, complemented
2#13072517C2116yesmaximal, direct product factor
3C2×#10622599C211yesmaximal, characteristic, complemented
4C2×#10622607C211yesmaximal, characteristic, complemented
5C2×#10622835C211yesmaximal, characteristic, complemented
6C2×#10622836C211yesmaximal, characteristic
7C2×#10622558C211yesmaximal, characteristic, complemented
8C2×#10622564C211yesmaximal, characteristic, complemented
9C2×#10622546C211yesmaximal, characteristic, complemented
10C2×#10622826C211yesmaximal, characteristic, complemented
11C2×#10622826C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×#10622824C211yesmaximal, characteristic, complemented
14C2×#10622825C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C22×C4×D4×C11C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C2×C4×D4×C11—28no—
24C2×C4×D4×C11C2218yescomplemented
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic
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
44C2×#66936—28no—
45C2×#66936C2218yescomplemented
46#10622836C2218yes—
47#10622835C2218yescomplemented
48#10622826C2218yescomplemented
49#10622826C2218yescomplemented
50#10622825C2218yescomplemented
51#10622824C2218yescomplemented
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62#10622607C2218yescomplemented
63#10622599C2218yescomplemented
64#10622569C2218yescomplemented
65#10622564C2218yescomplemented
66#10622558C2218yescomplemented
67C4×(C2×D11)⋊C4C2218yescomplemented
68#10622546C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C22×D4×C11—24no—
73C22×D4×C11—24no—
74C22×D4×C11—24no—
75C22×D4×C11C2314yes—
76C23×C4×C11—24no—
77C23×C4×C11—24no—
78C23×C4×C11—24no—
79C23×C4×C11—24no—
80C23×C4×C11—42no—
81C23×C4×C11—42no—
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2314yes—
84C23×C4×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—24no—
93C22×C22⋊D11—42no—
94C22×C22⋊D11—42no—
95C22×C22⋊D11C2314yes—
96C22×C22⋊D11C2314yes—
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C22×C4×D11—24no—
105C22×C4×D11—24no—
106C22×C4×D11—42no—
107C22×C4×D11C2314yes—
108C4×D4×C11—232no—
109C2×C11×C4⋊C4—24no—
110C2×C11×C4⋊C4C2314yes—
111C2×C11×C22⋊C4—24no—
112C2×C11×C22⋊C4D418yescomplemented
113C2×C11×C22⋊C4C2314yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C42×C11—24no—
116C2×C42×C11C2314yes—
117C2×C22⋊Dic11—24no—
118C2×C22⋊Dic11—24no—
119C2×C22⋊Dic11—42no—
120C2×C22⋊Dic11—42no—
121C2×C22⋊Dic11—42no—
122C2×C22⋊Dic11—42no—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C2×C22⋊Dic11C2314yes—
129C2×(C2×D11)⋊C4—24no—
130C2×(C2×D11)⋊C4—24no—
131C2×(C2×D11)⋊C4—24no—
132C2×(C2×D11)⋊C4—42no—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×C4⋊Dic11—24no—
138C2×C4⋊Dic11—42no—
139C2×C4⋊Dic11C2314yes—
140C2×C4⋊Dic11C2314yes—
141C2×Dic11⋊C4—24no—
142C2×Dic11⋊C4—24no—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×C4×Dic11—42no—
146C2×C4×Dic11C2314yes—
147#66936—232no—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2457—111nomaximal, Sylow
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×C11C2×D414yes—
172C24×C11#4114yes—
173C24×C11C2412yes—
174C24×C11C2412yes—
175C24×C11C2411yescharacteristic
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11—22no—
181C23×D11—22no—
182C23×D11#4114yes—
183C23×D11C2412yes—
184C2×D4×C11—232no—
185C2×D4×C11—28no—
186C2×D4×C11—28no—
187C2×D4×C11—28no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—28no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—28no—
201C22×C4×C11—28no—
202C22×C4×C11—28no—
203C22×C4×C11—44no—
204C22×C4×C11—44no—
205C22×C4×C11—416no—
206C22×C4×C11—416no—
207C22×C4×C11C2×D414yes—
208C22×C4×C11C2×D414yes—
209C22×C4×C11#4114yes—
210C22×C4×C11#4114yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C2×C22⋊D11—28no—
217C2×C22⋊D11—28no—
218C2×C22⋊D11—28no—
219C2×C22⋊D11—28no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—416no—
223C2×C22⋊D11—416no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—22no—
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×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C22×Dic11C2412yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C2×C4×D11—28no—
253C2×C4×D11—28no—
254C2×C4×D11—44no—
255C2×C4×D11—416no—
256C11×C4⋊C4—28no—
257C11×C22⋊C4—28no—
258C11×C22⋊C4C2×D4116yescomplemented
259C42×C11—28no—
260C22⋊Dic11—28no—
261C22⋊Dic11—28no—
262C22⋊Dic11—44no—
263C22⋊Dic11—44no—
264C22⋊Dic11—44no—
265C22⋊Dic11—44no—
266(C2×D11)⋊C4—28no—
267(C2×D11)⋊C4—28no—
268(C2×D11)⋊C4—28no—
269(C2×D11)⋊C4—44no—
270C4⋊Dic11—28no—
271C4⋊Dic11—44no—
272Dic11⋊C4—28no—
273Dic11⋊C4—28no—
274C4×Dic11—44no—
275C22×#123—111no—
276C22×C4×D4D1111yescharacteristic, complemented
277#2457—1116no—
278C2×#400—111no—
279C2×#396—111no—
280C2×#394—111no—
281C2×#392—111no—
282C2×#388—111no—
283C2×#388—111no—
284C2×#387—111no—
285C2×#386—111no—
286C2×#386—111no—
287C2×#386—111no—
288C2×#381—111no—
289C2×#380—111no—
290C2×C4×C22⋊C4—111no—
291C23×C11—28no—
292C23×C11—28no—
293C23×C11—28no—
294C23×C11—28no—
295C23×C11—28no—
296C23×C11—28no—
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×C11C22×D414yes—
318C23×C11C22×D412yes—
319C23×C11C2×#4114yes—
320C23×C11C2×#4112yes—
321C23×C11C2×#4112yes—
322C23×C11C2×#4112yes—
323C23×C11C2×#4112yes—
324C23×C11H(5,𝔽2)12yes—
325C23×C11H(5,𝔽2)12yes—
326C23×C11C2511yescharacteristic
327C22×D11—28no—
328C22×D11—28no—
329C22×D11—28no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11—44no—
339C22×D11—44no—
340C22×D11C2×#4114yes—
341D4×C11—232no—
342C2×C4×C11—28no—
343C2×C4×C11—28no—
344C2×C4×C11—28no—
345C2×C4×C11—28no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—416no—
358C2×C4×C11—416no—
359C2×C4×C11—44no—
360C2×C4×C11C22×D414yes—
361C2×C4×C11C22×D414yes—
362C2×C4×C11C2×#4114yes—
363C2×C4×C11C2×#4114yes—
364C22⋊D11—416no—
365C22⋊D11—416no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—44no—
388C2×Dic11—44no—
389C2×Dic11—44no—
390C2×Dic11—44no—
391C2×Dic11—44no—
392C2×Dic11—44no—
393C2×Dic11—44no—
394C4×D11—416no—
395C23×D4—111no—
396C23×D4—111no—
397C23×D4C2×D1111yescharacteristic
398C24×C4—111no—
399C24×C4C2×D1111yescharacteristic
400C24×C4C2×D1111yescharacteristic
401C2×#123—118no—
402C2×#123—228no—
403C2×C4×D4—28no—
404C2×C4×D4C2×D1118yescomplemented
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
407C22×C4⋊C4—111no—
408C22×C4⋊C4—111no—
409C22×C4⋊C4C2×D1111yescharacteristic
410C22×C22⋊C4—111no—
411C22×C22⋊C4—111no—
412C22×C22⋊C4—111no—
413C22×C22⋊C4—111no—
414C22×C22⋊C4—111no—
415C22×C22⋊C4—111no—
416C22×C22⋊C4—111no—
417C22×C22⋊C4—111no—
418C22×C22⋊C4—111no—
419C22×C22⋊C4—111no—
420C22×C22⋊C4C2×D1111yescharacteristic
421C22×C22⋊C4C2×D1111yescharacteristic
422C22×C42—111no—
423C22×C42C2×D1111yescharacteristic
424#400—118no—
425#396—118no—
426#394—118no—
427#392—118no—
428#388—118no—
429#388—118no—
430#387—118no—
431#386—118no—
432#386—118no—
433#386—118no—
434#381—118no—
435#380—118no—
436C4×C22⋊C4—118no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95—111no—
444C2×#95—111no—
445C2×#95—111no—
446C2×#95—111no—
447C22×C11—24no—
448C22×C11—24no—
449C22×C11—24no—
450C22×C11—24no—
451C22×C11—24no—
452C22×C11—24no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—416no—
462C22×C11—416no—
463C22×C11#52514yes—
464C22×C11#52914yes—
465C22×C11#54014yes—
466C22×C11#54614yes—
467C22×C11#54614yes—
468C22×C11#55114yes—
469C22×C11#55314yes—
470C22×C11C23×D411yescharacteristic
471C22×C11C22×#4111yescharacteristic
472C22×C11C22×#4111yescharacteristic
473C22×C11C22×#4111yescharacteristic
474C22×C11C22×#4111yescharacteristic
475C22×C11C2×H(5,𝔽2)11yescharacteristic
476C22×C11C2×H(5,𝔽2)11yescharacteristic
477C2×D11—24no—
478C2×D11—24no—
479C2×D11—24no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—416no—
485C4×C11—24no—
486C4×C11—24no—
487C4×C11—24no—
488C4×C11—24no—
489C4×C11—42no—
490Dic11—42no—
491Dic11—42no—
492Dic11—42no—
493Dic11—42no—
494Dic11—42no—
495Dic11—42no—
496Dic11—42no—
497C25—111no—
498C25C22×D1111yescharacteristic
499C25C22×D1111yescharacteristic
500C22×D4—24no—
501C22×D4—24no—
502C22×D4—24no—
503C22×D4—114no—
504C22×D4—114no—
505C22×D4—224no—
506C22×D4—224no—
507C22×D4—224no—
508C22×D4—224no—
509C22×D4—442no—
510C22×D4—442no—
511C22×D4C22×D1114yes—
512C23×C4—24no—
513C23×C4—24no—
514C23×C4—24no—
515C23×C4—24no—
516C23×C4—42no—
517C23×C4—42no—
518C23×C4—111no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4—111no—
524C23×C4—111no—
525C23×C4—114no—
526C23×C4—224no—
527C23×C4—224no—
528C23×C4—442no—
529C23×C4C22×D1111yescharacteristic
530C23×C4C22×D1114yes—
531C23×C4C22×D1114yes—
532C23×C4C22×D1111yescharacteristic
533C23×C4C22×D1111yescharacteristic
534C23×C4C22×D1111yescharacteristic
535C23×C4C22×D1111yescharacteristic
536#123—2232no—
537C4×D4—232no—
538C2×C4⋊C4—24no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—114no—
541C2×C4⋊C4—114no—
542C2×C4⋊C4—114no—
543C2×C4⋊C4—224no—
544C2×C4⋊C4—224no—
545C2×C4⋊C4—224no—
546C2×C4⋊C4—442no—
547C2×C4⋊C4C22×D1114yes—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—114no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—114no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—114no—
557C2×C22⋊C4—114no—
558C2×C22⋊C4—114no—
559C2×C22⋊C4—224no—
560C2×C22⋊C4—224no—
561C2×C22⋊C4—224no—
562C2×C22⋊C4—224no—
563C2×C22⋊C4—224no—
564C2×C22⋊C4—442no—
565C2×C22⋊C4—442no—
566C2×C22⋊C4—442no—
567C2×C22⋊C4—442no—
568C2×C22⋊C4—442no—
569C2×C22⋊C4C22⋊D1118yescomplemented
570C2×C22⋊C4C22×D1114yes—
571C2×C22⋊C4C22×D1114yes—
572C2×C42—24no—
573C2×C42—114no—
574C2×C42—442no—
575C2×C42C22×D1114yes—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95—114no—
581#95—114no—
582#95—114no—
583#95—114no—
584#95—114no—
585#95—114no—
586C2×C11—44no—
587C2×C11—44no—
588C2×C11#245718yescomplemented
589C2×C11C2×#52511yescharacteristic
590C2×C11C2×#52911yescharacteristic
591C2×C11C2×#54011yescharacteristic
592C2×C11C2×#54611yescharacteristic
593C2×C11C2×#54611yescharacteristic
594C2×C11C2×#55111yescharacteristic
595C2×C11C2×#55311yescharacteristic
596D11—44no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—114no—
610C24—112no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24—222no—
616C24—222no—
617C24#433914yes—
618C24C2×C22⋊D1114yes—
619C24C23×D1112yes—
620C24C23×D1112yes—
621C24C23×D1111yescharacteristic
622C2×D4—232no—
623C2×D4—28no—
624C2×D4—28no—
625C2×D4—28no—
626C2×D4—228no—
627C2×D4—228no—
628C2×D4—228no—
629C2×D4—228no—
630C2×D4—444no—
631C2×D4—444no—
632C2×D4—4416no—
633C2×D4—4416no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—28no—
646C22×C4—28no—
647C22×C4—28no—
648C22×C4—28no—
649C22×C4—44no—
650C22×C4—44no—
651C22×C4—416no—
652C22×C4—416no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—112no—
660C22×C4—228no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—222no—
665C22×C4—222no—
666C22×C4—222no—
667C22×C4—222no—
668C22×C4—222no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—222no—
674C22×C4—222no—
675C22×C4—222no—
676C22×C4—222no—
677C22×C4—222no—
678C22×C4—222no—
679C22×C4—222no—
680C22×C4—222no—
681C22×C4—222no—
682C22×C4—228no—
683C22×C4—444no—
684C22×C4—4416no—
685C22×C4#433914yes—
686C22×C4#434114yes—
687C22×C4C2×C22⋊D1114yes—
688C22×C4C2×C22⋊D1114yes—
689C22×C4C23×D1112yes—
690C22×C4C23×D1112yes—
691C22×C4C23×D1112yes—
692C22×C4C23×D1112yes—
693C22×C4C23×D1112yes—
694C4⋊C4—28no—
695C4⋊C4—228no—
696C4⋊C4—228no—
697C4⋊C4—228no—
698C4⋊C4—444no—
699C22⋊C4—28no—
700C22⋊C4—228no—
701C22⋊C4—228no—
702C22⋊C4—228no—
703C22⋊C4—228no—
704C22⋊C4—228no—
705C22⋊C4—444no—
706C22⋊C4—444no—
707C22⋊C4—444no—
708C22⋊C4—444no—
709C22⋊C4—444no—
710C22⋊C4C2×C22⋊D11116yescomplemented
711C42—28no—
712C42—444no—
713C11C2×#245711yescharacteristic, complemented, Sylow
714C23—28no—
715C23—28no—
716C23—28no—
717C23—28no—
718C23—28no—
719C23—28no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—114no—
741C23—228no—
742C23—228no—
743C23—228no—
744C23—222no—
745C23—222no—
746C23—222no—
747C23—222no—
748C23—222no—
749C23—222no—
750C23—444no—
751C23—444no—
752C23—444no—
753C23—444no—
754C23C2×#433914yes—
755C23C2×#433912yes—
756C23C2×#433912yes—
757C23C2×#434112yes—
758C23#6703712yes—
759C23#41×D1112yes—
760C23#6704212yes—
761C23C22×C22⋊D1114yes—
762C23C22×C22⋊D1112yes—
763C23C24×D1111yescharacteristic
764D4—232no—
765D4—4416no—
766D4—4416no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—28no—
770C2×C4—28no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—416no—
783C2×C4—416no—
784C2×C4—44no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—222no—
788C2×C4—222no—
789C2×C4—222no—
790C2×C4—222no—
791C2×C4—222no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—4416no—
807C2×C4—444no—
808C2×C4—444no—
809C2×C4—444no—
810C2×C4—444no—
811C2×C4—444no—
812C2×C4—444no—
813C2×C4—444no—
814C2×C4C2×#433914yes—
815C2×C4C2×#434114yes—
816C2×C4C22×C22⋊D1114yes—
817C2×C4C22×C22⋊D1114yes—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—416no—
831C22—416no—
832C22—42no—
833C22—42no—
834C22—224no—
835C22—224no—
836C22—224no—
837C22—442no—
838C22—442no—
839C22—442no—
840C22—4416no—
841C22—442no—
842C22#1062308714yes—
843C22#1062308814yes—
844C22#1062309314yes—
845C22#1062309614yes—
846C22#1062332214yes—
847C22#1062333714yes—
848C22#1062336014yes—
849C22C22×#433911yescharacteristic
850C22C22×#433911yescharacteristic
851C22C22×#434111yescharacteristic
852C22C2×#6703711yescharacteristic
853C22C2×#41×D1111yescharacteristic
854C22C2×#6704211yescharacteristic
855C22C23×C22⋊D1111yescharacteristic
856C4—24no—
857C4—24no—
858C4—24no—
859C4—24no—
860C4—42no—
861C4—442no—
862C4—442no—
863C4—442no—
864C4—442no—
865C4—442no—
866C4—442no—
867C4—442no—
868C2—44no—
869C2—44no—
870C2—444no—
871C2#1307251718yesdirect product factor
872C2C2×#1062332211yescharacteristic
873C2C2×#1062308811yescharacteristic
874C2C2×#1062309311yescharacteristic
875C2C2×#1062336011yescharacteristic
876C2C2×#1062333711yescharacteristic
877C2C2×#1062308711yescharacteristic
878C2C2×#1062309611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
socleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC22×C4×D4D11
hypocenterC11C2×#2457
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#66936C2semidirect
2. #13072517C2direct (N × H)
3. C2×#10622599C2semidirect
4. C2×#10622607C2semidirect
5. C2×#10622835C2semidirect
7. C2×#10622558C2semidirect
8. C2×#10622564C2semidirect
9. C2×#10622546C2semidirect
10. C2×#10622826C2semidirect
11. C2×#10622826C2semidirect
12. C2×#10622569C2semidirect
13. C2×#10622824C2semidirect
14. C2×#10622825C2semidirect
15. C2×C4×(C2×D11)⋊C4C2semidirect
16. C22×C4×D4×C11C2semidirect
24. C2×C4×D4×C11C22semidirect
45. C2×#66936C22semidirect
47. #10622835C22semidirect
48. #10622826C22semidirect
49. #10622826C22semidirect
50. #10622825C22semidirect
51. #10622824C22semidirect
62. #10622607C22semidirect
63. #10622599C22semidirect
64. #10622569C22semidirect
65. #10622564C22semidirect
66. #10622558C22semidirect
67. C4×(C2×D11)⋊C4C22semidirect
68. #10622546C22semidirect
112. C2×C11×C22⋊C4D4semidirect
258. C11×C22⋊C4C2×D4semidirect
276. C22×C4×D4D11semidirect
404. C2×C4×D4C2×D11semidirect
569. C2×C22⋊C4C22⋊D11semidirect
588. C2×C11#2457semidirect
710. C22⋊C4C2×C22⋊D11semidirect
713. C11C2×#2457semidirect
871. C2#13072517direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669362
#130725172
C2×#106225992
C2×#106226072
C2×#106228352
C2×#106228362
C2×#106225582
C2×#106225642
C2×#106225462
C2×#106228262
C2×#106225692
C2×#106228242
C2×#106228252
C2×C4×(C2×D11)⋊C42
C22×C4×D4×C112
C2×#245711