Finite Group Databasebeta

← C2×#13071380 #14912639

Subgroups — C2×#13071380 #14912639

Order 2816.

3414 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66948C211yesmaximal, characteristic
2#13071380C2116yesmaximal, direct product factor
3C2×#10622552C211yesmaximal, characteristic, complemented
4C2×#10622601C211yesmaximal, characteristic, complemented
5C2×#10622283C211yesmaximal, characteristic, complemented
6C2×#10622603C211yesmaximal, characteristic, complemented
7C2×#10622594C211yesmaximal, characteristic, complemented
8C2×#10622278C211yesmaximal, characteristic, complemented
9C2×#10622278C211yesmaximal, characteristic, complemented
10C2×#10622278C211yesmaximal, characteristic, complemented
11C2×#10622278C211yesmaximal, characteristic, complemented
12C2×#10622277C211yesmaximal, characteristic, complemented
13C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
14C2×#10622279C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#387C211yesmaximal, characteristic, complemented
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C2×#66948C4116yescomplemented
43C2×#66948C2218yes—
44C11×#387C2218yescomplemented
45C2×C11×#95C2211yescharacteristic
46C2×C11×#95C2211yescharacteristic
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55#10622603C2218yescomplemented
56#10622601C2218yescomplemented
57#10622594C2218yescomplemented
58#10622552C2218yescomplemented
59C4×(C2×D11)⋊C4C2218yescomplemented
60#10622283C2218yescomplemented
61#10622279C2218yescomplemented
62#10622279C2218yescomplemented
63#10622278C2218yescomplemented
64#10622278C2218yescomplemented
65#10622278C2218yescomplemented
66#10622278C2218yescomplemented
67#10622277C2218yescomplemented
68C24×D11C2311yescharacteristic
69C24×D11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C22×D44—42no—
84C22×D44—42no—
85C22×D44—42no—
86C22×D44—42no—
87C22×D44—42no—
88C22×D44—42no—
89C22×D44C2×C418yes—
90C22×D44C2×C418yescomplemented
91C22×D44C2×C418yescomplemented
92C22×D44C2314yes—
93C22×D44C2314yes—
94C22×D44C2314yes—
95C22×C4×D11—24no—
96C22×C4×D11—24no—
97C22×C4×D11—42no—
98C22×C4×D11—42no—
99C22×C4×D11—42no—
100C22×C4×D11—42no—
101C22×C4×D11—42no—
102C22×C4×D11—42no—
103C22×C4×D11C2×C418yescomplemented
104C22×C4×D11C2314yes—
105C22×C4×D11C2314yes—
106C22×C4×D11C2314yes—
107C2×C11×C4⋊C4—42no—
108C2×C11×C4⋊C4C2×C418yescomplemented
109C2×C11×C4⋊C4C2314yes—
110C2×C11×C4⋊C4C2314yes—
111C2×C42×C11—42no—
112C2×C42×C11C2314yes—
113C2×(C2×D11)⋊C4—24no—
114C2×(C2×D11)⋊C4—24no—
115C2×(C2×D11)⋊C4—24no—
116C2×(C2×D11)⋊C4—24no—
117C2×(C2×D11)⋊C4—42no—
118C2×(C2×D11)⋊C4—42no—
119C2×(C2×D11)⋊C4—42no—
120C2×(C2×D11)⋊C4—42no—
121C2×(C2×D11)⋊C4—42no—
122C2×(C2×D11)⋊C4—42no—
123C2×(C2×D11)⋊C4C2×C418yescomplemented
124C2×(C2×D11)⋊C4C2×C418yescomplemented
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×C4⋊Dic11—42no—
138C2×C4⋊Dic11C2314yes—
139C2×C4×Dic11—42no—
140C2×C4×Dic11—42no—
141C2×C4×Dic11—42no—
142C2×C4×Dic11C2314yes—
143C2×C4×Dic11C2314yes—
144C2×C4×Dic11C2314yes—
145#66948C2×C4164yescomplemented
146C11×#95C2314yes—
147C11×#95C2314yes—
148C11×#95C2314yes—
149C11×#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C2×#2333—111nomaximal, Sylow
157C24×C11C2411yescharacteristic
158C23×D11—22no—
159C23×D11—22no—
160C23×D11—22no—
161C23×D11—22no—
162C23×D11—22no—
163C23×D11—22no—
164C23×D11—22no—
165C23×D11—22no—
166C23×D11—22no—
167C23×D11—22no—
168C23×D11—22no—
169C23×D11—22no—
170C23×D11—22no—
171C23×D11—22no—
172C23×D11—22no—
173C23×D11—22no—
174C23×D11—22no—
175C23×D11—22no—
176C23×D11C22×C414yes—
177C23×D11C22×C414yes—
178C23×D11C22×C414yes—
179C23×D11C2412yes—
180C23×D11C2412yes—
181C23×D11C2412yes—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
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—22no—
198C22×C4×C11—22no—
199C22×C4×C11C22×C414yes—
200C22×C4×C11C22×C414yes—
201C22×C4×C11C22×C414yes—
202C22×C4×C11#4114yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11C22×C414yes—
224C22×Dic11#4114yes—
225C22×Dic11C2412yes—
226C22×Dic11C2412yes—
227C22×Dic11C2412yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C2×D44—416no—
231C2×D44—416no—
232C2×D44—416no—
233C2×D44—44no—
234C2×D44—44no—
235C2×D44—44no—
236C2×D44—44no—
237C2×D44—44no—
238C2×D44—44no—
239C2×D44C22×C4116yes—
240C2×D44C22×C4116yescomplemented
241C2×D44C22×C4116yescomplemented
242C2×C4×D11—28no—
243C2×C4×D11—28no—
244C2×C4×D11—416no—
245C2×C4×D11—44no—
246C2×C4×D11—44no—
247C2×C4×D11—44no—
248C2×C4×D11—44no—
249C2×C4×D11—44no—
250C2×C4×D11—44no—
251C2×C4×D11—416no—
252C2×C4×D11—416no—
253C2×C4×D11C22×C4116yescomplemented
254C11×C4⋊C4—44no—
255C11×C4⋊C4C22×C4116yescomplemented
256C42×C11—44no—
257(C2×D11)⋊C4—28no—
258(C2×D11)⋊C4—28no—
259(C2×D11)⋊C4—28no—
260(C2×D11)⋊C4—28no—
261(C2×D11)⋊C4—44no—
262(C2×D11)⋊C4—44no—
263(C2×D11)⋊C4—44no—
264(C2×D11)⋊C4—44no—
265(C2×D11)⋊C4—44no—
266(C2×D11)⋊C4—44no—
267(C2×D11)⋊C4C22×C4116yescomplemented
268(C2×D11)⋊C4C22×C4116yescomplemented
269C4⋊Dic11—44no—
270C4×Dic11—44no—
271C4×Dic11—44no—
272C4×Dic11—44no—
273C22×#121—111no—
274#2333—1116no—
275C2×#390—111no—
276C2×#390—111no—
277C2×#388—111no—
278C2×#388—111no—
279C2×#387—111no—
280C2×#387D1111yescharacteristic, complemented
281C2×#386—111no—
282C2×#386—111no—
283C2×#386—111no—
284C2×#386—111no—
285C2×#381—111no—
286C2×C4×C22⋊C4—111no—
287C2×C4×C22⋊C4—111no—
288C2×C4×C22⋊C4—111no—
289C23×C11C23×C412yes—
290C23×C11C2×#4112yes—
291C23×C11C2×#4112yes—
292C23×C11H(5,𝔽2)12yes—
293C23×C11H(5,𝔽2)12yes—
294C23×C11H(5,𝔽2)12yes—
295C23×C11H(5,𝔽2)12yes—
296C23×C11C2511yescharacteristic
297C22×D11—28no—
298C22×D11—28no—
299C22×D11—28no—
300C22×D11—28no—
301C22×D11—28no—
302C22×D11—28no—
303C22×D11—28no—
304C22×D11—28no—
305C22×D11—28no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—44no—
325C22×D11—44no—
326C22×D11—44no—
327C22×D11—44no—
328C22×D11—44no—
329C22×D11—44no—
330C22×D11—44no—
331C22×D11—44no—
332C22×D11—44no—
333C22×D11—44no—
334C22×D11—44no—
335C22×D11—44no—
336C22×D11C23×C414yes—
337C22×D11C23×C414yes—
338C22×D11C23×C414yes—
339C2×C4×C11—28no—
340C2×C4×C11—28no—
341C2×C4×C11—28no—
342C2×C4×C11—28no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
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—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—44no—
361C2×C4×C11—44no—
362C2×C4×C11—44no—
363C2×C4×C11C23×C414yes—
364C2×C4×C11C23×C414yes—
365C2×C4×C11C23×C414yes—
366C2×C4×C11C2×#4114yes—
367C2×Dic11—28no—
368C2×Dic11—28no—
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—44no—
383C2×Dic11—44no—
384C2×Dic11—44no—
385C2×Dic11C23×C414yes—
386C2×Dic11C2×#4114yes—
387D44—416no—
388D44—416no—
389D44—416no—
390C4×D11—416no—
391C4×D11—416no—
392C4×D11—416no—
393C23×D4—111no—
394C23×D4—111no—
395C23×D4—111no—
396C24×C4—111no—
397C24×C4—111no—
398C24×C4—111no—
399C2×#121—118no—
400C2×#121—1116no—
401C22×C4⋊C4—111no—
402C22×C4⋊C4C2×D1111yescharacteristic
403C22×C4⋊C4C2×D1111yescharacteristic
404C22×C22⋊C4—111no—
405C22×C22⋊C4—111no—
406C22×C22⋊C4—111no—
407C22×C22⋊C4—111no—
408C22×C22⋊C4—111no—
409C22×C22⋊C4—111no—
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×C42—111no—
417C22×C42—111no—
418C22×C42—111no—
419C22×C42C2×D1111yescharacteristic
420#390—118no—
421#390—118no—
422#388—118no—
423#388—118no—
424#387—118no—
425#387C2×D1118yescomplemented
426#386—118no—
427#386—118no—
428#386—118no—
429#386—118no—
430#381—118no—
431C4×C22⋊C4—118no—
432C4×C22⋊C4—118no—
433C4×C22⋊C4—118no—
434C2×#95—111no—
435C2×#95—111no—
436C2×#95—111no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95C2×D1111yescharacteristic
441C2×#95C2×D1111yescharacteristic
442C2×#95C2×D1111yescharacteristic
443C2×#95C2×D1111yescharacteristic
444C22×C11C4×#4114yes—
445C22×C11#51814yes—
446C22×C11#51814yes—
447C22×C11#53814yes—
448C22×C11#53814yes—
449C22×C11#54014yes—
450C22×C11#54014yes—
451C22×C11C24×C411yescharacteristic
452C22×C11C22×#4111yescharacteristic
453C22×C11C22×#4111yescharacteristic
454C22×C11C2×H(5,𝔽2)11yescharacteristic
455C22×C11C2×H(5,𝔽2)11yescharacteristic
456C22×C11C2×H(5,𝔽2)11yescharacteristic
457C22×C11C2×H(5,𝔽2)11yescharacteristic
458C2×D11—24no—
459C2×D11—24no—
460C2×D11—24no—
461C2×D11—24no—
462C2×D11—24no—
463C2×D11—24no—
464C2×D11—24no—
465C2×D11—24no—
466C2×D11—24no—
467C2×D11—416no—
468C2×D11—416no—
469C2×D11—416no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C4×C11—24no—
483C4×C11—24no—
484C4×C11—24no—
485C4×C11—24no—
486C4×C11—42no—
487C4×C11—42no—
488C4×C11—42no—
489Dic11—24no—
490Dic11—24no—
491Dic11—42no—
492Dic11—42no—
493Dic11—42no—
494C25—111no—
495C25—111no—
496C25—111no—
497C22×D4—118no—
498C22×D4—118no—
499C22×D4—118no—
500C22×D4—114no—
501C22×D4—114no—
502C22×D4—114no—
503C22×D4—442no—
504C22×D4—442no—
505C22×D4—442no—
506C22×D4—442no—
507C22×D4—442no—
508C22×D4—442no—
509C23×C4—111no—
510C23×C4—111no—
511C23×C4—118no—
512C23×C4—114no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—114no—
517C23×C4—114no—
518C23×C4—224no—
519C23×C4—224no—
520C23×C4—442no—
521C23×C4—442no—
522C23×C4—442no—
523C23×C4—442no—
524C23×C4—442no—
525C23×C4—442no—
526C23×C4C22×D1111yescharacteristic
527C23×C4C22×D1111yescharacteristic
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1111yescharacteristic
530C23×C4C22×D1111yescharacteristic
531C23×C4C22×D1111yescharacteristic
532C23×C4C22×D1111yescharacteristic
533#121—1164no—
534C2×C4⋊C4—42no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—442no—
537C2×C4⋊C4C4×D1118yescomplemented
538C2×C4⋊C4C22×D1114yes—
539C2×C4⋊C4C22×D1114yes—
540C2×C22⋊C4—118no—
541C2×C22⋊C4—118no—
542C2×C22⋊C4—114no—
543C2×C22⋊C4—114no—
544C2×C22⋊C4—114no—
545C2×C22⋊C4—114no—
546C2×C22⋊C4—114no—
547C2×C22⋊C4—114no—
548C2×C22⋊C4—114no—
549C2×C22⋊C4—114no—
550C2×C22⋊C4—114no—
551C2×C22⋊C4—114no—
552C2×C22⋊C4—114no—
553C2×C22⋊C4—114no—
554C2×C22⋊C4—224no—
555C2×C22⋊C4—224no—
556C2×C22⋊C4—224no—
557C2×C22⋊C4—224no—
558C2×C22⋊C4—442no—
559C2×C22⋊C4—442no—
560C2×C22⋊C4—442no—
561C2×C22⋊C4—442no—
562C2×C22⋊C4—442no—
563C2×C22⋊C4—442no—
564C2×C42—42no—
565C2×C42—114no—
566C2×C42—114no—
567C2×C42—114no—
568C2×C42—442no—
569C2×C42—442no—
570C2×C42—442no—
571C2×C42C22×D1114yes—
572#95—114no—
573#95—114no—
574#95—114no—
575#95—114no—
576#95—114no—
577#95—114no—
578#95C22×D1114yes—
579#95C22×D1114yes—
580#95C22×D1114yes—
581#95C22×D1114yes—
582C2×C11#233318yescomplemented
583C2×C11C2×C4×#4111yescharacteristic
584C2×C11C2×#51811yescharacteristic
585C2×C11C2×#51811yescharacteristic
586C2×C11C2×#53811yescharacteristic
587C2×C11C2×#53811yescharacteristic
588C2×C11C2×#54011yescharacteristic
589C2×C11C2×#54011yescharacteristic
590D11—44no—
591D11—44no—
592D11—44no—
593C24—114no—
594C24—114no—
595C24—114no—
596C24—112no—
597C24—112no—
598C24—112no—
599C24—222no—
600C24—222no—
601C24—222no—
602C24—222no—
603C24—222no—
604C24—222no—
605C24—222no—
606C24—222no—
607C24—222no—
608C24—222no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24—222no—
616C24—222no—
617C24C23×D1111yescharacteristic
618C2×D4—1116no—
619C2×D4—1116no—
620C2×D4—1116no—
621C2×D4—4416no—
622C2×D4—4416no—
623C2×D4—4416no—
624C2×D4—444no—
625C2×D4—444no—
626C2×D4—444no—
627C2×D4—444no—
628C2×D4—444no—
629C2×D4—444no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
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—22no—
646C22×C4—22no—
647C22×C4—114no—
648C22×C4—114no—
649C22×C4—112no—
650C22×C4—112no—
651C22×C4—1116no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—228no—
656C22×C4—222no—
657C22×C4—222no—
658C22×C4—222no—
659C22×C4—222no—
660C22×C4—222no—
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—228no—
670C22×C4—4416no—
671C22×C4—444no—
672C22×C4—444no—
673C22×C4—444no—
674C22×C4—444no—
675C22×C4—444no—
676C22×C4—444no—
677C22×C4—4416no—
678C22×C4—4416no—
679C22×C4C2×C4×D1114yes—
680C22×C4C2×C4×D1114yes—
681C22×C4C2×C4×D1114yes—
682C22×C4#434314yes—
683C22×C4C23×D1112yes—
684C22×C4C23×D1112yes—
685C22×C4C23×D1112yes—
686C22×C4C23×D1112yes—
687C22×C4C23×D1112yes—
688C22×C4C23×D1112yes—
689C22×C4C23×D1112yes—
690C4⋊C4—44no—
691C4⋊C4—444no—
692C4⋊C4C2×C4×D11116yescomplemented
693C22⋊C4—1116no—
694C22⋊C4—1116no—
695C22⋊C4—228no—
696C22⋊C4—228no—
697C22⋊C4—228no—
698C22⋊C4—228no—
699C22⋊C4—444no—
700C22⋊C4—444no—
701C22⋊C4—444no—
702C22⋊C4—444no—
703C22⋊C4—444no—
704C22⋊C4—444no—
705C42—44no—
706C42—444no—
707C42—444no—
708C42—444no—
709C11C2×#233311yescharacteristic, complemented, Sylow
710C23—114no—
711C23—114no—
712C23—114no—
713C23—228no—
714C23—228no—
715C23—228no—
716C23—228no—
717C23—228no—
718C23—228no—
719C23—228no—
720C23—228no—
721C23—228no—
722C23—222no—
723C23—222no—
724C23—222no—
725C23—222no—
726C23—222no—
727C23—222no—
728C23—222no—
729C23—222no—
730C23—222no—
731C23—222no—
732C23—222no—
733C23—222no—
734C23—222no—
735C23—222no—
736C23—222no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—444no—
741C23—444no—
742C23—444no—
743C23—444no—
744C23—444no—
745C23—444no—
746C23—444no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23—444no—
752C23C22×C4×D1112yes—
753C23#6703712yes—
754C23C2×#434312yes—
755C23#41×D1112yes—
756C23#6704212yes—
757C23#6704212yes—
758C23#6704212yes—
759C23C24×D1111yescharacteristic
760D4—4416no—
761D4—4416no—
762D4—4416no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
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—22no—
783C2×C4—22no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—114no—
788C2×C4—114no—
789C2×C4—228no—
790C2×C4—228no—
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—4416no—
805C2×C4—4416no—
806C2×C4—4416no—
807C2×C4—444no—
808C2×C4—444no—
809C2×C4—444no—
810C2×C4C22×C4×D1114yes—
811C2×C4C22×C4×D1114yes—
812C2×C4C22×C4×D1114yes—
813C2×C4C2×#434314yes—
814C22—224no—
815C22—224no—
816C22—224no—
817C22—224no—
818C22—224no—
819C22—224no—
820C22—224no—
821C22—224no—
822C22—224no—
823C22—4416no—
824C22—4416no—
825C22—4416no—
826C22—442no—
827C22—442no—
828C22—442no—
829C22—442no—
830C22—442no—
831C22—442no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—442no—
838C22#1062305214yes—
839C22#1062307614yes—
840C22C4×#434314yes—
841C22#1062317514yes—
842C22#1062319414yes—
843C22#1062322914yes—
844C22#1062323514yes—
845C22C23×C4×D1111yescharacteristic
846C22C2×#6703711yescharacteristic
847C22C22×#434311yescharacteristic
848C22C2×#41×D1111yescharacteristic
849C22C2×#6704211yescharacteristic
850C22C2×#6704211yescharacteristic
851C22C2×#6704211yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—24no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—224no—
860C4—224no—
861C4—442no—
862C4—442no—
863C4—442no—
864C2—444no—
865C2—444no—
866C2—444no—
867C2#1307138018yesdirect product factor
868C2C2×C4×#434311yescharacteristic
869C2C2×#1062307611yescharacteristic
870C2C2×#1062305211yescharacteristic
871C2C2×#1062323511yescharacteristic
872C2C2×#1062317511yescharacteristic
873C2C2×#1062319411yescharacteristic
874C2C2×#1062322911yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#387C2
socleC24×C11C24
prime radicalC22×#66948C2
cosocleC23×C11C25
hypercenterC2×#387D11
hypocenterC11C2×#2333
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #13071380C2direct (N × H)
3. C2×#10622552C2semidirect
4. C2×#10622601C2semidirect
5. C2×#10622283C2semidirect
6. C2×#10622603C2semidirect
7. C2×#10622594C2semidirect
8. C2×#10622278C2semidirect
9. C2×#10622278C2semidirect
10. C2×#10622278C2semidirect
11. C2×#10622278C2semidirect
12. C2×#10622277C2semidirect
13. C2×C4×(C2×D11)⋊C4C2semidirect
14. C2×#10622279C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#387C2semidirect
42. C2×#66948C4semidirect
44. C11×#387C22semidirect
55. #10622603C22semidirect
56. #10622601C22semidirect
57. #10622594C22semidirect
58. #10622552C22semidirect
59. C4×(C2×D11)⋊C4C22semidirect
60. #10622283C22semidirect
61. #10622279C22semidirect
62. #10622279C22semidirect
63. #10622278C22semidirect
64. #10622278C22semidirect
65. #10622278C22semidirect
66. #10622278C22semidirect
67. #10622277C22semidirect
90. C22×D44C2×C4semidirect
91. C22×D44C2×C4semidirect
103. C22×C4×D11C2×C4semidirect
108. C2×C11×C4⋊C4C2×C4semidirect
123. C2×(C2×D11)⋊C4C2×C4semidirect
124. C2×(C2×D11)⋊C4C2×C4semidirect
145. #66948C2×C4semidirect
240. C2×D44C22×C4semidirect
241. C2×D44C22×C4semidirect
253. C2×C4×D11C22×C4semidirect
255. C11×C4⋊C4C22×C4semidirect
267. (C2×D11)⋊C4C22×C4semidirect
268. (C2×D11)⋊C4C22×C4semidirect
280. C2×#387D11semidirect
425. #387C2×D11semidirect
537. C2×C4⋊C4C4×D11semidirect
582. C2×C11#2333semidirect
692. C4⋊C4C2×C4×D11semidirect
709. C11C2×#2333semidirect
867. C2#13071380direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669482
#130713802
C2×#106225522
C2×#106226012
C2×#106222832
C2×#106226032
C2×#106225942
C2×#106222782
C2×#106222772
C2×C4×(C2×D11)⋊C42
C2×#106222792
C2×C11×#3872
C2×#233311