Finite Group Databasebeta

← C2×#13071767 #14916364

Subgroups — C2×#13071767 #14916364

Order 2816.

3302 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×#66992C211yesmaximal, characteristic
2#13071767C2116yesmaximal, direct product factor
3C2×#10622570C211yesmaximal, characteristic, complemented
4C2×#10622558C211yesmaximal, characteristic, complemented
5C2×#10622553C211yesmaximal, characteristic, complemented
6C2×#10622546C211yesmaximal, characteristic, complemented
7C2×#10622591C211yesmaximal, characteristic, complemented
8C2×#10622833C211yesmaximal, characteristic, complemented
9C2×#10622571C211yesmaximal, characteristic, complemented
10C2×#10622569C211yesmaximal, characteristic, complemented
11C2×#10622569C211yesmaximal, characteristic, complemented
12C2×#10622559C211yesmaximal, characteristic, complemented
13C2×#10622602C211yesmaximal, characteristic, complemented
14C2×#10622556C211yesmaximal, characteristic, complemented
15C2×#10622555C211yesmaximal, characteristic, complemented
16C2×C11×#390C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C2×#66992C4116yescomplemented
34C2×#66992C2218yes—
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×(C2×D11)⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C11×#390C2218yescomplemented
45#10622833C2218yescomplemented
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
55C2×C11⋊#95C2211yescharacteristic
56#10622602C2218yescomplemented
57#10622591C2218yescomplemented
58#10622571C2218yescomplemented
59#10622570C2218yescomplemented
60#10622569C2218yescomplemented
61#10622569C2218yescomplemented
62#10622559C2218yescomplemented
63#10622558C2218yescomplemented
64#10622556C2218yescomplemented
65#10622555C2218yescomplemented
66#10622553C2218yescomplemented
67#10622546C2218yescomplemented
68C25×C11C2311yescharacteristic
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C22×D4×C11—42no—
72C22×D4×C11—42no—
73C22×D4×C11C2×C418yescomplemented
74C22×D4×C11C2314yes—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—42no—
81C22×C22⋊D11—42no—
82C22×C22⋊D11—42no—
83C22×C22⋊D11—42no—
84C22×C22⋊D11C2×C418yes—
85C22×C22⋊D11C2×C418yescomplemented
86C22×C22⋊D11C2314yes—
87C22×C22⋊D11C2314yes—
88C23×Dic11—42no—
89C23×Dic11—42no—
90C23×Dic11—42no—
91C23×Dic11—42no—
92C23×Dic11—42no—
93C23×Dic11C2×C418yescomplemented
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2314yes—
102C23×Dic11C2314yes—
103C22×C4×D11—42no—
104C22×C4×D11—42no—
105C22×C4×D11—42no—
106C22×C4×D11C2314yes—
107C2×C11×C4⋊C4—42no—
108C2×C11×C4⋊C4C2314yes—
109C2×C11×C22⋊C4—42no—
110C2×C11×C22⋊C4—42no—
111C2×C11×C22⋊C4—42no—
112C2×C11×C22⋊C4—42no—
113C2×C11×C22⋊C4C2314yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C42×C11—42no—
118C2×C42×C11C2314yes—
119C2×C22⋊Dic11—42no—
120C2×C22⋊Dic11—42no—
121C2×C22⋊Dic11—42no—
122C2×C22⋊Dic11C2×C418yescomplemented
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127#66992C2×C4164yescomplemented
128C2×(C2×D11)⋊C4—42no—
129C2×(C2×D11)⋊C4—42no—
130C2×(C2×D11)⋊C4—42no—
131C2×(C2×D11)⋊C4C2×C418yescomplemented
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×Dic11⋊C4—42no—
137C2×Dic11⋊C4—42no—
138C2×Dic11⋊C4—42no—
139C2×Dic11⋊C4C2×C418yescomplemented
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×C4×Dic11—42no—
145C2×C4×Dic11C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C2×#2377—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×C11C22×C414yes—
170C24×C11C22×C414yes—
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×D11C22×C414yes—
181C23×D11C2412yes—
182C2×D4×C11—416no—
183C2×D4×C11—44no—
184C2×D4×C11—44no—
185C2×D4×C11C22×C4116yescomplemented
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×C11—22no—
200C22×C4×C11C22×C414yes—
201C22×C4×C11C2412yes—
202C22×C4×C11C2412yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C2×C22⋊D11—416no—
207C2×C22⋊D11—416no—
208C2×C22⋊D11—44no—
209C2×C22⋊D11—44no—
210C2×C22⋊D11—44no—
211C2×C22⋊D11—44no—
212C2×C22⋊D11C22×C4116yes—
213C2×C22⋊D11C22×C4116yescomplemented
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×Dic11—22no—
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—416no—
233C22×Dic11—44no—
234C22×Dic11—44no—
235C22×Dic11—44no—
236C22×Dic11—44no—
237C22×Dic11—44no—
238C22×Dic11—416no—
239C22×Dic11C22×C414yes—
240C22×Dic11C22×C414yes—
241C22×Dic11C22×C414yes—
242C22×Dic11C22×C4116yescomplemented
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C22×Dic11C2412yes—
249C22×Dic11C2412yes—
250C2×C4×D11—44no—
251C2×C4×D11—44no—
252C2×C4×D11—44no—
253C2×C4×D11—416no—
254C11×C4⋊C4—44no—
255C11×C22⋊C4—44no—
256C11×C22⋊C4—44no—
257C11×C22⋊C4—44no—
258C11×C22⋊C4—44no—
259C42×C11—44no—
260C22⋊Dic11—44no—
261C22⋊Dic11—44no—
262C22⋊Dic11—44no—
263C22⋊Dic11C22×C4116yescomplemented
264(C2×D11)⋊C4—44no—
265(C2×D11)⋊C4—44no—
266(C2×D11)⋊C4—44no—
267(C2×D11)⋊C4C22×C4116yescomplemented
268Dic11⋊C4—44no—
269Dic11⋊C4—44no—
270Dic11⋊C4—44no—
271Dic11⋊C4C22×C4116yescomplemented
272C4×Dic11—44no—
273C22×#121—111no—
274#2377—1116no—
275C2×#390—111no—
276C2×#390D1111yescharacteristic, complemented
277C2×#388—111no—
278C2×#388—111no—
279C2×#387—111no—
280C2×#387—111no—
281C2×#386—111no—
282C2×#386—111no—
283C2×#386—111no—
284C2×#386—111no—
285C2×#385—111no—
286C2×#385—111no—
287C2×#381—111no—
288C2×#380—111no—
289C23×C11—28no—
290C23×C11—28no—
291C23×C11—28no—
292C23×C11—28no—
293C23×C11—28no—
294C23×C11—28no—
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—44no—
308C23×C11—44no—
309C23×C11—44no—
310C23×C11—44no—
311C23×C11—44no—
312C23×C11—44no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11C23×C414yes—
316C23×C11C23×C414yes—
317C23×C11C23×C412yes—
318C23×C11H(5,𝔽2)12yes—
319C23×C11H(5,𝔽2)12yes—
320C23×C11H(5,𝔽2)12yes—
321C23×C11H(5,𝔽2)12yes—
322C23×C11H(5,𝔽2)12yes—
323C23×C112−1+412yes—
324C23×C11C2511yescharacteristic
325C22×D11—28no—
326C22×D11—28no—
327C22×D11—28no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—44no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11C23×C414yes—
339D4×C11—416no—
340C2×C4×C11—28no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
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—44no—
356C2×C4×C11—44no—
357C2×C4×C11—44no—
358C2×C4×C11—44no—
359C2×C4×C11C23×C414yes—
360C22⋊D11—416no—
361C22⋊D11—416no—
362C2×Dic11—28no—
363C2×Dic11—28no—
364C2×Dic11—28no—
365C2×Dic11—22no—
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—416no—
384C2×Dic11—416no—
385C2×Dic11—44no—
386C2×Dic11—44no—
387C2×Dic11—44no—
388C2×Dic11—44no—
389C2×Dic11C23×C414yes—
390C2×Dic11C23×C414yes—
391C2×Dic11C23×C414yes—
392C4×D11—416no—
393C23×D4—111no—
394C23×D4—111no—
395C23×D4C2×D1111yescharacteristic
396C24×C4—111no—
397C24×C4—111no—
398C24×C4—111no—
399C2×#121—118no—
400C2×#121—1116no—
401C22×C4⋊C4—111no—
402C22×C4⋊C4—111no—
403C22×C4⋊C4—111no—
404C22×C4⋊C4—111no—
405C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic
415C22×C22⋊C4C2×D1111yescharacteristic
416C22×C22⋊C4C2×D1111yescharacteristic
417C22×C22⋊C4C2×D1111yescharacteristic
418C22×C42—111no—
419C22×C42C2×D1111yescharacteristic
420#390—118no—
421#390C2×D1118yescomplemented
422#388—118no—
423#388—118no—
424#387—118no—
425#387—118no—
426#386—118no—
427#386—118no—
428#386—118no—
429#386—118no—
430#385—118no—
431#385—118no—
432#381—118no—
433#380—118no—
434C2×#95—111no—
435C2×#95—111no—
436C2×#95—111no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95—111no—
444C22×C11—24no—
445C22×C11—24no—
446C22×C11—24no—
447C22×C11—24no—
448C22×C11—24no—
449C22×C11—24no—
450C22×C11—416no—
451C22×C11—416no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11#51814yes—
461C22×C11#51814yes—
462C22×C11#52014yes—
463C22×C11#56014yes—
464C22×C11#56014yes—
465C22×C11#56214yes—
466C22×C11#56214yes—
467C22×C11C24×C411yescharacteristic
468C22×C11C2×H(5,𝔽2)11yescharacteristic
469C22×C11C2×H(5,𝔽2)11yescharacteristic
470C22×C11C2×H(5,𝔽2)11yescharacteristic
471C22×C11C2×H(5,𝔽2)11yescharacteristic
472C22×C11C2×H(5,𝔽2)11yescharacteristic
473C22×C11C2×2−1+411yescharacteristic
474C2×D11—24no—
475C2×D11—24no—
476C2×D11—24no—
477C2×D11—416no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C4×C11—24no—
483C4×C11—42no—
484C4×C11—42no—
485C4×C11—42no—
486C4×C11—42no—
487Dic11—24no—
488Dic11—24no—
489Dic11—24no—
490Dic11—42no—
491Dic11—42no—
492Dic11—42no—
493Dic11—42no—
494C25—111no—
495C25C22×D1111yescharacteristic
496C25C22×D1111yescharacteristic
497C22×D4—42no—
498C22×D4—42no—
499C22×D4—118no—
500C22×D4—118no—
501C22×D4—114no—
502C22×D4—114no—
503C22×D4—442no—
504C22×D4—442no—
505C22×D4—442no—
506C22×D4—442no—
507C22×D4C4×D1118yescomplemented
508C22×D4C22×D1114yes—
509C23×C4—111no—
510C23×C4—111no—
511C23×C4—111no—
512C23×C4—118no—
513C23×C4—114no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—111no—
517C23×C4—111no—
518C23×C4—114no—
519C23×C4—114no—
520C23×C4—442no—
521C23×C4—442no—
522C23×C4—442no—
523C23×C4—442no—
524C23×C4—442no—
525C23×C4—442no—
526C23×C4—442no—
527C23×C4—442no—
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—118no—
536C2×C4⋊C4—114no—
537C2×C4⋊C4—114no—
538C2×C4⋊C4—114no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—442no—
541C2×C4⋊C4—442no—
542C2×C4⋊C4—442no—
543C2×C4⋊C4C22×D1114yes—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—118no—
549C2×C22⋊C4—114no—
550C2×C22⋊C4—118no—
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—442no—
559C2×C22⋊C4—442no—
560C2×C22⋊C4—442no—
561C2×C22⋊C4—442no—
562C2×C22⋊C4—442no—
563C2×C22⋊C4—442no—
564C2×C22⋊C4C22×D1114yes—
565C2×C22⋊C4C22×D1114yes—
566C2×C22⋊C4C22×D1114yes—
567C2×C22⋊C4C22×D1114yes—
568C2×C42—42no—
569C2×C42—114no—
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#95—114no—
579#95—114no—
580#95—114no—
581#95—114no—
582C2×C11—44no—
583C2×C11—44no—
584C2×C11#237718yescomplemented
585C2×C11C2×#51811yescharacteristic
586C2×C11C2×#51811yescharacteristic
587C2×C11C2×#52011yescharacteristic
588C2×C11C2×#56011yescharacteristic
589C2×C11C2×#56011yescharacteristic
590C2×C11C2×#56211yescharacteristic
591C2×C11C2×#56211yescharacteristic
592D11—44no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—114no—
606C24—112no—
607C24—222no—
608C24—222no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24C2×C4×D1114yes—
614C24C2×C4×D1114yes—
615C24C23×D1112yes—
616C24C23×D1112yes—
617C24C23×D1111yescharacteristic
618C2×D4—44no—
619C2×D4—44no—
620C2×D4—416no—
621C2×D4—1116no—
622C2×D4—1116no—
623C2×D4—4416no—
624C2×D4—4416no—
625C2×D4—444no—
626C2×D4—444no—
627C2×D4—444no—
628C2×D4—444no—
629C2×D4C2×C4×D11116yescomplemented
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—114no—
645C22×C4—114no—
646C22×C4—114no—
647C22×C4—112no—
648C22×C4—112no—
649C22×C4—112no—
650C22×C4—1116no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—222no—
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—222no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—444no—
674C22×C4—444no—
675C22×C4—444no—
676C22×C4—4416no—
677C22×C4—4416no—
678C22×C4—444no—
679C22×C4—444no—
680C22×C4—444no—
681C22×C4—444no—
682C22×C4—444no—
683C22×C4—4416no—
684C22×C4C2×C4×D1114yes—
685C22×C4C23×D1112yes—
686C22×C4C23×D1112yes—
687C22×C4C23×D1112yes—
688C22×C4C23×D1112yes—
689C22×C4C23×D1112yes—
690C4⋊C4—44no—
691C4⋊C4—1116no—
692C4⋊C4—444no—
693C4⋊C4—444no—
694C4⋊C4—444no—
695C22⋊C4—44no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—44no—
699C22⋊C4—1116no—
700C22⋊C4—1116no—
701C22⋊C4—444no—
702C22⋊C4—444no—
703C22⋊C4—444no—
704C22⋊C4—444no—
705C22⋊C4—444no—
706C22⋊C4—444no—
707C42—44no—
708C42—444no—
709C11C2×#237711yescharacteristic, complemented, Sylow
710C23—28no—
711C23—28no—
712C23—28no—
713C23—28no—
714C23—28no—
715C23—28no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—114no—
737C23—228no—
738C23—228no—
739C23—228no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—222no—
745C23—222no—
746C23—444no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23C22×C4×D1114yes—
751C23C22×C4×D1114yes—
752C23C22×C4×D1112yes—
753C23#6703712yes—
754C23#6703712yes—
755C23#6703712yes—
756C23#6703712yes—
757C23#6704212yes—
758C23#6704312yes—
759C23C24×D1111yescharacteristic
760D4—416no—
761D4—4416no—
762D4—4416no—
763C2×C4—28no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
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—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—114no—
783C2×C4—114no—
784C2×C4—114no—
785C2×C4—228no—
786C2×C4—228no—
787C2×C4—228no—
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—4416no—
808C2×C4—4416no—
809C2×C4—444no—
810C2×C4—444no—
811C2×C4—444no—
812C2×C4—444no—
813C2×C4C22×C4×D1114yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—416no—
829C22—416no—
830C22—224no—
831C22—224no—
832C22—224no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—4416no—
838C22#1062301714yes—
839C22#1062307614yes—
840C22#1062307714yes—
841C22#1062315114yes—
842C22#1062315214yes—
843C22#1062321514yes—
844C22#1062325114yes—
845C22C23×C4×D1111yescharacteristic
846C22C2×#6703711yescharacteristic
847C22C2×#6703711yescharacteristic
848C22C2×#6703711yescharacteristic
849C22C2×#6703711yescharacteristic
850C22C2×#6704211yescharacteristic
851C22C2×#6704311yescharacteristic
852C4—24no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—224no—
858C4—224no—
859C4—224no—
860C4—442no—
861C4—442no—
862C4—442no—
863C4—442no—
864C2—44no—
865C2—44no—
866C2—444no—
867C2#1307176718yesdirect product factor
868C2C2×#1062307611yescharacteristic
869C2C2×#1062301711yescharacteristic
870C2C2×#1062307711yescharacteristic
871C2C2×#1062325111yescharacteristic
872C2C2×#1062315111yescharacteristic
873C2C2×#1062321511yescharacteristic
874C2C2×#1062315211yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#390C2
socleC24×C11C24
prime radicalC22×#66992C2
cosocleC23×C11C25
hypercenterC2×#390D11
hypocenterC11C2×#2377
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. #13071767C2direct (N × H)
3. C2×#10622570C2semidirect
4. C2×#10622558C2semidirect
5. C2×#10622553C2semidirect
6. C2×#10622546C2semidirect
7. C2×#10622591C2semidirect
8. C2×#10622833C2semidirect
9. C2×#10622571C2semidirect
10. C2×#10622569C2semidirect
11. C2×#10622569C2semidirect
12. C2×#10622559C2semidirect
13. C2×#10622602C2semidirect
14. C2×#10622556C2semidirect
15. C2×#10622555C2semidirect
16. C2×C11×#390C2semidirect
33. C2×#66992C4semidirect
44. C11×#390C22semidirect
45. #10622833C22semidirect
56. #10622602C22semidirect
57. #10622591C22semidirect
58. #10622571C22semidirect
59. #10622570C22semidirect
60. #10622569C22semidirect
61. #10622569C22semidirect
62. #10622559C22semidirect
63. #10622558C22semidirect
64. #10622556C22semidirect
65. #10622555C22semidirect
66. #10622553C22semidirect
67. #10622546C22semidirect
73. C22×D4×C11C2×C4semidirect
85. C22×C22⋊D11C2×C4semidirect
93. C23×Dic11C2×C4semidirect
122. C2×C22⋊Dic11C2×C4semidirect
127. #66992C2×C4semidirect
131. C2×(C2×D11)⋊C4C2×C4semidirect
139. C2×Dic11⋊C4C2×C4semidirect
185. C2×D4×C11C22×C4semidirect
213. C2×C22⋊D11C22×C4semidirect
242. C22×Dic11C22×C4semidirect
263. C22⋊Dic11C22×C4semidirect
267. (C2×D11)⋊C4C22×C4semidirect
271. Dic11⋊C4C22×C4semidirect
276. C2×#390D11semidirect
421. #390C2×D11semidirect
507. C22×D4C4×D11semidirect
584. C2×C11#2377semidirect
629. C2×D4C2×C4×D11semidirect
709. C11C2×#2377semidirect
867. C2#13071767direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669922
#130717672
C2×#106225702
C2×#106225582
C2×#106225532
C2×#106225462
C2×#106225912
C2×#106228332
C2×#106225712
C2×#106225692
C2×#106225592
C2×#106226022
C2×#106225562
C2×#106225552
C2×C11×#3902
C2×#237711