Finite Group Databasebeta

← C2×#13071769 #14916366

Subgroups — C2×#13071769 #14916366

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×#66937C211yesmaximal, characteristic
2#13071769C2116yesmaximal, direct product factor
3C2×#10622552C211yesmaximal, characteristic, complemented
4C2×#10622570C211yesmaximal, characteristic, complemented
5C2×#10622283C211yesmaximal, characteristic, complemented
6C2×#10622268C211yesmaximal, characteristic, complemented
7C2×#10622546C211yesmaximal, characteristic, complemented
8C2×#10622278C211yesmaximal, characteristic, complemented
9C2×#10622571C211yesmaximal, characteristic, complemented
10C2×#10622571C211yesmaximal, characteristic, complemented
11C2×#10622569C211yesmaximal, characteristic, complemented
12C2×#10622563C211yesmaximal, characteristic, complemented
13C2×#10622602C211yesmaximal, characteristic, complemented
14C2×#10622277C211yesmaximal, characteristic, complemented
15C2×#10622600C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C42×C11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C2×#66937C4116yescomplemented
43C2×#66937C2218yes—
44C11×#388C2218yescomplemented
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#10622602C2218yescomplemented
56#10622600C2218yescomplemented
57#10622571C2218yescomplemented
58#10622571C2218yescomplemented
59#10622570C2218yescomplemented
60#10622569C2218yescomplemented
61#10622563C2218yescomplemented
62#10622552C2218yescomplemented
63#10622546C2218yescomplemented
64#10622283C2218yescomplemented
65#10622278C2218yescomplemented
66#10622277C2218yescomplemented
67#10622268C2218yescomplemented
68C25×C11C2311yescharacteristic
69C24×D11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11—42no—
78C22×C22⋊D11—42no—
79C22×C22⋊D11—42no—
80C22×C22⋊D11—42no—
81C22×C22⋊D11C2×C418yes—
82C22×C22⋊D11C2×C418yescomplemented
83C22×C22⋊D11C2314yes—
84C22×C22⋊D11C2314yes—
85C23×Dic11—42no—
86C23×Dic11—42no—
87C23×Dic11—42no—
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2314yes—
95C22×D44—42no—
96C22×D44—42no—
97C22×D44C2×C418yescomplemented
98C22×D44C2314yes—
99C22×C4×D11—42no—
100C22×C4×D11—42no—
101C22×C4×D11—42no—
102C22×C4×D11—42no—
103C22×C4×D11—42no—
104C22×C4×D11C2×C418yescomplemented
105C22×C4×D11C2314yes—
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⋊C4C2×C418yescomplemented
112C2×C11×C22⋊C4C2314yes—
113C2×C11×C22⋊C4C2314yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C42×C11—42no—
116C2×C42×C11C2314yes—
117C2×C22⋊Dic11—42no—
118C2×C22⋊Dic11C2314yes—
119C2×(C2×D11)⋊C4—42no—
120C2×(C2×D11)⋊C4—42no—
121C2×(C2×D11)⋊C4—42no—
122C2×(C2×D11)⋊C4—42no—
123C2×(C2×D11)⋊C4—42no—
124C2×(C2×D11)⋊C4—42no—
125C2×(C2×D11)⋊C4—42no—
126C2×(C2×D11)⋊C4C2×C418yescomplemented
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×C4⋊Dic11—42no—
136C2×C4⋊Dic11—42no—
137C2×C4⋊Dic11C2314yes—
138C2×C4⋊Dic11C2314yes—
139C2×Dic11⋊C4—42no—
140C2×Dic11⋊C4C2×C418yescomplemented
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×C4×Dic11—42no—
144C2×C4×Dic11C2314yes—
145#66937C2×C4164yescomplemented
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×C11C22×C414yes—
164C24×C11C2412yes—
165C24×C11C2411yescharacteristic
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×D11—22no—
177C23×D11—22no—
178C23×D11C22×C414yes—
179C23×D11C22×C414yes—
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×C11C22×C414yes—
199C22×C4×C11C22×C414yes—
200C22×C4×C11C2412yes—
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—44no—
231C22×Dic11—44no—
232C22×Dic11—44no—
233C22×Dic11—416no—
234C22×Dic11C22×C414yes—
235C22×Dic11C22×C414yes—
236C22×Dic11C2412yes—
237C22×Dic11C2412yes—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C2×D44—416no—
243C2×D44—44no—
244C2×D44—44no—
245C2×D44C22×C4116yescomplemented
246C2×C4×D11—416no—
247C2×C4×D11—44no—
248C2×C4×D11—44no—
249C2×C4×D11—44no—
250C2×C4×D11—44no—
251C2×C4×D11—44no—
252C2×C4×D11—416no—
253C2×C4×D11C22×C4116yescomplemented
254C11×C4⋊C4—44no—
255C11×C22⋊C4—44no—
256C11×C22⋊C4—44no—
257C11×C22⋊C4C22×C4116yescomplemented
258C42×C11—44no—
259C22⋊Dic11—44no—
260(C2×D11)⋊C4—44no—
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
268C4⋊Dic11—44no—
269C4⋊Dic11—44no—
270Dic11⋊C4—44no—
271Dic11⋊C4C22×C4116yescomplemented
272C4×Dic11—44no—
273C22×#121—111no—
274#2377—1116no—
275C2×#390—111no—
276C2×#390—111no—
277C2×#388—111no—
278C2×#388D1111yescharacteristic, complemented
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—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—44no—
299C23×C11—44no—
300C23×C11—44no—
301C23×C11—44no—
302C23×C11C23×C414yes—
303C23×C11C23×C412yes—
304C23×C11H(5,𝔽2)12yes—
305C23×C11H(5,𝔽2)12yes—
306C23×C11H(5,𝔽2)12yes—
307C23×C11H(5,𝔽2)12yes—
308C23×C11H(5,𝔽2)12yes—
309C23×C112−1+412yes—
310C23×C11C2511yescharacteristic
311C22×D11—28no—
312C22×D11—28no—
313C22×D11—28no—
314C22×D11—28no—
315C22×D11—28no—
316C22×D11—28no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—44no—
330C22×D11—44no—
331C22×D11—44no—
332C22×D11—44no—
333C22×D11—44no—
334C22×D11—44no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11C23×C414yes—
338C22×D11C23×C414yes—
339C2×C4×C11—28no—
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—22no—
356C2×C4×C11—22no—
357C2×C4×C11—44no—
358C2×C4×C11—44no—
359C2×C4×C11—44no—
360C2×C4×C11—44no—
361C2×C4×C11C23×C414yes—
362C2×C4×C11C23×C414yes—
363C22⋊D11—416no—
364C22⋊D11—416no—
365C2×Dic11—28no—
366C2×Dic11—28no—
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—44no—
385C2×Dic11—44no—
386C2×Dic11—44no—
387C2×Dic11—44no—
388C2×Dic11C23×C414yes—
389C2×Dic11C23×C414yes—
390D44—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⋊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⋊C4—111no—
415C22×C22⋊C4C2×D1111yescharacteristic
416C22×C22⋊C4C2×D1111yescharacteristic
417C22×C22⋊C4C2×D1111yescharacteristic
418C22×C42—111no—
419C22×C42C2×D1111yescharacteristic
420#390—118no—
421#390—118no—
422#388—118no—
423#388C2×D1118yescomplemented
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×#95C2×D1111yescharacteristic
443C2×#95C2×D1111yescharacteristic
444C22×C11—24no—
445C22×C11—24no—
446C22×C11—24no—
447C22×C11—416no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11#51814yes—
453C22×C11#51814yes—
454C22×C11#52014yes—
455C22×C11#56014yes—
456C22×C11#56014yes—
457C22×C11#56214yes—
458C22×C11#56214yes—
459C22×C11C24×C411yescharacteristic
460C22×C11C2×H(5,𝔽2)11yescharacteristic
461C22×C11C2×H(5,𝔽2)11yescharacteristic
462C22×C11C2×H(5,𝔽2)11yescharacteristic
463C22×C11C2×H(5,𝔽2)11yescharacteristic
464C22×C11C2×H(5,𝔽2)11yescharacteristic
465C22×C11C2×2−1+411yescharacteristic
466C2×D11—24no—
467C2×D11—24no—
468C2×D11—24no—
469C2×D11—24no—
470C2×D11—24no—
471C2×D11—24no—
472C2×D11—416no—
473C2×D11—416no—
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—42no—
485C4×C11—42no—
486C4×C11—42no—
487C4×C11—42no—
488Dic11—24no—
489Dic11—24no—
490Dic11—42no—
491Dic11—42no—
492Dic11—42no—
493Dic11—42no—
494C25—111no—
495C25—111no—
496C25C22×D1111yescharacteristic
497C22×D4—118no—
498C22×D4—118no—
499C22×D4—114no—
500C22×D4—114no—
501C22×D4—118no—
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—111no—
517C23×C4—114no—
518C23×C4—114no—
519C23×C4—442no—
520C23×C4—442no—
521C23×C4—442no—
522C23×C4—442no—
523C23×C4—442no—
524C23×C4—442no—
525C23×C4—442no—
526C23×C4—442no—
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—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—118no—
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—114no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—442no—
557C2×C22⋊C4—442no—
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⋊C4C4×D1118yescomplemented
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#95C22×D1114yes—
581#95C22×D1114yes—
582C2×C11—44no—
583C2×C11#237718yescomplemented
584C2×C11C2×#51811yescharacteristic
585C2×C11C2×#51811yescharacteristic
586C2×C11C2×#52011yescharacteristic
587C2×C11C2×#56011yescharacteristic
588C2×C11C2×#56011yescharacteristic
589C2×C11C2×#56211yescharacteristic
590C2×C11C2×#56211yescharacteristic
591D11—44no—
592D11—44no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—114no—
600C24—114no—
601C24—112no—
602C24—112no—
603C24—222no—
604C24—222no—
605C24—222no—
606C24—222no—
607C24—222no—
608C24—222no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24C2×C4×D1114yes—
616C24C23×D1112yes—
617C24C23×D1111yescharacteristic
618C2×D4—1116no—
619C2×D4—1116no—
620C2×D4—1116no—
621C2×D4—4416no—
622C2×D4—444no—
623C2×D4—444no—
624C2×D4—4416no—
625C2×D4—4416no—
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—114no—
647C22×C4—114no—
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—4416no—
672C22×C4—444no—
673C22×C4—444no—
674C22×C4—444no—
675C22×C4—444no—
676C22×C4—444no—
677C22×C4—4416no—
678C22×C4—444no—
679C22×C4—444no—
680C22×C4—444no—
681C22×C4—4416no—
682C22×C4C2×C4×D1114yes—
683C22×C4C2×C4×D1114yes—
684C22×C4C23×D1112yes—
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—1116no—
698C22⋊C4—444no—
699C22⋊C4—444no—
700C22⋊C4—444no—
701C22⋊C4—444no—
702C22⋊C4—444no—
703C22⋊C4—444no—
704C22⋊C4—444no—
705C22⋊C4—444no—
706C22⋊C4C2×C4×D11116yescomplemented
707C42—44no—
708C42—444no—
709C11C2×#237711yescharacteristic, complemented, Sylow
710C23—28no—
711C23—28no—
712C23—28no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—114no—
724C23—114no—
725C23—228no—
726C23—228no—
727C23—228no—
728C23—228no—
729C23—228no—
730C23—228no—
731C23—222no—
732C23—222no—
733C23—222no—
734C23—222no—
735C23—222no—
736C23—222no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—444no—
744C23—444no—
745C23—444no—
746C23—444no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23C22×C4×D1114yes—
752C23C22×C4×D1112yes—
753C23#6703712yes—
754C23#6703712yes—
755C23#6704212yes—
756C23#6704212yes—
757C23#6704212yes—
758C23#6704312yes—
759C23C24×D1111yescharacteristic
760D4—4416no—
761D4—4416no—
762D4—4416no—
763C2×C4—28no—
764C2×C4—28no—
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—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—114no—
786C2×C4—114no—
787C2×C4—228no—
788C2×C4—228no—
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—4416no—
806C2×C4—4416no—
807C2×C4—4416no—
808C2×C4—444no—
809C2×C4—444no—
810C2×C4—444no—
811C2×C4—444no—
812C2×C4C22×C4×D1114yes—
813C2×C4C22×C4×D1114yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—416no—
822C22—224no—
823C22—224no—
824C22—224no—
825C22—224no—
826C22—224no—
827C22—224no—
828C22—442no—
829C22—442no—
830C22—442no—
831C22—442no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—4416no—
837C22—4416no—
838C22#1062305414yes—
839C22#1062307614yes—
840C22#1062307614yes—
841C22#1062315114yes—
842C22#1062319814yes—
843C22#1062321514yes—
844C22#1062324214yes—
845C22C23×C4×D1111yescharacteristic
846C22C2×#6703711yescharacteristic
847C22C2×#6703711yescharacteristic
848C22C2×#6704211yescharacteristic
849C22C2×#6704211yescharacteristic
850C22C2×#6704211yescharacteristic
851C22C2×#6704311yescharacteristic
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—224no—
859C4—224no—
860C4—442no—
861C4—442no—
862C4—442no—
863C4—442no—
864C2—44no—
865C2—444no—
866C2—444no—
867C2#1307176918yesdirect product factor
868C2C2×#1062307611yescharacteristic
869C2C2×#1062307611yescharacteristic
870C2C2×#1062305411yescharacteristic
871C2C2×#1062315111yescharacteristic
872C2C2×#1062324211yescharacteristic
873C2C2×#1062321511yescharacteristic
874C2C2×#1062319811yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC22×#66937C2
cosocleC23×C11C25
hypercenterC2×#388D11
hypocenterC11C2×#2377
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #13071769C2direct (N × H)
3. C2×#10622552C2semidirect
4. C2×#10622570C2semidirect
5. C2×#10622283C2semidirect
6. C2×#10622268C2semidirect
7. C2×#10622546C2semidirect
8. C2×#10622278C2semidirect
9. C2×#10622571C2semidirect
10. C2×#10622571C2semidirect
11. C2×#10622569C2semidirect
12. C2×#10622563C2semidirect
13. C2×#10622602C2semidirect
14. C2×#10622277C2semidirect
15. C2×#10622600C2semidirect
16. C2×C11×#388C2semidirect
42. C2×#66937C4semidirect
44. C11×#388C22semidirect
55. #10622602C22semidirect
56. #10622600C22semidirect
57. #10622571C22semidirect
58. #10622571C22semidirect
59. #10622570C22semidirect
60. #10622569C22semidirect
61. #10622563C22semidirect
62. #10622552C22semidirect
63. #10622546C22semidirect
64. #10622283C22semidirect
65. #10622278C22semidirect
66. #10622277C22semidirect
67. #10622268C22semidirect
82. C22×C22⋊D11C2×C4semidirect
97. C22×D44C2×C4semidirect
104. C22×C4×D11C2×C4semidirect
111. C2×C11×C22⋊C4C2×C4semidirect
126. C2×(C2×D11)⋊C4C2×C4semidirect
140. C2×Dic11⋊C4C2×C4semidirect
145. #66937C2×C4semidirect
213. C2×C22⋊D11C22×C4semidirect
245. C2×D44C22×C4semidirect
253. C2×C4×D11C22×C4semidirect
257. C11×C22⋊C4C22×C4semidirect
267. (C2×D11)⋊C4C22×C4semidirect
271. Dic11⋊C4C22×C4semidirect
278. C2×#388D11semidirect
423. #388C2×D11semidirect
564. C2×C22⋊C4C4×D11semidirect
583. C2×C11#2377semidirect
706. C22⋊C4C2×C4×D11semidirect
709. C11C2×#2377semidirect
867. C2#13071769direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669372
#130717692
C2×#106225522
C2×#106225702
C2×#106222832
C2×#106222682
C2×#106225462
C2×#106222782
C2×#106225712
C2×#106225692
C2×#106225632
C2×#106226022
C2×#106222772
C2×#106226002
C2×C11×#3882
C2×#237711