Finite Group Databasebeta

← C2×#13072663 #14921458

Subgroups — C2×#13072663 #14921458

Order 2816.

3330 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×#66946C211yesmaximal, characteristic, complemented
2#13072663C2116yesmaximal, direct product factor
3C2×#10622605C211yesmaximal, characteristic, complemented
4C2×#10622604C211yesmaximal, characteristic, complemented
5C2×#10622574C211yesmaximal, characteristic, complemented
6C2×#10622573C211yesmaximal, characteristic
7C2×#10622570C211yesmaximal, characteristic, complemented
8C2×#10622553C211yesmaximal, characteristic, complemented
9C2×#10622557C211yesmaximal, characteristic, complemented
10C2×#10622594C211yesmaximal, characteristic, complemented
11C2×#10622591C211yesmaximal, characteristic, complemented
12C2×#10622569C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622600C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C22×C11×#126C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C2×C11×#126—28no—
23C2×C11×#126C2218yescomplemented
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C22×C42×C11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
41C22×C4⋊Dic11C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C2×#66946—28no—
47C2×#66946C2218yescomplemented
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#10622605C2218yescomplemented
57#10622604C2218yescomplemented
58#10622600C2218yescomplemented
59#10622594C2218yescomplemented
60#10622591C2218yescomplemented
61#10622574C2218yescomplemented
62#10622573C2218yes—
63#10622570C2218yescomplemented
64#10622569C2218yescomplemented
65#10622569C2218yescomplemented
66#10622557C2218yescomplemented
67#10622553C2218yescomplemented
68C4×(C2×D11)⋊C4C2218yescomplemented
69C25×C11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C22×C22⋊D11—24no—
79C22×C22⋊D11—24no—
80C22×C22⋊D11—24no—
81C22×C22⋊D11—42no—
82C22×C22⋊D11—42no—
83C22×C22⋊D11—42no—
84C22×C22⋊D11C2314yes—
85C22×C22⋊D11C2314yes—
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C22×D44—24no—
93C22×D44—24no—
94C22×D44—24no—
95C22×D44C2314yes—
96C22×C4×D11—24no—
97C22×C4×D11—24no—
98C22×C4×D11—24no—
99C22×C4×D11—24no—
100C22×C4×D11—42no—
101C22×C4×D11—42no—
102C22×C4×D11C2314yes—
103C22×C4×D11C2314yes—
104C11×#126—232no—
105C2×C11×C4⋊C4—24no—
106C2×C11×C4⋊C4—24no—
107C2×C11×C4⋊C4D418yescomplemented
108C2×C11×C4⋊C4C2314yes—
109C2×C11×C4⋊C4C2314yes—
110C2×C11×C4⋊C4C2314yes—
111C2×C11×C22⋊C4—24no—
112C2×C11×C22⋊C4—24no—
113C2×C11×C22⋊C4—24no—
114C2×C11×C22⋊C4C2314yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C42×C11—24no—
118C2×C42×C11C2314yes—
119C2×C22⋊Dic11—24no—
120C2×C22⋊Dic11—42no—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123C2×(C2×D11)⋊C4—24no—
124C2×(C2×D11)⋊C4—24no—
125C2×(C2×D11)⋊C4—24no—
126C2×(C2×D11)⋊C4—24no—
127C2×(C2×D11)⋊C4—24no—
128C2×(C2×D11)⋊C4—42no—
129C2×(C2×D11)⋊C4—42no—
130C2×(C2×D11)⋊C4—42no—
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×(C2×D11)⋊C4C2314yes—
138C2×(C2×D11)⋊C4C2314yes—
139C2×C4⋊Dic11—42no—
140C2×C4⋊Dic11C2314yes—
141C2×Dic11⋊C4—24no—
142C2×Dic11⋊C4—42no—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×C4×Dic11—24no—
146C2×C4×Dic11—42no—
147C2×C4×Dic11C2314yes—
148C2×C4×Dic11C2314yes—
149#66946—232no—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2467—111nomaximal, Sylow
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11—22no—
166C24×C11C2412yes—
167C24×C11C2411yescharacteristic
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×D11—22no—
179C23×D11—22no—
180C23×D11#4114yes—
181C23×D11#4114yes—
182C23×D11C2412yes—
183C23×D11C2412yes—
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×C11C2×D414yes—
200C22×C4×C11C2×D414yes—
201C22×C4×C11C2×D414yes—
202C22×C4×C11C2412yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C2×C22⋊D11—28no—
209C2×C22⋊D11—28no—
210C2×C22⋊D11—28no—
211C2×C22⋊D11—44no—
212C2×C22⋊D11—44no—
213C2×C22⋊D11—44no—
214C2×C22⋊D11—416no—
215C2×C22⋊D11—416no—
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#4114yes—
233C22×Dic11#4114yes—
234C22×Dic11C2412yes—
235C22×Dic11C2412yes—
236C22×Dic11C2412yes—
237C22×Dic11C2412yes—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240C2×D44—232no—
241C2×D44—28no—
242C2×D44—28no—
243C2×D44—28no—
244C2×C4×D11—28no—
245C2×C4×D11—28no—
246C2×C4×D11—28no—
247C2×C4×D11—28no—
248C2×C4×D11—44no—
249C2×C4×D11—44no—
250C2×C4×D11—416no—
251C2×C4×D11—416no—
252C11×C4⋊C4—28no—
253C11×C4⋊C4—28no—
254C11×C4⋊C4C2×D4116yescomplemented
255C11×C22⋊C4—28no—
256C11×C22⋊C4—28no—
257C11×C22⋊C4—28no—
258C42×C11—28no—
259C22⋊Dic11—28no—
260C22⋊Dic11—44no—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—28no—
263(C2×D11)⋊C4—28no—
264(C2×D11)⋊C4—28no—
265(C2×D11)⋊C4—28no—
266(C2×D11)⋊C4—44no—
267(C2×D11)⋊C4—44no—
268(C2×D11)⋊C4—44no—
269C4⋊Dic11—44no—
270Dic11⋊C4—28no—
271Dic11⋊C4—44no—
272C4×Dic11—28no—
273C4×Dic11—44no—
274C22×#126D1111yescharacteristic, complemented
275C22×C4×D4—111no—
276#2467—1116no—
277C2×#399—111no—
278C2×#394—111no—
279C2×#394—111no—
280C2×#392—111no—
281C2×#390—111no—
282C2×#388—111no—
283C2×#388—111no—
284C2×#387—111no—
285C2×#387—111no—
286C2×#386—111no—
287C2×#386—111no—
288C2×#380—111no—
289C2×C4×C22⋊C4—111no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—44no—
298C23×C11—44no—
299C23×C11—44no—
300C23×C11—44no—
301C23×C11—44no—
302C23×C11—44no—
303C23×C11—44no—
304C23×C11C22×D412yes—
305C23×C11C2×#4112yes—
306C23×C11C2×#4112yes—
307C23×C11C2×#4112yes—
308C23×C11C2×#4112yes—
309C23×C11H(5,𝔽2)12yes—
310C23×C11H(5,𝔽2)12yes—
311C23×C11C2511yescharacteristic
312C22×D11—28no—
313C22×D11—28no—
314C22×D11—28no—
315C22×D11—28no—
316C22×D11—28no—
317C22×D11—28no—
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—22no—
330C22×D11—44no—
331C22×D11—44no—
332C22×D11—44no—
333C22×D11—44no—
334C22×D11—44no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11C2×#4114yes—
339C22×D11C2×#4114yes—
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—44no—
359C2×C4×C11—44no—
360C2×C4×C11—44no—
361C2×C4×C11C22×D414yes—
362C2×C4×C11C22×D414yes—
363C2×C4×C11C22×D414yes—
364C22⋊D11—416no—
365C22⋊D11—416no—
366C2×Dic11—28no—
367C2×Dic11—28no—
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—44no—
385C2×Dic11—44no—
386C2×Dic11—44no—
387C2×Dic11—44no—
388C2×Dic11C2×#4114yes—
389C2×Dic11C2×#4114yes—
390D44—232no—
391C4×D11—416no—
392C4×D11—416no—
393C23×D4—111no—
394C23×D4—111no—
395C23×D4—111no—
396C24×C4—111no—
397C24×C4—111no—
398C2×#126—28no—
399C2×#126C2×D1118yescomplemented
400C2×C4×D4—118no—
401C2×C4×D4—228no—
402C22×C4⋊C4—111no—
403C22×C4⋊C4—111no—
404C22×C4⋊C4—111no—
405C22×C4⋊C4C2×D1111yescharacteristic
406C22×C4⋊C4C2×D1111yescharacteristic
407C22×C4⋊C4C2×D1111yescharacteristic
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×C22⋊C4—111no—
417C22×C22⋊C4—111no—
418C22×C22⋊C4C2×D1111yescharacteristic
419C22×C22⋊C4C2×D1111yescharacteristic
420C22×C22⋊C4C2×D1111yescharacteristic
421C22×C42—111no—
422C22×C42—111no—
423C22×C42C2×D1111yescharacteristic
424#399—118no—
425#394—118no—
426#394—118no—
427#392—118no—
428#390—118no—
429#388—118no—
430#388—118no—
431#387—118no—
432#387—118no—
433#386—118no—
434#386—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—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—88no—
453C22×C11#52514yes—
454C22×C11#52914yes—
455C22×C11#53814yes—
456C22×C11#54614yes—
457C22×C11#55014yes—
458C22×C11#55114yes—
459C22×C11#55314yes—
460C22×C11C23×D411yescharacteristic
461C22×C11C22×#4111yescharacteristic
462C22×C11C22×#4111yescharacteristic
463C22×C11C22×#4111yescharacteristic
464C22×C11C22×#4111yescharacteristic
465C22×C11C2×H(5,𝔽2)11yescharacteristic
466C22×C11C2×H(5,𝔽2)11yescharacteristic
467C2×D11—24no—
468C2×D11—24no—
469C2×D11—24no—
470C2×D11—24no—
471C2×D11—24no—
472C2×D11—24no—
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—416no—
482C2×D11—416no—
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—
494Dic11—42no—
495C25—111no—
496C25—111no—
497C25C22×D1111yescharacteristic
498C22×D4—114no—
499C22×D4—114no—
500C22×D4—114no—
501C22×D4—224no—
502C22×D4—224no—
503C22×D4—224no—
504C22×D4—224no—
505C22×D4—224no—
506C22×D4—224no—
507C22×D4—442no—
508C22×D4—442no—
509C22×D4—442no—
510C23×C4—111no—
511C23×C4—111no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—114no—
517C23×C4—114no—
518C23×C4—224no—
519C23×C4—224no—
520C23×C4—224no—
521C23×C4—224no—
522C23×C4—442no—
523C23×C4—442no—
524C23×C4C22×D1111yescharacteristic
525C23×C4C22×D1111yescharacteristic
526C23×C4C22×D1111yescharacteristic
527C23×C4C22×D1111yescharacteristic
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1111yescharacteristic
530#126—232no—
531C4×D4—2232no—
532C2×C4⋊C4—24no—
533C2×C4⋊C4—24no—
534C2×C4⋊C4—114no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—114no—
537C2×C4⋊C4—224no—
538C2×C4⋊C4—442no—
539C2×C4⋊C4—442no—
540C2×C4⋊C4C22⋊D1118yescomplemented
541C2×C4⋊C4C22×D1114yes—
542C2×C4⋊C4C22×D1114yes—
543C2×C4⋊C4C22×D1114yes—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
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—114no—
557C2×C22⋊C4—224no—
558C2×C22⋊C4—224no—
559C2×C22⋊C4—224no—
560C2×C22⋊C4—224no—
561C2×C22⋊C4—224no—
562C2×C22⋊C4—224no—
563C2×C22⋊C4—442no—
564C2×C22⋊C4—442no—
565C2×C22⋊C4—442no—
566C2×C22⋊C4—442no—
567C2×C22⋊C4C22×D1114yes—
568C2×C22⋊C4C22×D1114yes—
569C2×C22⋊C4C22×D1114yes—
570C2×C42—24no—
571C2×C42—114no—
572C2×C42—114no—
573C2×C42—224no—
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—
584C2×C11—82no—
585C2×C11#246718yescomplemented
586C2×C11C2×#52511yescharacteristic
587C2×C11C2×#52911yescharacteristic
588C2×C11C2×#53811yescharacteristic
589C2×C11C2×#54611yescharacteristic
590C2×C11C2×#55011yescharacteristic
591C2×C11C2×#55111yescharacteristic
592C2×C11C2×#55311yescharacteristic
593D11—44no—
594D11—44no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—114no—
603C24—114no—
604C24—112no—
605C24—112no—
606C24—222no—
607C24—222no—
608C24—222no—
609C24—222no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24—222no—
616C24—222no—
617C24—222no—
618C24C23×D1112yes—
619C24C23×D1111yescharacteristic
620C2×D4—228no—
621C2×D4—228no—
622C2×D4—2232no—
623C2×D4—228no—
624C2×D4—228no—
625C2×D4—228no—
626C2×D4—228no—
627C2×D4—444no—
628C2×D4—444no—
629C2×D4—444no—
630C2×D4—4416no—
631C2×D4—4416no—
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—112no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—228no—
656C22×C4—228no—
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—228no—
674C22×C4—228no—
675C22×C4—444no—
676C22×C4—444no—
677C22×C4—4416no—
678C22×C4—4416no—
679C22×C4C2×C22⋊D1114yes—
680C22×C4C2×C22⋊D1114yes—
681C22×C4C2×C22⋊D1114yes—
682C22×C4C23×D1112yes—
683C22×C4C23×D1112yes—
684C22×C4C23×D1112yes—
685C22×C4C23×D1112yes—
686C22×C4C23×D1112yes—
687C22×C4C23×D1112yes—
688C4⋊C4—28no—
689C4⋊C4—28no—
690C4⋊C4—228no—
691C4⋊C4—444no—
692C4⋊C4—444no—
693C4⋊C4C2×C22⋊D11116yescomplemented
694C22⋊C4—28no—
695C22⋊C4—28no—
696C22⋊C4—28no—
697C22⋊C4—228no—
698C22⋊C4—228no—
699C22⋊C4—228no—
700C22⋊C4—228no—
701C22⋊C4—228no—
702C22⋊C4—228no—
703C22⋊C4—444no—
704C22⋊C4—444no—
705C22⋊C4—444no—
706C22⋊C4—444no—
707C42—28no—
708C42—228no—
709C42—444no—
710C11C2×#246711yescharacteristic, complemented, Sylow
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—114no—
726C23—114no—
727C23—228no—
728C23—228no—
729C23—228no—
730C23—228no—
731C23—228no—
732C23—228no—
733C23—222no—
734C23—222no—
735C23—222no—
736C23—222no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—222no—
745C23—444no—
746C23—444no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23—444no—
752C23—444no—
753C23#41×D1112yes—
754C23#41×D1112yes—
755C23#41×D1112yes—
756C23#41×D1112yes—
757C23#6704212yes—
758C23#6704212yes—
759C23C22×C22⋊D1112yes—
760C23C24×D1111yescharacteristic
761D4—2232no—
762D4—4416no—
763D4—4416no—
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—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—444no—
808C2×C4—444no—
809C2×C4—444no—
810C2×C4—444no—
811C2×C4C22×C22⋊D1114yes—
812C2×C4C22×C22⋊D1114yes—
813C2×C4C22×C22⋊D1114yes—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—88no—
822C22—224no—
823C22—224no—
824C22—224no—
825C22—224no—
826C22—224no—
827C22—224no—
828C22—442no—
829C22—4416no—
830C22—4416no—
831C22—442no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—442no—
838C22#1062323514yes—
839C22#1062323614yes—
840C22#1062323714yes—
841C22#1062324014yes—
842C22#1062335914yes—
843C22#1062336014yes—
844C22#1062336514yes—
845C22C2×#41×D1111yescharacteristic
846C22C2×#41×D1111yescharacteristic
847C22C2×#41×D1111yescharacteristic
848C22C2×#41×D1111yescharacteristic
849C22C2×#6704211yescharacteristic
850C22C2×#6704211yescharacteristic
851C22C23×C22⋊D1111yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—224no—
859C4—224no—
860C4—442no—
861C4—442no—
862C4—442no—
863C4—442no—
864C2—82no—
865C2—444no—
866C2—444no—
867C2#1307266318yesdirect product factor
868C2C2×#1062335911yescharacteristic
869C2C2×#1062323711yescharacteristic
870C2C2×#1062323511yescharacteristic
871C2C2×#1062336011yescharacteristic
872C2C2×#1062336511yescharacteristic
873C2C2×#1062323611yescharacteristic
874C2C2×#1062324011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#126C2
socleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC22×#126D11
hypocenterC11C2×#2467
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. C22×#66946C2semidirect
2. #13072663C2direct (N × H)
3. C2×#10622605C2semidirect
4. C2×#10622604C2semidirect
5. C2×#10622574C2semidirect
7. C2×#10622570C2semidirect
8. C2×#10622553C2semidirect
9. C2×#10622557C2semidirect
10. C2×#10622594C2semidirect
11. C2×#10622591C2semidirect
12. C2×#10622569C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622600C2semidirect
15. C2×C4×(C2×D11)⋊C4C2semidirect
16. C22×C11×#126C2semidirect
23. C2×C11×#126C22semidirect
47. C2×#66946C22semidirect
56. #10622605C22semidirect
57. #10622604C22semidirect
58. #10622600C22semidirect
59. #10622594C22semidirect
60. #10622591C22semidirect
61. #10622574C22semidirect
63. #10622570C22semidirect
64. #10622569C22semidirect
65. #10622569C22semidirect
66. #10622557C22semidirect
67. #10622553C22semidirect
68. C4×(C2×D11)⋊C4C22semidirect
107. C2×C11×C4⋊C4D4semidirect
254. C11×C4⋊C4C2×D4semidirect
274. C22×#126D11semidirect
399. C2×#126C2×D11semidirect
540. C2×C4⋊C4C22⋊D11semidirect
585. C2×C11#2467semidirect
693. C4⋊C4C2×C22⋊D11semidirect
710. C11C2×#2467semidirect
867. C2#13072663direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669462
#130726632
C2×#106226052
C2×#106226042
C2×#106225742
C2×#106225732
C2×#106225702
C2×#106225532
C2×#106225572
C2×#106225942
C2×#106225912
C2×#106225692
C2×#106226002
C2×C4×(C2×D11)⋊C42
C22×C11×#1262
C2×#246711