Finite Group Databasebeta

← C2×#13072805 #14922137

Subgroups — C2×#13072805 #14922137

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×#66948C211yesmaximal, characteristic
2C22×#66945C211yesmaximal, characteristic, complemented
3#13072805C2116yesmaximal, direct product factor
4C2×#10622285C211yesmaximal, characteristic, complemented
5C2×#10622604C211yesmaximal, characteristic, complemented
6C2×#10622604C211yesmaximal, characteristic, complemented
7C2×#10622601C211yesmaximal, characteristic, complemented
8C2×#10622283C211yesmaximal, characteristic, complemented
9C2×#10622603C211yesmaximal, characteristic, complemented
10C2×#10622603C211yesmaximal, characteristic, complemented
11C2×#10622591C211yesmaximal, characteristic, complemented
12C2×#10622278C211yesmaximal, characteristic, complemented
13C2×#10622278C211yesmaximal, characteristic, complemented
14C2×#10622281C211yesmaximal, characteristic, complemented
15C2×#10622279C211yesmaximal, characteristic, complemented
16C2×C11×#398C211yesmaximal, characteristic, complemented
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C22×C4×Dic11C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C2×#66948—28no—
45C2×#66948C2218yes—
46C2×#66945—28no—
47C2×#66945C2218yescomplemented
48C11×#398C2218yescomplemented
49C2×C11×#95C2211yescharacteristic
50C2×C11×#95C2211yescharacteristic
51C2×C11×#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622604C2218yescomplemented
58#10622604C2218yescomplemented
59#10622603C2218yescomplemented
60#10622603C2218yescomplemented
61#10622601C2218yescomplemented
62#10622591C2218yescomplemented
63#10622285C2218yescomplemented
64#10622283C2218yescomplemented
65#10622281C2218yescomplemented
66#10622279C2218yescomplemented
67#10622278C2218yescomplemented
68#10622278C2218yescomplemented
69C24×D11C2311yescharacteristic
70C24×D11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C22×D44—24no—
85C22×D44—24no—
86C22×D44—24no—
87C22×D44—24no—
88C22×D44—24no—
89C22×D44—24no—
90C22×D44—42no—
91C22×D44—42no—
92C22×D44—42no—
93C22×D44C2314yes—
94C22×D44C2314yes—
95C22×D44C2314yes—
96C22×C4×D11—24no—
97C22×C4×D11—24no—
98C22×C4×D11—24no—
99C22×C4×D11—24no—
100C22×C4×D11—24no—
101C22×C4×D11—42no—
102C22×C4×D11C2314yes—
103C22×C4×D11C2314yes—
104C2×C11×C4⋊C4—24no—
105C2×C11×C4⋊C4—24no—
106C2×C11×C4⋊C4—42no—
107C2×C11×C4⋊C4—42no—
108C2×C11×C4⋊C4C2314yes—
109C2×C11×C4⋊C4C2314yes—
110C2×C11×C4⋊C4C2314yes—
111C2×C11×C4⋊C4C2314yes—
112C2×(C2×D11)⋊C4—24no—
113C2×(C2×D11)⋊C4—24no—
114C2×(C2×D11)⋊C4—24no—
115C2×(C2×D11)⋊C4—24no—
116C2×(C2×D11)⋊C4—24no—
117C2×(C2×D11)⋊C4—24no—
118C2×(C2×D11)⋊C4—24no—
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)⋊C4D418yes—
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×(C2×D11)⋊C4C2314yes—
138C2×C4⋊Dic11—24no—
139C2×C4⋊Dic11C2314yes—
140C2×Dic11⋊C4—24no—
141C2×Dic11⋊C4C2314yes—
142C2×C4×Dic11—24no—
143C2×C4×Dic11—24no—
144C2×C4×Dic11—42no—
145C2×C4×Dic11C2314yes—
146C2×C4×Dic11C2314yes—
147C2×C4×Dic11C2314yes—
148#66948—232no—
149#66945—232no—
150C11×#95C2314yes—
151C11×#95C2314yes—
152C11×#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2476—111nomaximal, Sylow
159C24×C11C2411yescharacteristic
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×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11C2×D414yes—
180C23×D11#4114yes—
181C23×D11C2412yes—
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×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11C2×D414yes—
203C22×C4×C11#4114yes—
204C22×C4×C11#4114yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
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×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11C2×D414yes—
226C22×Dic11#4114yes—
227C22×Dic11C2412yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C22×Dic11C2412yes—
231C22×Dic11C2412yes—
232C2×D44—28no—
233C2×D44—28no—
234C2×D44—28no—
235C2×D44—28no—
236C2×D44—28no—
237C2×D44—28no—
238C2×D44—44no—
239C2×D44—44no—
240C2×D44—44no—
241C2×D44—416no—
242C2×D44—416no—
243C2×D44—416no—
244C2×C4×D11—232no—
245C2×C4×D11—28no—
246C2×C4×D11—28no—
247C2×C4×D11—28no—
248C2×C4×D11—28no—
249C2×C4×D11—28no—
250C2×C4×D11—44no—
251C2×C4×D11—416no—
252C11×C4⋊C4—28no—
253C11×C4⋊C4—28no—
254C11×C4⋊C4—44no—
255C11×C4⋊C4—44no—
256(C2×D11)⋊C4—28no—
257(C2×D11)⋊C4—28no—
258(C2×D11)⋊C4—28no—
259(C2×D11)⋊C4—28no—
260(C2×D11)⋊C4—28no—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—28no—
263(C2×D11)⋊C4—44no—
264(C2×D11)⋊C4—44no—
265(C2×D11)⋊C4—44no—
266(C2×D11)⋊C4—44no—
267(C2×D11)⋊C4—44no—
268(C2×D11)⋊C4C2×D4116yes—
269C4⋊Dic11—28no—
270Dic11⋊C4—28no—
271C4×Dic11—28no—
272C4×Dic11—28no—
273C4×Dic11—44no—
274C22×#121—111no—
275C22×#117—111no—
276#2476—1116no—
277C2×#398D1111yescharacteristic, complemented
278C2×#394—111no—
279C2×#394—111no—
280C2×#394—111no—
281C2×#390—111no—
282C2×#388—111no—
283C2×#388—111no—
284C2×#388—111no—
285C2×#387—111no—
286C2×#386—111no—
287C2×#386—111no—
288C2×#385—111no—
289C2×C4×C22⋊C4—111no—
290C23×C11C22×D412yes—
291C23×C11C2×#4112yes—
292C23×C11C2×#4112yes—
293C23×C11C2×#4112yes—
294C23×C11C2×#4112yes—
295C23×C11H(5,𝔽2)12yes—
296C23×C11H(5,𝔽2)12yes—
297C23×C11C2511yescharacteristic
298C22×D11—28no—
299C22×D11—28no—
300C22×D11—28no—
301C22×D11—28no—
302C22×D11—28no—
303C22×D11—28no—
304C22×D11—22no—
305C22×D11—22no—
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—44no—
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×D11—44no—
337C22×D11—44no—
338C22×D11C22×D414yes—
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—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—44no—
362C2×C4×C11—44no—
363C2×C4×C11—44no—
364C2×C4×C11—44no—
365C2×C4×C11C22×D414yes—
366C2×C4×C11C2×#4114yes—
367C2×C4×C11C2×#4114yes—
368C2×Dic11—28no—
369C2×Dic11—28no—
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—44no—
384C2×Dic11—44no—
385C2×Dic11—44no—
386C2×Dic11C22×D414yes—
387C2×Dic11C2×#4114yes—
388D44—416no—
389D44—416no—
390D44—416no—
391C4×D11—232no—
392C4×D11—416no—
393C23×D4—111no—
394C23×D4—111no—
395C23×D4—111no—
396C24×C4—111no—
397C24×C4—111no—
398C2×#121—118no—
399C2×#121—228no—
400C2×#117—118no—
401C2×#117—228no—
402C22×C4⋊C4—111no—
403C22×C4⋊C4—111no—
404C22×C4⋊C4C2×D1111yescharacteristic
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⋊C4—111no—
419C22×C22⋊C4—111no—
420C22×C22⋊C4—111no—
421C22×C42—111no—
422C22×C42—111no—
423C22×C42—111no—
424#398C2×D1118yescomplemented
425#394—118no—
426#394—118no—
427#394—118no—
428#390—118no—
429#388—118no—
430#388—118no—
431#388—118no—
432#387—118no—
433#386—118no—
434#386—118no—
435#385—118no—
436C4×C22⋊C4—118no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95C2×D1111yescharacteristic
443C2×#95C2×D1111yescharacteristic
444C2×#95C2×D1111yescharacteristic
445C22×C11#52514yes—
446C22×C11#52914yes—
447C22×C11#54014yes—
448C22×C11#54614yes—
449C22×C11#54614yes—
450C22×C11#55314yes—
451C22×C11#55514yes—
452C22×C11C23×D411yescharacteristic
453C22×C11C22×#4111yescharacteristic
454C22×C11C22×#4111yescharacteristic
455C22×C11C22×#4111yescharacteristic
456C22×C11C22×#4111yescharacteristic
457C22×C11C2×H(5,𝔽2)11yescharacteristic
458C22×C11C2×H(5,𝔽2)11yescharacteristic
459C2×D11—24no—
460C2×D11—24no—
461C2×D11—24no—
462C2×D11—24no—
463C2×D11—24no—
464C2×D11—24no—
465C2×D11—42no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—416no—
474C2×D11—416no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—88no—
483C4×C11—24no—
484C4×C11—24no—
485C4×C11—24no—
486C4×C11—42no—
487C4×C11—42no—
488C4×C11—42no—
489C4×C11—42no—
490Dic11—24no—
491Dic11—24no—
492Dic11—42no—
493Dic11—42no—
494Dic11—42no—
495C25—111no—
496C25—111no—
497C25—111no—
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—114no—
516C23×C4—114no—
517C23×C4—224no—
518C23×C4—224no—
519C23×C4—224no—
520C23×C4—224no—
521C23×C4—224no—
522C23×C4—442no—
523C23×C4C22×D1111yescharacteristic
524C23×C4C22×D1111yescharacteristic
525C23×C4C22×D1111yescharacteristic
526C23×C4C22×D1111yescharacteristic
527C23×C4C22×D1111yescharacteristic
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1111yescharacteristic
530#121—2232no—
531#117—2232no—
532C2×C4⋊C4—24no—
533C2×C4⋊C4—24no—
534C2×C4⋊C4—42no—
535C2×C4⋊C4—42no—
536C2×C4⋊C4—114no—
537C2×C4⋊C4—114no—
538C2×C4⋊C4—224no—
539C2×C4⋊C4—224no—
540C2×C4⋊C4C22×D1114yes—
541C2×C4⋊C4C22×D1114yes—
542C2×C4⋊C4C22×D1114yes—
543C2×C4⋊C4C22×D1114yes—
544C2×C22⋊C4—118no—
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—114no—
555C2×C22⋊C4—114no—
556C2×C22⋊C4—114no—
557C2×C22⋊C4—114no—
558C2×C22⋊C4—224no—
559C2×C22⋊C4—224no—
560C2×C22⋊C4—224no—
561C2×C22⋊C4—224no—
562C2×C22⋊C4—224no—
563C2×C22⋊C4—224no—
564C2×C22⋊C4—224no—
565C2×C22⋊C4—442no—
566C2×C22⋊C4—442no—
567C2×C22⋊C4—442no—
568C2×C22⋊C4—442no—
569C2×C22⋊C4—442no—
570C2×C42—114no—
571C2×C42—114no—
572C2×C42—114no—
573C2×C42—224no—
574C2×C42—224no—
575C2×C42—442no—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95—114no—
581#95C22×D1114yes—
582#95C22×D1114yes—
583#95C22×D1114yes—
584C2×C11#247618yescomplemented
585C2×C11C2×#52511yescharacteristic
586C2×C11C2×#52911yescharacteristic
587C2×C11C2×#54011yescharacteristic
588C2×C11C2×#54611yescharacteristic
589C2×C11C2×#54611yescharacteristic
590C2×C11C2×#55311yescharacteristic
591C2×C11C2×#55511yescharacteristic
592D11—44no—
593D11—44no—
594D11—82no—
595C24—114no—
596C24—114no—
597C24—112no—
598C24—112no—
599C24—112no—
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—
617C24—222no—
618C24—222no—
619C24C23×D1111yescharacteristic
620C2×D4—228no—
621C2×D4—228no—
622C2×D4—228no—
623C2×D4—228no—
624C2×D4—228no—
625C2×D4—228no—
626C2×D4—444no—
627C2×D4—444no—
628C2×D4—444no—
629C2×D4—4416no—
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—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—114no—
651C22×C4—114no—
652C22×C4—112no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—228no—
658C22×C4—228no—
659C22×C4—228no—
660C22×C4—2232no—
661C22×C4—222no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—222no—
665C22×C4—228no—
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—228no—
676C22×C4—444no—
677C22×C4—4416no—
678C22×C4D4×D1114yes—
679C22×C4#434314yes—
680C22×C4#434314yes—
681C22×C4C23×D1112yes—
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—44no—
691C4⋊C4—44no—
692C4⋊C4—228no—
693C4⋊C4—228no—
694C22⋊C4—1116no—
695C22⋊C4—228no—
696C22⋊C4—228no—
697C22⋊C4—228no—
698C22⋊C4—228no—
699C22⋊C4—228no—
700C22⋊C4—228no—
701C22⋊C4—228no—
702C22⋊C4—444no—
703C22⋊C4—444no—
704C22⋊C4—444no—
705C22⋊C4—444no—
706C22⋊C4—444no—
707C42—228no—
708C42—228no—
709C42—444no—
710C11C2×#247611yescharacteristic, complemented, Sylow
711C23—114no—
712C23—114no—
713C23—228no—
714C23—228no—
715C23—228no—
716C23—228no—
717C23—222no—
718C23—222no—
719C23—222no—
720C23—222no—
721C23—222no—
722C23—222no—
723C23—222no—
724C23—222no—
725C23—222no—
726C23—222no—
727C23—222no—
728C23—222no—
729C23—228no—
730C23—228no—
731C23—222no—
732C23—222no—
733C23—222no—
734C23—222no—
735C23—222no—
736C23—222no—
737C23—222no—
738C23—444no—
739C23—444no—
740C23—444no—
741C23—444no—
742C23—444no—
743C23—444no—
744C23—444no—
745C23—444no—
746C23—444no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23—444no—
752C23—444no—
753C23C2×D4×D1112yes—
754C23#6703712yes—
755C23C2×#434312yes—
756C23C2×#434312yes—
757C23#41×D1112yes—
758C23#41×D1112yes—
759C23#6704212yes—
760C23C24×D1111yescharacteristic
761D4—4416no—
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—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—114no—
790C2×C4—114no—
791C2×C4—2232no—
792C2×C4—228no—
793C2×C4—228no—
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—222no—
807C2×C4—4416no—
808C2×C4—444no—
809C2×C4—444no—
810C2×C4—444no—
811C2×C4C2×D4×D1114yes—
812C2×C4C2×#434314yes—
813C2×C4C2×#434314yes—
814C22—224no—
815C22—224no—
816C22—224no—
817C22—224no—
818C22—224no—
819C22—224no—
820C22—442no—
821C22—442no—
822C22—442no—
823C22—442no—
824C22—442no—
825C22—442no—
826C22—442no—
827C22—4416no—
828C22—4416no—
829C22—442no—
830C22—442no—
831C22—442no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—442no—
837C22—888no—
838C22#1062314114yes—
839C22#1062315814yes—
840C22#1062316114yes—
841C22#1062319414yes—
842C22#1062322214yes—
843C22#1062322614yes—
844C22#1062326514yes—
845C22C22×D4×D1111yescharacteristic
846C22C2×#6703711yescharacteristic
847C22C22×#434311yescharacteristic
848C22C22×#434311yescharacteristic
849C22C2×#41×D1111yescharacteristic
850C22C2×#41×D1111yescharacteristic
851C22C2×#6704211yescharacteristic
852C4—24no—
853C4—24no—
854C4—24no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—224no—
860C4—224no—
861C4—442no—
862C4—442no—
863C4—442no—
864C2—444no—
865C2—444no—
866C2—882no—
867C2#1307280518yesdirect product factor
868C2C2×#1062315811yescharacteristic
869C2C2×#1062322211yescharacteristic
870C2C2×#1062319411yescharacteristic
871C2C2×#1062314111yescharacteristic
872C2C2×#1062316111yescharacteristic
873C2C2×#1062322611yescharacteristic
874C2C2×#1062326511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#398C2
socleC24×C11C24
prime radicalC22×#66948C2
hypercenterC2×#398D11
hypocenterC11C2×#2476
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
2. C22×#66945C2semidirect
3. #13072805C2direct (N × H)
4. C2×#10622285C2semidirect
5. C2×#10622604C2semidirect
6. C2×#10622604C2semidirect
7. C2×#10622601C2semidirect
8. C2×#10622283C2semidirect
9. C2×#10622603C2semidirect
10. C2×#10622603C2semidirect
11. C2×#10622591C2semidirect
12. C2×#10622278C2semidirect
13. C2×#10622278C2semidirect
14. C2×#10622281C2semidirect
15. C2×#10622279C2semidirect
16. C2×C11×#398C2semidirect
47. C2×#66945C22semidirect
48. C11×#398C22semidirect
57. #10622604C22semidirect
58. #10622604C22semidirect
59. #10622603C22semidirect
60. #10622603C22semidirect
61. #10622601C22semidirect
62. #10622591C22semidirect
63. #10622285C22semidirect
64. #10622283C22semidirect
65. #10622281C22semidirect
66. #10622279C22semidirect
67. #10622278C22semidirect
68. #10622278C22semidirect
277. C2×#398D11semidirect
424. #398C2×D11semidirect
584. C2×C11#2476semidirect
710. C11C2×#2476semidirect
867. C2#13072805direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669482
C22×#669452
#130728052
C2×#106222852
C2×#106226042
C2×#106226012
C2×#106222832
C2×#106226032
C2×#106225912
C2×#106222782
C2×#106222812
C2×#106222792
C2×C11×#3982
C2×#247611