Finite Group Databasebeta

← C2×#13073677 #14923847

Subgroups — C2×#13073677 #14923847

Order 2816.

3158 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66932C211yesmaximal, characteristic, complemented
2C22×#66988C211yesmaximal, characteristic, complemented
3#13073677C2116yesmaximal, direct product factor
4C2×#10622274C211yesmaximal, characteristic, complemented
5C2×#10622561C211yesmaximal, characteristic, complemented
6C2×#10622835C211yesmaximal, characteristic, complemented
7C2×#10622834C211yesmaximal, characteristic, complemented
8C2×#10622834C211yesmaximal, characteristic, complemented
9C2×#10622834C211yesmaximal, characteristic, complemented
10C2×#10622558C211yesmaximal, characteristic, complemented
11C2×#10622564C211yesmaximal, characteristic, complemented
12C2×#10622557C211yesmaximal, characteristic, complemented
13C2×#10622833C211yesmaximal, characteristic, complemented
14C2×#10622262C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#392C211yesmaximal, characteristic
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C2×#66988—28no—
36C2×#66988C2218yescomplemented
37C22×C4⋊Dic11C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2211yescharacteristic
46C22×C4×Dic11C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48C2×#66932—28no—
49C2×#66932C2218yescomplemented
50C11×#392C2218yes—
51C2×C11×#95C2211yescharacteristic
52#10622835C2218yescomplemented
53#10622834C2218yescomplemented
54#10622834C2218yescomplemented
55#10622834C2218yescomplemented
56#10622833C2218yescomplemented
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62#10622564C2218yescomplemented
63#10622561C2218yescomplemented
64#10622558C2218yescomplemented
65#10622557C2218yescomplemented
66C22⋊C4×Dic11C2218yescomplemented
67#10622274C2218yescomplemented
68#10622262C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C25×C11C2311yescharacteristic
72C22×D4×C11—24no—
73C22×D4×C11—24no—
74C22×D4×C11—24no—
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—42no—
78C22×D4×C11—42no—
79C22×D4×C11—42no—
80C22×D4×C11—42no—
81C22×D4×C11C2314yes—
82C22×D4×C11C2314yes—
83C22×D4×C11C2314yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×Dic11—24no—
89C23×Dic11—24no—
90C23×Dic11—42no—
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2314yes—
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C2×C11×C22⋊C4—24no—
101C2×C11×C22⋊C4—24no—
102C2×C11×C22⋊C4—24no—
103C2×C11×C22⋊C4C2314yes—
104C2×C11×C22⋊C4C2314yes—
105C2×C11×C22⋊C4C2314yes—
106C2×C22⋊Dic11—24no—
107C2×C22⋊Dic11—24no—
108C2×C22⋊Dic11—24no—
109C2×C22⋊Dic11—24no—
110C2×C22⋊Dic11—24no—
111C2×C22⋊Dic11—24no—
112C2×C22⋊Dic11—24no—
113C2×C22⋊Dic11—24no—
114C2×C22⋊Dic11—42no—
115C2×C22⋊Dic11—42no—
116C2×C22⋊Dic11—42no—
117C2×C22⋊Dic11C2314yes—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128#66988—232no—
129C2×C4⋊Dic11—24no—
130C2×C4⋊Dic11—42no—
131C2×C4⋊Dic11—42no—
132C2×C4⋊Dic11C2314yes—
133C2×C4⋊Dic11C2314yes—
134C2×C4⋊Dic11C2314yes—
135C2×Dic11⋊C4—24no—
136C2×Dic11⋊C4—24no—
137C2×Dic11⋊C4—24no—
138C2×Dic11⋊C4D418yescomplemented
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×C4×Dic11—24no—
144C2×C4×Dic11—24no—
145C2×C4×Dic11—42no—
146C2×C4×Dic11—42no—
147C2×C4×Dic11C2314yes—
148C2×C4×Dic11C2314yes—
149C2×C4×Dic11C2314yes—
150C2×C4×Dic11C2314yes—
151#66932—232no—
152C11×#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2554—111nomaximal, Sylow
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×C11—22no—
170C24×C11—22no—
171C24×C11—22no—
172C24×C11—22no—
173C24×C11—22no—
174C24×C11—22no—
175C24×C11—22no—
176C24×C11—22no—
177C24×C11—22no—
178C24×C11—22no—
179C24×C11#4114yes—
180C24×C11C2412yes—
181C24×C11C2412yes—
182C24×C11C2412yes—
183C24×C11C2411yescharacteristic
184C2×D4×C11—28no—
185C2×D4×C11—28no—
186C2×D4×C11—28no—
187C2×D4×C11—28no—
188C2×D4×C11—28no—
189C2×D4×C11—44no—
190C2×D4×C11—44no—
191C2×D4×C11—44no—
192C2×D4×C11—44no—
193C2×D4×C11—416no—
194C2×D4×C11—416no—
195C2×D4×C11—416no—
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×C11—22no—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11C2×D414yes—
206C22×C4×C11#4114yes—
207C22×C4×C11#4114yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C22×Dic11—28no—
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×Dic11—28no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—44no—
236C22×Dic11—416no—
237C22×Dic11C2×D414yes—
238C22×Dic11C2×D414yes—
239C22×Dic11#4114yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C11×C22⋊C4—28no—
249C11×C22⋊C4—28no—
250C11×C22⋊C4—28no—
251C22⋊Dic11—28no—
252C22⋊Dic11—28no—
253C22⋊Dic11—28no—
254C22⋊Dic11—28no—
255C22⋊Dic11—28no—
256C22⋊Dic11—28no—
257C22⋊Dic11—28no—
258C22⋊Dic11—28no—
259C22⋊Dic11—44no—
260C22⋊Dic11—44no—
261C22⋊Dic11—44no—
262C4⋊Dic11—28no—
263C4⋊Dic11—44no—
264C4⋊Dic11—44no—
265Dic11⋊C4—28no—
266Dic11⋊C4—28no—
267Dic11⋊C4—28no—
268Dic11⋊C4C2×D4116yescomplemented
269C4×Dic11—28no—
270C4×Dic11—28no—
271C4×Dic11—44no—
272C4×Dic11—44no—
273C22×#126—111no—
274C22×#123—111no—
275#2554—1116no—
276C2×#398—111no—
277C2×#396—111no—
278C2×#394—111no—
279C2×#392D1111yescharacteristic
280C2×#390—111no—
281C2×#390—111no—
282C2×#390—111no—
283C2×#388—111no—
284C2×#388—111no—
285C2×#388—111no—
286C2×#386—111no—
287C2×C4×C4⋊C4—111no—
288C2×C4×C22⋊C4—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—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—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—44no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11—44no—
317C23×C11—44no—
318C23×C11—44no—
319C23×C11—44no—
320C23×C11—44no—
321C23×C11—44no—
322C23×C11—44no—
323C23×C11—44no—
324C23×C11—44no—
325C23×C11—44no—
326C23×C11—44no—
327C23×C11—44no—
328C23×C11—44no—
329C23×C11—44no—
330C23×C11C22×D412yes—
331C23×C11C2×#4114yes—
332C23×C11C2×#4112yes—
333C23×C11C2×#4112yes—
334C23×C11C2×#4112yes—
335C23×C11C2×#4112yes—
336C23×C11H(5,𝔽2)12yes—
337C23×C11H(5,𝔽2)12yes—
338C23×C11C2511yescharacteristic
339D4×C11—416no—
340D4×C11—416no—
341D4×C11—416no—
342C2×C4×C11—28no—
343C2×C4×C11—28no—
344C2×C4×C11—28no—
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—44no—
355C2×C4×C11C22×D414yes—
356C2×C4×C11C2×#4114yes—
357C2×C4×C11C2×#4114yes—
358C2×Dic11—28no—
359C2×Dic11—28no—
360C2×Dic11—28no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
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—416no—
383C2×Dic11—44no—
384C2×Dic11—44no—
385C2×Dic11—44no—
386C2×Dic11—44no—
387C2×Dic11—44no—
388C2×Dic11C22×D414yes—
389C2×Dic11C22×D414yes—
390C2×Dic11C2×#4114yes—
391C23×D4C2×D1111yescharacteristic
392C23×D4C2×D1111yescharacteristic
393C23×D4C2×D1111yescharacteristic
394C24×C4—111no—
395C2×#126—118no—
396C2×#126—228no—
397C2×#123—118no—
398C2×#123—228no—
399C22×C4⋊C4—111no—
400C22×C4⋊C4—111no—
401C22×C4⋊C4—111no—
402C22×C4⋊C4—111no—
403C22×C4⋊C4—111no—
404C22×C4⋊C4—111no—
405C22×C4⋊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×C22⋊C4—111no—
417C22×C22⋊C4C2×D1111yescharacteristic
418C22×C22⋊C4C2×D1111yescharacteristic
419C22×C22⋊C4C2×D1111yescharacteristic
420C22×C42—111no—
421C22×C42—111no—
422C22×C42—111no—
423C22×C42—111no—
424#398—118no—
425#396—118no—
426#394—118no—
427#392C2×D1118yes—
428#390—118no—
429#390—118no—
430#390—118no—
431#388—118no—
432#388—118no—
433#388—118no—
434#386—118no—
435C4×C4⋊C4—118no—
436C4×C22⋊C4—118no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95C2×D1111yescharacteristic
443C22×C11—24no—
444C22×C11—24no—
445C22×C11—24no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—416no—
451C22×C11—42no—
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—42no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—88no—
466C22×C11—88no—
467C22×C11#52914yes—
468C22×C11#53214yes—
469C22×C11#53814yes—
470C22×C11#54614yes—
471C22×C11#55014yes—
472C22×C11#55114yes—
473C22×C11#55314yes—
474C22×C11C23×D411yescharacteristic
475C22×C11C22×#4111yescharacteristic
476C22×C11C22×#4111yescharacteristic
477C22×C11C22×#4111yescharacteristic
478C22×C11C22×#4111yescharacteristic
479C22×C11C2×H(5,𝔽2)11yescharacteristic
480C22×C11C2×H(5,𝔽2)11yescharacteristic
481C4×C11—24no—
482C4×C11—24no—
483C4×C11—24no—
484C4×C11—42no—
485Dic11—24no—
486Dic11—24no—
487Dic11—24no—
488Dic11—42no—
489Dic11—42no—
490Dic11—42no—
491Dic11—42no—
492Dic11—42no—
493C25C22×D1111yescharacteristic
494C25C22×D1111yescharacteristic
495C25C22×D1111yescharacteristic
496C22×D4—24no—
497C22×D4—24no—
498C22×D4—24no—
499C22×D4—24no—
500C22×D4—24no—
501C22×D4—42no—
502C22×D4—42no—
503C22×D4—42no—
504C22×D4—42no—
505C22×D4C22×D1114yes—
506C22×D4C22×D1114yes—
507C22×D4C22×D1114yes—
508C23×C4—111no—
509C23×C4—111no—
510C23×C4—111no—
511C23×C4—111no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—114no—
517C23×C4—224no—
518C23×C4—224no—
519C23×C4—442no—
520C23×C4C22×D1111yescharacteristic
521C23×C4C22×D1111yescharacteristic
522C23×C4C22×D1111yescharacteristic
523C23×C4C22×D1111yescharacteristic
524#126—2232no—
525#123—2232no—
526C2×C4⋊C4—118no—
527C2×C4⋊C4—114no—
528C2×C4⋊C4—114no—
529C2×C4⋊C4—114no—
530C2×C4⋊C4—114no—
531C2×C4⋊C4—114no—
532C2×C4⋊C4—114no—
533C2×C4⋊C4—114no—
534C2×C4⋊C4—224no—
535C2×C4⋊C4—224no—
536C2×C4⋊C4—224no—
537C2×C4⋊C4—224no—
538C2×C4⋊C4—442no—
539C2×C4⋊C4—442no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
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—224no—
559C2×C22⋊C4—224no—
560C2×C22⋊C4—224no—
561C2×C22⋊C4—224no—
562C2×C22⋊C4—442no—
563C2×C22⋊C4—442no—
564C2×C22⋊C4—442no—
565C2×C22⋊C4C22×D1114yes—
566C2×C22⋊C4C22×D1114yes—
567C2×C22⋊C4C22×D1114yes—
568C2×C42—114no—
569C2×C42—114no—
570C2×C42—114no—
571C2×C42—114no—
572C2×C42—224no—
573C2×C42—224no—
574C2×C42—442no—
575C2×C42—442no—
576#95—114no—
577#95—114no—
578#95—114no—
579#95—114no—
580#95—114no—
581#95C22×D1114yes—
582C2×C11—44no—
583C2×C11—82no—
584C2×C11—82no—
585C2×C11#255418yescomplemented
586C2×C11C2×#52911yescharacteristic
587C2×C11C2×#53211yescharacteristic
588C2×C11C2×#53811yescharacteristic
589C2×C11C2×#54611yescharacteristic
590C2×C11C2×#55011yescharacteristic
591C2×C11C2×#55111yescharacteristic
592C2×C11C2×#55311yescharacteristic
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—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24#434114yes—
614C24C23×D1112yes—
615C24C23×D1112yes—
616C24C23×D1112yes—
617C24C23×D1111yescharacteristic
618C2×D4—28no—
619C2×D4—28no—
620C2×D4—28no—
621C2×D4—28no—
622C2×D4—28no—
623C2×D4—44no—
624C2×D4—44no—
625C2×D4—44no—
626C2×D4—44no—
627C2×D4—416no—
628C2×D4—416no—
629C2×D4—416no—
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—114no—
640C22×C4—114no—
641C22×C4—114no—
642C22×C4—112no—
643C22×C4—112no—
644C22×C4—112no—
645C22×C4—112no—
646C22×C4—112no—
647C22×C4—112no—
648C22×C4—112no—
649C22×C4—112no—
650C22×C4—228no—
651C22×C4—222no—
652C22×C4—222no—
653C22×C4—222no—
654C22×C4—222no—
655C22×C4—222no—
656C22×C4—222no—
657C22×C4—222no—
658C22×C4—222no—
659C22×C4—222no—
660C22×C4—222no—
661C22×C4—222no—
662C22×C4—228no—
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—4416no—
675C22×C4D4×D1114yes—
676C22×C4#434114yes—
677C22×C4#434114yes—
678C22×C4C23×D1112yes—
679C22×C4C23×D1112yes—
680C22×C4C23×D1112yes—
681C22×C4C23×D1112yes—
682C4⋊C4—1116no—
683C4⋊C4—228no—
684C4⋊C4—228no—
685C4⋊C4—228no—
686C4⋊C4—228no—
687C4⋊C4—444no—
688C4⋊C4—444no—
689C22⋊C4—28no—
690C22⋊C4—28no—
691C22⋊C4—28no—
692C22⋊C4—228no—
693C22⋊C4—228no—
694C22⋊C4—228no—
695C22⋊C4—228no—
696C22⋊C4—228no—
697C22⋊C4—228no—
698C22⋊C4—228no—
699C22⋊C4—228no—
700C22⋊C4—444no—
701C22⋊C4—444no—
702C22⋊C4—444no—
703C42—228no—
704C42—228no—
705C42—444no—
706C42—444no—
707C11C2×#255411yescharacteristic, complemented, Sylow
708C23—28no—
709C23—28no—
710C23—28no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
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—22no—
729C23—22no—
730C23—22no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23C2×D4×D1112yes—
750C23C2×#434114yes—
751C23C2×#434112yes—
752C23C2×#434112yes—
753C23C2×#434112yes—
754C23#6703712yes—
755C23#6703712yes—
756C23#41×D1112yes—
757C23C24×D1111yescharacteristic
758D4—416no—
759D4—416no—
760D4—416no—
761C2×C4—28no—
762C2×C4—28no—
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—44no—
774C2×C4—114no—
775C2×C4—114no—
776C2×C4—114no—
777C2×C4—228no—
778C2×C4—228no—
779C2×C4—228no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—222no—
784C2×C4—222no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—222no—
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—4416no—
802C2×C4—444no—
803C2×C4—444no—
804C2×C4—444no—
805C2×C4—444no—
806C2×C4—444no—
807C2×C4C2×D4×D1114yes—
808C2×C4C2×#434114yes—
809C2×C4C2×#434114yes—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—416no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—88no—
833C22—88no—
834C22#1062311814yes—
835C22#1062312214yes—
836C22#1062312414yes—
837C22#1062313014yes—
838C22#1062313114yes—
839C22#1062314514yes—
840C22#1062324714yes—
841C22C22×D4×D1111yescharacteristic
842C22C22×#434111yescharacteristic
843C22C22×#434111yescharacteristic
844C22C22×#434111yescharacteristic
845C22C2×#6703711yescharacteristic
846C22C2×#6703711yescharacteristic
847C22C2×#41×D1111yescharacteristic
848C4—24no—
849C4—24no—
850C4—24no—
851C4—42no—
852C4—224no—
853C4—224no—
854C4—224no—
855C4—442no—
856C4—442no—
857C4—442no—
858C4—442no—
859C4—442no—
860C2—44no—
861C2—82no—
862C2—82no—
863C2#1307367718yesdirect product factor
864C2C2×#1062313111yescharacteristic
865C2C2×#1062324711yescharacteristic
866C2C2×#1062312411yescharacteristic
867C2C2×#1062312211yescharacteristic
868C2C2×#1062313011yescharacteristic
869C2C2×#1062311811yescharacteristic
870C2C2×#1062314511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
Fitting, prime radicalC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2554
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#66932C2semidirect
2. C22×#66988C2semidirect
3. #13073677C2direct (N × H)
4. C2×#10622274C2semidirect
5. C2×#10622561C2semidirect
6. C2×#10622835C2semidirect
7. C2×#10622834C2semidirect
8. C2×#10622834C2semidirect
9. C2×#10622834C2semidirect
10. C2×#10622558C2semidirect
11. C2×#10622564C2semidirect
12. C2×#10622557C2semidirect
13. C2×#10622833C2semidirect
14. C2×#10622262C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
36. C2×#66988C22semidirect
49. C2×#66932C22semidirect
52. #10622835C22semidirect
53. #10622834C22semidirect
54. #10622834C22semidirect
55. #10622834C22semidirect
56. #10622833C22semidirect
62. #10622564C22semidirect
63. #10622561C22semidirect
64. #10622558C22semidirect
65. #10622557C22semidirect
66. C22⋊C4×Dic11C22semidirect
67. #10622274C22semidirect
68. #10622262C22semidirect
138. C2×Dic11⋊C4D4semidirect
268. Dic11⋊C4C2×D4semidirect
585. C2×C11#2554semidirect
707. C11C2×#2554semidirect
863. C2#13073677direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669322
C22×#669882
#130736772
C2×#106222742
C2×#106225612
C2×#106228352
C2×#106228342
C2×#106225582
C2×#106225642
C2×#106225572
C2×#106228332
C2×#106222622
C2×C22⋊C4×Dic112
C2×C11×#3922
C2×#255411