Finite Group Databasebeta

← C2×#13072554 #14921416

Subgroups — C2×#13072554 #14921416

Order 2816.

3394 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66938C211yesmaximal, characteristic, complemented
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3#13072554C2116yesmaximal, direct product factor
4C2×#10622572C211yesmaximal, characteristic, complemented
5C2×#10622560C211yesmaximal, characteristic, complemented
6C2×#10622836C211yesmaximal, characteristic
7C2×#10622587C211yesmaximal, characteristic, complemented
8C2×#10622603C211yesmaximal, characteristic, complemented
9C2×#10622557C211yesmaximal, characteristic, complemented
10C2×#10622557C211yesmaximal, characteristic, complemented
11C2×#10622265C211yesmaximal, characteristic, complemented
12C2×#10622833C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622277C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#394C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×Dic22C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C2×#66938—28no—
43C2×#66938C2218yescomplemented
44C2×(C22⋊D11)⋊C4—28no—
45C2×(C22⋊D11)⋊C4C2218yescomplemented
46C11×#394C2218yescomplemented
47C2×C11×#95C2211yescharacteristic
48#10622836C2218yes—
49#10622833C2218yescomplemented
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59#10622603C2218yescomplemented
60#10622587C2218yescomplemented
61#10622572C2218yescomplemented
62#10622569C2218yescomplemented
63#10622560C2218yescomplemented
64#10622557C2218yescomplemented
65#10622557C2218yescomplemented
66C22⋊C4×Dic11C2218yescomplemented
67#10622277C2218yescomplemented
68#10622265C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C22×D4×C11—24no—
73C22×D4×C11—42no—
74C22×D4×C11—42no—
75C22×D4×C11C2314yes—
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—24no—
82C22×C22⋊D11—24no—
83C22×C22⋊D11—24no—
84C22×C22⋊D11—24no—
85C22×C22⋊D11—24no—
86C22×C22⋊D11—42no—
87C22×C22⋊D11C2314yes—
88C22×C22⋊D11C2314yes—
89C23×Dic11—24no—
90C23×Dic11—24no—
91C23×Dic11—42no—
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2314yes—
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C22×C4×D11—24no—
101C22×C4×D11—24no—
102C22×C4×D11—42no—
103C22×C4×D11C2314yes—
104C22×Dic22—24no—
105C22×Dic22—24no—
106C22×Dic22—42no—
107C22×Dic22C2314yes—
108C2×C11×C4⋊C4—42no—
109C2×C11×C4⋊C4C2314yes—
110C2×C11×C22⋊C4—24no—
111C2×C11×C22⋊C4—24no—
112C2×C11×C22⋊C4—24no—
113C2×C11×C22⋊C4—42no—
114C2×C11×C22⋊C4C2314yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2314yes—
117C2×C11×C22⋊C4C2314yes—
118C2×C22⋊Dic11—24no—
119C2×C22⋊Dic11—24no—
120C2×C22⋊Dic11—24no—
121C2×C22⋊Dic11—24no—
122C2×C22⋊Dic11—42no—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128C2×(C2×D11)⋊C4—24no—
129C2×(C2×D11)⋊C4—42no—
130C2×(C2×D11)⋊C4—42no—
131C2×(C2×D11)⋊C4D418yescomplemented
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×Dic11⋊C4—24no—
137C2×Dic11⋊C4—24no—
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2314yes—
140C2×C4×Dic11—24no—
141C2×C4×Dic11—24no—
142C2×C4×Dic11—42no—
143C2×C4×Dic11C2314yes—
144C2×C4×Dic11C2314yes—
145C2×C4×Dic11C2314yes—
146#66938—232no—
147(C22⋊D11)⋊C4—232no—
148C11×#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2459—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#4114yes—
173C24×C11C2412yes—
174C24×C11C2412yes—
175C24×C11C2411yescharacteristic
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—22no—
179C23×D11—22no—
180C23×D11—22no—
181C23×D11—22no—
182C23×D11C2×D414yes—
183C23×D11C2412yes—
184C2×D4×C11—28no—
185C2×D4×C11—44no—
186C2×D4×C11—44no—
187C2×D4×C11—416no—
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×C11C2412yes—
204C22×C4×C11C2412yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C2×C22⋊D11—232no—
209C2×C22⋊D11—28no—
210C2×C22⋊D11—28no—
211C2×C22⋊D11—28no—
212C2×C22⋊D11—28no—
213C2×C22⋊D11—28no—
214C2×C22⋊D11—44no—
215C2×C22⋊D11—416no—
216C22×Dic11—28no—
217C22×Dic11—28no—
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—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—44no—
236C22×Dic11—416no—
237C22×Dic11C2×D414yes—
238C22×Dic11#4114yes—
239C22×Dic11#4114yes—
240C22×Dic11#4114yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C2×C4×D11—28no—
249C2×C4×D11—28no—
250C2×C4×D11—44no—
251C2×C4×D11—416no—
252C2×Dic22—28no—
253C2×Dic22—28no—
254C2×Dic22—44no—
255C2×Dic22—416no—
256C11×C4⋊C4—44no—
257C11×C22⋊C4—28no—
258C11×C22⋊C4—28no—
259C11×C22⋊C4—28no—
260C11×C22⋊C4—44no—
261C22⋊Dic11—28no—
262C22⋊Dic11—28no—
263C22⋊Dic11—28no—
264C22⋊Dic11—28no—
265C22⋊Dic11—44no—
266(C2×D11)⋊C4—28no—
267(C2×D11)⋊C4—44no—
268(C2×D11)⋊C4—44no—
269(C2×D11)⋊C4C2×D4116yescomplemented
270Dic11⋊C4—28no—
271Dic11⋊C4—28no—
272C4×Dic11—28no—
273C4×Dic11—28no—
274C4×Dic11—44no—
275C22×#124—111no—
276C22×C4×D4—111no—
277#2459—1116no—
278C2×#394—111no—
279C2×#394D1111yescharacteristic, complemented
280C2×#393—111no—
281C2×#392—111no—
282C2×#391—111no—
283C2×#388—111no—
284C2×#388—111no—
285C2×#388—111no—
286C2×#387—111no—
287C2×#386—111no—
288C2×#386—111no—
289C2×#381—111no—
290C2×C4×C22⋊C4—111no—
291C23×C11—28no—
292C23×C11—28no—
293C23×C11—28no—
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—44no—
308C23×C11—44no—
309C23×C11—44no—
310C23×C11—44no—
311C23×C11—44no—
312C23×C11—44no—
313C23×C11—44no—
314C23×C11—44no—
315C23×C11—44no—
316C23×C11—44no—
317C23×C11—44no—
318C23×C11C22×D412yes—
319C23×C11C2×#4114yes—
320C23×C11C2×#4112yes—
321C23×C11C2×#4112yes—
322C23×C11C2×#4112yes—
323C23×C11C2×#4112yes—
324C23×C11H(5,𝔽2)12yes—
325C23×C11H(5,𝔽2)12yes—
326C23×C11C2511yescharacteristic
327C22×D11—28no—
328C22×D11—28no—
329C22×D11—28no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11—44no—
339C22×D11—44no—
340C22×D11C22×D414yes—
341D4×C11—416no—
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—44no—
358C2×C4×C11—44no—
359C2×C4×C11—44no—
360C2×C4×C11—44no—
361C2×C4×C11C22×D414yes—
362C22⋊D11—232no—
363C22⋊D11—416no—
364C2×Dic11—28no—
365C2×Dic11—28no—
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—22no—
385C2×Dic11—416no—
386C2×Dic11—44no—
387C2×Dic11—44no—
388C2×Dic11—44no—
389C2×Dic11C22×D414yes—
390C2×Dic11C2×#4114yes—
391C2×Dic11C2×#4114yes—
392C2×Dic11C2×#4114yes—
393C4×D11—416no—
394Dic22—416no—
395C23×Q8—111no—
396C23×D4—111no—
397C23×D4—111no—
398C23×D4C2×D1111yescharacteristic
399C24×C4—111no—
400C24×C4—111no—
401C2×#124—118no—
402C2×#124—228no—
403C2×C4×D4—118no—
404C2×C4×D4—228no—
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
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⋊C4C2×D1111yescharacteristic
418C22×C22⋊C4C2×D1111yescharacteristic
419C22×C22⋊C4C2×D1111yescharacteristic
420C22×C22⋊C4C2×D1111yescharacteristic
421C22×C42—111no—
422C22×C42—111no—
423C22×C42—111no—
424#394—118no—
425#394C2×D1118yescomplemented
426#393—118no—
427#392—118no—
428#391—118no—
429#388—118no—
430#388—118no—
431#388—118no—
432#387—118no—
433#386—118no—
434#386—118no—
435#381—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—
445C2×#95—111no—
446C2×#95C2×D1111yescharacteristic
447C22×C11—24no—
448C22×C11—24no—
449C22×C11—24no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—416no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—88no—
463C22×C11#52514yes—
464C22×C11#52914yes—
465C22×C11#53814yes—
466C22×C11#54614yes—
467C22×C11#54614yes—
468C22×C11#55514yes—
469C22×C11#55914yes—
470C22×C11C23×D411yescharacteristic
471C22×C11C22×#4111yescharacteristic
472C22×C11C22×#4111yescharacteristic
473C22×C11C22×#4111yescharacteristic
474C22×C11C22×#4111yescharacteristic
475C22×C11C2×H(5,𝔽2)11yescharacteristic
476C22×C11C2×H(5,𝔽2)11yescharacteristic
477C2×D11—24no—
478C2×D11—24no—
479C2×D11—24no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—416no—
485C4×C11—24no—
486C4×C11—42no—
487C4×C11—42no—
488C4×C11—42no—
489C4×C11—42no—
490Dic11—24no—
491Dic11—24no—
492Dic11—24no—
493Dic11—24no—
494Dic11—42no—
495Dic11—42no—
496Dic11—42no—
497C25—111no—
498C25C22×D1111yescharacteristic
499C25C22×D1111yescharacteristic
500C22×Q8—114no—
501C22×Q8—224no—
502C22×Q8—224no—
503C22×Q8—442no—
504C22×D4—24no—
505C22×D4—42no—
506C22×D4—42no—
507C22×D4—114no—
508C22×D4—114no—
509C22×D4—224no—
510C22×D4—224no—
511C22×D4—224no—
512C22×D4—224no—
513C22×D4—224no—
514C22×D4—442no—
515C22×D4C22×D1114yes—
516C23×C4—111no—
517C23×C4—111no—
518C23×C4—111no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—111no—
522C23×C4—111no—
523C23×C4—114no—
524C23×C4—114no—
525C23×C4—224no—
526C23×C4—224no—
527C23×C4—224no—
528C23×C4—224no—
529C23×C4—442no—
530C23×C4—442no—
531C23×C4C22×D1111yescharacteristic
532C23×C4C22×D1111yescharacteristic
533C23×C4C22×D1111yescharacteristic
534C23×C4C22×D1111yescharacteristic
535C23×C4C22×D1111yescharacteristic
536#124—2232no—
537C4×D4—2232no—
538C2×C4⋊C4—42no—
539C2×C4⋊C4—114no—
540C2×C4⋊C4—114no—
541C2×C4⋊C4—224no—
542C2×C4⋊C4—224no—
543C2×C4⋊C4C22×D1114yes—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—118no—
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—442no—
564C2×C22⋊C4—442no—
565C2×C22⋊C4—442no—
566C2×C22⋊C4C22×D1114yes—
567C2×C22⋊C4C22×D1114yes—
568C2×C22⋊C4C22×D1114yes—
569C2×C22⋊C4C22×D1114yes—
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#95—114no—
582#95—114no—
583#95—114no—
584#95—114no—
585#95C22×D1114yes—
586C2×C11—44no—
587C2×C11—82no—
588C2×C11#245918yescomplemented
589C2×C11C2×#52511yescharacteristic
590C2×C11C2×#52911yescharacteristic
591C2×C11C2×#53811yescharacteristic
592C2×C11C2×#54611yescharacteristic
593C2×C11C2×#54611yescharacteristic
594C2×C11C2×#55511yescharacteristic
595C2×C11C2×#55911yescharacteristic
596D11—44no—
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—114no—
611C24—112no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24—222no—
616C24—222no—
617C24—222no—
618C24#434114yes—
619C24C23×D1112yes—
620C24C23×D1112yes—
621C24C23×D1111yescharacteristic
622C2×Q8—228no—
623C2×Q8—228no—
624C2×Q8—444no—
625C2×Q8—4416no—
626C2×D4—28no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—416no—
630C2×D4—228no—
631C2×D4—228no—
632C2×D4—228no—
633C2×D4—2232no—
634C2×D4—228no—
635C2×D4—228no—
636C2×D4—444no—
637C2×D4—4416no—
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—22no—
651C22×C4—22no—
652C22×C4—114no—
653C22×C4—114no—
654C22×C4—114no—
655C22×C4—114no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—112no—
660C22×C4—112no—
661C22×C4—112no—
662C22×C4—112no—
663C22×C4—228no—
664C22×C4—228no—
665C22×C4—228no—
666C22×C4—228no—
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—222no—
676C22×C4—222no—
677C22×C4—222no—
678C22×C4—222no—
679C22×C4—222no—
680C22×C4—222no—
681C22×C4—222no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—444no—
685C22×C4—4416no—
686C22×C4—444no—
687C22×C4—4416no—
688C22×C4D4×D1114yes—
689C22×C4C23×D1112yes—
690C22×C4C23×D1112yes—
691C22×C4C23×D1112yes—
692C22×C4C23×D1112yes—
693C22×C4C23×D1112yes—
694C4⋊C4—44no—
695C4⋊C4—228no—
696C4⋊C4—228no—
697C22⋊C4—28no—
698C22⋊C4—28no—
699C22⋊C4—28no—
700C22⋊C4—44no—
701C22⋊C4—1116no—
702C22⋊C4—228no—
703C22⋊C4—228no—
704C22⋊C4—228no—
705C22⋊C4—228no—
706C22⋊C4—228no—
707C22⋊C4—444no—
708C22⋊C4—444no—
709C22⋊C4—444no—
710C42—228no—
711C42—228no—
712C42—444no—
713C11C2×#245911yescharacteristic, complemented, Sylow
714C23—28no—
715C23—28no—
716C23—28no—
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—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—114no—
742C23—228no—
743C23—228no—
744C23—228no—
745C23—222no—
746C23—222no—
747C23—222no—
748C23—222no—
749C23—222no—
750C23—222no—
751C23—444no—
752C23—444no—
753C23—444no—
754C23—444no—
755C23C2×D4×D1112yes—
756C23C2×#434114yes—
757C23C2×#434112yes—
758C23#6703712yes—
759C23#6703712yes—
760C23#41×D1112yes—
761C23#41×D1112yes—
762C23#41×D1112yes—
763C23C24×D1111yescharacteristic
764Q8—4416no—
765D4—416no—
766D4—2232no—
767D4—4416no—
768C2×C4—28no—
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—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—114no—
788C2×C4—114no—
789C2×C4—114no—
790C2×C4—114no—
791C2×C4—228no—
792C2×C4—228no—
793C2×C4—228no—
794C2×C4—228no—
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—222no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—222no—
811C2×C4—222no—
812C2×C4—4416no—
813C2×C4—4416no—
814C2×C4—444no—
815C2×C4—444no—
816C2×C4—444no—
817C2×C4C2×D4×D1114yes—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—42no—
822C22—42no—
823C22—416no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—88no—
834C22—224no—
835C22—224no—
836C22—224no—
837C22—442no—
838C22—442no—
839C22—442no—
840C22—442no—
841C22—4416no—
842C22#1062312414yes—
843C22#1062313714yes—
844C22#1062314114yes—
845C22#1062314314yes—
846C22#1062318014yes—
847C22#1062319514yes—
848C22#1062320114yes—
849C22C22×D4×D1111yescharacteristic
850C22C22×#434111yescharacteristic
851C22C2×#6703711yescharacteristic
852C22C2×#6703711yescharacteristic
853C22C2×#41×D1111yescharacteristic
854C22C2×#41×D1111yescharacteristic
855C22C2×#41×D1111yescharacteristic
856C4—24no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—224no—
862C4—224no—
863C4—224no—
864C4—224no—
865C4—442no—
866C4—442no—
867C4—442no—
868C2—44no—
869C2—82no—
870C2—444no—
871C2#1307255418yesdirect product factor
872C2C2×#1062313711yescharacteristic
873C2C2×#1062318011yescharacteristic
874C2C2×#1062312411yescharacteristic
875C2C2×#1062314111yescharacteristic
876C2C2×#1062314311yescharacteristic
877C2C2×#1062320111yescharacteristic
878C2C2×#1062319511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC2×#394D11
hypocenterC11C2×#2459
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66938C2semidirect
2. C22×(C22⋊D11)⋊C4C2semidirect
3. #13072554C2direct (N × H)
4. C2×#10622572C2semidirect
5. C2×#10622560C2semidirect
7. C2×#10622587C2semidirect
8. C2×#10622603C2semidirect
9. C2×#10622557C2semidirect
10. C2×#10622557C2semidirect
11. C2×#10622265C2semidirect
12. C2×#10622833C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622277C2semidirect
15. C2×C22⋊C4×Dic11C2semidirect
16. C2×C11×#394C2semidirect
43. C2×#66938C22semidirect
45. C2×(C22⋊D11)⋊C4C22semidirect
46. C11×#394C22semidirect
49. #10622833C22semidirect
59. #10622603C22semidirect
60. #10622587C22semidirect
61. #10622572C22semidirect
62. #10622569C22semidirect
63. #10622560C22semidirect
64. #10622557C22semidirect
65. #10622557C22semidirect
66. C22⋊C4×Dic11C22semidirect
67. #10622277C22semidirect
68. #10622265C22semidirect
131. C2×(C2×D11)⋊C4D4semidirect
269. (C2×D11)⋊C4C2×D4semidirect
279. C2×#394D11semidirect
425. #394C2×D11semidirect
588. C2×C11#2459semidirect
713. C11C2×#2459semidirect
871. C2#13072554direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669382
C22×(C22⋊D11)⋊C42
#130725542
C2×#106225722
C2×#106225602
C2×#106228362
C2×#106225872
C2×#106226032
C2×#106225572
C2×#106222652
C2×#106228332
C2×#106225692
C2×#106222772
C2×C22⋊C4×Dic112
C2×C11×#3942
C2×#245911