Finite Group Databasebeta

← C2×#13072673 #14921470

Subgroups — C2×#13072673 #14921470

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×#66932C211yesmaximal, characteristic, complemented
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3#13072673C2116yesmaximal, direct product factor
4C2×#10622605C211yesmaximal, characteristic, complemented
5C2×#10622574C211yesmaximal, characteristic, complemented
6C2×#10622572C211yesmaximal, characteristic, complemented
7C2×#10622836C211yesmaximal, characteristic
8C2×#10622558C211yesmaximal, characteristic, complemented
9C2×#10622557C211yesmaximal, characteristic, complemented
10C2×#10622594C211yesmaximal, characteristic, complemented
11C2×#10622546C211yesmaximal, characteristic, complemented
12C2×#10622833C211yesmaximal, characteristic, complemented
13C2×#10622569C211yesmaximal, characteristic, complemented
14C2×#10622555C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C2×C11×#390C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C42×C11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×C4×Dic11C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C2×(C22⋊D11)⋊C4—28no—
45C2×(C22⋊D11)⋊C4C2218yescomplemented
46C2×#66932—28no—
47C2×#66932C2218yescomplemented
48C11×#390C2218yescomplemented
49#10622836C2218yes—
50#10622833C2218yescomplemented
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#10622605C2218yescomplemented
60#10622594C2218yescomplemented
61#10622574C2218yescomplemented
62#10622572C2218yescomplemented
63#10622569C2218yescomplemented
64#10622558C2218yescomplemented
65#10622557C2218yescomplemented
66#10622555C2218yescomplemented
67C4×(C2×D11)⋊C4C2218yescomplemented
68#10622546C2218yescomplemented
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C24×D11C2311yescharacteristic
72C22×D4×C11—24no—
73C22×D4×C11—24no—
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—42no—
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×Dic11C2311yescharacteristic
96C23×Dic11C2314yes—
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C22×C4×D11—24no—
101C22×C4×D11—24no—
102C22×C4×D11—42no—
103C22×C4×D11C2314yes—
104C2×C11×C4⋊C4—24no—
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C22⋊C4—24no—
107C2×C11×C22⋊C4—24no—
108C2×C11×C22⋊C4—42no—
109C2×C11×C22⋊C4—42no—
110C2×C11×C22⋊C4C2314yes—
111C2×C11×C22⋊C4C2314yes—
112C2×C11×C22⋊C4C2314yes—
113C2×C11×C22⋊C4C2314yes—
114C2×C42×C11—42no—
115C2×C42×C11C2314yes—
116C2×C22⋊Dic11—24no—
117C2×C22⋊Dic11—24no—
118C2×C22⋊Dic11—24no—
119C2×C22⋊Dic11—24no—
120C2×C22⋊Dic11—42no—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126C2×(C2×D11)⋊C4—24no—
127C2×(C2×D11)⋊C4—24no—
128C2×(C2×D11)⋊C4—24no—
129C2×(C2×D11)⋊C4—42no—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×C4⋊Dic11—24no—
135C2×C4⋊Dic11C2314yes—
136C2×Dic11⋊C4—24no—
137C2×Dic11⋊C4—42no—
138C2×Dic11⋊C4—42no—
139C2×Dic11⋊C4D418yescomplemented
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×C4×Dic11—24no—
145C2×C4×Dic11—24no—
146C2×C4×Dic11C2314yes—
147C2×C4×Dic11C2314yes—
148(C22⋊D11)⋊C4—232no—
149#66932—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×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×D11#4114yes—
183C23×D11C2412yes—
184C2×D4×C11—28no—
185C2×D4×C11—28no—
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×C11C2×D414yes—
202C22×C4×C11#4114yes—
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—44no—
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—22no—
236C22×Dic11—44no—
237C22×Dic11—416no—
238C22×Dic11C2×D414yes—
239C22×Dic11C2×D414yes—
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—
252C11×C4⋊C4—28no—
253C11×C22⋊C4—28no—
254C11×C22⋊C4—28no—
255C11×C22⋊C4—44no—
256C11×C22⋊C4—44no—
257C42×C11—44no—
258C22⋊Dic11—28no—
259C22⋊Dic11—28no—
260C22⋊Dic11—28no—
261C22⋊Dic11—28no—
262C22⋊Dic11—44no—
263(C2×D11)⋊C4—28no—
264(C2×D11)⋊C4—28no—
265(C2×D11)⋊C4—28no—
266(C2×D11)⋊C4—44no—
267C4⋊Dic11—28no—
268Dic11⋊C4—28no—
269Dic11⋊C4—44no—
270Dic11⋊C4—44no—
271Dic11⋊C4C2×D4116yescomplemented
272C4×Dic11—28no—
273C4×Dic11—28no—
274C22×#126—111no—
275C22×C4×D4—111no—
276#2467—1116no—
277C2×#399—111no—
278C2×#394—111no—
279C2×#394—111no—
280C2×#392—111no—
281C2×#390D1111yescharacteristic, complemented
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—28no—
291C23×C11—28no—
292C23×C11—28no—
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—44no—
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×C11C22×D412yes—
318C23×C11C2×#4114yes—
319C23×C11C2×#4112yes—
320C23×C11C2×#4112yes—
321C23×C11C2×#4112yes—
322C23×C11C2×#4112yes—
323C23×C11H(5,𝔽2)12yes—
324C23×C11H(5,𝔽2)12yes—
325C23×C11C2511yescharacteristic
326C22×D11—28no—
327C22×D11—28no—
328C22×D11—28no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—44no—
336C22×D11—44no—
337C22×D11—44no—
338C22×D11—44no—
339C22×D11C2×#4114yes—
340D4×C11—416no—
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—44no—
357C2×C4×C11—44no—
358C2×C4×C11—44no—
359C2×C4×C11C22×D414yes—
360C2×C4×C11C2×#4114yes—
361C22⋊D11—232no—
362C22⋊D11—416no—
363C2×Dic11—28no—
364C2×Dic11—28no—
365C2×Dic11—28no—
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—22no—
383C2×Dic11—22no—
384C2×Dic11—416no—
385C2×Dic11—44no—
386C2×Dic11—44no—
387C2×Dic11—44no—
388C2×Dic11—44no—
389C2×Dic11C22×D414yes—
390C2×Dic11C22×D414yes—
391C2×Dic11C2×#4114yes—
392C4×D11—416no—
393C23×D4—111no—
394C23×D4—111no—
395C23×D4C2×D1111yescharacteristic
396C24×C4—111no—
397C24×C4—111no—
398C2×#126—118no—
399C2×#126—228no—
400C2×C4×D4—118no—
401C2×C4×D4—228no—
402C22×C4⋊C4—111no—
403C22×C4⋊C4—111no—
404C22×C4⋊C4—111no—
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×C42C2×D1111yescharacteristic
424#399—118no—
425#394—118no—
426#394—118no—
427#392—118no—
428#390C2×D1118yescomplemented
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—24no—
446C22×C11—24no—
447C22×C11—24no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—416no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—88no—
461C22×C11#52514yes—
462C22×C11#52914yes—
463C22×C11#53814yes—
464C22×C11#54614yes—
465C22×C11#55014yes—
466C22×C11#55114yes—
467C22×C11#55314yes—
468C22×C11C23×D411yescharacteristic
469C22×C11C22×#4111yescharacteristic
470C22×C11C22×#4111yescharacteristic
471C22×C11C22×#4111yescharacteristic
472C22×C11C22×#4111yescharacteristic
473C22×C11C2×H(5,𝔽2)11yescharacteristic
474C22×C11C2×H(5,𝔽2)11yescharacteristic
475C2×D11—24no—
476C2×D11—24no—
477C2×D11—24no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—416no—
483C4×C11—24no—
484C4×C11—24no—
485C4×C11—42no—
486C4×C11—42no—
487C4×C11—42no—
488Dic11—24no—
489Dic11—24no—
490Dic11—24no—
491Dic11—42no—
492Dic11—42no—
493Dic11—42no—
494Dic11—42no—
495C25—111no—
496C25C22×D1111yescharacteristic
497C25C22×D1111yescharacteristic
498C22×D4—24no—
499C22×D4—24no—
500C22×D4—42no—
501C22×D4—114no—
502C22×D4—114no—
503C22×D4—224no—
504C22×D4—224no—
505C22×D4—224no—
506C22×D4—224no—
507C22×D4—442no—
508C22×D4—442no—
509C22×D4C22×D1114yes—
510C23×C4—111no—
511C23×C4—111no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—111no—
517C23×C4—114no—
518C23×C4—114no—
519C23×C4—224no—
520C23×C4—224no—
521C23×C4—224no—
522C23×C4—224no—
523C23×C4—442no—
524C23×C4—442no—
525C23×C4C22×D1111yescharacteristic
526C23×C4C22×D1111yescharacteristic
527C23×C4C22×D1111yescharacteristic
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1111yescharacteristic
530#126—2232no—
531C4×D4—2232no—
532C2×C4⋊C4—24no—
533C2×C4⋊C4—118no—
534C2×C4⋊C4—114no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4—114no—
537C2×C4⋊C4—114no—
538C2×C4⋊C4—114no—
539C2×C4⋊C4—224no—
540C2×C4⋊C4—224no—
541C2×C4⋊C4—442no—
542C2×C4⋊C4—442no—
543C2×C4⋊C4C22×D1114yes—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
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—224no—
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—42no—
571C2×C42—114no—
572C2×C42—114no—
573C2×C42—224no—
574C2×C42—224no—
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—44no—
585C2×C11—82no—
586C2×C11#246718yescomplemented
587C2×C11C2×#52511yescharacteristic
588C2×C11C2×#52911yescharacteristic
589C2×C11C2×#53811yescharacteristic
590C2×C11C2×#54611yescharacteristic
591C2×C11C2×#55011yescharacteristic
592C2×C11C2×#55111yescharacteristic
593C2×C11C2×#55311yescharacteristic
594D11—44no—
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—114no—
609C24—112no—
610C24—222no—
611C24—222no—
612C24—222no—
613C24—222no—
614C24—222no—
615C24—222no—
616C24#433914yes—
617C24C23×D1112yes—
618C24C23×D1112yes—
619C24C23×D1111yescharacteristic
620C2×D4—28no—
621C2×D4—28no—
622C2×D4—44no—
623C2×D4—416no—
624C2×D4—228no—
625C2×D4—228no—
626C2×D4—2232no—
627C2×D4—228no—
628C2×D4—228no—
629C2×D4—444no—
630C2×D4—444no—
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—114no—
646C22×C4—114no—
647C22×C4—114no—
648C22×C4—112no—
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—228no—
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—222no—
674C22×C4—222no—
675C22×C4—222no—
676C22×C4—228no—
677C22×C4—444no—
678C22×C4—4416no—
679C22×C4—444no—
680C22×C4—4416no—
681C22×C4D4×D1114yes—
682C22×C4#434114yes—
683C22×C4C23×D1112yes—
684C22×C4C23×D1112yes—
685C22×C4C23×D1112yes—
686C22×C4C23×D1112yes—
687C22×C4C23×D1112yes—
688C4⋊C4—28no—
689C4⋊C4—1116no—
690C4⋊C4—228no—
691C4⋊C4—228no—
692C4⋊C4—444no—
693C4⋊C4—444no—
694C22⋊C4—28no—
695C22⋊C4—28no—
696C22⋊C4—44no—
697C22⋊C4—44no—
698C22⋊C4—228no—
699C22⋊C4—228no—
700C22⋊C4—228no—
701C22⋊C4—228no—
702C22⋊C4—228no—
703C22⋊C4—228no—
704C22⋊C4—228no—
705C22⋊C4—444no—
706C22⋊C4—444no—
707C42—44no—
708C42—228no—
709C42—228no—
710C11C2×#246711yescharacteristic, complemented, Sylow
711C23—28no—
712C23—28no—
713C23—28no—
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—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—114no—
739C23—228no—
740C23—228no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—222no—
745C23—222no—
746C23—222no—
747C23—228no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23—444no—
752C23C2×#433914yes—
753C23C2×#433912yes—
754C23C2×D4×D1112yes—
755C23C2×#434112yes—
756C23#6703712yes—
757C23#6703712yes—
758C23#41×D1112yes—
759C23#41×D1112yes—
760C23C24×D1111yescharacteristic
761D4—416no—
762D4—2232no—
763D4—4416no—
764C2×C4—28no—
765C2×C4—28no—
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—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—114no—
783C2×C4—114no—
784C2×C4—114no—
785C2×C4—228no—
786C2×C4—228no—
787C2×C4—228no—
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—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—4416no—
807C2×C4—4416no—
808C2×C4—444no—
809C2×C4—444no—
810C2×C4—444no—
811C2×C4—444no—
812C2×C4C2×D4×D1114yes—
813C2×C4C2×#434114yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—416no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—88no—
830C22—224no—
831C22—224no—
832C22—224no—
833C22—442no—
834C22—442no—
835C22—4416no—
836C22—442no—
837C22—442no—
838C22#1062302614yes—
839C22#1062307114yes—
840C22#1062307814yes—
841C22#1062314114yes—
842C22#1062314414yes—
843C22#1062321114yes—
844C22#1062324914yes—
845C22C22×#433911yescharacteristic
846C22C22×D4×D1111yescharacteristic
847C22C22×#434111yescharacteristic
848C22C2×#6703711yescharacteristic
849C22C2×#6703711yescharacteristic
850C22C2×#41×D1111yescharacteristic
851C22C2×#41×D1111yescharacteristic
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—224no—
858C4—224no—
859C4—224no—
860C4—442no—
861C4—442no—
862C4—442no—
863C4—442no—
864C2—44no—
865C2—82no—
866C2—444no—
867C2#1307267318yesdirect product factor
868C2C2×#1062307811yescharacteristic
869C2C2×#1062321111yescharacteristic
870C2C2×#1062314411yescharacteristic
871C2C2×#1062314111yescharacteristic
872C2C2×#1062324911yescharacteristic
873C2C2×#1062302611yescharacteristic
874C2C2×#1062307111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#390C2
socleC24×C11C24
prime radicalC2×#10622836C2
hypercenterC2×#390D11
hypocenterC11C2×#2467
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C22×#66932C2semidirect
2. C22×(C22⋊D11)⋊C4C2semidirect
3. #13072673C2direct (N × H)
4. C2×#10622605C2semidirect
5. C2×#10622574C2semidirect
6. C2×#10622572C2semidirect
8. C2×#10622558C2semidirect
9. C2×#10622557C2semidirect
10. C2×#10622594C2semidirect
11. C2×#10622546C2semidirect
12. C2×#10622833C2semidirect
13. C2×#10622569C2semidirect
14. C2×#10622555C2semidirect
15. C2×C4×(C2×D11)⋊C4C2semidirect
16. C2×C11×#390C2semidirect
45. C2×(C22⋊D11)⋊C4C22semidirect
47. C2×#66932C22semidirect
48. C11×#390C22semidirect
50. #10622833C22semidirect
59. #10622605C22semidirect
60. #10622594C22semidirect
61. #10622574C22semidirect
62. #10622572C22semidirect
63. #10622569C22semidirect
64. #10622558C22semidirect
65. #10622557C22semidirect
66. #10622555C22semidirect
67. C4×(C2×D11)⋊C4C22semidirect
68. #10622546C22semidirect
139. C2×Dic11⋊C4D4semidirect
271. Dic11⋊C4C2×D4semidirect
281. C2×#390D11semidirect
428. #390C2×D11semidirect
586. C2×C11#2467semidirect
710. C11C2×#2467semidirect
867. C2#13072673direct (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×(C22⋊D11)⋊C42
#130726732
C2×#106226052
C2×#106225742
C2×#106225722
C2×#106228362
C2×#106225582
C2×#106225572
C2×#106225942
C2×#106225462
C2×#106228332
C2×#106225692
C2×#106225552
C2×C4×(C2×D11)⋊C42
C2×C11×#3902
C2×#246711