Finite Group Databasebeta

← C2×#13072525 #14921892

Subgroups — C2×#13072525 #14921892

Order 2816.

3438 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×#66947C211yesmaximal, characteristic, complemented
2C22×C4×D44C211yesmaximal, characteristic, complemented
3#13072525C2116yesmaximal, direct product factor
4C2×#10622273C211yesmaximal, characteristic, complemented
5C2×#10622607C211yesmaximal, characteristic, complemented
6C2×#10622604C211yesmaximal, characteristic, complemented
7C2×#10622284C211yesmaximal, characteristic
8C2×#10622603C211yesmaximal, characteristic, complemented
9C2×#10622282C211yesmaximal, characteristic, complemented
10C2×#10622278C211yesmaximal, characteristic, complemented
11C2×#10622278C211yesmaximal, characteristic, complemented
12C2×#10622278C211yesmaximal, characteristic, complemented
13C2×#10622277C211yesmaximal, characteristic, complemented
14C2×#10622280C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C2×C11×#387C211yesmaximal, characteristic, complemented
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C2×#66947—28no—
43C2×#66947C2218yescomplemented
44C2×C4×D44—28no—
45C2×C4×D44C2218yescomplemented
46C11×#387C2218yescomplemented
47C2×C11×#95C2211yescharacteristic
48C2×C11×#95C2211yescharacteristic
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#10622607C2218yescomplemented
58#10622604C2218yescomplemented
59#10622603C2218yescomplemented
60C4×(C2×D11)⋊C4C2218yescomplemented
61#10622284C2218yes—
62#10622282C2218yescomplemented
63#10622280C2218yescomplemented
64#10622278C2218yescomplemented
65#10622278C2218yescomplemented
66#10622278C2218yescomplemented
67#10622277C2218yescomplemented
68#10622273C2218yescomplemented
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—24no—
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—24no—
102C22×C4×D11—42no—
103C22×C4×D11—42no—
104C22×C4×D11—42no—
105C22×C4×D11C2314yes—
106C22×C4×D11C2314yes—
107C22×C4×D11C2314yes—
108C2×C11×C4⋊C4—24no—
109C2×C11×C4⋊C4—24no—
110C2×C11×C4⋊C4C2314yes—
111C2×C11×C4⋊C4C2314yes—
112C2×C42×C11—24no—
113C2×C42×C11C2314yes—
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—24no—
120C2×(C2×D11)⋊C4—42no—
121C2×(C2×D11)⋊C4—42no—
122C2×(C2×D11)⋊C4—42no—
123C2×(C2×D11)⋊C4—42no—
124C2×(C2×D11)⋊C4—42no—
125C2×(C2×D11)⋊C4D418yescomplemented
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⋊C4—42no—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×C4×Dic11—42no—
145C2×C4×Dic11C2314yes—
146#66947—232no—
147C4×D44—232no—
148C11×#95C2314yes—
149C11×#95C2314yes—
150C11×#95C2314yes—
151C11×#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2457—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×D11C2×D414yes—
179C23×D11#4114yes—
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×Dic11—22no—
226C22×Dic11C2×D414yes—
227C22×Dic11C2412yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C22×Dic11C2412yes—
231C22×Dic11C2412yes—
232C2×D44—232no—
233C2×D44—28no—
234C2×D44—28no—
235C2×D44—28no—
236C2×D44—28no—
237C2×D44—28no—
238C2×D44—28no—
239C2×D44—28no—
240C2×D44—44no—
241C2×D44—44no—
242C2×D44—416no—
243C2×D44—416no—
244C2×C4×D11—28no—
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—44no—
252C2×C4×D11—44no—
253C2×C4×D11—416no—
254C2×C4×D11—416no—
255C2×C4×D11—416no—
256C11×C4⋊C4—28no—
257C11×C4⋊C4—28no—
258C42×C11—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—28no—
264(C2×D11)⋊C4—28no—
265(C2×D11)⋊C4—44no—
266(C2×D11)⋊C4—44no—
267(C2×D11)⋊C4—44no—
268(C2×D11)⋊C4—44no—
269(C2×D11)⋊C4—44no—
270(C2×D11)⋊C4C2×D4116yescomplemented
271C4⋊Dic11—28no—
272Dic11⋊C4—28no—
273Dic11⋊C4—44no—
274C4×Dic11—44no—
275C22×#123—111no—
276C22×C4×D4—111no—
277#2457—1116no—
278C2×#400—111no—
279C2×#396—111no—
280C2×#394—111no—
281C2×#392—111no—
282C2×#388—111no—
283C2×#388—111no—
284C2×#387D1111yescharacteristic, complemented
285C2×#386—111no—
286C2×#386—111no—
287C2×#386—111no—
288C2×#381—111no—
289C2×#380—111no—
290C2×C4×C22⋊C4—111no—
291C23×C11C22×D412yes—
292C23×C11C2×#4112yes—
293C23×C11C2×#4112yes—
294C23×C11C2×#4112yes—
295C23×C11C2×#4112yes—
296C23×C11H(5,𝔽2)12yes—
297C23×C11H(5,𝔽2)12yes—
298C23×C11C2511yescharacteristic
299C22×D11—28no—
300C22×D11—28no—
301C22×D11—28no—
302C22×D11—28no—
303C22×D11—28no—
304C22×D11—28no—
305C22×D11—28no—
306C22×D11—28no—
307C22×D11—28no—
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—22no—
324C22×D11—22no—
325C22×D11—22no—
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—
340C22×D11C2×#4114yes—
341C2×C4×C11—28no—
342C2×C4×C11—28no—
343C2×C4×C11—28no—
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—22no—
362C2×C4×C11—44no—
363C2×C4×C11—44no—
364C2×C4×C11—44no—
365C2×C4×C11—44no—
366C2×C4×C11C22×D414yes—
367C2×C4×C11C2×#4114yes—
368C2×C4×C11C2×#4114yes—
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—22no—
384C2×Dic11—44no—
385C2×Dic11—44no—
386C2×Dic11—44no—
387C2×Dic11—44no—
388C2×Dic11C22×D414yes—
389D44—232no—
390D44—416no—
391D44—416no—
392C4×D11—416no—
393C4×D11—416no—
394C4×D11—416no—
395C23×D4—111no—
396C23×D4—111no—
397C23×D4—111no—
398C24×C4—111no—
399C24×C4—111no—
400C24×C4—111no—
401C2×#123—118no—
402C2×#123—228no—
403C2×C4×D4—118no—
404C2×C4×D4—228no—
405C22×C4⋊C4—111no—
406C22×C4⋊C4—111no—
407C22×C4⋊C4—111no—
408C22×C4⋊C4C2×D1111yescharacteristic
409C22×C4⋊C4C2×D1111yescharacteristic
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×C22⋊C4—111no—
422C22×C42—111no—
423C22×C42C2×D1111yescharacteristic
424#400—118no—
425#396—118no—
426#394—118no—
427#392—118no—
428#388—118no—
429#388—118no—
430#387C2×D1118yescomplemented
431#386—118no—
432#386—118no—
433#386—118no—
434#381—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×#95C2×D1111yescharacteristic
444C2×#95C2×D1111yescharacteristic
445C2×#95C2×D1111yescharacteristic
446C2×#95C2×D1111yescharacteristic
447C22×C11#52514yes—
448C22×C11#52914yes—
449C22×C11#54014yes—
450C22×C11#54614yes—
451C22×C11#54614yes—
452C22×C11#55114yes—
453C22×C11#55314yes—
454C22×C11C23×D411yescharacteristic
455C22×C11C22×#4111yescharacteristic
456C22×C11C22×#4111yescharacteristic
457C22×C11C22×#4111yescharacteristic
458C22×C11C22×#4111yescharacteristic
459C22×C11C2×H(5,𝔽2)11yescharacteristic
460C22×C11C2×H(5,𝔽2)11yescharacteristic
461C2×D11—24no—
462C2×D11—24no—
463C2×D11—24no—
464C2×D11—24no—
465C2×D11—24no—
466C2×D11—24no—
467C2×D11—24no—
468C2×D11—24no—
469C2×D11—24no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—42no—
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—42no—
482C2×D11—416no—
483C2×D11—416no—
484C2×D11—416no—
485C4×C11—24no—
486C4×C11—24no—
487C4×C11—24no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11—42no—
491C4×C11—42no—
492Dic11—24no—
493Dic11—42no—
494Dic11—42no—
495Dic11—42no—
496Dic11—42no—
497C25—111no—
498C25—111no—
499C25—111no—
500C22×D4—114no—
501C22×D4—114no—
502C22×D4—114no—
503C22×D4—224no—
504C22×D4—224no—
505C22×D4—224no—
506C22×D4—224no—
507C22×D4—224no—
508C22×D4—224no—
509C22×D4—224no—
510C22×D4—442no—
511C22×D4—442no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4—111no—
517C23×C4—114no—
518C23×C4—114no—
519C23×C4—114no—
520C23×C4—224no—
521C23×C4—224no—
522C23×C4—224no—
523C23×C4—224no—
524C23×C4—224no—
525C23×C4—224no—
526C23×C4—442no—
527C23×C4—442no—
528C23×C4—442no—
529C23×C4C22×D1111yescharacteristic
530C23×C4C22×D1111yescharacteristic
531C23×C4C22×D1111yescharacteristic
532C23×C4C22×D1111yescharacteristic
533C23×C4C22×D1111yescharacteristic
534C23×C4C22×D1111yescharacteristic
535C23×C4C22×D1111yescharacteristic
536#123—2232no—
537C4×D4—2232no—
538C2×C4⋊C4—24no—
539C2×C4⋊C4—24no—
540C2×C4⋊C4—114no—
541C2×C4⋊C4—114no—
542C2×C4⋊C4—114no—
543C2×C4⋊C4—224no—
544C2×C4⋊C4—224no—
545C2×C4⋊C4—442no—
546C2×C4⋊C4C22×D1114yes—
547C2×C4⋊C4C22×D1114yes—
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—114no—
559C2×C22⋊C4—114no—
560C2×C22⋊C4—114no—
561C2×C22⋊C4—224no—
562C2×C22⋊C4—224no—
563C2×C22⋊C4—224no—
564C2×C22⋊C4—224no—
565C2×C22⋊C4—224no—
566C2×C22⋊C4—224no—
567C2×C22⋊C4—442no—
568C2×C22⋊C4—442no—
569C2×C22⋊C4—442no—
570C2×C22⋊C4—442no—
571C2×C22⋊C4—442no—
572C2×C42—24no—
573C2×C42—114no—
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#95C22×D1114yes—
583#95C22×D1114yes—
584#95C22×D1114yes—
585#95C22×D1114yes—
586C2×C11#245718yescomplemented
587C2×C11C2×#52511yescharacteristic
588C2×C11C2×#52911yescharacteristic
589C2×C11C2×#54011yescharacteristic
590C2×C11C2×#54611yescharacteristic
591C2×C11C2×#54611yescharacteristic
592C2×C11C2×#55111yescharacteristic
593C2×C11C2×#55311yescharacteristic
594D11—44no—
595D11—44no—
596D11—44no—
597C24—114no—
598C24—114no—
599C24—114no—
600C24—112no—
601C24—112no—
602C24—112no—
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—
619C24—222no—
620C24—222no—
621C24C23×D1111yescharacteristic
622C2×D4—228no—
623C2×D4—228no—
624C2×D4—2232no—
625C2×D4—228no—
626C2×D4—228no—
627C2×D4—228no—
628C2×D4—228no—
629C2×D4—228no—
630C2×D4—444no—
631C2×D4—444no—
632C2×D4—4416no—
633C2×D4—4416no—
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—22no—
651C22×C4—22no—
652C22×C4—114no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—228no—
659C22×C4—228no—
660C22×C4—228no—
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—228no—
676C22×C4—228no—
677C22×C4—228no—
678C22×C4—444no—
679C22×C4—444no—
680C22×C4—444no—
681C22×C4—4416no—
682C22×C4—4416no—
683C22×C4—4416no—
684C22×C4#433914yes—
685C22×C4D4×D1114yes—
686C22×C4#434314yes—
687C22×C4C23×D1112yes—
688C22×C4C23×D1112yes—
689C22×C4C23×D1112yes—
690C22×C4C23×D1112yes—
691C22×C4C23×D1112yes—
692C22×C4C23×D1112yes—
693C22×C4C23×D1112yes—
694C4⋊C4—28no—
695C4⋊C4—28no—
696C4⋊C4—228no—
697C4⋊C4—228no—
698C4⋊C4—444no—
699C22⋊C4—1116no—
700C22⋊C4—228no—
701C22⋊C4—228no—
702C22⋊C4—228no—
703C22⋊C4—228no—
704C22⋊C4—228no—
705C22⋊C4—228no—
706C22⋊C4—444no—
707C22⋊C4—444no—
708C22⋊C4—444no—
709C22⋊C4—444no—
710C22⋊C4—444no—
711C42—28no—
712C42—444no—
713C11C2×#245711yescharacteristic, complemented, Sylow
714C23—114no—
715C23—114no—
716C23—114no—
717C23—228no—
718C23—228no—
719C23—228no—
720C23—228no—
721C23—228no—
722C23—228no—
723C23—228no—
724C23—228no—
725C23—222no—
726C23—222no—
727C23—222no—
728C23—222no—
729C23—222no—
730C23—222no—
731C23—222no—
732C23—222no—
733C23—222no—
734C23—222no—
735C23—222no—
736C23—222no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—228no—
744C23—444no—
745C23—444no—
746C23—444no—
747C23—444no—
748C23—444no—
749C23—444no—
750C23—444no—
751C23—444no—
752C23—444no—
753C23—444no—
754C23—444no—
755C23—444no—
756C23C2×#433912yes—
757C23C2×D4×D1112yes—
758C23C2×#434312yes—
759C23#41×D1112yes—
760C23#41×D1112yes—
761C23#6704212yes—
762C23#6704212yes—
763C23C24×D1111yescharacteristic
764D4—2232no—
765D4—4416no—
766D4—4416no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—28no—
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—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—114no—
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—222no—
808C2×C4—4416no—
809C2×C4—4416no—
810C2×C4—4416no—
811C2×C4—444no—
812C2×C4—444no—
813C2×C4—444no—
814C2×C4—444no—
815C2×C4C2×#433914yes—
816C2×C4C2×D4×D1114yes—
817C2×C4C2×#434314yes—
818C22—224no—
819C22—224no—
820C22—224no—
821C22—224no—
822C22—224no—
823C22—224no—
824C22—224no—
825C22—224no—
826C22—224no—
827C22—442no—
828C22—442no—
829C22—442no—
830C22—442no—
831C22—442no—
832C22—442no—
833C22—442no—
834C22—442no—
835C22—442no—
836C22—4416no—
837C22—4416no—
838C22—4416no—
839C22—442no—
840C22—442no—
841C22—442no—
842C22#1062306614yes—
843C22#1062307814yes—
844C22#1062311114yes—
845C22#1062316114yes—
846C22#1062318514yes—
847C22#1062322614yes—
848C22#1062323614yes—
849C22C22×#433911yescharacteristic
850C22C22×D4×D1111yescharacteristic
851C22C22×#434311yescharacteristic
852C22C2×#41×D1111yescharacteristic
853C22C2×#41×D1111yescharacteristic
854C22C2×#6704211yescharacteristic
855C22C2×#6704211yescharacteristic
856C4—24no—
857C4—24no—
858C4—24no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—224no—
864C4—442no—
865C4—442no—
866C4—442no—
867C4—442no—
868C2—444no—
869C2—444no—
870C2—444no—
871C2#1307252518yesdirect product factor
872C2C2×#1062307811yescharacteristic
873C2C2×#1062311111yescharacteristic
874C2C2×#1062306611yescharacteristic
875C2C2×#1062316111yescharacteristic
876C2C2×#1062318511yescharacteristic
877C2C2×#1062323611yescharacteristic
878C2C2×#1062322611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#387C2
socleC24×C11C24
prime radicalC2×#10622284C2
hypercenterC2×#387D11
hypocenterC11C2×#2457
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#66947C2semidirect
2. C22×C4×D44C2semidirect
3. #13072525C2direct (N × H)
4. C2×#10622273C2semidirect
5. C2×#10622607C2semidirect
6. C2×#10622604C2semidirect
8. C2×#10622603C2semidirect
9. C2×#10622282C2semidirect
10. C2×#10622278C2semidirect
11. C2×#10622278C2semidirect
12. C2×#10622278C2semidirect
13. C2×#10622277C2semidirect
14. C2×#10622280C2semidirect
15. C2×C4×(C2×D11)⋊C4C2semidirect
16. C2×C11×#387C2semidirect
43. C2×#66947C22semidirect
45. C2×C4×D44C22semidirect
46. C11×#387C22semidirect
57. #10622607C22semidirect
58. #10622604C22semidirect
59. #10622603C22semidirect
60. C4×(C2×D11)⋊C4C22semidirect
62. #10622282C22semidirect
63. #10622280C22semidirect
64. #10622278C22semidirect
65. #10622278C22semidirect
66. #10622278C22semidirect
67. #10622277C22semidirect
68. #10622273C22semidirect
125. C2×(C2×D11)⋊C4D4semidirect
270. (C2×D11)⋊C4C2×D4semidirect
284. C2×#387D11semidirect
430. #387C2×D11semidirect
586. C2×C11#2457semidirect
713. C11C2×#2457semidirect
871. C2#13072525direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669472
C22×C4×D442
#130725252
C2×#106222732
C2×#106226072
C2×#106226042
C2×#106222842
C2×#106226032
C2×#106222822
C2×#106222782
C2×#106222772
C2×#106222802
C2×C4×(C2×D11)⋊C42
C2×C11×#3872
C2×#245711