Finite Group Databasebeta

← C2×#13072347 #14921221

Subgroups — C2×#13072347 #14921221

Order 2816.

4002 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66988C211yesmaximal, characteristic, complemented
2C22×D4×Dic11C211yesmaximal, characteristic, complemented
3C23×Dic11⋊C4C211yesmaximal, characteristic, complemented
4#13072347C2116yesmaximal, direct product factor
5C2×#10622562C211yesmaximal, characteristic, complemented
6C2×#10622596C211yesmaximal, characteristic, complemented
7C2×#10622565C211yesmaximal, characteristic, complemented
8C2×#10622835C211yesmaximal, characteristic, complemented
9C2×#10622557C211yesmaximal, characteristic, complemented
10C2×#10622591C211yesmaximal, characteristic, complemented
11C2×#10622833C211yesmaximal, characteristic, complemented
12C2×#10622833C211yesmaximal, characteristic, complemented
13C2×#10622833C211yesmaximal, characteristic, complemented
14C2×#10622823C211yesmaximal, characteristic, complemented
15C2×#10622559C211yesmaximal, characteristic, complemented
16C22×C11×#121C211yesmaximal, characteristic
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C24×C4×C11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C24×Dic11C2211yescharacteristic
23C24×Dic11C2211yescharacteristic
24C2×C11×#121—28no—
25C2×C11×#121C2218yes—
26C22×C11×C4⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C22×C22⋊Dic11C2211yescharacteristic
37C22×C22⋊Dic11C2211yescharacteristic
38C2×#66988—28no—
39C2×#66988C2218yescomplemented
40C2×D4×Dic11—28no—
41C2×D4×Dic11C2218yescomplemented
42C22×C4⋊Dic11C2211yescharacteristic
43C22×Dic11⋊C4—28no—
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×Dic11⋊C4C2211yescharacteristic
50C22×Dic11⋊C4C2218yescomplemented
51C22×C4×Dic11C2211yescharacteristic
52#10622835C2218yescomplemented
53#10622833C2218yescomplemented
54#10622833C2218yescomplemented
55#10622833C2218yescomplemented
56#10622823C2218yescomplemented
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61C2×C11⋊#95C2211yescharacteristic
62C2×C11⋊#95C2211yescharacteristic
63C2×C11⋊#95C2211yescharacteristic
64C2×C11⋊#95C2211yescharacteristic
65#10622596C2218yescomplemented
66#10622591C2218yescomplemented
67#10622565C2218yescomplemented
68#10622562C2218yescomplemented
69#10622559C2218yescomplemented
70#10622557C2218yescomplemented
71C25×C11C2311yescharacteristic
72C25×C11C2311yescharacteristic
73C25×C11C2311yescharacteristic
74C22×D4×C11—24no—
75C22×D4×C11—24no—
76C22×D4×C11—24no—
77C22×D4×C11—24no—
78C22×D4×C11—24no—
79C22×D4×C11—24no—
80C22×D4×C11—24no—
81C22×D4×C11—42no—
82C22×D4×C11D418yes—
83C22×D4×C11C2314yes—
84C22×D4×C11C2314yes—
85C22×D4×C11C2314yes—
86C23×C4×C11—24no—
87C23×C4×C11—24no—
88C23×C4×C11—42no—
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2314yes—
92C23×C4×C11C2311yescharacteristic
93C23×C4×C11C2311yescharacteristic
94C23×Dic11—24no—
95C23×Dic11—24no—
96C23×Dic11—24no—
97C23×Dic11—24no—
98C23×Dic11—24no—
99C23×Dic11—24no—
100C23×Dic11—24no—
101C23×Dic11—42no—
102C23×Dic11—42no—
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C23×Dic11C2314yes—
109C23×Dic11C2314yes—
110C23×Dic11C2314yes—
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2311yescharacteristic
114C11×#121—232no—
115C2×C11×C4⋊C4—24no—
116C2×C11×C4⋊C4C2314yes—
117C2×C11×C22⋊C4—24no—
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4C2314yes—
120C2×C11×C22⋊C4C2314yes—
121C2×C22⋊Dic11—24no—
122C2×C22⋊Dic11—24no—
123C2×C22⋊Dic11—24no—
124C2×C22⋊Dic11—24no—
125C2×C22⋊Dic11—24no—
126C2×C22⋊Dic11—24no—
127C2×C22⋊Dic11—24no—
128C2×C22⋊Dic11—24no—
129C2×C22⋊Dic11—42no—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134C2×C22⋊Dic11C2314yes—
135C2×C22⋊Dic11C2314yes—
136C2×C22⋊Dic11C2314yes—
137C2×C22⋊Dic11C2314yes—
138C2×C22⋊Dic11C2314yes—
139#66988—232no—
140D4×Dic11—232no—
141C2×C4⋊Dic11—24no—
142C2×C4⋊Dic11C2314yes—
143C2×Dic11⋊C4—24no—
144C2×Dic11⋊C4—24no—
145C2×Dic11⋊C4—24no—
146C2×Dic11⋊C4—24no—
147C2×Dic11⋊C4—232no—
148C2×Dic11⋊C4—42no—
149C2×Dic11⋊C4D418yescomplemented
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C2×Dic11⋊C4C2314yes—
155C2×Dic11⋊C4C2314yes—
156C2×C4×Dic11—24no—
157C2×C4×Dic11C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C11⋊#95C2314yes—
166C2×#2443—111nomaximal, Sylow
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—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—22no—
183C24×C11—22no—
184C24×C11C2×D414yes—
185C24×C11C2×D414yes—
186C24×C11#4114yes—
187C24×C11#4114yes—
188C24×C11C2412yes—
189C24×C11C2412yes—
190C24×C11C2412yes—
191C24×C11C2411yescharacteristic
192C2×D4×C11—232no—
193C2×D4×C11—28no—
194C2×D4×C11—28no—
195C2×D4×C11—28no—
196C2×D4×C11—28no—
197C2×D4×C11—28no—
198C2×D4×C11—28no—
199C2×D4×C11—28no—
200C2×D4×C11—44no—
201C2×D4×C11—416no—
202C2×D4×C11—416no—
203C2×D4×C11C2×D4116yes—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—28no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—28no—
216C22×C4×C11—44no—
217C22×C4×C11—416no—
218C22×C4×C11C2×D414yes—
219C22×C4×C11C2×D414yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×Dic11—232no—
225C22×Dic11—28no—
226C22×Dic11—28no—
227C22×Dic11—28no—
228C22×Dic11—28no—
229C22×Dic11—22no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—28no—
238C22×Dic11—28no—
239C22×Dic11—28no—
240C22×Dic11—22no—
241C22×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11—22no—
246C22×Dic11—22no—
247C22×Dic11—22no—
248C22×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11—22no—
251C22×Dic11—22no—
252C22×Dic11—22no—
253C22×Dic11—44no—
254C22×Dic11—44no—
255C22×Dic11—416no—
256C22×Dic11—416no—
257C22×Dic11C2×D414yes—
258C22×Dic11C2×D414yes—
259C22×Dic11#4114yes—
260C22×Dic11C2412yes—
261C22×Dic11C2412yes—
262C22×Dic11C2412yes—
263C22×Dic11C2412yes—
264C22×Dic11C2412yes—
265C22×Dic11C2412yes—
266C22×Dic11C2412yes—
267C22×Dic11C2412yes—
268C11×C4⋊C4—28no—
269C11×C22⋊C4—28no—
270C11×C22⋊C4—28no—
271C22⋊Dic11—28no—
272C22⋊Dic11—28no—
273C22⋊Dic11—28no—
274C22⋊Dic11—28no—
275C22⋊Dic11—28no—
276C22⋊Dic11—28no—
277C22⋊Dic11—28no—
278C22⋊Dic11—28no—
279C22⋊Dic11—44no—
280C4⋊Dic11—28no—
281Dic11⋊C4—28no—
282Dic11⋊C4—28no—
283Dic11⋊C4—28no—
284Dic11⋊C4—28no—
285Dic11⋊C4—44no—
286Dic11⋊C4C2×D4116yescomplemented
287C4×Dic11—28no—
288C22×#123—111no—
289C22×#121D1111yescharacteristic
290C22×C4×D4—111no—
291C23×C4⋊C4—111no—
292#2443—1116no—
293C2×#399—111no—
294C2×#398—111no—
295C2×#397—111no—
296C2×#394—111no—
297C2×#388—111no—
298C2×#387—111no—
299C2×#386—111no—
300C2×#386—111no—
301C2×#386—111no—
302C2×#385—111no—
303C2×#385—111no—
304C23×C11—28no—
305C23×C11—28no—
306C23×C11—28no—
307C23×C11—28no—
308C23×C11—28no—
309C23×C11—28no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—28no—
315C23×C11—28no—
316C23×C11—28no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—44no—
331C23×C11—44no—
332C23×C11—44no—
333C23×C11—44no—
334C23×C11—44no—
335C23×C11—44no—
336C23×C11—44no—
337C23×C11—44no—
338C23×C11—44no—
339C23×C11—44no—
340C23×C11—44no—
341C23×C11#123116yescomplemented
342C23×C11C22×D412yes—
343C23×C11C22×D414yes—
344C23×C11C22×D414yes—
345C23×C11C22×D412yes—
346C23×C11C2×#4114yes—
347C23×C11C2×#4114yes—
348C23×C11C2×#4112yes—
349C23×C11C2×#4112yes—
350C23×C11C2×#4112yes—
351C23×C11H(5,𝔽2)12yes—
352C23×C112−1+412yes—
353C23×C11C2511yescharacteristic
354D4×C11—232no—
355D4×C11—416no—
356D4×C11—416no—
357C2×C4×C11—28no—
358C2×C4×C11—28no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—416no—
370C2×C4×C11—44no—
371C2×C4×C11—44no—
372C2×C4×C11C22×D414yes—
373C2×C4×C11C22×D414yes—
374C2×Dic11—232no—
375C2×Dic11—28no—
376C2×Dic11—28no—
377C2×Dic11—28no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—416no—
400C2×Dic11—416no—
401C2×Dic11—44no—
402C2×Dic11—44no—
403C2×Dic11—44no—
404C2×Dic11—44no—
405C2×Dic11—44no—
406C2×Dic11C22×D414yes—
407C2×Dic11C22×D414yes—
408C2×Dic11C2×#4114yes—
409C23×D4C2×D1111yescharacteristic
410C23×D4C2×D1111yescharacteristic
411C23×D4C2×D1111yescharacteristic
412C24×C4—111no—
413C24×C4—111no—
414C24×C4—111no—
415C24×C4C2×D1111yescharacteristic
416C2×#123—118no—
417C2×#123—228no—
418C2×#121—28no—
419C2×#121C2×D1118yes—
420C2×C4×D4—118no—
421C2×C4×D4—228no—
422C22×C4⋊C4—111no—
423C22×C4⋊C4—111no—
424C22×C4⋊C4—111no—
425C22×C4⋊C4—111no—
426C22×C4⋊C4—111no—
427C22×C4⋊C4—118no—
428C22×C4⋊C4—111no—
429C22×C4⋊C4—111no—
430C22×C4⋊C4—228no—
431C22×C4⋊C4C2×D1111yescharacteristic
432C22×C22⋊C4—111no—
433C22×C22⋊C4—111no—
434C22×C22⋊C4—111no—
435C22×C22⋊C4—111no—
436C22×C22⋊C4—111no—
437C22×C22⋊C4—111no—
438C22×C22⋊C4—111no—
439C22×C22⋊C4—111no—
440C22×C22⋊C4—111no—
441C22×C22⋊C4C2×D1111yescharacteristic
442C22×C22⋊C4C2×D1111yescharacteristic
443C22×C42—111no—
444#399—118no—
445#398—118no—
446#397—118no—
447#394—118no—
448#388—118no—
449#387—118no—
450#386—118no—
451#386—118no—
452#386—118no—
453#385—118no—
454#385—118no—
455C2×#95—111no—
456C2×#95—111no—
457C2×#95—111no—
458C2×#95—111no—
459C2×#95—111no—
460C2×#95—111no—
461C2×#95—111no—
462C2×#95—111no—
463C22×C11—24no—
464C22×C11—24no—
465C22×C11—24no—
466C22×C11—24no—
467C22×C11—24no—
468C22×C11—232no—
469C22×C11—24no—
470C22×C11—24no—
471C22×C11—24no—
472C22×C11—24no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—416no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—88no—
486C22×C11C2×#12314yes—
487C22×C11C2×#12318yescomplemented
488C22×C11#52514yes—
489C22×C11#53914yes—
490C22×C11D4214yes—
491C22×C11#54714yes—
492C22×C11#54814yes—
493C22×C11#55314yes—
494C22×C11C23×D411yescharacteristic
495C22×C11C23×D411yescharacteristic
496C22×C11C22×#4111yescharacteristic
497C22×C11C22×#4111yescharacteristic
498C22×C11C22×#4111yescharacteristic
499C22×C11C2×H(5,𝔽2)11yescharacteristic
500C22×C11C2×2−1+411yescharacteristic
501C4×C11—24no—
502C4×C11—24no—
503C4×C11—42no—
504C4×C11—42no—
505Dic11—24no—
506Dic11—24no—
507Dic11—24no—
508Dic11—42no—
509Dic11—42no—
510Dic11—42no—
511Dic11—42no—
512Dic11—42no—
513C25C22×D1111yescharacteristic
514C25C22×D1111yescharacteristic
515C25C22×D1111yescharacteristic
516C22×D4—24no—
517C22×D4—24no—
518C22×D4—24no—
519C22×D4—24no—
520C22×D4—24no—
521C22×D4—24no—
522C22×D4—24no—
523C22×D4—42no—
524C22×D4C22⋊D1118yes—
525C22×D4C22×D1114yes—
526C22×D4C22×D1114yes—
527C22×D4C22×D1114yes—
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—42no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—111no—
534C23×C4—114no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4—111no—
539C23×C4—111no—
540C23×C4—114no—
541C23×C4—114no—
542C23×C4—224no—
543C23×C4—224no—
544C23×C4—224no—
545C23×C4—224no—
546C23×C4—224no—
547C23×C4—224no—
548C23×C4—224no—
549C23×C4—442no—
550C23×C4—442no—
551C23×C4C22×D1111yescharacteristic
552C23×C4C22×D1111yescharacteristic
553C23×C4C22×D1114yes—
554C23×C4C22×D1111yescharacteristic
555C23×C4C22×D1111yescharacteristic
556#123—2232no—
557#121—232no—
558C4×D4—2232no—
559C2×C4⋊C4—24no—
560C2×C4⋊C4—118no—
561C2×C4⋊C4—114no—
562C2×C4⋊C4—114no—
563C2×C4⋊C4—114no—
564C2×C4⋊C4—114no—
565C2×C4⋊C4—114no—
566C2×C4⋊C4—114no—
567C2×C4⋊C4—114no—
568C2×C4⋊C4—2232no—
569C2×C4⋊C4—224no—
570C2×C4⋊C4—224no—
571C2×C4⋊C4—224no—
572C2×C4⋊C4—224no—
573C2×C4⋊C4—224no—
574C2×C4⋊C4—442no—
575C2×C4⋊C4C22×D1114yes—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—114no—
579C2×C22⋊C4—114no—
580C2×C22⋊C4—114no—
581C2×C22⋊C4—114no—
582C2×C22⋊C4—114no—
583C2×C22⋊C4—114no—
584C2×C22⋊C4—114no—
585C2×C22⋊C4—114no—
586C2×C22⋊C4—114no—
587C2×C22⋊C4—224no—
588C2×C22⋊C4—224no—
589C2×C22⋊C4—224no—
590C2×C22⋊C4—224no—
591C2×C22⋊C4—224no—
592C2×C22⋊C4—224no—
593C2×C22⋊C4—224no—
594C2×C22⋊C4—224no—
595C2×C22⋊C4—442no—
596C2×C22⋊C4C22×D1114yes—
597C2×C22⋊C4C22×D1114yes—
598C2×C42—114no—
599C2×C42—224no—
600#95—114no—
601#95—114no—
602#95—114no—
603#95—114no—
604#95—114no—
605#95—114no—
606#95—114no—
607#95—114no—
608C2×C11—28no—
609C2×C11—44no—
610C2×C11—82no—
611C2×C11#244318yescomplemented
612C2×C11C22×#12311yescharacteristic
613C2×C11C2×#52511yescharacteristic
614C2×C11C2×#53911yescharacteristic
615C2×C11C2×D4211yescharacteristic
616C2×C11C2×#54711yescharacteristic
617C2×C11C2×#54811yescharacteristic
618C2×C11C2×#55311yescharacteristic
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24#434114yes—
637C24#434114yes—
638C24C2×C22⋊D1114yes—
639C24C2×C22⋊D1114yes—
640C24C23×D1112yes—
641C24C23×D1112yes—
642C24C23×D1112yes—
643C24C23×D1111yescharacteristic
644C2×D4—232no—
645C2×D4—28no—
646C2×D4—28no—
647C2×D4—28no—
648C2×D4—28no—
649C2×D4—28no—
650C2×D4—28no—
651C2×D4—28no—
652C2×D4—44no—
653C2×D4—416no—
654C2×D4—416no—
655C2×D4C2×C22⋊D11116yes—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—28no—
667C22×C4—28no—
668C22×C4—44no—
669C22×C4—416no—
670C22×C4—114no—
671C22×C4—114no—
672C22×C4—114no—
673C22×C4—112no—
674C22×C4—112no—
675C22×C4—112no—
676C22×C4—112no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—228no—
682C22×C4—228no—
683C22×C4—228no—
684C22×C4—228no—
685C22×C4—2232no—
686C22×C4—222no—
687C22×C4—228no—
688C22×C4—222no—
689C22×C4—222no—
690C22×C4—222no—
691C22×C4—222no—
692C22×C4—222no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—222no—
696C22×C4—222no—
697C22×C4—222no—
698C22×C4—222no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—222no—
702C22×C4—222no—
703C22×C4—222no—
704C22×C4—222no—
705C22×C4—222no—
706C22×C4—222no—
707C22×C4—222no—
708C22×C4—228no—
709C22×C4—228no—
710C22×C4—444no—
711C22×C4—444no—
712C22×C4—4416no—
713C22×C4—4416no—
714C22×C4D4×D1114yes—
715C22×C4C2×C22⋊D1114yes—
716C22×C4C23×D1112yes—
717C22×C4C23×D1112yes—
718C22×C4C23×D1112yes—
719C22×C4C23×D1112yes—
720C4⋊C4—28no—
721C4⋊C4—1116no—
722C4⋊C4—228no—
723C4⋊C4—228no—
724C4⋊C4—228no—
725C4⋊C4—228no—
726C4⋊C4—228no—
727C4⋊C4—444no—
728C22⋊C4—28no—
729C22⋊C4—28no—
730C22⋊C4—228no—
731C22⋊C4—228no—
732C22⋊C4—228no—
733C22⋊C4—228no—
734C22⋊C4—228no—
735C22⋊C4—228no—
736C22⋊C4—228no—
737C22⋊C4—228no—
738C22⋊C4—444no—
739C42—228no—
740C11C2×#244311yescharacteristic, complemented, Sylow
741C23—28no—
742C23—28no—
743C23—28no—
744C23—28no—
745C23—28no—
746C23—28no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—28no—
752C23—28no—
753C23—28no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23#66988116yescomplemented
779C23C2×D4×D1112yes—
780C23C2×#434114yes—
781C23C2×#434114yes—
782C23C2×#434112yes—
783C23C2×#434112yes—
784C23#6703712yes—
785C23#41×D1112yes—
786C23#6704312yes—
787C23C22×C22⋊D1114yes—
788C23C22×C22⋊D1114yes—
789C23C22×C22⋊D1112yes—
790C23C24×D1111yescharacteristic
791D4—232no—
792D4—416no—
793D4—416no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—416no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—114no—
810C2×C4—114no—
811C2×C4—114no—
812C2×C4—2232no—
813C2×C4—228no—
814C2×C4—228no—
815C2×C4—228no—
816C2×C4—222no—
817C2×C4—222no—
818C2×C4—222no—
819C2×C4—222no—
820C2×C4—222no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—222no—
835C2×C4—222no—
836C2×C4—222no—
837C2×C4—4416no—
838C2×C4—4416no—
839C2×C4—444no—
840C2×C4—444no—
841C2×C4—444no—
842C2×C4—444no—
843C2×C4—444no—
844C2×C4C2×D4×D1114yes—
845C2×C4C22×C22⋊D1114yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—24no—
851C22—232no—
852C22—24no—
853C22—24no—
854C22—24no—
855C22—24no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—416no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—88no—
869C22#1062312914yes—
870C22#1062313214yes—
871C22#1062313314yes—
872C22#1062313714yes—
873C22C2×#6698814yes—
874C22C2×#6698818yescomplemented
875C22D4×C22⋊D1114yes—
876C22#1062335514yes—
877C22C22×D4×D1111yescharacteristic
878C22C22×#434111yescharacteristic
879C22C22×#434111yescharacteristic
880C22C2×#6703711yescharacteristic
881C22C2×#41×D1111yescharacteristic
882C22C2×#6704311yescharacteristic
883C22C23×C22⋊D1111yescharacteristic
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—224no—
889C4—224no—
890C4—224no—
891C4—442no—
892C4—442no—
893C4—442no—
894C4—442no—
895C4—442no—
896C2—28no—
897C2—44no—
898C2—82no—
899C2#1307234718yesdirect product factor
900C2C22×#6698811yescharacteristic
901C2C2×#1062313711yescharacteristic
902C2C2×#1062313311yescharacteristic
903C2C2×D4×C22⋊D1111yescharacteristic
904C2C2×#1062335511yescharacteristic
905C2C2×#1062312911yescharacteristic
906C2C2×#1062313211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
Fitting, prime radicalC22×C11×#121C2
socleC24×C11C24
hypercenterC22×#121D11
hypocenterC11C2×#2443
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#66988C2semidirect
2. C22×D4×Dic11C2semidirect
3. C23×Dic11⋊C4C2semidirect
4. #13072347C2direct (N × H)
5. C2×#10622562C2semidirect
6. C2×#10622596C2semidirect
7. C2×#10622565C2semidirect
8. C2×#10622835C2semidirect
9. C2×#10622557C2semidirect
10. C2×#10622591C2semidirect
11. C2×#10622833C2semidirect
12. C2×#10622833C2semidirect
13. C2×#10622833C2semidirect
14. C2×#10622823C2semidirect
15. C2×#10622559C2semidirect
39. C2×#66988C22semidirect
41. C2×D4×Dic11C22semidirect
50. C22×Dic11⋊C4C22semidirect
52. #10622835C22semidirect
53. #10622833C22semidirect
54. #10622833C22semidirect
55. #10622833C22semidirect
56. #10622823C22semidirect
65. #10622596C22semidirect
66. #10622591C22semidirect
67. #10622565C22semidirect
68. #10622562C22semidirect
69. #10622559C22semidirect
70. #10622557C22semidirect
149. C2×Dic11⋊C4D4semidirect
286. Dic11⋊C4C2×D4semidirect
341. C23×C11#123semidirect
487. C22×C11C2×#123semidirect
611. C2×C11#2443semidirect
740. C11C2×#2443semidirect
778. C23#66988semidirect
874. C22C2×#66988semidirect
899. C2#13072347direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669882
C22×D4×Dic112
C23×Dic11⋊C42
#130723472
C2×#106225622
C2×#106225962
C2×#106225652
C2×#106228352
C2×#106225572
C2×#106225912
C2×#106228332
C2×#106228232
C2×#106225592
C22×C11×#1212
C2×#244311