Finite Group Databasebeta

← C2×#13072288 #14922414

Subgroups — C2×#13072288 #14922414

Order 2816.

3006 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66930C211yesmaximal, characteristic
2#13072288C2116yesmaximal, direct product factor
3C2×#10622595C211yesmaximal, characteristic, complemented
4C2×#10622597C211yesmaximal, characteristic, complemented
5C2×#10622597C211yesmaximal, characteristic, complemented
6C2×#10622842C211yesmaximal, characteristic, complemented
7C2×#10622843C211yesmaximal, characteristic, complemented
8C2×#10622586C211yesmaximal, characteristic, complemented
9C2×#10622591C211yesmaximal, characteristic, complemented
10C2×#10622591C211yesmaximal, characteristic, complemented
11C2×#10622563C211yesmaximal, characteristic
12C2×#10622823C211yesmaximal, characteristic
13C2×#10622556C211yesmaximal, characteristic
14C2×#10622555C211yesmaximal, characteristic
15C22×C11⋊#95C211yesmaximal, characteristic
16C22×C11×C22⋊Q8C211yesmaximal, characteristic
17C23×Q8×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C2×C11×C22⋊Q8—28no—
22C2×C11×C22⋊Q8C2218yes—
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C2×#66930—28no—
41C2×#66930C2218yes—
42#10622843C2218yescomplemented
43#10622842C2218yescomplemented
44#10622823C2218yes—
45C2×C11⋊#95C2218yes—
46C2×C11⋊#95C2211yescharacteristic
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
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60#10622597C2218yescomplemented
61#10622597C2218yescomplemented
62#10622595C2218yescomplemented
63#10622591C2218yescomplemented
64#10622591C2218yescomplemented
65#10622586C2218yescomplemented
66#10622563C2218yes—
67#10622556C2218yes—
68#10622555C2218yes—
69C25×C11C2311yescharacteristic
70C22×Q8×C11—24no—
71C22×Q8×C11—24no—
72C22×Q8×C11—42no—
73C22×Q8×C11C2314yes—
74C23×C4×C11—24no—
75C23×C4×C11—24no—
76C23×C4×C11—42no—
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2314yes—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×Dic11—24no—
85C23×Dic11—24no—
86C23×Dic11—24no—
87C23×Dic11—24no—
88C23×Dic11—42no—
89C23×Dic11Q818yescomplemented
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2314yes—
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2314yes—
99C23×Dic11C2311yescharacteristic
100C11×C22⋊Q8—232no—
101C2×C11×C4⋊C4—24no—
102C2×C11×C4⋊C4—24no—
103C2×C11×C4⋊C4—24no—
104C2×C11×C4⋊C4C2314yes—
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C4⋊C4C2314yes—
107C2×C11×C22⋊C4—24no—
108C2×C11×C22⋊C4D418yes—
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2314yes—
111C2×C22⋊Dic11—24no—
112C2×C22⋊Dic11—24no—
113C2×C22⋊Dic11C2314yes—
114C2×C22⋊Dic11C2314yes—
115C2×C4⋊Dic11—24no—
116C2×C4⋊Dic11—42no—
117C2×C4⋊Dic11C2314yes—
118C2×C4⋊Dic11C2314yes—
119C2×Dic11⋊C4—24no—
120C2×Dic11⋊C4—24no—
121C2×Dic11⋊C4—24no—
122C2×Dic11⋊C4—24no—
123C2×Dic11⋊C4—42no—
124C2×Dic11⋊C4—42no—
125C2×Dic11⋊C4C2314yes—
126C2×Dic11⋊C4C2314yes—
127C2×Dic11⋊C4C2314yes—
128C2×Dic11⋊C4C2314yes—
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2314yes—
131C2×C4×Dic11—24no—
132C2×C4×Dic11—24no—
133C2×C4×Dic11C2314yes—
134C2×C4×Dic11C2314yes—
135#66930—232no—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C2×#2438—111nomaximal, Sylow
151C24×C11—22no—
152C24×C11—22no—
153C24×C11—22no—
154C24×C11—22no—
155C24×C11C2×D414yes—
156C24×C11C2×Q814yes—
157C24×C11#4114yes—
158C24×C11C2412yes—
159C24×C11C2411yescharacteristic
160C2×Q8×C11—28no—
161C2×Q8×C11—28no—
162C2×Q8×C11—44no—
163C2×Q8×C11—416no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—28no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—28no—
181C22×C4×C11—44no—
182C22×C4×C11—416no—
183C22×C4×C11C2×D414yes—
184C22×C4×C11C2×D414yes—
185C22×C4×C11#4114yes—
186C22×C4×C11C2412yes—
187C22×C4×C11C2412yes—
188C22×C4×C11C2412yes—
189C22×C4×C11C2412yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2412yes—
192C22×Dic11—28no—
193C22×Dic11—232no—
194C22×Dic11—28no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—28no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—28no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—44no—
219C22×Dic11—416no—
220C22×Dic11C2×Q814yes—
221C22×Dic11C2×Q814yes—
222C22×Dic11C2×Q8116yescomplemented
223C22×Dic11#4114yes—
224C22×Dic11C2412yes—
225C22×Dic11C2412yes—
226C22×Dic11C2412yes—
227C22×Dic11C2412yes—
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C22×Dic11C2412yes—
231C22×Dic11C2412yes—
232C11×C4⋊C4—28no—
233C11×C4⋊C4—28no—
234C11×C4⋊C4—28no—
235C11×C22⋊C4—28no—
236C11×C22⋊C4C2×D4116yes—
237C22⋊Dic11—28no—
238C22⋊Dic11—28no—
239C4⋊Dic11—28no—
240C4⋊Dic11—44no—
241Dic11⋊C4—28no—
242Dic11⋊C4—28no—
243Dic11⋊C4—28no—
244Dic11⋊C4—28no—
245Dic11⋊C4—44no—
246Dic11⋊C4—44no—
247C4×Dic11—28no—
248C4×Dic11—28no—
249C22×C22⋊Q8D1111yescharacteristic
250C22×#117—111no—
251#2438—1116no—
252C2×#400—111no—
253C2×#398—111no—
254C2×#398—111no—
255C2×#395—111no—
256C2×#391—111no—
257C2×#389—111no—
258C2×#387—111no—
259C2×#387—111no—
260C2×#385—111no—
261C2×#385—111no—
262C2×#381—111no—
263C2×#380—111no—
264C22×#95—111no—
265C23×C11—28no—
266C23×C11—28no—
267C23×C11—28no—
268C23×C11—28no—
269C23×C11—28no—
270C23×C11—28no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11C22⋊Q8116yes—
276C23×C11C22×D414yes—
277C23×C11C22×D412yes—
278C23×C11C22×Q814yes—
279C23×C11C22×Q812yes—
280C23×C11C2×#4112yes—
281C23×C11C2×#4114yes—
282C23×C11C2×#4112yes—
283C23×C11C2×#4112yes—
284C23×C11H(5,𝔽2)12yes—
285C23×C112−1+412yes—
286C23×C11C2511yescharacteristic
287Q8×C11—416no—
288C2×C4×C11—28no—
289C2×C4×C11—28no—
290C2×C4×C11—28no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—416no—
307C2×C4×C11—44no—
308C2×C4×C11—44no—
309C2×C4×C11—44no—
310C2×C4×C11C22×D414yes—
311C2×C4×C11C22×D414yes—
312C2×C4×C11C2×#4114yes—
313C2×Dic11—28no—
314C2×Dic11—28no—
315C2×Dic11—232no—
316C2×Dic11—28no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—416no—
339C2×Dic11—44no—
340C2×Dic11—44no—
341C2×Dic11—44no—
342C2×Dic11—44no—
343C2×Dic11—44no—
344C2×Dic11C22×Q814yes—
345C2×Dic11C22×Q814yes—
346C2×Dic11C2×#4114yes—
347C23×Q8C2×D1111yescharacteristic
348C24×C4—111no—
349C24×C4—111no—
350C24×C4C2×D1111yescharacteristic
351C2×C22⋊Q8—28no—
352C2×C22⋊Q8C2×D1118yes—
353C2×#117—118no—
354C2×#117—228no—
355C22×C4⋊C4—111no—
356C22×C4⋊C4—111no—
357C22×C4⋊C4—111no—
358C22×C4⋊C4—111no—
359C22×C4⋊C4—111no—
360C22×C4⋊C4—111no—
361C22×C4⋊C4—111no—
362C22×C4⋊C4—111no—
363C22×C4⋊C4C2×D1111yescharacteristic
364C22×C4⋊C4C2×D1111yescharacteristic
365C22×C4⋊C4C2×D1111yescharacteristic
366C22×C22⋊C4—111no—
367C22×C22⋊C4—111no—
368C22×C22⋊C4C2×D1111yescharacteristic
369C22×C22⋊C4C2×D1111yescharacteristic
370C22×C42—111no—
371C22×C42—111no—
372#400—118no—
373#398—118no—
374#398—118no—
375#395—118no—
376#391—118no—
377#389—118no—
378#387—118no—
379#387—118no—
380#385—118no—
381#385—118no—
382#381—118no—
383#380—118no—
384C2×#95—111no—
385C2×#95—111no—
386C2×#95—111no—
387C2×#95—111no—
388C2×#95—111no—
389C2×#95—111no—
390C2×#95—111no—
391C2×#95—111no—
392C2×#95—111no—
393C2×#95—111no—
394C2×#95—118no—
395C2×#95—111no—
396C2×#95—111no—
397C2×#95—111no—
398C2×#95—111no—
399C22×C11—24no—
400C22×C11—24no—
401C22×C11—232no—
402C22×C11—24no—
403C22×C11—24no—
404C22×C11—24no—
405C22×C11—24no—
406C22×C11C2×C22⋊Q818yes—
407C22×C11C2×C22⋊Q814yes—
408C22×C11#53314yes—
409C22×C11#54414yes—
410C22×C11#54614yes—
411C22×C11#54714yes—
412C22×C11#55114yes—
413C22×C11#55214yes—
414C22×C11C23×D411yescharacteristic
415C22×C11C23×Q811yescharacteristic
416C22×C11C22×#4111yescharacteristic
417C22×C11C22×#4111yescharacteristic
418C22×C11C22×#4111yescharacteristic
419C22×C11C2×H(5,𝔽2)11yescharacteristic
420C22×C11C2×2−1+411yescharacteristic
421C4×C11—24no—
422C4×C11—24no—
423C4×C11—24no—
424C4×C11—42no—
425C4×C11—42no—
426C4×C11—42no—
427Dic11—24no—
428Dic11—24no—
429Dic11—24no—
430Dic11—42no—
431Dic11—42no—
432Dic11—42no—
433Dic11—42no—
434Dic11—42no—
435C25C22×D1111yescharacteristic
436C22×Q8—24no—
437C22×Q8—24no—
438C22×Q8—42no—
439C22×Q8C22×D1114yes—
440C23×C4—24no—
441C23×C4—24no—
442C23×C4—42no—
443C23×C4—118no—
444C23×C4—114no—
445C23×C4—111no—
446C23×C4—111no—
447C23×C4—111no—
448C23×C4—111no—
449C23×C4—111no—
450C23×C4—111no—
451C23×C4—111no—
452C23×C4—111no—
453C23×C4—114no—
454C23×C4—224no—
455C23×C4—224no—
456C23×C4—224no—
457C23×C4—224no—
458C23×C4—442no—
459C23×C4C22×D1111yescharacteristic
460C23×C4C22×D1111yescharacteristic
461C23×C4C22×D1111yescharacteristic
462C23×C4C22×D1114yes—
463C23×C4C22×D1111yescharacteristic
464C23×C4C22×D1111yescharacteristic
465C23×C4C22×D1111yescharacteristic
466C22⋊Q8—232no—
467#117—2232no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—114no—
472C2×C4⋊C4—114no—
473C2×C4⋊C4—114no—
474C2×C4⋊C4—114no—
475C2×C4⋊C4—114no—
476C2×C4⋊C4—114no—
477C2×C4⋊C4—114no—
478C2×C4⋊C4—114no—
479C2×C4⋊C4—224no—
480C2×C4⋊C4—224no—
481C2×C4⋊C4—224no—
482C2×C4⋊C4—224no—
483C2×C4⋊C4—224no—
484C2×C4⋊C4—442no—
485C2×C4⋊C4—442no—
486C2×C4⋊C4—442no—
487C2×C4⋊C4C22×D1114yes—
488C2×C4⋊C4C22×D1114yes—
489C2×C4⋊C4C22×D1114yes—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—114no—
492C2×C22⋊C4—114no—
493C2×C22⋊C4—224no—
494C2×C22⋊C4—224no—
495C2×C22⋊C4C22⋊D1118yes—
496C2×C22⋊C4C22×D1114yes—
497C2×C22⋊C4C22×D1114yes—
498C2×C42—114no—
499C2×C42—114no—
500C2×C42—224no—
501C2×C42—224no—
502#95—114no—
503#95—114no—
504#95—114no—
505#95—114no—
506#95—114no—
507#95—114no—
508#95—114no—
509#95—114no—
510#95—114no—
511#95—114no—
512#95—114no—
513#95—114no—
514#95—114no—
515#95—114no—
516C2×C11—28no—
517C2×C11#243818yescomplemented
518C2×C11C22×C22⋊Q811yescharacteristic
519C2×C11C2×#53311yescharacteristic
520C2×C11C2×#54411yescharacteristic
521C2×C11C2×#54611yescharacteristic
522C2×C11C2×#54711yescharacteristic
523C2×C11C2×#55111yescharacteristic
524C2×C11C2×#55211yescharacteristic
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24Q8×D1114yes—
530C24#434314yes—
531C24C2×C22⋊D1114yes—
532C24C23×D1112yes—
533C24C23×D1111yescharacteristic
534C2×Q8—28no—
535C2×Q8—28no—
536C2×Q8—44no—
537C2×Q8—416no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—44no—
556C22×C4—416no—
557C22×C4—114no—
558C22×C4—114no—
559C22×C4—1116no—
560C22×C4—114no—
561C22×C4—112no—
562C22×C4—112no—
563C22×C4—112no—
564C22×C4—112no—
565C22×C4—112no—
566C22×C4—112no—
567C22×C4—112no—
568C22×C4—112no—
569C22×C4—228no—
570C22×C4—2232no—
571C22×C4—222no—
572C22×C4—228no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—228no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—228no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—444no—
596C22×C4—4416no—
597C22×C4#434114yes—
598C22×C4C2×C22⋊D1114yes—
599C22×C4C2×C22⋊D1114yes—
600C22×C4C23×D1112yes—
601C22×C4C23×D1112yes—
602C22×C4C23×D1112yes—
603C22×C4C23×D1112yes—
604C22×C4C23×D1112yes—
605C22×C4C23×D1112yes—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—228no—
610C4⋊C4—228no—
611C4⋊C4—228no—
612C4⋊C4—228no—
613C4⋊C4—228no—
614C4⋊C4—444no—
615C4⋊C4—444no—
616C4⋊C4—444no—
617C22⋊C4—28no—
618C22⋊C4—228no—
619C22⋊C4—228no—
620C22⋊C4C2×C22⋊D11116yes—
621C42—228no—
622C42—228no—
623C11C2×#243811yescharacteristic, complemented, Sylow
624C23—28no—
625C23—28no—
626C23—28no—
627C23—28no—
628C23—28no—
629C23—28no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23#66999116yes—
635C23C2×#434112yes—
636C23#6703712yes—
637C23C2×Q8×D1114yes—
638C23C2×Q8×D1112yes—
639C23C2×#434314yes—
640C23C2×#434312yes—
641C23#41×D1112yes—
642C23#6704312yes—
643C23C22×C22⋊D1114yes—
644C23C22×C22⋊D1112yes—
645C23C24×D1111yescharacteristic
646Q8—416no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—28no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—416no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—114no—
670C2×C4—114no—
671C2×C4—114no—
672C2×C4—2232no—
673C2×C4—228no—
674C2×C4—228no—
675C2×C4—228no—
676C2×C4—222no—
677C2×C4—222no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—4416no—
698C2×C4—444no—
699C2×C4—444no—
700C2×C4—444no—
701C2×C4—444no—
702C2×C4—444no—
703C2×C4C2×#434114yes—
704C2×C4C22×C22⋊D1114yes—
705C2×C4C22×C22⋊D1114yes—
706C22—24no—
707C22—24no—
708C22—24no—
709C22—24no—
710C22—232no—
711C22—24no—
712C22—24no—
713C22#1062315314yes—
714C22#1062315414yes—
715C22#1062316814yes—
716C22#1062317314yes—
717C22#1062333714yes—
718C22C2×#6699918yes—
719C22C2×#6699914yes—
720C22#1062335514yes—
721C22C22×#434111yescharacteristic
722C22C2×#6703711yescharacteristic
723C22C22×Q8×D1111yescharacteristic
724C22C22×#434311yescharacteristic
725C22C2×#41×D1111yescharacteristic
726C22C2×#6704311yescharacteristic
727C22C23×C22⋊D1111yescharacteristic
728C4—24no—
729C4—24no—
730C4—24no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—224no—
735C4—224no—
736C4—224no—
737C4—442no—
738C4—442no—
739C4—442no—
740C4—442no—
741C4—442no—
742C2—28no—
743C2#1307228818yesdirect product factor
744C2C22×#6699911yescharacteristic
745C2C2×#1062315311yescharacteristic
746C2C2×#1062315411yescharacteristic
747C2C2×#1062333711yescharacteristic
748C2C2×#1062335511yescharacteristic
749C2C2×#1062316811yescharacteristic
750C2C2×#1062317311yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×C22⋊Q8C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#2438
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13072288C2direct (N × H)
3. C2×#10622595C2semidirect
4. C2×#10622597C2semidirect
5. C2×#10622597C2semidirect
6. C2×#10622842C2semidirect
7. C2×#10622843C2semidirect
8. C2×#10622586C2semidirect
9. C2×#10622591C2semidirect
10. C2×#10622591C2semidirect
42. #10622843C22semidirect
43. #10622842C22semidirect
60. #10622597C22semidirect
61. #10622597C22semidirect
62. #10622595C22semidirect
63. #10622591C22semidirect
64. #10622591C22semidirect
65. #10622586C22semidirect
89. C23×Dic11Q8semidirect
222. C22×Dic11C2×Q8semidirect
517. C2×C11#2438semidirect
623. C11C2×#2438semidirect
743. C2#13072288direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669302
#130722882
C2×#106225952
C2×#106225972
C2×#106228422
C2×#106228432
C2×#106225862
C2×#106225912
C2×#106225632
C2×#106228232
C2×#106225562
C2×#106225552
C22×C11⋊#952
C22×C11×C22⋊Q82
C2×#243811