Finite Group Databasebeta

← C2×#13072335 #14921857

Subgroups — C2×#13072335 #14921857

Order 2816.

2942 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66942C211yesmaximal, characteristic, complemented
2C22×C4⋊C4×D11C211yesmaximal, characteristic
3#13072335C2116yesmaximal, direct product factor
4C2×#10622273C211yesmaximal, characteristic, complemented
5C2×#10622599C211yesmaximal, characteristic, complemented
6C2×#10622270C211yesmaximal, characteristic, complemented
7C2×#10622585C211yesmaximal, characteristic, complemented
8C2×#10622585C211yesmaximal, characteristic, complemented
9C2×#10622602C211yesmaximal, characteristic
10C2×#10622602C211yesmaximal, characteristic
11C2×#10622263C211yesmaximal, characteristic, complemented
12C2×#10622280C211yesmaximal, characteristic
13C2×#10622280C211yesmaximal, characteristic
14C2×#10622600C211yesmaximal, characteristic
15C2×#10622279C211yesmaximal, characteristic
16C2×C11×#398C211yesmaximal, characteristic, complemented
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
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×C4⋊C4×D11—28no—
41C2×C4⋊C4×D11C2218yes—
42C2×#66942—28no—
43C2×#66942C2218yescomplemented
44C11×#398C2218yescomplemented
45C2×C11×#95C2211yescharacteristic
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
57#10622602C2218yes—
58#10622602C2218yes—
59#10622600C2218yes—
60#10622599C2218yescomplemented
61#10622585C2218yescomplemented
62#10622585C2218yescomplemented
63#10622280C2218yes—
64#10622280C2218yes—
65#10622279C2218yes—
66#10622273C2218yescomplemented
67#10622270C2218yescomplemented
68#10622263C2218yescomplemented
69C24×D11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C22×C4×D11—24no—
85C22×C4×D11—24no—
86C22×C4×D11—24no—
87C22×C4×D11—24no—
88C22×C4×D11—24no—
89C22×C4×D11—24no—
90C22×C4×D11—42no—
91C22×C4×D11—42no—
92C22×C4×D11Q818yes—
93C22×C4×D11C2314yes—
94C22×C4×D11C2314yes—
95C22×C4×D11C2314yes—
96C2×C11×C4⋊C4—24no—
97C2×C11×C4⋊C4—24no—
98C2×C11×C4⋊C4—42no—
99C2×C11×C4⋊C4—42no—
100C2×C11×C4⋊C4C2314yes—
101C2×C11×C4⋊C4C2314yes—
102C2×C11×C4⋊C4C2314yes—
103C2×C11×C4⋊C4C2314yes—
104C2×(C2×D11)⋊C4—24no—
105C2×(C2×D11)⋊C4—24no—
106C2×(C2×D11)⋊C4—24no—
107C2×(C2×D11)⋊C4—24no—
108C2×(C2×D11)⋊C4C2314yes—
109C2×(C2×D11)⋊C4C2314yes—
110C2×(C2×D11)⋊C4C2314yes—
111C2×(C2×D11)⋊C4C2314yes—
112C2×C4⋊Dic11—24no—
113C2×C4⋊Dic11—24no—
114C2×C4⋊Dic11C2314yes—
115C2×C4⋊Dic11C2314yes—
116C2×Dic11⋊C4—24no—
117C2×Dic11⋊C4—24no—
118C2×Dic11⋊C4—24no—
119C2×Dic11⋊C4—24no—
120C2×Dic11⋊C4—24no—
121C2×Dic11⋊C4—42no—
122C2×Dic11⋊C4—42no—
123C2×Dic11⋊C4D418yes—
124C2×Dic11⋊C4C2314yes—
125C2×Dic11⋊C4C2314yes—
126C2×Dic11⋊C4C2314yes—
127C2×Dic11⋊C4C2314yes—
128C2×Dic11⋊C4C2314yes—
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2314yes—
131C2×Dic11⋊C4C2314yes—
132C2×C4×Dic11—24no—
133C2×C4×Dic11—24no—
134C2×C4×Dic11C2314yes—
135C2×C4×Dic11C2314yes—
136C4⋊C4×D11—232no—
137#66942—232no—
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×#2442—111nomaximal, Sylow
151C24×C11C2411yescharacteristic
152C23×D11—22no—
153C23×D11—22no—
154C23×D11—22no—
155C23×D11—22no—
156C23×D11C2×Q814yes—
157C23×D11#4114yes—
158C23×D11#4114yes—
159C23×D11C2412yes—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
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—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11C2×D414yes—
180C22×C4×C11C2×Q814yes—
181C22×C4×C11C2412yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2412yes—
185C22×C4×C11C2412yes—
186C22×C4×C11C2412yes—
187C22×C4×C11C2412yes—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11C2×D414yes—
206C22×Dic11C2×D414yes—
207C22×Dic11C2×Q814yes—
208C22×Dic11#4114yes—
209C22×Dic11C2412yes—
210C22×Dic11C2412yes—
211C22×Dic11C2412yes—
212C22×Dic11C2412yes—
213C22×Dic11C2412yes—
214C22×Dic11C2412yes—
215C22×Dic11C2412yes—
216C2×C4×D11—232no—
217C2×C4×D11—28no—
218C2×C4×D11—28no—
219C2×C4×D11—28no—
220C2×C4×D11—28no—
221C2×C4×D11—28no—
222C2×C4×D11—28no—
223C2×C4×D11—44no—
224C2×C4×D11—44no—
225C2×C4×D11—416no—
226C2×C4×D11—416no—
227C2×C4×D11C2×Q8116yes—
228C11×C4⋊C4—28no—
229C11×C4⋊C4—28no—
230C11×C4⋊C4—44no—
231C11×C4⋊C4—44no—
232(C2×D11)⋊C4—28no—
233(C2×D11)⋊C4—28no—
234(C2×D11)⋊C4—28no—
235(C2×D11)⋊C4—28no—
236C4⋊Dic11—28no—
237C4⋊Dic11—28no—
238Dic11⋊C4—28no—
239Dic11⋊C4—28no—
240Dic11⋊C4—28no—
241Dic11⋊C4—28no—
242Dic11⋊C4—28no—
243Dic11⋊C4—44no—
244Dic11⋊C4—44no—
245Dic11⋊C4C2×D4116yes—
246C4×Dic11—28no—
247C4×Dic11—28no—
248C22×#125—111no—
249C23×C4⋊C4—111no—
250#2442—1116no—
251C2×#400—111no—
252C2×#400—111no—
253C2×#398—111no—
254C2×#398D1111yescharacteristic, complemented
255C2×#389—111no—
256C2×#389—111no—
257C2×#385—111no—
258C2×#385—111no—
259C2×#382—111no—
260C2×#380—111no—
261C2×#380—111no—
262C2×#380—111no—
263C2×C4×C22⋊C4—111no—
264C23×C11C22×D412yes—
265C23×C11C22×Q812yes—
266C23×C11C2×#4112yes—
267C23×C11C2×#4112yes—
268C23×C11C2×#4112yes—
269C23×C11H(5,𝔽2)12yes—
270C23×C112−1+412yes—
271C23×C11C2511yescharacteristic
272C22×D11—28no—
273C22×D11—28no—
274C22×D11—28no—
275C22×D11—28no—
276C22×D11—28no—
277C22×D11—28no—
278C22×D11—22no—
279C22×D11—22no—
280C22×D11—22no—
281C22×D11—22no—
282C22×D11#125116yescomplemented
283C22×D11C22×Q814yes—
284C22×D11C2×#4114yes—
285C22×D11C2×#4114yes—
286C2×C4×C11—28no—
287C2×C4×C11—28no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
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—22no—
307C2×C4×C11—44no—
308C2×C4×C11—44no—
309C2×C4×C11—44no—
310C2×C4×C11—44no—
311C2×C4×C11—44no—
312C2×C4×C11C22×D414yes—
313C2×C4×C11C22×Q814yes—
314C2×Dic11—28no—
315C2×Dic11—22no—
316C2×Dic11—22no—
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—44no—
333C2×Dic11—44no—
334C2×Dic11—44no—
335C2×Dic11—44no—
336C2×Dic11—44no—
337C2×Dic11C22⋊Q8116yes—
338C2×Dic11C22×D414yes—
339C2×Dic11C22×D414yes—
340C2×Dic11C22×Q814yes—
341C2×Dic11C2×#4114yes—
342C4×D11—232no—
343C4×D11—416no—
344C4×D11—416no—
345C24×C4—111no—
346C24×C4—111no—
347C24×C4—111no—
348C2×#125—118no—
349C2×#125—228no—
350C22×C4⋊C4—111no—
351C22×C4⋊C4—111no—
352C22×C4⋊C4—111no—
353C22×C4⋊C4—111no—
354C22×C4⋊C4—111no—
355C22×C4⋊C4—111no—
356C22×C4⋊C4—111no—
357C22×C4⋊C4—111no—
358C22×C4⋊C4—111no—
359C22×C4⋊C4—111no—
360C22×C4⋊C4—118no—
361C22×C4⋊C4—228no—
362C22×C4⋊C4C2×D1111yescharacteristic
363C22×C4⋊C4C2×D1111yescharacteristic
364C22×C4⋊C4C2×D1111yescharacteristic
365C22×C4⋊C4C2×D1111yescharacteristic
366C22×C22⋊C4—111no—
367C22×C22⋊C4—111no—
368C22×C22⋊C4—111no—
369C22×C22⋊C4—111no—
370C22×C42—111no—
371C22×C42—111no—
372#400—118no—
373#400—118no—
374#398—118no—
375#398C2×D1118yescomplemented
376#389—118no—
377#389—118no—
378#385—118no—
379#385—118no—
380#382—118no—
381#380—118no—
382#380—118no—
383#380—118no—
384C4×C22⋊C4—118no—
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×#95C2×D1111yescharacteristic
395C2×#95C2×D1111yescharacteristic
396C2×#95C2×D1111yescharacteristic
397C22×C11C2×C22⋊Q814yes—
398C22×C11C2×#12514yes—
399C22×C11#54414yes—
400C22×C11#54614yes—
401C22×C11#54814yes—
402C22×C11#55214yes—
403C22×C11#55314yes—
404C22×C11C23×D411yescharacteristic
405C22×C11C23×Q811yescharacteristic
406C22×C11C22×#4111yescharacteristic
407C22×C11C22×#4111yescharacteristic
408C22×C11C22×#4111yescharacteristic
409C22×C11C2×H(5,𝔽2)11yescharacteristic
410C22×C11C2×2−1+411yescharacteristic
411C2×D11—24no—
412C2×D11—24no—
413C2×D11—24no—
414C2×D11—24no—
415C2×D11—232no—
416C2×D11—24no—
417C2×D11—24no—
418C2×D11C2×#12518yescomplemented
419C4×C11—24no—
420C4×C11—24no—
421C4×C11—42no—
422C4×C11—42no—
423C4×C11—42no—
424C4×C11—42no—
425C4×C11—42no—
426Dic11—24no—
427Dic11—42no—
428Dic11—42no—
429Dic11—42no—
430Dic11—42no—
431Dic11—42no—
432Dic11C2×C22⋊Q818yes—
433C25—111no—
434C23×C4—111no—
435C23×C4—111no—
436C23×C4—118no—
437C23×C4—114no—
438C23×C4—111no—
439C23×C4—111no—
440C23×C4—111no—
441C23×C4—111no—
442C23×C4—111no—
443C23×C4—114no—
444C23×C4—114no—
445C23×C4—224no—
446C23×C4—224no—
447C23×C4—224no—
448C23×C4—224no—
449C23×C4—224no—
450C23×C4—224no—
451C23×C4—442no—
452C23×C4—442no—
453C23×C4C22×D1111yescharacteristic
454C23×C4C22×D1111yescharacteristic
455C23×C4C22×D1111yescharacteristic
456C23×C4C22×D1111yescharacteristic
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459C23×C4C22×D1111yescharacteristic
460#125—2232no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—118no—
466C2×C4⋊C4—114no—
467C2×C4⋊C4—114no—
468C2×C4⋊C4—114no—
469C2×C4⋊C4—114no—
470C2×C4⋊C4—114no—
471C2×C4⋊C4—114no—
472C2×C4⋊C4—114no—
473C2×C4⋊C4—114no—
474C2×C4⋊C4—114no—
475C2×C4⋊C4—114no—
476C2×C4⋊C4—2232no—
477C2×C4⋊C4—224no—
478C2×C4⋊C4—224no—
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⋊C4C22×D1114yes—
487C2×C4⋊C4C22×D1114yes—
488C2×C4⋊C4C22×D1114yes—
489C2×C4⋊C4C22×D1114yes—
490C2×C22⋊C4—114no—
491C2×C22⋊C4—114no—
492C2×C22⋊C4—114no—
493C2×C22⋊C4—114no—
494C2×C22⋊C4—224no—
495C2×C22⋊C4—224no—
496C2×C22⋊C4—224no—
497C2×C22⋊C4—224no—
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#95C22×D1114yes—
512#95C22×D1114yes—
513#95C22×D1114yes—
514C2×C11#244218yescomplemented
515C2×C11C22×C22⋊Q811yescharacteristic
516C2×C11C22×#12511yescharacteristic
517C2×C11C2×#54411yescharacteristic
518C2×C11C2×#54611yescharacteristic
519C2×C11C2×#54811yescharacteristic
520C2×C11C2×#55211yescharacteristic
521C2×C11C2×#55311yescharacteristic
522D11—28no—
523C24—114no—
524C24—114no—
525C24—114no—
526C24—112no—
527C24—222no—
528C24—222no—
529C24—222no—
530C24—222no—
531C24C23×D1111yescharacteristic
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
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—114no—
552C22×C4—114no—
553C22×C4—114no—
554C22×C4—112no—
555C22×C4—114no—
556C22×C4—112no—
557C22×C4—1116no—
558C22×C4—112no—
559C22×C4—112no—
560C22×C4—112no—
561C22×C4—112no—
562C22×C4—112no—
563C22×C4—228no—
564C22×C4—2232no—
565C22×C4—228no—
566C22×C4—228no—
567C22×C4—228no—
568C22×C4—228no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
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—444no—
588C22×C4—444no—
589C22×C4—4416no—
590C22×C4—4416no—
591C22×C4D4×D1114yes—
592C22×C4Q8×D1114yes—
593C22×C4C23×D1112yes—
594C22×C4C23×D1112yes—
595C22×C4C23×D1112yes—
596C22×C4C23×D1112yes—
597C22×C4C23×D1112yes—
598C22×C4C23×D1112yes—
599C22×C4C23×D1112yes—
600C4⋊C4—28no—
601C4⋊C4—28no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—1116no—
605C4⋊C4—228no—
606C4⋊C4—228no—
607C4⋊C4—228no—
608C4⋊C4—228no—
609C4⋊C4—228no—
610C4⋊C4—228no—
611C4⋊C4—228no—
612C4⋊C4—444no—
613C4⋊C4—444no—
614C22⋊C4—228no—
615C22⋊C4—228no—
616C22⋊C4—228no—
617C22⋊C4—228no—
618C42—228no—
619C42—228no—
620C11C2×#244211yescharacteristic, complemented, Sylow
621C23—114no—
622C23—114no—
623C23—114no—
624C23—1116no—
625C23—228no—
626C23—228no—
627C23—228no—
628C23—228no—
629C23—222no—
630C23—222no—
631C23—228no—
632C23—222no—
633C23—222no—
634C23—228no—
635C23C2×D4×D1112yes—
636C23#6703712yes—
637C23C2×Q8×D1112yes—
638C23#6704012yes—
639C23#41×D1112yes—
640C23#41×D1112yes—
641C23#41×D1112yes—
642C23C24×D1111yescharacteristic
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
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—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—1116no—
670C2×C4—114no—
671C2×C4—114no—
672C2×C4—114no—
673C2×C4—114no—
674C2×C4—2232no—
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—4416no—
694C2×C4—4416no—
695C2×C4—444no—
696C2×C4—444no—
697C2×C4—444no—
698C2×C4—444no—
699C2×C4—444no—
700C2×C4C2×D4×D1114yes—
701C2×C4C2×Q8×D1114yes—
702C22—118no—
703C22—224no—
704C22—224no—
705C22—224no—
706C22—224no—
707C22—2232no—
708C22—224no—
709C22—224no—
710C22#1062314114yes—
711C22D11×C22⋊Q814yes—
712C22#1062316414yes—
713C22#1062319214yes—
714C22D11×#12514yes—
715C22#1062322414yes—
716C22#1062326014yes—
717C22C22×D4×D1111yescharacteristic
718C22C2×#6703711yescharacteristic
719C22C22×Q8×D1111yescharacteristic
720C22C2×#6704011yescharacteristic
721C22C2×#41×D1111yescharacteristic
722C22C2×#41×D1111yescharacteristic
723C22C2×#41×D1111yescharacteristic
724C4—24no—
725C4—24no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—118no—
732C4—224no—
733C4—442no—
734C4—442no—
735C4—442no—
736C4—442no—
737C4—442no—
738C2—228no—
739C2#1307233518yesdirect product factor
740C2C2×D11×C22⋊Q811yescharacteristic
741C2C2×D11×#12511yescharacteristic
742C2C2×#1062326011yescharacteristic
743C2C2×#1062314111yescharacteristic
744C2C2×#1062316411yescharacteristic
745C2C2×#1062322411yescharacteristic
746C2C2×#1062319211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#398C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#398D11
hypocenterC11C2×#2442
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#66942C2semidirect
3. #13072335C2direct (N × H)
4. C2×#10622273C2semidirect
5. C2×#10622599C2semidirect
6. C2×#10622270C2semidirect
7. C2×#10622585C2semidirect
8. C2×#10622585C2semidirect
11. C2×#10622263C2semidirect
16. C2×C11×#398C2semidirect
43. C2×#66942C22semidirect
44. C11×#398C22semidirect
60. #10622599C22semidirect
61. #10622585C22semidirect
62. #10622585C22semidirect
66. #10622273C22semidirect
67. #10622270C22semidirect
68. #10622263C22semidirect
254. C2×#398D11semidirect
282. C22×D11#125semidirect
375. #398C2×D11semidirect
418. C2×D11C2×#125semidirect
514. C2×C11#2442semidirect
620. C11C2×#2442semidirect
739. C2#13072335direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669422
C22×C4⋊C4×D112
#130723352
C2×#106222732
C2×#106225992
C2×#106222702
C2×#106225852
C2×#106226022
C2×#106222632
C2×#106222802
C2×#106226002
C2×#106222792
C2×C11×#3982
C2×#244211