Finite Group Databasebeta

← C2×#13071640 #14913311

Subgroups — C2×#13071640 #14913311

Order 2816.

3310 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×#66931C211yesmaximal, characteristic
2C22×#66940C211yesmaximal, characteristic, complemented
3C22×#66930C211yesmaximal, characteristic
4#13071640C2116yesmaximal, direct product factor
5C2×#10622259C211yesmaximal, characteristic, complemented
6C2×#10622260C211yesmaximal, characteristic, complemented
7C2×#10622564C211yesmaximal, characteristic
8C2×#10622557C211yesmaximal, characteristic
9C2×#10622557C211yesmaximal, characteristic
10C2×#10622267C211yesmaximal, characteristic, complemented
11C2×#10622591C211yesmaximal, characteristic, complemented
12C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
13C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
14C2×#10622262C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic
16C2×C11×#388C211yesmaximal, characteristic
17C24×Dic11C2211yescharacteristic
18C23×Dic22C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C22×C4×Dic11C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C2×#66940—28no—
43C2×#66940C2218yescomplemented
44C2×#66931C4116yescomplemented
45C2×#66931C2218yes—
46C2×#66930—28no—
47C2×#66930C2218yes—
48C11×#388C2218yes—
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
59#10622591C2218yescomplemented
60#10622564C2218yes—
61#10622557C2218yes—
62#10622557C2218yes—
63C22⋊C4×Dic11C2218yes—
64C4×C4⋊Dic11C2218yescomplemented
65C4×Dic11⋊C4C2218yescomplemented
66#10622267C2218yescomplemented
67#10622262C2218yescomplemented
68#10622260C2218yescomplemented
69#10622259C2218yescomplemented
70C25×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×Dic11—24no—
78C23×Dic11—24no—
79C23×Dic11C2×C418yes—
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2314yes—
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C22×Dic22—24no—
90C22×Dic22—24no—
91C22×Dic22C2×C418yes—
92C22×Dic22C2314yes—
93C2×C11×C4⋊C4—24no—
94C2×C11×C4⋊C4C2314yes—
95C2×C11×C22⋊C4—24no—
96C2×C11×C22⋊C4—24no—
97C2×C11×C22⋊C4C2×C418yes—
98C2×C11×C22⋊C4C2314yes—
99C2×C11×C22⋊C4C2314yes—
100C2×C11×C22⋊C4C2314yes—
101C2×C42×C11—24no—
102C2×C42×C11C2314yes—
103C2×C22⋊Dic11—24no—
104C2×C22⋊Dic11—24no—
105C2×C22⋊Dic11C2×C418yes—
106C2×C22⋊Dic11C2314yes—
107C2×C22⋊Dic11C2314yes—
108C2×C22⋊Dic11C2314yes—
109C2×C4⋊Dic11—24no—
110C2×C4⋊Dic11C2×C418yes—
111C2×C4⋊Dic11C2314yes—
112C2×C4⋊Dic11C2314yes—
113C2×Dic11⋊C4—24no—
114C2×Dic11⋊C4—24no—
115C2×Dic11⋊C4—24no—
116C2×Dic11⋊C4C2×C418yes—
117C2×Dic11⋊C4C2×C418yes—
118C2×Dic11⋊C4D418yes—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2314yes—
125C2×C4×Dic11—24no—
126C2×C4×Dic11—24no—
127C2×C4×Dic11—24no—
128C2×C4×Dic11—24no—
129C2×C4×Dic11—24no—
130C2×C4×Dic11—24no—
131C2×C4×Dic11—24no—
132C2×C4×Dic11C2314yes—
133C2×C4×Dic11C2314yes—
134C2×C4×Dic11C2314yes—
135C2×C4×Dic11C2314yes—
136C2×C4×Dic11C2314yes—
137C2×C4×Dic11C2314yes—
138C2×C4×Dic11C2314yes—
139#66940—232no—
140#66931C2×C4164yescomplemented
141#66930—232no—
142C11×#95C2314yes—
143C11×#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C2×#2362—111nomaximal, Sylow
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—22no—
156C24×C11—22no—
157C24×C11—22no—
158C24×C11—22no—
159C24×C11C22×C414yes—
160C24×C11C2412yes—
161C24×C11C2411yescharacteristic
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×C11C22×C414yes—
177C22×C4×C11C22×C414yes—
178C22×C4×C11C2×D414yes—
179C22×C4×C11#4114yes—
180C22×C4×C11C2412yes—
181C22×C4×C11C2412yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2412yes—
185C22×C4×C11C2412yes—
186C22×Dic11—232no—
187C22×Dic11—28no—
188C22×Dic11—28no—
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×Dic11C22×C4116yes—
206C22×Dic11C22×C414yes—
207C22×Dic11C22×C414yes—
208C22×Dic11C22×C414yes—
209C22×Dic11C22×C414yes—
210C22×Dic11C2×D414yes—
211C22×Dic11C2×D414yes—
212C22×Dic11#4114yes—
213C22×Dic11#4114yes—
214C22×Dic11C2412yes—
215C22×Dic11C2412yes—
216C22×Dic11C2412yes—
217C22×Dic11C2412yes—
218C22×Dic11C2412yes—
219C22×Dic11C2412yes—
220C22×Dic11C2412yes—
221C22×Dic11C2412yes—
222C2×Dic22—232no—
223C2×Dic22—28no—
224C2×Dic22—28no—
225C2×Dic22C22×C4116yes—
226C11×C4⋊C4—28no—
227C11×C22⋊C4—28no—
228C11×C22⋊C4—28no—
229C11×C22⋊C4C22×C4116yes—
230C42×C11—28no—
231C22⋊Dic11—28no—
232C22⋊Dic11—28no—
233C22⋊Dic11C22×C4116yes—
234C4⋊Dic11—28no—
235C4⋊Dic11C22×C4116yes—
236Dic11⋊C4—28no—
237Dic11⋊C4—28no—
238Dic11⋊C4—28no—
239Dic11⋊C4C22×C4116yes—
240Dic11⋊C4C22×C4116yes—
241Dic11⋊C4C2×D4116yes—
242C4×Dic11—28no—
243C4×Dic11—28no—
244C4×Dic11—28no—
245C4×Dic11—28no—
246C4×Dic11—28no—
247C4×Dic11—28no—
248C4×Dic11—28no—
249C22×C22⋊Q8—111no—
250C22×C4×Q8—111no—
251C22×#117—111no—
252#2362—1116no—
253C2×#391—111no—
254C2×#389—111no—
255C2×#388—111no—
256C2×#388—111no—
257C2×#388—111no—
258C2×#388D1111yescharacteristic
259C2×#387—111no—
260C2×#387—111no—
261C2×C4×C4⋊C4—111no—
262C2×C4×C4⋊C4—111no—
263C2×C4×C4⋊C4—111no—
264C2×C4×C22⋊C4—111no—
265C23×C11—28no—
266C23×C11—28no—
267C23×C11—28no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—44no—
275C23×C11—44no—
276C23×C11—44no—
277C23×C11—44no—
278C23×C11C23×C414yes—
279C23×C11C23×C412yes—
280C23×C11C22×D412yes—
281C23×C11C2×#4112yes—
282C23×C11C2×#4112yes—
283C23×C11C2×#4112yes—
284C23×C112−1+412yes—
285C23×C112−1+412yes—
286C23×C11C2511yescharacteristic
287C2×C4×C11—28no—
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—44no—
306C2×C4×C11—44no—
307C2×C4×C11C23×C414yes—
308C2×C4×C11C23×C414yes—
309C2×C4×C11C22×D414yes—
310C2×C4×C11C2×#4114yes—
311C2×Dic11—28no—
312C2×Dic11—28no—
313C2×Dic11—28no—
314C2×Dic11—28no—
315C2×Dic11—28no—
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—232no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—44no—
334C2×Dic11—44no—
335C2×Dic11C4×D4116yes—
336C2×Dic11C23×C414yes—
337C2×Dic11C23×C414yes—
338C2×Dic11C23×C414yes—
339C2×Dic11C23×C414yes—
340C2×Dic11C22×D414yes—
341C2×Dic11C22×D414yes—
342C2×Dic11C2×#4114yes—
343C2×Dic11C2×#4114yes—
344Dic22—232no—
345C23×Q8—111no—
346C24×C4—111no—
347C2×C22⋊Q8—118no—
348C2×C22⋊Q8—1116no—
349C2×C4×Q8—118no—
350C2×C4×Q8—228no—
351C2×#117—118no—
352C2×#117—228no—
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—111no—
361C22×C4⋊C4C2×D1111yescharacteristic
362C22×C22⋊C4—111no—
363C22×C22⋊C4—111no—
364C22×C22⋊C4—111no—
365C22×C22⋊C4C2×D1111yescharacteristic
366C22×C22⋊C4C2×D1111yescharacteristic
367C22×C22⋊C4C2×D1111yescharacteristic
368C22×C42—111no—
369C22×C42—111no—
370C22×C42—111no—
371C22×C42—111no—
372C22×C42—111no—
373C22×C42—111no—
374C22×C42—111no—
375C22×C42C2×D1111yescharacteristic
376#391—118no—
377#389—118no—
378#388—118no—
379#388—118no—
380#388—118no—
381#388C2×D1118yes—
382#387—118no—
383#387—118no—
384C4×C4⋊C4—118no—
385C4×C4⋊C4—118no—
386C4×C4⋊C4—118no—
387C4×C22⋊C4—118no—
388C2×#95—111no—
389C2×#95—111no—
390C2×#95—111no—
391C2×#95—111no—
392C2×#95—111no—
393C2×#95—111no—
394C2×#95—111no—
395C2×#95—111no—
396C2×#95C2×D1111yescharacteristic
397C2×#95C2×D1111yescharacteristic
398C22×C11—24no—
399C22×C11—24no—
400C22×C11—24no—
401C22×C11—416no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11C2×C4×D414yes—
407C22×C11C4×#4114yes—
408C22×C11#51914yes—
409C22×C11#54714yes—
410C22×C11#54814yes—
411C22×C11#55214yes—
412C22×C11#55614yes—
413C22×C11C24×C411yescharacteristic
414C22×C11C23×D411yescharacteristic
415C22×C11C22×#4111yescharacteristic
416C22×C11C22×#4111yescharacteristic
417C22×C11C22×#4111yescharacteristic
418C22×C11C2×2−1+411yescharacteristic
419C22×C11C2×2−1+411yescharacteristic
420C4×C11—24no—
421C4×C11—24no—
422C4×C11—24no—
423C4×C11—24no—
424C4×C11—42no—
425C4×C11—42no—
426Dic11—24no—
427Dic11—24no—
428Dic11—24no—
429Dic11—24no—
430Dic11—24no—
431Dic11—42no—
432Dic11—42no—
433Dic11C2×C4×D418yes—
434C25C22×D1111yescharacteristic
435C22×Q8—118no—
436C22×Q8—114no—
437C22×Q8—224no—
438C22×Q8—224no—
439C23×C4—111no—
440C23×C4—118no—
441C23×C4—114no—
442C23×C4—111no—
443C23×C4—111no—
444C23×C4—111no—
445C23×C4—111no—
446C23×C4—111no—
447C23×C4—111no—
448C23×C4—111no—
449C23×C4—224no—
450C23×C4—224no—
451C23×C4C22×D1111yescharacteristic
452C23×C4C22×D1111yescharacteristic
453C23×C4C22×D1111yescharacteristic
454C23×C4C22×D1111yescharacteristic
455C23×C4C22×D1111yescharacteristic
456C23×C4C22×D1111yescharacteristic
457C22⋊Q8—1164no—
458C4×Q8—2232no—
459#117—2232no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—118no—
462C2×C4⋊C4—118no—
463C2×C4⋊C4—118no—
464C2×C4⋊C4—118no—
465C2×C4⋊C4—114no—
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—224no—
474C2×C4⋊C4—224no—
475C2×C4⋊C4—224no—
476C2×C4⋊C4—224no—
477C2×C4⋊C4C22×D1114yes—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—118no—
481C2×C22⋊C4—114no—
482C2×C22⋊C4—114no—
483C2×C22⋊C4—114no—
484C2×C22⋊C4—224no—
485C2×C22⋊C4—224no—
486C2×C22⋊C4C4×D1118yes—
487C2×C22⋊C4C22×D1114yes—
488C2×C22⋊C4C22×D1114yes—
489C2×C22⋊C4C22×D1114yes—
490C2×C42—24no—
491C2×C42—114no—
492C2×C42—114no—
493C2×C42—114no—
494C2×C42—114no—
495C2×C42—114no—
496C2×C42—114no—
497C2×C42—114no—
498C2×C42—224no—
499C2×C42—224no—
500C2×C42—224no—
501C2×C42—224no—
502C2×C42—224no—
503C2×C42—224no—
504C2×C42—224no—
505C2×C42C22×D1114yes—
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#95C22×D1114yes—
515#95C22×D1114yes—
516C2×C11—44no—
517C2×C11#236218yescomplemented
518C2×C11C22×C4×D411yescharacteristic
519C2×C11C2×C4×#4111yescharacteristic
520C2×C11C2×#51911yescharacteristic
521C2×C11C2×#54711yescharacteristic
522C2×C11C2×#54811yescharacteristic
523C2×C11C2×#55211yescharacteristic
524C2×C11C2×#55611yescharacteristic
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24C2×C4×D1114yes—
532C24C23×D1112yes—
533C24C23×D1111yescharacteristic
534C2×Q8—1116no—
535C2×Q8—228no—
536C2×Q8—2232no—
537C2×Q8—228no—
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—114no—
553C22×C4—114no—
554C22×C4—114no—
555C22×C4—112no—
556C22×C4—114no—
557C22×C4—114no—
558C22×C4—114no—
559C22×C4—1116no—
560C22×C4—114no—
561C22×C4—114no—
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—228no—
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—222no—
587C22×C4—222no—
588C22×C4C2×C4×D1114yes—
589C22×C4C2×C4×D1114yes—
590C22×C4D4×D1114yes—
591C22×C4#434114yes—
592C22×C4C23×D1112yes—
593C22×C4C23×D1112yes—
594C22×C4C23×D1112yes—
595C22×C4C23×D1112yes—
596C22×C4C23×D1112yes—
597C22×C4C23×D1112yes—
598C4⋊C4—28no—
599C4⋊C4—1116no—
600C4⋊C4—1116no—
601C4⋊C4—1116no—
602C4⋊C4—1116no—
603C4⋊C4—228no—
604C4⋊C4—228no—
605C4⋊C4—228no—
606C4⋊C4—228no—
607C22⋊C4—28no—
608C22⋊C4—28no—
609C22⋊C4—1116no—
610C22⋊C4—228no—
611C22⋊C4—228no—
612C22⋊C4C2×C4×D11116yes—
613C42—28no—
614C42—228no—
615C42—228no—
616C42—228no—
617C42—228no—
618C42—228no—
619C42—228no—
620C42—228no—
621C11C2×#236211yescharacteristic, complemented, Sylow
622C23—28no—
623C23—28no—
624C23—28no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23C22×C4×D1114yes—
636C23C22×C4×D1112yes—
637C23C2×D4×D1112yes—
638C23C2×#434112yes—
639C23#41×D1112yes—
640C23#41×D1112yes—
641C23#6704312yes—
642C23#6704312yes—
643C23C24×D1111yescharacteristic
644Q8—2232no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—28no—
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—44no—
664C2×C4—44no—
665C2×C4—1116no—
666C2×C4—114no—
667C2×C4—114no—
668C2×C4—114no—
669C2×C4—114no—
670C2×C4—114no—
671C2×C4—114no—
672C2×C4—114no—
673C2×C4—114no—
674C2×C4—2232no—
675C2×C4—228no—
676C2×C4—228no—
677C2×C4—228no—
678C2×C4—228no—
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—228no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—444no—
697C2×C4—444no—
698C2×C4C22×C4×D1114yes—
699C2×C4C22×C4×D1114yes—
700C2×C4C2×D4×D1114yes—
701C2×C4C2×#434114yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—42no—
706C22—416no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22#1062304714yes—
711C22C4×#434114yes—
712C22C4×D4×D1114yes—
713C22#1062314214yes—
714C22#1062318114yes—
715C22#1062320814yes—
716C22#1062323314yes—
717C22C23×C4×D1111yescharacteristic
718C22C22×D4×D1111yescharacteristic
719C22C22×#434111yescharacteristic
720C22C2×#41×D1111yescharacteristic
721C22C2×#41×D1111yescharacteristic
722C22C2×#6704311yescharacteristic
723C22C2×#6704311yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—118no—
731C4—224no—
732C4—224no—
733C4—224no—
734C4—224no—
735C4—224no—
736C4—442no—
737C4—442no—
738C2—44no—
739C2#1307164018yesdirect product factor
740C2C2×C4×D4×D1111yescharacteristic
741C2C2×C4×#434111yescharacteristic
742C2C2×#1062304711yescharacteristic
743C2C2×#1062314211yescharacteristic
744C2C2×#1062320811yescharacteristic
745C2C2×#1062318111yescharacteristic
746C2C2×#1062323311yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC25×C11C23
cosocleC23×C11C25
hypercenterC2×#388D11
hypocenterC11C2×#2362
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#66940C2semidirect
4. #13071640C2direct (N × H)
5. C2×#10622259C2semidirect
6. C2×#10622260C2semidirect
10. C2×#10622267C2semidirect
11. C2×#10622591C2semidirect
12. C2×C4×Dic11⋊C4C2semidirect
13. C2×C4×C4⋊Dic11C2semidirect
14. C2×#10622262C2semidirect
43. C2×#66940C22semidirect
44. C2×#66931C4semidirect
59. #10622591C22semidirect
64. C4×C4⋊Dic11C22semidirect
65. C4×Dic11⋊C4C22semidirect
66. #10622267C22semidirect
67. #10622262C22semidirect
68. #10622260C22semidirect
69. #10622259C22semidirect
140. #66931C2×C4semidirect
517. C2×C11#2362semidirect
621. C11C2×#2362semidirect
739. C2#13071640direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669312
C22×#669402
C22×#669302
#130716402
C2×#106222592
C2×#106222602
C2×#106225642
C2×#106225572
C2×#106222672
C2×#106225912
C2×C4×Dic11⋊C42
C2×C4×C4⋊Dic112
C2×#106222622
C2×C22⋊C4×Dic112
C2×C11×#3882
C2×#236211