Finite Group Databasebeta

← C2×#13071392 #14912652

Subgroups — C2×#13071392 #14912652

Order 2816.

2614 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66932C211yesmaximal, characteristic
2#13071392C2116yesmaximal, direct product factor
3C2×#10622586C211yesmaximal, characteristic, complemented
4C2×#10622585C211yesmaximal, characteristic, complemented
5C2×#10622558C211yesmaximal, characteristic
6C2×#10622558C211yesmaximal, characteristic
7C2×#10622564C211yesmaximal, characteristic
8C2×#10622268C211yesmaximal, characteristic, complemented
9C2×#10622267C211yesmaximal, characteristic, complemented
10C2×#10622591C211yesmaximal, characteristic, complemented
11C2×#10622823C211yesmaximal, characteristic
12C2×#10622263C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
14C2×#10622262C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic11C211yesmaximal, characteristic
16C2×C11×#385C211yesmaximal, characteristic
17C24×C4×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C2×#66932C4116yescomplemented
41C2×#66932C2218yes—
42C11×#385C2218yes—
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
45#10622823C2218yes—
46C4×C22⋊Dic11C2218yes—
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#10622591C2218yescomplemented
58C4⋊C4×Dic11C2218yescomplemented
59#10622586C2218yescomplemented
60#10622585C2218yescomplemented
61#10622564C2218yes—
62#10622558C2218yes—
63#10622558C2218yes—
64#10622268C2218yescomplemented
65#10622267C2218yescomplemented
66#10622263C2218yescomplemented
67#10622262C2218yescomplemented
68C25×C11C2311yescharacteristic
69C23×C4×C11—24no—
70C23×C4×C11—42no—
71C23×C4×C11—42no—
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2314yes—
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C2×C11×C4⋊C4—24no—
88C2×C11×C4⋊C4—42no—
89C2×C11×C4⋊C4C2314yes—
90C2×C11×C4⋊C4C2314yes—
91C2×C11×C22⋊C4—42no—
92C2×C11×C22⋊C4C2×C418yes—
93C2×C11×C22⋊C4C2314yes—
94C2×C11×C22⋊C4C2314yes—
95C2×C22⋊Dic11—24no—
96C2×C22⋊Dic11—42no—
97C2×C22⋊Dic11C2×C418yes—
98C2×C22⋊Dic11C2×C418yes—
99C2×C22⋊Dic11C2314yes—
100C2×C22⋊Dic11C2314yes—
101C2×C22⋊Dic11C2314yes—
102C2×C22⋊Dic11C2314yes—
103C2×C4⋊Dic11—24no—
104C2×C4⋊Dic11C2×C418yescomplemented
105C2×C4⋊Dic11C2314yes—
106C2×C4⋊Dic11C2314yes—
107C2×Dic11⋊C4—24no—
108C2×Dic11⋊C4—42no—
109C2×Dic11⋊C4—42no—
110C2×Dic11⋊C4—42no—
111C2×Dic11⋊C4C2×C418yescomplemented
112C2×Dic11⋊C4C2×C418yescomplemented
113C2×Dic11⋊C4C2314yes—
114C2×Dic11⋊C4C2314yes—
115C2×Dic11⋊C4C2314yes—
116C2×Dic11⋊C4C2314yes—
117C2×Dic11⋊C4C2314yes—
118C2×Dic11⋊C4C2314yes—
119C2×C4×Dic11—24no—
120C2×C4×Dic11—42no—
121C2×C4×Dic11—42no—
122C2×C4×Dic11—42no—
123C2×C4×Dic11—42no—
124C2×C4×Dic11C2×C418yescomplemented
125C2×C4×Dic11C2314yes—
126C2×C4×Dic11C2314yes—
127C2×C4×Dic11C2314yes—
128C2×C4×Dic11C2314yes—
129C2×C4×Dic11C2314yes—
130C2×C4×Dic11C2314yes—
131#66932C2×C4164yescomplemented
132C11×#95C2314yes—
133C11×#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C2×#2334—111nomaximal, Sylow
145C24×C11—22no—
146C24×C11—22no—
147C24×C11—22no—
148C24×C11—22no—
149C24×C11—22no—
150C24×C11—22no—
151C24×C11C22×C414yes—
152C24×C11C2412yes—
153C24×C11C2411yescharacteristic
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
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—28no—
170C22×C4×C11—44no—
171C22×C4×C11—44no—
172C22×C4×C11—416no—
173C22×C4×C11C22×C414yes—
174C22×C4×C11C22×C414yes—
175C22×C4×C11#4114yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2412yes—
178C22×C4×C11C2412yes—
179C22×C4×C11C2412yes—
180C22×C4×C11C2412yes—
181C22×C4×C11C2412yes—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
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×Dic11C22×C414yes—
202C22×Dic11C22×C414yes—
203C22×Dic11C22×C414yes—
204C22×Dic11C22×C414yes—
205C22×Dic11#4114yes—
206C22×Dic11C2412yes—
207C22×Dic11C2412yes—
208C22×Dic11C2412yes—
209C22×Dic11C2412yes—
210C22×Dic11C2412yes—
211C22×Dic11C2412yes—
212C22×Dic11C2412yes—
213C22×Dic11C2412yes—
214C11×C4⋊C4—28no—
215C11×C4⋊C4—44no—
216C11×C22⋊C4—44no—
217C11×C22⋊C4C22×C4116yes—
218C22⋊Dic11—28no—
219C22⋊Dic11—44no—
220C22⋊Dic11C22×C4116yes—
221C22⋊Dic11C22×C4116yes—
222C4⋊Dic11—28no—
223C4⋊Dic11C22×C4116yescomplemented
224Dic11⋊C4—28no—
225Dic11⋊C4—44no—
226Dic11⋊C4—44no—
227Dic11⋊C4—44no—
228Dic11⋊C4C22×C4116yescomplemented
229Dic11⋊C4C22×C4116yescomplemented
230C4×Dic11—28no—
231C4×Dic11—44no—
232C4×Dic11—44no—
233C4×Dic11—44no—
234C4×Dic11—44no—
235C4×Dic11C22×C4116yescomplemented
236C22×#126—111no—
237#2334—1116no—
238C2×#389—111no—
239C2×#389—111no—
240C2×#388—111no—
241C2×#388—111no—
242C2×#388—111no—
243C2×#387—111no—
244C2×#387—111no—
245C2×#387—111no—
246C2×#385—111no—
247C2×#385D1111yescharacteristic
248C2×#382—111no—
249C2×C4×C4⋊C4—111no—
250C2×C4×C4⋊C4—111no—
251C2×C4×C22⋊C4—111no—
252C23×C11—28no—
253C23×C11—28no—
254C23×C11—28no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—44no—
262C23×C11—44no—
263C23×C11—44no—
264C23×C11—44no—
265C23×C11C23×C414yes—
266C23×C11C23×C412yes—
267C23×C11C2×#4112yes—
268C23×C11C2×#4112yes—
269C23×C11H(5,𝔽2)12yes—
270C23×C11H(5,𝔽2)12yes—
271C23×C112−1+412yes—
272C23×C112−1+412yes—
273C23×C11C2511yescharacteristic
274C2×C4×C11—28no—
275C2×C4×C11—28no—
276C2×C4×C11—28no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—416no—
293C2×C4×C11—44no—
294C2×C4×C11—44no—
295C2×C4×C11—44no—
296C2×C4×C11C23×C414yes—
297C2×C4×C11C23×C414yes—
298C2×C4×C11C2×#4114yes—
299C2×Dic11—28no—
300C2×Dic11—28no—
301C2×Dic11—28no—
302C2×Dic11—28no—
303C2×Dic11—28no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
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—44no—
324C2×Dic11—44no—
325C2×Dic11—44no—
326C2×Dic11C23×C414yes—
327C2×Dic11C23×C414yes—
328C2×Dic11C23×C414yes—
329C2×Dic11C23×C414yes—
330C2×Dic11C2×#4114yes—
331C24×C4C2×D1111yescharacteristic
332C2×#126—118no—
333C2×#126—1116no—
334C22×C4⋊C4—111no—
335C22×C4⋊C4—111no—
336C22×C4⋊C4—111no—
337C22×C4⋊C4—111no—
338C22×C4⋊C4—111no—
339C22×C4⋊C4—111no—
340C22×C4⋊C4—111no—
341C22×C4⋊C4—111no—
342C22×C4⋊C4C2×D1111yescharacteristic
343C22×C4⋊C4C2×D1111yescharacteristic
344C22×C22⋊C4—111no—
345C22×C22⋊C4—111no—
346C22×C22⋊C4—111no—
347C22×C22⋊C4—111no—
348C22×C22⋊C4C2×D1111yescharacteristic
349C22×C22⋊C4C2×D1111yescharacteristic
350C22×C42—111no—
351C22×C42—111no—
352C22×C42—111no—
353C22×C42—111no—
354C22×C42—111no—
355C22×C42—111no—
356#389—118no—
357#389—118no—
358#388—118no—
359#388—118no—
360#388—118no—
361#387—118no—
362#387—118no—
363#387—118no—
364#385—118no—
365#385C2×D1118yes—
366#382—118no—
367C4×C4⋊C4—118no—
368C4×C4⋊C4—118no—
369C4×C22⋊C4—118no—
370C2×#95—111no—
371C2×#95—111no—
372C2×#95—111no—
373C2×#95—111no—
374C2×#95—111no—
375C2×#95—111no—
376C2×#95—111no—
377C2×#95—111no—
378C2×#95—111no—
379C2×#95—111no—
380C2×#95C2×D1111yescharacteristic
381C2×#95C2×D1111yescharacteristic
382C22×C11—24no—
383C22×C11—24no—
384C22×C11—24no—
385C22×C11—416no—
386C22×C11—42no—
387C22×C11—42no—
388C22×C11—42no—
389C22×C11—42no—
390C22×C11C4×#4114yes—
391C22×C11#52014yes—
392C22×C11#52014yes—
393C22×C11#53814yes—
394C22×C11#53914yes—
395C22×C11#54114yes—
396C22×C11#54214yes—
397C22×C11C24×C411yescharacteristic
398C22×C11C22×#4111yescharacteristic
399C22×C11C22×#4111yescharacteristic
400C22×C11C2×H(5,𝔽2)11yescharacteristic
401C22×C11C2×H(5,𝔽2)11yescharacteristic
402C22×C11C2×2−1+411yescharacteristic
403C22×C11C2×2−1+411yescharacteristic
404C4×C11—24no—
405C4×C11—24no—
406C4×C11—24no—
407C4×C11—42no—
408C4×C11—42no—
409C4×C11—42no—
410Dic11—24no—
411Dic11—24no—
412Dic11—24no—
413Dic11—24no—
414Dic11—24no—
415Dic11—42no—
416Dic11—42no—
417Dic11—42no—
418C25C22×D1111yescharacteristic
419C23×C4—24no—
420C23×C4—42no—
421C23×C4—42no—
422C23×C4—111no—
423C23×C4—111no—
424C23×C4—111no—
425C23×C4—111no—
426C23×C4—111no—
427C23×C4—111no—
428C23×C4—111no—
429C23×C4—111no—
430C23×C4C22×D1111yescharacteristic
431C23×C4C22×D1111yescharacteristic
432C23×C4C22×D1111yescharacteristic
433C23×C4C22×D1111yescharacteristic
434C23×C4C22×D1111yescharacteristic
435C23×C4C22×D1111yescharacteristic
436C23×C4C22×D1114yes—
437#126—1164no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—42no—
440C2×C4⋊C4—118no—
441C2×C4⋊C4—118no—
442C2×C4⋊C4—118no—
443C2×C4⋊C4—114no—
444C2×C4⋊C4—114no—
445C2×C4⋊C4—114no—
446C2×C4⋊C4—114no—
447C2×C4⋊C4—114no—
448C2×C4⋊C4—114no—
449C2×C4⋊C4—114no—
450C2×C4⋊C4—114no—
451C2×C4⋊C4—224no—
452C2×C4⋊C4—224no—
453C2×C4⋊C4—442no—
454C2×C4⋊C4—442no—
455C2×C4⋊C4—442no—
456C2×C4⋊C4C22×D1114yes—
457C2×C4⋊C4C22×D1114yes—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—118no—
460C2×C22⋊C4—118no—
461C2×C22⋊C4—114no—
462C2×C22⋊C4—114no—
463C2×C22⋊C4—114no—
464C2×C22⋊C4—114no—
465C2×C22⋊C4—224no—
466C2×C22⋊C4—442no—
467C2×C22⋊C4C4×D1118yes—
468C2×C22⋊C4C22×D1114yes—
469C2×C22⋊C4C22×D1114yes—
470C2×C42—118no—
471C2×C42—114no—
472C2×C42—114no—
473C2×C42—114no—
474C2×C42—114no—
475C2×C42—114no—
476C2×C42—114no—
477C2×C42—224no—
478C2×C42—442no—
479C2×C42—442no—
480C2×C42—442no—
481C2×C42—442no—
482#95—114no—
483#95—114no—
484#95—114no—
485#95—114no—
486#95—114no—
487#95—114no—
488#95—114no—
489#95—114no—
490#95—114no—
491#95—114no—
492#95C22×D1114yes—
493#95C22×D1114yes—
494C2×C11—44no—
495C2×C11#233418yescomplemented
496C2×C11C2×C4×#4111yescharacteristic
497C2×C11C2×#52011yescharacteristic
498C2×C11C2×#52011yescharacteristic
499C2×C11C2×#53811yescharacteristic
500C2×C11C2×#53911yescharacteristic
501C2×C11C2×#54111yescharacteristic
502C2×C11C2×#54211yescharacteristic
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24C2×C4×D1114yes—
510C24C23×D1112yes—
511C24C23×D1111yescharacteristic
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—28no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—416no—
531C22×C4—114no—
532C22×C4—114no—
533C22×C4—114no—
534C22×C4—114no—
535C22×C4—114no—
536C22×C4—112no—
537C22×C4—112no—
538C22×C4—112no—
539C22×C4—112no—
540C22×C4—112no—
541C22×C4—112no—
542C22×C4—112no—
543C22×C4—112no—
544C22×C4—222no—
545C22×C4—222no—
546C22×C4—222no—
547C22×C4—222no—
548C22×C4—222no—
549C22×C4—222no—
550C22×C4—222no—
551C22×C4—222no—
552C22×C4—222no—
553C22×C4—222no—
554C22×C4—222no—
555C22×C4—222no—
556C22×C4—222no—
557C22×C4—222no—
558C22×C4—222no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4C2×C4×D1114yes—
564C22×C4C2×C4×D1114yes—
565C22×C4#434114yes—
566C22×C4C23×D1112yes—
567C22×C4C23×D1112yes—
568C22×C4C23×D1112yes—
569C22×C4C23×D1112yes—
570C22×C4C23×D1112yes—
571C22×C4C23×D1112yes—
572C4⋊C4—28no—
573C4⋊C4—44no—
574C4⋊C4—1116no—
575C4⋊C4—1116no—
576C4⋊C4—1116no—
577C4⋊C4—228no—
578C4⋊C4—228no—
579C4⋊C4—444no—
580C4⋊C4—444no—
581C4⋊C4—444no—
582C22⋊C4—44no—
583C22⋊C4—1116no—
584C22⋊C4—1116no—
585C22⋊C4—228no—
586C22⋊C4—444no—
587C22⋊C4C2×C4×D11116yes—
588C42—1116no—
589C42—228no—
590C42—444no—
591C42—444no—
592C42—444no—
593C42—444no—
594C11C2×#233411yescharacteristic, complemented, Sylow
595C23—28no—
596C23—28no—
597C23—28no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23C22×C4×D1114yes—
609C23C22×C4×D1112yes—
610C23C2×#434112yes—
611C23#6703712yes—
612C23#6703712yes—
613C23#6704012yes—
614C23#41×D1112yes—
615C23#6704312yes—
616C23C24×D1111yescharacteristic
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—416no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—114no—
640C2×C4—114no—
641C2×C4—114no—
642C2×C4—114no—
643C2×C4—114no—
644C2×C4—228no—
645C2×C4—228no—
646C2×C4—228no—
647C2×C4—228no—
648C2×C4—228no—
649C2×C4—222no—
650C2×C4—222no—
651C2×C4—222no—
652C2×C4—222no—
653C2×C4—222no—
654C2×C4—222no—
655C2×C4—222no—
656C2×C4—222no—
657C2×C4—222no—
658C2×C4—222no—
659C2×C4—222no—
660C2×C4—222no—
661C2×C4—222no—
662C2×C4—222no—
663C2×C4—222no—
664C2×C4—222no—
665C2×C4—222no—
666C2×C4—222no—
667C2×C4—222no—
668C2×C4—444no—
669C2×C4—444no—
670C2×C4—444no—
671C2×C4C22×C4×D1114yes—
672C2×C4C22×C4×D1114yes—
673C2×C4C2×#434114yes—
674C22—24no—
675C22—24no—
676C22—24no—
677C22—416no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22#1062303514yes—
683C22C4×#434114yes—
684C22#1062307714yes—
685C22#1062312414yes—
686C22#1062315614yes—
687C22#1062316914yes—
688C22#1062319314yes—
689C22C23×C4×D1111yescharacteristic
690C22C22×#434111yescharacteristic
691C22C2×#6703711yescharacteristic
692C22C2×#6703711yescharacteristic
693C22C2×#6704011yescharacteristic
694C22C2×#41×D1111yescharacteristic
695C22C2×#6704311yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—224no—
703C4—224no—
704C4—224no—
705C4—224no—
706C4—224no—
707C4—442no—
708C4—442no—
709C4—442no—
710C2—44no—
711C2#1307139218yesdirect product factor
712C2C2×C4×#434111yescharacteristic
713C2C2×#1062307711yescharacteristic
714C2C2×#1062303511yescharacteristic
715C2C2×#1062312411yescharacteristic
716C2C2×#1062316911yescharacteristic
717C2C2×#1062315611yescharacteristic
718C2C2×#1062319311yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#385C2
socleC24×C11C24
prime radicalC25×C11C23
cosocleC23×C11C25
hypercenterC2×#385D11
hypocenterC11C2×#2334
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. #13071392C2direct (N × H)
3. C2×#10622586C2semidirect
4. C2×#10622585C2semidirect
8. C2×#10622268C2semidirect
9. C2×#10622267C2semidirect
10. C2×#10622591C2semidirect
12. C2×#10622263C2semidirect
13. C2×C4⋊C4×Dic11C2semidirect
14. C2×#10622262C2semidirect
40. C2×#66932C4semidirect
57. #10622591C22semidirect
58. C4⋊C4×Dic11C22semidirect
59. #10622586C22semidirect
60. #10622585C22semidirect
64. #10622268C22semidirect
65. #10622267C22semidirect
66. #10622263C22semidirect
67. #10622262C22semidirect
104. C2×C4⋊Dic11C2×C4semidirect
111. C2×Dic11⋊C4C2×C4semidirect
112. C2×Dic11⋊C4C2×C4semidirect
124. C2×C4×Dic11C2×C4semidirect
131. #66932C2×C4semidirect
223. C4⋊Dic11C22×C4semidirect
228. Dic11⋊C4C22×C4semidirect
229. Dic11⋊C4C22×C4semidirect
235. C4×Dic11C22×C4semidirect
495. C2×C11#2334semidirect
594. C11C2×#2334semidirect
711. C2#13071392direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669322
#130713922
C2×#106225862
C2×#106225852
C2×#106225582
C2×#106225642
C2×#106222682
C2×#106222672
C2×#106225912
C2×#106228232
C2×#106222632
C2×C4⋊C4×Dic112
C2×#106222622
C2×C4×C22⋊Dic112
C2×C11×#3852
C2×#233411