Finite Group Databasebeta

← C2×#13071780 #14916378

Subgroups — C2×#13071780 #14916378

Order 2816.

2566 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66950C211yesmaximal, characteristic
2#13071780C2116yesmaximal, direct product factor
3C2×#10622259C211yesmaximal, characteristic, complemented
4C2×#10622259C211yesmaximal, characteristic, complemented
5C2×#10622541C211yesmaximal, characteristic, complemented
6C2×#10622586C211yesmaximal, characteristic, complemented
7C2×#10622283C211yesmaximal, characteristic
8C2×#10622553C211yesmaximal, characteristic
9C2×#10622603C211yesmaximal, characteristic
10C2×#10622282C211yesmaximal, characteristic
11C2×#10622594C211yesmaximal, characteristic, complemented
12C2×#10622266C211yesmaximal, characteristic, complemented
13C2×#10622267C211yesmaximal, characteristic, complemented
14C2×#10622277C211yesmaximal, characteristic
15C2×#10622280C211yesmaximal, characteristic
16C2×C11×#387C211yesmaximal, characteristic, complemented
17C23×C4×D11C2211yescharacteristic
18C23×Dic22C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C2×#66950C4116yescomplemented
39C2×#66950C2218yes—
40C11×#387C2218yescomplemented
41C2×C11×#95C2211yescharacteristic
42C2×C11×#95C2211yescharacteristic
43C2×C11×#95C2211yescharacteristic
44C2×C11×#95C2211yescharacteristic
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
55#10622603C2218yes—
56#10622594C2218yescomplemented
57#10622586C2218yescomplemented
58#10622553C2218yes—
59#10622541C2218yescomplemented
60#10622283C2218yes—
61#10622282C2218yes—
62#10622280C2218yes—
63#10622277C2218yes—
64#10622267C2218yescomplemented
65#10622266C2218yescomplemented
66#10622259C2218yescomplemented
67#10622259C2218yescomplemented
68C24×D11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C22×C4×D11—42no—
84C22×C4×D11—42no—
85C22×C4×D11C2×C418yes—
86C22×C4×D11C2314yes—
87C22×Dic22—42no—
88C22×Dic22—42no—
89C22×Dic22C2×C418yes—
90C22×Dic22C2314yes—
91C2×C11×C4⋊C4—42no—
92C2×C11×C4⋊C4C2×C418yes—
93C2×C11×C4⋊C4C2314yes—
94C2×C11×C4⋊C4C2314yes—
95C2×C42×C11—42no—
96C2×C42×C11C2314yes—
97C2×(C2×D11)⋊C4—42no—
98C2×(C2×D11)⋊C4—42no—
99C2×(C2×D11)⋊C4—42no—
100C2×(C2×D11)⋊C4—42no—
101C2×(C2×D11)⋊C4C2×C418yes—
102C2×(C2×D11)⋊C4C2×C418yes—
103C2×(C2×D11)⋊C4C2314yes—
104C2×(C2×D11)⋊C4C2314yes—
105C2×(C2×D11)⋊C4C2314yes—
106C2×(C2×D11)⋊C4C2314yes—
107C2×(C2×D11)⋊C4C2314yes—
108C2×(C2×D11)⋊C4C2314yes—
109C2×C4⋊Dic11—42no—
110C2×C4⋊Dic11C2×C418yes—
111C2×C4⋊Dic11C2×C418yes—
112C2×C4⋊Dic11C2314yes—
113C2×C4⋊Dic11C2314yes—
114C2×C4⋊Dic11C2314yes—
115C2×Dic11⋊C4—42no—
116C2×Dic11⋊C4—42no—
117C2×Dic11⋊C4—42no—
118C2×Dic11⋊C4—42no—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2314yes—
123C2×C4×Dic11—42no—
124C2×C4×Dic11—42no—
125C2×C4×Dic11—42no—
126C2×C4×Dic11C2314yes—
127C2×C4×Dic11C2314yes—
128C2×C4×Dic11C2314yes—
129#66950C2×C4164yescomplemented
130C11×#95C2314yes—
131C11×#95C2314yes—
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×#2378—111nomaximal, Sylow
145C24×C11C2411yescharacteristic
146C23×D11—22no—
147C23×D11—22no—
148C23×D11—22no—
149C23×D11—22no—
150C23×D11—22no—
151C23×D11—22no—
152C23×D11C22×C414yes—
153C23×D11C2412yes—
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—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11C22×C414yes—
173C22×C4×C11C22×C414yes—
174C22×C4×C11C22×C414yes—
175C22×C4×C11C2412yes—
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×Dic11C22×C414yes—
201C22×Dic11C22×C414yes—
202C22×Dic11C22×C414yes—
203C22×Dic11C2412yes—
204C22×Dic11C2412yes—
205C22×Dic11C2412yes—
206C22×Dic11C2412yes—
207C22×Dic11C2412yes—
208C22×Dic11C2412yes—
209C22×Dic11C2412yes—
210C2×C4×D11—416no—
211C2×C4×D11—44no—
212C2×C4×D11—44no—
213C2×C4×D11C22×C4116yes—
214C2×Dic22—416no—
215C2×Dic22—44no—
216C2×Dic22—44no—
217C2×Dic22C22×C4116yes—
218C11×C4⋊C4—44no—
219C11×C4⋊C4C22×C4116yes—
220C42×C11—44no—
221(C2×D11)⋊C4—44no—
222(C2×D11)⋊C4—44no—
223(C2×D11)⋊C4—44no—
224(C2×D11)⋊C4—44no—
225(C2×D11)⋊C4C22×C4116yes—
226(C2×D11)⋊C4C22×C4116yes—
227C4⋊Dic11—44no—
228C4⋊Dic11C22×C4116yes—
229C4⋊Dic11C22×C4116yes—
230Dic11⋊C4—44no—
231Dic11⋊C4—44no—
232Dic11⋊C4—44no—
233Dic11⋊C4—44no—
234C4×Dic11—44no—
235C4×Dic11—44no—
236C4×Dic11—44no—
237C22×C22⋊Q8—111no—
238#2378—1116no—
239C2×#391—111no—
240C2×#391—111no—
241C2×#389—111no—
242C2×#389—111no—
243C2×#388—111no—
244C2×#388—111no—
245C2×#388—111no—
246C2×#388—111no—
247C2×#387—111no—
248C2×#387—111no—
249C2×#387—111no—
250C2×#387D1111yescharacteristic, complemented
251C2×#381—111no—
252C2×#380—111no—
253C23×C11C23×C412yes—
254C23×C11H(5,𝔽2)12yes—
255C23×C11H(5,𝔽2)12yes—
256C23×C11H(5,𝔽2)12yes—
257C23×C112−1+412yes—
258C23×C112−1+412yes—
259C23×C112−1+412yes—
260C23×C11C2511yescharacteristic
261C22×D11—28no—
262C22×D11—28no—
263C22×D11—28no—
264C22×D11—22no—
265C22×D11—22no—
266C22×D11—22no—
267C22×D11—22no—
268C22×D11—22no—
269C22×D11—22no—
270C22×D11—44no—
271C22×D11—44no—
272C22×D11—44no—
273C22×D11—44no—
274C22×D11C23×C414yes—
275C2×C4×C11—28no—
276C2×C4×C11—28no—
277C2×C4×C11—28no—
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—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—44no—
297C2×C4×C11—44no—
298C2×C4×C11—44no—
299C2×C4×C11—44no—
300C2×C4×C11C23×C414yes—
301C2×C4×C11C23×C414yes—
302C2×C4×C11C23×C414yes—
303C2×Dic11—28no—
304C2×Dic11—28no—
305C2×Dic11—28no—
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—22no—
324C2×Dic11—44no—
325C2×Dic11—44no—
326C2×Dic11—44no—
327C2×Dic11—44no—
328C2×Dic11C23×C414yes—
329C2×Dic11C23×C414yes—
330C2×Dic11C23×C414yes—
331C4×D11—416no—
332Dic22—416no—
333C23×Q8—111no—
334C24×C4—111no—
335C2×C22⋊Q8—118no—
336C2×C22⋊Q8—1116no—
337C22×C4⋊C4—111no—
338C22×C4⋊C4—111no—
339C22×C4⋊C4—111no—
340C22×C4⋊C4—111no—
341C22×C4⋊C4—111no—
342C22×C4⋊C4—111no—
343C22×C4⋊C4—111no—
344C22×C4⋊C4C2×D1111yescharacteristic
345C22×C4⋊C4C2×D1111yescharacteristic
346C22×C22⋊C4—111no—
347C22×C22⋊C4—111no—
348C22×C22⋊C4—111no—
349C22×C22⋊C4—111no—
350C22×C22⋊C4—111no—
351C22×C22⋊C4—111no—
352C22×C42—111no—
353C22×C42—111no—
354C22×C42—111no—
355C22×C42C2×D1111yescharacteristic
356#391—118no—
357#391—118no—
358#389—118no—
359#389—118no—
360#388—118no—
361#388—118no—
362#388—118no—
363#388—118no—
364#387—118no—
365#387—118no—
366#387—118no—
367#387C2×D1118yescomplemented
368#381—118no—
369#380—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
382C2×#95C2×D1111yescharacteristic
383C2×#95C2×D1111yescharacteristic
384C22×C11#51814yes—
385C22×C11#51914yes—
386C22×C11#52014yes—
387C22×C11#56214yes—
388C22×C11#56214yes—
389C22×C11#56314yes—
390C22×C11#56314yes—
391C22×C11C24×C411yescharacteristic
392C22×C11C2×H(5,𝔽2)11yescharacteristic
393C22×C11C2×H(5,𝔽2)11yescharacteristic
394C22×C11C2×H(5,𝔽2)11yescharacteristic
395C22×C11C2×2−1+411yescharacteristic
396C22×C11C2×2−1+411yescharacteristic
397C22×C11C2×2−1+411yescharacteristic
398C2×D11—24no—
399C2×D11—24no—
400C2×D11—24no—
401C2×D11—416no—
402C2×D11—42no—
403C2×D11—42no—
404C2×D11—42no—
405C2×D11—42no—
406C4×C11—24no—
407C4×C11—24no—
408C4×C11—24no—
409C4×C11—42no—
410C4×C11—42no—
411C4×C11—42no—
412C4×C11—42no—
413Dic11—24no—
414Dic11—24no—
415Dic11—24no—
416Dic11—42no—
417Dic11—42no—
418Dic11—42no—
419Dic11—42no—
420C25—111no—
421C22×Q8—118no—
422C22×Q8—114no—
423C22×Q8—442no—
424C22×Q8—442no—
425C23×C4—111no—
426C23×C4—111no—
427C23×C4—111no—
428C23×C4—118no—
429C23×C4—114no—
430C23×C4—111no—
431C23×C4—111no—
432C23×C4—111no—
433C23×C4—111no—
434C23×C4—442no—
435C23×C4—442no—
436C23×C4C22×D1111yescharacteristic
437C23×C4C22×D1111yescharacteristic
438C23×C4C22×D1111yescharacteristic
439C23×C4C22×D1111yescharacteristic
440C23×C4C22×D1111yescharacteristic
441C23×C4C22×D1111yescharacteristic
442C23×C4C22×D1111yescharacteristic
443C22⋊Q8—1164no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—118no—
446C2×C4⋊C4—118no—
447C2×C4⋊C4—114no—
448C2×C4⋊C4—114no—
449C2×C4⋊C4—114no—
450C2×C4⋊C4—114no—
451C2×C4⋊C4—114no—
452C2×C4⋊C4—114no—
453C2×C4⋊C4—114no—
454C2×C4⋊C4—442no—
455C2×C4⋊C4—442no—
456C2×C4⋊C4—442no—
457C2×C4⋊C4—442no—
458C2×C4⋊C4—442no—
459C2×C4⋊C4C4×D1118yes—
460C2×C4⋊C4C22×D1114yes—
461C2×C4⋊C4C22×D1114yes—
462C2×C22⋊C4—118no—
463C2×C22⋊C4—118no—
464C2×C22⋊C4—114no—
465C2×C22⋊C4—114no—
466C2×C22⋊C4—114no—
467C2×C22⋊C4—114no—
468C2×C22⋊C4—114no—
469C2×C22⋊C4—114no—
470C2×C22⋊C4—442no—
471C2×C22⋊C4—442no—
472C2×C22⋊C4—442no—
473C2×C22⋊C4—442no—
474C2×C42—42no—
475C2×C42—114no—
476C2×C42—114no—
477C2×C42—114no—
478C2×C42—442no—
479C2×C42—442no—
480C2×C42—442no—
481C2×C42C22×D1114yes—
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—
494#95C22×D1114yes—
495#95C22×D1114yes—
496C2×C11#237818yescomplemented
497C2×C11C2×#51811yescharacteristic
498C2×C11C2×#51911yescharacteristic
499C2×C11C2×#52011yescharacteristic
500C2×C11C2×#56211yescharacteristic
501C2×C11C2×#56211yescharacteristic
502C2×C11C2×#56311yescharacteristic
503C2×C11C2×#56311yescharacteristic
504D11—44no—
505C24—114no—
506C24—112no—
507C24—222no—
508C24—222no—
509C24—222no—
510C24—222no—
511C24—222no—
512C24—222no—
513C24C23×D1111yescharacteristic
514C2×Q8—1116no—
515C2×Q8—4416no—
516C2×Q8—444no—
517C2×Q8—444no—
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—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—114no—
537C22×C4—114no—
538C22×C4—114no—
539C22×C4—112no—
540C22×C4—112no—
541C22×C4—112no—
542C22×C4—1116no—
543C22×C4—112no—
544C22×C4—112no—
545C22×C4—112no—
546C22×C4—112no—
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×C4—222no—
564C22×C4—222no—
565C22×C4—4416no—
566C22×C4—444no—
567C22×C4—444no—
568C22×C4C2×C4×D1114yes—
569C22×C4C2×C4×D1114yes—
570C22×C4C2×C4×D1114yes—
571C22×C4C23×D1112yes—
572C22×C4C23×D1112yes—
573C22×C4C23×D1112yes—
574C22×C4C23×D1112yes—
575C22×C4C23×D1112yes—
576C22×C4C23×D1112yes—
577C22×C4C23×D1112yes—
578C4⋊C4—44no—
579C4⋊C4—1116no—
580C4⋊C4—1116no—
581C4⋊C4—444no—
582C4⋊C4—444no—
583C4⋊C4—444no—
584C4⋊C4—444no—
585C4⋊C4—444no—
586C4⋊C4C2×C4×D11116yes—
587C22⋊C4—1116no—
588C22⋊C4—1116no—
589C22⋊C4—444no—
590C22⋊C4—444no—
591C22⋊C4—444no—
592C22⋊C4—444no—
593C42—44no—
594C42—444no—
595C42—444no—
596C42—444no—
597C11C2×#237811yescharacteristic, complemented, Sylow
598C23—114no—
599C23—228no—
600C23—228no—
601C23—228no—
602C23—222no—
603C23—222no—
604C23—222no—
605C23—222no—
606C23—222no—
607C23—222no—
608C23—444no—
609C23—444no—
610C23—444no—
611C23—444no—
612C23C22×C4×D1112yes—
613C23#6703712yes—
614C23#6704012yes—
615C23#6704212yes—
616C23#6704212yes—
617C23#6704312yes—
618C23#6704312yes—
619C23C24×D1111yescharacteristic
620Q8—4416no—
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—28no—
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—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—114no—
647C2×C4—114no—
648C2×C4—114no—
649C2×C4—228no—
650C2×C4—228no—
651C2×C4—228no—
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—222no—
669C2×C4—222no—
670C2×C4—4416no—
671C2×C4—444no—
672C2×C4—444no—
673C2×C4—444no—
674C2×C4—444no—
675C2×C4C22×C4×D1114yes—
676C2×C4C22×C4×D1114yes—
677C2×C4C22×C4×D1114yes—
678C22—224no—
679C22—224no—
680C22—224no—
681C22—442no—
682C22—442no—
683C22—442no—
684C22—442no—
685C22—4416no—
686C22#1062305214yes—
687C22#1062307714yes—
688C22#1062310314yes—
689C22#1062317814yes—
690C22#1062319814yes—
691C22#1062323014yes—
692C22#1062324314yes—
693C22C23×C4×D1111yescharacteristic
694C22C2×#6703711yescharacteristic
695C22C2×#6704011yescharacteristic
696C22C2×#6704211yescharacteristic
697C22C2×#6704211yescharacteristic
698C22C2×#6704311yescharacteristic
699C22C2×#6704311yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—224no—
708C4—224no—
709C4—224no—
710C4—442no—
711C4—442no—
712C4—442no—
713C4—442no—
714C2—444no—
715C2#1307178018yesdirect product factor
716C2C2×#1062305211yescharacteristic
717C2C2×#1062310311yescharacteristic
718C2C2×#1062307711yescharacteristic
719C2C2×#1062317811yescharacteristic
720C2C2×#1062319811yescharacteristic
721C2C2×#1062324311yescharacteristic
722C2C2×#1062323011yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#387C2
socleC24×C11C24
prime radicalC24×D11C23
cosocleC23×C11C25
hypercenterC2×#387D11
hypocenterC11C2×#2378
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #13071780C2direct (N × H)
3. C2×#10622259C2semidirect
4. C2×#10622259C2semidirect
5. C2×#10622541C2semidirect
6. C2×#10622586C2semidirect
11. C2×#10622594C2semidirect
12. C2×#10622266C2semidirect
13. C2×#10622267C2semidirect
16. C2×C11×#387C2semidirect
38. C2×#66950C4semidirect
40. C11×#387C22semidirect
56. #10622594C22semidirect
57. #10622586C22semidirect
59. #10622541C22semidirect
64. #10622267C22semidirect
65. #10622266C22semidirect
66. #10622259C22semidirect
67. #10622259C22semidirect
129. #66950C2×C4semidirect
250. C2×#387D11semidirect
367. #387C2×D11semidirect
496. C2×C11#2378semidirect
597. C11C2×#2378semidirect
715. C2#13071780direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669502
#130717802
C2×#106222592
C2×#106225412
C2×#106225862
C2×#106222832
C2×#106225532
C2×#106226032
C2×#106222822
C2×#106225942
C2×#106222662
C2×#106222672
C2×#106222772
C2×#106222802
C2×C11×#3872
C2×#237811