Finite Group Databasebeta

← C2×#13071423 #14912686

Subgroups — C2×#13071423 #14912686

Order 2816.

3046 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66938C211yesmaximal, characteristic
2#13071423C2116yesmaximal, direct product factor
3C2×#10622542C211yesmaximal, characteristic, complemented
4C2×#10622259C211yesmaximal, characteristic, complemented
5C2×#10622558C211yesmaximal, characteristic, complemented
6C2×#10622283C211yesmaximal, characteristic, complemented
7C2×#10622283C211yesmaximal, characteristic, complemented
8C2×#10622571C211yesmaximal, characteristic
9C2×#10622569C211yesmaximal, characteristic
10C2×#10622563C211yesmaximal, characteristic, complemented
11C2×#10622602C211yesmaximal, characteristic, complemented
12C2×#10622264C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C2×C11×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C22×C4⋊Dic11C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C2×#66938C4116yescomplemented
41C2×#66938C2218yes—
42C11×#388C2218yescomplemented
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#10622602C2218yescomplemented
56C4⋊C4×Dic11C2218yescomplemented
57#10622571C2218yes—
58#10622569C2218yes—
59#10622563C2218yescomplemented
60#10622558C2218yescomplemented
61C22⋊C4×Dic11C2218yescomplemented
62C4×(C2×D11)⋊C4C2218yescomplemented
63#10622542C2218yescomplemented
64#10622283C2218yescomplemented
65#10622283C2218yescomplemented
66#10622264C2218yescomplemented
67#10622259C2218yescomplemented
68C25×C11C2311yescharacteristic
69C24×D11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C22×C22⋊D11—42no—
77C22×C22⋊D11—42no—
78C22×C22⋊D11C2×C418yes—
79C22×C22⋊D11C2314yes—
80C23×Dic11—24no—
81C23×Dic11—42no—
82C23×Dic11—42no—
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2314yes—
91C22×C4×D11—24no—
92C22×C4×D11—42no—
93C22×C4×D11—42no—
94C22×C4×D11C2314yes—
95C22×Dic22—42no—
96C22×Dic22—42no—
97C22×Dic22C2×C418yescomplemented
98C22×Dic22C2314yes—
99C2×C11×C4⋊C4—24no—
100C2×C11×C4⋊C4C2314yes—
101C2×C11×C22⋊C4—24no—
102C2×C11×C22⋊C4—42no—
103C2×C11×C22⋊C4C2×C418yescomplemented
104C2×C11×C22⋊C4C2314yes—
105C2×C11×C22⋊C4C2314yes—
106C2×C11×C22⋊C4C2314yes—
107C2×C42×C11—42no—
108C2×C42×C11C2314yes—
109C2×C22⋊Dic11—42no—
110C2×C22⋊Dic11C2×C418yescomplemented
111C2×C22⋊Dic11C2314yes—
112C2×C22⋊Dic11C2314yes—
113C2×(C2×D11)⋊C4—24no—
114C2×(C2×D11)⋊C4—42no—
115C2×(C2×D11)⋊C4—42no—
116C2×(C2×D11)⋊C4C2×C418yescomplemented
117C2×(C2×D11)⋊C4C2×C418yescomplemented
118C2×(C2×D11)⋊C4C2314yes—
119C2×(C2×D11)⋊C4C2314yes—
120C2×(C2×D11)⋊C4C2314yes—
121C2×(C2×D11)⋊C4C2314yes—
122C2×(C2×D11)⋊C4C2314yes—
123C2×C4⋊Dic11—24no—
124C2×C4⋊Dic11—42no—
125C2×C4⋊Dic11C2314yes—
126C2×C4⋊Dic11C2314yes—
127C2×Dic11⋊C4—42no—
128C2×Dic11⋊C4C2314yes—
129C2×C4×Dic11—42no—
130C2×C4×Dic11—42no—
131C2×C4×Dic11—42no—
132C2×C4×Dic11C2×C418yescomplemented
133C2×C4×Dic11C2314yes—
134C2×C4×Dic11C2314yes—
135C2×C4×Dic11C2314yes—
136C2×C4×Dic11C2314yes—
137#66938C2×C4164yescomplemented
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×#2337—111nomaximal, Sylow
151C24×C11—22no—
152C24×C11—22no—
153C24×C11—22no—
154C24×C11—22no—
155C24×C11—22no—
156C24×C11—22no—
157C24×C11C22×C414yes—
158C24×C11C2412yes—
159C24×C11C2411yescharacteristic
160C23×D11—22no—
161C23×D11—22no—
162C23×D11—22no—
163C23×D11—22no—
164C23×D11—22no—
165C23×D11—22no—
166C23×D11C22×C414yes—
167C23×D11C2412yes—
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×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11C22×C414yes—
184C22×C4×C11C22×C414yes—
185C22×C4×C11#4114yes—
186C22×C4×C11C2412yes—
187C22×C4×C11C2412yes—
188C22×C4×C11C2412yes—
189C22×C4×C11C2412yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2412yes—
192C2×C22⋊D11—416no—
193C2×C22⋊D11—44no—
194C2×C22⋊D11—44no—
195C2×C22⋊D11C22×C4116yes—
196C22×Dic11—28no—
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×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—44no—
215C22×Dic11—44no—
216C22×Dic11—416no—
217C22×Dic11C22×C414yes—
218C22×Dic11C22×C414yes—
219C22×Dic11C22×C414yes—
220C22×Dic11#4114yes—
221C22×Dic11C2412yes—
222C22×Dic11C2412yes—
223C22×Dic11C2412yes—
224C22×Dic11C2412yes—
225C22×Dic11C2412yes—
226C22×Dic11C2412yes—
227C22×Dic11C2412yes—
228C2×C4×D11—28no—
229C2×C4×D11—44no—
230C2×C4×D11—44no—
231C2×C4×D11—416no—
232C2×Dic22—416no—
233C2×Dic22—44no—
234C2×Dic22—44no—
235C2×Dic22C22×C4116yescomplemented
236C11×C4⋊C4—28no—
237C11×C22⋊C4—28no—
238C11×C22⋊C4—44no—
239C11×C22⋊C4C22×C4116yescomplemented
240C42×C11—44no—
241C22⋊Dic11—44no—
242C22⋊Dic11C22×C4116yescomplemented
243(C2×D11)⋊C4—28no—
244(C2×D11)⋊C4—44no—
245(C2×D11)⋊C4—44no—
246(C2×D11)⋊C4C22×C4116yescomplemented
247(C2×D11)⋊C4C22×C4116yescomplemented
248C4⋊Dic11—28no—
249C4⋊Dic11—44no—
250Dic11⋊C4—44no—
251C4×Dic11—44no—
252C4×Dic11—44no—
253C4×Dic11—44no—
254C4×Dic11C22×C4116yescomplemented
255C22×#124—111no—
256#2337—1116no—
257C2×#391—111no—
258C2×#391—111no—
259C2×#388—111no—
260C2×#388—111no—
261C2×#388—111no—
262C2×#388D1111yescharacteristic, complemented
263C2×#386—111no—
264C2×#386—111no—
265C2×#385—111no—
266C2×#385—111no—
267C2×#383—111no—
268C2×C4×C4⋊C4—111no—
269C2×C4×C22⋊C4—111no—
270C2×C4×C22⋊C4—111no—
271C23×C11—28no—
272C23×C11—28no—
273C23×C11—28no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—44no—
281C23×C11—44no—
282C23×C11—44no—
283C23×C11—44no—
284C23×C11C23×C414yes—
285C23×C11C23×C412yes—
286C23×C11C2×#4112yes—
287C23×C11C2×#4112yes—
288C23×C11H(5,𝔽2)12yes—
289C23×C11H(5,𝔽2)12yes—
290C23×C11H(5,𝔽2)12yes—
291C23×C112−1+412yes—
292C23×C11C2511yescharacteristic
293C22×D11—28no—
294C22×D11—28no—
295C22×D11—28no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—44no—
303C22×D11—44no—
304C22×D11—44no—
305C22×D11—44no—
306C22×D11C23×C414yes—
307C2×C4×C11—28no—
308C2×C4×C11—28no—
309C2×C4×C11—28no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—44no—
326C2×C4×C11—44no—
327C2×C4×C11—44no—
328C2×C4×C11C23×C414yes—
329C2×C4×C11C23×C414yes—
330C2×C4×C11C2×#4114yes—
331C22⋊D11—416no—
332C2×Dic11—28no—
333C2×Dic11—28no—
334C2×Dic11—28no—
335C2×Dic11—28no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—22no—
353C2×Dic11—416no—
354C2×Dic11—44no—
355C2×Dic11—44no—
356C2×Dic11—44no—
357C2×Dic11C23×C414yes—
358C2×Dic11C23×C414yes—
359C2×Dic11C23×C414yes—
360C2×Dic11C2×#4114yes—
361C4×D11—416no—
362Dic22—416no—
363C23×Q8—111no—
364C23×D4—111no—
365C24×C4—111no—
366C24×C4—111no—
367C2×#124—118no—
368C2×#124—1116no—
369C22×C4⋊C4—111no—
370C22×C4⋊C4—111no—
371C22×C4⋊C4—111no—
372C22×C4⋊C4C2×D1111yescharacteristic
373C22×C22⋊C4—111no—
374C22×C22⋊C4—111no—
375C22×C22⋊C4—111no—
376C22×C22⋊C4—111no—
377C22×C22⋊C4—111no—
378C22×C22⋊C4—111no—
379C22×C22⋊C4—111no—
380C22×C22⋊C4C2×D1111yescharacteristic
381C22×C22⋊C4C2×D1111yescharacteristic
382C22×C22⋊C4C2×D1111yescharacteristic
383C22×C42—111no—
384C22×C42—111no—
385C22×C42—111no—
386C22×C42—111no—
387C22×C42C2×D1111yescharacteristic
388#391—118no—
389#391—118no—
390#388—118no—
391#388—118no—
392#388—118no—
393#388C2×D1118yescomplemented
394#386—118no—
395#386—118no—
396#385—118no—
397#385—118no—
398#383—118no—
399C4×C4⋊C4—118no—
400C4×C22⋊C4—118no—
401C4×C22⋊C4—118no—
402C2×#95—111no—
403C2×#95—111no—
404C2×#95—111no—
405C2×#95—111no—
406C2×#95—111no—
407C2×#95—111no—
408C2×#95—111no—
409C2×#95—111no—
410C2×#95—111no—
411C2×#95—111no—
412C2×#95C2×D1111yescharacteristic
413C2×#95C2×D1111yescharacteristic
414C22×C11—24no—
415C22×C11—24no—
416C22×C11—24no—
417C22×C11—416no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11C4×#4114yes—
423C22×C11#51814yes—
424C22×C11#52014yes—
425C22×C11#53814yes—
426C22×C11#53814yes—
427C22×C11#54214yes—
428C22×C11#54214yes—
429C22×C11C24×C411yescharacteristic
430C22×C11C22×#4111yescharacteristic
431C22×C11C22×#4111yescharacteristic
432C22×C11C2×H(5,𝔽2)11yescharacteristic
433C22×C11C2×H(5,𝔽2)11yescharacteristic
434C22×C11C2×H(5,𝔽2)11yescharacteristic
435C22×C11C2×2−1+411yescharacteristic
436C2×D11—24no—
437C2×D11—24no—
438C2×D11—24no—
439C2×D11—416no—
440C2×D11—42no—
441C2×D11—42no—
442C2×D11—42no—
443C2×D11—42no—
444C4×C11—24no—
445C4×C11—24no—
446C4×C11—24no—
447C4×C11—42no—
448C4×C11—42no—
449C4×C11—42no—
450Dic11—24no—
451Dic11—24no—
452Dic11—24no—
453Dic11—24no—
454Dic11—42no—
455Dic11—42no—
456Dic11—42no—
457C25—111no—
458C25C22×D1111yescharacteristic
459C22×Q8—118no—
460C22×Q8—114no—
461C22×Q8—442no—
462C22×Q8—442no—
463C22×D4—118no—
464C22×D4—114no—
465C22×D4—442no—
466C22×D4—442no—
467C23×C4—111no—
468C23×C4—111no—
469C23×C4—111no—
470C23×C4—111no—
471C23×C4—111no—
472C23×C4—111no—
473C23×C4—111no—
474C23×C4—114no—
475C23×C4—114no—
476C23×C4—224no—
477C23×C4—224no—
478C23×C4—442no—
479C23×C4—442no—
480C23×C4—442no—
481C23×C4—442no—
482C23×C4C22×D1111yescharacteristic
483C23×C4C22×D1111yescharacteristic
484C23×C4C22×D1111yescharacteristic
485C23×C4C22×D1111yescharacteristic
486C23×C4C22×D1111yescharacteristic
487C23×C4C22×D1111yescharacteristic
488#124—1164no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—114no—
491C2×C4⋊C4—114no—
492C2×C4⋊C4—114no—
493C2×C4⋊C4—224no—
494C2×C4⋊C4—442no—
495C2×C4⋊C4—442no—
496C2×C4⋊C4C22×D1114yes—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—118no—
500C2×C22⋊C4—114no—
501C2×C22⋊C4—118no—
502C2×C22⋊C4—118no—
503C2×C22⋊C4—114no—
504C2×C22⋊C4—114no—
505C2×C22⋊C4—114no—
506C2×C22⋊C4—114no—
507C2×C22⋊C4—114no—
508C2×C22⋊C4—114no—
509C2×C22⋊C4—224no—
510C2×C22⋊C4—442no—
511C2×C22⋊C4—442no—
512C2×C22⋊C4—442no—
513C2×C22⋊C4C4×D1118yescomplemented
514C2×C22⋊C4C22×D1114yes—
515C2×C22⋊C4C22×D1114yes—
516C2×C22⋊C4C22×D1114yes—
517C2×C42—42no—
518C2×C42—118no—
519C2×C42—114no—
520C2×C42—114no—
521C2×C42—114no—
522C2×C42—114no—
523C2×C42—442no—
524C2×C42—442no—
525C2×C42—442no—
526C2×C42C22×D1114yes—
527#95—114no—
528#95—114no—
529#95—114no—
530#95—114no—
531#95—114no—
532#95—114no—
533#95—114no—
534#95—114no—
535#95—114no—
536#95—114no—
537#95C22×D1114yes—
538#95C22×D1114yes—
539C2×C11—44no—
540C2×C11#233718yescomplemented
541C2×C11C2×C4×#4111yescharacteristic
542C2×C11C2×#51811yescharacteristic
543C2×C11C2×#52011yescharacteristic
544C2×C11C2×#53811yescharacteristic
545C2×C11C2×#53811yescharacteristic
546C2×C11C2×#54211yescharacteristic
547C2×C11C2×#54211yescharacteristic
548D11—44no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—114no—
556C24—112no—
557C24—222no—
558C24—222no—
559C24—222no—
560C24—222no—
561C24—222no—
562C24—222no—
563C24C2×C4×D1114yes—
564C24C23×D1112yes—
565C24C23×D1111yescharacteristic
566C2×Q8—1116no—
567C2×Q8—4416no—
568C2×Q8—444no—
569C2×Q8—444no—
570C2×D4—1116no—
571C2×D4—4416no—
572C2×D4—444no—
573C2×D4—444no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—114no—
590C22×C4—114no—
591C22×C4—114no—
592C22×C4—114no—
593C22×C4—112no—
594C22×C4—112no—
595C22×C4—112no—
596C22×C4—112no—
597C22×C4—112no—
598C22×C4—112no—
599C22×C4—112no—
600C22×C4—228no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—228no—
619C22×C4—444no—
620C22×C4—444no—
621C22×C4—4416no—
622C22×C4—444no—
623C22×C4—444no—
624C22×C4—4416no—
625C22×C4C2×C4×D1114yes—
626C22×C4C2×C4×D1114yes—
627C22×C4#434114yes—
628C22×C4C23×D1112yes—
629C22×C4C23×D1112yes—
630C22×C4C23×D1112yes—
631C22×C4C23×D1112yes—
632C22×C4C23×D1112yes—
633C22×C4C23×D1112yes—
634C4⋊C4—28no—
635C4⋊C4—228no—
636C4⋊C4—444no—
637C4⋊C4—444no—
638C22⋊C4—28no—
639C22⋊C4—44no—
640C22⋊C4—1116no—
641C22⋊C4—1116no—
642C22⋊C4—1116no—
643C22⋊C4—228no—
644C22⋊C4—444no—
645C22⋊C4—444no—
646C22⋊C4—444no—
647C22⋊C4C2×C4×D11116yescomplemented
648C42—44no—
649C42—1116no—
650C42—444no—
651C42—444no—
652C42—444no—
653C11C2×#233711yescharacteristic, complemented, Sylow
654C23—28no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—114no—
668C23—228no—
669C23—228no—
670C23—228no—
671C23—222no—
672C23—222no—
673C23—222no—
674C23—222no—
675C23—222no—
676C23—222no—
677C23—444no—
678C23—444no—
679C23—444no—
680C23—444no—
681C23C22×C4×D1114yes—
682C23C22×C4×D1112yes—
683C23C2×#434112yes—
684C23#6703712yes—
685C23#41×D1112yes—
686C23#6704212yes—
687C23#6704212yes—
688C23#6704312yes—
689C23C24×D1111yescharacteristic
690Q8—4416no—
691D4—4416no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—114no—
714C2×C4—114no—
715C2×C4—114no—
716C2×C4—114no—
717C2×C4—228no—
718C2×C4—228no—
719C2×C4—228no—
720C2×C4—228no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—4416no—
739C2×C4—4416no—
740C2×C4—444no—
741C2×C4—444no—
742C2×C4—444no—
743C2×C4C22×C4×D1114yes—
744C2×C4C22×C4×D1114yes—
745C2×C4C2×#434114yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—416no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—224no—
755C22—224no—
756C22—224no—
757C22—4416no—
758C22—442no—
759C22—442no—
760C22—442no—
761C22—442no—
762C22#1062305414yes—
763C22C4×#434114yes—
764C22#1062307614yes—
765C22#1062314814yes—
766C22#1062319314yes—
767C22#1062321314yes—
768C22#1062323514yes—
769C22C23×C4×D1111yescharacteristic
770C22C22×#434111yescharacteristic
771C22C2×#6703711yescharacteristic
772C22C2×#41×D1111yescharacteristic
773C22C2×#6704211yescharacteristic
774C22C2×#6704211yescharacteristic
775C22C2×#6704311yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—224no—
783C4—224no—
784C4—224no—
785C4—224no—
786C4—442no—
787C4—442no—
788C4—442no—
789C2—44no—
790C2—444no—
791C2#1307142318yesdirect product factor
792C2C2×C4×#434111yescharacteristic
793C2C2×#1062307611yescharacteristic
794C2C2×#1062305411yescharacteristic
795C2C2×#1062314811yescharacteristic
796C2C2×#1062323511yescharacteristic
797C2C2×#1062319311yescharacteristic
798C2C2×#1062321311yescharacteristic
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
cosocleC23×C11C25
hypercenterC2×#388D11
hypocenterC11C2×#2337
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #13071423C2direct (N × H)
3. C2×#10622542C2semidirect
4. C2×#10622259C2semidirect
5. C2×#10622558C2semidirect
6. C2×#10622283C2semidirect
7. C2×#10622283C2semidirect
10. C2×#10622563C2semidirect
11. C2×#10622602C2semidirect
12. C2×#10622264C2semidirect
13. C2×C4⋊C4×Dic11C2semidirect
14. C2×C22⋊C4×Dic11C2semidirect
15. C2×C4×(C2×D11)⋊C4C2semidirect
16. C2×C11×#388C2semidirect
40. C2×#66938C4semidirect
42. C11×#388C22semidirect
55. #10622602C22semidirect
56. C4⋊C4×Dic11C22semidirect
59. #10622563C22semidirect
60. #10622558C22semidirect
61. C22⋊C4×Dic11C22semidirect
62. C4×(C2×D11)⋊C4C22semidirect
63. #10622542C22semidirect
64. #10622283C22semidirect
65. #10622283C22semidirect
66. #10622264C22semidirect
67. #10622259C22semidirect
97. C22×Dic22C2×C4semidirect
103. C2×C11×C22⋊C4C2×C4semidirect
110. C2×C22⋊Dic11C2×C4semidirect
116. C2×(C2×D11)⋊C4C2×C4semidirect
117. C2×(C2×D11)⋊C4C2×C4semidirect
132. C2×C4×Dic11C2×C4semidirect
137. #66938C2×C4semidirect
235. C2×Dic22C22×C4semidirect
239. C11×C22⋊C4C22×C4semidirect
242. C22⋊Dic11C22×C4semidirect
246. (C2×D11)⋊C4C22×C4semidirect
247. (C2×D11)⋊C4C22×C4semidirect
254. C4×Dic11C22×C4semidirect
262. C2×#388D11semidirect
393. #388C2×D11semidirect
513. C2×C22⋊C4C4×D11semidirect
540. C2×C11#2337semidirect
647. C22⋊C4C2×C4×D11semidirect
653. C11C2×#2337semidirect
791. C2#13071423direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669382
#130714232
C2×#106225422
C2×#106222592
C2×#106225582
C2×#106222832
C2×#106225712
C2×#106225692
C2×#106225632
C2×#106226022
C2×#106222642
C2×C4⋊C4×Dic112
C2×C22⋊C4×Dic112
C2×C4×(C2×D11)⋊C42
C2×C11×#3882
C2×#233711