Finite Group Databasebeta

← C2×#13072212 #14921787

Subgroups — C2×#13072212 #14921787

Order 2816.

3246 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic, complemented
2C22×#66931C211yesmaximal, characteristic
3C22×#66931C211yesmaximal, characteristic
4C22×C4×Dic22C211yesmaximal, characteristic, complemented
5#13072212C2116yesmaximal, direct product factor
6C2×#10622597C211yesmaximal, characteristic, complemented
7C2×#10622274C211yesmaximal, characteristic, complemented
8C2×#10622561C211yesmaximal, characteristic
9C2×#10622561C211yesmaximal, characteristic
10C2×#10622259C211yesmaximal, characteristic, complemented
11C2×#10622541C211yesmaximal, characteristic, complemented
12C2×#10622260C211yesmaximal, characteristic, complemented
13C2×#10622260C211yesmaximal, characteristic, complemented
14C2×#10622564C211yesmaximal, characteristic
15C2×C22⋊C4×Dic11C211yesmaximal, characteristic
16C2×C11×#388C211yesmaximal, characteristic
17C24×Dic11C2211yescharacteristic
18C23×Dic22C2211yescharacteristic
19C23×Dic22C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×Dic11⋊C4C2211yescharacteristic
38C22×Dic11⋊C4C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×C4×Dic11C2211yescharacteristic
42C22×C4×Dic11C2211yescharacteristic
43C22×C4×Dic11C2211yescharacteristic
44C2×#66941—28no—
45C2×#66941C2218yescomplemented
46C2×#66931—28no—
47C2×#66931—28no—
48C2×#66931C2218yes—
49C2×#66931C2218yes—
50C2×C4×Dic22—28no—
51C2×C4×Dic22C2218yescomplemented
52C11×#388C2218yes—
53C2×C11×#95C2211yescharacteristic
54C2×C11×#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57C2×C11⋊#95C2211yescharacteristic
58C2×C11⋊#95C2211yescharacteristic
59C2×C11⋊#95C2211yescharacteristic
60C2×C11⋊#95C2211yescharacteristic
61#10622597C2218yescomplemented
62#10622564C2218yes—
63#10622561C2218yes—
64#10622561C2218yes—
65C22⋊C4×Dic11C2218yes—
66#10622541C2218yescomplemented
67#10622274C2218yescomplemented
68#10622260C2218yescomplemented
69#10622260C2218yescomplemented
70#10622259C2218yescomplemented
71C25×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×Dic11—24no—
79C23×Dic11—24no—
80C23×Dic11—24no—
81C23×Dic11C2314yes—
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C22×Dic22—24no—
91C22×Dic22—24no—
92C22×Dic22—24no—
93C22×Dic22—24no—
94C22×Dic22—24no—
95C22×Dic22D418yes—
96C22×Dic22C2314yes—
97C22×Dic22C2314yes—
98C2×C11×C4⋊C4—24no—
99C2×C11×C4⋊C4C2314yes—
100C2×C11×C22⋊C4—24no—
101C2×C11×C22⋊C4—24no—
102C2×C11×C22⋊C4Q818yescomplemented
103C2×C11×C22⋊C4C2314yes—
104C2×C11×C22⋊C4C2314yes—
105C2×C11×C22⋊C4C2314yes—
106C2×C42×C11—24no—
107C2×C42×C11C2314yes—
108C2×C22⋊Dic11—24no—
109C2×C22⋊Dic11—24no—
110C2×C22⋊Dic11—24no—
111C2×C22⋊Dic11C2314yes—
112C2×C22⋊Dic11C2314yes—
113C2×C22⋊Dic11C2314yes—
114C2×C4⋊Dic11—24no—
115C2×C4⋊Dic11—24no—
116C2×C4⋊Dic11—24no—
117C2×C4⋊Dic11—24no—
118C2×C4⋊Dic11—24no—
119C2×C4⋊Dic11C2314yes—
120C2×C4⋊Dic11C2314yes—
121C2×C4⋊Dic11C2314yes—
122C2×C4⋊Dic11C2314yes—
123C2×C4⋊Dic11C2314yes—
124C2×Dic11⋊C4—24no—
125C2×Dic11⋊C4—24no—
126C2×Dic11⋊C4—24no—
127C2×Dic11⋊C4—24no—
128C2×Dic11⋊C4—24no—
129C2×Dic11⋊C4—24no—
130C2×Dic11⋊C4—24no—
131C2×Dic11⋊C4D418yes—
132C2×Dic11⋊C4C2314yes—
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2314yes—
135C2×Dic11⋊C4C2314yes—
136C2×Dic11⋊C4C2314yes—
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2314yes—
140C2×C4×Dic11—24no—
141C2×C4×Dic11—24no—
142C2×C4×Dic11—24no—
143C2×C4×Dic11C2314yes—
144C2×C4×Dic11C2314yes—
145C2×C4×Dic11C2314yes—
146#66941—232no—
147#66931—232no—
148#66931—232no—
149C4×Dic22—232no—
150C11×#95C2314yes—
151C11×#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C2×#2429—111nomaximal, Sylow
159C24×C11—22no—
160C24×C11—22no—
161C24×C11—22no—
162C24×C11—22no—
163C24×C11—22no—
164C24×C11—22no—
165C24×C11C2×Q814yes—
166C24×C11C2412yes—
167C24×C11C2411yescharacteristic
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×C11C2×D414yes—
183C22×C4×C11C2×D414yes—
184C22×C4×C11C2×Q814yes—
185C22×C4×C11C2×Q814yes—
186C22×C4×C11C2412yes—
187C22×C4×C11C2412yes—
188C22×C4×C11C2412yes—
189C22×C4×C11C2412yes—
190C22×C4×C11C2412yes—
191C22×C4×C11C2412yes—
192C22×Dic11—28no—
193C22×Dic11—28no—
194C22×Dic11—28no—
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×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—416no—
214C22×Dic11C2×D414yes—
215C22×Dic11C2×D414yes—
216C22×Dic11C2×D414yes—
217C22×Dic11C2×D414yes—
218C22×Dic11#4114yes—
219C22×Dic11#4114yes—
220C22×Dic11C2412yes—
221C22×Dic11C2412yes—
222C22×Dic11C2412yes—
223C22×Dic11C2412yes—
224C22×Dic11C2412yes—
225C22×Dic11C2412yes—
226C22×Dic11C2412yes—
227C22×Dic11C2412yes—
228C2×Dic22—232no—
229C2×Dic22—28no—
230C2×Dic22—28no—
231C2×Dic22—28no—
232C2×Dic22—28no—
233C2×Dic22—28no—
234C2×Dic22—416no—
235C2×Dic22C2×D4116yes—
236C11×C4⋊C4—28no—
237C11×C22⋊C4—28no—
238C11×C22⋊C4—28no—
239C11×C22⋊C4C2×Q8116yescomplemented
240C42×C11—28no—
241C22⋊Dic11—28no—
242C22⋊Dic11—28no—
243C22⋊Dic11—28no—
244C4⋊Dic11—28no—
245C4⋊Dic11—28no—
246C4⋊Dic11—28no—
247C4⋊Dic11—28no—
248C4⋊Dic11—28no—
249Dic11⋊C4—28no—
250Dic11⋊C4—28no—
251Dic11⋊C4—28no—
252Dic11⋊C4—28no—
253Dic11⋊C4—28no—
254Dic11⋊C4—28no—
255Dic11⋊C4—28no—
256Dic11⋊C4C2×D4116yes—
257C4×Dic11—28no—
258C4×Dic11—28no—
259C4×Dic11—28no—
260C22×C4⋊Q8—111no—
261C22×C22⋊Q8—111no—
262C22×C22⋊Q8—111no—
263C22×C4×Q8—111no—
264#2429—1116no—
265C2×#398—111no—
266C2×#398—111no—
267C2×#396—111no—
268C2×#396—111no—
269C2×#391—111no—
270C2×#389—111no—
271C2×#389—111no—
272C2×#389—111no—
273C2×#388—111no—
274C2×#388D1111yescharacteristic
275C2×C4×C22⋊C4—111no—
276C23×C11—28no—
277C23×C11—28no—
278C23×C11—28no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—44no—
286C23×C11—44no—
287C23×C11—44no—
288C23×C11—44no—
289C23×C11C22×D412yes—
290C23×C11C22×D412yes—
291C23×C11C22×Q814yes—
292C23×C11C22×Q812yes—
293C23×C11C2×#4112yes—
294C23×C11C2×#4112yes—
295C23×C112−1+412yes—
296C23×C112−1+412yes—
297C23×C11C2511yescharacteristic
298C2×C4×C11—28no—
299C2×C4×C11—28no—
300C2×C4×C11—28no—
301C2×C4×C11—28no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
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—44no—
317C2×C4×C11—44no—
318C2×C4×C11C22×D414yes—
319C2×C4×C11C22×D414yes—
320C2×C4×C11C22×Q814yes—
321C2×C4×C11C22×Q814yes—
322C2×Dic11—28no—
323C2×Dic11—28no—
324C2×Dic11—28no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—44no—
344C2×Dic11—44no—
345C2×Dic11—44no—
346C2×Dic11—44no—
347C2×Dic11—416no—
348C2×Dic11#121116yes—
349C2×Dic11C22×D414yes—
350C2×Dic11C22×D414yes—
351C2×Dic11C22×D414yes—
352C2×Dic11C22×D414yes—
353C2×Dic11C2×#4114yes—
354C2×Dic11C2×#4114yes—
355Dic22—232no—
356Dic22—416no—
357C23×Q8—111no—
358C23×Q8—111no—
359C24×C4—111no—
360C2×C4⋊Q8—118no—
361C2×C4⋊Q8—228no—
362C2×C22⋊Q8—118no—
363C2×C22⋊Q8—118no—
364C2×C22⋊Q8—228no—
365C2×C22⋊Q8—228no—
366C2×C4×Q8—118no—
367C2×C4×Q8—228no—
368C22×C4⋊C4—111no—
369C22×C4⋊C4—111no—
370C22×C4⋊C4—111no—
371C22×C4⋊C4—111no—
372C22×C4⋊C4—111no—
373C22×C4⋊C4—111no—
374C22×C4⋊C4—111no—
375C22×C4⋊C4—111no—
376C22×C4⋊C4—111no—
377C22×C4⋊C4—111no—
378C22×C4⋊C4—111no—
379C22×C4⋊C4—111no—
380C22×C4⋊C4—111no—
381C22×C4⋊C4C2×D1111yescharacteristic
382C22×C22⋊C4—111no—
383C22×C22⋊C4—111no—
384C22×C22⋊C4—111no—
385C22×C22⋊C4C2×D1111yescharacteristic
386C22×C22⋊C4C2×D1111yescharacteristic
387C22×C22⋊C4C2×D1111yescharacteristic
388C22×C42—111no—
389C22×C42—111no—
390C22×C42—111no—
391C22×C42C2×D1111yescharacteristic
392#398—118no—
393#398—118no—
394#396—118no—
395#396—118no—
396#391—118no—
397#389—118no—
398#389—118no—
399#389—118no—
400#388—118no—
401#388C2×D1118yes—
402C4×C22⋊C4—118no—
403C2×#95—111no—
404C2×#95—111no—
405C2×#95—111no—
406C2×#95—111no—
407C2×#95—111no—
408C2×#95—111no—
409C2×#95C2×D1111yescharacteristic
410C2×#95C2×D1111yescharacteristic
411C22×C11—24no—
412C22×C11—24no—
413C22×C11—24no—
414C22×C11—42no—
415C22×C11—416no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11C2×#12114yes—
420C22×C11#53314yes—
421C22×C11#54114yes—
422C22×C11#54714yes—
423C22×C11#54814yes—
424C22×C11D4×Q814yes—
425C22×C11D4×Q814yes—
426C22×C11C23×D411yescharacteristic
427C22×C11C23×D411yescharacteristic
428C22×C11C23×Q811yescharacteristic
429C22×C11C22×#4111yescharacteristic
430C22×C11C22×#4111yescharacteristic
431C22×C11C2×2−1+411yescharacteristic
432C22×C11C2×2−1+411yescharacteristic
433C4×C11—24no—
434C4×C11—24no—
435C4×C11—24no—
436C4×C11—24no—
437C4×C11—42no—
438C4×C11—42no—
439Dic11—24no—
440Dic11—24no—
441Dic11—24no—
442Dic11—42no—
443Dic11—42no—
444Dic11—42no—
445Dic11—42no—
446Dic11C2×#12118yes—
447C25C22×D1111yescharacteristic
448C22×Q8—118no—
449C22×Q8—114no—
450C22×Q8—114no—
451C22×Q8—224no—
452C22×Q8—224no—
453C22×Q8—224no—
454C22×Q8—224no—
455C22×Q8—224no—
456C23×C4—111no—
457C23×C4—111no—
458C23×C4—111no—
459C23×C4—111no—
460C23×C4—114no—
461C23×C4—111no—
462C23×C4—111no—
463C23×C4—111no—
464C23×C4—111no—
465C23×C4—224no—
466C23×C4—224no—
467C23×C4—224no—
468C23×C4C22×D1111yescharacteristic
469C23×C4C22×D1111yescharacteristic
470C23×C4C22×D1111yescharacteristic
471C23×C4C22×D1111yescharacteristic
472C23×C4C22×D1111yescharacteristic
473C23×C4C22×D1111yescharacteristic
474C4⋊Q8—2232no—
475C22⋊Q8—2232no—
476C22⋊Q8—2232no—
477C4×Q8—2232no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—118no—
480C2×C4⋊C4—114no—
481C2×C4⋊C4—114no—
482C2×C4⋊C4—114no—
483C2×C4⋊C4—114no—
484C2×C4⋊C4—114no—
485C2×C4⋊C4—114no—
486C2×C4⋊C4—114no—
487C2×C4⋊C4—114no—
488C2×C4⋊C4—114no—
489C2×C4⋊C4—114no—
490C2×C4⋊C4—114no—
491C2×C4⋊C4—114no—
492C2×C4⋊C4—114no—
493C2×C4⋊C4—224no—
494C2×C4⋊C4—224no—
495C2×C4⋊C4—224no—
496C2×C4⋊C4—224no—
497C2×C4⋊C4—224no—
498C2×C4⋊C4—224no—
499C2×C4⋊C4—224no—
500C2×C4⋊C4—224no—
501C2×C4⋊C4—224no—
502C2×C4⋊C4—224no—
503C2×C4⋊C4—224no—
504C2×C4⋊C4—224no—
505C2×C4⋊C4C22×D1114yes—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—114no—
509C2×C22⋊C4—114no—
510C2×C22⋊C4—114no—
511C2×C22⋊C4—224no—
512C2×C22⋊C4—224no—
513C2×C22⋊C4—224no—
514C2×C22⋊C4Dic2218yescomplemented
515C2×C22⋊C4C22×D1114yes—
516C2×C22⋊C4C22×D1114yes—
517C2×C22⋊C4C22×D1114yes—
518C2×C42—24no—
519C2×C42—114no—
520C2×C42—114no—
521C2×C42—114no—
522C2×C42—224no—
523C2×C42—224no—
524C2×C42—224no—
525C2×C42C22×D1114yes—
526#95—114no—
527#95—114no—
528#95—114no—
529#95—114no—
530#95—114no—
531#95—114no—
532#95C22×D1114yes—
533#95C22×D1114yes—
534C2×C11—44no—
535C2×C11#242918yescomplemented
536C2×C11C22×#12111yescharacteristic
537C2×C11C2×#53311yescharacteristic
538C2×C11C2×#54111yescharacteristic
539C2×C11C2×#54711yescharacteristic
540C2×C11C2×#54811yescharacteristic
541C2×C11C2×D4×Q811yescharacteristic
542C2×C11C2×D4×Q811yescharacteristic
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24C2×Dic2214yes—
550C24C23×D1112yes—
551C24C23×D1111yescharacteristic
552C2×Q8—1116no—
553C2×Q8—228no—
554C2×Q8—2232no—
555C2×Q8—228no—
556C2×Q8—228no—
557C2×Q8—228no—
558C2×Q8—228no—
559C2×Q8—4416no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—114no—
575C22×C4—114no—
576C22×C4—114no—
577C22×C4—112no—
578C22×C4—114no—
579C22×C4—114no—
580C22×C4—114no—
581C22×C4—112no—
582C22×C4—112no—
583C22×C4—112no—
584C22×C4—112no—
585C22×C4—112no—
586C22×C4—112no—
587C22×C4—112no—
588C22×C4—228no—
589C22×C4—228no—
590C22×C4—228no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—222no—
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—4416no—
610C22×C4C2×Dic2214yes—
611C22×C4C2×Dic2214yes—
612C22×C4D4×D1114yes—
613C22×C4D4×D1114yes—
614C22×C4C23×D1112yes—
615C22×C4C23×D1112yes—
616C22×C4C23×D1112yes—
617C22×C4C23×D1112yes—
618C22×C4C23×D1112yes—
619C22×C4C23×D1112yes—
620C4⋊C4—28no—
621C4⋊C4—1116no—
622C4⋊C4—228no—
623C4⋊C4—228no—
624C4⋊C4—228no—
625C4⋊C4—228no—
626C4⋊C4—228no—
627C4⋊C4—228no—
628C4⋊C4—228no—
629C4⋊C4—228no—
630C4⋊C4—228no—
631C4⋊C4—228no—
632C4⋊C4—228no—
633C4⋊C4—228no—
634C22⋊C4—28no—
635C22⋊C4—28no—
636C22⋊C4—228no—
637C22⋊C4—228no—
638C22⋊C4—228no—
639C22⋊C4C2×Dic22116yescomplemented
640C42—28no—
641C42—228no—
642C42—228no—
643C42—228no—
644C11C2×#242911yescharacteristic, complemented, Sylow
645C23—28no—
646C23—28no—
647C23—28no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23C22×Dic2214yes—
659C23C22×Dic2212yes—
660C23C2×D4×D1112yes—
661C23C2×D4×D1112yes—
662C23#41×D1112yes—
663C23#41×D1112yes—
664C23#6704312yes—
665C23#6704312yes—
666C23C24×D1111yescharacteristic
667Q8—2232no—
668Q8—4416no—
669C2×C4—28no—
670C2×C4—28no—
671C2×C4—28no—
672C2×C4—28no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—1116no—
690C2×C4—114no—
691C2×C4—114no—
692C2×C4—114no—
693C2×C4—114no—
694C2×C4—114no—
695C2×C4—114no—
696C2×C4—228no—
697C2×C4—228no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—228no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—4416no—
718C2×C4—444no—
719C2×C4—444no—
720C2×C4—444no—
721C2×C4—444no—
722C2×C4C22×Dic2214yes—
723C2×C4C22×Dic2214yes—
724C2×C4C2×D4×D1114yes—
725C2×C4C2×D4×D1114yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—416no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22#1062304814yes—
735C22D4×Dic2214yes—
736C22D4×Dic2214yes—
737C22D11×#12114yes—
738C22#1062318614yes—
739C22#1062320814yes—
740C22#1062323214yes—
741C22C23×Dic2211yescharacteristic
742C22C22×D4×D1111yescharacteristic
743C22C22×D4×D1111yescharacteristic
744C22C2×#41×D1111yescharacteristic
745C22C2×#41×D1111yescharacteristic
746C22C2×#6704311yescharacteristic
747C22C2×#6704311yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—118no—
755C4—224no—
756C4—224no—
757C4—224no—
758C4—442no—
759C4—442no—
760C4—442no—
761C4—442no—
762C2—44no—
763C2#1307221218yesdirect product factor
764C2C2×D11×#12111yescharacteristic
765C2C2×#1062304811yescharacteristic
766C2C2×#1062323211yescharacteristic
767C2C2×#1062318611yescharacteristic
768C2C2×#1062320811yescharacteristic
769C2C2×D4×Dic2211yescharacteristic
770C2C2×D4×Dic2211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#388C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#388D11
hypocenterC11C2×#2429
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#66941C2semidirect
4. C22×C4×Dic22C2semidirect
5. #13072212C2direct (N × H)
6. C2×#10622597C2semidirect
7. C2×#10622274C2semidirect
10. C2×#10622259C2semidirect
11. C2×#10622541C2semidirect
12. C2×#10622260C2semidirect
13. C2×#10622260C2semidirect
45. C2×#66941C22semidirect
51. C2×C4×Dic22C22semidirect
61. #10622597C22semidirect
66. #10622541C22semidirect
67. #10622274C22semidirect
68. #10622260C22semidirect
69. #10622260C22semidirect
70. #10622259C22semidirect
102. C2×C11×C22⋊C4Q8semidirect
239. C11×C22⋊C4C2×Q8semidirect
514. C2×C22⋊C4Dic22semidirect
535. C2×C11#2429semidirect
639. C22⋊C4C2×Dic22semidirect
644. C11C2×#2429semidirect
763. C2#13072212direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669412
C22×#669312
C22×C4×Dic222
#130722122
C2×#106225972
C2×#106222742
C2×#106225612
C2×#106222592
C2×#106225412
C2×#106222602
C2×#106225642
C2×C22⋊C4×Dic112
C2×C11×#3882
C2×#242911