Finite Group Databasebeta

← C2×#13082233 #15660865

Subgroups — C2×#13082233 #15660865

Order 2816.

7706 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
1#13082233C2132yesmaximal, direct product factor
2C2×#10623100C211yesmaximal, characteristic, complemented
3C2×#10623099C213yesmaximal, complemented
4C2×#10623112C213yesmaximal, complemented
5C2×#10623044C213yesmaximal, complemented
6C2×Q8×C22⋊D11C211yesmaximal, characteristic, complemented
7C2×#10623107C211yesmaximal, characteristic, complemented
8C2×#10623348C211yesmaximal, characteristic, complemented
9C2×#10623038C213yesmaximal, complemented
10C2×#10623109C213yesmaximal, complemented
11C2×#10623111C213yesmaximal, complemented
12C2×#10623010C213yesmaximal, complemented
13C2×C4×#4343C211yesmaximal, characteristic, complemented
14C2×C4×#4339C213yesmaximal, complemented
15C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C11C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C22×#4343C2211yescharacteristic
19C22×Q8×D11C2211yescharacteristic
20C22×#4339C2213yes—
21C2×C4×Q8×C11C2213yes—
22C2×C4×Q8×C11C2213yes—
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×Q8×C11C22116yescomplemented
26C22×C11×C4⋊C4C2213yes—
27C22×C42×C11C2213yes—
28#10623348C22116yescomplemented
29Q8×C22⋊D11C22116yescomplemented
30C2×#67000C2213yes—
31C2×#66999C2213yes—
32C2×#66999C2213yes—
33C2×Q8×Dic11C2211yescharacteristic
34C2×Q8×Dic11C2211yescharacteristic
35C2×#66997C2213yes—
36C2×#66983C2213yes—
37C2×#66982C2216yes—
38C2×C4×C22⋊D11C2213yes—
39C2×C4×C22⋊D11C2213yes—
40C2×C4×C22⋊D11C2211yescharacteristic
41C2×C4×C22⋊D11C2213yes—
42C2×#66979C2213yes—
43C2×#66977C2213yes—
44#10623112C22148yescomplemented
45#10623111C22148yescomplemented
46#10623109C22148yescomplemented
47#10623107C22116yescomplemented
48C4×#4343C22116yescomplemented
49C4×Q8×D11C22116yescomplemented
50#10623100C22116yescomplemented
51#10623099C22148yescomplemented
52#10623044C22148yescomplemented
53C2×#66951C2216yes—
54C2×#66950C2213yes—
55C2×#66949C2216yes—
56#10623038C22148yescomplemented
57C2×#66948C2213yes—
58C2×#66947C2216yes—
59C2×#66946C2213yes—
60C2×#66945C2213yes—
61C2×C4⋊C4×D11C2213yes—
62C2×#66943C2213yes—
63C2×#66942C2216yes—
64C2×#66941C2213yes—
65C2×#66940C2213yes—
66#10623010C22148yescomplemented
67C2×#66929C2216yes—
68C2×#66928C2213yes—
69C4×#4339C22148yescomplemented
70C2×C4×D44C2213yes—
71C2×C4×D44C2213yes—
72C2×C4×D44C2213yes—
73C2×#66925C2213yes—
74C2×#66925C2216yes—
75C2×#66925C2213yes—
76C2×C42×D11C2213yes—
77C2×C42×D11C2213yes—
78C2×#66923C2213yes—
79C2×C4×Dic22C2213yes—
80C2×C4×Dic22C2213yes—
81C2×C4×Dic22C2213yes—
82C22×Q8×C11—28no—
83C22×Q8×C11C2313yes—
84C22×Q8×C11C2318yes—
85C22×Q8×C11C2311yescharacteristic
86C23×C4×C11C2313yes—
87C23×C4×C11C2313yes—
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11C2313yes—
90C22×C22⋊D11C2311yescharacteristic
91C2×#4343—28no—
92C2×#4343C2318yes—
93C2×Q8×D11—28no—
94C2×Q8×D11C2318yes—
95C2×#4339—224no—
96C2×#4339C23124yes—
97C22×D44C2313yes—
98C22×D44C2313yes—
99C22×C4×D11C2311yescharacteristic
100C22×C4×D11C2313yes—
101C22×C4×D11C2313yes—
102C22×C4×D11C2313yes—
103C22×C4×D11C2313yes—
104C22×C4×D11C2313yes—
105C22×Dic22C2313yes—
106C22×Dic22C2313yes—
107C4×Q8×C11C23124yes—
108C4×Q8×C11C2318yes—
109C4×Q8×C11C2318yes—
110C4×Q8×C11C23124yes—
111C2×C11×C4⋊C4C2313yes—
112C2×C11×C4⋊C4C2313yes—
113C2×C11×C4⋊C4C2316yes—
114C2×C11×C4⋊C4C23124yes—
115C2×C42×C11C2313yes—
116C2×C42×C11C2313yes—
117C2×C42×C11C2313yes—
118C2×C42×C11C2313yes—
119C2×C42×C11C23124yes—
120C2×C22⋊Dic11C2313yes—
121C2×C22⋊Dic11C2311yescharacteristic
122#67000C23124yes—
123#66999C23124yes—
124#66999C23124yes—
125Q8×Dic11C2318yes—
126Q8×Dic11C2318yes—
127#66997C23124yes—
128#66983C23124yes—
129#66982C23148yes—
130C4×C22⋊D11C2318yes—
131C4×C22⋊D11C23124yes—
132C4×C22⋊D11C23124yes—
133C4×C22⋊D11C23124yes—
134C2×(C2×D11)⋊C4C2311yescharacteristic
135C2×(C2×D11)⋊C4C2313yes—
136C2×(C2×D11)⋊C4C2313yes—
137C2×(C2×D11)⋊C4C2313yes—
138C2×(C2×D11)⋊C4C2316yes—
139C2×(C2×D11)⋊C4C2316yes—
140C2×(C2×D11)⋊C4C2316yes—
141#66979C23124yes—
142C2×C4⋊Dic11C2313yes—
143C2×C4⋊Dic11C2313yes—
144C2×C4⋊Dic11C2313yes—
145C2×C4⋊Dic11C2313yes—
146#66977C23124yes—
147C2×Dic11⋊C4C2311yescharacteristic
148C2×Dic11⋊C4C2313yes—
149C2×Dic11⋊C4C2313yes—
150C2×Dic11⋊C4C2313yes—
151C2×Dic11⋊C4C2316yes—
152C2×Dic11⋊C4C2316yes—
153C2×Dic11⋊C4C2316yes—
154C2×C4×Dic11C2311yescharacteristic
155C2×C4×Dic11C2313yes—
156C2×C4×Dic11C2313yes—
157C2×C4×Dic11C2313yes—
158C2×C4×Dic11C2313yes—
159C2×C4×Dic11C2313yes—
160#66951C23148yes—
161#66950C23124yes—
162#66949C23148yes—
163#66948C23124yes—
164#66947C23148yes—
165#66946C23124yes—
166#66945C23124yes—
167C4⋊C4×D11C23124yes—
168#66943C23124yes—
169#66942C23148yes—
170#66941C23124yes—
171#66940C23124yes—
172#66929C23148yes—
173#66928C23124yes—
174C4×D44C23124yes—
175C4×D44C23124yes—
176C4×D44C23124yes—
177#66925C23124yes—
178#66925C23124yes—
179#66925C23148yes—
180C42×D11C23124yes—
181C42×D11C23124yes—
182#66923C23124yes—
183C4×Dic22C23124yes—
184C4×Dic22C23124yes—
185C4×Dic22C23124yes—
186C2×#3482—111nomaximal, Sylow
187C24×C11C2411yescharacteristic
188C23×D11C2413yes—
189C23×D11C2411yescharacteristic
190C2×Q8×C11—232no—
191C2×Q8×C11—212no—
192C2×Q8×C11#4118yescomplemented
193C2×Q8×C11C24112yes—
194C2×Q8×C11C2414yes—
195C22×C4×C11—212no—
196C22×C4×C11—212no—
197C22×C4×C11—24no—
198C22×C4×C11C2413yes—
199C22×C4×C11C2411yescharacteristic
200C22×C4×C11C2413yes—
201C22×C4×C11C2413yes—
202C22×C4×C11C24112yes—
203C22×C4×C11C24112yes—
204C22×C4×C11C2414yes—
205C22×C4×C11C2413yes—
206C22×C4×C11C2411yescharacteristic
207C2×C22⋊D11—212no—
208C2×C22⋊D11#4118yescomplemented
209C2×C22⋊D11C24112yes—
210C2×C22⋊D11C2414yes—
211C22×Dic11C2411yescharacteristic
212C22×Dic11C2411yescharacteristic
213C22×Dic11C2413yes—
214C22×Dic11C2413yes—
215C22×Dic11C2413yes—
216C22×Dic11C2411yescharacteristic
217#4343—232no—
218Q8×D11—232no—
219#4339—296no—
220C2×D44—212no—
221C2×D44—212no—
222C2×D44C24112yes—
223C2×D44C24112yes—
224C2×C4×D11—212no—
225C2×C4×D11—212no—
226C2×C4×D11—212no—
227C2×C4×D11—212no—
228C2×C4×D11—24no—
229C2×C4×D11—212no—
230C2×C4×D11C2414yes—
231C2×C4×D11C24112yes—
232C2×C4×D11C24112yes—
233C2×C4×D11C24112yes—
234C2×C4×D11C24112yes—
235C2×C4×D11C24112yes—
236C2×Dic22—212no—
237C2×Dic22—212no—
238C2×Dic22C24112yes—
239C2×Dic22C24112yes—
240C11×C4⋊C4C24112yes—
241C11×C4⋊C4C24112yes—
242C11×C4⋊C4C24124yes—
243C42×C11C24112yes—
244C42×C11C24112yes—
245C42×C11C24112yes—
246C42×C11C24112yes—
247C22⋊Dic11C24112yes—
248C22⋊Dic11C2414yes—
249(C2×D11)⋊C4C2414yes—
250(C2×D11)⋊C4C24112yes—
251(C2×D11)⋊C4C24112yes—
252(C2×D11)⋊C4C24112yes—
253(C2×D11)⋊C4C24124yes—
254(C2×D11)⋊C4C24124yes—
255(C2×D11)⋊C4C24124yes—
256C4⋊Dic11C24112yes—
257C4⋊Dic11C24112yes—
258C4⋊Dic11C24112yes—
259C4⋊Dic11C24112yes—
260Dic11⋊C4C2414yes—
261Dic11⋊C4C24112yes—
262Dic11⋊C4C24112yes—
263Dic11⋊C4C24112yes—
264Dic11⋊C4C24124yes—
265Dic11⋊C4C24124yes—
266Dic11⋊C4C24124yes—
267C4×Dic11C2414yes—
268C4×Dic11C24112yes—
269C4×Dic11C24112yes—
270C4×Dic11C24112yes—
271C4×Dic11C24112yes—
272C4×Dic11C24112yes—
273#3482—1132no—
274C2×#557—111no—
275C2×#556—113no—
276C2×#552—113no—
277C2×#552—113no—
278C2×D4×Q8—111no—
279C2×#548—111no—
280C2×#548—111no—
281C2×#547—113no—
282C2×#533—113no—
283C2×#529—113no—
284C2×#529—113no—
285C2×C4×#41—113no—
286C2×C4×#41—111no—
287C22×C4×Q8—111no—
288C22×C4×Q8D1111yescharacteristic, complemented
289C23×C11—22no—
290C23×C11—22no—
291C23×C11C2×#4114yes—
292C23×C11C2512yes—
293C23×C11C2511yescharacteristic
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—26no—
297C22×D11—26no—
298C22×D11—26no—
299C22×D11C2×#4114yes—
300C22×D11C2516yes—
301C22×D11C2512yes—
302Q8×C11—224no—
303Q8×C11C2×#41116yescomplemented
304C2×C4×C11—26no—
305C2×C4×C11—26no—
306C2×C4×C11—224no—
307C2×C4×C11—26no—
308C2×C4×C11—22no—
309C2×C4×C11—224no—
310C2×C4×C11—28no—
311C2×C4×C11C2×#41112yes—
312C2×C4×C112−1+414yes—
313C2×C4×C11C2516yes—
314C2×C4×C11C2512yes—
315C2×C4×C11C2516yes—
316C2×C4×C11C2516yes—
317C2×C4×C11C2516yes—
318C2×C4×C11C2512yes—
319C22⋊D11—224no—
320C22⋊D11C2×#41116yescomplemented
321C2×Dic11—26no—
322C2×Dic11—26no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—26no—
326C2×Dic11C2×#4114yes—
327C2×Dic11C2512yes—
328C2×Dic11C2512yes—
329C2×Dic11C2516yes—
330C2×Dic11C2516yes—
331C2×Dic11C2516yes—
332C2×Dic11C2512yes—
333D44—224no—
334D44—224no—
335C4×D11—224no—
336C4×D11—224no—
337C4×D11—224no—
338C4×D11—28no—
339C4×D11—224no—
340C4×D11—224no—
341Dic22—224no—
342Dic22—224no—
343C22×#41—111no—
344C22×#41—113no—
345C23×Q8—111no—
346C23×Q8C2×D1111yescharacteristic
347#557—1116no—
348#556—1148no—
349#552—1148no—
350#552—1148no—
351D4×Q8—1116no—
352#548—1116no—
353#548—1116no—
354#547—1148no—
355#533—1148no—
356C2×C4⋊Q8—113no—
357C2×C4⋊Q8—113no—
358#529—1148no—
359#529—1148no—
360C2×#126—116no—
361C2×#126—116no—
362C2×#125—116no—
363C2×#125—113no—
364C2×#125—113no—
365C2×#124—113no—
366C2×#124—113no—
367C2×#123—116no—
368C2×#123—116no—
369C2×C22⋊Q8—113no—
370C2×C22⋊Q8—113no—
371C2×C22⋊Q8—113no—
372C2×C22⋊Q8—116no—
373C2×C22⋊Q8—113no—
374C2×#121—113no—
375C2×#121—113no—
376C4×#41—1116no—
377C4×#41—1148no—
378C2×C4×Q8—111no—
379C2×C4×Q8—111no—
380C2×C4×Q8—1116no—
381C2×C4×Q8—113no—
382C2×C4×Q8—113no—
383C2×C4×Q8—113no—
384C2×C4×Q8—113no—
385C2×C4×Q8C2×D1111yescharacteristic
386C2×C4×Q8C2×D1113yes—
387C2×C4×Q8C2×D1111yescharacteristic
388C2×C4×Q8C2×D1113yes—
389C2×C4×Q8C2×D11116yescomplemented
390C2×C4×D4—111no—
391C2×C4×D4—113no—
392C2×C4×D4—113no—
393C2×C4×D4—113no—
394C2×C4×D4—113no—
395C2×C4×D4—113no—
396C2×C4×D4—113no—
397C2×C4×D4—113no—
398C2×#117—113no—
399C2×#117—113no—
400C2×#117—113no—
401C2×#117—113no—
402C2×#117—116no—
403C22×C4⋊C4—113no—
404C22×C4⋊C4C2×D1113yes—
405C22×C42—113no—
406C22×C42—113no—
407C22×C42C2×D1113yes—
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—28no—
411C22×C11C22×#4112yes—
412C22×C11C22×#4114yes—
413C22×C11C22×#4112yes—
414C22×C11C2×2−1+412yes—
415C22×C11C2611yescharacteristic
416C2×D11—22no—
417C2×D11—22no—
418C2×D11—28no—
419C2×D11—26no—
420C2×D11—26no—
421C2×D11—26no—
422C2×D11—412no—
423C2×D11C22×#4114yes—
424C4×C11—26no—
425C4×C11—26no—
426C4×C11—26no—
427C4×C11—22no—
428C4×C11C22×#41112yes—
429C4×C11C2×2−1+414yes—
430Dic11—26no—
431Dic11—26no—
432Dic11—22no—
433Dic11—22no—
434Dic11—26no—
435Dic11C22×#4114yes—
436C2×#41—118no—
437C2×#41—1124no—
438C2×#41—2224no—
439C2×#41—228no—
440C22×Q8—28no—
441C22×Q8—118no—
442C22×Q8—113no—
443C22×Q8—113no—
444C22×Q8—228no—
445C22×Q8C22×D1113yes—
446C22×Q8C22×D1118yes—
447C22×Q8C22×D1111yescharacteristic
448C22×D4—111no—
449C22×D4—113no—
450C22×D4—113no—
451C22×D4—113no—
452C23×C4—113no—
453C23×C4—113no—
454C23×C4—113no—
455C23×C4—113no—
456C23×C4—113no—
457C23×C4—111no—
458C23×C4C22×D1113yes—
459C23×C4C22×D1113yes—
460C23×C4C22×D1111yescharacteristic
461C4⋊Q8—1124no—
462C4⋊Q8—1124no—
463#126—1148no—
464#126—1148no—
465#125—1124no—
466#125—1148no—
467#125—1124no—
468#124—1124no—
469#124—1124no—
470#123—1148no—
471#123—1148no—
472C22⋊Q8—1124no—
473C22⋊Q8—1124no—
474C22⋊Q8—1124no—
475C22⋊Q8—1148no—
476C22⋊Q8—1124no—
477#121—1124no—
478#121—1124no—
479C4×Q8—118no—
480C4×Q8—118no—
481C4×Q8—1124no—
482C4×Q8—1124no—
483C4×Q8—1124no—
484C4×Q8—1124no—
485C4×Q8C22×D1118yes—
486C4×Q8C22×D11124yes—
487C4×Q8C22×D1118yes—
488C4×Q8C22×D11124yes—
489C4×D4—118no—
490C4×D4—1124no—
491C4×D4—1124no—
492C4×D4—1124no—
493C4×D4—1124no—
494C4×D4—1124no—
495C4×D4—1124no—
496C4×D4—1124no—
497#117—1124no—
498#117—1124no—
499#117—1124no—
500#117—1124no—
501#117—1148no—
502C2×C4⋊C4—113no—
503C2×C4⋊C4—116no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—113no—
506C2×C4⋊C4—113no—
507C2×C4⋊C4—113no—
508C2×C4⋊C4—113no—
509C2×C4⋊C4—113no—
510C2×C4⋊C4—113no—
511C2×C4⋊C4—116no—
512C2×C4⋊C4—116no—
513C2×C4⋊C4—1124no—
514C2×C4⋊C4C22×D1113yes—
515C2×C4⋊C4C22×D1113yes—
516C2×C4⋊C4C22×D1116yes—
517C2×C4⋊C4C22×D11124yes—
518C2×C22⋊C4—111no—
519C2×C22⋊C4—113no—
520C2×C22⋊C4—111no—
521C2×C22⋊C4—113no—
522C2×C22⋊C4—116no—
523C2×C22⋊C4—113no—
524C2×C22⋊C4—113no—
525C2×C22⋊C4—116no—
526C2×C22⋊C4—116no—
527C2×C42—113no—
528C2×C42—113no—
529C2×C42—113no—
530C2×C42—113no—
531C2×C42—113no—
532C2×C42—111no—
533C2×C42—1124no—
534C2×C42—1124no—
535C2×C42C22×D1113yes—
536C2×C42C22×D1113yes—
537C2×C42C22×D11124yes—
538C2×C42C22×D1113yes—
539C2×C42C22×D1113yes—
540C2×C11—24no—
541C2×C11#348214yescomplemented
542C2×C11C23×#4111yescharacteristic
543C2×C11C23×#4111yescharacteristic
544C2×C11C22×2−1+411yescharacteristic
545D11—24no—
546D11—46no—
547C24—111no—
548C24—113no—
549C24C23×D1111yescharacteristic
550#41—2296no—
551#41—2232no—
552C2×Q8—232no—
553C2×Q8—212no—
554C2×Q8—1112no—
555C2×Q8—1112no—
556C2×Q8—2212no—
557C2×Q8—2232no—
558C2×Q8—2212no—
559C2×Q8#433918yescomplemented
560C2×Q8C23×D11112yes—
561C2×Q8C23×D1114yes—
562C2×D4—118no—
563C2×D4—114no—
564C2×D4—1112no—
565C2×D4—1112no—
566C2×D4—1112no—
567C2×D4—2212no—
568C2×D4—2212no—
569C2×D4—2212no—
570C22×C4—212no—
571C22×C4—212no—
572C22×C4—24no—
573C22×C4—111no—
574C22×C4—111no—
575C22×C4—111no—
576C22×C4—113no—
577C22×C4—113no—
578C22×C4—113no—
579C22×C4—114no—
580C22×C4—1112no—
581C22×C4—1112no—
582C22×C4—1112no—
583C22×C4—1112no—
584C22×C4—1112no—
585C22×C4—2212no—
586C22×C4—2212no—
587C22×C4—2212no—
588C22×C4—2212no—
589C22×C4—224no—
590C22×C4—2212no—
591C22×C4C23×D1113yes—
592C22×C4C23×D1111yescharacteristic
593C22×C4C23×D1114yes—
594C22×C4C23×D1113yes—
595C22×C4C23×D1113yes—
596C22×C4C23×D11112yes—
597C22×C4C23×D11112yes—
598C22×C4C23×D1113yes—
599C22×C4C23×D1111yescharacteristic
600C4⋊C4—1112no—
601C4⋊C4—1124no—
602C4⋊C4—114no—
603C4⋊C4—1112no—
604C4⋊C4—1112no—
605C4⋊C4—1112no—
606C4⋊C4—1112no—
607C4⋊C4—1112no—
608C4⋊C4—1112no—
609C4⋊C4—1124no—
610C4⋊C4—1124no—
611C4⋊C4C23×D11112yes—
612C4⋊C4C23×D11112yes—
613C4⋊C4C23×D11124yes—
614C22⋊C4—114no—
615C22⋊C4—1112no—
616C22⋊C4—114no—
617C22⋊C4—1112no—
618C22⋊C4—1124no—
619C22⋊C4—1112no—
620C22⋊C4—1112no—
621C22⋊C4—1124no—
622C22⋊C4—1124no—
623C42—114no—
624C42—1112no—
625C42—1112no—
626C42—1112no—
627C42—1112no—
628C42—1112no—
629C42C23×D11112yes—
630C42C23×D11112yes—
631C42C23×D11112yes—
632C42C23×D11112yes—
633C11C2×#348211yescharacteristic, complemented, Sylow
634C23—22no—
635C23—22no—
636C23—114no—
637C23—112no—
638C23—116no—
639C23—222no—
640C23—222no—
641C23—226no—
642C23—226no—
643C23—226no—
644C23#41×D1114yes—
645C23C24×D1112yes—
646C23C24×D1111yescharacteristic
647Q8—224no—
648Q8—2224no—
649Q8—2224no—
650Q8C2×#4339116yescomplemented
651D4—1116no—
652D4—2224no—
653D4—2224no—
654D4—2224no—
655C2×C4—26no—
656C2×C4—22no—
657C2×C4—26no—
658C2×C4—26no—
659C2×C4—224no—
660C2×C4—224no—
661C2×C4—28no—
662C2×C4—114no—
663C2×C4—112no—
664C2×C4—112no—
665C2×C4—112no—
666C2×C4—116no—
667C2×C4—116no—
668C2×C4—116no—
669C2×C4—2224no—
670C2×C4—2224no—
671C2×C4—222no—
672C2×C4—226no—
673C2×C4—222no—
674C2×C4—226no—
675C2×C4—226no—
676C2×C4—2224no—
677C2×C4—2224no—
678C2×C4—228no—
679C2×C4—2224no—
680C2×C4C2×#4339112yes—
681C2×C4#6704014yes—
682C2×C4C24×D1116yes—
683C2×C4C24×D1112yes—
684C2×C4C24×D1116yes—
685C2×C4C24×D1116yes—
686C2×C4C24×D1116yes—
687C2×C4C24×D1112yes—
688C22—22no—
689C22—22no—
690C22—28no—
691C22—114no—
692C22—222no—
693C22—222no—
694C22—228no—
695C22—226no—
696C22—226no—
697C22—226no—
698C22—4412no—
699C22C22×#433912yes—
700C22C2×#6704012yes—
701C22C2×#41×D1114yes—
702C22C2×#41×D1112yes—
703C22C25×D1111yescharacteristic
704C4—26no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—114no—
709C4—226no—
710C4—222no—
711C4—226no—
712C4—222no—
713C4—226no—
714C4C22×#4339112yes—
715C4C2×#6704014yes—
716C2—24no—
717C2—224no—
718C2—446no—
719C2#1308223314yesdirect product factor
720C2C22×#41×D1111yescharacteristic
721C2C23×#433911yescharacteristic
722C2C22×#6704011yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C4×Q8×C11C2
socleC23×C11C25
hypercenterC22×C4×Q8D11
hypocenterC11C2×#3482
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #13082233C2direct (N × H)
2. C2×#10623100C2semidirect
3. C2×#10623099C2semidirect
4. C2×#10623112C2semidirect
5. C2×#10623044C2semidirect
6. C2×Q8×C22⋊D11C2semidirect
7. C2×#10623107C2semidirect
8. C2×#10623348C2semidirect
9. C2×#10623038C2semidirect
10. C2×#10623109C2semidirect
11. C2×#10623111C2semidirect
12. C2×#10623010C2semidirect
13. C2×C4×#4343C2semidirect
14. C2×C4×#4339C2semidirect
15. C2×C4×Q8×D11C2semidirect
16. C22×C4×Q8×C11C2semidirect
25. C2×C4×Q8×C11C22semidirect
28. #10623348C22semidirect
29. Q8×C22⋊D11C22semidirect
44. #10623112C22semidirect
45. #10623111C22semidirect
46. #10623109C22semidirect
47. #10623107C22semidirect
48. C4×#4343C22semidirect
49. C4×Q8×D11C22semidirect
50. #10623100C22semidirect
51. #10623099C22semidirect
52. #10623044C22semidirect
56. #10623038C22semidirect
66. #10623010C22semidirect
69. C4×#4339C22semidirect
192. C2×Q8×C11#41semidirect
208. C2×C22⋊D11#41semidirect
288. C22×C4×Q8D11semidirect
303. Q8×C11C2×#41semidirect
320. C22⋊D11C2×#41semidirect
389. C2×C4×Q8C2×D11semidirect
541. C2×C11#3482semidirect
559. C2×Q8#4339semidirect
633. C11C2×#3482semidirect
650. Q8C2×#4339semidirect
719. C2#13082233direct (N × H)

Maximal subgroups

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

subgroupindex
#130822332
C2×#106231002
C2×#106230992
C2×#106231122
C2×#106230442
C2×Q8×C22⋊D112
C2×#106231072
C2×#106233482
C2×#106230382
C2×#106231092
C2×#106231112
C2×#106230102
C2×C4×#43432
C2×C4×#43392
C2×C4×Q8×D112
C22×C4×Q8×C112
C2×#348211