Finite Group Databasebeta

← C2×#13082206 #15660827

Subgroups — C2×#13082206 #15660827

Order 2816.

7802 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082206C2132yesmaximal, direct product factor
2C2×#10623212C213yesmaximal, complemented
3C2×#10623100C211yesmaximal, characteristic, complemented
4C2×#10623172C213yesmaximal, complemented
5C2×#10623149C213yesmaximal, complemented
6C2×#10623096C213yesmaximal, complemented
7C2×#10623365C211yesmaximal, characteristic, complemented
8C2×#10623348C211yesmaximal, characteristic, complemented
9C2×#10623127C213yesmaximal, complemented
10C2×#10623155C213yesmaximal, complemented
11C2×#10623211C213yesmaximal, complemented
12C2×#41×Dic11C211yesmaximal, characteristic, complemented
13C2×C4×#4343C211yesmaximal, characteristic, complemented
14C2×C4×#4341C213yesmaximal, complemented
15C22×Q8×Dic11C211yesmaximal, characteristic, complemented
16C2×C11×#548C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×Q8×C11C2211yescharacteristic
19C22×#4343C2211yescharacteristic
20C22×#4341C2213yes—
21C11×#548C22116yescomplemented
22C2×C11×#124C2213yes—
23C2×C11×C22⋊Q8C2213yes—
24C2×C11×#121C2213yes—
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×D4×C11C2213yes—
27#10623365C22116yescomplemented
28#41×Dic11C22116yescomplemented
29#10623348C22116yescomplemented
30C2×#67000C2213yes—
31C2×#66999C2213yes—
32C2×Q8×Dic11C2213yes—
33C2×Q8×Dic11C2213yes—
34C2×Q8×Dic11C2211yescharacteristic
35C2×Q8×Dic11C2211yescharacteristic
36C2×Q8×Dic11C2211yescharacteristic
37C2×Q8×Dic11C22116yescomplemented
38C2×#66993C2213yes—
39C2×#66992C2216yes—
40C2×#66991C2213yes—
41C2×D4×Dic11C2213yes—
42C2×D4×Dic11C2213yes—
43C2×D4×Dic11C2213yes—
44C2×#66983C2213yes—
45C2×#66983C2213yes—
46C2×C4×C22⋊D11C2213yes—
47C2×C4×C22⋊D11C2213yes—
48C2×#66979C2213yes—
49C22×C4⋊Dic11C2213yes—
50C22×C4×Dic11C2213yes—
51C22×C4×Dic11C2213yes—
52#10623212C22148yescomplemented
53#10623211C22148yescomplemented
54#10623172C22148yescomplemented
55#10623155C22148yescomplemented
56#10623149C22148yescomplemented
57#10623127C22148yescomplemented
58C4×#4343C22116yescomplemented
59#10623100C22116yescomplemented
60#10623096C22148yescomplemented
61C4×#4341C22148yescomplemented
62C2×#66951C2216yes—
63C2×#66946C2213yes—
64C2×#66945C2213yes—
65C2×#66945C2213yes—
66C2×#66943C2213yes—
67C2×#66941C2213yes—
68C2×#66940C2213yes—
69C2×#66939C2216yes—
70C2×#66938C2216yes—
71C2×#66936C2216yes—
72C2×(C22⋊D11)⋊C4C2216yes—
73C2×(C22⋊D11)⋊C4C2213yes—
74C2×(C22⋊D11)⋊C4C2213yes—
75C2×#66932C2216yes—
76C2×#66930C2213yes—
77C2×#66930C2211yescharacteristic
78C2×C4×D44C2213yes—
79C2×C42×D11C2213yes—
80C2×#66923C2213yes—
81C2×C4×Dic22C2213yes—
82C2×C11×#41—28no—
83C2×C11×#41C2318yes—
84C22×Q8×C11—28no—
85C22×Q8×C11C2313yes—
86C22×Q8×C11C2318yes—
87C22×Q8×C11C2311yescharacteristic
88C22×D4×C11C2313yes—
89C22×D4×C11C2313yes—
90C23×C4×C11C2313yes—
91C23×C4×C11C2313yes—
92C22×C22⋊D11C2313yes—
93C22×C22⋊D11C2313yes—
94C22×C22⋊D11C2316yes—
95C23×Dic11C2313yes—
96C23×Dic11C2313yes—
97C23×Dic11C2313yes—
98C23×Dic11C2311yescharacteristic
99C2×#4343—28no—
100C2×#4343C2318yes—
101C2×#4341—224no—
102C2×#4341C23124yes—
103C22×D44C2313yes—
104C22×C4×D11C2313yes—
105C22×C4×D11C2313yes—
106C22×C4×D11C2313yes—
107C22×Dic22C2313yes—
108C11×#124C23124yes—
109C11×C22⋊Q8C23124yes—
110C11×#121C23124yes—
111C4×Q8×C11C2318yes—
112C4×D4×C11C23124yes—
113C2×C11×C4⋊C4C2313yes—
114C2×C11×C4⋊C4C2313yes—
115C2×C11×C22⋊C4C2311yescharacteristic
116C2×C11×C22⋊C4C2313yes—
117C2×C11×C22⋊C4C2316yes—
118C2×C42×C11C2313yes—
119C2×C22⋊Dic11C2313yes—
120C2×C22⋊Dic11C2311yescharacteristic
121C2×C22⋊Dic11C2316yes—
122#67000C23124yes—
123#66999C23124yes—
124Q8×Dic11C2318yes—
125Q8×Dic11C2318yes—
126Q8×Dic11C23124yes—
127Q8×Dic11C23124yes—
128Q8×Dic11C2318yes—
129#66993C23124yes—
130#66992C23148yes—
131#66991C23124yes—
132D4×Dic11C23124yes—
133D4×Dic11C23124yes—
134D4×Dic11C23124yes—
135#66983C23124yes—
136#66983C23124yes—
137C4×C22⋊D11C23124yes—
138C4×C22⋊D11C23124yes—
139C2×(C2×D11)⋊C4C2316yes—
140C2×(C2×D11)⋊C4C2316yes—
141C2×(C2×D11)⋊C4C2313yes—
142C2×(C2×D11)⋊C4C2313yes—
143#66979C23124yes—
144C2×C4⋊Dic11C2313yes—
145C2×C4⋊Dic11C2313yes—
146C2×C4⋊Dic11C2313yes—
147C2×C4⋊Dic11C2313yes—
148C2×C4⋊Dic11C2316yes—
149C2×C4⋊Dic11C23124yes—
150C2×Dic11⋊C4C2311yescharacteristic
151C2×Dic11⋊C4C2313yes—
152C2×Dic11⋊C4C2316yes—
153C2×Dic11⋊C4C2313yes—
154C2×Dic11⋊C4C2311yescharacteristic
155C2×C4×Dic11C2313yes—
156C2×C4×Dic11C2313yes—
157C2×C4×Dic11C2311yescharacteristic
158C2×C4×Dic11C2313yes—
159C2×C4×Dic11C2313yes—
160C2×C4×Dic11C2313yes—
161C2×C4×Dic11C2311yescharacteristic
162C2×C4×Dic11C2313yes—
163C2×C4×Dic11C2313yes—
164C2×C4×Dic11C23124yes—
165C2×C4×Dic11C23124yes—
166#66951C23148yes—
167#66946C23124yes—
168#66945C23124yes—
169#66945C23124yes—
170#66943C23124yes—
171#66941C23124yes—
172#66940C23124yes—
173#66939C23148yes—
174#66938C23148yes—
175#66936C23148yes—
176(C22⋊D11)⋊C4C23124yes—
177(C22⋊D11)⋊C4C23124yes—
178(C22⋊D11)⋊C4C23148yes—
179#66932C23148yes—
180#66930C2318yes—
181#66930C23124yes—
182C4×D44C23124yes—
183C42×D11C23124yes—
184#66923C23124yes—
185C4×Dic22C23124yes—
186C2×#3480—111nomaximal, Sylow
187C24×C11C2413yes—
188C24×C11C2411yescharacteristic
189C23×D11C2413yes—
190C11×#41—232no—
191C2×Q8×C11—232no—
192C2×Q8×C11—212no—
193C2×Q8×C11#4118yescomplemented
194C2×Q8×C11C24112yes—
195C2×Q8×C11C2414yes—
196C2×D4×C11—212no—
197C2×D4×C11—212no—
198C2×D4×C11C24112yes—
199C2×D4×C11C24112yes—
200C22×C4×C11—212no—
201C22×C4×C11—212no—
202C22×C4×C11C2411yescharacteristic
203C22×C4×C11C2413yes—
204C22×C4×C11C24112yes—
205C22×C4×C11C24112yes—
206C22×C4×C11C2411yescharacteristic
207C22×C4×C11C2413yes—
208C22×C4×C11C2413yes—
209C2×C22⋊D11—212no—
210C2×C22⋊D11—212no—
211C2×C22⋊D11—412no—
212C2×C22⋊D11C24112yes—
213C2×C22⋊D11C24112yes—
214C2×C22⋊D11C24124yes—
215C22×Dic11—212no—
216C22×Dic11—46no—
217C22×Dic11—46no—
218C22×Dic11#4118yescomplemented
219C22×Dic11C24112yes—
220C22×Dic11C2411yescharacteristic
221C22×Dic11C2411yescharacteristic
222C22×Dic11C2413yes—
223C22×Dic11C2413yes—
224C22×Dic11C2413yes—
225C22×Dic11C24112yes—
226C22×Dic11C24112yes—
227C22×Dic11C2411yescharacteristic
228C22×Dic11C2411yescharacteristic
229C22×Dic11C2414yes—
230#4343—232no—
231#4341—296no—
232C2×D44—212no—
233C2×D44C24112yes—
234C2×C4×D11—212no—
235C2×C4×D11—212no—
236C2×C4×D11—46no—
237C2×C4×D11C24112yes—
238C2×C4×D11C24112yes—
239C2×C4×D11C24112yes—
240C2×Dic22—212no—
241C2×Dic22C24112yes—
242C11×C4⋊C4C24112yes—
243C11×C4⋊C4C24112yes—
244C11×C22⋊C4C2414yes—
245C11×C22⋊C4C24112yes—
246C11×C22⋊C4C24124yes—
247C42×C11C24112yes—
248C22⋊Dic11C24112yes—
249C22⋊Dic11C2414yes—
250C22⋊Dic11C24124yes—
251(C2×D11)⋊C4C24124yes—
252(C2×D11)⋊C4C24124yes—
253(C2×D11)⋊C4C24112yes—
254(C2×D11)⋊C4C24112yes—
255C4⋊Dic11C24112yes—
256C4⋊Dic11C24112yes—
257C4⋊Dic11C24112yes—
258C4⋊Dic11C24112yes—
259C4⋊Dic11C24124yes—
260Dic11⋊C4C2414yes—
261Dic11⋊C4C24112yes—
262Dic11⋊C4C24124yes—
263Dic11⋊C4C24112yes—
264Dic11⋊C4C2414yes—
265C4×Dic11C24112yes—
266C4×Dic11C24112yes—
267C4×Dic11C2414yes—
268C4×Dic11C24112yes—
269C4×Dic11C24112yes—
270C4×Dic11C24112yes—
271C4×Dic11C2414yes—
272C4×Dic11C24112yes—
273C4×Dic11C24112yes—
274#3480—1132no—
275C2×#559—113no—
276C2×#557—111no—
277C2×#556—113no—
278C2×#553—113no—
279C2×#553—113no—
280C2×#550—111no—
281C2×#548—111no—
282C2×#548D1111yescharacteristic, complemented
283C2×#532—113no—
284C2×#529—113no—
285C2×#529—113no—
286C2×C4×#41—111no—
287C2×C4×#41—111no—
288C2×C4×#41—113no—
289C22×C4×Q8—111no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—26no—
293C23×C11—26no—
294C23×C11—26no—
295C23×C11C2×#4114yes—
296C23×C11C2516yes—
297C23×C11C2512yes—
298C23×C11C2511yescharacteristic
299C22×D11—26no—
300C22×D11—26no—
301C22×D11—26no—
302C22×D11C2516yes—
303Q8×C11—224no—
304Q8×C11C2×#41116yescomplemented
305D4×C11—224no—
306D4×C11—224no—
307C2×C4×C11—26no—
308C2×C4×C11—22no—
309C2×C4×C11—26no—
310C2×C4×C11—22no—
311C2×C4×C11—224no—
312C2×C4×C11—224no—
313C2×C4×C11C2×#41112yes—
314C2×C4×C11C2512yes—
315C2×C4×C11C2516yes—
316C2×C4×C11C2512yes—
317C2×C4×C11C2516yes—
318C2×C4×C11C2516yes—
319C22⋊D11—224no—
320C22⋊D11—224no—
321C22⋊D11—424no—
322C2×Dic11—26no—
323C2×Dic11—22no—
324C2×Dic11—26no—
325C2×Dic11—22no—
326C2×Dic11—26no—
327C2×Dic11—224no—
328C2×Dic11—412no—
329C2×Dic11—412no—
330C2×Dic11C2×#4114yes—
331C2×Dic11C2×#4114yes—
332C2×Dic11C2×#41116yescomplemented
333C2×Dic11C2512yes—
334C2×Dic11C2512yes—
335C2×Dic11C2516yes—
336C2×Dic11C2516yes—
337C2×Dic11C2516yes—
338C2×Dic11C2512yes—
339C2×Dic11C2512yes—
340D44—224no—
341C4×D11—224no—
342C4×D11—224no—
343C4×D11—412no—
344Dic22—224no—
345C22×#41—111no—
346C22×#41—113no—
347C22×#41C2×D1111yescharacteristic
348C23×Q8C2×D1111yescharacteristic
349#559—1148no—
350#557—1116no—
351#556—1148no—
352#553—1148no—
353#553—1148no—
354#550—1116no—
355#548—1116no—
356#548C2×D11116yescomplemented
357#532—1148no—
358C2×C4⋊Q8—113no—
359C2×#127—113no—
360#529—1148no—
361#529—1148no—
362C2×#126—116no—
363C2×#126—116no—
364C2×#125—113no—
365C2×#125—113no—
366C2×#124—113no—
367C2×#124—116no—
368C2×#124C2×D1113yes—
369C2×#123—116no—
370C2×#123—116no—
371C2×C22⋊Q8—113no—
372C2×C22⋊Q8C2×D1113yes—
373C2×#121—113no—
374C2×#121—116no—
375C2×#121—113no—
376C2×#121—113no—
377C2×#121C2×D1113yes—
378C4×#41—1116no—
379C4×#41—1116no—
380C4×#41—1148no—
381C2×C4×Q8—111no—
382C2×C4×Q8—113no—
383C2×C4×Q8—111no—
384C2×C4×Q8—113no—
385C2×C4×Q8—1116no—
386C2×C4×Q8—111no—
387C2×C4×Q8—113no—
388C2×C4×Q8—113no—
389C2×C4×Q8C2×D1111yescharacteristic
390C2×C4×D4—113no—
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×C4×D4—116no—
399C2×C4×D4—113no—
400C2×C4×D4C2×D1113yes—
401C2×#117—113no—
402C2×#117—113no—
403C2×#117—113no—
404C2×#117—111no—
405C2×#117—113no—
406C22×C4⋊C4—113no—
407C22×C42—113no—
408C22×C42—113no—
409C22×C42—113no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—28no—
413C22×C11—26no—
414C22×C11—26no—
415C22×C11—26no—
416C22×C11—412no—
417C22×C11C22×#4112yes—
418C22×C11C22×#4114yes—
419C22×C11C22×#4112yes—
420C22×C11#58512yes—
421C22×C11C2611yescharacteristic
422C2×D11—26no—
423C2×D11—26no—
424C2×D11—26no—
425C2×D11—412no—
426C4×C11—22no—
427C4×C11—26no—
428C4×C11—26no—
429C4×C11—22no—
430C4×C11C22×#41112yes—
431Dic11—26no—
432Dic11—22no—
433Dic11—26no—
434Dic11—22no—
435Dic11—26no—
436Dic11C22×#4114yes—
437Dic11C22×#4114yes—
438C2×#41—28no—
439C2×#41—118no—
440C2×#41—1124no—
441C2×#41—2224no—
442C2×#41—228no—
443C2×#41C22×D1118yes—
444C22×Q8—28no—
445C22×Q8—113no—
446C22×Q8C22×D1113yes—
447C22×Q8C22×D1118yes—
448C22×Q8C22×D1111yescharacteristic
449C22×D4—113no—
450C22×D4—113no—
451C22×D4—116no—
452C22×D4—113no—
453C22×D4C22×D1113yes—
454C22×D4C22×D1113yes—
455C23×C4—111no—
456C23×C4—113no—
457C23×C4—113no—
458C23×C4—113no—
459C23×C4—113no—
460C23×C4—113no—
461C23×C4—113no—
462C23×C4C22×D1113yes—
463C23×C4C22×D1113yes—
464C4⋊Q8—1124no—
465#127—1124no—
466#126—1148no—
467#126—1148no—
468#125—1124no—
469#125—1124no—
470#124—1124no—
471#124—1148no—
472#124C22×D11124yes—
473#123—1148no—
474#123—1148no—
475C22⋊Q8—1124no—
476C22⋊Q8C22×D11124yes—
477#121—1124no—
478#121—1148no—
479#121—1124no—
480#121—1124no—
481#121C22×D11124yes—
482C4×Q8—118no—
483C4×Q8—1124no—
484C4×Q8—118no—
485C4×Q8—1124no—
486C4×Q8—118no—
487C4×Q8—1124no—
488C4×Q8—1124no—
489C4×Q8C22×D1118yes—
490C4×D4—1124no—
491C4×D4—1124no—
492C4×D4—1124no—
493C4×D4—1124no—
494C4×D4—1124no—
495C4×D4—1124no—
496C4×D4—1124no—
497C4×D4—1124no—
498C4×D4—1148no—
499C4×D4—1124no—
500C4×D4C22×D11124yes—
501#117—1124no—
502#117—1124no—
503#117—1124no—
504#117—118no—
505#117—1124no—
506C2×C4⋊C4—113no—
507C2×C4⋊C4—113no—
508C2×C4⋊C4—116no—
509C2×C4⋊C4—1124no—
510C2×C4⋊C4—111no—
511C2×C4⋊C4—111no—
512C2×C4⋊C4—113no—
513C2×C4⋊C4—113no—
514C2×C4⋊C4—113no—
515C2×C4⋊C4—113no—
516C2×C4⋊C4—116no—
517C2×C4⋊C4C22×D1113yes—
518C2×C4⋊C4C22×D1113yes—
519C2×C22⋊C4—111no—
520C2×C22⋊C4—113no—
521C2×C22⋊C4—116no—
522C2×C22⋊C4—113no—
523C2×C22⋊C4—116no—
524C2×C22⋊C4—113no—
525C2×C22⋊C4—116no—
526C2×C22⋊C4C22×D1111yescharacteristic
527C2×C22⋊C4C22×D1113yes—
528C2×C22⋊C4C22×D1116yes—
529C2×C42—111no—
530C2×C42—111no—
531C2×C42—113no—
532C2×C42—113no—
533C2×C42—113no—
534C2×C42—113no—
535C2×C42—113no—
536C2×C42—113no—
537C2×C42—113no—
538C2×C42—1124no—
539C2×C42—1124no—
540C2×C42—1124no—
541C2×C42C22×D1113yes—
542C2×C11—24no—
543C2×C11—46no—
544C2×C11#348014yescomplemented
545C2×C11C23×#4111yescharacteristic
546C2×C11C23×#4111yescharacteristic
547C2×C11C2×#58511yescharacteristic
548D11—46no—
549C24—113no—
550C24C23×D1113yes—
551C24C23×D1111yescharacteristic
552#41—232no—
553#41—2296no—
554#41—2232no—
555C2×Q8—232no—
556C2×Q8—212no—
557C2×Q8—1112no—
558C2×Q8—2212no—
559C2×Q8#434118yescomplemented
560C2×Q8C23×D11112yes—
561C2×Q8C23×D1114yes—
562C2×D4—212no—
563C2×D4—212no—
564C2×D4—1112no—
565C2×D4—1112no—
566C2×D4—1124no—
567C2×D4—1112no—
568C2×D4—2212no—
569C2×D4—2212no—
570C2×D4—2212no—
571C2×D4—4412no—
572C2×D4C23×D11112yes—
573C2×D4C23×D11112yes—
574C22×C4—212no—
575C22×C4—212no—
576C22×C4—118no—
577C22×C4—114no—
578C22×C4—111no—
579C22×C4—111no—
580C22×C4—1112no—
581C22×C4—111no—
582C22×C4—111no—
583C22×C4—113no—
584C22×C4—113no—
585C22×C4—113no—
586C22×C4—1112no—
587C22×C4—1112no—
588C22×C4—1112no—
589C22×C4—1112no—
590C22×C4—1112no—
591C22×C4—2212no—
592C22×C4—2212no—
593C22×C4—2212no—
594C22×C4—446no—
595C22×C4—446no—
596C22×C4—446no—
597C22×C4C23×D11112yes—
598C22×C4C23×D11112yes—
599C22×C4C23×D1111yescharacteristic
600C22×C4C23×D1113yes—
601C22×C4C23×D1111yescharacteristic
602C22×C4C23×D1113yes—
603C22×C4C23×D1113yes—
604C4⋊C4—1112no—
605C4⋊C4—1112no—
606C4⋊C4—1124no—
607C4⋊C4—114no—
608C4⋊C4—114no—
609C4⋊C4—1112no—
610C4⋊C4—1112no—
611C4⋊C4—1112no—
612C4⋊C4—1112no—
613C4⋊C4—1124no—
614C4⋊C4C23×D11112yes—
615C4⋊C4C23×D11112yes—
616C22⋊C4—114no—
617C22⋊C4—1112no—
618C22⋊C4—1124no—
619C22⋊C4—1112no—
620C22⋊C4—1124no—
621C22⋊C4—1112no—
622C22⋊C4—1124no—
623C22⋊C4C23×D1114yes—
624C22⋊C4C23×D11112yes—
625C22⋊C4C23×D11124yes—
626C42—114no—
627C42—114no—
628C42—1112no—
629C42—1112no—
630C42—1112no—
631C42—1112no—
632C42—1112no—
633C42—1112no—
634C42—1112no—
635C42C23×D11112yes—
636C11C2×#348011yescharacteristic, complemented, Sylow
637C23—22no—
638C23—22no—
639C23—26no—
640C23—26no—
641C23—26no—
642C23—116no—
643C23—226no—
644C23—226no—
645C23—226no—
646C23#41×D1114yes—
647C23C24×D1116yes—
648C23C24×D1112yes—
649C23C24×D1111yescharacteristic
650Q8—224no—
651Q8—2224no—
652Q8C2×#4341116yescomplemented
653D4—224no—
654D4—224no—
655D4—2224no—
656D4—2224no—
657D4—2224no—
658D4—4424no—
659C2×C4—22no—
660C2×C4—26no—
661C2×C4—26no—
662C2×C4—22no—
663C2×C4—224no—
664C2×C4—224no—
665C2×C4—114no—
666C2×C4—114no—
667C2×C4—1116no—
668C2×C4—112no—
669C2×C4—112no—
670C2×C4—112no—
671C2×C4—112no—
672C2×C4—116no—
673C2×C4—116no—
674C2×C4—116no—
675C2×C4—2224no—
676C2×C4—2224no—
677C2×C4—222no—
678C2×C4—226no—
679C2×C4—226no—
680C2×C4—222no—
681C2×C4—226no—
682C2×C4—2224no—
683C2×C4—4412no—
684C2×C4—4412no—
685C2×C4—4412no—
686C2×C4C2×#4341112yes—
687C2×C4C24×D1112yes—
688C2×C4C24×D1116yes—
689C2×C4C24×D1112yes—
690C2×C4C24×D1116yes—
691C2×C4C24×D1116yes—
692C22—22no—
693C22—22no—
694C22—28no—
695C22—26no—
696C22—26no—
697C22—26no—
698C22—412no—
699C22—226no—
700C22—226no—
701C22—226no—
702C22—4412no—
703C22C22×#434112yes—
704C22C2×#41×D1114yes—
705C22C2×#41×D1112yes—
706C22#1062345712yes—
707C22C25×D1111yescharacteristic
708C4—26no—
709C4—22no—
710C4—26no—
711C4—22no—
712C4—114no—
713C4—114no—
714C4—226no—
715C4—222no—
716C4—226no—
717C4—222no—
718C4—226no—
719C4C22×#4341112yes—
720C2—24no—
721C2—46no—
722C2—446no—
723C2#1308220614yesdirect product factor
724C2C22×#41×D1111yescharacteristic
725C2C23×#434111yescharacteristic
726C2C2×#1062345711yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#548C2
socleC23×C11C25
hypercenterC2×#548D11
hypocenterC11C2×#3480
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #13082206C2direct (N × H)
2. C2×#10623212C2semidirect
3. C2×#10623100C2semidirect
4. C2×#10623172C2semidirect
5. C2×#10623149C2semidirect
6. C2×#10623096C2semidirect
7. C2×#10623365C2semidirect
8. C2×#10623348C2semidirect
9. C2×#10623127C2semidirect
10. C2×#10623155C2semidirect
11. C2×#10623211C2semidirect
12. C2×#41×Dic11C2semidirect
13. C2×C4×#4343C2semidirect
14. C2×C4×#4341C2semidirect
15. C22×Q8×Dic11C2semidirect
16. C2×C11×#548C2semidirect
21. C11×#548C22semidirect
27. #10623365C22semidirect
28. #41×Dic11C22semidirect
29. #10623348C22semidirect
37. C2×Q8×Dic11C22semidirect
52. #10623212C22semidirect
53. #10623211C22semidirect
54. #10623172C22semidirect
55. #10623155C22semidirect
56. #10623149C22semidirect
57. #10623127C22semidirect
58. C4×#4343C22semidirect
59. #10623100C22semidirect
60. #10623096C22semidirect
61. C4×#4341C22semidirect
193. C2×Q8×C11#41semidirect
218. C22×Dic11#41semidirect
282. C2×#548D11semidirect
304. Q8×C11C2×#41semidirect
332. C2×Dic11C2×#41semidirect
356. #548C2×D11semidirect
544. C2×C11#3480semidirect
559. C2×Q8#4341semidirect
636. C11C2×#3480semidirect
652. Q8C2×#4341semidirect
723. C2#13082206direct (N × H)

Maximal subgroups

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

subgroupindex
#130822062
C2×#106232122
C2×#106231002
C2×#106231722
C2×#106231492
C2×#106230962
C2×#106233652
C2×#106233482
C2×#106231272
C2×#106231552
C2×#106232112
C2×#41×Dic112
C2×C4×#43432
C2×C4×#43412
C22×Q8×Dic112
C2×C11×#5482
C2×#348011