Finite Group Databasebeta

← C2×#13082265 #15661939

Subgroups — C2×#13082265 #15661939

Order 2816.

11254 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67043C211yesmaximal, characteristic, complemented
2C23×Q8×D11C211yesmaximal, characteristic, complemented
3#13082265C2132yesmaximal, direct product factor
4C2×#10623258C214yesmaximal, complemented
5C2×#10623163C214yesmaximal, complemented
6C2×#10623164C214yesmaximal, complemented
7C2×#10623208C214yesmaximal, complemented
8C2×#10623347C211yesmaximal, characteristic, complemented
9C2×#10623179C214yesmaximal, complemented
10C2×#10623055C211yesmaximal, characteristic, complemented
11C2×#10623187C214yesmaximal, complemented
12C2×#10623359C211yesmaximal, characteristic, complemented
13C2×#10623047C211yesmaximal, characteristic, complemented
14C2×C11×#536C211yesmaximal, characteristic, complemented
15C22×C11×#41C2211yescharacteristic
16C23×Q8×C11C2211yescharacteristic
17C2×#67043—216no—
18C2×#67043C22116yescomplemented
19C22×Q8×D11—216no—
20C22×Q8×D11C2214yes—
21C22×Q8×D11C2214yes—
22C22×Q8×D11C22116yescomplemented
23C22×Q8×D11C2212yescomplemented
24C22×#4341C2214yes—
25C22×#4341C2212yescomplemented
26C22×#4339C2211yescharacteristic
27C22×#4339C2212yescomplemented
28C23×C4×D11C2211yescharacteristic
29C23×C4×D11C2212yes—
30C23×Dic22C2212yes—
31C23×Dic22C2211yescharacteristic
32C23×Dic22C2212yescomplemented
33C11×#536C22116yescomplemented
34C2×C11×C4⋊Q8C2212yescomplemented
35C2×C11×#124C2212yescomplemented
36C2×C11×#123C2214yes—
37C2×C11×C22⋊Q8C2214yescomplemented
38C2×C11×#117C2211yescharacteristic
39#10623359C22116yescomplemented
40#10623347C22116yescomplemented
41C2×#67000C2212yescomplemented
42C2×#66999C2212yes—
43C2×#66999C2214yescomplemented
44C2×#66997C2212yescomplemented
45C2×#66991C2212yes—
46C2×#66990C2212yes—
47C2×#66988C2212yes—
48C2×#66982C2214yes—
49C2×C4×C22⋊D11C2214yes—
50C2×#66979C2211yescharacteristic
51#10623258C22164yescomplemented
52#10623208C22164yescomplemented
53#10623187C22164yescomplemented
54#10623179C22164yescomplemented
55#10623164C22164yescomplemented
56#10623163C22164yescomplemented
57#10623055C22116yescomplemented
58#10623047C22116yescomplemented
59C2×#66950C2212yes—
60C2×#66949C2218yes—
61C2×#66949C2218yescomplemented
62C2×#66948C2212yes—
63C2×#66946C2218yes—
64C2×#66941C2218yescomplemented
65C2×#66940C2214yescomplemented
66C2×#66939C2212yes—
67C2×#66938C2218yescomplemented
68C2×#66937C2218yes—
69C2×#66935C2212yes—
70C2×(C22⋊D11)⋊C4C2218yes—
71C2×#66931C2218yescomplemented
72C2×#66930C2214yes—
73C2×C4×D44C2214yes—
74C2×C4×Dic22C2214yescomplemented
75C24×D11C2311yescharacteristic
76C2×C11×#41—28no—
77C2×C11×#41C2318yes—
78C22×Q8×C11—28no—
79C22×Q8×C11C2312yes—
80C22×Q8×C11C2311yescharacteristic
81C22×Q8×C11C2312yes—
82C22×Q8×C11C2318yes—
83C22×D4×C11C2312yes—
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11C2312yes—
86C23×C4×C11C2312yes—
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11C2314yes—
89C22×C22⋊D11C2312yes—
90C22×C22⋊D11C2314yes—
91C23×Dic11C2314yes—
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2312yes—
94#67043—2128no—
95C2×Q8×D11—232no—
96C2×Q8×D11—232no—
97C2×Q8×D11—216no—
98C2×Q8×D11—2128no—
99C2×Q8×D11C23132yes—
100C2×Q8×D11C23132yes—
101C2×Q8×D11C23116yescomplemented
102C2×#4341—232no—
103C2×#4341—216no—
104C2×#4341C23132yes—
105C2×#4341C23116yescomplemented
106C2×#4339—28no—
107C2×#4339—216no—
108C2×#4339C2318yes—
109C2×#4339C23116yescomplemented
110C22×D44C2314yes—
111C22×D44C2311yescharacteristic
112C22×C4×D11—28no—
113C22×C4×D11—216no—
114C22×C4×D11C2312yes—
115C22×C4×D11C2312yes—
116C22×C4×D11C2318yes—
117C22×C4×D11C2314yes—
118C22×C4×D11C2312yes—
119C22×C4×D11C2318yes—
120C22×C4×D11C23116yes—
121C22×Dic22—216no—
122C22×Dic22—216no—
123C22×Dic22D4116yescomplemented
124C22×Dic22C2318yes—
125C22×Dic22C2314yes—
126C22×Dic22C2311yescharacteristic
127C22×Dic22C23116yes—
128C22×Dic22C2312yes—
129C22×Dic22C2312yes—
130C22×Dic22C2318yes—
131C22×Dic22C23116yescomplemented
132C11×C4⋊Q8C23116yescomplemented
133C11×#124C23116yescomplemented
134C11×#123C23132yes—
135C11×C22⋊Q8C23132yescomplemented
136C11×#117C2318yes—
137C2×C11×C4⋊C4C2312yes—
138C2×C11×C4⋊C4C2318yes—
139C2×C11×C22⋊C4C2312yes—
140C2×C11×C22⋊C4C2318yes—
141C2×C42×C11C2312yes—
142C2×C22⋊Dic11C2312yes—
143C2×C22⋊Dic11C2314yes—
144#67000C23116yescomplemented
145#66999C23116yes—
146#66999C23132yescomplemented
147#66997C23116yescomplemented
148#66991C23116yes—
149#66990C23116yes—
150#66988C23116yes—
151#66982C23132yes—
152C4×C22⋊D11C23132yes—
153C2×(C2×D11)⋊C4C2314yes—
154C2×(C2×D11)⋊C4C2314yes—
155C2×(C2×D11)⋊C4C2318yes—
156C2×(C2×D11)⋊C4C2314yes—
157#66979C2318yes—
158C2×C4⋊Dic11C2312yes—
159C2×C4⋊Dic11C2314yes—
160C2×Dic11⋊C4C2318yes—
161C2×Dic11⋊C4C2318yes—
162C2×Dic11⋊C4C2314yes—
163C2×C4×Dic11C2318yes—
164C2×C4×Dic11C2312yes—
165#66950C23116yes—
166#66949C23164yes—
167#66949C23164yescomplemented
168#66948C23116yes—
169#66946C23164yes—
170#66941C23164yescomplemented
171#66940C23132yescomplemented
172#66939C23116yes—
173#66938C23164yescomplemented
174#66937C23164yes—
175#66935C23116yes—
176(C22⋊D11)⋊C4C23164yes—
177#66931C23164yescomplemented
178#66930C23132yes—
179C4×D44C23132yes—
180C4×Dic22C23132yescomplemented
181C2×#3486—111nomaximal, Sylow
182C24×C11C2412yes—
183C24×C11C2411yescharacteristic
184C23×D11—24no—
185C23×D11—28no—
186C23×D11C2414yes—
187C23×D11C2412yes—
188C23×D11C2412yes—
189C11×#41—232no—
190C2×Q8×C11—28no—
191C2×Q8×C11—28no—
192C2×Q8×C11—232no—
193C2×Q8×C11—24no—
194C2×Q8×C11C2418yes—
195C2×Q8×C11C2414yes—
196C2×Q8×C11C2418yes—
197C2×D4×C11—28no—
198C2×D4×C11—24no—
199C2×D4×C11C2418yes—
200C2×D4×C11C2414yes—
201C22×C4×C11—28no—
202C22×C4×C11—28no—
203C22×C4×C11C2×D418yes—
204C22×C4×C11C2414yes—
205C22×C4×C11C2414yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2418yes—
208C22×C4×C11C2418yes—
209C22×C4×C11C2411yescharacteristic
210C22×C4×C11C2411yescharacteristic
211C22×C4×C11C2414yes—
212C2×C22⋊D11—216no—
213C2×C22⋊D11—28no—
214C2×C22⋊D11—216no—
215C2×C22⋊D11C24116yes—
216C2×C22⋊D11C2418yes—
217C2×C22⋊D11C24116yes—
218C22×Dic11—216no—
219C22×Dic11—24no—
220C22×Dic11C2×D4116yes—
221C22×Dic11C24116yes—
222C22×Dic11C2414yes—
223C22×Dic11C2414yes—
224C22×Dic11C2412yes—
225C22×Dic11C2412yes—
226C22×Dic11C2418yes—
227C22×Dic11C2414yes—
228Q8×D11—2128no—
229Q8×D11—2128no—
230Q8×D11—264no—
231#4341—2128no—
232#4341—264no—
233#4339—264no—
234#4339—232no—
235C2×D44—216no—
236C2×D44—24no—
237C2×D44C24116yes—
238C2×D44C2414yes—
239C2×C4×D11—232no—
240C2×C4×D11—264no—
241C2×C4×D11—216no—
242C2×C4×D11—28no—
243C2×C4×D11—28no—
244C2×C4×D11—232no—
245C2×C4×D11—28no—
246C2×C4×D11C2418yes—
247C2×C4×D11C2418yes—
248C2×C4×D11C24132yes—
249C2×C4×D11C24116yes—
250C2×C4×D11C2418yes—
251C2×Dic22—216no—
252C2×Dic22—232no—
253C2×Dic22—264no—
254C2×Dic22—264no—
255C2×Dic22—24no—
256C2×Dic22C2×D4116yes—
257C2×Dic22C2×D4116yes—
258C2×Dic22C2×D4164yescomplemented
259C2×Dic22C24132yes—
260C2×Dic22C24116yes—
261C2×Dic22C2414yes—
262C2×Dic22C2418yes—
263C2×Dic22C2418yes—
264C11×C4⋊C4C2418yes—
265C11×C4⋊C4C24132yes—
266C11×C22⋊C4C2418yes—
267C11×C22⋊C4C24132yes—
268C42×C11C2418yes—
269C22⋊Dic11C2418yes—
270C22⋊Dic11C24116yes—
271(C2×D11)⋊C4C24116yes—
272(C2×D11)⋊C4C24116yes—
273(C2×D11)⋊C4C24132yes—
274(C2×D11)⋊C4C24116yes—
275C4⋊Dic11C2418yes—
276C4⋊Dic11C24116yes—
277Dic11⋊C4C24132yes—
278Dic11⋊C4C24132yes—
279Dic11⋊C4C24116yes—
280C4×Dic11C24132yes—
281C4×Dic11C2418yes—
282C22×2−1+4—111no—
283C24×Q8—111no—
284#3486—1132no—
285C2×D4×Q8—114no—
286C2×D4×Q8—114no—
287C2×#548—114no—
288C2×#548—114no—
289C2×#536—111no—
290C2×#536—114no—
291C2×#536D1111yescharacteristic, complemented
292C2×#525—111no—
293C2×#525—114no—
294C2×#525—111no—
295C2×#519—111no—
296C23×C11—24no—
297C23×C11—24no—
298C23×C11—28no—
299C23×C11C22×D414yes—
300C23×C11C2514yes—
301C23×C11C2512yes—
302C23×C11C2511yescharacteristic
303C22×D11—232no—
304C22×D11—28no—
305C22×D11—24no—
306C22×D11—24no—
307C22×D11—216no—
308C22×D11—24no—
309C22×D11—28no—
310C22×D112−1+418yescomplemented
311C22×D11C2514yes—
312C22×D11C2514yes—
313Q8×C11—216no—
314Q8×C11—216no—
315Q8×C11—28no—
316D4×C11—216no—
317D4×C11—28no—
318C2×C4×C11—24no—
319C2×C4×C11—216no—
320C2×C4×C11—28no—
321C2×C4×C11—28no—
322C2×C4×C11—216no—
323C2×C4×C11C22×D414yes—
324C2×C4×C11C22×D414yes—
325C2×C4×C11C22×D4116yes—
326C2×C4×C11C2518yes—
327C2×C4×C11C2518yes—
328C2×C4×C11C2514yes—
329C2×C4×C11C2512yes—
330C2×C4×C11C2512yes—
331C22⋊D11—216no—
332C22⋊D11—232no—
333C22⋊D11—232no—
334C2×Dic11—28no—
335C2×Dic11—24no—
336C2×Dic11—24no—
337C2×Dic11—28no—
338C2×Dic11—232no—
339C2×Dic11C22×D4116yes—
340C2×Dic11C22×D4132yes—
341C2×Dic11C2518yes—
342C2×Dic11C2514yes—
343C2×Dic11C2514yes—
344C2×Dic11C2518yes—
345D44—232no—
346D44—28no—
347C4×D11—216no—
348C4×D11—216no—
349C4×D11—216no—
350C4×D11—264no—
351C4×D11—232no—
352Dic22—28no—
353Dic22—232no—
354Dic22—264no—
355Dic22C22×D4132yes—
356Dic22C22×D4132yes—
357C2×2−1+4—1116no—
358C2×2−1+4—2216no—
359C22×#41—114no—
360C22×#41—112no—
361C22×#41—111no—
362C22×#41—112no—
363C22×#41C2×D1111yescharacteristic
364C23×Q8—114no—
365C23×Q8—114no—
366C23×Q8—1116no—
367C23×Q8—112no—
368C23×Q8—111no—
369C23×Q8—112no—
370C23×Q8—112no—
371C23×Q8—2216no—
372C23×Q8C2×D1111yescharacteristic
373C24×C4—112no—
374C24×C4—111no—
375D4×Q8—1164no—
376D4×Q8—1164no—
377#548—1164no—
378#548—1164no—
379#536—1116no—
380#536—1164no—
381#536C2×D11116yescomplemented
382C2×C4⋊Q8—112no—
383C2×C4⋊Q8—118no—
384C2×C4⋊Q8C2×D1112yescomplemented
385C2×#124—112no—
386C2×#124—118no—
387C2×#124C2×D1112yescomplemented
388#525—1116no—
389#525—1164no—
390#525—1116no—
391C2×#123—112no—
392C2×#123—114no—
393C2×#123—112no—
394C2×#123C2×D1114yes—
395C2×C22⋊Q8—112no—
396C2×C22⋊Q8—114no—
397C2×C22⋊Q8—118no—
398C2×C22⋊Q8—118no—
399C2×C22⋊Q8—112no—
400C2×C22⋊Q8—118no—
401C2×C22⋊Q8C2×D1114yescomplemented
402C2×#121—112no—
403C2×#121—112no—
404C2×#121—118no—
405C2×#120—112no—
406C2×#120—112no—
407#519—1116no—
408C2×C4×Q8—114no—
409C2×C4×Q8—114no—
410C2×C4×D4—114no—
411C2×C4×D4—118no—
412C2×C4×D4—118no—
413C2×C4×D4—114no—
414C2×#117—111no—
415C2×#117—114no—
416C2×#117C2×D1111yescharacteristic
417C22×C11—24no—
418C22×C11—28no—
419C22×C11—24no—
420C22×C11—28no—
421C22×C11—48no—
422C22×C11C23×D414yes—
423C22×C11C23×D412yes—
424C22×C11C2×2−1+414yes—
425C22×C11C2611yescharacteristic
426C2×D11—232no—
427C2×D11—24no—
428C2×D11—24no—
429C2×D11—216no—
430C2×D11—24no—
431C2×D11—28no—
432C2×D11—48no—
433C2×D11C2×2−1+418yescomplemented
434C4×C11—24no—
435C4×C11—28no—
436C4×C11—28no—
437C4×C11C23×D414yes—
438C4×C11C23×D414yes—
439Dic11—24no—
440Dic11—24no—
441Dic11—28no—
442Dic11C23×D4116yes—
443C25—111no—
4442−1+4—22128no—
445C2×#41—28no—
446C2×#41—1132no—
447C2×#41—1116no—
448C2×#41—118no—
449C2×#41—1116no—
450C2×#41—2216no—
451C2×#41—2232no—
452C2×#41—2216no—
453C2×#41—228no—
454C2×#41C22×D1118yes—
455C22×Q8—28no—
456C22×Q8—1132no—
457C22×Q8—1132no—
458C22×Q8—1116no—
459C22×Q8—1116no—
460C22×Q8—112no—
461C22×Q8—112no—
462C22×Q8—118no—
463C22×Q8—118no—
464C22×Q8—114no—
465C22×Q8—111no—
466C22×Q8—1116no—
467C22×Q8—1116no—
468C22×Q8—2216no—
469C22×Q8—2216no—
470C22×Q8—2232no—
471C22×Q8—2232no—
472C22×Q8—22128no—
473C22×Q8—2216no—
474C22×Q8C22×D1112yes—
475C22×Q8C22×D1111yescharacteristic
476C22×Q8C22×D1112yes—
477C22×Q8C22×D1118yes—
478C22×D4—114no—
479C22×D4—112no—
480C22×D4—114no—
481C22×D4—114no—
482C22×D4—111no—
483C22×D4C22×D1112yes—
484C22×D4C22×D1111yescharacteristic
485C23×C4—112no—
486C23×C4—114no—
487C23×C4—111no—
488C23×C4—118no—
489C23×C4—112no—
490C23×C4—112no—
491C23×C4—114no—
492C23×C4—112no—
493C23×C4—1116no—
494C23×C4—118no—
495C23×C4—2216no—
496C23×C4—228no—
497C23×C4C22×D1112yes—
498C23×C4C22×D1112yes—
499C23×C4C22×D1111yescharacteristic
500C4⋊Q8—1116no—
501C4⋊Q8—1164no—
502C4⋊Q8C22×D11116yescomplemented
503#124—1116no—
504#124—1164no—
505#124C22×D11116yescomplemented
506#123—1116no—
507#123—1132no—
508#123—1116no—
509#123C22×D11132yes—
510C22⋊Q8—1116no—
511C22⋊Q8—1132no—
512C22⋊Q8—1164no—
513C22⋊Q8—1116no—
514C22⋊Q8—1164no—
515C22⋊Q8—1164no—
516C22⋊Q8C22×D11132yescomplemented
517#121—1116no—
518#121—1116no—
519#121—1164no—
520#120—1116no—
521#120—1116no—
522C4×Q8—1132no—
523C4×Q8—1132no—
524C4×D4—1132no—
525C4×D4—1164no—
526C4×D4—1164no—
527C4×D4—1132no—
528#117—118no—
529#117—1132no—
530#117C22×D1118yes—
531C2×C4⋊C4—118no—
532C2×C4⋊C4—112no—
533C2×C4⋊C4—114no—
534C2×C4⋊C4—118no—
535C2×C4⋊C4—114no—
536C2×C4⋊C4C22×D1112yes—
537C2×C4⋊C4C22×D1118yes—
538C2×C22⋊C4—112no—
539C2×C22⋊C4—114no—
540C2×C22⋊C4—114no—
541C2×C22⋊C4—114no—
542C2×C22⋊C4—118no—
543C2×C22⋊C4—114no—
544C2×C22⋊C4C22×D1112yes—
545C2×C22⋊C4C22×D1118yes—
546C2×C42—118no—
547C2×C42—112no—
548C2×C42C22×D1112yes—
549C2×C11—24no—
550C2×C11—44no—
551C2×C11#348614yescomplemented
552C2×C11C24×D411yescharacteristic
553C2×C11C22×2−1+412yes—
554D11—28no—
555D11—44no—
556C24—112no—
557C24—114no—
558C24—112no—
559C24—228no—
560C24—224no—
561C24C23×D1112yes—
562C24C23×D1111yescharacteristic
563#41—232no—
564#41—2264no—
565#41—22128no—
566#41—2264no—
567#41—2232no—
568C2×Q8—28no—
569C2×Q8—28no—
570C2×Q8—232no—
571C2×Q8—24no—
572C2×Q8—1116no—
573C2×Q8—1116no—
574C2×Q8—1164no—
575C2×Q8—118no—
576C2×Q8—118no—
577C2×Q8—1132no—
578C2×Q8—1116no—
579C2×Q8—114no—
580C2×Q8—2232no—
581C2×Q8—2264no—
582C2×Q8—2216no—
583C2×Q8—2264no—
584C2×Q8—22128no—
585C2×Q8—22128no—
586C2×Q8—2264no—
587C2×Q8—224no—
588C2×Q8C23×D1118yes—
589C2×Q8C23×D1114yes—
590C2×Q8C23×D1118yes—
591C2×D4—28no—
592C2×D4—24no—
593C2×D4—1116no—
594C2×D4—118no—
595C2×D4—1116no—
596C2×D4—1116no—
597C2×D4—114no—
598C2×D4—2216no—
599C2×D4—2216no—
600C2×D4—2216no—
601C2×D4—228no—
602C2×D4—224no—
603C2×D4C23×D1118yes—
604C2×D4C23×D1114yes—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—1116no—
608C22×C4—118no—
609C22×C4—114no—
610C22×C4—1116no—
611C22×C4—114no—
612C22×C4—114no—
613C22×C4—112no—
614C22×C4—112no—
615C22×C4—1132no—
616C22×C4—118no—
617C22×C4—118no—
618C22×C4—1116no—
619C22×C4—118no—
620C22×C4—2232no—
621C22×C4—2264no—
622C22×C4—2216no—
623C22×C4—2216no—
624C22×C4—224no—
625C22×C4—228no—
626C22×C4—228no—
627C22×C4—2232no—
628C22×C4—228no—
629C22×C4D4×D1118yes—
630C22×C4C23×D1118yes—
631C22×C4C23×D1118yes—
632C22×C4C23×D1114yes—
633C22×C4C23×D1114yes—
634C22×C4C23×D1112yes—
635C22×C4C23×D1114yes—
636C22×C4C23×D1111yescharacteristic
637C22×C4C23×D1111yescharacteristic
638C4⋊C4—1132no—
639C4⋊C4—118no—
640C4⋊C4—1116no—
641C4⋊C4—1132no—
642C4⋊C4—1116no—
643C4⋊C4C23×D1118yes—
644C4⋊C4C23×D11132yes—
645C22⋊C4—118no—
646C22⋊C4—1116no—
647C22⋊C4—1116no—
648C22⋊C4—1116no—
649C22⋊C4—1132no—
650C22⋊C4—1116no—
651C22⋊C4C23×D1118yes—
652C22⋊C4C23×D11132yes—
653C42—1132no—
654C42—118no—
655C42C23×D1118yes—
656C11C2×#348611yescharacteristic, complemented, Sylow
657C23—24no—
658C23—24no—
659C23—28no—
660C23—118no—
661C23—114no—
662C23—114no—
663C23—2216no—
664C23—2232no—
665C23—228no—
666C23—224no—
667C23—224no—
668C23—224no—
669C23—228no—
670C23C2×D4×D1114yes—
671C23C24×D1114yes—
672C23C24×D1112yes—
673C23C24×D1111yescharacteristic
674Q8—216no—
675Q8—216no—
676Q8—28no—
677Q8—1132no—
678Q8—1132no—
679Q8—2264no—
680Q8—2232no—
681Q8—228no—
682D4—216no—
683D4—28no—
684D4—2232no—
685D4—2232no—
686D4—2232no—
687D4—2216no—
688D4—228no—
689C2×C4—24no—
690C2×C4—216no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—216no—
694C2×C4—1116no—
695C2×C4—1132no—
696C2×C4—118no—
697C2×C4—118no—
698C2×C4—114no—
699C2×C4—114no—
700C2×C4—2264no—
701C2×C4—2232no—
702C2×C4—2232no—
703C2×C4—224no—
704C2×C4—228no—
705C2×C4—224no—
706C2×C4—228no—
707C2×C4—2216no—
708C2×C4—2216no—
709C2×C4—2216no—
710C2×C4C2×D4×D1114yes—
711C2×C4C2×D4×D1114yes—
712C2×C4C2×D4×D11116yes—
713C2×C4C24×D1118yes—
714C2×C4C24×D1118yes—
715C2×C4C24×D1114yes—
716C2×C4C24×D1112yes—
717C2×C4C24×D1112yes—
718C22—24no—
719C22—28no—
720C22—24no—
721C22—28no—
722C22—48no—
723C22—118no—
724C22—2232no—
725C22—224no—
726C22—224no—
727C22—2216no—
728C22—224no—
729C22—228no—
730C22—448no—
731C22C22×D4×D1114yes—
732C22C22×D4×D1112yes—
733C22D11×2−1+414yes—
734C22C25×D1111yescharacteristic
735C4—24no—
736C4—28no—
737C4—28no—
738C4—1116no—
739C4—224no—
740C4—224no—
741C4—228no—
742C4C22×D4×D1114yes—
743C4C22×D4×D1114yes—
744C2—24no—
745C2—44no—
746C2—228no—
747C2—444no—
748C2#1308226514yesdirect product factor
749C2C23×D4×D1111yescharacteristic
750C2C2×D11×2−1+412yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#536C2
socleC23×C11C25
hypercenterC2×#536D11
hypocenterC11C2×#3486
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C22×#67043C2semidirect
2. C23×Q8×D11C2semidirect
3. #13082265C2direct (N × H)
4. C2×#10623258C2semidirect
5. C2×#10623163C2semidirect
6. C2×#10623164C2semidirect
7. C2×#10623208C2semidirect
8. C2×#10623347C2semidirect
9. C2×#10623179C2semidirect
10. C2×#10623055C2semidirect
11. C2×#10623187C2semidirect
12. C2×#10623359C2semidirect
13. C2×#10623047C2semidirect
14. C2×C11×#536C2semidirect
18. C2×#67043C22semidirect
22. C22×Q8×D11C22semidirect
23. C22×Q8×D11C22semidirect
25. C22×#4341C22semidirect
27. C22×#4339C22semidirect
32. C23×Dic22C22semidirect
33. C11×#536C22semidirect
34. C2×C11×C4⋊Q8C22semidirect
35. C2×C11×#124C22semidirect
37. C2×C11×C22⋊Q8C22semidirect
39. #10623359C22semidirect
40. #10623347C22semidirect
41. C2×#67000C22semidirect
43. C2×#66999C22semidirect
44. C2×#66997C22semidirect
51. #10623258C22semidirect
52. #10623208C22semidirect
53. #10623187C22semidirect
54. #10623179C22semidirect
55. #10623164C22semidirect
56. #10623163C22semidirect
57. #10623055C22semidirect
58. #10623047C22semidirect
61. C2×#66949C22semidirect
64. C2×#66941C22semidirect
65. C2×#66940C22semidirect
67. C2×#66938C22semidirect
71. C2×#66931C22semidirect
74. C2×C4×Dic22C22semidirect
101. C2×Q8×D11C23semidirect
105. C2×#4341C23semidirect
109. C2×#4339C23semidirect
123. C22×Dic22D4semidirect
131. C22×Dic22C23semidirect
132. C11×C4⋊Q8C23semidirect
133. C11×#124C23semidirect
135. C11×C22⋊Q8C23semidirect
144. #67000C23semidirect
146. #66999C23semidirect
147. #66997C23semidirect
167. #66949C23semidirect
170. #66941C23semidirect
171. #66940C23semidirect
173. #66938C23semidirect
177. #66931C23semidirect
180. C4×Dic22C23semidirect
258. C2×Dic22C2×D4semidirect
291. C2×#536D11semidirect
310. C22×D112−1+4semidirect
381. #536C2×D11semidirect
384. C2×C4⋊Q8C2×D11semidirect
387. C2×#124C2×D11semidirect
401. C2×C22⋊Q8C2×D11semidirect
433. C2×D11C2×2−1+4semidirect
502. C4⋊Q8C22×D11semidirect
505. #124C22×D11semidirect
516. C22⋊Q8C22×D11semidirect
551. C2×C11#3486semidirect
656. C11C2×#3486semidirect
748. C2#13082265direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670432
C23×Q8×D112
#130822652
C2×#106232582
C2×#106231632
C2×#106231642
C2×#106232082
C2×#106233472
C2×#106231792
C2×#106230552
C2×#106231872
C2×#106233592
C2×#106230472
C2×C11×#5362
C2×#348611