Finite Group Databasebeta

← C2×#13081058 #15632306

Subgroups — C2×#13081058 #15632306

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623072C211yesmaximal, characteristic, complemented
2C2×#10623086C211yesmaximal, characteristic
3#13081058C2116yesmaximal, direct product factor
4C2×#10622315C211yesmaximal, characteristic, complemented
5C2×#10622335C211yesmaximal, characteristic, complemented
6C2×#10622350C211yesmaximal, characteristic, complemented
7C2×#10622334C211yesmaximal, characteristic, complemented
8C2×#10622349C211yesmaximal, characteristic, complemented
9C2×#10622463C211yesmaximal, characteristic, complemented
10C2×#10622460C211yesmaximal, characteristic, complemented
11C2×#10622747C211yesmaximal, characteristic, complemented
12C2×#10622727C211yesmaximal, characteristic, complemented
13C2×#10622323C211yesmaximal, characteristic, complemented
14C2×#10622734C211yesmaximal, characteristic, complemented
15C22×#66882C211yesmaximal, characteristic, complemented
16C2×C11×#435C211yesmaximal, characteristic, complemented
17C22×#4341—21no—
18C22×C11×M16C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66988—21no—
22C2×#66983C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C2×#66979C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C2×#66977C2211yescharacteristic
29C2×#66977C2211yescharacteristic
30C22×#4314C2211yescharacteristic
31#10623086—24no—
32#10623086C2218yes—
33#10623072—24no—
34#10623072C2218yescomplemented
35C2×#66950—21no—
36C2×#66942—21no—
37C2×#66939—21no—
38C2×#66939—21no—
39C2×#66932—21no—
40C2×#66930—21no—
41C2×C4×D44C2211yescharacteristic
42C2×#66923C2211yescharacteristic
43C2×#66922C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C11×#435C2218yescomplemented
46C2×C11×C4⋊C8C2211yescharacteristic
47C2×C11×C22⋊C8C2211yescharacteristic
48C2×C11×C22⋊C8C2211yescharacteristic
49C2×C11×#97C2211yescharacteristic
50#10622747C2218yescomplemented
51#10622734C2218yescomplemented
52#10622727C2218yescomplemented
53C2×#66885C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×#66885C2211yescharacteristic
56C2×#66882C2211yescharacteristic
57C2×#66882C2211yescharacteristic
58C2×#66882C2211yescharacteristic
59C2×#66882C2211yescharacteristic
60C2×#66882C2211yescharacteristic
61C2×#66882C2211yescharacteristic
62C2×#66882C2218yescomplemented
63C2×#66881C2211yescharacteristic
64C2×#66881C2211yescharacteristic
65C2×#66881C2211yescharacteristic
66C2×#66880C2211yescharacteristic
67C2×#66880C2211yescharacteristic
68C2×#66880C2211yescharacteristic
69#10622463C2218yescomplemented
70#10622460C2218yescomplemented
71#10622350C2218yescomplemented
72#10622349C2218yescomplemented
73#10622335C2218yescomplemented
74#10622334C2218yescomplemented
75#10622323C2218yescomplemented
76#10622315C2218yescomplemented
77C22×D4×C11D411yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C23×Dic11—21no—
83C23×Dic11—21no—
84C23×Dic11—21no—
85C2×#4341—28no—
86C2×#4341—48no—
87C22×D44C2311yescharacteristic
88C22×C4×D11—21no—
89C22×Dic22—21no—
90C22×Dic22C2311yescharacteristic
91C2×C11×M16—24no—
92C2×C11×M16C2314yes—
93C22×C8×C11—24no—
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2314yes—
98C22×C8×C11C2311yescharacteristic
99C4×D4×C11D414yes—
100C4×D4×C11C2314yes—
101C2×C11×C4⋊C4D411yescharacteristic
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108#66988—28no—
109#66983—22no—
110#66983—22no—
111#66983C2314yes—
112#66983C2314yes—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116#66979—22no—
117#66979C2314yes—
118C2×C4⋊Dic11—21no—
119C2×C4⋊Dic11—21no—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11—22no—
123C2×C4⋊Dic11—22no—
124C2×C4⋊Dic11—22no—
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2314yes—
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2314yes—
133C2×C4⋊Dic11C2314yes—
134#66977—22no—
135#66977—22no—
136#66977C2314yes—
137#66977C2314yes—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×C4×Dic11—21no—
144C2×C4×Dic11—21no—
145C2×#4314—24no—
146C2×#4314C2314yes—
147#66950—28no—
148#66942—28no—
149#66939—28no—
150#66939—28no—
151#66932—28no—
152#66930—28no—
153C4×D44—22no—
154C4×D44C2314yes—
155#66923—22no—
156#66923C2314yes—
157#66922—22no—
158#66922C2314yes—
159C4×Dic22—22no—
160C4×Dic22C2314yes—
161C11×C4⋊C8C2314yes—
162C11×C22⋊C8C2314yes—
163C11×C22⋊C8C2314yes—
164C11×#97C2314yes—
165#66885C2314yes—
166#66885C2314yes—
167#66885C2314yes—
168#66882C2314yes—
169#66882C2314yes—
170#66882C2314yes—
171#66882C2314yes—
172#66882C2314yes—
173#66882C2314yes—
174#66881C2314yes—
175#66881C2314yes—
176#66881C2314yes—
177#66880C2314yes—
178#66880C2314yes—
179#66880C2314yes—
180C2×#3343—111nomaximal, Sylow
181C24×C11C2×D411yescharacteristic
182C24×C11C2×D411yescharacteristic
183C23×D11—21no—
184C2×D4×C11—24no—
185C2×D4×C11C2×D414yes—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D412yes—
195C22×C4×C11C2×D412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2411yescharacteristic
199C2×C22⋊D11—24no—
200C2×C22⋊D11—24no—
201C2×C22⋊D11—44no—
202C2×C22⋊D11—44no—
203C22×Dic11—24no—
204C22×Dic11—24no—
205C22×Dic11—24no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—44no—
214C22×Dic11—44no—
215C22×Dic11—44no—
216#4341—432no—
217C2×D44—21no—
218C2×D44—22no—
219C2×D44—22no—
220C2×D44C2412yes—
221C2×C4×D11—24no—
222C2×C4×D11—44no—
223C2×Dic22—21no—
224C2×Dic22—24no—
225C2×Dic22—22no—
226C2×Dic22—22no—
227C2×Dic22—44no—
228C2×Dic22C2412yes—
229C11×M16—28no—
230C2×C8×C11—28no—
231C2×C8×C11—22no—
232C2×C8×C11—22no—
233C2×C8×C11—22no—
234C2×C8×C11#4114yescomplemented
235C2×C8×C11C2412yes—
236C2×C8×C11C2412yes—
237C2×C8×C11C2412yes—
238C2×C8×C11C2412yes—
239C11×C4⋊C4C2×D414yes—
240C11×C22⋊C4C2×D414yes—
241C11×C22⋊C4C2×D414yes—
242C42×C11C2×D412yes—
243C42×C11C2412yes—
244C22⋊Dic11—24no—
245C22⋊Dic11—24no—
246C22⋊Dic11—24no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250C4⋊Dic11—21no—
251C4⋊Dic11—21no—
252C4⋊Dic11—21no—
253C4⋊Dic11—24no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11—21no—
257C4⋊Dic11—24no—
258C4⋊Dic11—24no—
259C4⋊Dic11—24no—
260C4⋊Dic11C2412yes—
261C4⋊Dic11C2412yes—
262C4⋊Dic11C2412yes—
263C4⋊Dic11C2412yes—
264C4⋊Dic11C2412yes—
265C4⋊Dic11C2412yes—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269Dic11⋊C4—24no—
270Dic11⋊C4—24no—
271C4×Dic11—24no—
272C4×Dic11—24no—
273#4314—28no—
274C2×#552—111no—
275C2×#547—111no—
276#3343—1116no—
277C2×#501—111no—
278C2×#484—111no—
279C2×#482—111no—
280C2×#483—111no—
281C2×#480—111no—
282C2×#477—111no—
283C2×#478—111no—
284C2×#468—111no—
285C2×#465—111no—
286C2×#440—111no—
287C2×#435D1111yescharacteristic, complemented
288C2×#428—111no—
289C22×#107—111no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11AGL(1,ℤ/8)14yes—
296C23×C11C22×D412yes—
297C23×C11C22×D412yes—
298C23×C11C22×D411yescharacteristic
299C22×D11—22no—
300C22×D11—42no—
301C22×D11—42no—
302C22×D11—42no—
303D4×C11—28no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—24no—
309C2×C4×C11—24no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11C22×D412yes—
315C2×C4×C11C22×D412yes—
316C2×C4×C11C22×D412yes—
317C2×C4×C11C22×D412yes—
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C2×#4112yes—
320C2×C4×C112−1+412yes—
321C2×C4×C11C2511yescharacteristic
322C22⋊D11—48no—
323C22⋊D11—48no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—48no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—48no—
337C2×Dic11—48no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341D44—22no—
342D44—22no—
343D44—42no—
344C4×D11—48no—
345Dic22—22no—
346Dic22—22no—
347Dic22—48no—
348Dic22—42no—
349C8×C11—22no—
350C8×C11—22no—
351C8×C11—22no—
352C8×C11C2×#4114yescomplemented
353C22×#41—221no—
354C22×SD16—111no—
355C22×M16C2×D1111yescharacteristic
356C23×C8C2×D1111yescharacteristic
357#552—118no—
358#552—224no—
359#547—118no—
360#547—224no—
361C2×C4⋊Q8—111no—
362C2×#126—221no—
363C2×#125—111no—
364C2×#125—221no—
365C2×#123—221no—
366C2×#123—221no—
367C2×#123—221no—
368C2×C22⋊Q8—111no—
369C2×C22⋊Q8—111no—
370C2×C22⋊Q8—221no—
371C2×#121—111no—
372C2×#121—111no—
373C2×C4×Q8—111no—
374C2×C4×D4—111no—
375C2×C4×D4C2×D1111yescharacteristic
376C2×#117—111no—
377C2×#117—221no—
378C22×C4⋊C4—111no—
379C22×C4⋊C4—111no—
380C22×C4⋊C4—111no—
381#501—118no—
382#484—118no—
383#483—118no—
384#482—118no—
385#480—118no—
386#478—118no—
387#477—118no—
388#468—118no—
389#465—118no—
390#440—118no—
391#435C2×D1118yescomplemented
392#428—118no—
393C2×#107—111no—
394C2×#107—111no—
395C2×#107—111no—
396C2×#107—111no—
397C2×#107—118no—
398C2×#107—111no—
399C2×#107—111no—
400C2×#106—111no—
401C2×#106—111no—
402C2×#106—111no—
403C2×C4⋊C8C2×D1111yescharacteristic
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#102—111no—
408C2×#102—111no—
409C2×#102—111no—
410C2×C22⋊C8C2×D1111yescharacteristic
411C2×C22⋊C8C2×D1111yescharacteristic
412C2×#97C2×D1111yescharacteristic
413C22×C11—28no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—22no—
419C22×C11—44no—
420C22×C11#54712yes—
421C22×C11C2×AGL(1,ℤ/8)14yes—
422C22×C11C2×AGL(1,ℤ/8)12yes—
423C22×C11#57812yes—
424C22×C11C23×D411yescharacteristic
425C2×D11—42no—
426C2×D11—42no—
427C2×D11—42no—
428C2×D11—84no—
429C4×C11—22no—
430C4×C11—22no—
431C4×C11—22no—
432C4×C11—22no—
433C4×C11#54712yes—
434C4×C11C22×#4111yescharacteristic
435C4×C11C2×2−1+411yescharacteristic
436Dic11—42no—
437Dic11—42no—
438Dic11—42no—
439Dic11—42no—
440Dic11—42no—
441Dic11—42no—
442Dic11—42no—
443C2×#41—228no—
444C2×#41—448no—
445C22×Q8—111no—
446C22×Q8—221no—
447C22×D4—111no—
448C22×D4—221no—
449C22×D4—221no—
450C22×D4D4411yescharacteristic
451C23×C4—221no—
452C23×C4—221no—
453C23×C4—221no—
454C23×C4—221no—
455C23×C4C22×D1111yescharacteristic
456C23×C4C22×D1111yescharacteristic
457C2×SD16—114no—
458C2×SD16—224no—
459C2×M16—24no—
460C2×M16C22×D1114yes—
461C22×C8—24no—
462C22×C8C22×D1111yescharacteristic
463C22×C8C22×D1114yes—
464C22×C8C22×D1111yescharacteristic
465C22×C8C22×D1111yescharacteristic
466C22×C8C22×D1111yescharacteristic
467C4⋊Q8—114no—
468C4⋊Q8—222no—
469#126—228no—
470#125—114no—
471#125—228no—
472#125—222no—
473#123—228no—
474#123—228no—
475#123—228no—
476C22⋊Q8—114no—
477C22⋊Q8—114no—
478C22⋊Q8—222no—
479C22⋊Q8—222no—
480C22⋊Q8—228no—
481#121—114no—
482#121—114no—
483#121—222no—
484#121—222no—
485C4×Q8—114no—
486C4×Q8—222no—
487C4×D4—114no—
488C4×D4—222no—
489C4×D4D4414yes—
490C4×D4C22×D1114yes—
491#117—114no—
492#117—222no—
493#117—228no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—111no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—111no—
499C2×C4⋊C4—114no—
500C2×C4⋊C4—114no—
501C2×C4⋊C4—114no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4—221no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—222no—
507C2×C4⋊C4—222no—
508C2×C4⋊C4—222no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4—221no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4—221no—
515C2×C4⋊C4D4411yescharacteristic
516C2×C22⋊C4—221no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4D4411yescharacteristic
523C2×C22⋊C4D4411yescharacteristic
524C2×C42—221no—
525C2×C42—221no—
526C2×C42C22×D1111yescharacteristic
527#107—114no—
528#107—114no—
529#107—114no—
530#107—114no—
531#107—114no—
532#107—114no—
533#106—114no—
534#106—114no—
535#106—114no—
536C4⋊C8C22×D1114yes—
537#103—114no—
538#103—114no—
539#103—114no—
540#102—114no—
541#102—114no—
542#102—114no—
543C22⋊C8C22×D1114yes—
544C22⋊C8C22×D1114yes—
545#97C22×D1114yes—
546C2×C11—24no—
547C2×C11—42no—
548C2×C11#334314yescomplemented
549C2×C11C2×#54711yescharacteristic
550C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
551C2×C11C2×#57811yescharacteristic
552D11—82no—
553C24—221no—
554C24C2×D4411yescharacteristic
555C24C2×D4411yescharacteristic
556#41—4432no—
557C2×Q8—112no—
558C2×Q8—221no—
559C2×Q8—224no—
560C2×Q8—222no—
561C2×Q8—222no—
562C2×Q8—444no—
563C2×D4—24no—
564C2×D4—112no—
565C2×D4—224no—
566C2×D4—224no—
567C2×D4—221no—
568C2×D4—222no—
569C2×D4—222no—
570C2×D4—444no—
571C2×D4—444no—
572C2×D4C2×D4414yes—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—224no—
578C22×C4—224no—
579C22×C4—224no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—224no—
588C22×C4—444no—
589C22×C4—444no—
590C22×C4—444no—
591C22×C4—444no—
592C22×C4C2×D4412yes—
593C22×C4C2×D4412yes—
594C22×C4C2×D4411yescharacteristic
595C22×C4C2×D4411yescharacteristic
596C22×C4C2×D4411yescharacteristic
597C22×C4C2×D4411yescharacteristic
598C22×C4C23×D1112yes—
599C22×C4C23×D1112yes—
600C22×C4C23×D1111yescharacteristic
601SD16—228no—
602M16—28no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—28no—
607C2×C8#434114yescomplemented
608C2×C8C23×D1112yes—
609C2×C8C23×D1112yes—
610C2×C8C23×D1112yes—
611C2×C8C23×D1112yes—
612C4⋊C4—112no—
613C4⋊C4—112no—
614C4⋊C4—112no—
615C4⋊C4—112no—
616C4⋊C4—112no—
617C4⋊C4—112no—
618C4⋊C4—221no—
619C4⋊C4—221no—
620C4⋊C4—221no—
621C4⋊C4—221no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—221no—
625C4⋊C4—224no—
626C4⋊C4—221no—
627C4⋊C4—224no—
628C4⋊C4—224no—
629C4⋊C4—224no—
630C4⋊C4—224no—
631C4⋊C4—224no—
632C4⋊C4—224no—
633C4⋊C4C2×D4414yes—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C22⋊C4—224no—
639C22⋊C4—224no—
640C22⋊C4C2×D4414yes—
641C22⋊C4C2×D4414yes—
642C42—224no—
643C42—224no—
644C42C2×D4412yes—
645C42C23×D1112yes—
646C11C2×#334311yescharacteristic, complemented, Sylow
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—222no—
653C23—442no—
654C23—442no—
655C23—442no—
656C23#6696114yes—
657C23C22×D4412yes—
658C23C22×D4412yes—
659C23C22×D4411yescharacteristic
660Q8—222no—
661Q8—222no—
662Q8—448no—
663Q8—442no—
664D4—28no—
665D4—222no—
666D4—222no—
667D4—448no—
668D4—448no—
669D4—442no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—448no—
688C2×C4—448no—
689C2×C4—442no—
690C2×C4—442no—
691C2×C4—442no—
692C2×C4—448no—
693C2×C4—448no—
694C2×C4—442no—
695C2×C4—442no—
696C2×C4—442no—
697C2×C4—442no—
698C2×C4C22×D4412yes—
699C2×C4C22×D4412yes—
700C2×C4C22×D4412yes—
701C2×C4C22×D4412yes—
702C2×C4C22×D4411yescharacteristic
703C2×C4C2×#434112yes—
704C2×C4#6704312yes—
705C2×C4C24×D1111yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8C2×#434114yescomplemented
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—442no—
718C22—442no—
719C22—442no—
720C22—884no—
721C22#1062308612yes—
722C22C2×#6696114yes—
723C22C2×#6696112yes—
724C22#1062328412yes—
725C22C23×D4411yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—442no—
731C4—442no—
732C4—442no—
733C4—442no—
734C4—442no—
735C4—442no—
736C4—442no—
737C4#1062308612yes—
738C4C22×#434111yescharacteristic
739C4C2×#6704311yescharacteristic
740C2—24no—
741C2—42no—
742C2—882no—
743C2#1308105814yesdirect product factor
744C2C2×#1062308611yescharacteristic
745C2C22×#6696111yescharacteristic
746C2C2×#1062328411yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#435C2
socleC23×C11C22×D4
prime radicalC2×#10623086C2
hypercenterC2×#435D11
hypocenterC11C2×#3343
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#10623072C2semidirect
3. #13081058C2direct (N × H)
4. C2×#10622315C2semidirect
5. C2×#10622335C2semidirect
6. C2×#10622350C2semidirect
7. C2×#10622334C2semidirect
8. C2×#10622349C2semidirect
9. C2×#10622463C2semidirect
10. C2×#10622460C2semidirect
11. C2×#10622747C2semidirect
12. C2×#10622727C2semidirect
13. C2×#10622323C2semidirect
14. C2×#10622734C2semidirect
15. C22×#66882C2semidirect
16. C2×C11×#435C2semidirect
34. #10623072C22semidirect
45. C11×#435C22semidirect
50. #10622747C22semidirect
51. #10622734C22semidirect
52. #10622727C22semidirect
62. C2×#66882C22semidirect
69. #10622463C22semidirect
70. #10622460C22semidirect
71. #10622350C22semidirect
72. #10622349C22semidirect
73. #10622335C22semidirect
74. #10622334C22semidirect
75. #10622323C22semidirect
76. #10622315C22semidirect
234. C2×C8×C11#41semidirect
287. C2×#435D11semidirect
352. C8×C11C2×#41semidirect
391. #435C2×D11semidirect
548. C2×C11#3343semidirect
607. C2×C8#4341semidirect
646. C11C2×#3343semidirect
709. C8C2×#4341semidirect
743. C2#13081058direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230722
C2×#106230862
#130810582
C2×#106223152
C2×#106223352
C2×#106223502
C2×#106223342
C2×#106223492
C2×#106224632
C2×#106224602
C2×#106227472
C2×#106227272
C2×#106223232
C2×#106227342
C22×#668822
C2×C11×#4352
C2×#334311