Finite Group Databasebeta

← C2×#13081103 #15632354

Subgroups — C2×#13081103 #15632354

Order 2816.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623074C211yesmaximal, characteristic, complemented
2C2×#10623096C211yesmaximal, characteristic
3#13081103C2116yesmaximal, direct product factor
4C2×#10622315C211yesmaximal, characteristic, complemented
5C2×#10622335C211yesmaximal, characteristic, complemented
6C2×#10622348C211yesmaximal, characteristic, complemented
7C2×#10622336C211yesmaximal, characteristic, complemented
8C2×#10622349C211yesmaximal, characteristic, complemented
9C2×#10622442C211yesmaximal, characteristic, complemented
10C2×#10622459C211yesmaximal, 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×C11×M16C2211yescharacteristic
18C23×C8×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66992—21no—
21C2×D4×Dic11—21no—
22C2×#66983C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C2×#66979C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2211yescharacteristic
28C2×#66977C2211yescharacteristic
29C2×#66977C2211yescharacteristic
30C22×#4314C2211yescharacteristic
31#10623096—24no—
32#10623096C2218yes—
33#10623074—24no—
34#10623074C2218yescomplemented
35C2×#66951—21no—
36C2×#66943—21no—
37C2×#66936—21no—
38C2×(C22⋊D11)⋊C4—21no—
39C2×#66931—21no—
40C2×#66931—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#10622459C2218yescomplemented
70#10622442C2218yescomplemented
71#10622349C2218yescomplemented
72#10622348C2218yescomplemented
73#10622336C2218yescomplemented
74#10622335C2218yescomplemented
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—
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×Dic22—21no—
88C22×Dic22C2311yescharacteristic
89C2×C11×M16—24no—
90C2×C11×M16C2314yes—
91C22×C8×C11—24no—
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2314yes—
96C22×C8×C11C2311yescharacteristic
97C4×D4×C11D414yes—
98C4×D4×C11C2314yes—
99C2×C11×C4⋊C4D411yescharacteristic
100C2×C11×C22⋊C4D411yescharacteristic
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106#66992—28no—
107D4×Dic11—28no—
108#66983—22no—
109#66983—22no—
110#66983C2314yes—
111#66983C2314yes—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115#66979—22no—
116#66979C2314yes—
117C2×C4⋊Dic11—21no—
118C2×C4⋊Dic11—21no—
119C2×C4⋊Dic11—21no—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—22no—
122C2×C4⋊Dic11—22no—
123C2×C4⋊Dic11—22no—
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2314yes—
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2314yes—
132C2×C4⋊Dic11C2314yes—
133#66977—22no—
134#66977—22no—
135#66977C2314yes—
136#66977C2314yes—
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C2×Dic11⋊C4—21no—
142C2×C4×Dic11—21no—
143C2×C4×Dic11—21no—
144C2×#4314—24no—
145C2×#4314C2314yes—
146#66951—28no—
147#66943—28no—
148#66936—28no—
149(C22⋊D11)⋊C4—28no—
150#66931—28no—
151#66931—28no—
152C4×D44—22no—
153C4×D44C2314yes—
154#66923—22no—
155#66923C2314yes—
156#66922—22no—
157#66922C2314yes—
158C4×Dic22—22no—
159C4×Dic22C2314yes—
160C11×C4⋊C8C2314yes—
161C11×C22⋊C8C2314yes—
162C11×C22⋊C8C2314yes—
163C11×#97C2314yes—
164#66885C2314yes—
165#66885C2314yes—
166#66885C2314yes—
167#66882C2314yes—
168#66882C2314yes—
169#66882C2314yes—
170#66882C2314yes—
171#66882C2314yes—
172#66882C2314yes—
173#66881C2314yes—
174#66881C2314yes—
175#66881C2314yes—
176#66880C2314yes—
177#66880C2314yes—
178#66880C2314yes—
179C2×#3346—111nomaximal, Sylow
180C24×C11C2×D411yescharacteristic
181C24×C11C2×D411yescharacteristic
182C23×D11—21no—
183C2×D4×C11—24no—
184C2×D4×C11C2×D414yes—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D412yes—
194C22×C4×C11C2×D412yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2411yescharacteristic
198C2×C22⋊D11—24no—
199C2×C22⋊D11—24no—
200C2×C22⋊D11—44no—
201C2×C22⋊D11—82no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—24no—
210C22×Dic11—24no—
211C22×Dic11—24no—
212C22×Dic11—82no—
213C22×Dic11—82no—
214C22×Dic11—82no—
215C2×D44—21no—
216C2×D44—22no—
217C2×D44—22no—
218C2×D44C2412yes—
219C2×C4×D11—24no—
220C2×C4×D11—82no—
221C2×Dic22—21no—
222C2×Dic22—24no—
223C2×Dic22—22no—
224C2×Dic22—22no—
225C2×Dic22—82no—
226C2×Dic22C2412yes—
227C11×M16—28no—
228C2×C8×C11—28no—
229C2×C8×C11—22no—
230C2×C8×C11—22no—
231C2×C8×C11—22no—
232C2×C8×C11#4114yes—
233C2×C8×C11C2412yes—
234C2×C8×C11C2412yes—
235C2×C8×C11C2412yes—
236C2×C8×C11C2412yes—
237C11×C4⋊C4C2×D414yes—
238C11×C22⋊C4C2×D414yes—
239C11×C22⋊C4C2×D414yes—
240C42×C11C2×D412yes—
241C42×C11C2412yes—
242C22⋊Dic11—24no—
243C22⋊Dic11—24no—
244C22⋊Dic11—24no—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—24no—
248C4⋊Dic11—21no—
249C4⋊Dic11—21no—
250C4⋊Dic11—21no—
251C4⋊Dic11—24no—
252C4⋊Dic11—21no—
253C4⋊Dic11—21no—
254C4⋊Dic11—21no—
255C4⋊Dic11—24no—
256C4⋊Dic11—24no—
257C4⋊Dic11—24no—
258C4⋊Dic11C2412yes—
259C4⋊Dic11C2412yes—
260C4⋊Dic11C2412yes—
261C4⋊Dic11C2412yes—
262C4⋊Dic11C2412yes—
263C4⋊Dic11C2412yes—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269C4×Dic11—24no—
270C4×Dic11—24no—
271#4314—28no—
272C2×#554—111no—
273C2×#553—111no—
274#3346—1116no—
275C2×#501—111no—
276C2×#484—111no—
277C2×#481—111no—
278C2×#485—111no—
279C2×#480—111no—
280C2×#479—111no—
281C2×#474—111no—
282C2×#468—111no—
283C2×#465—111no—
284C2×#440—111no—
285C2×#435D1111yescharacteristic, complemented
286C2×#428—111no—
287C22×#107—111no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11#13714yes—
294C23×C11C22×D412yes—
295C23×C11C22×D412yes—
296C23×C11C22×D411yescharacteristic
297C22×D11—22no—
298C22×D11—42no—
299C22×D11—42no—
300C22×D11—42no—
301D4×C11—28no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—24no—
307C2×C4×C11—24no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11C22×D412yes—
313C2×C4×C11C22×D412yes—
314C2×C4×C11C22×D412yes—
315C2×C4×C11C22×D412yes—
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C2×#4112yes—
318C2×C4×C112−1+412yes—
319C2×C4×C11C2511yescharacteristic
320C22⋊D11—48no—
321C22⋊D11—84no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—84no—
337C2×Dic11—84no—
338C2×Dic11—84no—
339D44—22no—
340D44—22no—
341D44—42no—
342C4×D11—84no—
343Dic22—22no—
344Dic22—22no—
345Dic22—42no—
346Dic22—84no—
347C8×C11—22no—
348C8×C11—22no—
349C8×C11—22no—
350C8×C11C2×#4114yes—
351C22×SD16—111no—
352C22×M16C2×D1111yescharacteristic
353C23×C8C2×D1111yescharacteristic
354#554—118no—
355#554—224no—
356#553—118no—
357#553—224no—
358C2×C4⋊Q8—111no—
359C2×#126—221no—
360C2×#125—111no—
361C2×#125—221no—
362C2×#123—221no—
363C2×C22⋊Q8—111no—
364C2×C22⋊Q8—111no—
365C2×C22⋊Q8—221no—
366C2×C22⋊Q8—221no—
367C2×#121—111no—
368C2×#121—111no—
369C2×#121—221no—
370C2×C4×Q8—111no—
371C2×C4×D4—111no—
372C2×C4×D4—221no—
373C2×C4×D4—221no—
374C2×C4×D4C2×D1111yescharacteristic
375C2×#117—111no—
376C22×C4⋊C4—111no—
377C22×C4⋊C4—111no—
378C22×C4⋊C4—111no—
379#501—118no—
380#485—118no—
381#484—118no—
382#481—118no—
383#480—118no—
384#479—118no—
385#474—118no—
386#468—118no—
387#465—118no—
388#440—118no—
389#435C2×D1118yescomplemented
390#428—118no—
391C2×#107—111no—
392C2×#107—111no—
393C2×#107—111no—
394C2×#107—111no—
395C2×#107—118no—
396C2×#107—111no—
397C2×#107—111no—
398C2×#106—111no—
399C2×#106—111no—
400C2×#106—111no—
401C2×C4⋊C8C2×D1111yescharacteristic
402C2×#103—111no—
403C2×#103—111no—
404C2×#103—111no—
405C2×#102—111no—
406C2×#102—111no—
407C2×#102—111no—
408C2×C22⋊C8C2×D1111yescharacteristic
409C2×C22⋊C8C2×D1111yescharacteristic
410C2×#97C2×D1111yescharacteristic
411C22×C11—28no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—44no—
418C22×C11#54712yes—
419C22×C11C2×#13714yes—
420C22×C11C2×#13712yes—
421C22×C11#57612yes—
422C22×C11C23×D411yescharacteristic
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—84no—
427C4×C11—22no—
428C4×C11—22no—
429C4×C11—22no—
430C4×C11—22no—
431C4×C11#54712yes—
432C4×C11C22×#4111yescharacteristic
433C4×C11C2×2−1+411yescharacteristic
434Dic11—42no—
435Dic11—42no—
436Dic11—42no—
437Dic11—42no—
438Dic11—42no—
439Dic11—42no—
440Dic11—42no—
441C22×Q8—111no—
442C22×Q8—221no—
443C22×D4—111no—
444C22×D4—221no—
445C22×D4—221no—
446C22×D4D4411yescharacteristic
447C23×C4—221no—
448C23×C4—221no—
449C23×C4—221no—
450C23×C4—221no—
451C23×C4C22×D1111yescharacteristic
452C23×C4C22×D1111yescharacteristic
453C2×SD16—114no—
454C2×SD16—224no—
455C2×M16—24no—
456C2×M16C22×D1114yes—
457C22×C8—24no—
458C22×C8C22×D1111yescharacteristic
459C22×C8C22×D1114yes—
460C22×C8C22×D1111yescharacteristic
461C22×C8C22×D1111yescharacteristic
462C22×C8C22×D1111yescharacteristic
463C4⋊Q8—114no—
464C4⋊Q8—222no—
465#126—228no—
466#125—114no—
467#125—228no—
468#125—222no—
469#123—228no—
470C22⋊Q8—114no—
471C22⋊Q8—114no—
472C22⋊Q8—222no—
473C22⋊Q8—222no—
474C22⋊Q8—228no—
475C22⋊Q8—228no—
476#121—114no—
477#121—114no—
478#121—228no—
479#121—222no—
480#121—222no—
481C4×Q8—114no—
482C4×Q8—222no—
483C4×D4—114no—
484C4×D4—228no—
485C4×D4—228no—
486C4×D4—222no—
487C4×D4D4414yes—
488C4×D4C22×D1114yes—
489#117—114no—
490#117—222no—
491C2×C4⋊C4—111no—
492C2×C4⋊C4—111no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—114no—
497C2×C4⋊C4—114no—
498C2×C4⋊C4—114no—
499C2×C4⋊C4—111no—
500C2×C4⋊C4—221no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4—222no—
504C2×C4⋊C4—222no—
505C2×C4⋊C4—222no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—221no—
509C2×C4⋊C4—221no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4D4411yescharacteristic
513C2×C22⋊C4—221no—
514C2×C22⋊C4—221no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4D4411yescharacteristic
520C2×C22⋊C4D4411yescharacteristic
521C2×C42—221no—
522C2×C42—221no—
523C2×C42C22×D1111yescharacteristic
524#107—114no—
525#107—114no—
526#107—114no—
527#107—114no—
528#107—114no—
529#107—114no—
530#106—114no—
531#106—114no—
532#106—114no—
533C4⋊C8C22×D1114yes—
534#103—114no—
535#103—114no—
536#103—114no—
537#102—114no—
538#102—114no—
539#102—114no—
540C22⋊C8C22×D1114yes—
541C22⋊C8C22×D1114yes—
542#97C22×D1114yes—
543C2×C11—24no—
544C2×C11—42no—
545C2×C11#334614yescomplemented
546C2×C11C2×#54711yescharacteristic
547C2×C11C22×#13711yescharacteristic
548C2×C11C2×#57611yescharacteristic
549D11—82no—
550C24—221no—
551C24C2×D4411yescharacteristic
552C24C2×D4411yescharacteristic
553C2×Q8—112no—
554C2×Q8—221no—
555C2×Q8—224no—
556C2×Q8—222no—
557C2×Q8—222no—
558C2×Q8—882no—
559C2×D4—24no—
560C2×D4—112no—
561C2×D4—224no—
562C2×D4—224no—
563C2×D4—221no—
564C2×D4—222no—
565C2×D4—222no—
566C2×D4—444no—
567C2×D4—882no—
568C2×D4C2×D4414yes—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—221no—
579C22×C4—221no—
580C22×C4—224no—
581C22×C4—224no—
582C22×C4—224no—
583C22×C4—224no—
584C22×C4—882no—
585C22×C4—882no—
586C22×C4—882no—
587C22×C4—882no—
588C22×C4C2×D4412yes—
589C22×C4C2×D4412yes—
590C22×C4C2×D4411yescharacteristic
591C22×C4C2×D4411yescharacteristic
592C22×C4C2×D4411yescharacteristic
593C22×C4C2×D4411yescharacteristic
594C22×C4C23×D1112yes—
595C22×C4C23×D1112yes—
596C22×C4C23×D1111yescharacteristic
597SD16—228no—
598M16—28no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—28no—
603C2×C8#434114yes—
604C2×C8C23×D1112yes—
605C2×C8C23×D1112yes—
606C2×C8C23×D1112yes—
607C2×C8C23×D1112yes—
608C4⋊C4—112no—
609C4⋊C4—112no—
610C4⋊C4—112no—
611C4⋊C4—112no—
612C4⋊C4—112no—
613C4⋊C4—112no—
614C4⋊C4—221no—
615C4⋊C4—221no—
616C4⋊C4—221no—
617C4⋊C4—224no—
618C4⋊C4—224no—
619C4⋊C4—221no—
620C4⋊C4—221no—
621C4⋊C4—224no—
622C4⋊C4—221no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—224no—
626C4⋊C4—224no—
627C4⋊C4—224no—
628C4⋊C4—224no—
629C4⋊C4C2×D4414yes—
630C22⋊C4—224no—
631C22⋊C4—224no—
632C22⋊C4—224no—
633C22⋊C4—224no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C22⋊C4C2×D4414yes—
637C22⋊C4C2×D4414yes—
638C42—224no—
639C42—224no—
640C42C2×D4412yes—
641C42C23×D1112yes—
642C11C2×#334611yescharacteristic, complemented, Sylow
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—222no—
649C23—442no—
650C23—442no—
651C23—442no—
652C23#6696214yes—
653C23C22×D4412yes—
654C23C22×D4412yes—
655C23C22×D4411yescharacteristic
656Q8—222no—
657Q8—222no—
658Q8—442no—
659Q8—884no—
660D4—28no—
661D4—222no—
662D4—222no—
663D4—448no—
664D4—442no—
665D4—884no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—222no—
677C2×C4—222no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—442no—
684C2×C4—442no—
685C2×C4—442no—
686C2×C4—442no—
687C2×C4—442no—
688C2×C4—442no—
689C2×C4—442no—
690C2×C4—884no—
691C2×C4—884no—
692C2×C4—884no—
693C2×C4—884no—
694C2×C4C22×D4412yes—
695C2×C4C22×D4412yes—
696C2×C4C22×D4412yes—
697C2×C4C22×D4412yes—
698C2×C4C22×D4411yescharacteristic
699C2×C4C2×#434112yes—
700C2×C4#6704312yes—
701C2×C4C24×D1111yescharacteristic
702C8—22no—
703C8—22no—
704C8—22no—
705C8C2×#434114yes—
706C22—28no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—442no—
714C22—442no—
715C22—442no—
716C22—884no—
717C22#1062308612yes—
718C22C2×#6696214yes—
719C22C2×#6696212yes—
720C22#1062328312yes—
721C22C23×D4411yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—442no—
727C4—442no—
728C4—442no—
729C4—442no—
730C4—442no—
731C4—442no—
732C4—442no—
733C4#1062308612yes—
734C4C22×#434111yescharacteristic
735C4C2×#6704311yescharacteristic
736C2—24no—
737C2—42no—
738C2—882no—
739C2#1308110314yesdirect product factor
740C2C2×#1062308611yescharacteristic
741C2C22×#6696211yescharacteristic
742C2C2×#1062328311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#435C2
socleC23×C11C22×D4
prime radicalC2×#10623096C2
hypercenterC2×#435D11
hypocenterC11C2×#3346
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×#10623074C2semidirect
3. #13081103C2direct (N × H)
4. C2×#10622315C2semidirect
5. C2×#10622335C2semidirect
6. C2×#10622348C2semidirect
7. C2×#10622336C2semidirect
8. C2×#10622349C2semidirect
9. C2×#10622442C2semidirect
10. C2×#10622459C2semidirect
11. C2×#10622747C2semidirect
12. C2×#10622727C2semidirect
13. C2×#10622323C2semidirect
14. C2×#10622734C2semidirect
15. C22×#66882C2semidirect
16. C2×C11×#435C2semidirect
34. #10623074C22semidirect
45. C11×#435C22semidirect
50. #10622747C22semidirect
51. #10622734C22semidirect
52. #10622727C22semidirect
62. C2×#66882C22semidirect
69. #10622459C22semidirect
70. #10622442C22semidirect
71. #10622349C22semidirect
72. #10622348C22semidirect
73. #10622336C22semidirect
74. #10622335C22semidirect
75. #10622323C22semidirect
76. #10622315C22semidirect
285. C2×#435D11semidirect
389. #435C2×D11semidirect
545. C2×C11#3346semidirect
642. C11C2×#3346semidirect
739. C2#13081103direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230742
C2×#106230962
#130811032
C2×#106223152
C2×#106223352
C2×#106223482
C2×#106223362
C2×#106223492
C2×#106224422
C2×#106224592
C2×#106227472
C2×#106227272
C2×#106223232
C2×#106227342
C22×#668822
C2×C11×#4352
C2×#334611