Finite Group Databasebeta

← C2×#13081131 #15632384

Subgroups — C2×#13081131 #15632384

Order 2816.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623072C211yesmaximal, characteristic, complemented
2#13081131C2116yesmaximal, direct product factor
3C2×#10622693C211yesmaximal, characteristic, complemented
4C2×#10622647C211yesmaximal, characteristic, complemented
5C2×#10622609C211yesmaximal, characteristic, complemented
6C2×#10622609C211yesmaximal, characteristic, complemented
7C2×#10622648C211yesmaximal, characteristic, complemented
8C2×#10622707C211yesmaximal, characteristic, complemented
9C2×#10622622C211yesmaximal, characteristic, complemented
10C2×#10622655C211yesmaximal, characteristic, complemented
11C2×#10622654C211yesmaximal, characteristic, complemented
12C2×#10622631C211yesmaximal, characteristic, complemented
13C2×#10622624C211yesmaximal, characteristic, complemented
14C2×#10622608C211yesmaximal, characteristic, complemented
15C2×#10622611C211yesmaximal, characteristic, complemented
16C2×C11×#555C211yesmaximal, characteristic
17C11×#555—24no—
18C11×#555C2218yes—
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#124—21no—
21C2×C11×#124—21no—
22C2×C11×#121—21no—
23C2×C11×#121C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27C2×C11×#117—21no—
28C2×C11×#117C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic
30C2×#66988—21no—
31C22×#4324C2211yescharacteristic
32C2×#66979C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C2×#66977C2211yescharacteristic
35C2×#66977C2211yescharacteristic
36C22×#4318C2211yescharacteristic
37C23×C11⋊C8C2211yescharacteristic
38#10623072—24no—
39#10623072C2218yescomplemented
40C2×#66942—21no—
41C2×#66932—21no—
42C2×#66930—21no—
43C2×#66923C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46C2×#66896C2211yescharacteristic
47C2×#66896C2211yescharacteristic
48C2×C22⋊(C11⋊C8)C2211yescharacteristic
49C2×C22⋊(C11⋊C8)C2211yescharacteristic
50#10622707C2218yescomplemented
51#10622693C2218yescomplemented
52#10622655C2218yescomplemented
53#10622654C2218yescomplemented
54#10622648C2218yescomplemented
55#10622647C2218yescomplemented
56#10622631C2218yescomplemented
57#10622624C2218yescomplemented
58#10622622C2218yescomplemented
59#10622611C2218yescomplemented
60#10622609C2218yescomplemented
61#10622609C2218yescomplemented
62#10622608C2218yescomplemented
63C2×#66874C2211yescharacteristic
64C2×#66874C2211yescharacteristic
65C2×#66874C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69C2×#66872C2211yescharacteristic
70C2×#66872C2211yescharacteristic
71C2×#66871C2211yescharacteristic
72C2×#66871C2211yescharacteristic
73C2×#66871C2211yescharacteristic
74C2×#66871C2211yescharacteristic
75C2×C4⋊(C11⋊C8)C2211yescharacteristic
76C2×#66867C2211yescharacteristic
77C22×Q8×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11—21no—
80C22×D4×C11D411yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11—21no—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×Dic11—21no—
86C22×Dic22C2311yescharacteristic
87C11×C4⋊Q8—22no—
88C11×C4⋊Q8C2314yes—
89C11×#124—28no—
90C11×#124—28no—
91C11×#121—28no—
92C11×#121—22no—
93C11×#121—22no—
94C11×#121C2314yes—
95C11×#121C2314yes—
96C4×D4×C11—22no—
97C4×D4×C11D414yes—
98C4×D4×C11C2314yes—
99C4×D4×C11C2314yes—
100C11×#117—22no—
101C11×#117—22no—
102C11×#117—28no—
103C11×#117C2314yes—
104C11×#117C2314yes—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4D411yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4D411yescharacteristic
116C2×C11×C22⋊C4D411yescharacteristic
117C2×C42×C11—21no—
118C2×C42×C11—21no—
119C2×C42×C11C2311yescharacteristic
120C2×C22⋊Dic11—21no—
121C2×C22⋊Dic11—21no—
122C2×C22⋊Dic11—21no—
123#66988—28no—
124C2×#4324—24no—
125C2×#4324C2314yes—
126#66979—22no—
127#66979C2314yes—
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11—22no—
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
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×#4318—24no—
146C2×#4318C2314yes—
147C22×C11⋊C8—24no—
148C22×C11⋊C8C2311yescharacteristic
149C22×C11⋊C8C2311yescharacteristic
150C22×C11⋊C8C2311yescharacteristic
151C22×C11⋊C8C2314yes—
152C22×C11⋊C8C2311yescharacteristic
153#66942—28no—
154#66932—28no—
155#66930—28no—
156#66923—22no—
157#66923C2314yes—
158C4×Dic22—22no—
159C4×Dic22C2314yes—
160#66896C2314yes—
161#66896C2314yes—
162#66896C2314yes—
163C22⋊(C11⋊C8)C2314yes—
164C22⋊(C11⋊C8)C2314yes—
165#66874C2314yes—
166#66874C2314yes—
167#66874C2314yes—
168#66872C2314yes—
169#66872C2314yes—
170#66872C2314yes—
171#66872C2314yes—
172#66872C2314yes—
173#66871C2314yes—
174#66871C2314yes—
175#66871C2314yes—
176#66871C2314yes—
177C4⋊(C11⋊C8)C2314yes—
178#66867C2314yes—
179C2×#3348—111nomaximal, Sylow
180C24×C11—21no—
181C24×C11C2×D411yescharacteristic
182C24×C11C2×D411yescharacteristic
183C2×Q8×C11—24no—
184C2×Q8×C11—82no—
185C2×D4×C11—24no—
186C2×D4×C11—24no—
187C2×D4×C11—21no—
188C2×D4×C11—22no—
189C2×D4×C11—22no—
190C2×D4×C11—42no—
191C2×D4×C11—82no—
192C2×D4×C11—82no—
193C2×D4×C11C2×D414yes—
194C2×D4×C11C2412yes—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—24no—
203C22×C4×C11—44no—
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D412yes—
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2411yescharacteristic
213C22×Dic11—24no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—44no—
219C2×Dic22—21no—
220C2×Dic22—22no—
221C2×Dic22—22no—
222C2×Dic22C2412yes—
223C11×C4⋊C4—24no—
224C11×C4⋊C4—21no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4C2×D414yes—
228C11×C4⋊C4C2412yes—
229C11×C4⋊C4C2412yes—
230C11×C4⋊C4C2412yes—
231C11×C22⋊C4—24no—
232C11×C22⋊C4—24no—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—24no—
236C11×C22⋊C4C2×D414yes—
237C11×C22⋊C4C2×D414yes—
238C42×C11—24no—
239C42×C11—24no—
240C42×C11C2×D412yes—
241C42×C11C2412yes—
242C22⋊Dic11—24no—
243C22⋊Dic11—24no—
244C22⋊Dic11—24no—
245#4324—28no—
246C4⋊Dic11—21no—
247C4⋊Dic11—21no—
248C4⋊Dic11—21no—
249C4⋊Dic11—24no—
250C4⋊Dic11C2412yes—
251C4⋊Dic11C2412yes—
252C4⋊Dic11C2412yes—
253Dic11⋊C4—24no—
254Dic11⋊C4—24no—
255Dic11⋊C4—24no—
256Dic11⋊C4—24no—
257Dic11⋊C4—24no—
258C4×Dic11—24no—
259C4×Dic11—24no—
260#4318—28no—
261C2×C11⋊C8—28no—
262C2×C11⋊C8—22no—
263C2×C11⋊C8—22no—
264C2×C11⋊C8—22no—
265C2×C11⋊C8#4114yes—
266C2×C11⋊C8C2412yes—
267C2×C11⋊C8C2412yes—
268C2×C11⋊C8C2412yes—
269C2×C11⋊C8C2412yes—
270C2×#555D1111yescharacteristic
271C2×#552—111no—
272#3348—1116no—
273C2×#501—111no—
274C2×#481—111no—
275C2×#485—111no—
276C2×#485—111no—
277C2×#482—111no—
278C2×#475—111no—
279C2×#478—111no—
280C2×#468—111no—
281C2×#465—111no—
282C2×#440—111no—
283C2×#435—111no—
284C2×#428—111no—
285C2×#427—111no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—42no—
294C23×C11—42no—
295C23×C11—42no—
296C23×C11C22×D412yes—
297C23×C11C22×D412yes—
298C23×C11C22×D411yescharacteristic
299Q8×C11—84no—
300D4×C11—22no—
301D4×C11—22no—
302D4×C11—44no—
303D4×C11—42no—
304D4×C11—84no—
305D4×C11—84no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—24no—
311C2×C4×C11—24no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—48no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11C22×D412yes—
324C2×C4×C11C22×D412yes—
325C2×C4×C11C22×D412yes—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C2×#4112yes—
329C2×C4×C112−1+412yes—
330C2×C4×C11C2511yescharacteristic
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—48no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340Dic22—22no—
341Dic22—22no—
342Dic22—42no—
343C11⋊C8—22no—
344C11⋊C8—22no—
345C11⋊C8—22no—
346C11⋊C8C2×#4114yes—
347C22×SD16—111no—
348C22×M16—111no—
349C23×C8—111no—
350#555—24no—
351#555C2×D1118yes—
352#552—118no—
353#552—224no—
354C2×C4⋊Q8C2×D1111yescharacteristic
355C2×#126—221no—
356C2×#125—111no—
357C2×#125—221no—
358C2×#124—21no—
359C2×#124—21no—
360C2×#123—221no—
361C2×C22⋊Q8—111no—
362C2×C22⋊Q8—111no—
363C2×#121—21no—
364C2×#121C2×D1111yescharacteristic
365C2×#121C2×D1111yescharacteristic
366C2×C4×Q8—111no—
367C2×C4×D4C2×D1111yescharacteristic
368C2×C4×D4C2×D1111yescharacteristic
369C2×#117—21no—
370C2×#117—111no—
371C2×#117—221no—
372C2×#117C2×D1111yescharacteristic
373C2×#117C2×D1111yescharacteristic
374C22×C4⋊C4—111no—
375#501—118no—
376#485—118no—
377#485—118no—
378#482—118no—
379#481—118no—
380#478—118no—
381#475—118no—
382#468—118no—
383#465—118no—
384#440—118no—
385#435—118no—
386#428—118no—
387#427—118no—
388C2×#107—111no—
389C2×#107—111no—
390C2×#107—111no—
391C2×#107—111no—
392C2×#106—111no—
393C2×#106—111no—
394C2×#106—111no—
395C2×#106—111no—
396C2×#106—111no—
397C2×C4⋊C8—111no—
398C2×#103—111no—
399C2×#103—111no—
400C2×#103—111no—
401C2×#102—111no—
402C2×#102—111no—
403C2×#102—111no—
404C2×C22⋊C8—111no—
405C2×C22⋊C8—111no—
406C2×#97—111no—
407C22×C11—22no—
408C22×C11—22no—
409C22×C11—22no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—22no—
413C22×C11—44no—
414C22×C11—44no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—84no—
419C22×C11#54712yes—
420C22×C11#57512yes—
421C22×C11#57712yes—
422C22×C11C23×D411yescharacteristic
423C4×C11—22no—
424C4×C11—22no—
425C4×C11—22no—
426C4×C11—22no—
427C4×C11—42no—
428C4×C11—42no—
429C4×C11—42no—
430C4×C11#54712yes—
431C4×C11C22×#4111yescharacteristic
432C4×C11C2×2−1+411yescharacteristic
433Dic11—42no—
434Dic11—42no—
435Dic11—42no—
436Dic11—42no—
437C22×Q8—21no—
438C22×Q8—111no—
439C22×D4—21no—
440C22×D4—21no—
441C22×D4C22⋊D1111yescharacteristic
442C22×D4C22×D1111yescharacteristic
443C23×C4—21no—
444C23×C4—221no—
445C23×C4C22×D1111yescharacteristic
446C23×C4C22×D1111yescharacteristic
447C2×SD16—114no—
448C2×SD16—224no—
449C2×M16—114no—
450C2×M16—224no—
451C22×C8—111no—
452C22×C8—111no—
453C22×C8—114no—
454C22×C8—111no—
455C22×C8—111no—
456C22×C8—224no—
457C4⋊Q8—22no—
458C4⋊Q8C22×D1114yes—
459#126—228no—
460#125—114no—
461#125—228no—
462#125—222no—
463#124—28no—
464#124—28no—
465#123—228no—
466C22⋊Q8—114no—
467C22⋊Q8—114no—
468C22⋊Q8—222no—
469C22⋊Q8—222no—
470#121—28no—
471#121—22no—
472#121—22no—
473#121C22×D1114yes—
474#121C22×D1114yes—
475C4×Q8—114no—
476C4×Q8—222no—
477C4×D4—22no—
478C4×D4C22⋊D1114yes—
479C4×D4C22×D1114yes—
480C4×D4C22×D1114yes—
481#117—22no—
482#117—22no—
483#117—28no—
484#117—114no—
485#117—222no—
486#117—228no—
487#117C22×D1114yes—
488#117C22×D1114yes—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—111no—
491C2×C4⋊C4—111no—
492C2×C4⋊C4—114no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—221no—
495C2×C4⋊C4—222no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4—221no—
501C2×C4⋊C4C22⋊D1111yescharacteristic
502C2×C4⋊C4C22×D1111yescharacteristic
503C2×C4⋊C4C22×D1111yescharacteristic
504C2×C4⋊C4C22×D1111yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4C22⋊D1111yescharacteristic
514C2×C22⋊C4C22⋊D1111yescharacteristic
515C2×C42—21no—
516C2×C42—21no—
517C2×C42—221no—
518C2×C42—221no—
519C2×C42C22×D1111yescharacteristic
520#107—114no—
521#107—114no—
522#107—114no—
523#107—114no—
524#106—114no—
525#106—114no—
526#106—114no—
527#106—114no—
528#106—114no—
529C4⋊C8—114no—
530#103—114no—
531#103—114no—
532#103—114no—
533#102—114no—
534#102—114no—
535#102—114no—
536C22⋊C8—114no—
537C22⋊C8—114no—
538#97—114no—
539C2×C11—42no—
540C2×C11—42no—
541C2×C11—82no—
542C2×C11#334814yescomplemented
543C2×C11C2×#54711yescharacteristic
544C2×C11C2×#57511yescharacteristic
545C2×C11C2×#57711yescharacteristic
546C24—21no—
547C24C2×C22⋊D1111yescharacteristic
548C24C2×C22⋊D1111yescharacteristic
549C2×Q8—24no—
550C2×Q8—82no—
551C2×Q8—112no—
552C2×Q8—221no—
553C2×Q8—222no—
554C2×Q8—222no—
555C2×D4—24no—
556C2×D4—24no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—42no—
561C2×D4—82no—
562C2×D4—82no—
563C2×D4C2×C22⋊D1114yes—
564C2×D4C23×D1112yes—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—24no—
573C22×C4—44no—
574C22×C4—224no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—221no—
579C22×C4—444no—
580C22×C4C2×C22⋊D1112yes—
581C22×C4C2×C22⋊D1112yes—
582C22×C4C2×C22⋊D1111yescharacteristic
583C22×C4C2×C22⋊D1111yescharacteristic
584C22×C4C2×C22⋊D1111yescharacteristic
585C22×C4C2×C22⋊D1111yescharacteristic
586C22×C4C23×D1112yes—
587C22×C4C23×D1112yes—
588C22×C4C23×D1111yescharacteristic
589SD16—228no—
590M16—228no—
591C2×C8—114no—
592C2×C8—112no—
593C2×C8—112no—
594C2×C8—112no—
595C2×C8—112no—
596C2×C8—228no—
597C2×C8—222no—
598C2×C8—222no—
599C2×C8—222no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—112no—
605C4⋊C4—112no—
606C4⋊C4—112no—
607C4⋊C4—221no—
608C4⋊C4—221no—
609C4⋊C4—224no—
610C4⋊C4—221no—
611C4⋊C4—224no—
612C4⋊C4—224no—
613C4⋊C4—224no—
614C4⋊C4—224no—
615C4⋊C4—224no—
616C4⋊C4C2×C22⋊D1114yes—
617C4⋊C4C23×D1112yes—
618C4⋊C4C23×D1112yes—
619C4⋊C4C23×D1112yes—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—224no—
626C22⋊C4—224no—
627C22⋊C4—224no—
628C22⋊C4C2×C22⋊D1114yes—
629C22⋊C4C2×C22⋊D1114yes—
630C42—24no—
631C42—24no—
632C42—224no—
633C42—224no—
634C42C2×C22⋊D1112yes—
635C42C23×D1112yes—
636C11C2×#334811yescharacteristic, complemented, Sylow
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23C22×C22⋊D1112yes—
648C23C22×C22⋊D1112yes—
649C23C22×C22⋊D1111yescharacteristic
650Q8—84no—
651Q8—222no—
652Q8—222no—
653Q8—442no—
654D4—22no—
655D4—22no—
656D4—44no—
657D4—42no—
658D4—84no—
659D4—84no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—48no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—222no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—448no—
682C2×C4—442no—
683C2×C4—442no—
684C2×C4—442no—
685C2×C4—442no—
686C2×C4#41×D1112yes—
687C2×C4#6704312yes—
688C2×C4C22×C22⋊D1112yes—
689C2×C4C22×C22⋊D1112yes—
690C2×C4C22×C22⋊D1112yes—
691C2×C4C22×C22⋊D1112yes—
692C2×C4C22×C22⋊D1111yescharacteristic
693C2×C4C24×D1111yescharacteristic
694C8—114no—
695C8—222no—
696C8—222no—
697C8—222no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—84no—
710C22#1062335312yes—
711C22#1062335512yes—
712C22#1062336712yes—
713C22C23×C22⋊D1111yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—442no—
722C4—442no—
723C4—442no—
724C4—442no—
725C4#1062335512yes—
726C4C2×#41×D1111yescharacteristic
727C4C2×#6704311yescharacteristic
728C2—42no—
729C2—42no—
730C2—82no—
731C2#1308113114yesdirect product factor
732C2C2×#1062335511yescharacteristic
733C2C2×#1062335311yescharacteristic
734C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#555C2
socleC23×C11C22×D4
hypercenterC2×#555D11
hypocenterC11C2×#3348
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×#10623072C2semidirect
2. #13081131C2direct (N × H)
3. C2×#10622693C2semidirect
4. C2×#10622647C2semidirect
5. C2×#10622609C2semidirect
6. C2×#10622609C2semidirect
7. C2×#10622648C2semidirect
8. C2×#10622707C2semidirect
9. C2×#10622622C2semidirect
10. C2×#10622655C2semidirect
11. C2×#10622654C2semidirect
12. C2×#10622631C2semidirect
13. C2×#10622624C2semidirect
14. C2×#10622608C2semidirect
15. C2×#10622611C2semidirect
39. #10623072C22semidirect
50. #10622707C22semidirect
51. #10622693C22semidirect
52. #10622655C22semidirect
53. #10622654C22semidirect
54. #10622648C22semidirect
55. #10622647C22semidirect
56. #10622631C22semidirect
57. #10622624C22semidirect
58. #10622622C22semidirect
59. #10622611C22semidirect
60. #10622609C22semidirect
61. #10622609C22semidirect
62. #10622608C22semidirect
542. C2×C11#3348semidirect
636. C11C2×#3348semidirect
731. C2#13081131direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230722
#130811312
C2×#106226932
C2×#106226472
C2×#106226092
C2×#106226482
C2×#106227072
C2×#106226222
C2×#106226552
C2×#106226542
C2×#106226312
C2×#106226242
C2×#106226082
C2×#106226112
C2×C11×#5552
C2×#334811