Finite Group Databasebeta

← C2×#13081101 #15632352

Subgroups — C2×#13081101 #15632352

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
2#13081101C2116yesmaximal, direct product factor
3C2×#10622678C211yesmaximal, characteristic, complemented
4C2×#10622583C211yesmaximal, characteristic, complemented
5C2×#10622647C211yesmaximal, characteristic, complemented
6C2×#10622609C211yesmaximal, characteristic, complemented
7C2×#10622646C211yesmaximal, characteristic, complemented
8C2×#10622676C211yesmaximal, characteristic, complemented
9C2×#10622620C211yesmaximal, characteristic, complemented
10C2×#10622655C211yesmaximal, characteristic, complemented
11C2×#10622654C211yesmaximal, characteristic, complemented
12C2×#10622631C211yesmaximal, characteristic, complemented
13C2×#10622624C211yesmaximal, characteristic, complemented
14C2×#10622608C211yesmaximal, characteristic, complemented
15C22×#66871C211yesmaximal, characteristic, complemented
16C2×C11×#553C211yesmaximal, characteristic
17C11×#553—24no—
18C11×#553C2218yes—
19C2×C11×#126—21no—
20C2×C11×#125C2211yescharacteristic
21C2×C11×#123—21no—
22C2×C11×#121—21no—
23C2×C11×#121C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C2×C4×D4×C11—21no—
26C2×C4×D4×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C2×D4×Dic11—21no—
31C22×#4324C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C2×#66977C2211yescharacteristic
35C2×#66977C2211yescharacteristic
36C22×#4318C2211yescharacteristic
37C23×C11⋊C8C2211yescharacteristic
38#10623074—24no—
39#10623074C2218yescomplemented
40C2×#66943—21no—
41C2×#66931—21no—
42C2×#66931—21no—
43C2×#66922C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46C2×#66896C2211yescharacteristic
47C2×#66896C2211yescharacteristic
48C2×C22⋊(C11⋊C8)C2211yescharacteristic
49C2×C22⋊(C11⋊C8)C2211yescharacteristic
50#10622678C2218yescomplemented
51#10622676C2218yescomplemented
52#10622655C2218yescomplemented
53#10622654C2218yescomplemented
54#10622647C2218yescomplemented
55#10622646C2218yescomplemented
56#10622631C2218yescomplemented
57#10622624C2218yescomplemented
58#10622620C2218yescomplemented
59#10622609C2218yescomplemented
60#10622608C2218yescomplemented
61#10622583C2218yescomplemented
62C2×#66874C2211yescharacteristic
63C2×#66874C2211yescharacteristic
64C2×#66874C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66872C2211yescharacteristic
68C2×#66871C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71C2×#66871C2211yescharacteristic
72C2×#66871C2211yescharacteristic
73C2×#66871C2211yescharacteristic
74C2×#66871C2218yescomplemented
75C2×C4⋊(C11⋊C8)C2211yescharacteristic
76C2×#66867C2211yescharacteristic
77C22×D4×C11—21no—
78C22×D4×C11—21no—
79C22×D4×C11D411yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11—21no—
82C23×C4×C11—21no—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×Dic11—21no—
86C23×Dic11—21no—
87C22×Dic22—21no—
88C22×Dic22C2311yescharacteristic
89C11×#126—28no—
90C11×#125—22no—
91C11×#125C2314yes—
92C11×#123—28no—
93C11×#121—28no—
94C11×#121—22no—
95C11×#121—22no—
96C11×#121C2314yes—
97C11×#121C2314yes—
98C4×D4×C11—28no—
99C4×D4×C11—22no—
100C4×D4×C11D414yes—
101C4×D4×C11C2314yes—
102C4×D4×C11C2314yes—
103C11×#117—22no—
104C11×#117C2314yes—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—22no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4D411yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2314yes—
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C11×C22⋊C4D411yescharacteristic
119C2×C11×C22⋊C4D411yescharacteristic
120C2×C42×C11—21no—
121C2×C42×C11C2311yescharacteristic
122C2×C22⋊Dic11—21no—
123C2×C22⋊Dic11—21no—
124D4×Dic11—28no—
125C2×#4324—24no—
126C2×#4324C2314yes—
127C2×C4⋊Dic11—21no—
128C2×C4⋊Dic11—21no—
129C2×C4⋊Dic11—21no—
130C2×C4⋊Dic11—22no—
131C2×C4⋊Dic11—22no—
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2311yescharacteristic
134C2×C4⋊Dic11C2311yescharacteristic
135C2×C4⋊Dic11C2314yes—
136C2×C4⋊Dic11C2314yes—
137#66977—22no—
138#66977—22no—
139#66977C2314yes—
140#66977C2314yes—
141C2×Dic11⋊C4—21no—
142C2×Dic11⋊C4—21no—
143C2×Dic11⋊C4—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#66943—28no—
154#66931—28no—
155#66931—28no—
156#66922—22no—
157#66922C2314yes—
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#66871C2314yes—
172#66871C2314yes—
173#66871C2314yes—
174#66871C2314yes—
175#66871C2314yes—
176#66871C2314yes—
177C4⋊(C11⋊C8)C2314yes—
178#66867C2314yes—
179C2×#3346—111nomaximal, Sylow
180C24×C11—21no—
181C24×C11C2×D411yescharacteristic
182C24×C11C2×D411yescharacteristic
183C2×D4×C11—24no—
184C2×D4×C11—24no—
185C2×D4×C11—24no—
186C2×D4×C11—21no—
187C2×D4×C11—22no—
188C2×D4×C11—22no—
189C2×D4×C11—44no—
190C2×D4×C11—82no—
191C2×D4×C11C2×D414yes—
192C2×D4×C11C2412yes—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—22no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—24no—
201C22×C4×C11—24no—
202C22×C4×C11—82no—
203C22×C4×C11—82no—
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—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—24no—
218C22×Dic11—24no—
219C22×Dic11—82no—
220C22×Dic11—82no—
221C2×Dic22—21no—
222C2×Dic22—24no—
223C2×Dic22—22no—
224C2×Dic22—22no—
225C2×Dic22—82no—
226C2×Dic22C2412yes—
227C11×C4⋊C4—21no—
228C11×C4⋊C4—21no—
229C11×C4⋊C4—24no—
230C11×C4⋊C4—24no—
231C11×C4⋊C4—24no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4C2×D414yes—
234C11×C4⋊C4C2412yes—
235C11×C4⋊C4C2412yes—
236C11×C4⋊C4C2412yes—
237C11×C22⋊C4—24no—
238C11×C22⋊C4—24no—
239C11×C22⋊C4—24no—
240C11×C22⋊C4—24no—
241C11×C22⋊C4C2×D414yes—
242C11×C22⋊C4C2×D414yes—
243C42×C11—24no—
244C42×C11C2×D412yes—
245C42×C11C2412yes—
246C22⋊Dic11—24no—
247C22⋊Dic11—24no—
248#4324—28no—
249C4⋊Dic11—21no—
250C4⋊Dic11—21no—
251C4⋊Dic11—21no—
252C4⋊Dic11—24no—
253C4⋊Dic11—24no—
254C4⋊Dic11—24no—
255C4⋊Dic11C2412yes—
256C4⋊Dic11C2412yes—
257C4⋊Dic11C2412yes—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261C4×Dic11—24no—
262#4318—28no—
263C2×C11⋊C8—28no—
264C2×C11⋊C8—22no—
265C2×C11⋊C8—22no—
266C2×C11⋊C8—22no—
267C2×C11⋊C8#4114yes—
268C2×C11⋊C8C2412yes—
269C2×C11⋊C8C2412yes—
270C2×C11⋊C8C2412yes—
271C2×C11⋊C8C2412yes—
272C2×#554—111no—
273C2×#553D1111yescharacteristic
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×#435—111no—
286C2×#428—111no—
287C22×#107—111no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—42no—
295C23×C11—42no—
296C23×C11—42no—
297C23×C11#13714yes—
298C23×C11C22×D412yes—
299C23×C11C22×D412yes—
300C23×C11C22×D411yescharacteristic
301D4×C11—28no—
302D4×C11—22no—
303D4×C11—22no—
304D4×C11—48no—
305D4×C11—42no—
306D4×C11—84no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—24no—
312C2×C4×C11—24no—
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—22no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11—84no—
324C2×C4×C11—84no—
325C2×C4×C11C22×D412yes—
326C2×C4×C11C22×D412yes—
327C2×C4×C11C22×D412yes—
328C2×C4×C11C22×D412yes—
329C2×C4×C11C22×D411yescharacteristic
330C2×C4×C11C2×#4112yes—
331C2×C4×C112−1+412yes—
332C2×C4×C11C2511yescharacteristic
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—84no—
342C2×Dic11—84no—
343Dic22—22no—
344Dic22—22no—
345Dic22—42no—
346Dic22—84no—
347C11⋊C8—22no—
348C11⋊C8—22no—
349C11⋊C8—22no—
350C11⋊C8C2×#4114yes—
351C22×SD16—111no—
352C22×M16—111no—
353C23×C8—111no—
354#554—118no—
355#554—224no—
356#553—24no—
357#553C2×D1118yes—
358C2×C4⋊Q8—111no—
359C2×#126—21no—
360C2×#125—221no—
361C2×#125C2×D1111yescharacteristic
362C2×#123—21no—
363C2×C22⋊Q8—111no—
364C2×C22⋊Q8—111no—
365C2×C22⋊Q8—221no—
366C2×C22⋊Q8—221no—
367C2×#121—21no—
368C2×#121C2×D1111yescharacteristic
369C2×#121C2×D1111yescharacteristic
370C2×C4×Q8—111no—
371C2×C4×D4—21no—
372C2×C4×D4—221no—
373C2×C4×D4C2×D1111yescharacteristic
374C2×C4×D4C2×D1111yescharacteristic
375C2×#117C2×D1111yescharacteristic
376C22×C4⋊C4—111no—
377C22×C4⋊C4—111no—
378C22×C4⋊C4C2×D1111yescharacteristic
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#435—118no—
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⋊C8—111no—
402C2×#103—111no—
403C2×#103—111no—
404C2×#103—111no—
405C2×#102—111no—
406C2×#102—111no—
407C2×#102—111no—
408C2×C22⋊C8—111no—
409C2×C22⋊C8—111no—
410C2×#97—111no—
411C22×C11—28no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—44no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—84no—
422C22×C11#54712yes—
423C22×C11C2×#13714yes—
424C22×C11C2×#13712yes—
425C22×C11#57612yes—
426C22×C11C23×D411yescharacteristic
427C4×C11—22no—
428C4×C11—22no—
429C4×C11—22no—
430C4×C11—22no—
431C4×C11—42no—
432C4×C11—42no—
433C4×C11—42no—
434C4×C11#54712yes—
435C4×C11C22×#4111yescharacteristic
436C4×C11C2×2−1+411yescharacteristic
437Dic11—42no—
438Dic11—42no—
439Dic11—42no—
440Dic11—42no—
441C22×Q8—111no—
442C22×Q8—221no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4C22⋊D1111yescharacteristic
446C22×D4C22×D1111yescharacteristic
447C23×C4—21no—
448C23×C4—21no—
449C23×C4—221no—
450C23×C4—221no—
451C23×C4C22×D1111yescharacteristic
452C23×C4C22×D1111yescharacteristic
453C2×SD16—114no—
454C2×SD16—224no—
455C2×M16—114no—
456C2×M16—224no—
457C22×C8—111no—
458C22×C8—111no—
459C22×C8—114no—
460C22×C8—111no—
461C22×C8—111no—
462C22×C8—224no—
463C4⋊Q8—114no—
464C4⋊Q8—222no—
465#126—28no—
466#125—22no—
467#125—228no—
468#125C22×D1114yes—
469#123—28no—
470C22⋊Q8—114no—
471C22⋊Q8—114no—
472C22⋊Q8—222no—
473C22⋊Q8—222no—
474C22⋊Q8—228no—
475C22⋊Q8—228no—
476#121—28no—
477#121—22no—
478#121—22no—
479#121C22×D1114yes—
480#121C22×D1114yes—
481C4×Q8—114no—
482C4×Q8—222no—
483C4×D4—28no—
484C4×D4—22no—
485C4×D4—228no—
486C4×D4C22⋊D1114yes—
487C4×D4C22×D1114yes—
488C4×D4C22×D1114yes—
489#117—22no—
490#117C22×D1114yes—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—111no—
497C2×C4⋊C4—111no—
498C2×C4⋊C4—114no—
499C2×C4⋊C4—114no—
500C2×C4⋊C4—221no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4—222no—
503C2×C4⋊C4—222no—
504C2×C4⋊C4—221no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4C22⋊D1111yescharacteristic
509C2×C4⋊C4C22×D1111yescharacteristic
510C2×C4⋊C4C22×D1111yescharacteristic
511C2×C4⋊C4C22×D1114yes—
512C2×C4⋊C4C22×D1111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4C22⋊D1111yescharacteristic
520C2×C22⋊C4C22⋊D1111yescharacteristic
521C2×C42—21no—
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⋊C8—114no—
534#103—114no—
535#103—114no—
536#103—114no—
537#102—114no—
538#102—114no—
539#102—114no—
540C22⋊C8—114no—
541C22⋊C8—114no—
542#97—114no—
543C2×C11—24no—
544C2×C11—42no—
545C2×C11—82no—
546C2×C11#334614yescomplemented
547C2×C11C2×#54711yescharacteristic
548C2×C11C22×#13711yescharacteristic
549C2×C11C2×#57611yescharacteristic
550C24—21no—
551C24C2×C22⋊D1111yescharacteristic
552C24C2×C22⋊D1111yescharacteristic
553C2×Q8—112no—
554C2×Q8—221no—
555C2×Q8—224no—
556C2×Q8—222no—
557C2×Q8—222no—
558C2×Q8—882no—
559C2×D4—24no—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—44no—
566C2×D4—82no—
567C2×D4C2×C22⋊D1114yes—
568C2×D4C23×D1112yes—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—82no—
579C22×C4—82no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—224no—
585C22×C4—224no—
586C22×C4—882no—
587C22×C4—882no—
588C22×C4C2×C22⋊D1112yes—
589C22×C4C2×C22⋊D1112yes—
590C22×C4C2×C22⋊D1111yescharacteristic
591C22×C4C2×C22⋊D1111yescharacteristic
592C22×C4C2×C22⋊D1111yescharacteristic
593C22×C4C2×C22⋊D1111yescharacteristic
594C22×C4C23×D1112yes—
595C22×C4C23×D1112yes—
596C22×C4C23×D1111yescharacteristic
597SD16—228no—
598M16—228no—
599C2×C8—114no—
600C2×C8—112no—
601C2×C8—112no—
602C2×C8—112no—
603C2×C8—112no—
604C2×C8—228no—
605C2×C8—222no—
606C2×C8—222no—
607C2×C8—222no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—112no—
615C4⋊C4—112no—
616C4⋊C4—112no—
617C4⋊C4—221no—
618C4⋊C4—224no—
619C4⋊C4—224no—
620C4⋊C4—221no—
621C4⋊C4—221no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—224no—
626C4⋊C4C2×C22⋊D1114yes—
627C4⋊C4C23×D1112yes—
628C4⋊C4C23×D1112yes—
629C4⋊C4C23×D1112yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C22⋊C4C2×C22⋊D1114yes—
637C22⋊C4C2×C22⋊D1114yes—
638C42—24no—
639C42—224no—
640C42C2×C22⋊D1112yes—
641C42C23×D1112yes—
642C11C2×#334611yescharacteristic, complemented, Sylow
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23#6700414yes—
653C23C22×C22⋊D1112yes—
654C23C22×C22⋊D1112yes—
655C23C22×C22⋊D1111yescharacteristic
656Q8—222no—
657Q8—222no—
658Q8—442no—
659Q8—884no—
660D4—28no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—42no—
665D4—84no—
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—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—84no—
683C2×C4—84no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—442no—
689C2×C4—442no—
690C2×C4—442no—
691C2×C4—442no—
692C2×C4—884no—
693C2×C4—884no—
694C2×C4#41×D1112yes—
695C2×C4#6704312yes—
696C2×C4C22×C22⋊D1112yes—
697C2×C4C22×C22⋊D1112yes—
698C2×C4C22×C22⋊D1112yes—
699C2×C4C22×C22⋊D1112yes—
700C2×C4C22×C22⋊D1111yescharacteristic
701C2×C4C24×D1111yescharacteristic
702C8—114no—
703C8—222no—
704C8—222no—
705C8—222no—
706C22—28no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22C2×#6700414yes—
718C22C2×#6700412yes—
719C22#1062335512yes—
720C22#1062336612yes—
721C22C23×C22⋊D1111yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—442no—
730C4—442no—
731C4—442no—
732C4—442no—
733C4#1062335512yes—
734C4C2×#41×D1111yescharacteristic
735C4C2×#6704311yescharacteristic
736C2—24no—
737C2—42no—
738C2—82no—
739C2#1308110114yesdirect product factor
740C2C2×#1062335511yescharacteristic
741C2C22×#6700411yescharacteristic
742C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#553C2
socleC23×C11C22×D4
hypercenterC2×#553D11
hypocenterC11C2×#3346
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#10623074C2semidirect
2. #13081101C2direct (N × H)
3. C2×#10622678C2semidirect
4. C2×#10622583C2semidirect
5. C2×#10622647C2semidirect
6. C2×#10622609C2semidirect
7. C2×#10622646C2semidirect
8. C2×#10622676C2semidirect
9. C2×#10622620C2semidirect
10. C2×#10622655C2semidirect
11. C2×#10622654C2semidirect
12. C2×#10622631C2semidirect
13. C2×#10622624C2semidirect
14. C2×#10622608C2semidirect
15. C22×#66871C2semidirect
39. #10623074C22semidirect
50. #10622678C22semidirect
51. #10622676C22semidirect
52. #10622655C22semidirect
53. #10622654C22semidirect
54. #10622647C22semidirect
55. #10622646C22semidirect
56. #10622631C22semidirect
57. #10622624C22semidirect
58. #10622620C22semidirect
59. #10622609C22semidirect
60. #10622608C22semidirect
61. #10622583C22semidirect
74. C2×#66871C22semidirect
546. C2×C11#3346semidirect
642. C11C2×#3346semidirect
739. C2#13081101direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230742
#130811012
C2×#106226782
C2×#106225832
C2×#106226472
C2×#106226092
C2×#106226462
C2×#106226762
C2×#106226202
C2×#106226552
C2×#106226542
C2×#106226312
C2×#106226242
C2×#106226082
C22×#668712
C2×C11×#5532
C2×#334611