Finite Group Databasebeta

← C4×#10622652 #14760413

Subgroups — C4×#10622652 #14760413

Order 2816.

1170 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×#10622652C211yesmaximal, characteristic
2C2×C4×#4323C211yesmaximal, characteristic, complemented
3C2×C4×#4318C211yesmaximal, characteristic, complemented
4C4×#66983C211yesmaximal, characteristic, complemented
5#13069491C211yesmaximal, characteristic, complemented
6#13069356C211yesmaximal, characteristic, complemented
7#13069316C211yesmaximal, characteristic, complemented
8#13069312C211yesmaximal, characteristic, complemented
9#13069055C211yesmaximal, characteristic, complemented
10#13069052C211yesmaximal, characteristic, complemented
11#13068647C211yesmaximal, characteristic, complemented
12C4×#66872C211yesmaximal, characteristic, complemented
13C4×#66873C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C4×C11×#121C211yesmaximal, characteristic, complemented
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C2×C4×C22⋊D11—21no—
23C22×#4318C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C2×C4×D44C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#388—21no—
29C11×#386—21no—
30C11×#380C2211yescharacteristic
31C4×C11×C4⋊C4C2211yescharacteristic
32C4×C11×C22⋊C4—21no—
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36#10622826—21no—
37#10622825C2211yescharacteristic
38#10622652C418yesdirect product factor
39C4×#4323—24no—
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622553—21no—
47#10622552C2211yescharacteristic
48C4×(C2×D11)⋊C4—21no—
49C4×C4⋊Dic11C2211yescharacteristic
50#10622541C2211yescharacteristic
51C4×#4318—24no—
52C2×#66867C2211yescharacteristic
53C2×#66867C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C2×C4×C11⋊C8C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11D411yescharacteristic
66C23×C4×C11D411yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—21no—
69C22×D44C2311yescharacteristic
70C22×C4×D11—21no—
71C11×#121—22no—
72C11×#121C2×C414yescomplemented
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C4×D4×C11—44no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C42×C11—22no—
86C2×C42×C11—22no—
87C2×C42×C11—21no—
88C2×C42×C11D411yescharacteristic
89C2×C42×C11D411yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C22⋊Dic11—21no—
93C2×#4323—22no—
94C2×#4323—22no—
95C2×#4323C2×C414yescomplemented
96#66983—22no—
97#66983C2×C414yescomplemented
98C4×C22⋊D11—44no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×Dic11⋊C4—21no—
107C2×C4×Dic11—21no—
108C2×#4318—22no—
109C2×#4318—22no—
110C2×#4318—22no—
111C2×#4318—22no—
112C2×#4318—22no—
113C2×#4318C2×C414yescomplemented
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C4×D44—22no—
119C4×D44—22no—
120C11×#95—21no—
121C11×#95—21no—
122C11×#95—21no—
123#66896—22no—
124#66896—22no—
125#66896C2×C414yescomplemented
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129#66873—22no—
130#66873—22no—
131#66873C2×C414yescomplemented
132#66872—22no—
133#66872C2×C414yescomplemented
134#66871—22no—
135#66867—22no—
136#66867—22no—
137C4×C11⋊C8—22no—
138C4×C11⋊C8D414yescomplemented
139C4×#469—111nomaximal, Sylow
140C24×C11—21no—
141C24×C11C2×D411yescharacteristic
142C23×D11—21no—
143C2×D4×C11—24no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11C22×C412yes—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—41no—
164C22×C4×C11—41no—
165C22×C4×C11—42no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11C22×C412yes—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11#4112yes—
175C22×C4×C11C2411yescharacteristic
176C2×C22⋊D11—24no—
177C2×C22⋊D11—42no—
178C2×C22⋊D11—42no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44—21no—
186C2×D44—21no—
187C2×D44C22×C412yes—
188C2×C4×D11—42no—
189C2×C4×D11—42no—
190C2×C4×D11—42no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—42no—
197C11×C4⋊C4C22×C412yes—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—42no—
200C11×C22⋊C4—42no—
201C11×C22⋊C4—42no—
202C11×C22⋊C4—42no—
203C42×C11—22no—
204C42×C11—22no—
205C42×C11—21no—
206C42×C11—21no—
207C42×C11—42no—
208C42×C11C2×D412yes—
209C42×C11#4112yes—
210C22⋊Dic11—42no—
211#4323—28no—
212(C2×D11)⋊C4—24no—
213(C2×D11)⋊C4—42no—
214(C2×D11)⋊C4—42no—
215(C2×D11)⋊C4—42no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11C22×C412yes—
222Dic11⋊C4—42no—
223C4×Dic11—42no—
224#4318—28no—
225#4318—28no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8C22×C412yes—
233C2×C11⋊C8C22×C412yes—
234C2×C11⋊C8C2×D412yes—
235C2×C11⋊C8C2×D412yes—
236C2×C11⋊C8#4112yes—
237C2×C11⋊C8#4112yes—
238C2×#469—111no—
239C2×C4×D8—111no—
240C2×C4×M16—111no—
241C4×#121—111no—
242C4×#121D1111yescharacteristic, complemented
243#1972—111no—
244#1944—111no—
245#1936—111no—
246#1936—111no—
247#1895—111no—
248#1895—111no—
249#1809—111no—
250C4×#106—111no—
251C4×#102—111no—
252C4×#102—111no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—22no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11C4×D412yes—
267C23×C11C22×D411yescharacteristic
268C22×D11—22no—
269C22×D11—41no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275D4×C11—22no—
276D4×C11—22no—
277D4×C11—48no—
278D4×C11—41no—
279D4×C11—41no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—44no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—44no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—84no—
306C2×C4×C11C4×D412yes—
307C2×C4×C11#12112yes—
308C2×C4×C11#12112yes—
309C2×C4×C11AGL(1,ℤ/8)12yes—
310C2×C4×C11AGL(1,ℤ/8)12yes—
311C2×C4×C11C23×C411yescharacteristic
312C2×C4×C11C22×D411yescharacteristic
313C2×C4×C11C2×#4111yescharacteristic
314C2×C4×C11C2×#4111yescharacteristic
315C2×C4×C11C2×#4111yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C22⋊D11—48no—
318C2×Dic11—22no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327D44—22no—
328D44—22no—
329D44—41no—
330D44—41no—
331C4×D11—84no—
332C11⋊C8—22no—
333C11⋊C8—22no—
334C11⋊C8—22no—
335C11⋊C8C4×D414yescomplemented
336C22×D8—111no—
337C22×M16—111no—
338C22×M16—111no—
339C2×#121—111no—
340C2×#121C2×D1111yescharacteristic
341C2×C4×D4—21no—
342C2×C4×D4—111no—
343C2×C4×D4—221no—
344C2×C4×D4C2×D1111yescharacteristic
345C22×C42C2×D1111yescharacteristic
346#469—118no—
347C4×D8—224no—
348C2×#107—111no—
349C2×#106—111no—
350C2×#106—111no—
351C2×#102—111no—
352C2×#102—111no—
353C2×#102—111no—
354C2×#102—111no—
355C2×#102—111no—
356C2×#102—111no—
357C4×M16—224no—
358C2×#97—111no—
359C2×#97—111no—
360C2×C4×C8—111no—
361C2×C4×C8—111no—
362#390—111no—
363#390C2×D1111yescharacteristic
364#389—111no—
365#389C2×D1111yescharacteristic
366#388—21no—
367#388—221no—
368#386—21no—
369#386—221no—
370#380—111no—
371#380C2×D1111yescharacteristic
372C4×C4⋊C4—111no—
373C4×C4⋊C4C2×D1111yescharacteristic
374C4×C22⋊C4—21no—
375C4×C22⋊C4—221no—
376#340—111no—
377#340—111no—
378#340—111no—
379#340—111no—
380#340—111no—
381#340—111no—
382C22×C11—22no—
383C22×C11—22no—
384C22×C11—22no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—42no—
390C22×C11—42no—
391C22×C11—42no—
392C22×C11—81no—
393C22×C11—81no—
394C22×C11—81no—
395C22×C11—81no—
396C22×C11C2×C4×D411yescharacteristic
397C22×C11C2×#12111yescharacteristic
398C22×C11#53211yescharacteristic
399C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
400C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C11#57511yescharacteristic
402C22×C11#57511yescharacteristic
403C2×D11—42no—
404C2×D11—42no—
405C2×D11—42no—
406C2×D11—81no—
407C2×D11—81no—
408C2×D11—81no—
409C2×D11—81no—
410C4×C11—22no—
411C4×C11—22no—
412C4×C11—42no—
413C4×C11—41no—
414C4×C11—41no—
415C4×C11—81no—
416C4×C11—81no—
417C4×C11#46914yescomplemented
418C4×C11C2×C4×D411yescharacteristic
419C4×C11C4×#4111yescharacteristic
420C4×C11#52511yescharacteristic
421C4×C11#52911yescharacteristic
422Dic11—42no—
423Dic11—81no—
424Dic11—81no—
425C22×D4—21no—
426C22×D4—111no—
427C22×D4—221no—
428C22×D4C22×D1111yescharacteristic
429C23×C4—21no—
430C23×C4—221no—
431C23×C4C22⋊D1111yescharacteristic
432C23×C4C22⋊D1111yescharacteristic
433C23×C4C22×D1111yescharacteristic
434C2×D8—114no—
435C2×D8—222no—
436C2×D8—222no—
437C2×M16—114no—
438C2×M16—222no—
439C2×M16—222no—
440C2×M16—222no—
441C2×M16—222no—
442C2×M16—222no—
443C22×C8—111no—
444C22×C8—111no—
445C22×C8—111no—
446C22×C8—111no—
447#121—22no—
448#121—114no—
449#121—222no—
450#121C4×D1114yescomplemented
451C4×D4—22no—
452C4×D4—22no—
453C4×D4—44no—
454C4×D4—222no—
455C4×D4—222no—
456C4×D4—444no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—111no—
459C2×C4⋊C4—111no—
460C2×C4⋊C4—111no—
461C2×C4⋊C4—221no—
462C2×C4⋊C4C22×D1111yescharacteristic
463C2×C4⋊C4C22×D1111yescharacteristic
464C2×C4⋊C4C22×D1111yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—221no—
471C2×C22⋊C4—221no—
472C2×C22⋊C4—221no—
473C2×C22⋊C4—221no—
474C2×C22⋊C4—221no—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—21no—
478C2×C42—221no—
479C2×C42C22⋊D1111yescharacteristic
480C2×C42C22⋊D1111yescharacteristic
481C2×C42C22×D1111yescharacteristic
482C2×C42C22×D1111yescharacteristic
483#107—222no—
484#106—114no—
485#106—222no—
486#102—114no—
487#102—114no—
488#102—222no—
489#102—222no—
490#102—222no—
491#102—222no—
492#97—222no—
493#97—222no—
494C4×C8—114no—
495C4×C8—222no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—221no—
500#95—221no—
501#95—221no—
502C2×C11—42no—
503C2×C11—82no—
504C2×C11C4×#12111yescharacteristic
505C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
506C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
507C2×C11C2×#46911yescharacteristic
508C2×C11#305411yescharacteristic
509C2×C11#317111yescharacteristic
510C2×C11#317111yescharacteristic
511D11—82no—
512C24—21no—
513C24—221no—
514C24C2×C22⋊D1111yescharacteristic
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—112no—
524C2×D4—224no—
525C2×D4—221no—
526C2×D4—221no—
527C2×D4—221no—
528C2×D4—221no—
529C2×D4—221no—
530C2×D4—442no—
531C2×D4—442no—
532C2×D4C2×C4×D1112yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—221no—
550C22×C4—221no—
551C22×C4—221no—
552C22×C4—442no—
553C22×C4—442no—
554C22×C4—442no—
555C22×C4C2×C4×D1112yes—
556C22×C4#433912yes—
557C22×C4C2×C22⋊D1111yescharacteristic
558C22×C4C2×C22⋊D1111yescharacteristic
559C22×C4C2×C22⋊D1111yescharacteristic
560C22×C4C2×C22⋊D1111yescharacteristic
561C22×C4C2×C22⋊D1111yescharacteristic
562C22×C4C23×D1111yescharacteristic
563D8—228no—
564M16—228no—
565M16—228no—
566C2×C8—112no—
567C2×C8—112no—
568C2×C8—112no—
569C2×C8—112no—
570C2×C8—112no—
571C2×C8—112no—
572C2×C8—221no—
573C2×C8—221no—
574C2×C8—221no—
575C2×C8—221no—
576C2×C8—221no—
577C2×C8—221no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—42no—
584C4⋊C4—112no—
585C4⋊C4—221no—
586C4⋊C4—221no—
587C4⋊C4—221no—
588C4⋊C4—221no—
589C4⋊C4—221no—
590C4⋊C4—442no—
591C4⋊C4C2×C4×D1112yes—
592C22⋊C4—24no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—224no—
598C22⋊C4—442no—
599C22⋊C4—442no—
600C22⋊C4—442no—
601C22⋊C4—442no—
602C42—22no—
603C42—22no—
604C42—21no—
605C42—21no—
606C42—42no—
607C42—442no—
608C42D4×D1112yes—
609C42#434112yes—
610C11C4×#46911yescharacteristic, complemented, Sylow
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—222no—
625C23—441no—
626C23—441no—
627C23—441no—
628C23—441no—
629C23—441no—
630C23—441no—
631C23C4×C22⋊D1112yes—
632C23C22×C22⋊D1111yescharacteristic
633D4—22no—
634D4—22no—
635D4—48no—
636D4—41no—
637D4—41no—
638D4—222no—
639D4—222no—
640D4—448no—
641D4—441no—
642D4—441no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—44no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—44no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—84no—
669C2×C4—222no—
670C2×C4—441no—
671C2×C4—441no—
672C2×C4—441no—
673C2×C4—441no—
674C2×C4—441no—
675C2×C4—441no—
676C2×C4—441no—
677C2×C4—441no—
678C2×C4—884no—
679C2×C4C4×C22⋊D1112yes—
680C2×C4#6698512yes—
681C2×C4#6699212yes—
682C2×C4#6699212yes—
683C2×C4#6700212yes—
684C2×C4C22×C4×D1111yescharacteristic
685C2×C4C2×#433911yescharacteristic
686C2×C4C2×D4×D1111yescharacteristic
687C2×C4C2×#434111yescharacteristic
688C2×C4#41×D1111yescharacteristic
689C2×C4#41×D1111yescharacteristic
690C8—114no—
691C8—222no—
692C8—222no—
693C8—222no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—442no—
709C22—442no—
710C22—442no—
711C22—881no—
712C22—881no—
713C22—881no—
714C22—881no—
715C22C2×C4×C22⋊D1111yescharacteristic
716C22C2×#6698511yescharacteristic
717C22C2×#6699211yescharacteristic
718C22C2×#6700211yescharacteristic
719C22#1062335311yescharacteristic
720C22#1062335311yescharacteristic
721C22#1062336311yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—41no—
726C4—41no—
727C4—81no—
728C4—81no—
729C4—442no—
730C4—881no—
731C4—881no—
732C4#1062265214yesdirect product factor
733C4C4×#434111yescharacteristic
734C4#1062306911yescharacteristic
735C4C4×D4×D1111yescharacteristic
736C4#1062307811yescharacteristic
737C2—42no—
738C2—82no—
739C2—882no—
740C2C4×#6699211yescharacteristic
741C2C4×#6700211yescharacteristic
742C2C4×#6698511yescharacteristic
743C2C2×#1062265211yescharacteristic
744C2#1307822211yescharacteristic
745C2#1307920511yescharacteristic
746C2#1307921211yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#121C2
socleC23×C11C22×D4
prime radicalC2×#10622652C2
cosocleC22×C4×C11C24
hypercenterC4×#121D11
hypocenterC11C4×#469
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4323C2semidirect
3. C2×C4×#4318C2semidirect
4. C4×#66983C2semidirect
5. #13069491C2semidirect
6. #13069356C2semidirect
7. #13069316C2semidirect
8. #13069312C2semidirect
9. #13069055C2semidirect
10. #13069052C2semidirect
11. #13068647C2semidirect
12. C4×#66872C2semidirect
13. C4×#66873C2semidirect
14. C4×#66896C2semidirect
15. C4×C11×#121C2semidirect
38. #10622652C4direct (N × H)
72. C11×#121C2×C4semidirect
95. C2×#4323C2×C4semidirect
97. #66983C2×C4semidirect
113. C2×#4318C2×C4semidirect
125. #66896C2×C4semidirect
131. #66873C2×C4semidirect
133. #66872C2×C4semidirect
138. C4×C11⋊C8D4semidirect
242. C4×#121D11semidirect
335. C11⋊C8C4×D4semidirect
417. C4×C11#469semidirect
450. #121C4×D11semidirect
610. C11C4×#469semidirect
732. C4#10622652direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226522
C2×C4×#43232
C2×C4×#43182
C4×#669832
#130694912
#130693562
#130693162
#130693122
#130690552
#130690522
#130686472
C4×#668722
C4×#668732
C4×#668962
C4×C11×#1212
C4×#46911