Finite Group Databasebeta

← #14770255

Subgroups — #14770255

Order 2816.

1262 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#4318C211yesmaximal, characteristic, complemented
2C4×D4×Dic11C211yesmaximal, characteristic, complemented
3#13069594C211yesmaximal, characteristic, complemented
4#13069561C211yesmaximal, characteristic, complemented
5#13069060C212yesmaximal, complemented
6#13068919C212yesmaximal, complemented
7#13068715C212yesmaximal, complemented
8#13068636C211yesmaximal, characteristic, complemented
9C4×#66901C211yesmaximal, characteristic, complemented
10C2×#10622170C212yesmaximal, complemented
11C11×#3475C211yesmaximal, characteristic
12C11×#556C411yescharacteristic, complemented
13C11×#555C411yescharacteristic, complemented
14C11×#554C411yescharacteristic, complemented
15C11×#553C412yescomplemented
16C11×#552—21no—
17C11×#552C412yescomplemented
18C11×#551—22no—
19C11×#547C411yescharacteristic, complemented
20C11×#546—21no—
21C11×#533C2211yescharacteristic
22C11×#529—22no—
23C11×#529—21no—
24C11×#525C2212yes—
25C4×C11×#41—21no—
26C4×C11×#41C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C2×C11×#117C2212yes—
29C2×D4×Dic11—21no—
30C22×C4×Dic11C2212yes—
31C22×#4318C2212yes—
32C2×#66901C2211yescharacteristic
33C2×#66901C2211yescharacteristic
34C2×#66901C2212yes—
35C4×C22⋊Dic11C2212yes—
36#10622820C2212yes—
37#10622625—21no—
38#10622624—22no—
39D4×C11⋊C8—21no—
40C4⋊C4×Dic11—21no—
41C22⋊C4×Dic11—22no—
42C4×C4⋊Dic11C2211yescharacteristic
43C42×Dic11C2211yescharacteristic
44#10622537C2211yescharacteristic
45C4×#4318C2211yescharacteristic
46#10622170C2212yes—
47#10622170C2212yes—
48#10622170C2212yes—
49#10622170C2211yescharacteristic
50#10622170C2212yes—
51#10622170C2212yes—
52#10622170C2211yescharacteristic
53C2×C11×#41—21no—
54C2×C11×#41C2311yescharacteristic
55C22×D4×C11D411yescharacteristic
56C23×C4×C11C2312yes—
57C23×Dic11—22no—
58C11×C4⋊Q8C2×C411yescharacteristic, complemented
59C11×C4⋊Q8C2×C411yescharacteristic, complemented
60C11×#126—22no—
61C11×#126—22no—
62C11×#126—22no—
63C11×#125—22no—
64C11×#125—21no—
65C11×#125C2×C412yescomplemented
66C11×#124—21no—
67C11×#124—22no—
68C11×#123—22no—
69C11×#123—22no—
70C11×#123—22no—
71C11×#123—22no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8C2×C412yescomplemented
77C11×C22⋊Q8C2×C412yescomplemented
78C11×#121—22no—
79C11×#121—21no—
80C11×#121C2×C412yescomplemented
81C11×#121C2×C412yescomplemented
82C11×#120—22no—
83C4×Q8×C11—21no—
84C4×Q8×C11—21no—
85C4×Q8×C11—21no—
86C4×Q8×C11C2×C411yescharacteristic, complemented
87C4×Q8×C11C2×C411yescharacteristic, complemented
88C4×D4×C11—21no—
89C4×D4×C11—22no—
90C4×D4×C11—21no—
91C4×D4×C11—21no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11C2×C411yescharacteristic
95C4×D4×C11C2×C412yes—
96C4×D4×C11C2×C411yescharacteristic
97C4×D4×C11C2×C411yescharacteristic, complemented
98C4×D4×C11C2×C411yescharacteristic, complemented
99C4×D4×C11D411yescharacteristic
100C4×D4×C11D412yes—
101C4×D4×C11D411yescharacteristic
102C11×#117—22no—
103C11×#117—22no—
104C11×#117—21no—
105C11×#117—22no—
106C11×#117—21no—
107C11×#117C2×C412yescomplemented
108C11×#117C2×C412yescomplemented
109C11×#117C2311yescharacteristic
110C11×#117C2312yes—
111C2×C11×C4⋊C4C2×C412yescomplemented
112C2×C11×C4⋊C4C2×C412yescomplemented
113C2×C11×C4⋊C4D411yescharacteristic
114C2×C11×C22⋊C4—22no—
115C2×C11×C22⋊C4D412yes—
116C2×C42×C11—22no—
117C2×C42×C11—21no—
118C2×C42×C11C2311yescharacteristic
119C2×C22⋊Dic11—22no—
120D4×Dic11—28no—
121C2×C4⋊Dic11—21no—
122C2×C4×Dic11—21no—
123C2×C4×Dic11—24no—
124C2×C4×Dic11—21no—
125C2×C4×Dic11—22no—
126C2×C4×Dic11—42no—
127C2×C4×Dic11C2311yescharacteristic
128C2×C4×Dic11C2312yes—
129C2×C4×Dic11C2311yescharacteristic
130C2×#4318—22no—
131C2×#4318—24no—
132C2×#4318—42no—
133C2×#4318C2311yescharacteristic
134C2×#4318C2312yes—
135C2×#4318C2311yescharacteristic
136C22×C11⋊C8—22no—
137#66901—22no—
138#66901—22no—
139#66901—42no—
140C11⋊#95—21no—
141C11⋊#95—22no—
142C22⋊(C11⋊C8)—22no—
143C22⋊(C11⋊C8)—22no—
144C4⋊(C11⋊C8)—21no—
145C4⋊(C11⋊C8)—21no—
146#66867—21no—
147C4×C11⋊C8—21no—
148#22505—111nomaximal, Sylow
149C24×C11C2×D412yes—
150C11×#41—21no—
151C11×#41—21no—
152C11×#41—21no—
153C11×#41—21no—
154C11×#41—44no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11C22×C411yescharacteristic
158C2×D4×C11—24no—
159C2×D4×C11—22no—
160C2×D4×C11—21no—
161C2×D4×C11—22no—
162C2×D4×C11C22⋊C412yes—
163C2×D4×C11C22⋊C411yescharacteristic
164C2×D4×C11C22⋊C411yescharacteristic
165C2×D4×C11C22×C411yescharacteristic
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11C22×C412yes—
176C22×C4×C11C22×C412yes—
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2×D412yes—
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2411yescharacteristic
183C22×Dic11—28no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—22no—
187C22×Dic11—44no—
188C22×Dic11—44no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4C22⋊C411yescharacteristic
200C11×C4⋊C4C22⋊C411yescharacteristic
201C11×C4⋊C4C22⋊C412yes—
202C11×C4⋊C4C22×C411yescharacteristic
203C11×C4⋊C4C22×C411yescharacteristic
204C11×C4⋊C4C22×C412yes—
205C11×C4⋊C4C22×C412yes—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—21no—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—21no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4C22⋊C412yes—
217C11×C22⋊C4C22⋊C412yes—
218C11×C22⋊C4C22⋊C412yes—
219C11×C22⋊C4C22⋊C412yes—
220C42×C11—22no—
221C42×C11—21no—
222C42×C11—22no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—22no—
226C42×C11C22×C411yescharacteristic
227C42×C11C22×C411yescharacteristic
228C42×C11C2×D411yescharacteristic
229C42×C11C2×D411yescharacteristic
230C22⋊Dic11—28no—
231C4⋊Dic11—24no—
232C4×Dic11—24no—
233C4×Dic11—21no—
234C4×Dic11—22no—
235C4×Dic11—21no—
236C4×Dic11—22no—
237C4×Dic11—21no—
238C4×Dic11—44no—
239C4×Dic11—42no—
240C4×Dic11#4112yescomplemented
241#4318—21no—
242#4318—22no—
243#4318—21no—
244#4318—22no—
245#4318—21no—
246#4318—44no—
247#4318#4112yescomplemented
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—22no—
251C2×C11⋊C8—44no—
252#3475D1111yescharacteristic
253D4×M16—111no—
254C42×D4—111no—
255#1994—111no—
256#1986—111no—
257#1896—112no—
258#1871—112no—
259#1826—112no—
260#1806—111no—
261C4×#104—111no—
262C2×#339—112no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—24no—
266C23×C11—21no—
267C23×C11—42no—
268C23×C11C2×C22⋊C412yes—
269C23×C11C2×C22⋊C412yes—
270C23×C11C22×D411yescharacteristic
271Q8×C11—21no—
272Q8×C11—21no—
273Q8×C11—42no—
274Q8×C11—81no—
275D4×C11—24no—
276D4×C11—21no—
277D4×C11—21no—
278D4×C11—22no—
279D4×C11—41no—
280D4×C11—41no—
281D4×C11—44no—
282D4×C11—82no—
283D4×C11#10414yescomplemented
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—41no—
301C2×C4×C11—44no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—42no—
305C2×C4×C11—81no—
306C2×C4×C11—82no—
307C2×C4×C11C2×C22⋊C412yes—
308C2×C4×C11C2×C22⋊C411yescharacteristic
309C2×C4×C11C2×C22⋊C411yescharacteristic
310C2×C4×C11C2×C22⋊C411yescharacteristic
311C2×C4×C11C2×C22⋊C412yes—
312C2×C4×C11C2×C22⋊C411yescharacteristic
313C2×C4×C11C23×C411yescharacteristic
314C2×C4×C11C22×D411yescharacteristic
315C2×C4×C11C2×#4111yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11H(5,𝔽2)11yescharacteristic
318C2×C4×C112−1+411yescharacteristic
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—24no—
324C2×Dic11—416no—
325C2×Dic11—41no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—41no—
329C11⋊C8—22no—
330C11⋊C8—42no—
331C11⋊C8—41no—
332C22×M16—112no—
333#556Dic1111yescharacteristic, complemented
334#555Dic1111yescharacteristic, complemented
335#554Dic1111yescharacteristic, complemented
336#553Dic1112yescomplemented
337#552—21no—
338#552Dic1112yescomplemented
339#551—22no—
340#547Dic1111yescharacteristic, complemented
341#546—21no—
342#533C2×D1111yescharacteristic
343#529—22no—
344#529—21no—
345#525C2×D1112yes—
346C4×#41—21no—
347C4×#41C2×D1111yescharacteristic
348C2×C4×D4—221no—
349C2×C4×D4C2×D1111yescharacteristic
350C2×#117C2×D1112yes—
351C22×C42—112no—
352#436—221no—
353#435—222no—
354C8×D4—221no—
355#423—111no—
356C2×#104—111no—
357C2×#104—111no—
358C2×#104—112no—
359#407—112no—
360C4×M16—111no—
361C4×C4⋊C4—111no—
362C4×C4⋊C4—221no—
363C4×C22⋊C4—112no—
364C4×C22⋊C4—222no—
365C43—111no—
366#339—112no—
367#339—111no—
368#339—112no—
369#339—112no—
370#339—112no—
371#339—112no—
372#339—111no—
373C22×C11—22no—
374C22×C11—21no—
375C22×C11—21no—
376C22×C11—22no—
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—44no—
381C22×C11—44no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11C2×#10414yes—
386C22×C11C22×C22⋊C411yescharacteristic
387C22×C11#54611yescharacteristic
388C22×C11#54711yescharacteristic
389C4×C11—22no—
390C4×C11—22no—
391C4×C11—21no—
392C4×C11—21no—
393C4×C11—21no—
394C4×C11—41no—
395C4×C11—41no—
396C4×C11—42no—
397C4×C11—41no—
398C4×C11—42no—
399C4×C11C2×#10412yes—
400C4×C11C4×#4111yescharacteristic
401C4×C11#52011yescharacteristic
402C4×C11#54611yescharacteristic
403C4×C11#54711yescharacteristic
404Dic11—24no—
405Dic11—42no—
406Dic11—44no—
407C2×#41—21no—
408C2×#41C22×D1111yescharacteristic
409C22×D4C22⋊D1111yescharacteristic
410C23×C4—222no—
411C23×C4C22×D1112yes—
412C2×M16—111no—
413C2×M16—112no—
414C2×M16—111no—
415C2×M16—222no—
416C2×M16—224no—
417C2×M16—442no—
418C22×C8—222no—
419C4⋊Q8C2×Dic1111yescharacteristic, complemented
420C4⋊Q8C2×Dic1111yescharacteristic, complemented
421#126—22no—
422#126—22no—
423#126—22no—
424#125—22no—
425#125—21no—
426#125C2×Dic1112yescomplemented
427#124—21no—
428#124—22no—
429#123—22no—
430#123—22no—
431#123—22no—
432#123—22no—
433C22⋊Q8—21no—
434C22⋊Q8—21no—
435C22⋊Q8—21no—
436C22⋊Q8—22no—
437C22⋊Q8C2×Dic1112yescomplemented
438C22⋊Q8C2×Dic1112yescomplemented
439#121—22no—
440#121—21no—
441#121C2×Dic1112yescomplemented
442#121C2×Dic1112yescomplemented
443#120—22no—
444C4×Q8—21no—
445C4×Q8—21no—
446C4×Q8—21no—
447C4×Q8C2×Dic1111yescharacteristic, complemented
448C4×Q8C2×Dic1111yescharacteristic, complemented
449C4×D4—21no—
450C4×D4—22no—
451C4×D4—21no—
452C4×D4—21no—
453C4×D4—22no—
454C4×D4—22no—
455C4×D4—228no—
456C4×D4C2×Dic1111yescharacteristic
457C4×D4C2×Dic1112yes—
458C4×D4C2×Dic1111yescharacteristic
459C4×D4C2×Dic1111yescharacteristic, complemented
460C4×D4C2×Dic1111yescharacteristic, complemented
461C4×D4C22⋊D1111yescharacteristic
462C4×D4C22⋊D1112yes—
463C4×D4C22⋊D1111yescharacteristic
464#117—22no—
465#117—22no—
466#117—21no—
467#117—22no—
468#117—21no—
469#117C2×Dic1112yescomplemented
470#117C2×Dic1112yescomplemented
471#117C22×D1111yescharacteristic
472#117C22×D1112yes—
473C2×C4⋊C4—221no—
474C2×C4⋊C4C2×Dic1112yescomplemented
475C2×C4⋊C4C2×Dic1112yescomplemented
476C2×C4⋊C4C22⋊D1111yescharacteristic
477C2×C22⋊C4—22no—
478C2×C22⋊C4—222no—
479C2×C22⋊C4C22⋊D1112yes—
480C2×C42—22no—
481C2×C42—21no—
482C2×C42—111no—
483C2×C42—111no—
484C2×C42—112no—
485C2×C42—224no—
486C2×C42—221no—
487C2×C42—221no—
488C2×C42—222no—
489C2×C42—442no—
490C2×C42C22×D1111yescharacteristic
491C4⋊C8—221no—
492C4⋊C8—221no—
493#104—222no—
494#104—222no—
495#104—442no—
496C22⋊C8—222no—
497C22⋊C8—222no—
498#97—221no—
499C4×C8—221no—
500#95—222no—
501#95—221no—
502C2×C11—21no—
503C2×C11—21no—
504C2×C11—24no—
505C2×C11—42no—
506C2×C11—81no—
507C2×C11#233911yescharacteristic
508C2×C11C22×#10411yescharacteristic
509C2×C11#290111yescharacteristic
510C24C2×C22⋊D1112yes—
511#41—21no—
512#41—21no—
513#41—21no—
514#41—21no—
515#41—44no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8C22×Dic1111yescharacteristic
519C2×D4—24no—
520C2×D4—22no—
521C2×D4—21no—
522C2×D4—22no—
523C2×D4C22⋊Dic1112yes—
524C2×D4C22⋊Dic1111yescharacteristic
525C2×D4C22⋊Dic1111yescharacteristic
526C2×D4C22×Dic1111yescharacteristic
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—221no—
537C22×C4—228no—
538C22×C4—221no—
539C22×C4—222no—
540C22×C4—444no—
541C22×C4—444no—
542C22×C4C22×Dic1112yes—
543C22×C4C22×Dic1112yes—
544C22×C4C2×C22⋊D1112yes—
545C22×C4C2×C22⋊D1111yescharacteristic
546C22×C4C2×C22⋊D1112yes—
547C22×C4C2×C22⋊D1112yes—
548C22×C4C2×C22⋊D1111yescharacteristic
549C22×C4C23×D1111yescharacteristic
550M16—112no—
551M16—221no—
552M16—221no—
553M16—222no—
554M16—222no—
555M16—221no—
556M16—444no—
557C2×C8—221no—
558C2×C8—221no—
559C2×C8—222no—
560C2×C8—444no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—21no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—21no—
571C4⋊C4—224no—
572C4⋊C4C22⋊Dic1111yescharacteristic
573C4⋊C4C22⋊Dic1111yescharacteristic
574C4⋊C4C22⋊Dic1112yes—
575C4⋊C4C22×Dic1111yescharacteristic
576C4⋊C4C22×Dic1111yescharacteristic
577C4⋊C4C22×Dic1112yes—
578C4⋊C4C22×Dic1112yes—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—21no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—21no—
587C22⋊C4—21no—
588C22⋊C4—22no—
589C22⋊C4—228no—
590C22⋊C4C22⋊Dic1112yes—
591C22⋊C4C22⋊Dic1112yes—
592C22⋊C4C22⋊Dic1112yes—
593C22⋊C4C22⋊Dic1112yes—
594C42—22no—
595C42—21no—
596C42—22no—
597C42—21no—
598C42—21no—
599C42—22no—
600C42—112no—
601C42—224no—
602C42—221no—
603C42—221no—
604C42—222no—
605C42—222no—
606C42—221no—
607C42—444no—
608C42—442no—
609C42C22×Dic1111yescharacteristic
610C42C22×Dic1111yescharacteristic
611C42C2×C22⋊D1111yescharacteristic
612C42C2×C22⋊D1111yescharacteristic
613C11#2250511yescharacteristic, complemented, Sylow
614C23—22no—
615C23—24no—
616C23—22no—
617C23—21no—
618C23—42no—
619C23C2×C22⋊Dic1112yes—
620C23C2×C22⋊Dic1112yes—
621C23C22×C22⋊D1111yescharacteristic
622Q8—21no—
623Q8—21no—
624Q8—42no—
625Q8—81no—
626D4—24no—
627D4—21no—
628D4—21no—
629D4—22no—
630D4—41no—
631D4—44no—
632D4—41no—
633D4—82no—
634D4#6690114yescomplemented
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—41no—
652C2×C4—44no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—41no—
656C2×C4—81no—
657C2×C4—82no—
658C2×C4—222no—
659C2×C4—222no—
660C2×C4—222no—
661C2×C4—222no—
662C2×C4—224no—
663C2×C4—4416no—
664C2×C4—441no—
665C2×C4—442no—
666C2×C4—441no—
667C2×C4—442no—
668C2×C4C2×C22⋊Dic1112yes—
669C2×C4C2×C22⋊Dic1111yescharacteristic
670C2×C4C2×C22⋊Dic1111yescharacteristic
671C2×C4C2×C22⋊Dic1111yescharacteristic
672C2×C4C2×C22⋊Dic1112yes—
673C2×C4C2×C22⋊Dic1111yescharacteristic
674C2×C4#41×D1111yescharacteristic
675C2×C4#41×D1111yescharacteristic
676C2×C4#6704211yescharacteristic
677C2×C4#6704311yescharacteristic
678C2×C4C23×Dic1111yescharacteristic
679C2×C4C22×C22⋊D1111yescharacteristic
680C8—222no—
681C8—441no—
682C8—442no—
683C22—22no—
684C22—21no—
685C22—21no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—44no—
691C22—44no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22C2×#6690114yes—
696C22#1062335511yescharacteristic
697C22#1062336011yescharacteristic
698C22C22×C22⋊Dic1111yescharacteristic
699C4—22no—
700C4—22no—
701C4—21no—
702C4—21no—
703C4—21no—
704C4—41no—
705C4—41no—
706C4—42no—
707C4—41no—
708C4—42no—
709C4—224no—
710C4—444no—
711C4—442no—
712C4C2×#6690112yes—
713C4#1062335511yescharacteristic
714C4#41×Dic1111yescharacteristic
715C4#1062335811yescharacteristic
716C4#1062336011yescharacteristic
717C2—21no—
718C2—21no—
719C2—24no—
720C2—42no—
721C2—81no—
722C2#1307144611yescharacteristic
723C2C22×#6690111yescharacteristic
724C2#1307716311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3475C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenter#3475D11
hypocenterC11#22505
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. D4×#4318C2semidirect
2. C4×D4×Dic11C2semidirect
3. #13069594C2semidirect
4. #13069561C2semidirect
5. #13069060C2semidirect
6. #13068919C2semidirect
7. #13068715C2semidirect
8. #13068636C2semidirect
9. C4×#66901C2semidirect
10. C2×#10622170C2semidirect
12. C11×#556C4semidirect
13. C11×#555C4semidirect
14. C11×#554C4semidirect
15. C11×#553C4semidirect
17. C11×#552C4semidirect
19. C11×#547C4semidirect
58. C11×C4⋊Q8C2×C4semidirect
59. C11×C4⋊Q8C2×C4semidirect
65. C11×#125C2×C4semidirect
76. C11×C22⋊Q8C2×C4semidirect
77. C11×C22⋊Q8C2×C4semidirect
80. C11×#121C2×C4semidirect
81. C11×#121C2×C4semidirect
86. C4×Q8×C11C2×C4semidirect
87. C4×Q8×C11C2×C4semidirect
97. C4×D4×C11C2×C4semidirect
98. C4×D4×C11C2×C4semidirect
107. C11×#117C2×C4semidirect
108. C11×#117C2×C4semidirect
111. C2×C11×C4⋊C4C2×C4semidirect
112. C2×C11×C4⋊C4C2×C4semidirect
240. C4×Dic11#41semidirect
247. #4318#41semidirect
283. D4×C11#104semidirect
333. #556Dic11semidirect
334. #555Dic11semidirect
335. #554Dic11semidirect
336. #553Dic11semidirect
338. #552Dic11semidirect
340. #547Dic11semidirect
419. C4⋊Q8C2×Dic11semidirect
420. C4⋊Q8C2×Dic11semidirect
426. #125C2×Dic11semidirect
437. C22⋊Q8C2×Dic11semidirect
438. C22⋊Q8C2×Dic11semidirect
441. #121C2×Dic11semidirect
442. #121C2×Dic11semidirect
447. C4×Q8C2×Dic11semidirect
448. C4×Q8C2×Dic11semidirect
459. C4×D4C2×Dic11semidirect
460. C4×D4C2×Dic11semidirect
469. #117C2×Dic11semidirect
470. #117C2×Dic11semidirect
474. C2×C4⋊C4C2×Dic11semidirect
475. C2×C4⋊C4C2×Dic11semidirect
613. C11#22505semidirect
634. D4#66901semidirect

Maximal subgroups

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

subgroupindex
D4×#43182
C4×D4×Dic112
#130695942
#130695612
#130690602
#130689192
#130687152
#130686362
C4×#669012
C2×#106221702
C11×#34752
#2250511