Finite Group Databasebeta

← #14722007

Subgroups — #14722007

Order 2816.

896 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077636C211yesmaximal, characteristic, complemented
2#13077630C211yesmaximal, characteristic, complemented
3#13067251C211yesmaximal, characteristic, complemented
4#13067247C212yesmaximal, complemented
5#13067236C212yesmaximal, complemented
6#13067223C212yesmaximal, complemented
7#13067218C211yesmaximal, characteristic, complemented
8#13067218C211yesmaximal, characteristic, complemented
9#13067208C211yesmaximal, characteristic, complemented
10#13067204C212yesmaximal, complemented
11C11×#3512C211yesmaximal, characteristic
12C11×#553—22no—
13C11×#553—22no—
14C11×#553—21no—
15C11×#553—21no—
16C11×#552—21no—
17C11×#552—21no—
18C11×#541C412yes—
19C11×#540C412yes—
20C11×#537C411yescharacteristic
21C11×#537C411yescharacteristic
22C11×#532C2211yescharacteristic
23C11×#529C2212yes—
24C11×#529C2212yes—
25C2×C11×#125C2211yescharacteristic
26C11×#520C411yescharacteristic
27C11×#520C411yescharacteristic
28C4×C11×#41C2211yescharacteristic
29#10622637—21no—
30Q8×C11⋊C8—21no—
31#10622625—22no—
32#10622625—21no—
33#10622624—22no—
34D4×C11⋊C8—21no—
35#10622539C2211yescharacteristic
36#10622539C2212yes—
37#10622539C2211yescharacteristic
38#10622539C2212yes—
39C4×#4318C2211yescharacteristic
40C4×#4318C2212yes—
41C4×#4318C2211yescharacteristic
42C2×#66867C2212yes—
43#10622181C2212yes—
44#10622181C2212yes—
45#10622181C2212yes—
46#10622181C2212yes—
47#10622178C2211yescharacteristic
48#10622178C2212yes—
49#10622178C2211yescharacteristic
50#10622178C2211yescharacteristic
51#10622178C2211yescharacteristic
52#10622178C2212yes—
53C2×C11×#41C2×C411yescharacteristic
54C2×C11×#41C2×C411yescharacteristic
55C2×C11×#41C2×C411yescharacteristic
56C11×C4⋊Q8C2×C411yescharacteristic
57C11×#127C2×C411yescharacteristic
58C11×#126—22no—
59C11×#126—22no—
60C11×#126—22no—
61C11×#126—22no—
62C11×#125—22no—
63C11×#125—22no—
64C11×#125—21no—
65C11×#125—21no—
66C11×#125C2×C412yes—
67C11×#125C2312yes—
68C11×#124C2311yescharacteristic
69C11×#124C2311yescharacteristic
70C11×#123—22no—
71C11×#123—22no—
72C11×#123—22no—
73C11×#123—22no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8C2×C412yes—
77C11×C22⋊Q8C2×C412yes—
78C11×#121—21no—
79C11×#121—21no—
80C11×#121—22no—
81C11×#121—22no—
82C11×#121—21no—
83C11×#121—21no—
84C11×#121—22no—
85C11×#121—22no—
86C11×#121C2×C412yes—
87C11×#121C2×C412yes—
88C4×Q8×C11C2×C412yes—
89C4×Q8×C11C2×C412yes—
90C4×Q8×C11D411yescharacteristic
91C4×Q8×C11D411yescharacteristic
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C4×D4×C11—21no—
97C4×D4×C11—21no—
98C4×D4×C11C2×C412yes—
99C4×D4×C11C2×C412yes—
100C4×D4×C11D411yescharacteristic
101C4×D4×C11D412yes—
102C4×D4×C11D412yes—
103C4×D4×C11D411yescharacteristic
104C11×#117—21no—
105C11×#117—21no—
106C11×#117—22no—
107C11×#117—22no—
108C11×#117C2×C411yescharacteristic
109C11×#117C2×C412yes—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—21no—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4—21no—
114C2×C11×C4⋊C4C2×C411yescharacteristic
115C2×C11×C4⋊C4C2×C411yescharacteristic
116C2×C42×C11C2312yes—
117C2×C42×C11C2311yescharacteristic
118C2×#4318—21no—
119C2×#4318—21no—
120C2×#4318—22no—
121C22×C11⋊C8—22no—
122C22⋊(C11⋊C8)—22no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—22no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)—22no—
128C4⋊(C11⋊C8)—22no—
129C4⋊(C11⋊C8)—21no—
130#66867—22no—
131#66867C2311yescharacteristic
132#66867C2312yes—
133#66867C2311yescharacteristic
134#66867C2311yescharacteristic
135#66867C2312yes—
136#66867C2311yescharacteristic
137C4×C11⋊C8—21no—
138C4×C11⋊C8—22no—
139C4×C11⋊C8—21no—
140#17687—111nomaximal, Sylow
141C11×#41—42no—
142C11×#41—42no—
143C11×#41—42no—
144C2×Q8×C11C22⋊C411yescharacteristic
145C2×Q8×C11C22×C411yescharacteristic
146C2×Q8×C11C22×C411yescharacteristic
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11C22⋊C411yescharacteristic
154C2×D4×C11C22⋊C412yes—
155C2×D4×C11C22×C411yescharacteristic
156C2×D4×C11C22×C411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C22×C412yes—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D412yes—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4C22⋊C411yescharacteristic
182C11×C4⋊C4C22⋊C411yescharacteristic
183C11×C4⋊C4C22⋊C412yes—
184C11×C4⋊C4C22⋊C412yes—
185C11×C4⋊C4C22×C412yes—
186C11×C4⋊C4C22×C412yes—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—21no—
194C11×C22⋊C4—21no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4—21no—
197C11×C22⋊C4C22⋊C412yes—
198C11×C22⋊C4C22⋊C412yes—
199C11×C22⋊C4C22⋊C412yes—
200C42×C11—22no—
201C42×C11—22no—
202C42×C11C22×C412yes—
203C42×C11C22×C411yescharacteristic
204C42×C11C2×D412yes—
205C42×C11C2×D411yescharacteristic
206C42×C11C2×D411yescharacteristic
207C42×C11C2×D412yes—
208C42×C11C2411yescharacteristic
209#4318—42no—
210#4318—44no—
211#4318—42no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—22no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—22no—
218C2×C11⋊C8—44no—
219#3512D1111yescharacteristic
220#2971—111no—
221#2970—111no—
222#1536—111no—
223#1535—112no—
224#1532—112no—
225#1529—112no—
226#1528—111no—
227#1528—111no—
228#1525—111no—
229#1524—112no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11C2×C22⋊C412yes—
233C23×C11C2×C22⋊C411yescharacteristic
234Q8×C11—22no—
235Q8×C11—41no—
236Q8×C11—41no—
237D4×C11—22no—
238D4×C11—42no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—42no—
242D4×C11—42no—
243D4×C11—81no—
244D4×C11—81no—
245D4×C11—82no—
246D4×C11—82no—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—82no—
260C2×C4×C11—82no—
261C2×C4×C11—81no—
262C2×C4×C11—81no—
263C2×C4×C11C2×C22⋊C412yes—
264C2×C4×C11C2×C22⋊C412yes—
265C2×C4×C11C2×C22⋊C411yescharacteristic
266C2×C4×C11C2×C22⋊C411yescharacteristic
267C2×C4×C11C2×C22⋊C412yes—
268C2×C4×C11C2×C22⋊C411yescharacteristic
269C2×C4×C11C23×C411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C11⋊C8—22no—
273C11⋊C8—22no—
274C11⋊C8—42no—
275C11⋊C8—41no—
276C11⋊C8—42no—
277C11⋊C8—41no—
278#553—22no—
279#553—22no—
280#553—21no—
281#553—21no—
282#552—21no—
283#552—21no—
284#541Dic1112yes—
285#540Dic1112yes—
286#537Dic1111yescharacteristic
287#537Dic1111yescharacteristic
288#532C2×D1111yescharacteristic
289#529C2×D1112yes—
290#529C2×D1112yes—
291C2×#125C2×D1111yescharacteristic
292#520Dic1111yescharacteristic
293#520Dic1111yescharacteristic
294C4×#41C2×D1111yescharacteristic
295#446—221no—
296C8×Q8—221no—
297#436—222no—
298#436—221no—
299#435—222no—
300C8×D4—221no—
301#432—111no—
302#432—111no—
303#432—112no—
304#432—112no—
305C4×M16—111no—
306C4×M16—112no—
307C4×M16—111no—
308C2×#97—112no—
309#330—112no—
310#330—112no—
311#330—112no—
312#330—112no—
313#329—112no—
314#329—112no—
315#329—111no—
316#329—111no—
317#329—111no—
318#329—111no—
319C22×C11—21no—
320C22×C11—22no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11C22×C22⋊C411yescharacteristic
332C4×C11—21no—
333C4×C11—22no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—22no—
337C4×C11—22no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11#41312yes—
345C2×#41C2×Dic1111yescharacteristic
346C2×#41C2×Dic1111yescharacteristic
347C2×#41C2×Dic1111yescharacteristic
348C2×M16—221no—
349C2×M16—221no—
350C2×M16—222no—
351C22×C8—222no—
352C4⋊Q8C2×Dic1111yescharacteristic
353#127C2×Dic1111yescharacteristic
354#126—22no—
355#126—22no—
356#126—22no—
357#126—22no—
358#125—22no—
359#125—22no—
360#125—21no—
361#125—21no—
362#125C2×Dic1112yes—
363#125C22×D1112yes—
364#124C22×D1111yescharacteristic
365#124C22×D1111yescharacteristic
366#123—22no—
367#123—22no—
368#123—22no—
369#123—22no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8C2×Dic1112yes—
373C22⋊Q8C2×Dic1112yes—
374#121—21no—
375#121—21no—
376#121—22no—
377#121—22no—
378#121—21no—
379#121—21no—
380#121—22no—
381#121—22no—
382#121C2×Dic1112yes—
383#121C2×Dic1112yes—
384C4×Q8C2×Dic1112yes—
385C4×Q8C2×Dic1112yes—
386C4×Q8C22⋊D1111yescharacteristic
387C4×Q8C22⋊D1111yescharacteristic
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4C2×Dic1112yes—
395C4×D4C2×Dic1112yes—
396C4×D4C22⋊D1111yescharacteristic
397C4×D4C22⋊D1112yes—
398C4×D4C22⋊D1112yes—
399C4×D4C22⋊D1111yescharacteristic
400#117—21no—
401#117—21no—
402#117—22no—
403#117—22no—
404#117C2×Dic1111yescharacteristic
405#117C2×Dic1112yes—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4C2×Dic1111yescharacteristic
411C2×C4⋊C4C2×Dic1111yescharacteristic
412C2×C42C22×D1111yescharacteristic
413C2×C42C22×D1112yes—
414C4⋊C8—221no—
415C4⋊C8—222no—
416C4⋊C8—222no—
417C4⋊C8—221no—
418C22⋊C8—222no—
419C22⋊C8—221no—
420C22⋊C8—221no—
421C22⋊C8—222no—
422#97—111no—
423#97—112no—
424#97—111no—
425#97—112no—
426#97—111no—
427#97—111no—
428#97—222no—
429C4×C8—221no—
430C4×C8—222no—
431C4×C8—221no—
432C2×C11—41no—
433C2×C11—42no—
434C2×C11—81no—
435C2×C11—81no—
436C2×C11C2×#41311yescharacteristic
437C2×C11#290111yescharacteristic
438C2×C11#290111yescharacteristic
439#41—42no—
440#41—42no—
441#41—42no—
442C2×Q8C22⋊Dic1111yescharacteristic
443C2×Q8C22×Dic1111yescharacteristic
444C2×Q8C22×Dic1111yescharacteristic
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4C22⋊Dic1111yescharacteristic
452C2×D4C22⋊Dic1112yes—
453C2×D4C22×Dic1111yescharacteristic
454C2×D4C22×Dic1111yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4C22×Dic1111yescharacteristic
462C22×C4C22×Dic1112yes—
463C22×C4C2×C22⋊D1111yescharacteristic
464C22×C4C2×C22⋊D1111yescharacteristic
465C22×C4C2×C22⋊D1112yes—
466C22×C4C2×C22⋊D1112yes—
467M16—442no—
468M16—444no—
469M16—442no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—222no—
474C2×C8—221no—
475C2×C8—222no—
476C2×C8—444no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4C22⋊Dic1111yescharacteristic
490C4⋊C4C22⋊Dic1111yescharacteristic
491C4⋊C4C22⋊Dic1112yes—
492C4⋊C4C22⋊Dic1112yes—
493C4⋊C4C22×Dic1112yes—
494C4⋊C4C22×Dic1112yes—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4C22⋊Dic1112yes—
506C22⋊C4C22⋊Dic1112yes—
507C22⋊C4C22⋊Dic1112yes—
508C42—22no—
509C42—22no—
510C42C22×Dic1112yes—
511C42C22×Dic1111yescharacteristic
512C42C2×C22⋊D1112yes—
513C42C2×C22⋊D1111yescharacteristic
514C42C2×C22⋊D1111yescharacteristic
515C42C2×C22⋊D1112yes—
516C42C23×D1111yescharacteristic
517C11#1768711yescharacteristic, complemented, Sylow
518C23—21no—
519C23—21no—
520C23C2×C22⋊Dic1112yes—
521C23C2×C22⋊Dic1111yescharacteristic
522Q8—22no—
523Q8—41no—
524Q8—41no—
525D4—22no—
526D4—42no—
527D4—41no—
528D4—41no—
529D4—42no—
530D4—42no—
531D4—81no—
532D4—81no—
533D4—82no—
534D4—82no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—82no—
548C2×C4—82no—
549C2×C4—81no—
550C2×C4—81no—
551C2×C4C2×C22⋊Dic1112yes—
552C2×C4C2×C22⋊Dic1112yes—
553C2×C4C2×C22⋊Dic1111yescharacteristic
554C2×C4C2×C22⋊Dic1111yescharacteristic
555C2×C4C2×C22⋊Dic1112yes—
556C2×C4C2×C22⋊Dic1111yescharacteristic
557C2×C4C23×Dic1111yescharacteristic
558C2×C4C22×C22⋊D1111yescharacteristic
559C2×C4C22×C22⋊D1111yescharacteristic
560C8—222no—
561C8—222no—
562C8—442no—
563C8—441no—
564C8—442no—
565C8—441no—
566C22—21no—
567C22—22no—
568C22—21no—
569C22—21no—
570C22—22no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22C22×C22⋊Dic1111yescharacteristic
579C4—21no—
580C4—22no—
581C4—21no—
582C4—21no—
583C4—22no—
584C4—22no—
585C4—21no—
586C4—21no—
587C4—41no—
588C4—41no—
589C4—42no—
590C4—42no—
591C4#1062285012yes—
592C2—41no—
593C2—42no—
594C2—81no—
595C2—81no—
596C2C2×#1062285011yescharacteristic
597C2#1307716311yescharacteristic
598C2#1307716311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
Fitting, prime radicalC11×#3512C2
socleC22×C11C22×C22⋊C4
cosocleC42×C11C24
hypercenter#3512D11
hypocenterC11#17687
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3512

Complements

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

NH ≅ G/Ntype
1. #13077636C2semidirect
2. #13077630C2semidirect
3. #13067251C2semidirect
4. #13067247C2semidirect
5. #13067236C2semidirect
6. #13067223C2semidirect
7. #13067218C2semidirect
8. #13067218C2semidirect
9. #13067208C2semidirect
10. #13067204C2semidirect
517. C11#17687semidirect

Maximal subgroups

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

subgroupindex
#130776362
#130776302
#130672512
#130672472
#130672362
#130672232
#130672182
#130672082
#130672042
C11×#35122
#1768711