Finite Group Databasebeta

← #14723033

Subgroups — #14723033

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077583C211yesmaximal, characteristic
2#13077282C211yesmaximal, characteristic
3#13067407C211yesmaximal, characteristic, complemented
4#13067404C211yesmaximal, characteristic, complemented
5#13067402C211yesmaximal, characteristic, complemented
6#13067399C211yesmaximal, characteristic, complemented
7#13067397C211yesmaximal, characteristic, complemented
8#13067394C211yesmaximal, characteristic, complemented
9#13067384C211yesmaximal, characteristic, complemented
10#13067381C211yesmaximal, characteristic, complemented
11#13067377C211yesmaximal, characteristic, complemented
12#13067369C211yesmaximal, characteristic, complemented
13#13067366C211yesmaximal, characteristic, complemented
14#13067362C211yesmaximal, characteristic, complemented
15C11×#2925C211yesmaximal, characteristic
16C4×C11×#41C2211yescharacteristic
17C11×#433—21no—
18C11×#433—21no—
19C11×#432C2211yescharacteristic
20C11×#432C2211yescharacteristic
21C11×#431C2211yescharacteristic
22C11×#431C2211yescharacteristic
23C11×#423C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C11×#408—21no—
26C11×#405—21no—
27#10622847—21no—
28#10622637C411yescharacteristic
29#10622637C411yescharacteristic
30#10622625C411yescharacteristic
31#10622625C411yescharacteristic
32#10622624C411yescharacteristic
33#10622624C411yescharacteristic
34#10622624C411yescharacteristic
35#10622624C411yescharacteristic
36#10622613—21no—
37#10622613—21no—
38#10622610—21no—
39#10622539C2211yescharacteristic
40#10622539C2211yescharacteristic
41#10622538C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622538C2211yescharacteristic
44#10622538C2211yescharacteristic
45#10622538C2211yescharacteristic
46#10622537C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C4×#4318C2211yescharacteristic
49C4×#4318C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622118C2211yescharacteristic
52#10622118C2211yescharacteristic
53#10622118C2211yescharacteristic
54#10622118C2211yescharacteristic
55#10622118C2211yescharacteristic
56#10622118C2211yescharacteristic
57#10622118C2211yescharacteristic
58#10622118C2211yescharacteristic
59#10622117C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63#10622117C2211yescharacteristic
64#10622117C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41D411yescharacteristic
68C2×C11×M16—21no—
69C22×C8×C11—21no—
70C4×Q8×C11C2×C411yescharacteristic
71C4×Q8×C11Q811yescharacteristic
72C4×D4×C11C2×C411yescharacteristic
73C4×D4×C11C2×C411yescharacteristic
74C4×D4×C11C2×C411yescharacteristic
75C4×D4×C11Q811yescharacteristic
76C4×D4×C11Q811yescharacteristic
77C4×D4×C11Q811yescharacteristic
78C11×#117D411yescharacteristic
79C11×#117D411yescharacteristic
80C11×#117D411yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×#4318—21no—
85C2×#4318C2×C411yescharacteristic
86C2×#4318C2×C411yescharacteristic
87C2×#4318C2×C411yescharacteristic
88C2×#4318C2×C411yescharacteristic
89C22×C11⋊C8—21no—
90C22×C11⋊C8C2×C411yescharacteristic
91C22×C11⋊C8C2×C411yescharacteristic
92C11×C4⋊C8—21no—
93C11×C4⋊C8—21no—
94C11×C4⋊C8C2311yescharacteristic
95C11×C4⋊C8C2311yescharacteristic
96C11×C4⋊C8C2311yescharacteristic
97C11×C4⋊C8C2311yescharacteristic
98C11×C22⋊C8—21no—
99C11×C22⋊C8—21no—
100C11×C22⋊C8—21no—
101C11×C22⋊C8—21no—
102C11×#97—21no—
103C11×#97—21no—
104C4×C8×C11—21no—
105C4×C8×C11—21no—
106C22⋊(C11⋊C8)—21no—
107C22⋊(C11⋊C8)—21no—
108C22⋊(C11⋊C8)—21no—
109C22⋊(C11⋊C8)—21no—
110C22⋊(C11⋊C8)C2×C411yescharacteristic
111C22⋊(C11⋊C8)C2×C411yescharacteristic
112C22⋊(C11⋊C8)C2×C411yescharacteristic
113C22⋊(C11⋊C8)C2×C411yescharacteristic
114C22⋊(C11⋊C8)C2×C411yescharacteristic
115C22⋊(C11⋊C8)C2×C411yescharacteristic
116C4⋊(C11⋊C8)—21no—
117C4⋊(C11⋊C8)—21no—
118C4⋊(C11⋊C8)C2×C411yescharacteristic
119C4⋊(C11⋊C8)C2×C411yescharacteristic
120C4⋊(C11⋊C8)C2×C411yescharacteristic
121C4⋊(C11⋊C8)C2×C411yescharacteristic
122C4⋊(C11⋊C8)C2×C411yescharacteristic
123C4⋊(C11⋊C8)C2×C411yescharacteristic
124C4⋊(C11⋊C8)C2311yescharacteristic
125C4⋊(C11⋊C8)C2311yescharacteristic
126C4⋊(C11⋊C8)C2311yescharacteristic
127C4⋊(C11⋊C8)C2311yescharacteristic
128#66867—21no—
129#66867—21no—
130#66867C2×C411yescharacteristic
131#66867C2×C411yescharacteristic
132#66867C2×C411yescharacteristic
133#66867C2×C411yescharacteristic
134C4×C11⋊C8—21no—
135C4×C11⋊C8—21no—
136C4×C11⋊C8C2×C411yescharacteristic
137C4×C11⋊C8C2×C411yescharacteristic
138C4×C11⋊C8C2311yescharacteristic
139C4×C11⋊C8C2311yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142#17831—111nomaximal, Sylow
143C11×#41—41no—
144C11×#41—41no—
145C2×Q8×C11C4⋊C411yescharacteristic
146C2×D4×C11C4⋊C411yescharacteristic
147C2×D4×C11C4⋊C411yescharacteristic
148C2×D4×C11C4⋊C411yescharacteristic
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×Q811yescharacteristic
156C22×C4×C11C2×Q811yescharacteristic
157C22×C4×C11C2×Q811yescharacteristic
158C11×M16—42no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—42no—
164C11×C4⋊C4C4⋊C411yescharacteristic
165C11×C4⋊C4C4⋊C411yescharacteristic
166C11×C4⋊C4C4⋊C411yescharacteristic
167C11×C4⋊C4C4⋊C411yescharacteristic
168C11×C4⋊C4C4⋊C411yescharacteristic
169C11×C4⋊C4C4⋊C411yescharacteristic
170C11×C22⋊C4C4⋊C411yescharacteristic
171C11×C22⋊C4C4⋊C411yescharacteristic
172C11×C22⋊C4C4⋊C411yescharacteristic
173C11×C22⋊C4C4⋊C411yescharacteristic
174C11×C22⋊C4C4⋊C411yescharacteristic
175C11×C22⋊C4C4⋊C411yescharacteristic
176C42×C11C22×C411yescharacteristic
177C42×C11C22×C411yescharacteristic
178C42×C11C22×C411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11C2×Q811yescharacteristic
183C42×C11C2×Q811yescharacteristic
184C42×C11C2×Q811yescharacteristic
185C42×C11C2411yescharacteristic
186#4318—22no—
187#4318—22no—
188#4318—41no—
189#4318—41no—
190#4318—42no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—41no—
197C2×C11⋊C8—42no—
198C2×C11⋊C8C22×C411yescharacteristic
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206#2965—111no—
207#2925—111no—
208#2925D1111yescharacteristic
209#1574—111no—
210#1574—111no—
211#1573—111no—
212#1573—111no—
213#1572—111no—
214#1572—111no—
215#1569—111no—
216#1569—111no—
217#1568—111no—
218#1565—111no—
219#1565—111no—
220#1564—111no—
221C23×C11C2×C4⋊C411yescharacteristic
222C23×C11C2×C4⋊C411yescharacteristic
223C23×C11C2×C4⋊C411yescharacteristic
224Q8×C11—41no—
225D4×C11—41no—
226D4×C11—41no—
227D4×C11—41no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11C2×C4⋊C411yescharacteristic
244C2×C4×C11C2×C4⋊C411yescharacteristic
245C2×C4×C11C2×C4⋊C411yescharacteristic
246C2×C4×C11C2×C4⋊C411yescharacteristic
247C2×C4×C11C2×C4⋊C411yescharacteristic
248C2×C4×C11C2×C4⋊C411yescharacteristic
249C2×C4×C11C2×C4⋊C411yescharacteristic
250C2×C4×C11C2×C4⋊C411yescharacteristic
251C2×C4×C11C2×C4⋊C411yescharacteristic
252C2×C4×C11C23×C411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×Q811yescharacteristic
255C8×C11—41no—
256C8×C11—41no—
257C8×C11—41no—
258C8×C11—41no—
259C11⋊C8—21no—
260C11⋊C8—21no—
261C11⋊C8—21no—
262C11⋊C8—21no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8#13112yes—
271C4×#41C2×D1111yescharacteristic
272#446—111no—
273#446—111no—
274#436—111no—
275#436—111no—
276#435—111no—
277#435—111no—
278#435—111no—
279#435—111no—
280#433—21no—
281#433—21no—
282#433—221no—
283#433—221no—
284#432—111no—
285#432—111no—
286#432C2×D1111yescharacteristic
287#432C2×D1111yescharacteristic
288#431—111no—
289#431—111no—
290#431—111no—
291#431—111no—
292#431—111no—
293#431C2×D1111yescharacteristic
294#431C2×D1111yescharacteristic
295#423—111no—
296#423C2×D1111yescharacteristic
297C2×C4⋊C8—111no—
298C2×C4⋊C8C2×D1111yescharacteristic
299#408—21no—
300#408—221no—
301#405—21no—
302#405—221no—
303C4×M16—111no—
304C4×M16—111no—
305C2×C4×C8—111no—
306#335—111no—
307#335—111no—
308#335—111no—
309#335—111no—
310#335—111no—
311#335—111no—
312#335—111no—
313#335—111no—
314#334—111no—
315#334—111no—
316#334—111no—
317#334—111no—
318#334—111no—
319#334—111no—
320#334—111no—
321#334—111no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11C22×C4⋊C411yescharacteristic
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11C2×#13111yescharacteristic
343C4×C11#56811yescharacteristic
344C4×C11#57511yescharacteristic
345C4×C11#57511yescharacteristic
346C2×#41C22⋊D1111yescharacteristic
347C2×M16—21no—
348C2×M16—111no—
349C2×M16—111no—
350C2×M16—111no—
351C2×M16—111no—
352C2×M16—221no—
353C22×C8—21no—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8—221no—
357C4×Q8Dic2211yescharacteristic
358C4×Q8C4×D1111yescharacteristic
359C4×D4Dic2211yescharacteristic
360C4×D4Dic2211yescharacteristic
361C4×D4Dic2211yescharacteristic
362C4×D4C4×D1111yescharacteristic
363C4×D4C4×D1111yescharacteristic
364C4×D4C4×D1111yescharacteristic
365#117C22⋊D1111yescharacteristic
366#117C22⋊D1111yescharacteristic
367#117C22⋊D1111yescharacteristic
368C2×C42C22×D1111yescharacteristic
369C2×C42C22×D1111yescharacteristic
370C2×C42C22×D1111yescharacteristic
371C4⋊C8—21no—
372C4⋊C8—21no—
373C4⋊C8—111no—
374C4⋊C8—111no—
375C4⋊C8—111no—
376C4⋊C8—111no—
377C4⋊C8—111no—
378C4⋊C8—111no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—111no—
382C4⋊C8—111no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8C22×D1111yescharacteristic
386C4⋊C8C22×D1111yescharacteristic
387C4⋊C8C22×D1111yescharacteristic
388C4⋊C8C22×D1111yescharacteristic
389C22⋊C8—21no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392C22⋊C8—21no—
393C22⋊C8—111no—
394C22⋊C8—111no—
395C22⋊C8—111no—
396C22⋊C8—111no—
397C22⋊C8—111no—
398C22⋊C8—111no—
399C22⋊C8—221no—
400C22⋊C8—221no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403#97—21no—
404#97—21no—
405#97—111no—
406#97—111no—
407#97—111no—
408#97—111no—
409#97—221no—
410#97—221no—
411C4×C8—21no—
412C4×C8—21no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—111no—
417C4×C8—111no—
418C4×C8—111no—
419C4×C8—221no—
420C4×C8—221no—
421C2×C11—41no—
422C2×C11—41no—
423C2×C11—41no—
424C2×C11#290611yescharacteristic
425C2×C11#291111yescharacteristic
426C2×C11#291611yescharacteristic
427#41—41no—
428#41—41no—
429C2×Q8Dic11⋊C411yescharacteristic
430C2×D4Dic11⋊C411yescharacteristic
431C2×D4Dic11⋊C411yescharacteristic
432C2×D4Dic11⋊C411yescharacteristic
433C22×C4C2×Dic2211yescharacteristic
434C22×C4C2×Dic2211yescharacteristic
435C22×C4C2×Dic2211yescharacteristic
436C22×C4C2×C4×D1111yescharacteristic
437C22×C4C2×C4×D1111yescharacteristic
438C22×C4C2×C4×D1111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C2×C22⋊D1111yescharacteristic
442M16—42no—
443M16—222no—
444M16—222no—
445M16—441no—
446M16—441no—
447M16—442no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—42no—
453C2×C8—111no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—111no—
457C2×C8—111no—
458C2×C8—111no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—222no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—441no—
467C2×C8—442no—
468C4⋊C4Dic11⋊C411yescharacteristic
469C4⋊C4Dic11⋊C411yescharacteristic
470C4⋊C4Dic11⋊C411yescharacteristic
471C4⋊C4Dic11⋊C411yescharacteristic
472C4⋊C4Dic11⋊C411yescharacteristic
473C4⋊C4Dic11⋊C411yescharacteristic
474C22⋊C4Dic11⋊C411yescharacteristic
475C22⋊C4Dic11⋊C411yescharacteristic
476C22⋊C4Dic11⋊C411yescharacteristic
477C22⋊C4Dic11⋊C411yescharacteristic
478C22⋊C4Dic11⋊C411yescharacteristic
479C22⋊C4Dic11⋊C411yescharacteristic
480C42C2×Dic2211yescharacteristic
481C42C2×Dic2211yescharacteristic
482C42C2×Dic2211yescharacteristic
483C42C2×C4×D1111yescharacteristic
484C42C2×C4×D1111yescharacteristic
485C42C2×C4×D1111yescharacteristic
486C42C2×C22⋊D1111yescharacteristic
487C42C2×C22⋊D1111yescharacteristic
488C42C2×C22⋊D1111yescharacteristic
489C42C23×D1111yescharacteristic
490C11#1783111yescharacteristic, complemented, Sylow
491C23C2×Dic11⋊C411yescharacteristic
492C23C2×Dic11⋊C411yescharacteristic
493C23C2×Dic11⋊C411yescharacteristic
494Q8—41no—
495D4—41no—
496D4—41no—
497D4—41no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4C2×Dic11⋊C411yescharacteristic
514C2×C4C2×Dic11⋊C411yescharacteristic
515C2×C4C2×Dic11⋊C411yescharacteristic
516C2×C4C2×Dic11⋊C411yescharacteristic
517C2×C4C2×Dic11⋊C411yescharacteristic
518C2×C4C2×Dic11⋊C411yescharacteristic
519C2×C4C2×Dic11⋊C411yescharacteristic
520C2×C4C2×Dic11⋊C411yescharacteristic
521C2×C4C2×Dic11⋊C411yescharacteristic
522C2×C4C22×Dic2211yescharacteristic
523C2×C4C22×C4×D1111yescharacteristic
524C2×C4C22×C22⋊D1111yescharacteristic
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—112no—
530C8—221no—
531C8—221no—
532C8—221no—
533C8—221no—
534C8—221no—
535C8—221no—
536C8—221no—
537C8—441no—
538C8—441no—
539C8—441no—
540C8—441no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22C22×Dic11⋊C411yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4D11×#13111yescharacteristic
562C4#1062328111yescharacteristic
563C4#1062335311yescharacteristic
564C4#1062335311yescharacteristic
565C2—41no—
566C2—41no—
567C2—41no—
568C2#1307718211yescharacteristic
569C2#1307720511yescharacteristic
570C2#1307722511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2925C2
socleC22×C11C22×C4⋊C4
prime radicalC2×C11×#41D4
cosocleC42×C11C24
hypercenter#2925D11
hypocenterC11#17831
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2925

Complements

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

NH ≅ G/Ntype
3. #13067407C2semidirect
4. #13067404C2semidirect
5. #13067402C2semidirect
6. #13067399C2semidirect
7. #13067397C2semidirect
8. #13067394C2semidirect
9. #13067384C2semidirect
10. #13067381C2semidirect
11. #13067377C2semidirect
12. #13067369C2semidirect
13. #13067366C2semidirect
14. #13067362C2semidirect
490. C11#17831semidirect

Maximal subgroups

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

subgroupindex
#130775832
#130772822
#130674072
#130674042
#130674022
#130673992
#130673972
#130673942
#130673842
#130673812
#130673772
#130673692
#130673662
#130673622
C11×#29252
#1783111