Finite Group Databasebeta

← #14725638

Subgroups — #14725638

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079223C211yesmaximal, characteristic
2#13077563C211yesmaximal, characteristic, complemented
3#13067518C211yesmaximal, characteristic, complemented
4#13067511C211yesmaximal, characteristic, complemented
5#13067492C211yesmaximal, characteristic, complemented
6#13067487C211yesmaximal, characteristic, complemented
7#13067464C211yesmaximal, characteristic, complemented
8#13067452C211yesmaximal, characteristic, complemented
9#13067433C211yesmaximal, characteristic, complemented
10C8×#4324C211yesmaximal, characteristic, complemented
11#13067369C211yesmaximal, characteristic, complemented
12#13067036C211yesmaximal, characteristic, complemented
13#13067029C211yesmaximal, characteristic
14#13066919C211yesmaximal, characteristic, complemented
15C11×#2969C211yesmaximal, characteristic
16C11×#529C2211yescharacteristic
17#10623001C2211yescharacteristic
18C11×#446C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C11×#436—21no—
21C11×#436C2211yescharacteristic
22C11×#435—21no—
23C8×D4×C11C2211yescharacteristic
24C11×#433—21no—
25C11×#431C2211yescharacteristic
26C11×#405—21no—
27C4×C11×M16C2211yescharacteristic
28#10622735—21no—
29#10622732—21no—
30#10622682C411yescharacteristic
31#10622678C411yescharacteristic
32#10622673C411yescharacteristic
33#10622668C411yescharacteristic
34#10622665C411yescharacteristic
35#10622665C411yescharacteristic
36#10622655C411yescharacteristic
37#10622655C411yescharacteristic
38C4×#4326C2211yescharacteristic
39C4×#4326C2211yescharacteristic
40C4×#4324C2211yescharacteristic
41C4×#4324C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C4×#4318C2211yescharacteristic
44C4×#4318C2211yescharacteristic
45#10622314—21no—
46#10622314—21no—
47#10622292C2211yescharacteristic
48#10622292C2211yescharacteristic
49C8×Dic22C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic
52Q8⋊(C11⋊C8)C2211yescharacteristic
53D4⋊(C11⋊C8)C2211yescharacteristic
54D4⋊(C11⋊C8)C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622117C2211yescharacteristic
62#10622117C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×M16—21no—
68C2×C11×M16D411yescharacteristic
69C2×C11×M16D411yescharacteristic
70C22×C8×C11—21no—
71C11×#126—21no—
72C11×#125C2×C411yescharacteristic
73C11×#124C2×C411yescharacteristic
74C11×#123—21no—
75C11×C22⋊Q8C2×C411yescharacteristic
76C11×#121C2×C411yescharacteristic
77C4×Q8×C11C2311yescharacteristic
78C4×D4×C11—21no—
79C4×D4×C11C2311yescharacteristic
80C11×#117—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4326C2×C411yescharacteristic
83C2×#4326C2×C411yescharacteristic
84C2×#4324C2×C411yescharacteristic
85C2×#4324C2×C411yescharacteristic
86#66979—21no—
87#66977—21no—
88#66977C2×C411yescharacteristic
89#66977C2×C411yescharacteristic
90C2×#4318—21no—
91C2×#4318C2×C411yescharacteristic
92C2×#4318C2×C411yescharacteristic
93C22×C11⋊C8—21no—
94#66923—21no—
95#66922C2×C411yescharacteristic
96#66922C2×C411yescharacteristic
97C4×Dic22—21no—
98C4×Dic22C2311yescharacteristic
99C4×Dic22C2311yescharacteristic
100C11×C4⋊C8—21no—
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C22⋊C8—21no—
105C11×C22⋊C8—21no—
106C11×C22⋊C8—21no—
107C11×#97—21no—
108C11×#97D411yescharacteristic
109C11×#97D411yescharacteristic
110C4×C8×C11—21no—
111C4×C8×C11—21no—
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114#66899C2×C411yescharacteristic
115#66899C2×C411yescharacteristic
116#66896C2×C411yescharacteristic
117#66896C2×C411yescharacteristic
118#66879—21no—
119#66879—21no—
120Dic11⋊C8—21no—
121Dic11⋊C8—21no—
122Dic11⋊C8—21no—
123Dic11⋊C8—21no—
124C8×Dic11—21no—
125C8×Dic11—21no—
126#66874C2×C411yescharacteristic
127#66874C2×C411yescharacteristic
128#66874C2×C411yescharacteristic
129#66874C2×C411yescharacteristic
130#66872C2×C411yescharacteristic
131#66872C2×C411yescharacteristic
132#66871C2×C411yescharacteristic
133#66871C2×C411yescharacteristic
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137#66867—21no—
138#66867C2×C411yescharacteristic
139#66867C2×C411yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18077—111nomaximal, Sylow
145C2×Q8×C11C22×C411yescharacteristic
146C2×D4×C11—21no—
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C2×Dic22—21no—
153C2×Dic22C22×C411yescharacteristic
154C2×Dic22C22×C411yescharacteristic
155C11×M16—22no—
156C11×M16—41no—
157C11×M16—42no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—42no—
161C2×C8×C11C2×D411yescharacteristic
162C2×C8×C11C2×D411yescharacteristic
163C2×C8×C11C2×D411yescharacteristic
164C2×C8×C11C2×D411yescharacteristic
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4C22×C411yescharacteristic
170C11×C4⋊C4C22×C411yescharacteristic
171C11×C22⋊C4—21no—
172C11×C22⋊C4—21no—
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C42×C11—21no—
177C42×C11C22×C411yescharacteristic
178C42×C11C2×D411yescharacteristic
179C42×C11#4111yescharacteristic
180C42×C11C2411yescharacteristic
181C22⋊Dic11—21no—
182C22⋊Dic11—21no—
183#4326—22no—
184#4326—41no—
185#4324—22no—
186#4324—41no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11C22×C411yescharacteristic
191C4⋊Dic11C22×C411yescharacteristic
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198#4318—22no—
199#4318—41no—
200#4318—42no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—42no—
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C22×C411yescharacteristic
210#3172—111no—
211#2969D1111yescharacteristic
212#2962—111no—
213#1592—111no—
214#1591—111no—
215#1588—111no—
216#1587—111no—
217#1584—111no—
218#1582—111no—
219#1579—111no—
220C8×SD16—111no—
221#1565—111no—
222#1485—111no—
223#1483—111no—
224#1455—111no—
225C23×C11—21no—
226C23×C11C4×D411yescharacteristic
227Q8×C11—21no—
228Q8×C11—21no—
229D4×C11—21no—
230D4×C11—21no—
231D4×C11—81no—
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—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11C4×D411yescharacteristic
243C2×C4×C11C4×D411yescharacteristic
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11C23×C411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252Dic22—21no—
253Dic22—21no—
254Dic22—21no—
255Dic22—21no—
256Dic22—81no—
257C8×C11—21no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—41no—
261C8×C11—41no—
262C8×C11#13712yes—
263C11⋊C8—22no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8#13112yes—
271#533—111no—
272#529C2×D1111yescharacteristic
273#501—111no—
274#497—111no—
275#491—111no—
276#489—111no—
277#470—111no—
278#470—111no—
279#468—111no—
280#468—111no—
281#446—111no—
282#446—111no—
283#446—221no—
284#446—221no—
285#446C2×D1111yescharacteristic
286C8×Q8—111no—
287C8×Q8—111no—
288C8×Q8C2×D1111yescharacteristic
289C4×Q16—111no—
290C4×Q16—111no—
291C4×SD16—111no—
292C4×SD16—111no—
293#436—21no—
294#436C2×D1111yescharacteristic
295#435—21no—
296C8×D4C2×D1111yescharacteristic
297#433—21no—
298#431C2×D1111yescharacteristic
299#424—221no—
300C2×C4⋊C8—111no—
301#405—21no—
302#405—221no—
303C4×M16—111no—
304C4×M16—111no—
305C4×M16C2×D1111yescharacteristic
306#335—111no—
307#335—111no—
308#334—111no—
309#334—111no—
310Q8⋊C8—111no—
311Q8⋊C8—111no—
312Q8⋊C8—111no—
313Q8⋊C8—111no—
314Q8⋊C8—111no—
315Q8⋊C8—111no—
316D4⋊C8—111no—
317D4⋊C8—111no—
318#322—111no—
319#322—111no—
320#322—111no—
321C82—111no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11C2×C4×D411yescharacteristic
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11C2×#13111yescharacteristic
337C4×C11#56811yescharacteristic
338C4×C11C2×#13711yescharacteristic
339C4×C11#57511yescharacteristic
340Dic11—41no—
341Dic11—41no—
342Dic11—41no—
343Dic11—41no—
344C2×Q16—111no—
345C2×Q16—111no—
346C2×SD16—111no—
347C2×SD16—111no—
348C2×M16—21no—
349C2×M16—111no—
350C2×M16—111no—
351C2×M16—221no—
352C2×M16C22⋊D1111yescharacteristic
353C2×M16C22⋊D1111yescharacteristic
354C22×C8—21no—
355C22×C8—221no—
356C4⋊Q8—111no—
357C4⋊Q8—111no—
358#126—21no—
359#125—221no—
360#125C4×D1111yescharacteristic
361#124C4×D1111yescharacteristic
362#123—21no—
363C22⋊Q8—111no—
364C22⋊Q8—111no—
365C22⋊Q8—221no—
366C22⋊Q8C4×D1111yescharacteristic
367#121C4×D1111yescharacteristic
368C4×Q8—111no—
369C4×Q8—111no—
370C4×Q8—221no—
371C4×Q8C22×D1111yescharacteristic
372C4×D4—21no—
373C4×D4C22×D1111yescharacteristic
374#117—21no—
375#117—221no—
376C2×C42C22×D1111yescharacteristic
377#107—111no—
378#107—111no—
379#106—111no—
380#106—111no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—111no—
384C4⋊C8—111no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8—221no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390C4⋊C8C22×D1111yescharacteristic
391C4⋊C8C22×D1111yescharacteristic
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#103—111no—
398#102—111no—
399#102—111no—
400C22⋊C8—21no—
401C22⋊C8—21no—
402C22⋊C8—21no—
403#97—21no—
404#97—111no—
405#97—111no—
406#97—221no—
407#97—221no—
408#97—221no—
409#97C22⋊D1111yescharacteristic
410#97C22⋊D1111yescharacteristic
411C4×C8—21no—
412C4×C8—21no—
413C4×C8—111no—
414C4×C8—111no—
415C4×C8—111no—
416C4×C8—111no—
417C4×C8—221no—
418C4×C8—221no—
419C4×C8C22×D1111yescharacteristic
420C4×C8C22×D1111yescharacteristic
421C2×C11—41no—
422C2×C11—81no—
423C2×C11#293511yescharacteristic
424C2×C11C4×#13711yescharacteristic
425C2×C11#295611yescharacteristic
426C2×Q8—111no—
427C2×Q8—111no—
428C2×Q8—221no—
429C2×Q8C2×C4×D1111yescharacteristic
430C2×D4—21no—
431C2×D4C2×C4×D1111yescharacteristic
432C22×C4—21no—
433C22×C4C2×C4×D1111yescharacteristic
434C22×C4#433911yescharacteristic
435C22×C4C2×C22⋊D1111yescharacteristic
436Q16—222no—
437Q16—441no—
438SD16—222no—
439SD16—441no—
440M16—22no—
441M16—41no—
442M16—42no—
443M16—222no—
444M16—441no—
445M16—442no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—42no—
449C2×C8—111no—
450C2×C8—111no—
451C2×C8—111no—
452C2×C8—111no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—442no—
458C2×C8C2×C22⋊D1111yescharacteristic
459C2×C8C2×C22⋊D1111yescharacteristic
460C2×C8C2×C22⋊D1111yescharacteristic
461C2×C8C2×C22⋊D1111yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—111no—
467C4⋊C4—111no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4C2×C4×D1111yescharacteristic
476C4⋊C4C2×C4×D1111yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—221no—
483C22⋊C4—221no—
484C42—21no—
485C42—221no—
486C42—221no—
487C42C2×C4×D1111yescharacteristic
488C42#433911yescharacteristic
489C42C2×C22⋊D1111yescharacteristic
490C42C23×D1111yescharacteristic
491C11#1807711yescharacteristic, complemented, Sylow
492C23—21no—
493C23C4×C22⋊D1111yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—221no—
497Q8—221no—
498Q8—221no—
499Q8—221no—
500Q8—881no—
501D4—21no—
502D4—21no—
503D4—81no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4C4×C22⋊D1111yescharacteristic
519C2×C4C4×C22⋊D1111yescharacteristic
520C2×C4C4×C22⋊D1111yescharacteristic
521C2×C4C22×C4×D1111yescharacteristic
522C2×C4C2×#433911yescharacteristic
523C2×C4C22×C22⋊D1111yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—41no—
528C8—41no—
529C8—112no—
530C8—222no—
531C8—221no—
532C8—221no—
533C8—221no—
534C8—441no—
535C8—441no—
536C8—441no—
537C8#6700412yes—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22C2×C4×C22⋊D1111yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—441no—
553C4—441no—
554C4—441no—
555C4—441no—
556C4D11×#13111yescharacteristic
557C4#1062328111yescharacteristic
558C4#1062335311yescharacteristic
559C4C2×#6700411yescharacteristic
560C2—41no—
561C2—81no—
562C2#1307735811yescharacteristic
563C2C4×#6700411yescharacteristic
564C2#1307752311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2969C2
socleC22×C11C2×C4×D4
prime radicalC11×#121C2×C4
cosocleC42×C11C24
hypercenter#2969D11
hypocenterC11#18077
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2969

Complements

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

NH ≅ G/Ntype
2. #13077563C2semidirect
3. #13067518C2semidirect
4. #13067511C2semidirect
5. #13067492C2semidirect
6. #13067487C2semidirect
7. #13067464C2semidirect
8. #13067452C2semidirect
9. #13067433C2semidirect
10. C8×#4324C2semidirect
11. #13067369C2semidirect
12. #13067036C2semidirect
14. #13066919C2semidirect
491. C11#18077semidirect

Maximal subgroups

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

subgroupindex
#130792232
#130775632
#130675182
#130675112
#130674922
#130674872
#130674642
#130674522
#130674332
C8×#43242
#130673692
#130670362
#130670292
#130669192
C11×#29692
#1807711