Finite Group Databasebeta

← #14909515

Subgroups — #14909515

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078195C211yesmaximal, characteristic, complemented
2C2×#10622496C211yesmaximal, characteristic, complemented
3#13070818C211yesmaximal, characteristic, complemented
4#13070809C212yesmaximal, complemented
5#13070713C212yesmaximal, complemented
6#13070701C212yesmaximal, complemented
7#13070547C211yesmaximal, characteristic, complemented
8#13070540C212yesmaximal, complemented
9#13070527C211yesmaximal, characteristic, complemented
10D11×C22⋊C16C211yesmaximal, characteristic, complemented
11C11×#2233C211yesmaximal, characteristic, complemented
12C2×#66965C2211yescharacteristic, complemented
13C22×D88C2211yescharacteristic
14C22×C8×D11C2211yescharacteristic
15#10623137—21no—
16C2×#66948—21no—
17C11×#466C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19#10622770C2211yescharacteristic, complemented
20C2×#66890C2212yescomplemented
21#10622729C2211yescharacteristic
22#10622654—21no—
23C2×#66873—21no—
24C2×#66864C2212yescomplemented
25C2×C16×D11C2212yescomplemented
26#10622500C2211yescharacteristic, complemented
27#10622496—21no—
28#10622496—21no—
29#10622496C2212yes—
30#10622496C2212yes—
31#10622493C2211yescharacteristic, complemented
32#10622391—21no—
33#10622385—21no—
34C11×#367C2212yescomplemented
35C11×#357C2212yescomplemented
36C11×C22⋊C16C2211yescharacteristic
37C22⋊(C11⋊C16)C2211yescharacteristic
38#10622147C2212yescomplemented
39(C2×D11)⋊C16C2212yescomplemented
40#10622130C2212yescomplemented
41#10622129C2212yescomplemented
42#10622127C2212yescomplemented
43C2×#4341—21no—
44C22×D44—21no—
45C22×D44—41no—
46C22×C4×D11D411yescharacteristic
47C2×C11×D8C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×#121—21no—
50C2×C11×C4⋊C4—21no—
51#66991—21no—
52#66990—41no—
53D4×Dic11—41no—
54C2×#4324—21no—
55C2×(C2×D11)⋊C4—41no—
56#66977—21no—
57C22×C11⋊C8D411yescharacteristic
58#66965—42no—
59C2×Dic44C2311yescharacteristic
60C2×D88—21no—
61C2×D88—42no—
62C2×D88C2312yes—
63C2×C8×D11—42no—
64C2×C8×D11D411yescharacteristic
65C2×C8×D11D411yescharacteristic
66C2×C8×D11C2311yescharacteristic
67C2×C8×D11C2311yescharacteristic
68#66950—21no—
69#66948—22no—
70#66948—22no—
71#66948—41no—
72#66948—41no—
73#66945—21no—
74#66936—41no—
75(C22⋊D11)⋊C4—41no—
76C2×C11×C16C2312yes—
77C11×#107—21no—
78C11×#107C2311yescharacteristic
79C11×#107C2312yes—
80C11×#102—21no—
81#66896—21no—
82#66890—42no—
83#66882C2311yescharacteristic
84#66880—21no—
85C2×C11⋊C16C2312yes—
86#66874—21no—
87#66873—22no—
88#66873—22no—
89#66872—21no—
90#66864—42no—
91C16×D11—42no—
92#33754—111nomaximal, Sylow
93C23×D11—41no—
94C23×D11D811yescharacteristic
95C2×D4×C11—21no—
96C2×D4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C2×C22⋊D11—41no—
100C2×C22⋊D11—41no—
101C22×Dic11—41no—
102C22×Dic11D811yescharacteristic
103#4341—42no—
104#4341—42no—
105C2×D44—22no—
106C2×D44—42no—
107C2×D44—42no—
108C2×D44—42no—
109C2×D44—42no—
110C2×D44—41no—
111C2×D44—84no—
112C2×C4×D11—41no—
113C2×C4×D11—41no—
114C2×C4×D11D811yescharacteristic
115C2×C4×D11D811yescharacteristic
116C2×C4×D11C2×D411yescharacteristic
117C2×C4×D11C2×D411yescharacteristic
118C2×Dic22—21no—
119C11×D8—22no—
120C2×C8×C11—22no—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2411yescharacteristic
123C11×C4⋊C4—21no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—41no—
126C11×C22⋊C4—41no—
127C22⋊Dic11—41no—
128C22⋊Dic11—41no—
129#4324—42no—
130(C2×D11)⋊C4—42no—
131(C2×D11)⋊C4—42no—
132(C2×D11)⋊C4—41no—
133(C2×D11)⋊C4—41no—
134C4⋊Dic11—21no—
135C4⋊Dic11—41no—
136Dic11⋊C4—41no—
137C4×Dic11—41no—
138C2×C11⋊C8—41no—
139C2×C11⋊C8C2×D411yescharacteristic
140C2×C11⋊C8C2×D411yescharacteristic
141Dic44—22no—
142D88—22no—
143D88—22no—
144D88—42no—
145C8×D11—22no—
146C8×D11—22no—
147C8×D11—41no—
148C8×D11—41no—
149C11×C16—22no—
150C11⋊C16—22no—
151#3050—111no—
152C2×#466—111no—
153#2236—111no—
154#2234—112no—
155#2233D1111yescharacteristic, complemented
156#2217—112no—
157#2215—112no—
158#2187—111no—
159#2186—112no—
160#2184—111no—
161C2×C22⋊C16—111no—
162C23×C11—41no—
163C23×C11C2×D811yescharacteristic
164C22×D11—22no—
165C22×D11—22no—
166C22×D11—41no—
167C22×D11—42no—
168C22×D11—82no—
169C22×D11—82no—
170C22×D11—82no—
171C22×D11C2×D811yescharacteristic
172C22×D11C2×D811yescharacteristic
173D4×C11—41no—
174D4×C11—41no—
175D4×C11—82no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—82no—
181C2×C4×C11C2×D811yescharacteristic
182C2×C4×C11C22×D411yescharacteristic
183C22⋊D11—82no—
184C22⋊D11—82no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—82no—
189C2×Dic11C2×D811yescharacteristic
190C2×Dic11C2×D811yescharacteristic
191D44—42no—
192D44—42no—
193D44—82no—
194D44—84no—
195D44—84no—
196C4×D11—21no—
197C4×D11—21no—
198C4×D11—21no—
199C4×D11—21no—
200C4×D11—41no—
201C4×D11—41no—
202Dic22—41no—
203Dic22—41no—
204C8×C11—21no—
205C8×C11H(5,𝔽2)12yes—
206C11⋊C8—21no—
207C11⋊C8—21no—
208C2×#135—111no—
209C22×D8—111no—
210C23×C8—111no—
211#525—221no—
212C2×#121—221no—
213C2×SD32—112no—
214C2×D16—112no—
215C22×C16—112no—
216#467—111no—
217#467—111no—
218#466—111no—
219#466—112no—
220#466—112no—
221#466—221no—
222#466—221no—
223#466C2×D1111yescharacteristic
224#465—221no—
225#465—221no—
226#427—111no—
227C2×#107C2×D1111yescharacteristic
228#416—221no—
229C2×#102—221no—
230#367C2×D1112yescomplemented
231#366—112no—
232#358—112no—
233#357—112no—
234#357—112no—
235#357C2×D1112yescomplemented
236C22⋊C16—111no—
237C22⋊C16—112no—
238C22⋊C16C2×D1111yescharacteristic
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11#50812yes—
245C22×C11C22×D811yescharacteristic
246C2×D11—21no—
247C2×D11—21no—
248C2×D11—21no—
249C2×D11—21no—
250C2×D11—21no—
251C2×D11—44no—
252C2×D11—82no—
253C2×D11—82no—
254C2×D11—82no—
255C2×D11—164no—
256C2×D11#50912yes—
257C4×C11—21no—
258C4×C11—81no—
259C4×C11—82no—
260C4×C11#53411yescharacteristic
261C4×C11#57511yescharacteristic
262Dic11—21no—
263Dic11—21no—
264Dic11—81no—
265Dic11—81no—
266C2×#41—221no—
267C22×D4—221no—
268C22×D4—441no—
269C23×C4—111no—
270#135—442no—
271C2×Q16—111no—
272C2×SD16—221no—
273C2×D8—112no—
274C2×D8—221no—
275C2×D8—442no—
276C2×D8C22×D1111yescharacteristic
277C22×C8—111no—
278C22×C8—111no—
279C22×C8—111no—
280C22×C8—111no—
281C22×C8—111no—
282C22×C8—442no—
283C22×C8C22×D1111yescharacteristic
284#123—441no—
285C22⋊Q8—221no—
286C22⋊Q8—221no—
287#121—21no—
288#121—222no—
289#121—222no—
290#121—221no—
291#121—441no—
292#121—441no—
293#120—441no—
294C4×D4—441no—
295C4×D4—441no—
296#117—221no—
297C2×C4⋊C4—21no—
298C2×C22⋊C4—441no—
299SD32—442no—
300D16—442no—
301C2×C16—112no—
302C2×C16—442no—
303C2×C16C22×D1112yes—
304#107—21no—
305#107—111no—
306#107C22×D1111yescharacteristic
307#107C22×D1112yes—
308#106—221no—
309#103—221no—
310#103—221no—
311#102—21no—
312#102—222no—
313#102—222no—
314#102—221no—
315C2×C11—22no—
316C2×C11—161no—
317C2×C11#318611yescharacteristic
318C2×C11C2×#50811yescharacteristic
319C2×C11C2×#50911yescharacteristic
320D11—22no—
321D11—41no—
322D11—162no—
323C24—111no—
324C24—441no—
325#41—442no—
326#41—442no—
327C2×Q8—221no—
328C2×D4—21no—
329C2×D4—41no—
330C2×D4—222no—
331C2×D4—442no—
332C2×D4—442no—
333C2×D4—442no—
334C2×D4—442no—
335C2×D4—441no—
336C2×D4—441no—
337C2×D4—441no—
338C2×D4—884no—
339C22×C4—41no—
340C22×C4—111no—
341C22×C4—111no—
342C22×C4—111no—
343C22×C4—111no—
344C22×C4—111no—
345C22×C4—441no—
346C22×C4—441no—
347C22×C4—441no—
348C22×C4D4×D1111yescharacteristic
349Q16—222no—
350SD16—442no—
351D8—22no—
352D8—222no—
353D8—222no—
354D8—442no—
355C2×C8—22no—
356C2×C8—111no—
357C2×C8—111no—
358C2×C8—222no—
359C2×C8—222no—
360C2×C8—441no—
361C2×C8—441no—
362C2×C8—441no—
363C2×C8D4×D1111yescharacteristic
364C2×C8C23×D1111yescharacteristic
365C4⋊C4—21no—
366C4⋊C4—22no—
367C4⋊C4—41no—
368C4⋊C4—221no—
369C4⋊C4—441no—
370C4⋊C4—441no—
371C22⋊C4—41no—
372C22⋊C4—442no—
373C22⋊C4—442no—
374C22⋊C4—441no—
375C22⋊C4—441no—
376C22⋊C4—441no—
377C22⋊C4—441no—
378C42—441no—
379C16—22no—
380C16—222no—
381C11#3375411yescharacteristic, complemented, Sylow
382C23—41no—
383C23—111no—
384C23—111no—
385C23—222no—
386C23—222no—
387C23—441no—
388C23—442no—
389C23—882no—
390C23—882no—
391C23—882no—
392C23D8×D1111yescharacteristic
393Q8—441no—
394Q8—441no—
395D4—41no—
396D4—41no—
397D4—82no—
398D4—442no—
399D4—442no—
400D4—882no—
401D4—884no—
402D4—884no—
403D4—882no—
404D4—882no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—82no—
410C2×C4—111no—
411C2×C4—111no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—882no—
422C2×C4D8×D1111yescharacteristic
423C2×C4C2×D4×D1111yescharacteristic
424C8—21no—
425C8—221no—
426C8—221no—
427C8#6704212yes—
428C22—21no—
429C22—21no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—112no—
434C22—221no—
435C22—221no—
436C22—221no—
437C22—221no—
438C22—221no—
439C22—444no—
440C22—882no—
441C22—882no—
442C22—882no—
443C22—1764no—
444C22#1062252912yes—
445C22C2×D8×D1111yescharacteristic
446C4—21no—
447C4—81no—
448C4—82no—
449C4—221no—
450C4—221no—
451C4—881no—
452C4—881no—
453C4#1062318411yescharacteristic
454C4#1062330811yescharacteristic
455C2—22no—
456C2—161no—
457C2—222no—
458C2—441no—
459C2—1762no—
460C2#1307936611yescharacteristic
461C2C2×#1062252911yescharacteristic
462C2D11×#50911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2233C2
socleC22×C11C22×D8
hypercenter#2233D11
hypocenterC11#33754
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2233

Complements

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

NH ≅ G/Ntype
1. #13078195C2semidirect
2. C2×#10622496C2semidirect
3. #13070818C2semidirect
4. #13070809C2semidirect
5. #13070713C2semidirect
6. #13070701C2semidirect
7. #13070547C2semidirect
8. #13070540C2semidirect
9. #13070527C2semidirect
10. D11×C22⋊C16C2semidirect
11. C11×#2233C2semidirect
12. C2×#66965C22semidirect
19. #10622770C22semidirect
20. C2×#66890C22semidirect
24. C2×#66864C22semidirect
25. C2×C16×D11C22semidirect
26. #10622500C22semidirect
31. #10622493C22semidirect
34. C11×#367C22semidirect
35. C11×#357C22semidirect
38. #10622147C22semidirect
39. (C2×D11)⋊C16C22semidirect
40. #10622130C22semidirect
41. #10622129C22semidirect
42. #10622127C22semidirect
155. #2233D11semidirect
230. #367C2×D11semidirect
235. #357C2×D11semidirect
381. C11#33754semidirect

Maximal subgroups

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

subgroupindex
#130781952
C2×#106224962
#130708182
#130708092
#130707132
#130707012
#130705472
#130705402
#130705272
D11×C22⋊C162
C11×#22332
#3375411