Finite Group Databasebeta

← #14909518

Subgroups — #14909518

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#13078197C211yesmaximal, characteristic, complemented
2C2×#10622728C211yesmaximal, characteristic, complemented
3#13070819C211yesmaximal, characteristic, complemented
4#13070808C212yesmaximal, complemented
5#13070802C211yesmaximal, characteristic, complemented
6#13070712C212yesmaximal, complemented
7#13070702C212yesmaximal, complemented
8#13070547C211yesmaximal, characteristic, complemented
9#13070541C212yesmaximal, complemented
10#13070530C211yesmaximal, characteristic, complemented
11C2×C11×C22⋊C16C211yesmaximal, characteristic, complemented
12C23×C8×C11C2211yescharacteristic
13#10623322—21no—
14C2×#66983—21no—
15C2×#66957C2211yescharacteristic, complemented
16C22×D88C2211yescharacteristic
17C22×C11×C16C2212yescomplemented
18#10622729C2211yescharacteristic
19#10622729C2211yescharacteristic, complemented
20#10622728—21no—
21#10622728—21no—
22#10622728C2212yes—
23#10622728C2212yes—
24#10622728C2211yescharacteristic
25#10622728C2211yescharacteristic, complemented
26#10622727—21no—
27#10622727—21no—
28#10622726—21no—
29C2×#66885—21no—
30#10622719C2211yescharacteristic, complemented
31C2×#66882C2211yescharacteristic
32C2×#66864C2212yescomplemented
33C2×D176C2212yescomplemented
34C11×C22⋊C16C2211yescharacteristic
35C11×C22⋊C16C2211yescharacteristic
36C11×C22⋊C16C2212yescomplemented
37#10622147C2212yescomplemented
38#10622147C2212yescomplemented
39#10622147C2212yescomplemented
40#10622143C2212yescomplemented
41#10622142C2212yescomplemented
42#10622141C2212yescomplemented
43C23×C4×C11D411yescharacteristic
44C22×C22⋊D11—41no—
45C2×#4339—21no—
46C22×D44—21no—
47C22×C8×C11—42no—
48C22×C8×C11D411yescharacteristic
49C22×C8×C11D411yescharacteristic
50C22×C8×C11D411yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2311yescharacteristic
54#67006—41no—
55#66983—21no—
56#66983—21no—
57#66983—22no—
58#66983—22no—
59#66983—41no—
60#66983—41no—
61#66982—41no—
62C4×C22⋊D11—41no—
63C4×C22⋊D11—41no—
64C2×(C2×D11)⋊C4—41no—
65#66979—21no—
66C2×C4⋊Dic11—21no—
67#66977—21no—
68#66977—21no—
69C2×Dic44C2311yescharacteristic
70#66957—42no—
71C2×D88—21no—
72C2×D88—42no—
73C2×D88C2312yes—
74C2×D88C2311yescharacteristic
75C2×#4314—21no—
76C2×C11×C16—42no—
77C2×C11×C16C2312yes—
78C2×C11×C16C2312yes—
79#66885—22no—
80#66885—22no—
81#66885—21no—
82#66885—21no—
83#66882—21no—
84#66882C2312yes—
85#66882C2311yescharacteristic
86#66882C2311yescharacteristic
87#66881—21no—
88#66880—21no—
89#66880—21no—
90#66864—42no—
91D176—42no—
92#33754—111nomaximal, Sylow
93C24×C11D811yescharacteristic
94C23×D11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11D811yescharacteristic
98C22×C4×C11D811yescharacteristic
99C22×C4×C11D811yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C2×C22⋊D11—41no—
104C2×C22⋊D11—41no—
105C2×C22⋊D11—41no—
106C2×C22⋊D11—42no—
107C2×C22⋊D11—42no—
108C2×C22⋊D11—84no—
109C22×Dic11—41no—
110#4339—42no—
111#4339—42no—
112C2×D44—21no—
113C2×D44—22no—
114C2×D44—42no—
115C2×D44—42no—
116C2×D44—41no—
117C2×C4×D11—41no—
118C2×Dic22—21no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11—41no—
123C2×C8×C11—41no—
124C2×C8×C11—41no—
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2411yescharacteristic
129C22⋊Dic11—41no—
130C22⋊Dic11—41no—
131C22⋊Dic11—41no—
132(C2×D11)⋊C4—42no—
133(C2×D11)⋊C4—42no—
134(C2×D11)⋊C4—41no—
135(C2×D11)⋊C4—41no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11—22no—
139C4⋊Dic11—41no—
140Dic11⋊C4—41no—
141Dic11⋊C4—41no—
142C4×Dic11—41no—
143Dic44—22no—
144D88—22no—
145D88—22no—
146D88—22no—
147D88—42no—
148#4314—42no—
149C11×C16—22no—
150C11×C16—22no—
151#3050—111no—
152C2×#466—111no—
153#2236—111no—
154#2234—112no—
155#2233—111no—
156#2217—112no—
157#2215—112no—
158#2187—111no—
159#2186—112no—
160#2184—111no—
161C2×C22⋊C16D1111yescharacteristic, complemented
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—41no—
165C23×C11C2×D811yescharacteristic
166C23×C11C2×D811yescharacteristic
167C23×C11C2×D811yescharacteristic
168C22×D11—41no—
169C22×D11—42no—
170C22×D11—82no—
171C22×D11—82no—
172C22×D11—82no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11C2×D811yescharacteristic
183C2×C4×C11C2×D811yescharacteristic
184C2×C4×C11C2×D811yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C22⋊D11—82no—
187C22⋊D11—84no—
188C22⋊D11—82no—
189C22⋊D11—82no—
190C22⋊D11—84no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—42no—
195C2×Dic11—82no—
196D44—41no—
197D44—42no—
198D44—42no—
199D44—41no—
200D44—82no—
201C4×D11—82no—
202Dic22—41no—
203Dic22—41no—
204C8×C11—21no—
205C8×C11—21no—
206C8×C11—21no—
207C8×C11H(5,𝔽2)12yes—
208C2×#135—111no—
209C22×D8—111no—
210C23×C8C2×D1111yescharacteristic
211#525—221no—
212C2×#121—221no—
213C2×SD32—112no—
214C2×D16—112no—
215C22×C16C2×D1112yescomplemented
216#467—111no—
217#467—111no—
218#466—111no—
219#466—112no—
220#466—112no—
221#466—111no—
222#466—221no—
223#466—221no—
224#465—221no—
225#465—221no—
226#427—111no—
227C2×#107—111no—
228#416—221no—
229C2×#102—221no—
230#367—112no—
231#366—112no—
232#358—112no—
233#357—112no—
234#357—112no—
235#357—112no—
236C22⋊C16C2×D1111yescharacteristic
237C22⋊C16C2×D1111yescharacteristic
238C22⋊C16C2×D1112yescomplemented
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—44no—
247C22×C11#50812yes—
248C22×C11#50912yes—
249C22×C11C22×D811yescharacteristic
250C2×D11—82no—
251C2×D11—81no—
252C2×D11—82no—
253C2×D11—81no—
254C2×D11—82no—
255C2×D11—81no—
256C2×D11—164no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11#53411yescharacteristic
261C4×C11#57511yescharacteristic
262Dic11—81no—
263Dic11—82no—
264Dic11—81no—
265Dic11—81no—
266C2×#41—221no—
267C22×D4—221no—
268C22×D4—441no—
269C23×C4D4411yescharacteristic
270#135—442no—
271C2×Q16—111no—
272C2×SD16—221no—
273C2×D8—112no—
274C2×D8—111no—
275C2×D8—221no—
276C2×D8—442no—
277C22×C8—42no—
278C22×C8D4411yescharacteristic
279C22×C8D4411yescharacteristic
280C22×C8D4411yescharacteristic
281C22×C8C22×D1111yescharacteristic
282C22×C8C22×D1111yescharacteristic
283C22×C8C22×D1111yescharacteristic
284#123—441no—
285C22⋊Q8—221no—
286C22⋊Q8—221no—
287#121—222no—
288#121—222no—
289#121—221no—
290#121—221no—
291#121—441no—
292#121—441no—
293#120—441no—
294C4×D4—441no—
295C4×D4—441no—
296#117—221no—
297C2×C4⋊C4—221no—
298C2×C22⋊C4—441no—
299SD32—442no—
300D16—442no—
301C2×C16—42no—
302C2×C16C22×D1112yes—
303C2×C16C22×D1112yes—
304#107—111no—
305#107—111no—
306#107—112no—
307#107—221no—
308#106—221no—
309#103—221no—
310#103—221no—
311#102—222no—
312#102—222no—
313#102—221no—
314#102—221no—
315C2×C11—22no—
316C2×C11—22no—
317C2×C11—41no—
318C2×C11#318611yescharacteristic
319C2×C11C2×#50811yescharacteristic
320C2×C11C2×#50911yescharacteristic
321D11—161no—
322D11—162no—
323C24—441no—
324C24D8811yescharacteristic
325#41—442no—
326#41—442no—
327C2×Q8—221no—
328C2×D4—222no—
329C2×D4—221no—
330C2×D4—442no—
331C2×D4—442no—
332C2×D4—441no—
333C2×D4—441no—
334C2×D4—441no—
335C2×D4—442no—
336C2×D4—442no—
337C2×D4—441no—
338C2×D4—884no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—441no—
342C22×C4—441no—
343C22×C4D8811yescharacteristic
344C22×C4D8811yescharacteristic
345C22×C4D8811yescharacteristic
346C22×C4C2×D4411yescharacteristic
347C22×C4C2×D4411yescharacteristic
348C22×C4C2×D4411yescharacteristic
349Q16—222no—
350SD16—442no—
351D8—222no—
352D8—222no—
353D8—222no—
354D8—442no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—41no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8C2×D4411yescharacteristic
362C2×C8C2×D4411yescharacteristic
363C2×C8C2×D4411yescharacteristic
364C2×C8C23×D1111yescharacteristic
365C4⋊C4—222no—
366C4⋊C4—221no—
367C4⋊C4—221no—
368C4⋊C4—441no—
369C4⋊C4—441no—
370C4⋊C4—441no—
371C22⋊C4—441no—
372C22⋊C4—441no—
373C22⋊C4—441no—
374C22⋊C4—442no—
375C22⋊C4—442no—
376C22⋊C4—441no—
377C22⋊C4—441no—
378C42—441no—
379C16—22no—
380C16—22no—
381C11#3375411yescharacteristic, complemented, Sylow
382C23—22no—
383C23—22no—
384C23—41no—
385C23—441no—
386C23—442no—
387C23—882no—
388C23—882no—
389C23—882no—
390C23C2×D8811yescharacteristic
391C23C2×D8811yescharacteristic
392C23C2×D8811yescharacteristic
393Q8—441no—
394Q8—441no—
395D4—442no—
396D4—441no—
397D4—442no—
398D4—441no—
399D4—882no—
400D4—884no—
401D4—882no—
402D4—882no—
403D4—884no—
404D4—882no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—442no—
417C2×C4—441no—
418C2×C4—882no—
419C2×C4—882no—
420C2×C4C2×D8811yescharacteristic
421C2×C4C2×D8811yescharacteristic
422C2×C4C2×D8811yescharacteristic
423C2×C4C22×D4411yescharacteristic
424C8—21no—
425C8—21no—
426C8—21no—
427C8#6703712yes—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—44no—
436C22—881no—
437C22—882no—
438C22—881no—
439C22—882no—
440C22—882no—
441C22—881no—
442C22—1764no—
443C22#1062251712yes—
444C22#1062252112yes—
445C22C22×D8811yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—881no—
450C4—881no—
451C4—882no—
452C4—881no—
453C4#1062302411yescharacteristic
454C4#1062327911yescharacteristic
455C2—22no—
456C2—22no—
457C2—41no—
458C2—1762no—
459C2—1761no—
460C2#1307936711yescharacteristic
461C2C2×#1062251711yescharacteristic
462C2C2×#1062252111yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×C22⋊C16C2
socleC22×C11C22×D8
hypercenterC2×C22⋊C16D11
hypocenterC11#33754
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C2×C22⋊C16

Complements

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

NH ≅ G/Ntype
1. #13078197C2semidirect
2. C2×#10622728C2semidirect
3. #13070819C2semidirect
4. #13070808C2semidirect
5. #13070802C2semidirect
6. #13070712C2semidirect
7. #13070702C2semidirect
8. #13070547C2semidirect
9. #13070541C2semidirect
10. #13070530C2semidirect
11. C2×C11×C22⋊C16C2semidirect
15. C2×#66957C22semidirect
17. C22×C11×C16C22semidirect
19. #10622729C22semidirect
25. #10622728C22semidirect
30. #10622719C22semidirect
32. C2×#66864C22semidirect
33. C2×D176C22semidirect
36. C11×C22⋊C16C22semidirect
37. #10622147C22semidirect
38. #10622147C22semidirect
39. #10622147C22semidirect
40. #10622143C22semidirect
41. #10622142C22semidirect
42. #10622141C22semidirect
161. C2×C22⋊C16D11semidirect
215. C22×C16C2×D11semidirect
238. C22⋊C16C2×D11semidirect
381. C11#33754semidirect

Maximal subgroups

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

subgroupindex
#130781972
C2×#106227282
#130708192
#130708082
#130708022
#130707122
#130707022
#130705472
#130705412
#130705302
C2×C11×C22⋊C162
#3375411