Finite Group Databasebeta

← #14737356

Subgroups — #14737356

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079928C211yesmaximal, characteristic
2#13079757C211yesmaximal, characteristic, complemented
3#13079075C211yesmaximal, characteristic
4#13068110C212yesmaximal, complemented
5#13068088C212yesmaximal, complemented
6#13067986C212yesmaximal, complemented
7#13067964C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067266C211yesmaximal, characteristic
10C2×#10622120C211yesmaximal, characteristic, complemented
11C11×#2962C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×#66962—21no—
14C2×#66962—21no—
15#10623008C2211yescharacteristic
16C2×#66922C2211yescharacteristic
17C11×#446—22no—
18C11×#446C2212yes—
19C8×Q8×C11C2212yes—
20C11×#424—21no—
21C2×C11×C4⋊C8C2211yescharacteristic
22C11×#405—21no—
23C4×C11×M16C2211yescharacteristic
24#10622697—21no—
25#10622696—21no—
26#10622694—21no—
27#10622692—21no—
28#10622661—22no—
29#10622656—22no—
30#10622640C2212yes—
31#10622633C2212yes—
32#10622633C2212yes—
33#10622633C2212yes—
34#10622538C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622328—22no—
37#10622312C2212yes—
38#10622306C2212yes—
39#10622123C2211yescharacteristic
40#10622123C2211yescharacteristic
41#10622120C2211yescharacteristic
42#10622120C2211yescharacteristic
43#10622120C2212yes—
44#10622120C2212yes—
45#10622096C2212yes—
46#10622095C2212yes—
47C2×#4339—21no—
48C22×Dic22—21no—
49C2×C11×M16D411yescharacteristic
50C2×C11×M16D411yescharacteristic
51C22×C8×C11—21no—
52C11×C4⋊Q8D411yescharacteristic
53C11×C4⋊Q8D411yescharacteristic
54C11×#125—21no—
55C11×C22⋊Q8—21no—
56C11×C22⋊Q8D412yes—
57C4×Q8×C11—21no—
58C4×Q8×C11C2312yes—
59C11×#117—21no—
60C2×C42×C11C2311yescharacteristic
61C2×#4325—22no—
62#66983—21no—
63#66983—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C22×C11⋊C8—21no—
67#66962—44no—
68#66962—44no—
69C2×Dic44—22no—
70C2×Dic44—22no—
71C2×#4314—22no—
72C2×#4314—22no—
73#66928—21no—
74#66927C2311yescharacteristic
75C4×D44—21no—
76C4×D44—21no—
77#66922—21no—
78#66922—21no—
79#66922—21no—
80#66922C2312yes—
81#66922C2311yescharacteristic
82C11×C4⋊C8—22no—
83C11×C4⋊C8—22no—
84C11×C4⋊C8—21no—
85C11×C4⋊C8C2311yescharacteristic
86C11×C4⋊C8C2311yescharacteristic
87C11×#97—22no—
88C11×#97D412yes—
89C4×C8×C11—22no—
90C4×C8×C11C2312yes—
91#66899—22no—
92#66899—22no—
93#66899—22no—
94C22⋊(C11⋊C8)—21no—
95#66873—22no—
96#66872—22no—
97#66872—22no—
98#66872—22no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)C2312yes—
101C4⋊(C11⋊C8)C2311yescharacteristic
102C4⋊(C11⋊C8)C2311yescharacteristic
103C4×C11⋊C8—21no—
104#19239—111nomaximal, Sylow
105C2×Q8×C11—21no—
106C2×Q8×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C2×C22⋊D11—41no—
111C22×Dic11—41no—
112#4339—42no—
113#4339—42no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44—21no—
117C2×C4×D11—41no—
118C2×Dic22—22no—
119C2×Dic22—21no—
120C2×Dic22—41no—
121C2×Dic22—42no—
122C2×Dic22—42no—
123C11×M16—22no—
124C11×M16SD1614yescomplemented
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—42no—
128C2×C8×C11C2×D412yes—
129C2×C8×C11C2×D412yes—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4C2×D412yes—
136C11×C22⋊C4—22no—
137C42×C11—22no—
138C42×C11C2×D411yescharacteristic
139C42×C11C2×D411yescharacteristic
140C42×C11#4111yescharacteristic
141C42×C11C2411yescharacteristic
142#4325—82no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145C4⋊Dic11—22no—
146C4⋊Dic11—21no—
147C4⋊Dic11—22no—
148C4⋊Dic11—21no—
149C4⋊Dic11—41no—
150C4⋊Dic11—41no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—81no—
155Dic44—44no—
156Dic44—44no—
157#4314—44no—
158#4314—44no—
159#3246—111no—
160#3229—111no—
161#3152—111no—
162#2962D1111yescharacteristic, complemented
163#1690—112no—
164#1686—112no—
165#1670—112no—
166#1666—112no—
167#1565—111no—
168#1540—111no—
169C2×#332—111no—
170C23×C11#12111yescharacteristic
171C22×D11—41no—
172Q8×C11—22no—
173Q8×C11—22no—
174Q8×C11—81no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—41no—
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11C2×SD1612yes—
184C2×C4×C11AGL(1,ℤ/8)12yes—
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C22⋊D11—82no—
189C2×Dic11—42no—
190C2×Dic11—41no—
191C2×Dic11—82no—
192D44—41no—
193D44—41no—
194D44—41no—
195D44—41no—
196D44—81no—
197C4×D11—82no—
198Dic22—42no—
199Dic22—41no—
200Dic22—42no—
201Dic22—41no—
202Dic22—82no—
203C8×C11—22no—
204C8×C11—41no—
205C8×C11—41no—
206C8×C11C2×SD1614yes—
207C11⋊C8—41no—
208C11⋊C8—42no—
209C11⋊C8—41no—
210C2×#137—221no—
211C2×#137—221no—
212#533C2×D1111yescharacteristic
213#532—111no—
214C2×C4⋊Q8—111no—
215#498—221no—
216#497—222no—
217#494—112no—
218#492—112no—
219#487—221no—
220#483—222no—
221#476—221no—
222#475—112no—
223#475—112no—
224#475—112no—
225#465—222no—
226#461—221no—
227#460—112no—
228#446—22no—
229#446C2×D1112yes—
230C8×Q8C2×D1112yes—
231#431—111no—
232#424—21no—
233C2×C4⋊C8—111no—
234C2×C4⋊C8C2×D1111yescharacteristic
235#405—21no—
236C4×M16C2×D1111yescharacteristic
237#335—112no—
238#334—112no—
239#332—112no—
240#332—112no—
241#332—111no—
242#332—111no—
243#331—111no—
244#331—111no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11#46012yes—
248C22×C11C2×#12111yescharacteristic
249C2×D11—81no—
250C2×D11—81no—
251C2×D11—81no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—42no—
256C4×C11—42no—
257C4×C11#46012yes—
258C4×C11C22×SD1611yescharacteristic
259C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
260C4×C11#57711yescharacteristic
261C4×C11#57811yescharacteristic
262Dic11—82no—
263Dic11—81no—
264C2×#41—221no—
265C22×Q8—221no—
266#137—444no—
267#137—444no—
268C2×Q16—222no—
269C2×Q16—222no—
270C2×SD16—222no—
271C2×SD16—222no—
272C2×SD16—222no—
273C2×M16C22⋊D1111yescharacteristic
274C2×M16C22⋊D1111yescharacteristic
275C22×C8—21no—
276C22×C8—221no—
277C4⋊Q8—112no—
278C4⋊Q8—111no—
279C4⋊Q8—221no—
280C4⋊Q8—221no—
281C4⋊Q8—221no—
282C4⋊Q8D4411yescharacteristic
283C4⋊Q8D4411yescharacteristic
284#127—111no—
285#125—21no—
286#124—221no—
287C22⋊Q8—21no—
288C22⋊Q8D4412yes—
289#121—221no—
290#121—221no—
291C4×Q8—21no—
292C4×Q8C22×D1112yes—
293C4×D4—221no—
294C4×D4—221no—
295#117—21no—
296C2×C4⋊C4—221no—
297C2×C4⋊C4—221no—
298C2×C42C22×D1111yescharacteristic
299#106—222no—
300#106—222no—
301#106—222no—
302C4⋊C8—22no—
303C4⋊C8—22no—
304C4⋊C8—21no—
305C4⋊C8—111no—
306C4⋊C8—111no—
307C4⋊C8—112no—
308C4⋊C8—221no—
309C4⋊C8C22×D1111yescharacteristic
310C4⋊C8C22×D1111yescharacteristic
311#103—222no—
312#103—222no—
313#103—222no—
314#102—222no—
315C22⋊C8—221no—
316#97—22no—
317#97C22⋊D1112yes—
318C4×C8—22no—
319C4×C8—221no—
320C4×C8C22×D1112yes—
321C2×C11—22no—
322C2×C11C2×#46011yescharacteristic
323C2×C11#306311yescharacteristic
324C2×C11#306911yescharacteristic
325D11—161no—
326#41—442no—
327#41—442no—
328C2×Q8—21no—
329C2×Q8—221no—
330C2×Q8—222no—
331C2×Q8—441no—
332C2×Q8—442no—
333C2×Q8—442no—
334C2×Q8C2×D4412yes—
335C2×D4—221no—
336C2×D4—221no—
337C2×D4—221no—
338C2×D4—441no—
339C22×C4—441no—
340C22×C4—441no—
341C22×C4C2×D4411yescharacteristic
342C22×C4#433911yescharacteristic
343C22×C4C2×C22⋊D1111yescharacteristic
344Q16—444no—
345Q16—444no—
346SD16—444no—
347SD16—444no—
348SD16—882no—
349M16—22no—
350M16#432514yescomplemented
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—42no—
354C2×C8—221no—
355C2×C8—221no—
356C2×C8—222no—
357C2×C8—881no—
358C2×C8C2×C22⋊D1112yes—
359C2×C8C2×C22⋊D1112yes—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—222no—
366C4⋊C4—221no—
367C4⋊C4—222no—
368C4⋊C4—221no—
369C4⋊C4—441no—
370C4⋊C4—441no—
371C4⋊C4C2×D4412yes—
372C22⋊C4—22no—
373C22⋊C4—441no—
374C22⋊C4—441no—
375C42—22no—
376C42C2×D4411yescharacteristic
377C42#433911yescharacteristic
378C42C2×C22⋊D1111yescharacteristic
379C42C23×D1111yescharacteristic
380C11#1923911yescharacteristic, complemented, Sylow
381C23—441no—
382C23#6698311yescharacteristic
383Q8—22no—
384Q8—22no—
385Q8—81no—
386Q8—442no—
387Q8—441no—
388Q8—442no—
389Q8—441no—
390Q8—882no—
391D4—441no—
392D4—441no—
393D4—441no—
394D4—441no—
395D4—881no—
396D4—882no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—41no—
402C2×C4—441no—
403C2×C4—442no—
404C2×C4—882no—
405C2×C4—882no—
406C2×C4#6698311yescharacteristic
407C2×C4#6698311yescharacteristic
408C2×C4#6698311yescharacteristic
409C2×C4C2×#432512yes—
410C2×C4#6700212yes—
411C2×C4C22×D4411yescharacteristic
412C2×C4C2×#433911yescharacteristic
413C2×C4C22×C22⋊D1111yescharacteristic
414C8—22no—
415C8—41no—
416C8—41no—
417C8—442no—
418C8—441no—
419C8—441no—
420C8C2×#432514yes—
421C22—21no—
422C22—21no—
423C22—881no—
424C22—881no—
425C22—881no—
426C22#1062264012yes—
427C22C2×#6698311yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—42no—
432C4—42no—
433C4—881no—
434C4—882no—
435C4#1062264012yes—
436C4#1062328211yescharacteristic
437C4#1062328411yescharacteristic
438C4C22×#432511yescharacteristic
439C4C2×#6700211yescharacteristic
440C2—22no—
441C2—1761no—
442C2C2×#1062264011yescharacteristic
443C2#1307830711yescharacteristic
444C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2962C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#2962D11
hypocenterC11#19239
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
2. #13079757C2semidirect
4. #13068110C2semidirect
5. #13068088C2semidirect
6. #13067986C2semidirect
7. #13067964C2semidirect
8. #13067368C2semidirect
10. C2×#10622120C2semidirect
11. C11×#2962C2semidirect
124. C11×M16SD16semidirect
162. #2962D11semidirect
350. M16#4325semidirect
380. C11#19239semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130797572
#130790752
#130681102
#130680882
#130679862
#130679642
#130673682
#130672662
C2×#106221202
C11×#29622
#1923911