Finite Group Databasebeta

← #14737124

Subgroups — #14737124

Order 2816.

630 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079588C212yesmaximal, complemented
2#13079195C211yesmaximal, characteristic, complemented
3#13068184C212yesmaximal, complemented
4#13068177C212yesmaximal, complemented
5#13068010C211yesmaximal, characteristic, complemented
6#13068005C211yesmaximal, characteristic, complemented
7#13067976C211yesmaximal, characteristic, complemented
8#13067971C211yesmaximal, characteristic, complemented
9#13067364C211yesmaximal, characteristic, complemented
10#13067322C212yesmaximal, complemented
11C11×#2966C211yesmaximal, characteristic, complemented
12C11×#529C2211yescharacteristic
13#10623008C2212yes—
14C11×#446C2211yescharacteristic
15C8×Q8×C11C2211yescharacteristic
16C11×#436C2211yescharacteristic
17C11×#435—21no—
18C8×D4×C11—21no—
19C8×D4×C11C2211yescharacteristic
20C11×#433—21no—
21C11×#432C2211yescharacteristic
22C11×#405—21no—
23C2×C4×C8×C11C2211yescharacteristic
24#10622728—21no—
25#10622728—21no—
26#10622681—22no—
27#10622672—22no—
28#10622660—22no—
29#10622650—22no—
30#10622644C2212yes—
31#10622640C2212yes—
32#10622632C2212yes—
33#10622628C2212yes—
34#10622538C2212yes—
35#10622308C2211yescharacteristic
36#10622307C2212yes—
37C4×D88—21no—
38C4×D88—21no—
39#10622295C2211yescharacteristic
40#10622124C2212yes—
41#10622124C2212yes—
42#10622123C2212yes—
43#10622123C2212yes—
44#10622096C2211yescharacteristic
45#10622096C2211yescharacteristic
46#10622095C2212yes—
47C2×#4339—22no—
48C2×C11×M16—21no—
49C22×C8×C11—21no—
50C22×C8×C11D411yescharacteristic
51C22×C8×C11D411yescharacteristic
52C11×#126—21no—
53C11×#125D411yescharacteristic
54C11×#124D411yescharacteristic
55C11×#123—21no—
56C11×C22⋊Q8D411yescharacteristic
57C11×#121D411yescharacteristic
58C4×Q8×C11C2311yescharacteristic
59C4×D4×C11—21no—
60C4×D4×C11C2311yescharacteristic
61C11×#117—21no—
62C2×C42×C11C2311yescharacteristic
63C2×#4326—22no—
64C2×#4325—22no—
65C2×#4324—22no—
66C2×#4323—22no—
67#66983—22no—
68#66983—22no—
69C2×D88—21no—
70C2×D88—21no—
71#66928—22no—
72#66927C2312yes—
73C4×D44—22no—
74C4×D44—22no—
75#66922C2312yes—
76C11×C4⋊C8—21no—
77C11×C4⋊C8—21no—
78C11×C4⋊C8C2311yescharacteristic
79C11×C4⋊C8C2311yescharacteristic
80C11×C22⋊C8—21no—
81C11×C22⋊C8—21no—
82C11×C22⋊C8—21no—
83C11×#97—21no—
84C11×#97—21no—
85C4×C8×C11—21no—
86C4×C8×C11D411yescharacteristic
87C4×C8×C11D411yescharacteristic
88C4×C8×C11C2311yescharacteristic
89C4×C8×C11C2311yescharacteristic
90C22⋊(C11⋊C8)—22no—
91#66885—22no—
92#66885—22no—
93#66882—21no—
94#66882—21no—
95#66874—22no—
96#66874—22no—
97#66873—22no—
98#66873—22no—
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2312yes—
101C4×C11⋊C8—22no—
102#19219—111nomaximal, Sylow
103C2×Q8×C11C2×D411yescharacteristic
104C2×D4×C11—21no—
105C2×D4×C11C2×D411yescharacteristic
106C22×C4×C11—21no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C2×C22⋊D11—42no—
111#4339—82no—
112#4339—82no—
113C2×D44—22no—
114C2×D44—22no—
115C2×D44—22no—
116C2×C4×D11—42no—
117C2×Dic22—22no—
118C11×M16—42no—
119C2×C8×C11—22no—
120C2×C8×C11—21no—
121C2×C8×C11—21no—
122C2×C8×C11—41no—
123C2×C8×C11—42no—
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4C2×D411yescharacteristic
133C11×C4⋊C4C2×D411yescharacteristic
134C11×C22⋊C4—21no—
135C11×C22⋊C4—21no—
136C11×C22⋊C4—21no—
137C11×C22⋊C4—21no—
138C11×C22⋊C4—21no—
139C42×C11—21no—
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11#4111yescharacteristic
143C42×C11C2411yescharacteristic
144#4326—82no—
145#4325—82no—
146#4324—82no—
147#4323—82no—
148(C2×D11)⋊C4—42no—
149(C2×D11)⋊C4—42no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154D88—42no—
155D88—42no—
156#3212—112no—
157#3169—111no—
158#2966D1111yescharacteristic, complemented
159#1702—112no—
160#1701—112no—
161#1674—111no—
162#1673—111no—
163#1668—111no—
164#1667—111no—
165#1564—111no—
166#1553—112no—
167C23×C11—21no—
168C23×C11#12111yescharacteristic
169C22×D11—42no—
170Q8×C11—21no—
171Q8×C11—21no—
172D4×C11—21no—
173D4×C11—21no—
174D4×C11—42no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C22⋊D11—84no—
192C2×Dic11—42no—
193D44—42no—
194D44—42no—
195D44—42no—
196D44—42no—
197D44—82no—
198C4×D11—84no—
199Dic22—42no—
200Dic22—42no—
201C8×C11—21no—
202C8×C11—21no—
203C8×C11—21no—
204C8×C11—41no—
205C8×C11—41no—
206C8×C11#13512yes—
207C11⋊C8—42no—
208C11⋊C8—42no—
209#532—112no—
210#529C2×D1111yescharacteristic
211#500—111no—
212#495—222no—
213#493—111no—
214#488—222no—
215#486—112no—
216#466—221no—
217#466—221no—
218#462—112no—
219#461—112no—
220#460—112no—
221#459—112no—
222#452—222no—
223#449—222no—
224#446C2×D1111yescharacteristic
225C8×Q8C2×D1111yescharacteristic
226C4×D8—221no—
227C4×D8—221no—
228#436C2×D1111yescharacteristic
229#435—21no—
230C8×D4—21no—
231C8×D4C2×D1111yescharacteristic
232#433—21no—
233#432C2×D1111yescharacteristic
234#431—112no—
235#405—21no—
236C2×C4×C8C2×D1111yescharacteristic
237#335—111no—
238#335—111no—
239#334—112no—
240#332—112no—
241#332—112no—
242#331—112no—
243#331—112no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—41no—
248C22×C11—41no—
249C22×C11—41no—
250C22×C11C2×#12111yescharacteristic
251C2×D11—82no—
252C2×D11—82no—
253C2×D11—82no—
254C4×C11—21no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—41no—
259C4×C11—41no—
260C4×C11—41no—
261C4×C11C2×#13511yescharacteristic
262C4×C11#57511yescharacteristic
263C4×C11#57611yescharacteristic
264C4×C11#57611yescharacteristic
265Dic11—82no—
266C2×#41—222no—
267C2×Q16—222no—
268C2×SD16—222no—
269C2×SD16—222no—
270C2×D8—222no—
271C2×D8—221no—
272C2×D8—221no—
273C2×M16—21no—
274C22×C8—21no—
275C22×C8C22⋊D1111yescharacteristic
276C22×C8C22⋊D1111yescharacteristic
277C4⋊Q8—112no—
278#127—112no—
279#126—21no—
280#125D4411yescharacteristic
281#124—222no—
282#124D4411yescharacteristic
283#123—21no—
284C22⋊Q8D4411yescharacteristic
285#121—222no—
286#121—222no—
287#121D4411yescharacteristic
288C4×Q8C22×D1111yescharacteristic
289C4×D4—21no—
290C4×D4—222no—
291C4×D4—222no—
292C4×D4C22×D1111yescharacteristic
293#117—21no—
294C2×C42C22×D1111yescharacteristic
295#107—221no—
296#107—221no—
297C4⋊C8—21no—
298C4⋊C8—21no—
299C4⋊C8—112no—
300C4⋊C8—112no—
301C4⋊C8C22×D1111yescharacteristic
302C4⋊C8C22×D1111yescharacteristic
303#103—222no—
304#103—222no—
305#102—222no—
306#102—222no—
307#102—222no—
308#102—222no—
309C22⋊C8—21no—
310C22⋊C8—21no—
311C22⋊C8—21no—
312C22⋊C8—222no—
313#97—21no—
314#97—21no—
315C4×C8—21no—
316C4×C8—222no—
317C4×C8C22⋊D1111yescharacteristic
318C4×C8C22⋊D1111yescharacteristic
319C4×C8C22×D1111yescharacteristic
320C4×C8C22×D1111yescharacteristic
321C2×C11—41no—
322C2×C11—81no—
323C2×C11#303511yescharacteristic
324C2×C11#305811yescharacteristic
325C2×C11#306711yescharacteristic
326D11—162no—
327#41—882no—
328#41—882no—
329C2×Q8—222no—
330C2×Q8C2×D4411yescharacteristic
331C2×D4—21no—
332C2×D4—222no—
333C2×D4—222no—
334C2×D4—222no—
335C2×D4—442no—
336C2×D4C2×D4411yescharacteristic
337C22×C4—21no—
338C22×C4—442no—
339C22×C4C2×D4411yescharacteristic
340C22×C4#433911yescharacteristic
341C22×C4C2×C22⋊D1111yescharacteristic
342Q16—882no—
343SD16—882no—
344SD16—882no—
345D8—442no—
346D8—442no—
347D8—882no—
348M16—42no—
349C2×C8—22no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—41no—
353C2×C8—42no—
354C2×C8—222no—
355C2×C8—222no—
356C2×C8C2×C22⋊D1111yescharacteristic
357C2×C8C2×C22⋊D1111yescharacteristic
358C2×C8C2×C22⋊D1111yescharacteristic
359C2×C8C2×C22⋊D1111yescharacteristic
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—222no—
365C4⋊C4—222no—
366C4⋊C4C2×D4411yescharacteristic
367C4⋊C4C2×D4411yescharacteristic
368C22⋊C4—21no—
369C22⋊C4—21no—
370C22⋊C4—21no—
371C22⋊C4—21no—
372C22⋊C4—21no—
373C22⋊C4—442no—
374C22⋊C4—442no—
375C42—21no—
376C42C2×D4411yescharacteristic
377C42#433911yescharacteristic
378C42C2×C22⋊D1111yescharacteristic
379C42C23×D1111yescharacteristic
380C11#1921911yescharacteristic, complemented, Sylow
381C23—21no—
382C23—442no—
383C23#6698311yescharacteristic
384Q8—21no—
385Q8—21no—
386Q8—442no—
387Q8—442no—
388D4—21no—
389D4—21no—
390D4—42no—
391D4—442no—
392D4—442no—
393D4—442no—
394D4—442no—
395D4—882no—
396D4—884no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—442no—
408C2×C4—884no—
409C2×C4#6698311yescharacteristic
410C2×C4#6698311yescharacteristic
411C2×C4#6698311yescharacteristic
412C2×C4C22×D4411yescharacteristic
413C2×C4C2×#433911yescharacteristic
414C2×C4C22×C22⋊D1111yescharacteristic
415C8—21no—
416C8—21no—
417C8—21no—
418C8—41no—
419C8—41no—
420C8—442no—
421C8—442no—
422C8#6700312yes—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—882no—
430C22—882no—
431C22—882no—
432C22C2×#6698311yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—882no—
441C4#1062328311yescharacteristic
442C4#1062328311yescharacteristic
443C4C2×#6700311yescharacteristic
444C4#1062335311yescharacteristic
445C2—41no—
446C2—81no—
447C2—1762no—
448C2#1307807111yescharacteristic
449C2#1307826411yescharacteristic
450C2#1307833611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2966C2
socleC22×C11C2×#121
hypercenter#2966D11
hypocenterC11#19219
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
1. #13079588C2semidirect
2. #13079195C2semidirect
3. #13068184C2semidirect
4. #13068177C2semidirect
5. #13068010C2semidirect
6. #13068005C2semidirect
7. #13067976C2semidirect
8. #13067971C2semidirect
9. #13067364C2semidirect
10. #13067322C2semidirect
11. C11×#2966C2semidirect
158. #2966D11semidirect
380. C11#19219semidirect

Maximal subgroups

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

subgroupindex
#130795882
#130791952
#130681842
#130681772
#130680102
#130680052
#130679762
#130679712
#130673642
#130673222
C11×#29662
#1921911