Finite Group Databasebeta

← #14736882

Subgroups — #14736882

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079543C211yesmaximal, characteristic
2#13079541C211yesmaximal, characteristic
3C2×#10622691C211yesmaximal, characteristic, complemented
4#13077327C211yesmaximal, characteristic
5#13068128C214yesmaximal, complemented
6#13068004C214yesmaximal, complemented
7#13067362C211yesmaximal, characteristic, complemented
8#13067302C211yesmaximal, characteristic, complemented
9C11×#1549C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66960—21no—
12#10623008C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#423C2211yescharacteristic
16#10622840—22no—
17#10622742—21no—
18#10622698—21no—
19#10622696C2214yes—
20#10622694—21no—
21#10622691—21no—
22#10622691—21no—
23#10622691C2212yes—
24#10622691C2212yes—
25C2×#66871—21no—
26C2×#66871—21no—
27#10622538C2211yescharacteristic
28C2×C4×C11⋊C8C2211yescharacteristic
29#10622454C2214yes—
30#10622451—21no—
31#10622451C2212yes—
32#10622447—21no—
33#10622447C2212yes—
34#10622351—22no—
35#10622306—21no—
36#10622294—21no—
37C11×#332C2214yes—
38#10622124C2214yes—
39#10622118C2212yes—
40#10622117C2212yes—
41C22×Q8×C11—21no—
42C2×#4339—21no—
43C22×Dic22—21no—
44C2×C11×M16—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8C2312yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C42×C11C2311yescharacteristic
52C2×#4325—24no—
53#66983—21no—
54#66983D412yes—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C22×C11⋊C8D411yescharacteristic
58C22×C11⋊C8D411yescharacteristic
59#66960—44no—
60C2×#4314—24no—
61C2×#4313—22no—
62C2×C8×D11—22no—
63#66928—21no—
64#66927D411yescharacteristic
65C4×D44—21no—
66C4×D44C2312yes—
67#66922—21no—
68#66922—21no—
69#66922—21no—
70#66922D411yescharacteristic
71#66922C2312yes—
72C11×C4⋊C8—21no—
73C11×C4⋊C8C2312yes—
74C11×C4⋊C8C2312yes—
75C11×C22⋊C8—21no—
76C4×C8×C11—21no—
77#66899—24no—
78C22⋊(C11⋊C8)—21no—
79(C2×D11)⋊C8—22no—
80(C2×D11)⋊C8—22no—
81#66880—24no—
82#66871—22no—
83#66871—22no—
84#66871—22no—
85#66871—22no—
86C4⋊(C11⋊C8)C2312yes—
87C4×C11⋊C8—21no—
88C4×C11⋊C8D411yescharacteristic
89C4×C11⋊C8D411yescharacteristic
90C4×C11⋊C8C2311yescharacteristic
91C4×C11⋊C8C2311yescharacteristic
92#19192—111nomaximal, Sylow
93C2×Q8×C11—22no—
94C2×Q8×C11—41no—
95C2×Q8×C11—82no—
96C22×C4×C11—41no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C2×C22⋊D11—22no—
101C22×Dic11—41no—
102#4339—42no—
103#4339—42no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44C2×D412yes—
107C2×C4×D11—22no—
108C2×Dic22—21no—
109C2×Dic22—22no—
110C2×Dic22—41no—
111C2×Dic22—82no—
112C11×M16—42no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11#4111yescharacteristic
122C42×C11C2411yescharacteristic
123#4325—84no—
124(C2×D11)⋊C4—22no—
125(C2×D11)⋊C4—22no—
126C4⋊Dic11—21no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—41no—
130C4⋊Dic11—41no—
131C4⋊Dic11C2×D412yes—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8SD1614yescomplemented
135C2×C11⋊C8C2×D411yescharacteristic
136C2×C11⋊C8C2×D411yescharacteristic
137C2×C11⋊C8C2×D411yescharacteristic
138C2×C11⋊C8C2×D411yescharacteristic
139#4314—84no—
140#4313—44no—
141C8×D11—44no—
142#3206—111no—
143#3206—111no—
144C2×#500—111no—
145#2931—111no—
146#1693—114no—
147#1673—114no—
148#1564—111no—
149#1549—111no—
150#1549D1111yescharacteristic, complemented
151C23×C11#12111yescharacteristic
152C22×D11—22no—
153Q8×C11—44no—
154Q8×C11—82no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—42no—
158C2×C4×C11—82no—
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11C2×SD1612yes—
163C2×C4×C11#13712yes—
164C2×C4×C11C22×D411yescharacteristic
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11C2×#4111yescharacteristic
167C22⋊D11—44no—
168C2×Dic11—22no—
169C2×Dic11—42no—
170C2×Dic11—82no—
171D44—24no—
172D44—42no—
173D44—42no—
174C4×D11—42no—
175C4×D11—42no—
176Dic22—42no—
177Dic22—44no—
178Dic22—82no—
179C8×C11—42no—
180C8×C11—42no—
181C11⋊C8—21no—
182C11⋊C8—21no—
183C11⋊C8—42no—
184C11⋊C8C2×SD1612yes—
185C11⋊C8C2×SD1612yes—
186C2×#131—221no—
187#532—111no—
188C2×C4⋊Q8—111no—
189C2×C4⋊Q8C2×D1111yescharacteristic
190#500—112no—
191#500—112no—
192#500—221no—
193#500—221no—
194#492—221no—
195#492—221no—
196#487—221no—
197#487—221no—
198#461—114no—
199#461—114no—
200#448—222no—
201#448—222no—
202#436—112no—
203#436—221no—
204C8×D4—112no—
205C8×D4—221no—
206#431—111no—
207#431C2×D1111yescharacteristic
208C2×#107—221no—
209C2×#107—221no—
210#423C2×D1111yescharacteristic
211#408—221no—
212C2×C4×C8—111no—
213#335—112no—
214#334—112no—
215#332—114no—
216#332C2×D1114yes—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11#46112yes—
220C22×C11C2×#12111yescharacteristic
221C2×D11—42no—
222C2×D11—42no—
223C2×D11—42no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—82no—
227C4×C11#46112yes—
228C4×C11#47312yes—
229C4×C11C22×SD1611yescharacteristic
230C4×C11C2×#13711yescharacteristic
231C4×C11#57612yes—
232Dic11—42no—
233Dic11—82no—
234C2×#41—221no—
235C22×Q8—21no—
236C22×Q8—221no—
237C2×SD16—224no—
238C2×SD16—224no—
239#131—444no—
240C2×M16—21no—
241C2×M16—222no—
242C22×C8—111no—
243C22×C8—111no—
244C22×C8—222no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—21no—
248C4⋊Q8—111no—
249C4⋊Q8—112no—
250C4⋊Q8—221no—
251C4⋊Q8—221no—
252C4⋊Q8—221no—
253C4⋊Q8C22×D1112yes—
254#127—111no—
255#124—221no—
256#121—112no—
257#121—221no—
258C4×D4—112no—
259C4×D4—221no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—221no—
264C2×C42C22×D1111yescharacteristic
265#107—222no—
266#107—222no—
267#107—222no—
268#107—222no—
269C4⋊C8—21no—
270C4⋊C8—112no—
271C4⋊C8C22×D1112yes—
272C4⋊C8C22×D1112yes—
273#103—224no—
274#103—224no—
275C22⋊C8—21no—
276C22⋊C8—222no—
277C22⋊C8—222no—
278C22⋊C8—221no—
279C4×C8—21no—
280C4×C8—111no—
281C4×C8—111no—
282C4×C8—111no—
283C4×C8—111no—
284C4×C8—221no—
285C2×C11—22no—
286C2×C11C2×#46111yescharacteristic
287C2×C11#305811yescharacteristic
288C2×C11C2×#47311yescharacteristic
289D11—82no—
290#41—442no—
291#41—442no—
292C2×Q8—22no—
293C2×Q8—41no—
294C2×Q8—82no—
295C2×Q8—221no—
296C2×Q8—222no—
297C2×Q8—441no—
298C2×Q8—882no—
299C2×D4—112no—
300C2×D4—222no—
301C2×D4—221no—
302C2×D4—221no—
303C22×C4—41no—
304C22×C4—222no—
305C22×C4—441no—
306C22×C4#433911yescharacteristic
307C22×C4D4×D1111yescharacteristic
308C22×C4D4×D1111yescharacteristic
309SD16—884no—
310SD16—884no—
311M16—42no—
312M16—444no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—114no—
316C2×C8—111no—
317C2×C8—111no—
318C2×C8—111no—
319C2×C8—111no—
320C2×C8—222no—
321C2×C8—222no—
322C2×C8—444no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—112no—
328C4⋊C4—221no—
329C4⋊C4—222no—
330C4⋊C4—222no—
331C4⋊C4—441no—
332C4⋊C4—441no—
333C22⋊C4—222no—
334C22⋊C4—222no—
335C42#433911yescharacteristic
336C42D4×D1111yescharacteristic
337C42D4×D1111yescharacteristic
338C42C23×D1111yescharacteristic
339C11#1919211yescharacteristic, complemented, Sylow
340C23—222no—
341C23#6693711yescharacteristic
342Q8—44no—
343Q8—82no—
344Q8—442no—
345Q8—444no—
346Q8—882no—
347D4—224no—
348D4—444no—
349D4—442no—
350D4—442no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—42no—
354C2×C4—82no—
355C2×C4—222no—
356C2×C4—442no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4—882no—
360C2×C4#6693711yescharacteristic
361C2×C4#6693711yescharacteristic
362C2×C4#6693711yescharacteristic
363C2×C4SD16×D1112yes—
364C2×C4#6697112yes—
365C2×C4C2×#433911yescharacteristic
366C2×C4C2×D4×D1111yescharacteristic
367C2×C4C2×D4×D1111yescharacteristic
368C8—42no—
369C8—42no—
370C8—112no—
371C8—112no—
372C8—221no—
373C8—221no—
374C8—442no—
375C22—21no—
376C22—21no—
377C22—442no—
378C22—442no—
379C22—442no—
380C22#1062243112yes—
381C22C2×#6693711yescharacteristic
382C4—21no—
383C4—21no—
384C4—82no—
385C4—442no—
386C4—882no—
387C4#1062236812yes—
388C4#1062243112yes—
389C4C2×SD16×D1111yescharacteristic
390C4C2×#6697111yescharacteristic
391C4#1062330512yes—
392C2—22no—
393C2—882no—
394C2C2×#1062243111yescharacteristic
395C2#1307826311yescharacteristic
396C2C2×#1062236811yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1549C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#1549D11
hypocenterC11#19192
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
3. C2×#10622691C2semidirect
5. #13068128C2semidirect
6. #13068004C2semidirect
7. #13067362C2semidirect
8. #13067302C2semidirect
9. C11×#1549C2semidirect
134. C2×C11⋊C8SD16semidirect
150. #1549D11semidirect
339. C11#19192semidirect

Maximal subgroups

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

subgroupindex
#130795432
#130795412
C2×#106226912
#130773272
#130681282
#130680042
#130673622
#130673022
C11×#15492
#1919211