Finite Group Databasebeta

← #14807181

Subgroups — #14807181

Order 2816.

1068 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#13078998C211yesmaximal, characteristic, complemented
2#13078103C211yesmaximal, characteristic
3#13077012C211yesmaximal, characteristic, complemented
4#13069650C214yesmaximal
5#13069594C211yesmaximal, characteristic, complemented
6#13069461C211yesmaximal, characteristic, complemented
7#13069009C214yesmaximal, complemented
8C4×#66901C211yesmaximal, characteristic
9C11×#3509C211yesmaximal, characteristic
10C11×#557—22no—
11C11×#556—22no—
12C11×#552—24no—
13C11×#541—22no—
14C11×#536C2212yes—
15C11×#533—22no—
16C11×#533C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C11×#519C2212yes—
19C4×C11×#41C2211yescharacteristic
20C2×#67004C2212yes—
21C2×#66997C2214yes—
22C2×#66922C2211yescharacteristic
23C2×#66901C2212yes—
24C2×#66900C2214yes—
25#10622706—22no—
26#10622682—22no—
27#10622644—22no—
28#10622632—22no—
29#10622617C2214yes—
30#10622617C2212yes—
31#10622589—24no—
32C42×Dic11C2211yescharacteristic
33#10622537C2211yescharacteristic
34C4×#4318C2211yescharacteristic
35#10622170C2214yes—
36#10622170C2212yes—
37C2×C11×#41C2311yescharacteristic
38C22×Q8×C11C2312yes—
39C22×Dic22C2312yes—
40C11×C4⋊Q8—22no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—22no—
44C11×C4⋊Q8D412yes—
45C11×#126—28no—
46C11×#125—24no—
47C11×#125—28no—
48C11×#125D412yes—
49C11×#124—22no—
50C11×#123—24no—
51C11×C22⋊Q8—24no—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8—24no—
54C4×Q8×C11—24no—
55C4×Q8×C11—24no—
56C4×Q8×C11—24no—
57C4×Q8×C11—22no—
58C4×Q8×C11D412yes—
59C4×D4×C11—22no—
60C4×D4×C11D412yes—
61C11×#117—24no—
62C11×#117—24no—
63C11×#117—21no—
64C11×#117C2311yescharacteristic
65C11×#117C2312yes—
66C2×C11×C4⋊C4D414yes—
67C2×C42×C11—21no—
68C2×C42×C11C2311yescharacteristic
69#67004—44no—
70#66997—28no—
71#66997—44no—
72C2×#4326—22no—
73C2×#4324—22no—
74C2×C4⋊Dic11—22no—
75C2×Dic11⋊C4—28no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11C2312yes—
78C2×#4318C2312yes—
79C2×#4318C2312yes—
80#66922—22no—
81#66922—21no—
82#66922—21no—
83#66901—24no—
84#66900—44no—
85#66874—24no—
86#66874—28no—
87C4⋊(C11⋊C8)—22no—
88#66867—21no—
89C4×C11⋊C8—21no—
90#25589—111nomaximal, Sylow
91C11×#41—22no—
92C11×#41—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—24no—
97C2×Q8×C11—24no—
98C2×Q8×C11C2×D411yescharacteristic
99C2×D4×C11—21no—
100C2×D4×C11C2×D411yescharacteristic
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11C2×D414yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2411yescharacteristic
106C22×Dic11—22no—
107C22×Dic11—22no—
108C2×Dic22—22no—
109C2×Dic22—22no—
110C2×Dic22—24no—
111C2×Dic22—24no—
112C11×C4⋊C4—28no—
113C11×C4⋊C4—28no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—24no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4C2×D412yes—
120C11×C4⋊C4C2×D414yes—
121C11×C22⋊C4—28no—
122C11×C22⋊C4—21no—
123C11×C22⋊C4—22no—
124C11×C22⋊C4—22no—
125C42×C11—28no—
126C42×C11—22no—
127C42×C11—21no—
128C42×C11—22no—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D412yes—
132#4326—44no—
133#4324—44no—
134C4⋊Dic11—42no—
135C4⋊Dic11—42no—
136Dic11⋊C4—416no—
137C4×Dic11—28no—
138C4×Dic11—22no—
139C4×Dic11#4114yes—
140#4318—22no—
141#4318—22no—
142#4318—24no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145#3509D1111yescharacteristic
146#3139—111no—
147#3039—111no—
148#2868—111no—
149#2005—114no—
150#1994—111no—
151#1966—111no—
152#1886—114no—
153C4×#104—111no—
154C23×C11—21no—
155C23×C11C22×D411yescharacteristic
156Q8×C11—21no—
157Q8×C11—21no—
158Q8×C11—42no—
159Q8×C11—42no—
160Q8×C11—44no—
161Q8×C11—44no—
162D4×C11—21no—
163D4×C11—21no—
164D4×C11—42no—
165C2×C4×C11—24no—
166C2×C4×C11—22no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—21no—
170C2×C4×C11—28no—
171C2×C4×C11—42no—
172C2×C4×C11—44no—
173C2×C4×C11#12012yes—
174C2×C4×C11#12012yes—
175C2×C4×C11C22×D411yescharacteristic
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C2×#4112yes—
178C2×C4×C11H(5,𝔽2)12yes—
179C2×Dic11—28no—
180C2×Dic11—24no—
181C2×Dic11—42no—
182C2×Dic11—44no—
183Dic22—42no—
184Dic22—42no—
185Dic22—44no—
186C11⋊C8—42no—
187C11⋊C8—42no—
188C2×#137—112no—
189#557—22no—
190#556—22no—
191#552—24no—
192#541—22no—
193#536C2×D1112yes—
194#533—22no—
195#533C2×D1111yescharacteristic
196C2×C4⋊Q8—114no—
197C2×C4⋊Q8—111no—
198C2×C4⋊Q8C2×D1111yescharacteristic
199#519C2×D1112yes—
200C4×#41C2×D1111yescharacteristic
201#491—222no—
202#487—222no—
203#462—222no—
204#461—222no—
205#423—111no—
206C2×#104—112no—
207#419—114no—
208#419—112no—
209C2×#101—114no—
210C4×M16—111no—
211#384—224no—
212C43—111no—
213#339—112no—
214#339—114no—
215C22×C11—22no—
216C22×C11—41no—
217C22×C11—42no—
218C22×C11C2×#12011yescharacteristic
219C22×C11#54612yes—
220C4×C11—22no—
221C4×C11—44no—
222C4×C11—41no—
223C4×C11—42no—
224C4×C11—44no—
225C4×C11#45614yes—
226C4×C11#53211yescharacteristic
227C4×C11#53511yescharacteristic
228C4×C11#55012yes—
229Dic11—28no—
230Dic11—82no—
231C2×#41C22×D1111yescharacteristic
232C22×Q8—112no—
233C22×Q8C22×D1112yes—
234#137—444no—
235C2×Q16—222no—
236C2×SD16—222no—
237C2×M16—112no—
238C2×M16—112no—
239C4⋊Q8—22no—
240C4⋊Q8—21no—
241C4⋊Q8—21no—
242C4⋊Q8—22no—
243C4⋊Q8—228no—
244C4⋊Q8—222no—
245C4⋊Q8—221no—
246C4⋊Q8—221no—
247C4⋊Q8—444no—
248C4⋊Q8C22⋊D1112yes—
249#126—28no—
250#125—24no—
251#125—28no—
252#125C22⋊D1112yes—
253#124—22no—
254#123—24no—
255C22⋊Q8—24no—
256C22⋊Q8—22no—
257C22⋊Q8—24no—
258C4×Q8—24no—
259C4×Q8—24no—
260C4×Q8—24no—
261C4×Q8—22no—
262C4×Q8C22⋊D1112yes—
263C4×D4—22no—
264C4×D4C22⋊D1112yes—
265#117—24no—
266#117—24no—
267#117—21no—
268#117C22×D1111yescharacteristic
269#117C22×D1112yes—
270C2×C4⋊C4—228no—
271C2×C4⋊C4—222no—
272C2×C4⋊C4C22⋊D1114yes—
273C2×C42—21no—
274C2×C42—112no—
275C2×C42—222no—
276C2×C42C22×D1111yescharacteristic
277C4⋊C8—222no—
278#104—224no—
279#103—224no—
280#103—228no—
281#101—444no—
282#97—221no—
283C4×C8—221no—
284C2×C11—22no—
285C2×C11—81no—
286C2×C11#243111yescharacteristic
287C2×C11C2×#45612yes—
288#41—22no—
289#41—22no—
290C2×Q8—22no—
291C2×Q8—24no—
292C2×Q8—24no—
293C2×Q8—22no—
294C2×Q8—22no—
295C2×Q8—224no—
296C2×Q8—224no—
297C2×Q8—222no—
298C2×Q8—222no—
299C2×Q8C2×C22⋊D1111yescharacteristic
300C2×D4—21no—
301C2×D4C2×C22⋊D1111yescharacteristic
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—222no—
305C22×C4—222no—
306C22×C4C2×C22⋊D1114yes—
307C22×C4C2×C22⋊D1112yes—
308C22×C4C23×D1111yescharacteristic
309Q16—444no—
310SD16—444no—
311M16—222no—
312M16—222no—
313M16—224no—
314C2×C8—222no—
315C2×C8—222no—
316C4⋊C4—28no—
317C4⋊C4—28no—
318C4⋊C4—24no—
319C4⋊C4—24no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—24no—
323C4⋊C4—4416no—
324C4⋊C4—442no—
325C4⋊C4—442no—
326C4⋊C4C2×C22⋊D1112yes—
327C4⋊C4C2×C22⋊D1114yes—
328C22⋊C4—28no—
329C22⋊C4—21no—
330C22⋊C4—22no—
331C22⋊C4—22no—
332C42—28no—
333C42—22no—
334C42—21no—
335C42—22no—
336C42—114no—
337C42—228no—
338C42—222no—
339C42C2×C22⋊D1111yescharacteristic
340C42C2×C22⋊D1111yescharacteristic
341C42C2×C22⋊D1112yes—
342C11#2558911yescharacteristic, complemented, Sylow
343C23—21no—
344C23C22×C22⋊D1111yescharacteristic
345Q8—21no—
346Q8—21no—
347Q8—42no—
348Q8—42no—
349Q8—44no—
350Q8—44no—
351Q8—442no—
352Q8—442no—
353Q8—444no—
354D4—21no—
355D4—21no—
356D4—42no—
357C2×C4—24no—
358C2×C4—28no—
359C2×C4—22no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—44no—
365C2×C4—228no—
366C2×C4—224no—
367C2×C4—444no—
368C2×C4—442no—
369C2×C4#6700612yes—
370C2×C4#6700612yes—
371C2×C4#41×D1112yes—
372C2×C4#6704212yes—
373C2×C4C22×C22⋊D1111yescharacteristic
374C2×C4C22×C22⋊D1111yescharacteristic
375C8—442no—
376C8—442no—
377C22—22no—
378C22—41no—
379C22—42no—
380C22#1062336012yes—
381C22C2×#6700611yescharacteristic
382C4—22no—
383C4—44no—
384C4—41no—
385C4—42no—
386C4—44no—
387C4—228no—
388C4—882no—
389C4#1062285914yes—
390C4#1062336111yescharacteristic
391C4#1062336311yescharacteristic
392C4#1062336512yes—
393C2—22no—
394C2—81no—
395C2#1307223111yescharacteristic
396C2C2×#1062285912yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3509C2
socleC22×C11C2×#120
prime radicalC2×C11×#41C23
hypercenter#3509D11
hypocenterC11#25589
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. #13078998C2semidirect
3. #13077012C2semidirect
5. #13069594C2semidirect
6. #13069461C2semidirect
7. #13069009C2semidirect
342. C11#25589semidirect

Maximal subgroups

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

subgroupindex
#130789982
#130781032
#130770122
#130696502
#130695942
#130694612
#130690092
C4×#669012
C11×#35092
#2558911