Finite Group Databasebeta

← #14790025

Subgroups — #14790025

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082426C211yesmaximal, characteristic
2#13078421C212yesmaximal
3#13069961C212yesmaximal
4#13069777C212yesmaximal
5#13069593C212yesmaximal
6#13069010C212yesmaximal
7#13068830C212yesmaximal
8#13068612C211yesmaximal, characteristic
9C4×C11×C4⋊Q8C211yesmaximal, characteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C2×C4×Q8×C11C2211yescharacteristic
13#10623343C2212yes—
14#10623101—22no—
15#10623100—24no—
16Q8×Dic22—22no—
17#10623031—22no—
18#10623031C2212yes—
19#10623001—22no—
20#10623001C2212yes—
21C11×#391C2211yescharacteristic
22C11×#391C2211yescharacteristic
23C11×#389—22no—
24C11×#384C2211yescharacteristic
25C4×C11×C4⋊C4—22no—
26C43×C11C2211yescharacteristic
27C2×#66900C2212yes—
28#10622838C2214yes—
29#10622635—24no—
30#10622634—22no—
31#10622633—22no—
32#10622577C2214yes—
33#10622537C2212yes—
34#10622168C2212yes—
35#10622161C2214yes—
36#10622161C2214yes—
37C22×Q8×C11C2311yescharacteristic
38C22×Q8×C11C2311yescharacteristic
39C11×C4⋊Q8—22no—
40C11×C4⋊Q8Q814yescomplemented
41C4×Q8×C11—22no—
42C4×Q8×C11—22no—
43C4×Q8×C11—22no—
44C4×Q8×C11—22no—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D412yes—
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C42×C11—21no—
52C2×C42×C11—21no—
53C2×C42×C11—21no—
54C2×C42×C11D412yes—
55C2×C42×C11C2311yescharacteristic
56C2×C42×C11C2311yescharacteristic
57C2×C42×C11C2311yescharacteristic
58Q8×Dic11—24no—
59Q8×Dic11—24no—
60#66979—24no—
61#66979C2314yes—
62#66977—22no—
63#66977—24no—
64#66977—22no—
65C2×#4318C2314yes—
66#66943—28no—
67#66943—24no—
68#66941—28no—
69#66941—24no—
70#66923—24no—
71#66923D414yes—
72#66922—22no—
73#66922—22no—
74#66922D412yes—
75#66922D412yes—
76C4×Dic22—24no—
77C4×Dic22—24no—
78C4×Dic22—22no—
79C4×Dic22—22no—
80C11×#95—22no—
81C11×#95—22no—
82#66900—24no—
83#66899—24no—
84#66899—24no—
85#66872—24no—
86#66871—24no—
87C4⋊(C11⋊C8)—22no—
88C4⋊(C11⋊C8)—22no—
89#24315—111nomaximal, Sylow
90C2×Q8×C11—22no—
91C2×Q8×C11—21no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11—22no—
95C2×Q8×C11C2×Q812yes—
96C2×Q8×C11C2×Q812yes—
97C2×Q8×C11#4112yes—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C2×Dic22—24no—
108C2×Dic22—22no—
109C2×Dic22—22no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—28no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—44no—
115C11×C4⋊C4—42no—
116C42×C11—24no—
117C42×C11—22no—
118C42×C11—22no—
119C42×C11—21no—
120C42×C11—22no—
121C42×C11—42no—
122C42×C11—41no—
123C42×C11—41no—
124C42×C11C2×D412yes—
125C42×C11C2×D412yes—
126C42×C11C2×Q812yes—
127C22⋊Dic11—24no—
128C4⋊Dic11—24no—
129C4⋊Dic11—24no—
130C4⋊Dic11—24no—
131C4⋊Dic11—22no—
132C4⋊Dic11—22no—
133C4⋊Dic11C2×D414yes—
134C4⋊Dic11C2×D414yes—
135Dic11⋊C4—28no—
136Dic11⋊C4—24no—
137Dic11⋊C4—24no—
138C4×Dic11—28no—
139C4×Dic11—24no—
140#4318—24no—
141#4318—24no—
142C2×C11⋊C8—24no—
143#3502—111no—
144#3078—112no—
145C4×C4⋊Q8D1111yescharacteristic
146#2060—112no—
147#2028—112no—
148#1994—112no—
149#1886—112no—
150#1857—112no—
151#1801—111no—
152C23×C11C22×D411yescharacteristic
153Q8×C11—24no—
154Q8×C11—24no—
155Q8×C11—24no—
156Q8×C11—42no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11#12011yescharacteristic
175C2×C4×C11#12012yes—
176C2×C4×C11#12011yescharacteristic
177C2×C4×C11C22⋊Q814yes—
178C2×C4×C11C22×D412yes—
179C2×C4×C11C22×Q811yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C2×C4×C112−1+412yes—
182C2×Dic11—24no—
183C2×Dic11—24no—
184Dic22—44no—
185Dic22—82no—
186Dic22—84no—
187C11⋊C8—44no—
188Q82—222no—
189#557—224no—
190#557—222no—
191#544—112no—
192#544—222no—
193#533—112no—
194#533—222no—
195C2×C4⋊Q8C2×D1111yescharacteristic
196#519—112no—
197C2×C4×Q8C2×D1111yescharacteristic
198C2×C4×Q8C2×D1111yescharacteristic
199#479—224no—
200#477—222no—
201#475—222no—
202#428—114no—
203#423—112no—
204#419—114no—
205C2×#101—112no—
206#391C2×D1111yescharacteristic
207#391C2×D1111yescharacteristic
208#389—22no—
209#384C2×D1111yescharacteristic
210C4×C4⋊C4—22no—
211C43C2×D1111yescharacteristic
212#343—112no—
213#339—114no—
214#339—114no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11C2×#12011yescharacteristic
218C22×C11C2×C22⋊Q811yescharacteristic
219C22×C11#53611yescharacteristic
220C4×C11—24no—
221C4×C11—24no—
222C4×C11—21no—
223C4×C11—22no—
224C4×C11—42no—
225C4×C11—42no—
226C4×C11—42no—
227C4×C11—81no—
228C4×C11#45612yes—
229C4×C11#54812yes—
230C4×C11D4×Q812yes—
231Dic11—44no—
232Dic11—44no—
233C22×Q8C22×D1111yescharacteristic
234C22×Q8C22×D1111yescharacteristic
235C2×M16—114no—
236C4⋊Q8—22no—
237C4⋊Q8—112no—
238C4⋊Q8—112no—
239C4⋊Q8—222no—
240C4⋊Q8—222no—
241C4⋊Q8—224no—
242C4⋊Q8—228no—
243C4⋊Q8Dic2214yescomplemented
244#125—114no—
245#125—224no—
246#125—224no—
247#125—228no—
248C22⋊Q8—222no—
249C22⋊Q8—222no—
250C22⋊Q8—224no—
251C4×Q8—22no—
252C4×Q8—22no—
253C4×Q8—22no—
254C4×Q8—22no—
255C4×Q8—224no—
256C4×Q8—224no—
257C4×Q8—224no—
258C4×Q8—224no—
259C4×Q8—222no—
260C4×Q8—222no—
261#117—114no—
262#117—224no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4C22⋊D1112yes—
267C2×C4⋊C4C22×D1111yescharacteristic
268C2×C4⋊C4C22×D1111yescharacteristic
269C2×C42—21no—
270C2×C42—21no—
271C2×C42—21no—
272C2×C42C22⋊D1112yes—
273C2×C42C22×D1111yescharacteristic
274C2×C42C22×D1111yescharacteristic
275C2×C42C22×D1111yescharacteristic
276#107—224no—
277#106—224no—
278C4⋊C8—222no—
279C4⋊C8—222no—
280#103—224no—
281#103—224no—
282#101—224no—
283#95—22no—
284#95—22no—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11#240911yescharacteristic
288C2×C11C2×#45611yescharacteristic
289C2×C11#301811yescharacteristic
290C2×Q8—21no—
291C2×Q8—22no—
292C2×Q8—22no—
293C2×Q8—22no—
294C2×Q8—22no—
295C2×Q8—224no—
296C2×Q8—222no—
297C2×Q8—222no—
298C2×Q8C2×Dic2212yes—
299C2×Q8C2×Dic2212yes—
300C2×Q8#433912yes—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4C2×C22⋊D1112yes—
306C22×C4C2×C22⋊D1111yescharacteristic
307C22×C4C2×C22⋊D1112yes—
308C22×C4C2×C22⋊D1111yescharacteristic
309C22×C4C23×D1111yescharacteristic
310M16—224no—
311M16—224no—
312C2×C8—224no—
313C4⋊C4—28no—
314C4⋊C4—24no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—44no—
318C4⋊C4—42no—
319C4⋊C4—114no—
320C4⋊C4—114no—
321C4⋊C4—224no—
322C4⋊C4—224no—
323C4⋊C4—224no—
324C4⋊C4—228no—
325C4⋊C4—224no—
326C4⋊C4—222no—
327C4⋊C4—224no—
328C4⋊C4—222no—
329C22⋊C4—224no—
330C42—24no—
331C42—22no—
332C42—22no—
333C42—21no—
334C42—22no—
335C42—42no—
336C42—41no—
337C42—41no—
338C42—228no—
339C42—224no—
340C42C2×Dic2212yes—
341C42D4×D1112yes—
342C42D4×D1112yes—
343C11#2431511yescharacteristic, complemented, Sylow
344C23C22×C22⋊D1111yescharacteristic
345Q8—24no—
346Q8—24no—
347Q8—24no—
348Q8—42no—
349Q8—444no—
350Q8—882no—
351Q8—884no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—224no—
370C2×C4—224no—
371C2×C4#6697714yes—
372C2×C4#6699011yescharacteristic
373C2×C4#6699012yes—
374C2×C4#6699011yescharacteristic
375C2×C4C22×Dic2211yescharacteristic
376C2×C4C2×#433911yescharacteristic
377C2×C4C2×D4×D1112yes—
378C2×C4#6704312yes—
379C8—444no—
380C22—21no—
381C22—21no—
382C22C2×#6697711yescharacteristic
383C22C2×#6699011yescharacteristic
384C22#1062335611yescharacteristic
385C4—24no—
386C4—24no—
387C4—21no—
388C4—22no—
389C4—42no—
390C4—42no—
391C4—42no—
392C4—81no—
393C4—444no—
394C4—444no—
395C4#1062270812yes—
396C4D4×Dic2212yes—
397C4#1062308312yes—
398C2—21no—
399C2—21no—
400C2#1307198111yescharacteristic
401C2C2×#1062270811yescharacteristic
402C2#1307796411yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×C4⋊Q8C2
socleC22×C11C2×#120
prime radicalC23×C11C22×D4
hypercenterC4×C4⋊Q8D11
hypocenterC11#24315
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
40. C11×C4⋊Q8Q8semidirect
243. C4⋊Q8Dic22semidirect
343. C11#24315semidirect

Maximal subgroups

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

subgroupindex
#130824262
#130784212
#130699612
#130697772
#130695932
#130690102
#130688302
#130686122
C4×C11×C4⋊Q82
#2431511