Finite Group Databasebeta

← #14650140

Subgroups — #14650140

Order 2816.

466 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622703C211yesmaximal, characteristic
2#13077567C211yesmaximal, characteristic
3#13069606C211yesmaximal, characteristic
4#13067046C211yesmaximal, characteristic
5#13066490C211yesmaximal, characteristic
6#13066465C211yesmaximal, characteristic
7C11×#1548C211yesmaximal, characteristic
8C2×C11×C4⋊Q8C2211yescharacteristic
9C22×#4326C412yes—
10C2×C4×Dic22C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×#66899C412yes—
14#10622731—21no—
15M16×Dic11—21no—
16#10622703—21no—
17#10622703—21no—
18#10622703—21no—
19#10622703—21no—
20#10622537C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C4×#4318C2211yescharacteristic
23#10622444—21no—
24#10622443—21no—
25#10622441—22no—
26C11×#333—22no—
27#10622168—21no—
28#10622168—21no—
29#10622094—21no—
30#10622094—21no—
31C22×Q8×C11C2×C412yes—
32C22×Dic22C2×C411yescharacteristic
33C2×C11×M16—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C42×C11C2311yescharacteristic
41C2×#4326—22no—
42C2×#4326—22no—
43C2×#4326—44no—
44C2×C4⋊Dic11C2×C411yescharacteristic
45C2×Dic11⋊C4—21no—
46C2×C4×Dic11—21no—
47C2×#4318—21no—
48C2×#4318D411yescharacteristic
49C2×#4318D411yescharacteristic
50C22×C11⋊C8C2×C412yes—
51C4×Dic22—21no—
52C4×Dic22—21no—
53C4×Dic22D411yescharacteristic
54C4×Dic22D411yescharacteristic
55C4×Dic22D411yescharacteristic
56C4×Dic22D411yescharacteristic
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8D412yes—
60C11×C22⋊C8—21no—
61C4×C8×C11—21no—
62#66899—22no—
63#66899—22no—
64#66879—22no—
65Dic11⋊C8—22no—
66Dic11⋊C8—22no—
67C8×Dic11—22no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72#66867—21no—
73C4×C11⋊C8—21no—
74#9248—111nomaximal, Sylow
75C2×Q8×C11—22no—
76C2×Q8×C11—22no—
77C2×Q8×C11—42no—
78C2×Q8×C11—42no—
79C22×C4×C11—22no—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×Dic11—21no—
84C22×Dic11—21no—
85C2×Dic22—22no—
86C2×Dic22—21no—
87C2×Dic22—41no—
88C2×Dic22C22⋊C411yescharacteristic
89C2×Dic22C22⋊C411yescharacteristic
90C11×M16—41no—
91C11×M16—41no—
92C2×C8×C11—22no—
93C2×C8×C11—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11#4111yescharacteristic
102#4326—44no—
103#4326—44no—
104C4⋊Dic11—21no—
105C4⋊Dic11C22⋊C411yescharacteristic
106C4⋊Dic11C22⋊C411yescharacteristic
107Dic11⋊C4—21no—
108Dic11⋊C4—21no—
109Dic11⋊C4—21no—
110Dic11⋊C4—21no—
111C4×Dic11—21no—
112C4×Dic11—21no—
113C4×Dic11—21no—
114C4×Dic11—21no—
115#4318—21no—
116#4318—21no—
117#4318—21no—
118#4318—41no—
119#4318—41no—
120#4318Q1612yescomplemented
121C2×C11⋊C8—22no—
122C2×C11⋊C8—21no—
123C2×C11⋊C8—21no—
124C2×C11⋊C8—42no—
125C2×C11⋊C8—41no—
126C2×#462—111no—
127Q8×M16—111no—
128#1997—111no—
129#1548D1111yescharacteristic
130#1487—111no—
131#1292—111no—
132#1283—111no—
133C23×C11C4×D411yescharacteristic
134Q8×C11—42no—
135Q8×C11—42no—
136Q8×C11—82no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—41no—
140C2×C4×C11—42no—
141C2×C4×C11—82no—
142C2×C4×C11C2×C22⋊C411yescharacteristic
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12311yescharacteristic
148C2×C4×C11C2×Q1611yescharacteristic
149C2×C4×C11#13511yescharacteristic
150C2×C4×C11#13711yescharacteristic
151C2×C4×C11#13711yescharacteristic
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—42no—
157C2×Dic11—81no—
158Dic22—21no—
159Dic22—21no—
160Dic22—21no—
161Dic22—42no—
162Dic22#10012yes—
163C8×C11—42no—
164C8×C11—81no—
165C11⋊C8—22no—
166C11⋊C8—42no—
167C11⋊C8—41no—
168C11⋊C8—81no—
169C22×Q16—112no—
170C2×C4⋊Q8C2×D1111yescharacteristic
171C2×C4×Q8—111no—
172#462—221no—
173#462—221no—
174#462—221no—
175#462—221no—
176#446—221no—
177#446—222no—
178C8×Q8—221no—
179#431C2×D1111yescharacteristic
180#423—111no—
181#423—221no—
182#423C2×D1111yescharacteristic
183C2×C4⋊C8—111no—
184C2×#103—112no—
185C4×M16—111no—
186C4×M16—221no—
187#343—221no—
188#343—221no—
189#333—22no—
190Q8⋊C8—221no—
191Q8⋊C8—221no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11#38611yescharacteristic
195C22×C11C4×Q1611yescharacteristic
196C22×C11#44111yescharacteristic
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—82no—
201C4×C11C2×#10011yescharacteristic
202C4×C11#41311yescharacteristic
203C4×C11#45111yescharacteristic
204C4×C11#45211yescharacteristic
205C4×C11#46211yescharacteristic
206C4×C11#46411yescharacteristic
207Dic11—22no—
208Dic11—41no—
209Dic11—41no—
210Dic11—41no—
211C22×Q8—111no—
212C22×Q8C4×D1112yes—
213C2×Q16—222no—
214C2×Q16—222no—
215C2×Q16—444no—
216C2×M16—21no—
217C2×M16—111no—
218C2×M16—111no—
219C2×M16—221no—
220C22×C8—112no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4×Q8—111no—
226C4×Q8—111no—
227C4×Q8—111no—
228C4×Q8—111no—
229C4×Q8—221no—
230C4×Q8—221no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—221no—
235C2×C42—221no—
236C2×C42C22×D1111yescharacteristic
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—222no—
240C4⋊C8—222no—
241C4⋊C8—221no—
242C4⋊C8—221no—
243C4⋊C8—221no—
244C4⋊C8—221no—
245C4⋊C8C22⋊D1112yes—
246#103—222no—
247#103—222no—
248C22⋊C8—21no—
249#97—222no—
250#97—221no—
251C4×C8—21no—
252C4×C8—222no—
253C4×C8—221no—
254C2×C11—21no—
255C2×C11—21no—
256C2×C11#187811yescharacteristic
257C2×C11#190011yescharacteristic
258C2×C11#190211yescharacteristic
259C2×Q8—22no—
260C2×Q8—22no—
261C2×Q8—42no—
262C2×Q8—42no—
263C2×Q8—111no—
264C2×Q8—111no—
265C2×Q8—222no—
266C2×Q8—221no—
267C2×Q8—441no—
268C22×C4—22no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4C2×C4×D1111yescharacteristic
272C22×C4D4×D1111yescharacteristic
273C22×C4#434111yescharacteristic
274Q16—444no—
275Q16—444no—
276M16—41no—
277M16—41no—
278M16—112no—
279M16—221no—
280M16—221no—
281M16—221no—
282M16—441no—
283M16—441no—
284C2×C8—22no—
285C2×C8—41no—
286C2×C8—221no—
287C2×C8—222no—
288C2×C8—221no—
289C2×C8—442no—
290C2×C8—441no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—111no—
296C4⋊C4—111no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C42—221no—
303C42—221no—
304C42—221no—
305C42—221no—
306C42#433911yescharacteristic
307C42D4×D1111yescharacteristic
308C42D4×D1111yescharacteristic
309C42C2×C22⋊D1111yescharacteristic
310C11#924811yescharacteristic, complemented, Sylow
311C23(C22⋊D11)⋊C411yescharacteristic
312Q8—42no—
313Q8—42no—
314Q8—82no—
315Q8—112no—
316Q8—221no—
317Q8—221no—
318Q8—221no—
319Q8—442no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—82no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—442no—
330C2×C4—881no—
331C2×C4C22⋊C4×D1111yescharacteristic
332C2×C4#6693611yescharacteristic
333C2×C4#6693711yescharacteristic
334C2×C4#6696811yescharacteristic
335C2×C4#6696911yescharacteristic
336C2×C4Q16×D1111yescharacteristic
337C2×C4#6697111yescharacteristic
338C2×C4C4×C22⋊D1111yescharacteristic
339C2×C4#6699011yescharacteristic
340C2×C4#6699111yescharacteristic
341C8—42no—
342C8—81no—
343C8—222no—
344C8—441no—
345C8—442no—
346C8—881no—
347C22—21no—
348C22—21no—
349C22#1062240211yescharacteristic
350C22#1062240311yescharacteristic
351C22#1062256911yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—82no—
356C4—222no—
357C4—441no—
358C4—441no—
359C4—441no—
360C4D11×#10011yescharacteristic
361C4#1062235811yescharacteristic
362C4#1062240611yescharacteristic
363C4#1062241111yescharacteristic
364C4#1062278611yescharacteristic
365C4#1062279911yescharacteristic
366C2—21no—
367C2—21no—
368C2#1306895411yescharacteristic
369C2#1306907611yescharacteristic
370C2#1306908611yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1548C2
socleC22×C11#386
prime radicalC23×C11C4×D4
cosocleC2×C42×C11C23
hypercenter#1548D11
hypocenterC11#9248
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
120. #4318Q16semidirect
310. C11#9248semidirect

Maximal subgroups

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

subgroupindex
C2×#106227032
#130775672
#130696062
#130670462
#130664902
#130664652
C11×#15482
#924811