Finite Group Databasebeta

← #14645499

Subgroups — #14645499

Order 2816.

966 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 966 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×D44C211yesmaximal, characteristic
2#13068612C211yesmaximal, characteristic, complemented
3#13067287C212yesmaximal, complemented
4#13067042C212yesmaximal
5C11×#1461C211yesmaximal, characteristic, complemented
6C22×Q8×D11—21no—
7C2×C4×Q8×C11C2211yescharacteristic
8Q8×D44—24no—
9Q8×D44—24no—
10C2×#66950—21no—
11C2×#66950—22no—
12C2×C4×D44C412yes—
13C2×C4×D44C2211yescharacteristic
14C2×#66922C412yes—
15C2×#66922C2211yescharacteristic
16C11×#431C2212yes—
17C2×#66900—21no—
18#10622537C2212yes—
19C11×#324—22no—
20#10622168—21no—
21#10622124—24no—
22#10622097—24no—
23C22×Q8×C11D411yescharacteristic
24C2×Q8×D11—28no—
25C2×Q8×D11—44no—
26C2×Q8×D11—42no—
27C2×Q8×D11—42no—
28C22×D44C2×C411yescharacteristic
29C22×C4×D11—22no—
30C22×C4×D11—21no—
31C22×Dic22—22no—
32C22×Dic22—21no—
33C4×Q8×C11—22no—
34C4×Q8×C11—22no—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4D412yes—
37C2×C42×C11C2×C412yes—
38C2×C42×C11C2311yescharacteristic
39C2×(C2×D11)⋊C4—22no—
40C2×(C2×D11)⋊C4—21no—
41C2×C4⋊Dic11—22no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11C2×C411yescharacteristic
44C2×C4⋊Dic11C2×C412yes—
45C2×#4318—22no—
46#66950—28no—
47#66950—216no—
48C4×D44—24no—
49C4×D44—22no—
50C4×D44—24no—
51C4×D44D414yes—
52#66922—22no—
53#66922—24no—
54#66922—24no—
55#66922D414yes—
56C11×C4⋊C8—22no—
57C11×C22⋊C8—22no—
58C4×C8×C11—22no—
59#66900—42no—
60C4⋊(C11⋊C8)—22no—
61C4⋊(C11⋊C8)—22no—
62#8388—111nomaximal, Sylow
63C23×D11—21no—
64C2×Q8×C11—22no—
65C2×Q8×C11—22no—
66C2×Q8×C11D812yes—
67C2×Q8×C11SD1612yes—
68C22×C4×C11C22⋊C412yes—
69C22×C4×C11C22⋊C412yes—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—22no—
75Q8×D11—416no—
76Q8×D11—416no—
77C2×D44—24no—
78C2×D44—21no—
79C2×D44C22⋊C412yes—
80C2×C4×D11—28no—
81C2×C4×D11—24no—
82C2×C4×D11—44no—
83C2×C4×D11—44no—
84C2×C4×D11—41no—
85C2×C4×D11—41no—
86C2×C4×D11—42no—
87C2×Dic22—28no—
88C2×Dic22—24no—
89C2×Dic22—44no—
90C2×Dic22—44no—
91C2×Dic22—41no—
92C2×Dic22—41no—
93C2×Dic22—42no—
94C2×C8×C11—42no—
95C11×C4⋊C4—24no—
96C11×C4⋊C4—22no—
97C42×C11—22no—
98C42×C11—22no—
99C42×C11C2×D412yes—
100C42×C11C2×D412yes—
101(C2×D11)⋊C4—28no—
102(C2×D11)⋊C4—24no—
103C4⋊Dic11—28no—
104C4⋊Dic11—21no—
105C4⋊Dic11—22no—
106C4⋊Dic11—24no—
107C4⋊Dic11C22⋊C412yes—
108C4⋊Dic11C22⋊C414yes—
109#4318—42no—
110#4318—42no—
111C2×C11⋊C8—42no—
112C2×D4×Q8—111no—
113#1801—111no—
114#1546—112no—
115#1486—112no—
116#1461D1111yescharacteristic, complemented
117C23×C11C2×C22⋊C411yescharacteristic
118C22×D11—24no—
119C22×D11—22no—
120C22×D11—42no—
121C22×D11—41no—
122C22×D11—41no—
123Q8×C11—24no—
124Q8×C11—24no—
125C2×C4×C11—22no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11#10214yes—
132C2×C4×C11C2×C22⋊C411yescharacteristic
133C2×C4×C11C2×C22⋊C411yescharacteristic
134C2×C4×C11#12012yes—
135C2×C4×C11#12012yes—
136C2×C4×C11C2×D811yescharacteristic
137C2×C4×C11C2×SD1611yescharacteristic
138C2×C4×C11AGL(1,ℤ/8)12yes—
139C2×Dic11—22no—
140C2×Dic11—24no—
141C2×Dic11—41no—
142C2×Dic11—42no—
143C2×Dic11—41no—
144C2×Dic11—42no—
145D44—24no—
146D44—22no—
147D44#10114yescomplemented
148C4×D11—416no—
149C4×D11—44no—
150C4×D11—44no—
151Dic22—416no—
152Dic22—44no—
153Dic22—44no—
154C8×C11—82no—
155C11⋊C8—82no—
156C23×Q8—221no—
157D4×Q8—224no—
158D4×Q8—224no—
159C2×C4⋊Q8—111no—
160C2×C4⋊Q8—112no—
161C2×C22⋊Q8—221no—
162C2×C22⋊Q8—222no—
163C2×C4×Q8C2×D1111yescharacteristic
164C2×C4×D4—111no—
165C2×C4×D4—112no—
166#431C2×D1112yes—
167#423—112no—
168C2×#101—221no—
169#343—221no—
170#332—224no—
171D4⋊C8—224no—
172#324—22no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11#37911yescharacteristic
176C22×C11C2×#10211yescharacteristic
177C22×C11#41811yescharacteristic
178C2×D11—24no—
179C2×D11—44no—
180C2×D11—44no—
181C2×D11—42no—
182C2×D11—42no—
183C4×C11—22no—
184C4×C11—21no—
185C4×C11—24no—
186C4×C11—42no—
187C4×C11C2×#10112yes—
188C4×C11#44712yes—
189C4×C11#45012yes—
190Dic11—42no—
191Dic11—44no—
192C22×Q8—228no—
193C22×Q8—222no—
194C22×Q8—221no—
195C22×Q8—444no—
196C22×Q8—442no—
197C22×Q8—442no—
198C22×Q8D4411yescharacteristic
199C22×D4—111no—
200C23×C4—222no—
201C23×C4—221no—
202C2×M16—222no—
203C4⋊Q8—114no—
204C4⋊Q8—224no—
205C4⋊Q8—224no—
206C4⋊Q8—222no—
207C22⋊Q8—228no—
208C22⋊Q8—2216no—
209C4×Q8—22no—
210C4×Q8—22no—
211C4×D4—114no—
212C4×D4—224no—
213C4×D4—224no—
214C4×D4—222no—
215C2×C4⋊C4—111no—
216C2×C4⋊C4—112no—
217C2×C4⋊C4—222no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4D4411yescharacteristic
220C2×C4⋊C4C22⋊D1112yes—
221C2×C22⋊C4—222no—
222C2×C22⋊C4—221no—
223C2×C42C4×D1112yes—
224C2×C42C22×D1111yescharacteristic
225C4⋊C8—22no—
226C4⋊C8—222no—
227C4⋊C8—222no—
228#101—442no—
229C22⋊C8—22no—
230C4×C8—22no—
231C2×C11—21no—
232C2×C11—21no—
233C2×C11#178411yescharacteristic
234C2×C11#178611yescharacteristic
235C2×C11#179611yescharacteristic
236D11—44no—
237C24—221no—
238C2×Q8—22no—
239C2×Q8—22no—
240C2×Q8—228no—
241C2×Q8—224no—
242C2×Q8—444no—
243C2×Q8—4416no—
244C2×Q8—4416no—
245C2×Q8—444no—
246C2×Q8—441no—
247C2×Q8—441no—
248C2×Q8—442no—
249C2×Q8#431412yes—
250C2×Q8D8812yes—
251C2×D4—112no—
252C2×D4—224no—
253C2×D4—221no—
254C22×C4—228no—
255C22×C4—222no—
256C22×C4—221no—
257C22×C4—224no—
258C22×C4—444no—
259C22×C4—444no—
260C22×C4—441no—
261C22×C4—441no—
262C22×C4—442no—
263C22×C4(C2×D11)⋊C412yes—
264C22×C4(C2×D11)⋊C412yes—
265C22×C4C2×C4×D1111yescharacteristic
266C22×C4C2×D4411yescharacteristic
267C22×C4C2×C22⋊D1111yescharacteristic
268M16—442no—
269M16—442no—
270C2×C8—42no—
271C2×C8—442no—
272C4⋊C4—22no—
273C4⋊C4—24no—
274C4⋊C4—112no—
275C4⋊C4—114no—
276C4⋊C4—228no—
277C4⋊C4—221no—
278C4⋊C4—222no—
279C4⋊C4—224no—
280C22⋊C4—228no—
281C22⋊C4—224no—
282C42—22no—
283C42—22no—
284C42D4×D1112yes—
285C42D4×D1112yes—
286C11#838811yescharacteristic, complemented, Sylow
287C23—224no—
288C23—222no—
289C23—442no—
290C23—441no—
291C23—441no—
292C23C2×(C2×D11)⋊C411yescharacteristic
293Q8—24no—
294Q8—24no—
295Q8—4416no—
296Q8—444no—
297Q8—444no—
298D4—114no—
299D4—224no—
300D4—222no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—224no—
308C2×C4—222no—
309C2×C4—4416no—
310C2×C4—442no—
311C2×C4—441no—
312C2×C4—442no—
313C2×C4—441no—
314C2×C4—444no—
315C2×C4—444no—
316C2×C4#6688514yes—
317C2×C4C22⋊C4×D1111yescharacteristic
318C2×C4C22⋊C4×D1111yescharacteristic
319C2×C4#6693512yes—
320C2×C4C2×#431411yescharacteristic
321C2×C4C2×D8811yescharacteristic
322C2×C4#6696112yes—
323C2×C4#6699012yes—
324C8—82no—
325C8—882no—
326C22—21no—
327C22—21no—
328C22—224no—
329C22—444no—
330C22—444no—
331C22—442no—
332C22—442no—
333C22#1062256811yescharacteristic
334C22C2×#6688511yescharacteristic
335C22#1062274411yescharacteristic
336C4—24no—
337C4—22no—
338C4—21no—
339C4—42no—
340C4—444no—
341C4—442no—
342C4#1062234412yes—
343C4#1062234512yes—
344C4D11×#10112yes—
345C2—21no—
346C2—21no—
347C2—444no—
348C2#1306853811yescharacteristic
349C2#1306854811yescharacteristic
350C2#1306858911yescharacteristic
subgroupG/H
centerC22#10622568
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1461C2
socleC22×C11#379
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1461D11
hypocenterC11#8388
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
2. #13068612C2semidirect
3. #13067287C2semidirect
5. C11×#1461C2semidirect
116. #1461D11semidirect
147. D44#101semidirect
286. C11#8388semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×D442
#130686122
#130672872
#130670422
C11×#14612
#838811