Finite Group Databasebeta

← #14669254

Subgroups — #14669254

Order 2816.

976 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 976 conjugacy classes of subgroups — too many to draw. Only its 115 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×#10623356C211yesmaximal, characteristic
2C2×#10622110C214yesmaximal, complemented
3#13068544C211yesmaximal, characteristic
4C11×#1782C211yesmaximal, characteristic
5C22×C11×#41C2211yescharacteristic
6C23×Dic22C411yescharacteristic, complemented
7#10623356—28no—
8C2×#66997—21no—
9C2×#66989—21no—
10C2×#66988C412yescomplemented
11C2×#66988C2212yes—
12C2×#66979C411yescharacteristic, complemented
13C2×#66977—21no—
14C2×#66977—21no—
15C2×C11×#99—21no—
16C2×C11×#99C2212yes—
17C11×#381—21no—
18C2×#66900—21no—
19C2×#66897C2212yes—
20#10622820—21no—
21#10622110—28no—
22C2×C11×#41—24no—
23C2×C11×#41—42no—
24C2×C11×#41—42no—
25C22×Q8×C11D411yescharacteristic
26C22×D4×C11C2×C411yescharacteristic
27C22×D4×C11D411yescharacteristic
28C22×D4×C11C2311yescharacteristic
29C23×C4×C11C2×C411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C23×C4×C11D411yescharacteristic
32C23×Dic11C2×C412yes—
33C22×Dic22—21no—
34C22×Dic22—21no—
35C22×Dic22—24no—
36C22×Dic22—42no—
37C22×Dic22—42no—
38C2×C11×C22⋊C4—22no—
39C2×C22⋊Dic11—22no—
40C2×C22⋊Dic11—22no—
41C2×C22⋊Dic11C2×C412yes—
42#66997—28no—
43#66989—28no—
44#66988—24no—
45#66988—24no—
46#66988—24no—
47#66988D418yes—
48#66979—24no—
49C2×C4⋊Dic11—21no—
50#66977—28no—
51#66977—28no—
52C2×Dic11⋊C4—22no—
53C2×Dic11⋊C4—22no—
54C2×C4×Dic11—21no—
55C2×#4318—22no—
56C11×#99—24no—
57C11×#99—42no—
58C11×#95—42no—
59#66900—42no—
60#66897—24no—
61C22⋊(C11⋊C8)—42no—
62#12692—111nomaximal, Sylow
63C24×C11C22⋊C411yescharacteristic
64C24×C11C22×C411yescharacteristic
65C24×C11C2×D411yescharacteristic
66C11×#41—416no—
67C2×Q8×C11—22no—
68C2×Q8×C11—22no—
69C2×Q8×C11—41no—
70C2×D4×C11—22no—
71C2×D4×C11—22no—
72C2×D4×C11—22no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11C2×D414yes—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—42no—
89C22×C4×C11C22⋊C411yescharacteristic
90C22×C4×C11C22⋊C411yescharacteristic
91C22×C4×C11C22⋊C411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×Dic11—22no—
94C22×Dic11—22no—
95C22×Dic11—22no—
96C22×Dic11—42no—
97C22×Dic11—42no—
98C22×Dic11C22⋊C414yes—
99C2×Dic22—24no—
100C2×Dic22—24no—
101C2×Dic22—416no—
102C2×Dic22—42no—
103C2×Dic22—42no—
104C2×Dic22—42no—
105C2×Dic22—42no—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—42no—
108C22⋊Dic11—28no—
109C22⋊Dic11—22no—
110C22⋊Dic11—28no—
111C22⋊Dic11C22⋊C414yes—
112C4⋊Dic11—24no—
113Dic11⋊C4—28no—
114Dic11⋊C4—28no—
115C4×Dic11—24no—
116#4318—42no—
117#4318—42no—
118C2×C11⋊C8—42no—
119C2×#536—111no—
120C2×#352—114no—
121#1785—111no—
122#1782D1111yescharacteristic
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—42no—
131C23×C11—42no—
132C23×C11—42no—
133C23×C11C2×C22⋊C412yes—
134C23×C11C2×C22⋊C411yescharacteristic
135C23×C11#12012yes—
136Q8×C11—44no—
137D4×C11—44no—
138D4×C11—44no—
139D4×C11—44no—
140C2×C4×C11—28no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—44no—
151C2×C4×C11—44no—
152C2×C4×C11—82no—
153C2×C4×C11—84no—
154C2×C4×C11#9912yes—
155C2×C4×C11#9912yes—
156C2×C4×C11#12012yes—
157C2×Dic11—24no—
158C2×Dic11—24no—
159C2×Dic11—44no—
160C2×Dic11—44no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—44no—
164Dic22—48no—
165Dic22—48no—
166C11⋊C8—82no—
167C22×#41C2×D1111yescharacteristic
168C23×Q8—111no—
169#536—228no—
170C2×C4⋊Q8—221no—
171C2×#124—221no—
172C2×#123—112no—
173C2×#123—112no—
174C2×C22⋊Q8—221no—
175C2×C22⋊Q8—221no—
176C2×#117—111no—
177C2×#101—221no—
178C2×#100—112no—
179C2×#99—21no—
180C2×#99C2×D1112yes—
181#407—221no—
182#381—21no—
183#352—228no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—42no—
188C22×C11—42no—
189C22×C11—42no—
190C22×C11—42no—
191C22×C11—42no—
192C22×C11—42no—
193C22×C11—42no—
194C22×C11—41no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11#37911yescharacteristic
198C22×C11C2×#9911yescharacteristic
199C22×C11C2×#9911yescharacteristic
200C4×C11—22no—
201C4×C11—22no—
202C4×C11—22no—
203C4×C11—41no—
204C4×C11—162no—
205Dic11—44no—
206Dic11—44no—
207C2×#41—24no—
208C2×#41—42no—
209C2×#41—42no—
210C22×Q8—224no—
211C22×Q8—221no—
212C22×Q8—221no—
213C22×Q8—442no—
214C22×Q8—442no—
215C22×Q8D4411yescharacteristic
216C22×D4C4×D1111yescharacteristic
217C22×D4C22⋊D1111yescharacteristic
218C22×D4C22×D1111yescharacteristic
219C23×C4—112no—
220C23×C4C4×D1111yescharacteristic
221C23×C4D4411yescharacteristic
222C23×C4C22⋊D1111yescharacteristic
223C2×M16—222no—
224C4⋊Q8—228no—
225#124—228no—
226#123—118no—
227#123—224no—
228#123—224no—
229#123—224no—
230C22⋊Q8—228no—
231C22⋊Q8—228no—
232#117—224no—
233C2×C4⋊C4—222no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—222no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—112no—
238C2×C22⋊C4—222no—
239C2×C22⋊C4—222no—
240C2×C42—221no—
241#101—442no—
242#100—224no—
243#99—24no—
244#99—42no—
245C22⋊C8—442no—
246#95—42no—
247C2×C11—21no—
248C2×C11—21no—
249C2×C11—42no—
250C2×C11—42no—
251C2×C11—81no—
252C2×C11#178111yescharacteristic
253C2×C11#212312yes—
254C24(C2×D11)⋊C411yescharacteristic
255C24C2×C4×D1111yescharacteristic
256C24C2×C22⋊D1111yescharacteristic
257#41—416no—
258C2×Q8—22no—
259C2×Q8—22no—
260C2×Q8—41no—
261C2×Q8—224no—
262C2×Q8—224no—
263C2×Q8—4416no—
264C2×Q8—442no—
265C2×Q8—442no—
266C2×Q8—442no—
267C2×Q8—442no—
268C2×D4—22no—
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4D4×D1114yes—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—42no—
287C22×C4—114no—
288C22×C4—222no—
289C22×C4—222no—
290C22×C4—222no—
291C22×C4—442no—
292C22×C4—442no—
293C22×C4(C2×D11)⋊C411yescharacteristic
294C22×C4(C2×D11)⋊C411yescharacteristic
295C22×C4(C2×D11)⋊C411yescharacteristic
296C22×C4C2×D4411yescharacteristic
297M16—442no—
298M16—442no—
299C2×C8—442no—
300C4⋊C4—224no—
301C4⋊C4—228no—
302C4⋊C4—228no—
303C22⋊C4—42no—
304C22⋊C4—42no—
305C22⋊C4—114no—
306C22⋊C4—228no—
307C22⋊C4—222no—
308C22⋊C4—228no—
309C42—224no—
310C11#1269211yescharacteristic, complemented, Sylow
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23C22⋊C4×D1112yes—
322C23C2×(C2×D11)⋊C411yescharacteristic
323C23#6699012yes—
324Q8—44no—
325Q8—448no—
326Q8—448no—
327D4—44no—
328D4—44no—
329D4—44no—
330C2×C4—28no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—82no—
343C2×C4—84no—
344C2×C4—224no—
345C2×C4—224no—
346C2×C4—444no—
347C2×C4—444no—
348C2×C4—442no—
349C2×C4—442no—
350C2×C4—444no—
351C2×C4#6687012yes—
352C2×C4#6687012yes—
353C2×C4#6693512yes—
354C8—882no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—42no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—42no—
364C22—42no—
365C22—41no—
366C22—81no—
367C22—81no—
368C22C2×#6687011yescharacteristic
369C22C2×#6687011yescharacteristic
370C22#1062256811yescharacteristic
371C4—22no—
372C4—22no—
373C4—22no—
374C4—41no—
375C4—162no—
376C4—444no—
377C4—444no—
378C2—21no—
379C2—21no—
380C2—42no—
381C2—42no—
382C2—81no—
383C2#1306853011yescharacteristic
384C2#1307026912yes—
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
FittingC11×#1782C2
socleC22×C11C2×#99
prime radicalC22×C11×#41C22
cosocleC22×D4×C11C23
hypercenter#1782D11
hypocenterC11#12692
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #1782

Complements

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

NH ≅ G/Ntype
2. C2×#10622110C2semidirect
6. C23×Dic22C4semidirect
10. C2×#66988C4semidirect
12. C2×#66979C4semidirect
310. C11#12692semidirect

Maximal subgroups

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

subgroupindex
C2×#106233562
C2×#106221102
#130685442
C11×#17822
#1269211