Finite Group Databasebeta

← #14648844

Subgroups — #14648844

Order 2816.

484 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 95 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
1#13077700C211yesmaximal, characteristic
2#13071907C211yesmaximal, characteristic
3C4×#66888C211yesmaximal, characteristic
4#13067063C211yesmaximal, characteristic
5#13066510C211yesmaximal, characteristic
6#13066508C211yesmaximal, characteristic
7C11×#1491C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#432C2211yescharacteristic
11C4×C11×M16C2211yescharacteristic
12#10622842C411yescharacteristic
13#10622842C411yescharacteristic
14C2×#66888—21no—
15#10622596—21no—
16#10622593C411yescharacteristic
17#10622593C411yescharacteristic
18#10622592—21no—
19#10622545C2211yescharacteristic
20C4×Dic11⋊C4—21no—
21C4×Dic11⋊C4—21no—
22#10622539C2211yescharacteristic
23C4×#4318C2211yescharacteristic
24#10622441—22no—
25#10622332—21no—
26#10622331—21no—
27#10622314—22no—
28C11×Q8⋊C8—22no—
29#10622192—21no—
30Q8⋊(C11⋊C8)—22no—
31C22×Q8×C11C2×C411yescharacteristic
32C22×Dic22D411yescharacteristic
33C2×C11×M16—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C42×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C2×C4⋊Dic11D411yescharacteristic
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4C2×C411yescharacteristic
48C2×Dic11⋊C4C2×C411yescharacteristic
49C2×C4×Dic11—21no—
50C2×C4×Dic11D411yescharacteristic
51C2×C4×Dic11D411yescharacteristic
52C2×#4318—21no—
53C4×Dic22—21no—
54C4×Dic22—21no—
55C4×Dic22—21no—
56C4×Dic22—21no—
57C11×C4⋊C8D412yes—
58C11×C22⋊C8—21no—
59C11×#97—21no—
60C11×#97—21no—
61C4×C8×C11—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95C2×C411yescharacteristic
68C11⋊#95C2×C411yescharacteristic
69C22⋊(C11⋊C8)—21no—
70#66888—24no—
71#66879—22no—
72Dic11⋊C8—22no—
73Dic11⋊C8—22no—
74C8×Dic11—22no—
75C4⋊(C11⋊C8)D412yes—
76#66867—21no—
77#66867—21no—
78C4×C11⋊C8—21no—
79#9030—111nomaximal, Sylow
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—42no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11C22⋊C411yescharacteristic
91C22×Dic11C22⋊C411yescharacteristic
92C22×Dic11C22⋊C411yescharacteristic
93C22×Dic11C22⋊C411yescharacteristic
94C2×Dic22—22no—
95C2×Dic22—21no—
96C2×Dic22—21no—
97C2×Dic22—41no—
98C11×M16—22no—
99C11×M16—41no—
100C2×C8×C11—22no—
101C2×C8×C11—41no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C42×C11—41no—
107C42×C11—41no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111C42×C11#4111yescharacteristic
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114Dic11⋊C4—21no—
115Dic11⋊C4—21no—
116Dic11⋊C4—21no—
117Dic11⋊C4—21no—
118Dic11⋊C4—42no—
119Dic11⋊C4—42no—
120Dic11⋊C4—42no—
121Dic11⋊C4—42no—
122C4×Dic11—24no—
123C4×Dic11—21no—
124C4×Dic11—21no—
125C4×Dic11—21no—
126C4×Dic11—21no—
127#4318—22no—
128#4318—41no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—41no—
131#2983—111no—
132#2399—111no—
133C4×#101—111no—
134#1491—111no—
135#1491D1111yescharacteristic
136#1300—111no—
137#1300—111no—
138C23×C11C2×C22⋊C411yescharacteristic
139Q8×C11—22no—
140Q8×C11—22no—
141Q8×C11—41no—
142Q8×C11—41no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11C4×D411yescharacteristic
154C2×C4×C11C4×D411yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12311yescharacteristic
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—22no—
162C2×Dic11—22no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—21no—
167C2×Dic11—21no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11#10412yes—
175Dic22—42no—
176Dic22—42no—
177C8×C11—42no—
178C8×C11—42no—
179C11⋊C8—42no—
180C11⋊C8—42no—
181C2×C4×Q8—111no—
182C2×C4×Q8C2×D1111yescharacteristic
183#446—222no—
184#446—222no—
185#432—111no—
186#432—221no—
187#432C2×D1111yescharacteristic
188#431—221no—
189C2×#101—221no—
190C4×M16—111no—
191C4×M16C2×D1111yescharacteristic
192#398—111no—
193#398—111no—
194#398—221no—
195#395—111no—
196#395—111no—
197#395—221no—
198C4×C4⋊C4—221no—
199C4×C4⋊C4—221no—
200#376—111no—
201#343—221no—
202Q8⋊C8—22no—
203Q8⋊C8—222no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11#38611yescharacteristic
207C22×C11C2×#10411yescharacteristic
208C22×C11#42111yescharacteristic
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—42no—
215C4×C11—81no—
216C4×C11#45612yes—
217Dic11—22no—
218Dic11—42no—
219Dic11—42no—
220Dic11—41no—
221Dic11—41no—
222Dic11—41no—
223C22×Q8—111no—
224C22×Q8C4×D1111yescharacteristic
225C2×M16—21no—
226C2×M16—221no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×Q8—21no—
231C4×Q8—221no—
232C4×Q8—221no—
233C4×Q8—221no—
234C4×Q8—221no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—111no—
237C2×C4⋊C4—111no—
238C2×C4⋊C4—111no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4C4×D1111yescharacteristic
244C2×C42—21no—
245C2×C42—111no—
246C2×C42—111no—
247C2×C42—221no—
248C2×C42C22×D1111yescharacteristic
249C4⋊C8—112no—
250C4⋊C8—222no—
251C4⋊C8—222no—
252C4⋊C8C22⋊D1112yes—
253#101—224no—
254C22⋊C8—21no—
255C22⋊C8—221no—
256#97—21no—
257#97—21no—
258#97—222no—
259#97—221no—
260#97—221no—
261C4×C8—21no—
262C4×C8—222no—
263C4×C8—221no—
264#95—111no—
265#95—111no—
266#95—221no—
267#95—221no—
268#95—221no—
269#95—221no—
270#95—221no—
271C2×C11—21no—
272C2×C11—21no—
273C2×C11#187111yescharacteristic
274C2×C11#188611yescharacteristic
275C2×C11#189111yescharacteristic
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—42no—
279C2×Q8—222no—
280C2×Q8—221no—
281C2×Q8—221no—
282C2×Q8—441no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—111no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4C2×C4×D1111yescharacteristic
292C22×C4D4×D1111yescharacteristic
293C22×C4D4×D1111yescharacteristic
294M16—22no—
295M16—41no—
296M16—222no—
297M16—441no—
298C2×C8—22no—
299C2×C8—41no—
300C2×C8—222no—
301C2×C8—441no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—221no—
307C4⋊C4—221no—
308C4⋊C4—221no—
309C4⋊C4—221no—
310C4⋊C4—221no—
311C4⋊C4—221no—
312C4⋊C4—442no—
313C4⋊C4—442no—
314C4⋊C4—442no—
315C4⋊C4—442no—
316C42—41no—
317C42—41no—
318C42—224no—
319C42—221no—
320C42—221no—
321C42—221no—
322C42—221no—
323C42#433911yescharacteristic
324C42D4×D1111yescharacteristic
325C42#434111yescharacteristic
326C42C2×C22⋊D1111yescharacteristic
327C11#903011yescharacteristic, complemented, Sylow
328C23C22⋊C4×D1111yescharacteristic
329Q8—22no—
330Q8—22no—
331Q8—41no—
332Q8—41no—
333Q8—442no—
334Q8—442no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—112no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—222no—
349C2×C4—222no—
350C2×C4—221no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4(C22⋊D11)⋊C411yescharacteristic
362C2×C4#6693611yescharacteristic
363C2×C4#6693711yescharacteristic
364C2×C4C4×C22⋊D1111yescharacteristic
365C2×C4#6699011yescharacteristic
366C2×C4#6699111yescharacteristic
367C8—42no—
368C8—42no—
369C8—442no—
370C8—442no—
371C22—21no—
372C22—21no—
373C22D11×#10411yescharacteristic
374C22#1062243411yescharacteristic
375C22#1062256911yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—42no—
382C4—81no—
383C4—222no—
384C4—442no—
385C4—442no—
386C4—441no—
387C4—441no—
388C4—441no—
389C4#1062281812yes—
390C2—21no—
391C2—21no—
392C2#1306891511yescharacteristic
393C2#1306900611yescharacteristic
394C2#1306903111yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1491C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1491D11
hypocenterC11#9030
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
327. C11#9030semidirect

Maximal subgroups

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

subgroupindex
#130777002
#130719072
C4×#668882
#130670632
#130665102
#130665082
C11×#14912
#903011