Finite Group Databasebeta

← #14664060

Subgroups — #14664060

Order 2816.

448 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 83 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#13074436C211yesmaximal, characteristic
2#13068347C211yesmaximal, characteristic
3#13066927C211yesmaximal, characteristic
4#13066638C211yesmaximal, characteristic
5#13066637C211yesmaximal, characteristic
6#13066636C211yesmaximal, characteristic
7C11×#1351C211yesmaximal, characteristic
8C2×#66997C411yescharacteristic, complemented
9C2×#66930—21no—
10C2×#66930C2211yescharacteristic
11C11×#393C2211yescharacteristic
12#10622842C411yescharacteristic, complemented
13#10622562—21no—
14#10622560C2211yescharacteristic
15#10622555—21no—
16#10622331—21no—
17#10622271—21no—
18#10622269C411yescharacteristic, complemented
19#10622263C411yescharacteristic, complemented
20#10622260—21no—
21C11×#342C2211yescharacteristic
22C11×#323C2211yescharacteristic
23#10622165—21no—
24#10622164C2211yescharacteristic
25#10622163C2211yescharacteristic
26#10622107—21no—
27C22×Q8×C11C2×C411yescharacteristic
28C23×Dic11D411yescharacteristic
29C22×Dic22C2×C411yescharacteristic
30C2×C11×C22⋊C4—21no—
31C2×C11×C22⋊C4—21no—
32C2×C11×C22⋊C4C2311yescharacteristic
33C2×C22⋊Dic11—21no—
34C2×C22⋊Dic11—21no—
35C2×C22⋊Dic11D411yescharacteristic
36#66997—41no—
37#66997—41no—
38C2×C4⋊Dic11—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—41no—
44C2×Dic11⋊C4C2×C411yescharacteristic
45C2×Dic11⋊C4D411yescharacteristic
46C2×C4×Dic11—41no—
47C2×C4×Dic11C2×C411yescharacteristic
48C2×C4×Dic11D411yescharacteristic
49#66930—24no—
50#66930—41no—
51#66930—41no—
52#66930—42no—
53C11×C22⋊C8—21no—
54C11×#95—21no—
55C11×#95C2×C411yescharacteristic
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95C2×C411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62Dic11⋊C8—41no—
63C8×Dic11—41no—
64#11717—111nomaximal, Sylow
65C24×C11C2×D411yescharacteristic
66C2×Q8×C11—41no—
67C2×Q8×C11—81no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—41no—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—22no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—41no—
79C22×Dic11C22⋊C411yescharacteristic
80C22×Dic11C22⋊C411yescharacteristic
81C22×Dic11C22⋊C411yescharacteristic
82C22×Dic11C22⋊C411yescharacteristic
83C22×Dic11SD1612yes—
84C22×Dic11Q1612yes—
85C2×Dic22—41no—
86C2×Dic22—81no—
87C2×C8×C11—41no—
88C11×C22⋊C4—22no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—81no—
92C22⋊Dic11—22no—
93C22⋊Dic11—41no—
94C22⋊Dic11—41no—
95C22⋊Dic11—81no—
96C4⋊Dic11—81no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99Dic11⋊C4—44no—
100Dic11⋊C4—42no—
101Dic11⋊C4—41no—
102Dic11⋊C4—41no—
103Dic11⋊C4—42no—
104Dic11⋊C4—81no—
105C4×Dic11—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C4×Dic11—44no—
110C2×C11⋊C8—41no—
111#2628—111no—
112#1740—111no—
113#1458—111no—
114#1351—111no—
115#1351—111no—
116#1351—111no—
117#1351D1111yescharacteristic
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11C2×C22⋊C411yescharacteristic
123C23×C11C2×SD1611yescharacteristic
124C23×C11C2×Q1611yescharacteristic
125Q8×C11—82no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—81no—
138C2×C4×C11—81no—
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—22no—
142C2×Dic11—22no—
143C2×Dic11—22no—
144C2×Dic11—22no—
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—42no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—81no—
157C2×Dic11—81no—
158C2×Dic11#9911yescharacteristic
159C2×Dic11#9911yescharacteristic
160C2×Dic11#10312yes—
161C2×Dic11#10312yes—
162C2×Dic11#10412yes—
163Dic22—82no—
164C8×C11—81no—
165C11⋊C8—81no—
166C2×C4⋊Q8—111no—
167C2×#117—111no—
168C2×#117—221no—
169#431—221no—
170#400—221no—
171#399—221no—
172#395—111no—
173#395—111no—
174#393—111no—
175#393C2×D1111yescharacteristic
176#389—221no—
177#382—111no—
178#380—221no—
179#342—111no—
180#342—221no—
181#342C2×D1111yescharacteristic
182#324—221no—
183#323—111no—
184#323C2×D1111yescharacteristic
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—81no—
194C22×C11C2×#9911yescharacteristic
195C22×C11C2×#10311yescharacteristic
196C22×C11C2×#10411yescharacteristic
197C4×C11—41no—
198C4×C11—41no—
199C4×C11—81no—
200C4×C11—82no—
201C4×C11—81no—
202Dic11—22no—
203Dic11—41no—
204Dic11—41no—
205Dic11—81no—
206Dic11—82no—
207Dic11—81no—
208Dic11#32812yes—
209Dic11#32812yes—
210C22×Q8—111no—
211C22×Q8C4×D1111yescharacteristic
212C23×C4—111no—
213C4⋊Q8—441no—
214C4⋊Q8—441no—
215#117—224no—
216#117—441no—
217#117—441no—
218#117—442no—
219C2×C4⋊C4—111no—
220C2×C4⋊C4—111no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—441no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—111no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4C22×D1111yescharacteristic
233C2×C42—111no—
234C2×C42—111no—
235C2×C42—441no—
236C4⋊C8—441no—
237C22⋊C8—21no—
238C22⋊C8—221no—
239C4×C8—441no—
240#95—21no—
241#95—111no—
242#95—221no—
243#95—221no—
244#95—221no—
245#95—221no—
246#95C4×D1111yescharacteristic
247C2×C11—21no—
248C2×C11—21no—
249C2×C11—41no—
250C2×C11—41no—
251C2×C11C2×#32811yescharacteristic
252C2×C11#212211yescharacteristic
253C2×C11#212911yescharacteristic
254C24D4×D1111yescharacteristic
255C2×Q8—41no—
256C2×Q8—81no—
257C2×Q8—441no—
258C2×Q8—881no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—41no—
262C22×C4—111no—
263C22×C4—111no—
264C22×C4—112no—
265C22×C4—112no—
266C22×C4—111no—
267C22×C4—111no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—222no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—441no—
274C22×C4C2×C4×D1111yescharacteristic
275C22×C4D4×D1111yescharacteristic
276C2×C8—41no—
277C2×C8—441no—
278C4⋊C4—441no—
279C4⋊C4—441no—
280C4⋊C4—441no—
281C4⋊C4—441no—
282C4⋊C4—442no—
283C4⋊C4—442no—
284C4⋊C4—444no—
285C4⋊C4—881no—
286C4⋊C4—881no—
287C22⋊C4—22no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—81no—
291C22⋊C4—222no—
292C22⋊C4—441no—
293C22⋊C4—441no—
294C22⋊C4—881no—
295C42—221no—
296C42—221no—
297C42—221no—
298C42—221no—
299C42—444no—
300C11#1171711yescharacteristic, complemented, Sylow
301C23—21no—
302C23—21no—
303C23—41no—
304C23—41no—
305C23C22⋊C4×D1111yescharacteristic
306C23SD16×D1111yescharacteristic
307C23Q16×D1111yescharacteristic
308Q8—82no—
309Q8—882no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—111no—
324C2×C4—111no—
325C2×C4—112no—
326C2×C4—112no—
327C2×C4—112no—
328C2×C4—222no—
329C2×C4—222no—
330C2×C4—222no—
331C2×C4—222no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—442no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—881no—
346C2×C4—881no—
347C8—81no—
348C8—881no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—81no—
358C22D11×#9911yescharacteristic
359C22D11×#10311yescharacteristic
360C22D11×#10411yescharacteristic
361C4—41no—
362C4—41no—
363C4—81no—
364C4—82no—
365C4—81no—
366C4—112no—
367C4—112no—
368C4—222no—
369C4—441no—
370C4—441no—
371C4—881no—
372C4—882no—
373C4—881no—
374C2—21no—
375C2—21no—
376C2—41no—
377C2—41no—
378C2D11×#32811yescharacteristic
379C2#1307026411yescharacteristic
380C2#1307028911yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1351C2
socleC22×C11C2×#99
prime radicalC24×C11C2×D4
cosocleC2×C11×C22⋊C4C23
hypercenter#1351D11
hypocenterC11#11717
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1351

Complements

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

NH ≅ G/Ntype
8. C2×#66997C4semidirect
12. #10622842C4semidirect
18. #10622269C4semidirect
19. #10622263C4semidirect
300. C11#11717semidirect

Maximal subgroups

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

subgroupindex
#130744362
#130683472
#130669272
#130666382
#130666372
#130666362
C11×#13512
#1171711