Finite Group Databasebeta

← #14657008

Subgroups — #14657008

Order 2816.

414 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 75 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#13074277C211yesmaximal, characteristic
2#13068715C211yesmaximal, characteristic
3#13068693C211yesmaximal, characteristic
4#13066525C211yesmaximal, characteristic
5#13066470C211yesmaximal, characteristic
6#13066469C211yesmaximal, characteristic
7C11×#1826C211yesmaximal, characteristic
8C2×C11×#117C2211yescharacteristic
9C11×#407C2211yescharacteristic
10C4×C11×C22⋊C4C2211yescharacteristic
11#10622824C2211yescharacteristic
12#10622824C2211yescharacteristic
13C4×C22⋊Dic11C2211yescharacteristic
14#10622820C2211yescharacteristic
15#10622562—21no—
16#10622560—21no—
17#10622546—21no—
18#10622542—21no—
19#10622267—21no—
20#10622259—21no—
21C11×#339—21no—
22C11×#339—21no—
23#10622170—21no—
24#10622170—21no—
25#10622164—21no—
26#10622164—21no—
27C23×C4×C11C2311yescharacteristic
28C22×Dic22—21no—
29C2×C11×M16—21no—
30C11×#117—21no—
31C11×#117—21no—
32C11×#117—21no—
33C11×#117—21no—
34C2×C11×C4⋊C4Q811yescharacteristic, complemented
35C2×C11×C4⋊C4Q811yescharacteristic, complemented
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C42×C11—21no—
39C2×C42×C11D411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11D411yescharacteristic
44C2×C22⋊Dic11D411yescharacteristic
45C2×C4⋊Dic11—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×C4×Dic11D411yescharacteristic
49C2×C4×Dic11D411yescharacteristic
50C2×#4318—21no—
51C11×C22⋊C8—21no—
52C11×C22⋊C8—21no—
53C11×#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)—21no—
65#10387—111nomaximal, Sylow
66C24×C11C2×D411yescharacteristic
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×Q811yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—41no—
84C2×Dic22—42no—
85C2×Dic22—42no—
86C2×Dic22—81no—
87C11×M16—41no—
88C11×M16—41no—
89C2×C8×C11—41no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C22⋊C4—42no—
95C11×C22⋊C4—41no—
96C11×C22⋊C4—41no—
97C42×C11—41no—
98C42×C11—41no—
99C42×C11—41no—
100C42×C11—41no—
101C22⋊Dic11—41no—
102C22⋊Dic11—41no—
103C22⋊Dic11—41no—
104C22⋊Dic11—41no—
105C22⋊Dic11—42no—
106C4⋊Dic11—42no—
107Dic11⋊C4—42no—
108Dic11⋊C4—81no—
109C4×Dic11—41no—
110C4×Dic11—41no—
111#4318—41no—
112#4318—41no—
113C2×C11⋊C8—41no—
114#2607—111no—
115#1826—111no—
116#1826D1111yescharacteristic
117#1820—111no—
118#1306—111no—
119#1284—111no—
120#1284—111no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11#12011yescharacteristic
126C23×C11C22⋊Q811yescharacteristic
127C23×C11#12411yescharacteristic
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—22no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11C22⋊Q811yescharacteristic
147C2×C4×C11C22⋊Q811yescharacteristic
148C2×C4×C11#12411yescharacteristic
149C2×C4×C11#12411yescharacteristic
150C2×Dic11—22no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—81no—
163C2×Dic11—81no—
164C2×Dic11—81no—
165Dic22—84no—
166C8×C11—81no—
167C11⋊C8—81no—
168C2×#117C2×D1111yescharacteristic
169#407—111no—
170#407C2×D1111yescharacteristic
171#399—221no—
172#393—221no—
173#391—221no—
174#391—221no—
175#387—221no—
176#387—221no—
177#381—111no—
178#381—111no—
179C4×C22⋊C4—111no—
180C4×C22⋊C4C2×D1111yescharacteristic
181#342—221no—
182#342—221no—
183#339—21no—
184#339—21no—
185#339—221no—
186#339—221no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11#39311yescharacteristic
198C22×C11#45811yescharacteristic
199C22×C11#45811yescharacteristic
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—42no—
205C4×C11—81no—
206C4×C11—81no—
207C4×C11—81no—
208Dic11—42no—
209Dic11—81no—
210Dic11—81no—
211Dic11—81no—
212Dic11—161no—
213C22×Q8—221no—
214C23×C4C22×D1111yescharacteristic
215C2×M16—21no—
216C2×M16—221no—
217#117—21no—
218#117—21no—
219#117—21no—
220#117—21no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4Dic2211yescharacteristic, complemented
225C2×C4⋊C4Dic2211yescharacteristic, complemented
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—111no—
229C2×C22⋊C4—111no—
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C42—21no—
233C2×C42—111no—
234C2×C42—111no—
235C2×C42C22⋊D1111yescharacteristic
236C2×C42C22⋊D1111yescharacteristic
237C22⋊C8—21no—
238C22⋊C8—21no—
239C22⋊C8—221no—
240C22⋊C8—221no—
241#95—21no—
242#95—221no—
243#95—221no—
244#95—221no—
245#95—221no—
246#95—221no—
247#95—221no—
248#95—221no—
249#95—221no—
250#95—221no—
251C2×C11—21no—
252C2×C11—21no—
253C2×C11—41no—
254C2×C11—41no—
255C2×C11#203011yescharacteristic
256C2×C11#203111yescharacteristic
257C2×C11#203111yescharacteristic
258C24D4×D1111yescharacteristic
259C2×Q8—442no—
260C2×Q8—442no—
261C2×Q8—881no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—441no—
273C22×C4C2×Dic2211yescharacteristic
274C22×C4#433911yescharacteristic
275C22×C4D4×D1111yescharacteristic
276C22×C4#434111yescharacteristic
277C22×C4#434111yescharacteristic
278C22×C4C2×C22⋊D1111yescharacteristic
279M16—41no—
280M16—41no—
281M16—441no—
282M16—441no—
283C2×C8—41no—
284C2×C8—441no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—442no—
290C4⋊C4—442no—
291C4⋊C4—881no—
292C22⋊C4—42no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—442no—
296C22⋊C4—441no—
297C22⋊C4—441no—
298C22⋊C4—441no—
299C22⋊C4—441no—
300C42—41no—
301C42—41no—
302C42—41no—
303C42—41no—
304C42—441no—
305C42—441no—
306C11#1038711yescharacteristic, complemented, Sylow
307C23—21no—
308C23—21no—
309C23—41no—
310C23—41no—
311C23#6693111yescharacteristic
312C23#6693811yescharacteristic
313C23#6699011yescharacteristic
314Q8—884no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—222no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—881no—
346C2×C4—881no—
347C2×C4—881no—
348C2×C4#6693111yescharacteristic
349C2×C4#6693811yescharacteristic
350C2×C4#6697711yescharacteristic
351C2×C4#6698911yescharacteristic
352C8—81no—
353C8—881no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—81no—
363C22—81no—
364C22#1062256011yescharacteristic
365C22#1062266611yescharacteristic
366C22#1062266611yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—42no—
372C4—81no—
373C4—81no—
374C4—81no—
375C4—442no—
376C4—881no—
377C4—881no—
378C4—881no—
379C4—1761no—
380C2—21no—
381C2—21no—
382C2—41no—
383C2—41no—
384C2#1306978311yescharacteristic
385C2#1306978611yescharacteristic
386C2#1306978811yescharacteristic
subgroupG/H
centerC22#10622560
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1826C2
socleC22×C11#393
prime radicalC24×C11C2×D4
hypercenter#1826D11
hypocenterC11#10387
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
34. C2×C11×C4⋊C4Q8semidirect
35. C2×C11×C4⋊C4Q8semidirect
224. C2×C4⋊C4Dic22semidirect
225. C2×C4⋊C4Dic22semidirect
306. C11#10387semidirect

Maximal subgroups

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

subgroupindex
#130742772
#130687152
#130686932
#130665252
#130664702
#130664692
C11×#18262
#1038711