Finite Group Databasebeta

← #14656996

Subgroups — #14656996

Order 2816.

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

normal subgroups only

This group has 396 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#13074812C211yesmaximal, characteristic
2#13069602C211yesmaximal, characteristic
3#13067136C211yesmaximal, characteristic
4#13066523C211yesmaximal, characteristic
5#13066501C211yesmaximal, characteristic
6#13066468C211yesmaximal, characteristic
7C11×#1511C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C11×#407C2211yescharacteristic
10C11×#381C2211yescharacteristic
11#10622825C2211yescharacteristic
12C4×C22⋊Dic11C2211yescharacteristic
13C4×C22⋊Dic11C2211yescharacteristic
14#10622820C2211yescharacteristic
15#10622562—21no—
16#10622561—21no—
17#10622274—21no—
18#10622270—21no—
19#10622268—21no—
20#10622260—21no—
21C11×#328—21no—
22C11×#328—21no—
23#10622176—21no—
24#10622176—21no—
25#10622164—21no—
26#10622164—21no—
27C22×Q8×C11Q811yescharacteristic
28C23×C4×C11C2311yescharacteristic
29C2×C11×M16—21no—
30C11×C22⋊Q8—21no—
31C11×C22⋊Q8—21no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4Q811yescharacteristic
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11D411yescharacteristic
41C2×C22⋊Dic11D411yescharacteristic
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×C4×Dic11—21no—
50C2×C4×Dic11—21no—
51C2×#4318—21no—
52C11×C22⋊C8—21no—
53C11×C22⋊C8—21no—
54C11×#95—21no—
55C11×#95D411yescharacteristic
56C11×#95D411yescharacteristic
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95D411yescharacteristic
62C11⋊#95D411yescharacteristic
63C22⋊(C11⋊C8)—21no—
64C22⋊(C11⋊C8)—21no—
65#10385—111nomaximal, Sylow
66C24×C11C2×D411yescharacteristic
67C2×Q8×C11—21no—
68C2×Q8×C11—21no—
69C2×Q8×C11—81no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—81no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×Q811yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—41no—
86C11×M16—81no—
87C2×C8×C11—41no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—81no—
95C22⋊Dic11—22no—
96C22⋊Dic11—41no—
97C22⋊Dic11—41no—
98C22⋊Dic11—41no—
99C22⋊Dic11—42no—
100C4⋊Dic11—81no—
101C4⋊Dic11—81no—
102C4⋊Dic11—81no—
103Dic11⋊C4—42no—
104Dic11⋊C4—42no—
105Dic11⋊C4—81no—
106Dic11⋊C4—81no—
107C4×Dic11—81no—
108C4×Dic11—81no—
109#4318—81no—
110C2×C11⋊C8—41no—
111#2667—111no—
112#1996—111no—
113#1511D1111yescharacteristic
114#1508—111no—
115#1305—111no—
116#1297—111no—
117#1284—111no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11#12011yescharacteristic
123C23×C11C22⋊Q811yescharacteristic
124C23×C11#12411yescharacteristic
125Q8×C11—81no—
126Q8×C11—81no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
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—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—81no—
142C2×C4×C11—81no—
143C2×C4×C11C22⋊Q811yescharacteristic
144C2×C4×C11C22⋊Q811yescharacteristic
145C2×C4×C11#12411yescharacteristic
146C2×C4×C11#12411yescharacteristic
147C2×Dic11—22no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—42no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—81no—
161C2×Dic11—81no—
162C8×C11—81no—
163C11⋊C8—81no—
164C2×C22⋊Q8C2×D1111yescharacteristic
165#407—111no—
166#407C2×D1111yescharacteristic
167#399—221no—
168#398—221no—
169#398—221no—
170#396—221no—
171#389—221no—
172#387—221no—
173#381C2×D1111yescharacteristic
174#380—111no—
175C4×C22⋊C4—111no—
176C4×C22⋊C4—111no—
177#342—221no—
178#342—221no—
179#328—21no—
180#328—21no—
181#328—221no—
182#328—221no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—81no—
192C22×C11—81no—
193C22×C11#39311yescharacteristic
194C22×C11#45511yescharacteristic
195C22×C11#45611yescharacteristic
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—81no—
201C4×C11—81no—
202C4×C11—81no—
203C4×C11—81no—
204Dic11—42no—
205Dic11—81no—
206Dic11—81no—
207Dic11—81no—
208Dic11—82no—
209C22×Q8Dic2211yescharacteristic
210C23×C4C22×D1111yescharacteristic
211C2×M16—21no—
212C2×M16—221no—
213C22⋊Q8—21no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4—221no—
223C2×C4⋊C4—221no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4Dic2211yescharacteristic
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—221no—
233C2×C42—221no—
234C22⋊C8—21no—
235C22⋊C8—21no—
236C22⋊C8—221no—
237C22⋊C8—221no—
238#95—21no—
239#95—111no—
240#95—111no—
241#95—221no—
242#95—221no—
243#95—221no—
244#95—221no—
245#95C22⋊D1111yescharacteristic
246#95C22⋊D1111yescharacteristic
247C2×C11—21no—
248C2×C11—21no—
249C2×C11—41no—
250C2×C11—41no—
251C2×C11#202811yescharacteristic
252C2×C11#203111yescharacteristic
253C2×C11#203211yescharacteristic
254C24D4×D1111yescharacteristic
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—81no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—81no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—441no—
268C22×C4C2×Dic2211yescharacteristic
269C22×C4#433911yescharacteristic
270C22×C4D4×D1111yescharacteristic
271C22×C4#434111yescharacteristic
272C22×C4#434111yescharacteristic
273C22×C4C2×C22⋊D1111yescharacteristic
274M16—81no—
275M16—881no—
276C2×C8—41no—
277C2×C8—441no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—442no—
283C4⋊C4—442no—
284C4⋊C4—881no—
285C4⋊C4—881no—
286C4⋊C4—881no—
287C4⋊C4—881no—
288C4⋊C4—881no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—81no—
292C22⋊C4—222no—
293C22⋊C4—442no—
294C22⋊C4—441no—
295C22⋊C4—441no—
296C22⋊C4—441no—
297C42—881no—
298C42—881no—
299C11#1038511yescharacteristic, complemented, Sylow
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23#6693111yescharacteristic
305C23#6693811yescharacteristic
306C23#6699011yescharacteristic
307Q8—81no—
308Q8—81no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—222no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—442no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—881no—
339C2×C4—881no—
340C2×C4#6693111yescharacteristic
341C2×C4#6693811yescharacteristic
342C2×C4#6697711yescharacteristic
343C2×C4#6698911yescharacteristic
344C8—81no—
345C8—881no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22#1062256011yescharacteristic
357C22#1062281511yescharacteristic
358C22#1062281811yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—81no—
364C4—81no—
365C4—81no—
366C4—81no—
367C4—442no—
368C4—881no—
369C4—881no—
370C4—881no—
371C4—882no—
372C2—21no—
373C2—21no—
374C2—41no—
375C2—41no—
376C2#1306977511yescharacteristic
377C2#1306978611yescharacteristic
378C2#1306979311yescharacteristic
subgroupG/H
centerC22#10622560
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1511C2
socleC22×C11#393
prime radicalC24×C11C2×D4
hypercenter#1511D11
hypocenterC11#10385
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1511

Complements

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

NH ≅ G/Ntype
299. C11#10385semidirect

Maximal subgroups

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

subgroupindex
#130748122
#130696022
#130671362
#130665232
#130665012
#130664682
C11×#15112
#1038511