Finite Group Databasebeta

← #14655248

Subgroups — #14655248

Order 2816.

552 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 89 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#13079999C211yesmaximal, characteristic
2#13079073C211yesmaximal, characteristic
3#13069606C211yesmaximal, characteristic, complemented
4#13067211C211yesmaximal, characteristic, complemented
5#13067032C211yesmaximal, characteristic
6#13066507C211yesmaximal, characteristic, complemented
7C11×#3209C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66995—22no—
11#10623008C2211yescharacteristic
12C11×#494—21no—
13C11×#487—21no—
14C11×#462—22no—
15C11×#451—22no—
16C11×#431C2211yescharacteristic
17#10622705—21no—
18#10622700—21no—
19#10622699—22no—
20#10622698—21no—
21#10622696—21no—
22#10622662—22no—
23#10622640—21no—
24#10622634—21no—
25#10622537C2211yescharacteristic
26C4×#4318C2211yescharacteristic
27C4×#4318C2211yescharacteristic
28#10622181—22no—
29#10622168—22no—
30#10622121—22no—
31C22×Q8×C11D412yes—
32C2×#4339—21no—
33C2×C11×Q16—24no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D411yescharacteristic
39C11×C4⋊Q8D411yescharacteristic
40C11×#125—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C11×#117—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4326—24no—
50#66995—48no—
51C2×#4325—24no—
52C2×#4325—22no—
53#66983—21no—
54#66983—21no—
55C2×#4318—21no—
56C2×#4318—21no—
57C2×#4318D412yes—
58#66928—21no—
59#66927D411yescharacteristic
60C4×D44—21no—
61C4×D44—21no—
62#66922D411yescharacteristic
63C11×C4⋊C8D412yes—
64C11×#103—24no—
65C11×C22⋊C8—21no—
66C4×C8×C11—21no—
67#66899—22no—
68#66873—22no—
69#66871—22no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72#66867—21no—
73#66867D412yes—
74C4×C11⋊C8—21no—
75C4×C11⋊C8—21no—
76#10107—111nomaximal, Sylow
77C2×Q8×C11—21no—
78C2×Q8×C11—22no—
79C2×Q8×C11—22no—
80C2×Q8×C11—21no—
81C2×Q8×C11—44no—
82C22×C4×C11—22no—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C2×C22⋊D11—41no—
87#4339—44no—
88C2×D44—21no—
89C2×D44—21no—
90C2×D44—21no—
91C2×C4×D11—41no—
92C2×Dic22—21no—
93C11×Q16—84no—
94C2×C8×C11—22no—
95C11×C4⋊C4—21no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C22⋊C4—41no—
106C42×C11—41no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111#4326—48no—
112#4325—48no—
113#4325—82no—
114(C2×D11)⋊C4—41no—
115(C2×D11)⋊C4—41no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118#4318—24no—
119#4318—22no—
120#4318—42no—
121#4318—41no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—41no—
125#3254—111no—
126#3209D1111yescharacteristic, complemented
127#3152—111no—
128#1997—111no—
129#1526—111no—
130#1484—111no—
131#1299—111no—
132C23×C11#12111yescharacteristic
133C22×D11—41no—
134Q8×C11—44no—
135Q8×C11—42no—
136Q8×C11—44no—
137Q8×C11—41no—
138Q8×C11—41no—
139C2×C4×C11—22no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—82no—
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12711yescharacteristic
153C22⋊D11—82no—
154C2×Dic11—41no—
155D44—42no—
156D44—41no—
157D44—41no—
158D44—42no—
159C4×D11—82no—
160Dic22—42no—
161C8×C11—42no—
162C11⋊C8—24no—
163C11⋊C8—42no—
164C11⋊C8—42no—
165C2×#137—222no—
166#533C2×D1111yescharacteristic
167#532—111no—
168C2×C4⋊Q8C2×D1111yescharacteristic
169#497—222no—
170#494—21no—
171#494—221no—
172#492—221no—
173#487—21no—
174#477—221no—
175#474—221no—
176#468—222no—
177#462—22no—
178#461—221no—
179#460—221no—
180#451—22no—
181#431C2×D1111yescharacteristic
182#423—111no—
183C4×M16—111no—
184C4×M16—111no—
185#343—222no—
186#330—222no—
187D4⋊C8—222no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11#39211yescharacteristic
192C2×D11—81no—
193C2×D11—81no—
194C2×D11—81no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—82no—
199C4×C11—81no—
200C4×C11—81no—
201C4×C11#45312yes—
202C4×C11#45511yescharacteristic
203C4×C11#45611yescharacteristic
204C4×C11#47312yes—
205Dic11—81no—
206C2×#41—221no—
207C22×Q8C22⋊D1112yes—
208#137—448no—
209C2×Q16—24no—
210C2×Q16—224no—
211C2×SD16—224no—
212C2×SD16—222no—
213C2×M16—112no—
214C2×M16—221no—
215C2×M16—221no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—111no—
221C4⋊Q8C22⋊D1111yescharacteristic
222C4⋊Q8C22⋊D1111yescharacteristic
223#127—111no—
224#125—21no—
225#124—221no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228#121—221no—
229#121—221no—
230C4×Q8—21no—
231C4×Q8—21no—
232C4×D4—221no—
233C4×D4—221no—
234#117—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C42C22×D1111yescharacteristic
238#107—222no—
239C4⋊C8—221no—
240C4⋊C8—221no—
241C4⋊C8C22⋊D1112yes—
242#103—24no—
243#103—222no—
244#102—222no—
245C22⋊C8—21no—
246#97—112no—
247#97—221no—
248C4×C8—21no—
249C4×C8—221no—
250C4×C8—221no—
251C2×C11—41no—
252C2×C11#200211yescharacteristic
253C2×C11#200711yescharacteristic
254C2×C11#202011yescharacteristic
255D11—161no—
256#41—444no—
257C2×Q8—21no—
258C2×Q8—22no—
259C2×Q8—22no—
260C2×Q8—21no—
261C2×Q8—44no—
262C2×Q8—221no—
263C2×D4—221no—
264C2×D4—221no—
265C2×D4—221no—
266C2×D4—441no—
267C22×C4—22no—
268C22×C4—441no—
269C22×C4D4×D1111yescharacteristic
270C22×C4#434111yescharacteristic
271C22×C4C2×C22⋊D1111yescharacteristic
272Q16—84no—
273Q16—448no—
274SD16—448no—
275SD16—882no—
276M16—224no—
277M16—222no—
278M16—441no—
279M16—442no—
280C2×C8—22no—
281C2×C8—222no—
282C2×C8—222no—
283C2×C8—441no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C22⋊C4—41no—
297C22⋊C4—441no—
298C22⋊C4—441no—
299C42—41no—
300C42D4×D1111yescharacteristic
301C42D4×D1111yescharacteristic
302C42C2×C22⋊D1111yescharacteristic
303C42C2×C22⋊D1111yescharacteristic
304C11#1010711yescharacteristic, complemented, Sylow
305C23—441no—
306C23#6699211yescharacteristic
307Q8—44no—
308Q8—41no—
309Q8—41no—
310Q8—42no—
311Q8—44no—
312Q8—442no—
313D4—442no—
314D4—442no—
315D4—441no—
316D4—441no—
317D4—882no—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—82no—
326C2×C4—441no—
327C2×C4—882no—
328C2×C4#6699011yescharacteristic
329C2×C4#6699011yescharacteristic
330C2×C4#6699111yescharacteristic
331C2×C4#6699211yescharacteristic
332C2×C4#6699311yescharacteristic
333C2×C4#6700611yescharacteristic
334C8—42no—
335C8—224no—
336C8—442no—
337C8—442no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—881no—
342C22—881no—
343C22—881no—
344C22#1062283611yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—82no—
349C4—81no—
350C4—81no—
351C4—881no—
352C4#1062280512yes—
353C4#1062281511yescharacteristic
354C4#1062281811yescharacteristic
355C4#1062285412yes—
356C2—41no—
357C2—1761no—
358C2#1306962911yescharacteristic
359C2#1306966111yescharacteristic
360C2#1306973511yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3209C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#3209D11
hypocenterC11#10107
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3209

Complements

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

NH ≅ G/Ntype
3. #13069606C2semidirect
4. #13067211C2semidirect
6. #13066507C2semidirect
7. C11×#3209C2semidirect
126. #3209D11semidirect
304. C11#10107semidirect

Maximal subgroups

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

subgroupindex
#130799992
#130790732
#130696062
#130672112
#130670322
#130665072
C11×#32092
#1010711