Finite Group Databasebeta

← #14655378

Subgroups — #14655378

Order 2816.

454 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 81 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#13079806C211yesmaximal, characteristic
2#13079623C211yesmaximal, characteristic
3#13067089C211yesmaximal, characteristic, complemented
4#13067034C211yesmaximal, characteristic
5#13066972C211yesmaximal, characteristic, complemented
6#13066488C211yesmaximal, characteristic, complemented
7C11×#3166C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10#10623008C2211yescharacteristic
11C11×#501—21no—
12C11×#501—21no—
13C11×#499—22no—
14C11×#428—21no—
15C11×#428—21no—
16C4×C11×M16C2211yescharacteristic
17#10622702—21no—
18#10622699—21no—
19#10622680—21no—
20#10622679—22no—
21#10622678—21no—
22#10622660—22no—
23#10622644—21no—
24#10622640—21no—
25#10622581—21no—
26#10622580—21no—
27#10622539C2211yescharacteristic
28#10622539C2211yescharacteristic
29#10622538C2211yescharacteristic
30Q8⋊(C11⋊C8)—22no—
31#10622166—22no—
32#10622097—22no—
33C2×#4339—21no—
34C2×C11×M16—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×#125—21no—
38C11×#125—21no—
39C11×#125—21no—
40C11×#125—21no—
41C11×#125—21no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C11×#117—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C42×C11C2311yescharacteristic
52C2×#4326—22no—
53C2×#4325—22no—
54#66983—21no—
55#66983—21no—
56#66928—21no—
57#66927D411yescharacteristic
58C4×D44—21no—
59C4×D44—21no—
60#66922D411yescharacteristic
61C11×#107—22no—
62C11×#107—22no—
63C11×#106—22no—
64C11×#106—22no—
65C11×#97—21no—
66C4×C8×C11D412yes—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)D412yes—
70#66874—22no—
71#66873—22no—
72#66873—22no—
73#66873—22no—
74#66872—22no—
75#66871—22no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)D412yes—
79#66867—21no—
80#66867—21no—
81C4×C11⋊C8—21no—
82#10126—111nomaximal, Sylow
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C2×C22⋊D11—41no—
91#4339—82no—
92C2×D44—21no—
93C2×D44—21no—
94C2×D44—21no—
95C2×C4×D11—41no—
96C2×Dic22—21no—
97C11×M16—24no—
98C2×C8×C11—22no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C22⋊C4—41no—
114C42×C11—41no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119#4326—82no—
120#4325—82no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—41no—
128#3234—111no—
129#3216—111no—
130#3166D1111yescharacteristic, complemented
131#1497—111no—
132#1484—111no—
133#1470—111no—
134#1291—111no—
135C23×C11#12111yescharacteristic
136C22×D11—41no—
137Q8×C11—41no—
138Q8×C11—41no—
139Q8×C11—42no—
140C2×C4×C11—22no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—81no—
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12711yescharacteristic
155C22⋊D11—82no—
156C2×Dic11—41no—
157D44—42no—
158D44—42no—
159D44—42no—
160C4×D11—82no—
161Dic22—42no—
162C8×C11—24no—
163C11⋊C8—42no—
164C11⋊C8—42no—
165C11⋊C8—81no—
166#533C2×D1111yescharacteristic
167#532—111no—
168C2×#125C2×D1111yescharacteristic
169#501—21no—
170#501—21no—
171#501—221no—
172#499—22no—
173#497—221no—
174#490—221no—
175#489—221no—
176#481—221no—
177#480—221no—
178#478—222no—
179#462—221no—
180#460—221no—
181#452—222no—
182#432—111no—
183#432—111no—
184#431—111no—
185#428—21no—
186#428—21no—
187C4×M16C2×D1111yescharacteristic
188Q8⋊C8—222no—
189D4⋊C8—222no—
190#324—222no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11#39211yescharacteristic
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—81no—
198C4×C11—21no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—81no—
204C4×C11—81no—
205C4×C11—81no—
206C4×C11—81no—
207C4×C11#45612yes—
208Dic11—81no—
209C2×#41—221no—
210C2×Q16—222no—
211C2×SD16—222no—
212C2×M16—21no—
213C4⋊Q8—111no—
214C4⋊Q8C22⋊D1111yescharacteristic
215C4⋊Q8C22⋊D1111yescharacteristic
216#127—111no—
217#125—21no—
218#125—21no—
219#125—21no—
220#125—21no—
221#125—21no—
222#124—221no—
223C22⋊Q8—21no—
224C22⋊Q8—21no—
225#121—221no—
226#121—221no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×D4—221no—
230C4×D4—221no—
231#117—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4C22⋊D1111yescharacteristic
235C2×C4⋊C4C22⋊D1111yescharacteristic
236C2×C42C22×D1111yescharacteristic
237#107—22no—
238#107—22no—
239#107—222no—
240#106—22no—
241#106—22no—
242#106—222no—
243C4⋊C8—112no—
244C4⋊C8—221no—
245C4⋊C8—221no—
246#103—222no—
247#102—222no—
248#102—222no—
249#102—222no—
250C22⋊C8—112no—
251C22⋊C8—221no—
252C22⋊C8—221no—
253#97—21no—
254#97—221no—
255#97—221no—
256C4×C8—221no—
257C4×C8C22⋊D1112yes—
258C2×C11—41no—
259C2×C11#200511yescharacteristic
260C2×C11#200811yescharacteristic
261C2×C11#201711yescharacteristic
262D11—161no—
263#41—882no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—221no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—441no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—441no—
274C22×C4D4×D1111yescharacteristic
275C22×C4#434111yescharacteristic
276C22×C4C2×C22⋊D1111yescharacteristic
277Q16—882no—
278SD16—882no—
279M16—24no—
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—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C22⋊C4—41no—
301C22⋊C4—441no—
302C22⋊C4—441no—
303C42—41no—
304C42D4×D1111yescharacteristic
305C42D4×D1111yescharacteristic
306C42C2×C22⋊D1111yescharacteristic
307C42C2×C22⋊D1111yescharacteristic
308C11#1012611yescharacteristic, complemented, Sylow
309C23—441no—
310C23#6699211yescharacteristic
311Q8—41no—
312Q8—41no—
313Q8—42no—
314Q8—442no—
315D4—442no—
316D4—442no—
317D4—442no—
318D4—882no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—81no—
328C2×C4—441no—
329C2×C4—882no—
330C2×C4#6699011yescharacteristic
331C2×C4#6699011yescharacteristic
332C2×C4#6699111yescharacteristic
333C2×C4#6699211yescharacteristic
334C2×C4#6699311yescharacteristic
335C2×C4#6700611yescharacteristic
336C8—24no—
337C8—442no—
338C8—442no—
339C8—881no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—881no—
344C22—881no—
345C22—881no—
346C22#1062283611yescharacteristic
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—81no—
353C4—81no—
354C4—81no—
355C4—81no—
356C4—881no—
357C4#1062270812yes—
358C2—41no—
359C2—1761no—
360C2#1306965211yescharacteristic
361C2#1306966611yescharacteristic
362C2#1306971911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3166C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#3166D11
hypocenterC11#10126
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3166

Complements

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

NH ≅ G/Ntype
3. #13067089C2semidirect
5. #13066972C2semidirect
6. #13066488C2semidirect
7. C11×#3166C2semidirect
130. #3166D11semidirect
308. C11#10126semidirect

Maximal subgroups

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

subgroupindex
#130798062
#130796232
#130670892
#130670342
#130669722
#130664882
C11×#31662
#1012611