Finite Group Databasebeta

← #14673286

Subgroups — #14673286

Order 2816.

408 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 73 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#13070291C211yesmaximal, characteristic
2#13070270C211yesmaximal, characteristic
3#13069169C211yesmaximal, characteristic
4#13069139C211yesmaximal, characteristic
5#13068901C211yesmaximal, characteristic
6#13066745C211yesmaximal, characteristic
7C11×#3202C211yesmaximal, characteristic
8C11×#536C2211yescharacteristic
9C11×#536C2211yescharacteristic
10#10623350C2211yescharacteristic
11C11×#485—21no—
12C11×#485—21no—
13C11×#470—21no—
14C11×#467—21no—
15C11×#451—21no—
16C11×#451—21no—
17C11×#408C2211yescharacteristic
18#10622853C2211yescharacteristic
19#10622853C2211yescharacteristic
20#10622850C2211yescharacteristic
21C2×#66900—21no—
22#10622838—21no—
23#10622715—21no—
24#10622197—21no—
25#10622179—22no—
26#10622177—22no—
27#10622171—21no—
28#10622169—21no—
29C2×C11×#41C2311yescharacteristic
30C22×Q8×C11D411yescharacteristic
31C22×Q8×C11D411yescharacteristic
32C2×C11×Q16—21no—
33C2×C11×Q16—21no—
34C2×C11×M16D411yescharacteristic
35C22×C8×C11D411yescharacteristic
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×#124—21no—
39C11×#124—21no—
40C11×#123—21no—
41C11×#123—21no—
42C11×#123—21no—
43C11×#123—21no—
44C11×C22⋊Q8—21no—
45C11×C22⋊Q8—21no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8—21no—
48C11×#117D411yescharacteristic
49C11×#117D411yescharacteristic
50#67001—42no—
51#66979—21no—
52#66979—21no—
53C2×#4318—21no—
54C2×#4318—21no—
55C2×#4318—21no—
56C2×#4318—21no—
57C11×#107—21no—
58C11×#106—21no—
59C11×#103—21no—
60C11×#103—21no—
61C11×#103—21no—
62C11×#103—21no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8—21no—
65#66900—21no—
66#66900—42no—
67#66899—42no—
68#66898—21no—
69#66898—21no—
70#66898—21no—
71#66898D412yes—
72#66897—21no—
73Dic11⋊C8—42no—
74#13435—111nomaximal, Sylow
75C11×#41—41no—
76C11×#41—41no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—41no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×Q8×C11#4111yescharacteristic
86C2×D4×C11C2×D411yescharacteristic
87C2×D4×C11#4111yescharacteristic
88C2×D4×C11#4111yescharacteristic
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C11×Q16—81no—
95C11×Q16—81no—
96C11×M16—41no—
97C2×C8×C11—21no—
98C2×C8×C11—21no—
99C2×C8×C11—41no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C22⋊C4—21no—
107C11×C22⋊C4—21no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11—21no—
113C42×C11—21no—
114C22⋊Dic11—22no—
115C22⋊Dic11—41no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4×Dic11—41no—
119C4×Dic11—41no—
120#4318—22no—
121#4318—41no—
122#4318—41no—
123#4318—41no—
124#4318—41no—
125#4318—41no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—41no—
130#3202D1111yescharacteristic
131#2129—111no—
132#2123—111no—
133#1915—111no—
134#1909—111no—
135#1868—111no—
136#1395—111no—
137C23×C11#12111yescharacteristic
138C23×C11#12111yescharacteristic
139C23×C11#12311yescharacteristic
140Q8×C11—41no—
141Q8×C11—42no—
142Q8×C11—41no—
143Q8×C11—41no—
144Q8×C11—41no—
145Q8×C11—41no—
146Q8×C11—81no—
147D4×C11—41no—
148D4×C11—41no—
149D4×C11—41no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—81no—
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12311yescharacteristic
165C2×C4×C11#12411yescharacteristic
166C2×Dic11—42no—
167C2×Dic11—81no—
168C8×C11—41no—
169C8×C11—41no—
170C11⋊C8—42no—
171C11⋊C8—81no—
172#568—111no—
173#536C2×D1111yescharacteristic
174#536C2×D1111yescharacteristic
175#485—21no—
176#485—21no—
177#470—21no—
178#467—21no—
179#451—21no—
180#451—21no—
181#424—221no—
182#419—221no—
183#413—111no—
184C2×#101—221no—
185#410—111no—
186#410—111no—
187#408C2×D1111yescharacteristic
188#354—222no—
189#352—222no—
190#344—221no—
191#344—221no—
192H(3,ℤ/4)—221no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11#39411yescharacteristic
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—81no—
204C4×C11—81no—
205C4×C11—81no—
206C4×C11—81no—
207C4×C11B(4,𝔽2)11yescharacteristic
208C4×C11#45811yescharacteristic
209Dic11—82no—
210Dic11—161no—
211C2×#41C22×D1111yescharacteristic
212C22×Q8C22⋊D1111yescharacteristic
213C22×Q8C22⋊D1111yescharacteristic
214C2×Q16—21no—
215C2×Q16—21no—
216#131—442no—
217C2×M16—221no—
218C2×M16—221no—
219C2×M16—221no—
220C2×M16—221no—
221C2×M16C22⋊D1111yescharacteristic
222C22×C8C22⋊D1111yescharacteristic
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225#124—21no—
226#124—21no—
227#123—21no—
228#123—21no—
229#123—21no—
230#123—21no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235#117—221no—
236#117—221no—
237#117C22⋊D1111yescharacteristic
238#117C22⋊D1111yescharacteristic
239#107—21no—
240#106—21no—
241C4⋊C8—442no—
242#103—21no—
243#103—21no—
244#103—21no—
245#103—21no—
246#103—442no—
247#101—221no—
248#101—442no—
249#100—221no—
250#99—112no—
251#99—221no—
252#99—221no—
253#99—221no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C2×C11—21no—
257C2×C11—41no—
258C2×C11—41no—
259C2×C11—41no—
260C2×C11#204411yescharacteristic
261#41—41no—
262#41—41no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8#434111yescharacteristic
272C2×D4D4×D1111yescharacteristic
273C2×D4#434111yescharacteristic
274C2×D4#434111yescharacteristic
275C22×C4—21no—
276C22×C4—21no—
277C22×C4C2×C22⋊D1111yescharacteristic
278C22×C4C2×C22⋊D1111yescharacteristic
279C22×C4C2×C22⋊D1111yescharacteristic
280Q16—81no—
281Q16—81no—
282M16—41no—
283M16—222no—
284M16—441no—
285M16—441no—
286M16—441no—
287M16—441no—
288M16—441no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—41no—
292C2×C8—222no—
293C2×C8—222no—
294C2×C8—441no—
295C2×C8—441no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—222no—
311C22⋊C4—441no—
312C42—21no—
313C42—21no—
314C42—441no—
315C42—441no—
316C11#1343511yescharacteristic, complemented, Sylow
317C23#6698811yescharacteristic
318C23#6699111yescharacteristic
319C23#6699211yescharacteristic
320Q8—41no—
321Q8—42no—
322Q8—41no—
323Q8—41no—
324Q8—41no—
325Q8—41no—
326Q8—81no—
327D4—41no—
328D4—41no—
329D4—41no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—81no—
342C2×C4—442no—
343C2×C4—881no—
344C2×C4#6698811yescharacteristic
345C2×C4#6698911yescharacteristic
346C2×C4#6699211yescharacteristic
347C2×C4#6700611yescharacteristic
348C8—41no—
349C8—41no—
350C8—442no—
351C8—881no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22#1062283511yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—81no—
363C4—81no—
364C4—81no—
365C4—81no—
366C4—882no—
367C4—1761no—
368C4#1062285611yescharacteristic
369C4#1062285711yescharacteristic
370C2—21no—
371C2—41no—
372C2—41no—
373C2—41no—
374C2#1306986411yescharacteristic
subgroupG/H
centerC2#13069864
commutator, prime radical, cosocleC2×C11×#41C23
FrattiniC2×#41C22×D11
FittingC11×#3202C2
socleC2×C11#2044
hypercenter#3202D11
hypocenterC11#13435
LCSG ▷ C2×C11×#41 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #3202

Complements

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

NH ≅ G/Ntype
316. C11#13435semidirect

Maximal subgroups

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

subgroupindex
#130702912
#130702702
#130691692
#130691392
#130689012
#130667452
C11×#32022
#1343511