Finite Group Databasebeta

← #14670615

Subgroups — #14670615

Order 2816.

408 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 85 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#13077685C211yesmaximal, characteristic
2#13070299C211yesmaximal, characteristic
3#13068999C211yesmaximal, characteristic
4#13068836C211yesmaximal, characteristic, complemented
5#13066746C211yesmaximal, characteristic, complemented
6#13066745C211yesmaximal, characteristic, complemented
7C11×#1858C211yesmaximal, characteristic, complemented
8C11×#568C2211yescharacteristic
9#10623363C2211yescharacteristic
10C11×#430—21no—
11C11×#413C2211yescharacteristic
12C11×#408C2211yescharacteristic
13#10622853C2211yescharacteristic
14#10622850C2211yescharacteristic
15#10622847C2211yescharacteristic
16#10622752—21no—
17#10622740—21no—
18#10622737—21no—
19#10622724—21no—
20#10622343—21no—
21#10622341—21no—
22#10622340—21no—
23#10622332—21no—
24C11×#341—21no—
25#10622196—21no—
26#10622193—21no—
27#10622116C412yescomplemented
28#10622115C412yescomplemented
29C2×C11×#41C2311yescharacteristic
30C2×#4339D411yescharacteristic
31C11×#131—42no—
32C2×C11×M16—21no—
33C2×C11×M16—21no—
34C2×C11×M16—21no—
35C2×C11×M16—21no—
36C2×C11×M16D411yescharacteristic
37C22×C8×C11D411yescharacteristic
38#67000C2×C411yescharacteristic
39#66997C2×C411yescharacteristic
40#66993Q811yescharacteristic
41#66992—21no—
42#66992—21no—
43#66989Q811yescharacteristic
44C4×C22⋊D11—21no—
45C4×C22⋊D11—21no—
46#66979—21no—
47C2×C4×Dic11D411yescharacteristic
48C2×#4318—21no—
49C2×#4318D411yescharacteristic
50C22×C11⋊C8D411yescharacteristic
51C2×#4313—21no—
52C2×C8×D11—21no—
53C11×#108—42no—
54C11×#101C2×C412yes—
55C11×#100—21no—
56C11×C22⋊C8—21no—
57C11×C22⋊C8—21no—
58#66900C2×C412yes—
59#66898—21no—
60#66898—21no—
61#66897—21no—
62C22⋊(C11⋊C8)—21no—
63C22⋊(C11⋊C8)—21no—
64#66889—42no—
65#66886—42no—
66(C2×D11)⋊C8—21no—
67(C2×D11)⋊C8—21no—
68#66879—21no—
69#66879—21no—
70Dic11⋊C8—21no—
71Dic11⋊C8—21no—
72#12974—111nomaximal, Sylow
73C11×#41—41no—
74C11×#41—41no—
75C2×Q8×C11C22×C411yescharacteristic
76C2×D4×C11C2×Q811yescharacteristic
77C2×D4×C11#4111yescharacteristic
78C2×D4×C11#4111yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C2×C22⋊D11—21no—
83C2×C22⋊D11—21no—
84C2×C22⋊D11—21no—
85C22×Dic11—21no—
86#4339—41no—
87#4339—41no—
88C2×D44C4⋊C411yescharacteristic
89C2×C4×D11—21no—
90C2×Dic22C4⋊C411yescharacteristic
91C11×M16—22no—
92C11×M16—22no—
93C11×M16—22no—
94C11×M16—22no—
95C11×M16—41no—
96C11×M16—41no—
97C11×M16—41no—
98C2×C8×C11—21no—
99C2×C8×C11—21no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C2×C8×C11—41no—
104C2×C8×C11—41no—
105C22⋊Dic11—21no—
106C22⋊Dic11—21no—
107C22⋊Dic11—41no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4—21no—
110C4⋊Dic11—41no—
111Dic11⋊C4—21no—
112Dic11⋊C4—21no—
113C4×Dic11—21no—
114C4×Dic11—41no—
115C4×Dic11C4⋊C411yescharacteristic
116C4×Dic11C4⋊C411yescharacteristic
117#4318—22no—
118#4318—41no—
119#4318—41no—
120C2×C11⋊C8—21no—
121C2×C11⋊C8—21no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124#4313—81no—
125C8×D11—81no—
126#2980—111no—
127#2132—111no—
128#1884—111no—
129#1858—111no—
130#1858D1111yescharacteristic, complemented
131#1395—111no—
132#1395—111no—
133C23×C11C22⋊Q811yescharacteristic
134C23×C11C22⋊Q811yescharacteristic
135C23×C11#12311yescharacteristic
136C22×D11—21no—
137Q8×C11—41no—
138D4×C11—41no—
139D4×C11—41no—
140D4×C11—41no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11C2×C4⋊C411yescharacteristic
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11C4×D411yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C22⋊D11—81no—
152C22⋊D11—81no—
153C22⋊D11—81no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—81no—
158C2×Dic11—81no—
159D44—41no—
160C4×D11—41no—
161C4×D11—41no—
162Dic22—41no—
163C8×C11—42no—
164C8×C11—41no—
165C8×C11—42no—
166C8×C11—41no—
167C11⋊C8—42no—
168C11⋊C8—41no—
169C11⋊C8—41no—
170#568C2×D1111yescharacteristic
171#532—111no—
172#435—221no—
173#435—221no—
174#435—221no—
175#435—221no—
176#432—221no—
177#430—21no—
178#430—221no—
179#421—221no—
180#413—111no—
181#413C2×D1111yescharacteristic
182#410—111no—
183#408—111no—
184#408—221no—
185#408C2×D1111yescharacteristic
186#356—112no—
187#355—112no—
188#341—21no—
189#341—221no—
190#339—221no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11#38511yescharacteristic
198C2×D11—41no—
199C2×D11—41no—
200C2×D11—41no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11B(4,𝔽2)11yescharacteristic
205C4×C11#45811yescharacteristic
206Dic11—41no—
207Dic11—41no—
208Dic11—41no—
209Dic11—161no—
210C2×#41—111no—
211C2×#41C22×D1111yescharacteristic
212#131—42no—
213C2×M16—21no—
214C2×M16—21no—
215C2×M16—21no—
216C2×M16—21no—
217C2×M16—111no—
218C2×M16—221no—
219C2×M16—221no—
220C2×M16C22⋊D1111yescharacteristic
221C22×C8—111no—
222C22×C8—221no—
223C22×C8C22⋊D1111yescharacteristic
224C4⋊Q8—111no—
225#127—111no—
226#124—111no—
227#124—111no—
228#121—221no—
229#121—221no—
230C4×D4—221no—
231C4×D4—221no—
232#117—221no—
233C2×C42—111no—
234#108—42no—
235#108—442no—
236C4⋊C8—221no—
237C4⋊C8—221no—
238#104—442no—
239#101—112no—
240#101C4×D1112yes—
241#100—21no—
242#100—221no—
243#99—221no—
244#99—221no—
245C22⋊C8—21no—
246C22⋊C8—21no—
247C22⋊C8—221no—
248C22⋊C8—221no—
249C22⋊C8—221no—
250C22⋊C8—221no—
251#97—221no—
252#97—221no—
253C2×C11—21no—
254C2×C11—41no—
255C2×C11—41no—
256C2×C11—41no—
257C2×C11#186711yescharacteristic
258D11—81no—
259#41—41no—
260#41—41no—
261#41—441no—
262#41—441no—
263C2×Q8—111no—
264C2×Q8C2×C4×D1111yescharacteristic
265C2×D4—111no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4#433911yescharacteristic
270C2×D4Q8×D1111yescharacteristic
271C2×D4#434311yescharacteristic
272C22×C4—221no—
273C22×C4—221no—
274C22×C4D4×D1111yescharacteristic
275C22×C4D4×D1111yescharacteristic
276C22×C4C2×C22⋊D1111yescharacteristic
277M16—22no—
278M16—22no—
279M16—22no—
280M16—22no—
281M16—41no—
282M16—41no—
283M16—41no—
284M16—222no—
285M16—441no—
286M16—441no—
287M16—881no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—221no—
296C2×C8—221no—
297C2×C8—441no—
298C2×C8—441no—
299C2×C8—881no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—441no—
303C22⋊C4—221no—
304C22⋊C4—221no—
305C22⋊C4—221no—
306C22⋊C4—221no—
307C22⋊C4—441no—
308C42—111no—
309C42—111no—
310C42—221no—
311C42—441no—
312C11#1297411yescharacteristic, complemented, Sylow
313C23—221no—
314C23#6694711yescharacteristic
315C23#6694911yescharacteristic
316C23#6699911yescharacteristic
317Q8—41no—
318Q8—441no—
319D4—41no—
320D4—41no—
321D4—41no—
322D4—441no—
323D4—881no—
324D4—881no—
325D4—881no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—221no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—881no—
338C2×C4—881no—
339C2×C4C4⋊C4×D1111yescharacteristic
340C2×C4#6694611yescharacteristic
341C2×C4C4×C22⋊D1111yescharacteristic
342C2×C4#6699011yescharacteristic
343C8—42no—
344C8—41no—
345C8—42no—
346C8—41no—
347C8—442no—
348C8—441no—
349C8—441no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—441no—
357C22—441no—
358C22—441no—
359C22#1062260211yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—441no—
364C4—441no—
365C4—441no—
366C4—1761no—
367C4#1062264511yescharacteristic
368C4#1062266611yescharacteristic
369C2—21no—
370C2—41no—
371C2—41no—
372C2—41no—
373C2—881no—
374C2#1306889511yescharacteristic
subgroupG/H
centerC4#10622645
commutatorC2×Q8×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#1858C2
socleC2×C11#1867
prime radical#10623363C22
cosocleC2×C11×#41C23
hypercenter#1858D11
hypocenterC11#12974
LCSG ▷ C2×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1858

Complements

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

NH ≅ G/Ntype
4. #13068836C2semidirect
5. #13066746C2semidirect
6. #13066745C2semidirect
7. C11×#1858C2semidirect
27. #10622116C4semidirect
28. #10622115C4semidirect
130. #1858D11semidirect
312. C11#12974semidirect

Maximal subgroups

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

subgroupindex
#130776852
#130702992
#130689992
#130688362
#130667462
#130667452
C11×#18582
#1297411