Finite Group Databasebeta

← #14672915

Subgroups — #14672915

Order 2816.

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

normal subgroups only

This group has 648 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#13076562C211yesmaximal, characteristic, complemented
2#13068564C212yesmaximal
3#13066741C211yesmaximal, characteristic, complemented
4#13066735C212yesmaximal, complemented
5C11×#1792C211yesmaximal, characteristic
6C2×C11×H(5,𝔽2)C2211yescharacteristic
7C2×C11×#104—21no—
8C11×#417—21no—
9C2×C11×#100C2211yescharacteristic
10C11×#390C2211yescharacteristic
11#10622833—22no—
12#10622833C2212yes—
13C2×#66898—22no—
14C2×#66898C2212yes—
15#10622599—21no—
16#10622563—22no—
17#10622560—22no—
18#10622542—21no—
19C11×H(5,𝔽2)—22no—
20C11×H(5,𝔽2)—21no—
21C11×H(5,𝔽2)—42no—
22C11×H(5,𝔽2)Q812yescomplemented
23C2×C11×#41—21no—
24C2×C11×#41—41no—
25C22×D4×C11—22no—
26C22×D4×C11—41no—
27C22×D4×C11C2311yescharacteristic
28C23×Dic11D412yes—
29C22×Dic22—21no—
30C2×C11×M16—21no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C22⋊C4—22no—
33C2×C42×C11D411yescharacteristic
34C2×C22⋊Dic11—22no—
35C2×C22⋊Dic11—22no—
36C2×C22⋊Dic11—42no—
37C2×C22⋊Dic11D412yes—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C11×#104—42no—
41C11×#103—41no—
42C11×#102—41no—
43C11×#100—22no—
44#66898—22no—
45#66898—22no—
46#66898—44no—
47C11⋊#95—22no—
48C11⋊#95—21no—
49C11⋊#95—22no—
50C11⋊#95—22no—
51C11⋊#95—42no—
52#13377—111nomaximal, Sylow
53C24×C11—22no—
54C24×C11C2×D412yes—
55C11×#41—22no—
56C11×#41—22no—
57C11×#41—42no—
58C11×#41—41no—
59C11×#41—44no—
60C11×#41—42no—
61C11×#41—41no—
62C2×Q8×C11—21no—
63C2×D4×C11—21no—
64C2×D4×C11—24no—
65C2×D4×C11—24no—
66C2×D4×C11—41no—
67C2×D4×C11—41no—
68C2×D4×C11—42no—
69C2×D4×C11—42no—
70C2×D4×C11—42no—
71C2×D4×C11—42no—
72C2×D4×C11—44no—
73C2×D4×C11—41no—
74C2×D4×C11—42no—
75C2×D4×C11C2×Q811yescharacteristic
76C2×D4×C11#4111yescharacteristic
77C2×D4×C11#4112yes—
78C22×C4×C11—22no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C22×Dic11—22no—
84C22×Dic11—22no—
85C22×Dic11—42no—
86C22×Dic11—42no—
87C22×Dic11—82no—
88C2×Dic22—42no—
89C2×Dic22—81no—
90C2×Dic22—81no—
91C11×M16—41no—
92C11×M16—41no—
93C2×C8×C11—41no—
94C11×C4⋊C4—41no—
95C11×C22⋊C4—44no—
96C42×C11—41no—
97C22⋊Dic11—42no—
98C22⋊Dic11—42no—
99C22⋊Dic11—42no—
100C22⋊Dic11—82no—
101C22⋊Dic11—84no—
102C4⋊Dic11—81no—
103C4⋊Dic11—81no—
104#2804—111no—
105#1792D1111yescharacteristic
106#1790—112no—
107#1393—111no—
108#1390—112no—
109C23×C11—22no—
110C23×C11—22no—
111C23×C11—24no—
112C23×C11—42no—
113C23×C11—42no—
114C23×C11—42no—
115C23×C11—41no—
116C23×C11—82no—
117C23×C11—82no—
118C23×C11#12011yescharacteristic
119C23×C11C22⋊Q812yes—
120C23×C11#12412yes—
121Q8×C11—22no—
122Q8×C11—41no—
123D4×C11—22no—
124D4×C11—41no—
125D4×C11—41no—
126D4×C11—42no—
127D4×C11—41no—
128D4×C11—44no—
129D4×C11—44no—
130D4×C11—42no—
131D4×C11—42no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—22no—
135C2×C4×C11—24no—
136C2×C4×C11—42no—
137C2×C4×C11—42no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11—41no—
144C2×C4×C11C22⋊Q811yescharacteristic
145C2×C4×C11#12411yescharacteristic
146C2×Dic11—42no—
147C2×Dic11—42no—
148C2×Dic11—42no—
149C2×Dic11—42no—
150C2×Dic11—44no—
151C2×Dic11—42no—
152C2×Dic11—42no—
153C2×Dic11—82no—
154C2×Dic11—82no—
155C2×Dic11—82no—
156C2×Dic11—82no—
157Dic22—84no—
158C8×C11—81no—
159C2×H(5,𝔽2)C2×D1111yescharacteristic
160C2×#104—21no—
161#417—21no—
162C2×#100C2×D1111yescharacteristic
163C2×#99—112no—
164C2×#99—222no—
165#400—221no—
166#393—222no—
167#391—221no—
168#390C2×D1111yescharacteristic
169#386—112no—
170#386—222no—
171#385—222no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—22no—
175C22×C11—22no—
176C22×C11—42no—
177C22×C11—42no—
178C22×C11—42no—
179C22×C11—42no—
180C22×C11—42no—
181C22×C11—82no—
182C22×C11—84no—
183C22×C11—81no—
184C22×C11—81no—
185C22×C11—162no—
186C22×C11#39311yescharacteristic
187C22×C11B(4,𝔽2)11yescharacteristic
188C22×C11B(4,𝔽2)11yescharacteristic
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—42no—
192C4×C11—42no—
193C4×C11—81no—
194Dic11—82no—
195Dic11—82no—
196Dic11—162no—
197H(5,𝔽2)—22no—
198H(5,𝔽2)—21no—
199H(5,𝔽2)—42no—
200H(5,𝔽2)Dic2212yescomplemented
201C2×#41—21no—
202C2×#41—41no—
203C22×Q8—221no—
204C22×D4—22no—
205C22×D4—41no—
206C22×D4C22×D1111yescharacteristic
207C23×C4—112no—
208C2×M16—21no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4C22⋊D1111yescharacteristic
212C2×C22⋊C4—22no—
213C2×C22⋊C4—112no—
214C2×C22⋊C4—222no—
215C2×C22⋊C4—222no—
216C2×C22⋊C4—442no—
217C2×C42C22⋊D1111yescharacteristic
218#104—42no—
219#103—41no—
220#102—41no—
221#100—22no—
222#99—222no—
223#99—222no—
224#99—444no—
225#95—222no—
226#95—222no—
227#95—221no—
228#95—222no—
229#95—442no—
230C2×C11—21no—
231C2×C11—21no—
232C2×C11—42no—
233C2×C11—42no—
234C2×C11—82no—
235C2×C11#202911yescharacteristic
236C2×C11#219811yescharacteristic
237C2×C11#219911yescharacteristic
238C24—22no—
239C24D4×D1112yes—
240#41—22no—
241#41—22no—
242#41—42no—
243#41—41no—
244#41—44no—
245#41—42no—
246#41—41no—
247C2×Q8—21no—
248C2×Q8—442no—
249C2×Q8—881no—
250C2×Q8—881no—
251C2×D4—21no—
252C2×D4—24no—
253C2×D4—24no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—42no—
257C2×D4—42no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4—44no—
261C2×D4—42no—
262C2×D4—41no—
263C2×D4C2×Dic2211yescharacteristic
264C2×D4#433911yescharacteristic
265C2×D4#434112yes—
266C22×C4—22no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—41no—
270C22×C4—222no—
271C22×C4—222no—
272C22×C4—442no—
273C22×C4—442no—
274C22×C4—882no—
275C22×C4C2×C22⋊D1111yescharacteristic
276M16—41no—
277M16—41no—
278C2×C8—41no—
279C4⋊C4—41no—
280C4⋊C4—881no—
281C4⋊C4—881no—
282C22⋊C4—44no—
283C22⋊C4—442no—
284C22⋊C4—442no—
285C22⋊C4—442no—
286C22⋊C4—882no—
287C22⋊C4—884no—
288C42—41no—
289C11#1337711yescharacteristic, complemented, Sylow
290C23—22no—
291C23—22no—
292C23—24no—
293C23—42no—
294C23—42no—
295C23—42no—
296C23—41no—
297C23—82no—
298C23—82no—
299C23#6693112yes—
300C23#6693812yes—
301C23#6699011yescharacteristic
302Q8—22no—
303Q8—41no—
304Q8—884no—
305D4—22no—
306D4—41no—
307D4—41no—
308D4—42no—
309D4—41no—
310D4—44no—
311D4—44no—
312D4—42no—
313D4—42no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—24no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4—442no—
329C2×C4—442no—
330C2×C4—444no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4—882no—
334C2×C4—882no—
335C2×C4—882no—
336C2×C4—882no—
337C2×C4#6697711yescharacteristic
338C2×C4#6698911yescharacteristic
339C8—81no—
340C22—21no—
341C22—21no—
342C22—22no—
343C22—22no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22—42no—
348C22—42no—
349C22—82no—
350C22—84no—
351C22—81no—
352C22—81no—
353C22—162no—
354C22#1062256011yescharacteristic
355C22#1062264511yescharacteristic
356C22#1062264511yescharacteristic
357C4—21no—
358C4—21no—
359C4—42no—
360C4—42no—
361C4—81no—
362C4—882no—
363C4—882no—
364C4—1762no—
365C2—21no—
366C2—21no—
367C2—42no—
368C2—42no—
369C2—82no—
370C2#1306978011yescharacteristic
371C2#1307061111yescharacteristic
372C2#1307061611yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC22×D4×C11C23
FrattiniC22×D4C22×D11
FittingC11×#1792C2
socleC22×C11B(4,𝔽2)
prime radicalC2×C11×H(5,𝔽2)C22
hypercenter#1792D11
hypocenterC11#13377
LCSG ▷ C22×D4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1792

Complements

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

NH ≅ G/Ntype
1. #13076562C2semidirect
3. #13066741C2semidirect
4. #13066735C2semidirect
22. C11×H(5,𝔽2)Q8semidirect
200. H(5,𝔽2)Dic22semidirect
289. C11#13377semidirect

Maximal subgroups

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

subgroupindex
#130765622
#130685642
#130667412
#130667352
C11×#17922
#1337711