Finite Group Databasebeta

← #14672903

Subgroups — #14672903

Order 2816.

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

normal subgroups only

This group has 704 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#13074988C211yesmaximal, characteristic, complemented
2#13068564C212yesmaximal
3#13066741C211yesmaximal, characteristic, complemented
4#13066735C212yesmaximal, complemented
5C11×#1792C211yesmaximal, characteristic
6C2×C11×H(5,𝔽2)C2211yescharacteristic
7C2×#66931—22no—
8C2×C11×#104—21no—
9C11×#417—21no—
10C2×C11×#100C2211yescharacteristic
11C11×#390C2211yescharacteristic
12#10622833—22no—
13#10622833C2212yes—
14C2×#66898—22no—
15C2×#66898C2212yes—
16#10622592—21no—
17#10622561—22no—
18#10622541—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—
40C2×Dic11⋊C4—22no—
41C2×Dic11⋊C4—22no—
42#66931—48no—
43C11×#104—42no—
44C11×#103—41no—
45C11×#102—41no—
46C11×#100—22no—
47#66898—22no—
48#66898—22no—
49#66898—44no—
50C11⋊#95—21no—
51C11⋊#95—22no—
52C11⋊#95—42no—
53#13375—111nomaximal, Sylow
54C24×C11—22no—
55C24×C11C2×D412yes—
56C11×#41—22no—
57C11×#41—22no—
58C11×#41—42no—
59C11×#41—41no—
60C11×#41—44no—
61C11×#41—42no—
62C11×#41—41no—
63C2×Q8×C11—21no—
64C2×D4×C11—21no—
65C2×D4×C11—24no—
66C2×D4×C11—24no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11—42no—
70C2×D4×C11—42no—
71C2×D4×C11—42no—
72C2×D4×C11—42no—
73C2×D4×C11—44no—
74C2×D4×C11—41no—
75C2×D4×C11—42no—
76C2×D4×C11C2×Q811yescharacteristic
77C2×D4×C11#4111yescharacteristic
78C2×D4×C11#4112yes—
79C22×C4×C11—22no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—41no—
83C22×C4×C11C2×D411yescharacteristic
84C22×Dic11—22no—
85C22×Dic11—22no—
86C22×Dic11—42no—
87C22×Dic11—42no—
88C22×Dic11—44no—
89C2×Dic22—44no—
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—44no—
100C22⋊Dic11—42no—
101C22⋊Dic11—84no—
102C4⋊Dic11—24no—
103C4⋊Dic11—81no—
104Dic11⋊C4—44no—
105Dic11⋊C4—44no—
106#2683—111no—
107#1792D1111yescharacteristic
108#1790—112no—
109#1393—111no—
110#1390—112no—
111C23×C11—22no—
112C23×C11—22no—
113C23×C11—24no—
114C23×C11—42no—
115C23×C11—42no—
116C23×C11—42no—
117C23×C11—41no—
118C23×C11—82no—
119C23×C11—82no—
120C23×C11#12011yescharacteristic
121C23×C11C22⋊Q812yes—
122C23×C11#12412yes—
123Q8×C11—22no—
124Q8×C11—41no—
125D4×C11—22no—
126D4×C11—41no—
127D4×C11—41no—
128D4×C11—42no—
129D4×C11—41no—
130D4×C11—44no—
131D4×C11—44no—
132D4×C11—42no—
133D4×C11—42no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—22no—
137C2×C4×C11—24no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—41no—
146C2×C4×C11C22⋊Q811yescharacteristic
147C2×C4×C11#12411yescharacteristic
148C2×Dic11—24no—
149C2×Dic11—42no—
150C2×Dic11—42no—
151C2×Dic11—44no—
152C2×Dic11—42no—
153C2×Dic11—42no—
154C2×Dic11—42no—
155C2×Dic11—82no—
156C2×Dic11—82no—
157C2×Dic11—82no—
158C2×Dic11—82no—
159Dic22—84no—
160C8×C11—81no—
161C2×H(5,𝔽2)C2×D1111yescharacteristic
162C2×C22⋊Q8—222no—
163C2×#104—21no—
164#417—21no—
165C2×#100C2×D1111yescharacteristic
166C2×#99—112no—
167C2×#99—222no—
168#396—222no—
169#395—221no—
170#390C2×D1111yescharacteristic
171#389—221no—
172#386—112no—
173#386—222no—
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—22no—
177C22×C11—22no—
178C22×C11—42no—
179C22×C11—42no—
180C22×C11—42no—
181C22×C11—42no—
182C22×C11—42no—
183C22×C11—82no—
184C22×C11—84no—
185C22×C11—81no—
186C22×C11—81no—
187C22×C11—162no—
188C22×C11#39311yescharacteristic
189C22×C11B(4,𝔽2)11yescharacteristic
190C22×C11B(4,𝔽2)11yescharacteristic
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—42no—
194C4×C11—42no—
195C4×C11—81no—
196Dic11—44no—
197Dic11—82no—
198Dic11—162no—
199H(5,𝔽2)—22no—
200H(5,𝔽2)—21no—
201H(5,𝔽2)—42no—
202H(5,𝔽2)Dic2212yescomplemented
203C2×#41—21no—
204C2×#41—41no—
205C22×Q8—221no—
206C22×D4—22no—
207C22×D4—41no—
208C22×D4C22×D1111yescharacteristic
209C23×C4—112no—
210C2×M16—21no—
211C22⋊Q8—448no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—222no—
214C2×C4⋊C4—222no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4C22⋊D1111yescharacteristic
217C2×C22⋊C4—22no—
218C2×C22⋊C4—112no—
219C2×C22⋊C4—222no—
220C2×C22⋊C4—222no—
221C2×C22⋊C4—442no—
222C2×C42C22⋊D1111yescharacteristic
223#104—42no—
224#103—41no—
225#102—41no—
226#100—22no—
227#99—222no—
228#99—222no—
229#99—444no—
230#95—221no—
231#95—222no—
232#95—442no—
233C2×C11—21no—
234C2×C11—21no—
235C2×C11—42no—
236C2×C11—42no—
237C2×C11—82no—
238C2×C11#202911yescharacteristic
239C2×C11#219611yescharacteristic
240C2×C11#220111yescharacteristic
241C24—22no—
242C24D4×D1112yes—
243#41—22no—
244#41—22no—
245#41—42no—
246#41—41no—
247#41—44no—
248#41—42no—
249#41—41no—
250C2×Q8—21no—
251C2×Q8—444no—
252C2×Q8—881no—
253C2×D4—21no—
254C2×D4—24no—
255C2×D4—24no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4—42no—
261C2×D4—42no—
262C2×D4—44no—
263C2×D4—42no—
264C2×D4—41no—
265C2×D4C2×Dic2211yescharacteristic
266C2×D4#433911yescharacteristic
267C2×D4#434112yes—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4—222no—
273C22×C4—222no—
274C22×C4—444no—
275C22×C4—442no—
276C22×C4—442no—
277C22×C4C2×C22⋊D1111yescharacteristic
278M16—41no—
279M16—41no—
280C2×C8—41no—
281C4⋊C4—41no—
282C4⋊C4—224no—
283C4⋊C4—444no—
284C4⋊C4—444no—
285C4⋊C4—881no—
286C22⋊C4—44no—
287C22⋊C4—444no—
288C22⋊C4—442no—
289C22⋊C4—442no—
290C22⋊C4—442no—
291C22⋊C4—884no—
292C42—41no—
293C11#1337511yescharacteristic, complemented, Sylow
294C23—22no—
295C23—22no—
296C23—24no—
297C23—42no—
298C23—42no—
299C23—42no—
300C23—41no—
301C23—82no—
302C23—82no—
303C23#6693112yes—
304C23#6693812yes—
305C23#6699011yescharacteristic
306Q8—22no—
307Q8—41no—
308Q8—884no—
309D4—22no—
310D4—41no—
311D4—41no—
312D4—42no—
313D4—41no—
314D4—44no—
315D4—44no—
316D4—42no—
317D4—42no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—22no—
321C2×C4—24no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—224no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4—444no—
334C2×C4—442no—
335C2×C4—442no—
336C2×C4—442no—
337C2×C4—882no—
338C2×C4—882no—
339C2×C4—882no—
340C2×C4—882no—
341C2×C4#6697711yescharacteristic
342C2×C4#6698911yescharacteristic
343C8—81no—
344C22—21no—
345C22—21no—
346C22—22no—
347C22—22no—
348C22—42no—
349C22—42no—
350C22—42no—
351C22—42no—
352C22—42no—
353C22—82no—
354C22—84no—
355C22—81no—
356C22—81no—
357C22—162no—
358C22#1062256011yescharacteristic
359C22#1062264511yescharacteristic
360C22#1062264511yescharacteristic
361C4—21no—
362C4—21no—
363C4—42no—
364C4—42no—
365C4—81no—
366C4—444no—
367C4—882no—
368C4—1762no—
369C2—21no—
370C2—21no—
371C2—42no—
372C2—42no—
373C2—82no—
374C2#1306978011yescharacteristic
375C2#1307059911yescharacteristic
376C2#1307062811yescharacteristic
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#13375
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. #13074988C2semidirect
3. #13066741C2semidirect
4. #13066735C2semidirect
22. C11×H(5,𝔽2)Q8semidirect
202. H(5,𝔽2)Dic22semidirect
293. C11#13375semidirect

Maximal subgroups

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

subgroupindex
#130749882
#130685642
#130667412
#130667352
C11×#17922
#1337511