Finite Group Databasebeta

← #14657005

Subgroups — #14657005

Order 2816.

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

normal subgroups only

This group has 602 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#13074281C211yesmaximal, characteristic, complemented
2#13068560C212yesmaximal
3#13066524C211yesmaximal, characteristic, complemented
4#13066468C212yesmaximal, complemented
5C11×#1782C211yesmaximal, characteristic
6C22×C11×#41C2211yescharacteristic
7C2×C11×#99—21no—
8C2×C11×#99—21no—
9C11×#381C2211yescharacteristic
10C11×#381C2211yescharacteristic
11C2×#66901—22no—
12C2×#66901—22no—
13C4×C22⋊Dic11C2212yes—
14#10622820C2212yes—
15#10622562—21no—
16#10622560—21no—
17#10622268—22no—
18#10622259—22no—
19C2×C11×#41—22no—
20C2×C11×#41—22no—
21C2×C11×#41—42no—
22C2×C11×#41—42no—
23C22×Q8×C11Q811yescharacteristic, complemented
24C22×D4×C11—21no—
25C22×D4×C11Q811yescharacteristic, complemented
26C23×C4×C11—21no—
27C23×C4×C11C2311yescharacteristic
28C22×Dic22—21no—
29C2×C11×C22⋊C4—21no—
30C2×C11×C22⋊C4D411yescharacteristic
31C2×C11×C22⋊C4D411yescharacteristic
32C2×C22⋊Dic11—22no—
33C2×C4⋊Dic11—21no—
34C2×Dic11⋊C4—22no—
35C2×C4×Dic11D412yes—
36C2×C4×Dic11D412yes—
37C2×#4318—22no—
38C11×#99—42no—
39C11×#99—42no—
40C11×#95—22no—
41C11×#95—22no—
42#66901—44no—
43#66901—44no—
44C11⋊#95—21no—
45C11⋊#95—22no—
46C11⋊#95—21no—
47C11⋊#95—22no—
48C22⋊(C11⋊C8)—22no—
49C22⋊(C11⋊C8)—22no—
50#10386—111nomaximal, Sylow
51C24×C11—21no—
52C24×C11C2×D411yescharacteristic
53C11×#41—24no—
54C11×#41—24no—
55C11×#41—42no—
56C11×#41—42no—
57C11×#41—44no—
58C11×#41—44no—
59C2×Q8×C11—22no—
60C2×Q8×C11—42no—
61C2×D4×C11—22no—
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—42no—
65C2×D4×C11—41no—
66C2×D4×C11—41no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—42no—
75C22×C4×C11—42no—
76C22×C4×C11—42no—
77C22×C4×C11—41no—
78C22×C4×C11C2×D412yes—
79C22×C4×C11C2×Q811yescharacteristic
80C22×C4×C11#4112yes—
81C22×C4×C11#4111yescharacteristic
82C22×Dic11—22no—
83C22×Dic11—22no—
84C2×Dic22—44no—
85C2×Dic22—81no—
86C11×C22⋊C4—41no—
87C11×C22⋊C4—41no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C22⋊Dic11—44no—
91C4⋊Dic11—81no—
92Dic11⋊C4—44no—
93C4×Dic11—42no—
94C4×Dic11—42no—
95#4318—42no—
96#4318—42no—
97C2×C11⋊C8—42no—
98#2607—111no—
99#1789—112no—
100#1782D1111yescharacteristic
101#1306—111no—
102#1284—112no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—22no—
106C23×C11—42no—
107C23×C11—41no—
108C23×C11—41no—
109C23×C11—82no—
110C23×C11#12011yescharacteristic
111C23×C11C22⋊Q811yescharacteristic
112C23×C11#12411yescharacteristic
113Q8×C11—24no—
114Q8×C11—42no—
115D4×C11—24no—
116D4×C11—42no—
117D4×C11—42no—
118D4×C11—42no—
119D4×C11—42no—
120D4×C11—42no—
121C2×C4×C11—22no—
122C2×C4×C11—22no—
123C2×C4×C11—22no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—42no—
127C2×C4×C11—44no—
128C2×C4×C11—44no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—81no—
136C2×C4×C11—82no—
137C2×C4×C11C22⋊Q812yes—
138C2×C4×C11#12412yes—
139C2×Dic11—24no—
140C2×Dic11—42no—
141C2×Dic11—42no—
142C2×Dic11—42no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145Dic22—84no—
146C11⋊C8—82no—
147C22×#41C2×D1111yescharacteristic
148C2×#104—222no—
149C2×#104—222no—
150C2×#99—21no—
151C2×#99—21no—
152#407—112no—
153#399—221no—
154#393—221no—
155#391—222no—
156#387—222no—
157#381C2×D1111yescharacteristic
158#381C2×D1111yescharacteristic
159C4×C22⋊C4—112no—
160C22×C11—22no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—22no—
164C22×C11—22no—
165C22×C11—42no—
166C22×C11—81no—
167C22×C11—81no—
168C22×C11—82no—
169C22×C11—82no—
170C22×C11—82no—
171C22×C11#39311yescharacteristic
172C22×C11B(4,𝔽2)11yescharacteristic
173C22×C11B(4,𝔽2)11yescharacteristic
174C4×C11—22no—
175C4×C11—22no—
176C4×C11—42no—
177C4×C11—81no—
178C4×C11—81no—
179C4×C11—161no—
180Dic11—44no—
181Dic11—82no—
182C2×#41—22no—
183C2×#41—22no—
184C2×#41—42no—
185C2×#41—42no—
186C22×Q8—221no—
187C22×Q8Dic2211yescharacteristic, complemented
188C22×D4—21no—
189C22×D4Dic2211yescharacteristic, complemented
190C23×C4—21no—
191C23×C4C22×D1111yescharacteristic
192C2×M16—222no—
193C2×C4⋊C4—222no—
194C2×C4⋊C4—221no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4—222no—
197C2×C22⋊C4C22⋊D1111yescharacteristic
198C2×C22⋊C4C22⋊D1111yescharacteristic
199C2×C42—112no—
200C2×C42—112no—
201#104—444no—
202#104—444no—
203#99—42no—
204#99—42no—
205C22⋊C8—222no—
206C22⋊C8—222no—
207#95—22no—
208#95—22no—
209#95—221no—
210#95—222no—
211#95—221no—
212#95—222no—
213C2×C11—21no—
214C2×C11—21no—
215C2×C11—41no—
216C2×C11—41no—
217C2×C11—82no—
218C2×C11#202911yescharacteristic
219C2×C11#203112yes—
220C24—21no—
221C24C2×C22⋊D1111yescharacteristic
222#41—24no—
223#41—24no—
224#41—42no—
225#41—42no—
226#41—44no—
227#41—44no—
228C2×Q8—22no—
229C2×Q8—42no—
230C2×Q8—444no—
231C2×Q8—881no—
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—22no—
235C2×D4—42no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4—41no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—41no—
249C22×C4—222no—
250C22×C4—222no—
251C22×C4C2×Dic2211yescharacteristic
252C22×C4#433911yescharacteristic
253C22×C4D4×D1112yes—
254C22×C4#434112yes—
255M16—442no—
256M16—442no—
257C2×C8—442no—
258C4⋊C4—444no—
259C4⋊C4—881no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—444no—
265C42—442no—
266C42—442no—
267C11#1038611yescharacteristic, complemented, Sylow
268C23—21no—
269C23—21no—
270C23—22no—
271C23—42no—
272C23—41no—
273C23—41no—
274C23—82no—
275C23#6697711yescharacteristic
276C23#6698911yescharacteristic
277C23#6699011yescharacteristic
278Q8—24no—
279Q8—42no—
280Q8—884no—
281D4—24no—
282D4—42no—
283D4—42no—
284D4—42no—
285D4—42no—
286D4—42no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—81no—
302C2×C4—82no—
303C2×C4—224no—
304C2×C4—442no—
305C2×C4—442no—
306C2×C4—442no—
307C2×C4—442no—
308C2×C4—442no—
309C2×C4#6693112yes—
310C2×C4#6693812yes—
311C8—882no—
312C22—22no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—22no—
317C22—42no—
318C22—81no—
319C22—81no—
320C22—82no—
321C22—82no—
322C22—82no—
323C22#1062256011yescharacteristic
324C22#1062264511yescharacteristic
325C22#1062264511yescharacteristic
326C4—22no—
327C4—22no—
328C4—42no—
329C4—81no—
330C4—81no—
331C4—161no—
332C4—444no—
333C4—882no—
334C2—21no—
335C2—21no—
336C2—41no—
337C2—41no—
338C2—82no—
339C2#1306978011yescharacteristic
340C2#1306979012yes—
subgroupG/H
centerC22#10622560
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1782C2
socleC22×C11#393
prime radicalC22×C11×#41C22
hypercenter#1782D11
hypocenterC11#10386
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1782

Complements

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

NH ≅ G/Ntype
1. #13074281C2semidirect
3. #13066524C2semidirect
4. #13066468C2semidirect
23. C22×Q8×C11Q8semidirect
25. C22×D4×C11Q8semidirect
187. C22×Q8Dic22semidirect
189. C22×D4Dic22semidirect
267. C11#10386semidirect

Maximal subgroups

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

subgroupindex
#130742812
#130685602
#130665242
#130664682
C11×#17822
#1038611