Finite Group Databasebeta

← #14655579

Subgroups — #14655579

Order 2816.

574 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079538C211yesmaximal, characteristic
2C2×#10622312C211yesmaximal, characteristic, complemented
3#13079009C211yesmaximal, characteristic
4#13069604C211yesmaximal, characteristic, complemented
5#13067302C211yesmaximal, characteristic, complemented
6#13066453C211yesmaximal, characteristic, complemented
7C11×#1492C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C22×Dic44—22no—
10C2×#66922C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14#10622845—22no—
15#10622706—21no—
16#10622694—21no—
17#10622689—21no—
18#10622683—21no—
19#10622668—22no—
20#10622653—22no—
21#10622632—22no—
22#10622538C2211yescharacteristic
23C4×#4318C2211yescharacteristic
24#10622312—22no—
25#10622312—22no—
26C11×D4⋊C8—22no—
27#10622192—22no—
28#10622124—22no—
29C2×C11×#41—21no—
30C22×Dic22—21no—
31C22×Dic22D412yes—
32C2×C11×M16—21no—
33C22×C8×C11—21no—
34C11×C4⋊Q8D411yescharacteristic
35C11×#127D411yescharacteristic
36C11×#124—21no—
37C11×#121—21no—
38C11×#121—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4324—24no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×#4318D412yes—
48C2×Dic44—28no—
49C2×Dic44—48no—
50#66922—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57#66922D412yes—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C4×C8×C11—21no—
61C4×C8×C11D412yes—
62#66899—24no—
63#66896—24no—
64C22⋊(C11⋊C8)—21no—
65#66874—24no—
66C4⋊(C11⋊C8)D412yes—
67#66867—21no—
68C4×C11⋊C8—21no—
69C4×C11⋊C8—21no—
70#10154—111nomaximal, Sylow
71C11×#41—42no—
72C11×#41—42no—
73C2×Q8×C11—21no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C22×Dic11—22no—
83C22×Dic11—41no—
84C2×Dic22—22no—
85C2×Dic22—22no—
86C2×Dic22—22no—
87C2×Dic22—44no—
88C2×Dic22—44no—
89C2×Dic22—41no—
90C11×M16—42no—
91C2×C8×C11—24no—
92C2×C8×C11—22no—
93C2×C8×C11—41no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—21no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102#4324—84no—
103C4⋊Dic11—22no—
104C4⋊Dic11—22no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108C4⋊Dic11—41no—
109C4⋊Dic11—41no—
110C4⋊Dic11—41no—
111#4318—22no—
112#4318—22no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—22no—
115Dic44—416no—
116#3206—111no—
117C2×#494—111no—
118#3141—111no—
119#1997—111no—
120#1549—111no—
121#1492D1111yescharacteristic
122#1278—111no—
123C23×C11—41no—
124C23×C11#12111yescharacteristic
125Q8×C11—42no—
126D4×C11—42no—
127D4×C11—42no—
128D4×C11—42no—
129D4×C11—82no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—41no—
133C2×C4×C11—81no—
134C2×C4×C11—81no—
135C2×C4×C11#12011yescharacteristic
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12111yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12711yescharacteristic
141C2×C4×C11#13512yes—
142C2×C4×C11#13712yes—
143C2×Dic11—42no—
144C2×Dic11—42no—
145C2×Dic11—82no—
146C2×Dic11—82no—
147Dic22—44no—
148Dic22—44no—
149Dic22—44no—
150Dic22—82no—
151C8×C11—24no—
152C8×C11—81no—
153C11⋊C8—42no—
154C11⋊C8—42no—
155C22×Q16—222no—
156#532C2×D1111yescharacteristic
157C2×C4⋊Q8—111no—
158C2×C4⋊Q8—111no—
159#494—222no—
160#494—222no—
161#492—221no—
162#489—222no—
163#487—221no—
164#487—221no—
165#486—221no—
166#461—222no—
167#448—222no—
168#431—111no—
169#423C2×D1111yescharacteristic
170#417—222no—
171C4×M16—111no—
172C2×C4×C8C2×D1111yescharacteristic
173#343—222no—
174#332—222no—
175D4⋊C8—22no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—81no—
179C22×C11—81no—
180C22×C11—81no—
181C22×C11#39211yescharacteristic
182C22×C11#46412yes—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—81no—
186C4×C11#45212yes—
187C4×C11#45312yes—
188C4×C11#47312yes—
189C4×C11#49511yescharacteristic
190C4×C11#49711yescharacteristic
191Dic11—82no—
192Dic11—82no—
193C2×#41—21no—
194C22×Q8—112no—
195C22×Q8—221no—
196C2×Q16—228no—
197C2×Q16—448no—
198C2×SD16—224no—
199C2×M16—21no—
200C2×M16—112no—
201C22×C8—21no—
202C4⋊Q8—112no—
203C4⋊Q8—221no—
204C4⋊Q8—221no—
205C4⋊Q8—221no—
206C4⋊Q8—221no—
207C4⋊Q8—221no—
208C4⋊Q8—221no—
209C4⋊Q8—221no—
210C4⋊Q8D4411yescharacteristic
211#127D4411yescharacteristic
212#124—21no—
213#121—21no—
214#121—21no—
215C4×D4—21no—
216C4×D4—21no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C42C22×D1111yescharacteristic
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—112no—
225#103—224no—
226#103—224no—
227#102—224no—
228C22⋊C8—221no—
229#97—221no—
230C4×C8—21no—
231C4×C8—221no—
232C4×C8—221no—
233C4×C8C22⋊D1112yes—
234C2×C11—22no—
235C2×C11—161no—
236C2×C11#200211yescharacteristic
237C2×C11#201511yescharacteristic
238C2×C11#202011yescharacteristic
239#41—42no—
240#41—42no—
241C2×Q8—21no—
242C2×Q8—222no—
243C2×Q8—222no—
244C2×Q8—222no—
245C2×Q8—444no—
246C2×Q8—444no—
247C2×Q8—441no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—41no—
252C22×C4—41no—
253C22×C4—222no—
254C22×C4—441no—
255C22×C4#433911yescharacteristic
256C22×C4D4×D1111yescharacteristic
257C22×C4D4×D1111yescharacteristic
258Q16—4416no—
259SD16—884no—
260M16—42no—
261M16—222no—
262M16—222no—
263C2×C8—24no—
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—222no—
267C2×C8—222no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—222no—
271C4⋊C4—222no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C4⋊C4—441no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C42C2×D4411yescharacteristic
281C42D4×D1111yescharacteristic
282C42D4×D1111yescharacteristic
283C42C2×C22⋊D1111yescharacteristic
284C11#1015411yescharacteristic, complemented, Sylow
285C23—41no—
286C23#6693711yescharacteristic
287Q8—42no—
288Q8—444no—
289Q8—444no—
290Q8—444no—
291Q8—882no—
292D4—42no—
293D4—42no—
294D4—42no—
295D4—82no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—442no—
302C2×C4—442no—
303C2×C4—882no—
304C2×C4—882no—
305C2×C4#6693511yescharacteristic
306C2×C4#6693511yescharacteristic
307C2×C4#6693711yescharacteristic
308C2×C4#6696512yes—
309C2×C4#6696812yes—
310C2×C4#6698311yescharacteristic
311C2×C4#6699011yescharacteristic
312C2×C4#6699311yescharacteristic
313C8—24no—
314C8—81no—
315C8—442no—
316C8—442no—
317C22—21no—
318C22—21no—
319C22—81no—
320C22—81no—
321C22—81no—
322C22#1062238012yes—
323C22#1062257311yescharacteristic
324C4—21no—
325C4—21no—
326C4—81no—
327C4—882no—
328C4—882no—
329C4#1062239612yes—
330C4#1062243512yes—
331C4#1062275612yes—
332C4#1062276811yescharacteristic
333C4#1062278011yescharacteristic
334C2—22no—
335C2—161no—
336C2#1306963011yescharacteristic
337C2#1306971211yescharacteristic
338C2#1306973711yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1492C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#1492D11
hypocenterC11#10154
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. C2×#10622312C2semidirect
4. #13069604C2semidirect
5. #13067302C2semidirect
6. #13066453C2semidirect
284. C11#10154semidirect

Maximal subgroups

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

subgroupindex
#130795382
C2×#106223122
#130790092
#130696042
#130673022
#130664532
C11×#14922
#1015411