Finite Group Databasebeta

← #14657358

Subgroups — #14657358

Order 2816.

460 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#10622688C211yesmaximal, characteristic
2#13068609C211yesmaximal, characteristic, complemented
3#13067388C211yesmaximal, characteristic, complemented
4#13067284C211yesmaximal, characteristic
5#13067012C211yesmaximal, characteristic, complemented
6#13066512C211yesmaximal, characteristic, complemented
7C11×#1545C211yesmaximal, characteristic
8C2×C11×#127C2211yescharacteristic
9C22×#4324—21no—
10C2×C4×Dic22C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×#66896—21no—
14C2×#66888—21no—
15#10622688—22no—
16#10622688—22no—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C11×#331—22no—
21#10622192—21no—
22#10622182—22no—
23#10622118—22no—
24#10622094—22no—
25C22×D4×C11—21no—
26C22×D4×C11—21no—
27C22×D4×C11—21no—
28C22×Dic22D411yescharacteristic
29C2×C11×M16—21no—
30C11×#127—21no—
31C11×#127—21no—
32C11×#127—21no—
33C11×#127D412yes—
34C2×C42×C11C2311yescharacteristic
35C2×#4324—24no—
36C2×#4324—42no—
37C2×#4324—42no—
38C2×C4⋊Dic11D411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×C4×Dic11—21no—
41C2×#4318—21no—
42C22×C11⋊C8—21no—
43C4×Dic22—21no—
44C4×Dic22—21no—
45C4×Dic22—21no—
46C4×Dic22—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C22⋊C8—21no—
51C4×C8×C11—21no—
52#66896—24no—
53C22⋊(C11⋊C8)—21no—
54#66888—42no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)D412yes—
59C4⋊(C11⋊C8)D412yes—
60C4×C11⋊C8—21no—
61#10443—111nomaximal, Sylow
62C24×C11—41no—
63C2×D4×C11—22no—
64C2×D4×C11—22no—
65C2×D4×C11—22no—
66C2×D4×C11—41no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—82no—
74C2×D4×C11—82no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11#4111yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C22×Dic11—21no—
79C22×Dic11—21no—
80C2×Dic22—21no—
81C2×Dic22—21no—
82C2×Dic22—21no—
83C2×Dic22—21no—
84C2×Dic22—21no—
85C2×Dic22SD1612yes—
86C11×M16—41no—
87C11×M16—41no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11#4111yescharacteristic
94#4324—48no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99C4×Dic11—41no—
100C4×Dic11—41no—
101#4318—41no—
102#4318—41no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—22no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108C2×#460—111no—
109#1801—111no—
110#1570—111no—
111#1545—111no—
112#1545D1111yescharacteristic
113#1479—111no—
114#1301—111no—
115C23×C11—42no—
116C23×C11—82no—
117C23×C11—82no—
118C23×C11—81no—
119C23×C11—81no—
120C23×C11#12311yescharacteristic
121D4×C11—42no—
122D4×C11—42no—
123D4×C11—82no—
124D4×C11—82no—
125D4×C11—82no—
126D4×C11—81no—
127D4×C11—81no—
128D4×C11—82no—
129C2×C4×C11—22no—
130C2×C4×C11—41no—
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12311yescharacteristic
136C2×C4×C11#12411yescharacteristic
137C2×C4×C11C2×SD1611yescharacteristic
138C2×C4×C11#13511yescharacteristic
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×Dic11—22no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—81no—
146Dic22—22no—
147Dic22—22no—
148Dic22—41no—
149Dic22—41no—
150C8×C11—81no—
151C8×C11—81no—
152C11⋊C8—42no—
153C11⋊C8—42no—
154C11⋊C8—81no—
155C22×SD16—221no—
156C2×#127C2×D1111yescharacteristic
157C2×C4×Q8—111no—
158#460—222no—
159#460—222no—
160#431—111no—
161#431C2×D1111yescharacteristic
162#423—111no—
163#423C2×D1111yescharacteristic
164C2×C4⋊C8—111no—
165C2×#102—221no—
166C2×#101—221no—
167#343—221no—
168#334—222no—
169#331—22no—
170#331—222no—
171Q8⋊C8—222no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—82no—
175C22×C11—82no—
176C22×C11—82no—
177C22×C11—162no—
178C22×C11—162no—
179C22×C11#39411yescharacteristic
180C22×C11#48111yescharacteristic
181C22×C11#48211yescharacteristic
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11#44911yescharacteristic
186C4×C11#45011yescharacteristic
187C4×C11#46511yescharacteristic
188C4×C11#46911yescharacteristic
189C4×C11#47112yes—
190Dic11—42no—
191Dic11—81no—
192C22×Q8—111no—
193C22×D4—21no—
194C22×D4—21no—
195C22×D4—21no—
196C2×SD16—224no—
197C2×SD16—442no—
198C2×SD16—442no—
199C2×M16—21no—
200C2×M16—221no—
201C22×C8—221no—
202#127—21no—
203#127—21no—
204#127—21no—
205#127C22⋊D1112yes—
206C4×Q8—221no—
207C4×Q8—221no—
208C4×Q8—221no—
209C4×Q8—221no—
210C2×C4⋊C4—111no—
211C2×C4⋊C4—221no—
212C2×C42—221no—
213C2×C42C22×D1111yescharacteristic
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—112no—
218C4⋊C8—112no—
219C4⋊C8—221no—
220C4⋊C8—221no—
221C4⋊C8—221no—
222#102—224no—
223#101—442no—
224C22⋊C8—21no—
225C22⋊C8—221no—
226C4×C8—21no—
227C4×C8—221no—
228C2×C11—21no—
229C2×C11—21no—
230C2×C11—162no—
231C2×C11#203411yescharacteristic
232C2×C11#204611yescharacteristic
233C2×C11#204811yescharacteristic
234C24—41no—
235C2×Q8—112no—
236C2×Q8—221no—
237C2×Q8—221no—
238C2×Q8—221no—
239C2×Q8—221no—
240C2×Q8—221no—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4—22no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—82no—
252C2×D4—82no—
253C22×C4—221no—
254C22×C4—221no—
255C22×C4#433911yescharacteristic
256C22×C4D4×D1111yescharacteristic
257C22×C4#434111yescharacteristic
258SD16—448no—
259M16—41no—
260M16—41no—
261M16—441no—
262M16—441no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—222no—
266C2×C8—222no—
267C2×C8—441no—
268C2×C8—441no—
269C2×C8—441no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—441no—
273C4⋊C4—441no—
274C42—441no—
275C42—441no—
276C42#433911yescharacteristic
277C42D4×D1111yescharacteristic
278C42D4×D1111yescharacteristic
279C42C2×C22⋊D1111yescharacteristic
280C11#1044311yescharacteristic, complemented, Sylow
281C23—42no—
282C23—82no—
283C23—82no—
284C23—81no—
285C23—81no—
286C23#6693611yescharacteristic
287Q8—222no—
288Q8—222no—
289Q8—441no—
290Q8—441no—
291D4—42no—
292D4—42no—
293D4—82no—
294D4—82no—
295D4—82no—
296D4—82no—
297D4—81no—
298D4—81no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—222no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—881no—
306C2×C4#6693711yescharacteristic
307C2×C4#6693711yescharacteristic
308C2×C4#6693811yescharacteristic
309C2×C4#6696411yescharacteristic
310C2×C4#6696511yescharacteristic
311C2×C4SD16×D1111yescharacteristic
312C2×C4#6696711yescharacteristic
313C2×C4#6698211yescharacteristic
314C2×C4#6699011yescharacteristic
315C2×C4#6699211yescharacteristic
316C8—81no—
317C8—81no—
318C8—442no—
319C8—442no—
320C8—881no—
321C22—21no—
322C22—21no—
323C22—82no—
324C22—82no—
325C22—82no—
326C22—162no—
327C22—162no—
328C22#1062239011yescharacteristic
329C22#1062239711yescharacteristic
330C22#1062257211yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—442no—
335C4—881no—
336C4#1062236112yes—
337C4#1062239111yescharacteristic
338C4#1062239511yescharacteristic
339C4#1062277111yescharacteristic
340C4#1062278211yescharacteristic
341C2—21no—
342C2—21no—
343C2—162no—
344C2#1306980311yescharacteristic
345C2#1306987711yescharacteristic
346C2#1306988711yescharacteristic
subgroupG/H
centerC22#10622572
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1545C2
socleC22×C11#394
prime radicalC2×C11×#127C22
hypercenter#1545D11
hypocenterC11#10443
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1545

Complements

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

NH ≅ G/Ntype
2. #13068609C2semidirect
3. #13067388C2semidirect
5. #13067012C2semidirect
6. #13066512C2semidirect
280. C11#10443semidirect

Maximal subgroups

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

subgroupindex
C2×#106226882
#130686092
#130673882
#130672842
#130670122
#130665122
C11×#15452
#1044311