Finite Group Databasebeta

← #14656271

Subgroups — #14656271

Order 2816.

474 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079958C211yesmaximal, characteristic
2#13078421C211yesmaximal, characteristic
3#13069553C211yesmaximal, characteristic
4#13067071C211yesmaximal, characteristic
5#13067070C211yesmaximal, characteristic
6#13066490C211yesmaximal, characteristic
7C11×#3078C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#479—22no—
12C11×#477—21no—
13C11×#475—21no—
14C11×#428—21no—
15C11×#423C2211yescharacteristic
16C11×#419—21no—
17#10622838—21no—
18#10622704—21no—
19#10622703—21no—
20#10622664—22no—
21#10622644—21no—
22#10622635—22no—
23#10622634—21no—
24#10622634—21no—
25#10622633—21no—
26#10622577—21no—
27#10622537C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29C2×C4×C11⋊C8C2211yescharacteristic
30Q8⋊(C11⋊C8)—22no—
31#10622162—22no—
32#10622122—22no—
33C22×Q8×C11D411yescharacteristic
34C2×C11×M16—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×#125—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C11×#117—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C42×C11—21no—
50C2×C42×C11C2311yescharacteristic
51C2×#4326—22no—
52#66979—21no—
53#66977—21no—
54#66977—21no—
55C2×#4318—21no—
56C22×C11⋊C8—21no—
57C22×C11⋊C8D412yes—
58#66923—21no—
59#66922D411yescharacteristic
60#66922D411yescharacteristic
61C4×Dic22—21no—
62C4×Dic22—21no—
63C11×#107—22no—
64C11×#106—22no—
65C11×C4⋊C8—21no—
66C11×C4⋊C8D412yes—
67C11×#103—22no—
68C11×#103—22no—
69#66899—22no—
70#66899—22no—
71#66899—22no—
72#66874—22no—
73#66872—22no—
74#66871—22no—
75#66871—22no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)—21no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)D412yes—
80C4×C11⋊C8—21no—
81C4×C11⋊C8—21no—
82#10259—111nomaximal, Sylow
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11Q1612yescomplemented
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C2×Dic22—21no—
97C2×Dic22—21no—
98C11×M16—41no—
99C11×M16—41no—
100C2×C8×C11—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11—41no—
113C42×C11—41no—
114C42×C11—41no—
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C22⋊Dic11—41no—
120#4326—82no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125Dic11⋊C4—41no—
126Dic11⋊C4—41no—
127C4×Dic11—41no—
128#4318—41no—
129#4318—41no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—42no—
134C2×C11⋊C8—41no—
135C2×C11⋊C8—41no—
136#3249—111no—
137#3078—111no—
138#3078D1111yescharacteristic
139#1984—111no—
140#1493—111no—
141#1493—111no—
142#1292—111no—
143C23×C11#12111yescharacteristic
144Q8×C11—22no—
145Q8×C11—22no—
146Q8×C11—42no—
147Q8×C11—41no—
148Q8×C11—41no—
149Q8×C11—41no—
150Q8×C11—41no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—22no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12711yescharacteristic
167C2×C4×C11C2×Q1611yescharacteristic
168C2×C4×C11#13511yescharacteristic
169C2×C4×C11#13711yescharacteristic
170C2×C4×C11#13711yescharacteristic
171C2×Dic11—41no—
172C2×Dic11—41no—
173Dic22—42no—
174Dic22—41no—
175Dic22—41no—
176C8×C11—42no—
177C11⋊C8—42no—
178C11⋊C8—42no—
179C11⋊C8—42no—
180#533—111no—
181#533C2×D1111yescharacteristic
182C2×C4×Q8C2×D1111yescharacteristic
183#479—22no—
184#479—222no—
185#477—21no—
186#477—221no—
187#477—221no—
188#477—221no—
189#475—21no—
190#475—221no—
191#467—222no—
192#462—221no—
193#462—221no—
194#428—21no—
195#428—221no—
196#423—111no—
197#423C2×D1111yescharacteristic
198C2×C4⋊C8—111no—
199#419—21no—
200#419—221no—
201C2×C4×C8—111no—
202#336—222no—
203Q8⋊C8—222no—
204Q8⋊C8—222no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11#39211yescharacteristic
208C22×C11#46711yescharacteristic
209C22×C11#47011yescharacteristic
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—42no—
214C4×C11—81no—
215C4×C11—81no—
216C4×C11—81no—
217C4×C11#45111yescharacteristic
218C4×C11#45111yescharacteristic
219C4×C11#45211yescharacteristic
220C4×C11#45211yescharacteristic
221C4×C11#45511yescharacteristic
222C4×C11#45611yescharacteristic
223Dic11—81no—
224Dic11—81no—
225C22×Q8C22⋊D1111yescharacteristic
226C2×Q16—222no—
227C2×M16—21no—
228C2×M16—221no—
229C22×C8—112no—
230C22×C8—221no—
231C4⋊Q8—111no—
232C4⋊Q8—111no—
233C4⋊Q8C22⋊D1111yescharacteristic
234C4⋊Q8C22⋊D1111yescharacteristic
235#125—21no—
236#125—221no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C22⋊Q8—221no—
240C22⋊Q8—221no—
241C4×Q8—21no—
242C4×Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8—221no—
248C4×Q8—221no—
249#117—21no—
250#117—221no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4C22⋊D1111yescharacteristic
253C2×C42—21no—
254C2×C42C22×D1111yescharacteristic
255#107—22no—
256#107—222no—
257#107—222no—
258#106—22no—
259#106—222no—
260C4⋊C8—21no—
261C4⋊C8—112no—
262C4⋊C8—221no—
263C4⋊C8—221no—
264C4⋊C8—221no—
265C4⋊C8C22⋊D1112yes—
266#103—22no—
267#103—22no—
268#103—222no—
269#103—222no—
270#103—222no—
271#103—222no—
272C4×C8—221no—
273C4×C8—221no—
274C2×C11—21no—
275C2×C11—21no—
276C2×C11#200111yescharacteristic
277C2×C11#200711yescharacteristic
278C2×C11#201711yescharacteristic
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—221no—
287C2×Q8—221no—
288C2×Q8#432612yescomplemented
289C22×C4—21no—
290C22×C4—21no—
291C22×C4D4×D1111yescharacteristic
292C22×C4#434111yescharacteristic
293C22×C4C2×C22⋊D1111yescharacteristic
294Q16—882no—
295M16—41no—
296M16—41no—
297M16—441no—
298M16—441no—
299C2×C8—22no—
300C2×C8—222no—
301C2×C8—222no—
302C2×C8—222no—
303C2×C8—441no—
304C2×C8—441no—
305C2×C8—442no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—221no—
317C4⋊C4—221no—
318C4⋊C4—221no—
319C4⋊C4—221no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C22⋊C4—41no—
323C22⋊C4—441no—
324C42—41no—
325C42—41no—
326C42—41no—
327C42—441no—
328C42D4×D1111yescharacteristic
329C42D4×D1111yescharacteristic
330C42C2×C22⋊D1111yescharacteristic
331C42C2×C22⋊D1111yescharacteristic
332C11#1025911yescharacteristic, complemented, Sylow
333C23#6699211yescharacteristic
334Q8—22no—
335Q8—22no—
336Q8—42no—
337Q8—41no—
338Q8—41no—
339Q8—41no—
340Q8—41no—
341Q8—442no—
342Q8—441no—
343Q8—441no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4#6699011yescharacteristic
357C2×C4#6699011yescharacteristic
358C2×C4#6699111yescharacteristic
359C2×C4#6699211yescharacteristic
360C2×C4#6699311yescharacteristic
361C2×C4#6699511yescharacteristic
362C2×C4C2×#432611yescharacteristic
363C2×C4#6700311yescharacteristic
364C2×C4#6700411yescharacteristic
365C2×C4#6700611yescharacteristic
366C8—42no—
367C8—442no—
368C8—442no—
369C8—442no—
370C22—21no—
371C22—21no—
372C22#1062266411yescharacteristic
373C22#1062266511yescharacteristic
374C22#1062283611yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—42no—
379C4—81no—
380C4—81no—
381C4—81no—
382C4—881no—
383C4—881no—
384C4#1062266011yescharacteristic
385C4#1062266311yescharacteristic
386C4#1062281511yescharacteristic
387C4#1062281811yescharacteristic
388C4#1062284111yescharacteristic
389C4#1062285211yescharacteristic
390C2—21no—
391C2—21no—
392C2#1306962411yescharacteristic
393C2#1306966111yescharacteristic
394C2#1306971911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3078C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#3078D11
hypocenterC11#10259
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
90. C2×Q8×C11Q16semidirect
288. C2×Q8#4326semidirect
332. C11#10259semidirect

Maximal subgroups

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

subgroupindex
#130799582
#130784212
#130695532
#130670712
#130670702
#130664902
C11×#30782
#1025911