Finite Group Databasebeta

← #14655750

Subgroups — #14655750

Order 2816.

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

normal subgroups only

This group has 560 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#13079557C211yesmaximal, characteristic
2#13078421C211yesmaximal, characteristic, complemented
3#13067284C211yesmaximal, characteristic
4#13067018C211yesmaximal, characteristic, complemented
5#13066940C211yesmaximal, characteristic, complemented
6#13066513C211yesmaximal, characteristic, complemented
7C2×C11×#460C211yesmaximal, characteristic
8C22×C11×SD16—21no—
9C2×C11×#127C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11#10623001C2211yescharacteristic
12C11×#460—22no—
13C11×#460—22no—
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×#102—21no—
16#10622838—21no—
17#10622831—22no—
18#10622689—21no—
19#10622688—22no—
20#10622683—21no—
21#10622635—22no—
22#10622634—21no—
23#10622633—21no—
24#10622577—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622182—22no—
29#10622166—22no—
30#10622122—22no—
31C22×Q8×C11D411yescharacteristic
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C2×C11×SD16—24no—
36C2×C11×SD16—42no—
37C2×C11×SD16—42no—
38C22×C8×C11—21no—
39C11×#127—21no—
40C11×#127—21no—
41C11×#127—21no—
42C11×#127D412yes—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C42×C11—21no—
50C2×C42×C11C2311yescharacteristic
51C2×#4324—24no—
52#66979—21no—
53#66977—21no—
54#66977—21no—
55C2×#4318—21no—
56#66923—21no—
57#66922D411yescharacteristic
58#66922D411yescharacteristic
59C4×Dic22—21no—
60C4×Dic22—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63C11×#102—24no—
64#66899—22no—
65#66899—22no—
66#66896—24no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)D412yes—
69#66872—22no—
70#66871—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)D412yes—
75C4×C11⋊C8—21no—
76C4×C11⋊C8—21no—
77#10179—111nomaximal, Sylow
78C24×C11—41no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11SD1612yescomplemented
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—22no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—82no—
96C2×D4×C11—82no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C2×Dic22—21no—
103C2×Dic22—21no—
104C11×SD16—48no—
105C2×C8×C11—22no—
106C2×C8×C11—41no—
107C2×C8×C11—41no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C42×C11—41no—
113C42×C11—41no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C22⋊Dic11—41no—
119#4324—84no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124Dic11⋊C4—41no—
125Dic11⋊C4—41no—
126C4×Dic11—41no—
127#4318—41no—
128#4318—41no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—41no—
132#3208—111no—
133#3078—111no—
134C2×#460D1111yescharacteristic
135#1545—111no—
136#1481—111no—
137#1461—111no—
138#1301—111no—
139C23×C11—42no—
140C23×C11—82no—
141C23×C11—82no—
142C23×C11—81no—
143C23×C11—81no—
144C23×C11#12111yescharacteristic
145Q8×C11—22no—
146Q8×C11—22no—
147Q8×C11—41no—
148Q8×C11—41no—
149D4×C11—44no—
150D4×C11—42no—
151D4×C11—42no—
152D4×C11—82no—
153D4×C11—82no—
154D4×C11—81no—
155D4×C11—81no—
156D4×C11—82no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—81no—
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12011yescharacteristic
166C2×C4×C11#12011yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12711yescharacteristic
170C2×C4×C11C2×SD1611yescharacteristic
171C2×C4×C11#13511yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C11#13711yescharacteristic
174C2×Dic11—41no—
175C2×Dic11—41no—
176Dic22—42no—
177Dic22—42no—
178C8×C11—42no—
179C11⋊C8—42no—
180C11⋊C8—42no—
181C11⋊C8—81no—
182C22×SD16—21no—
183#533—111no—
184C2×#127C2×D1111yescharacteristic
185C2×C4×Q8C2×D1111yescharacteristic
186#492—221no—
187#486—221no—
188#479—222no—
189#477—221no—
190#475—221no—
191#460—22no—
192#460—22no—
193#460—222no—
194#450—222no—
195#431—111no—
196#431—111no—
197#428—221no—
198#423—111no—
199C2×C4⋊C8C2×D1111yescharacteristic
200#419—221no—
201C2×#102—21no—
202#331—222no—
203Q8⋊C8—222no—
204#324—222no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—82no—
208C22×C11—82no—
209C22×C11—82no—
210C22×C11—162no—
211C22×C11—162no—
212C22×C11#39211yescharacteristic
213C22×C11#46511yescharacteristic
214C22×C11#46811yescharacteristic
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—42no—
219C4×C11—81no—
220C4×C11#44811yescharacteristic
221C4×C11#44911yescharacteristic
222C4×C11#45011yescharacteristic
223C4×C11#45211yescharacteristic
224C4×C11#47112yes—
225Dic11—81no—
226Dic11—81no—
227C22×Q8C22⋊D1111yescharacteristic
228C22×D4—21no—
229C22×D4—21no—
230C22×D4—21no—
231C2×SD16—24no—
232C2×SD16—42no—
233C2×SD16—42no—
234C2×SD16—224no—
235C2×M16—221no—
236C22×C8—21no—
237C4⋊Q8—111no—
238C4⋊Q8—111no—
239#127—21no—
240#127—21no—
241#127—21no—
242#127C22⋊D1112yes—
243#125—221no—
244C22⋊Q8—221no—
245C22⋊Q8—221no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×Q8—221no—
251C4×Q8—221no—
252#117—221no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4C22⋊D1111yescharacteristic
255C2×C42—21no—
256C2×C42C22×D1111yescharacteristic
257#107—222no—
258#106—222no—
259C4⋊C8—21no—
260C4⋊C8—112no—
261C4⋊C8—221no—
262C4⋊C8—221no—
263C4⋊C8—221no—
264C4⋊C8C22⋊D1112yes—
265#103—222no—
266#103—222no—
267#102—24no—
268#102—224no—
269C22⋊C8—112no—
270C22⋊C8—221no—
271C4×C8—221no—
272C4×C8—221no—
273C2×C11—21no—
274C2×C11—21no—
275C2×C11—162no—
276C2×C11#200011yescharacteristic
277C2×C11#200811yescharacteristic
278C2×C11#201911yescharacteristic
279C24—41no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—221no—
286C2×Q8—221no—
287C2×Q8#432412yescomplemented
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—82no—
299C2×D4—82no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4D4×D1111yescharacteristic
303C22×C4#434111yescharacteristic
304C22×C4C2×C22⋊D1111yescharacteristic
305SD16—48no—
306SD16—884no—
307M16—441no—
308M16—441no—
309C2×C8—22no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—222no—
313C2×C8—222no—
314C2×C8—441no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—221no—
320C4⋊C4—221no—
321C4⋊C4—221no—
322C4⋊C4—221no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C22⋊C4—441no—
326C42—41no—
327C42—41no—
328C42—441no—
329C42D4×D1111yescharacteristic
330C42D4×D1111yescharacteristic
331C42C2×C22⋊D1111yescharacteristic
332C42C2×C22⋊D1111yescharacteristic
333C11#1017911yescharacteristic, complemented, Sylow
334C23—42no—
335C23—82no—
336C23—82no—
337C23—81no—
338C23—81no—
339C23#6699211yescharacteristic
340Q8—22no—
341Q8—22no—
342Q8—41no—
343Q8—41no—
344Q8—442no—
345Q8—442no—
346D4—44no—
347D4—42no—
348D4—42no—
349D4—82no—
350D4—82no—
351D4—82no—
352D4—81no—
353D4—81no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—81no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4#6698511yescharacteristic
364C2×C4C2×#432411yescharacteristic
365C2×C4#6699011yescharacteristic
366C2×C4#6699011yescharacteristic
367C2×C4#6699111yescharacteristic
368C2×C4#6699211yescharacteristic
369C2×C4#6699311yescharacteristic
370C2×C4#6700311yescharacteristic
371C2×C4#6700411yescharacteristic
372C2×C4#6700611yescharacteristic
373C8—42no—
374C8—442no—
375C8—442no—
376C8—881no—
377C22—21no—
378C22—21no—
379C22—82no—
380C22—82no—
381C22—82no—
382C22—162no—
383C22—162no—
384C22#1062265411yescharacteristic
385C22#1062265511yescharacteristic
386C22#1062283611yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—42no—
391C4—81no—
392C4—881no—
393C4—881no—
394C4#1062265011yescharacteristic
395C4#1062265311yescharacteristic
396C4#1062279012yes—
397C4#1062283111yescharacteristic
398C4#1062285211yescharacteristic
399C2—21no—
400C2—21no—
401C2—162no—
402C2#1306961911yescharacteristic
403C2#1306966711yescharacteristic
404C2#1306972811yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#460C2
socleC22×C11#392
prime radicalC2×C11×#127C22
hypercenterC2×#460D11
hypocenterC11#10179
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
2. #13078421C2semidirect
4. #13067018C2semidirect
5. #13066940C2semidirect
6. #13066513C2semidirect
84. C2×Q8×C11SD16semidirect
287. C2×Q8#4324semidirect
333. C11#10179semidirect

Maximal subgroups

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

subgroupindex
#130795572
#130784212
#130672842
#130670182
#130669402
#130665132
C2×C11×#4602
#1017911