Finite Group Databasebeta

← #14654549

Subgroups — #14654549

Order 2816.

500 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 99 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#13078417C211yesmaximal, characteristic
2#13073982C211yesmaximal, characteristic
3#13067180C211yesmaximal, characteristic
4#13067045C211yesmaximal, characteristic
5#13067012C211yesmaximal, characteristic
6#13066475C211yesmaximal, characteristic
7C11×#3104C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×C4×Dic22C2211yescharacteristic
11C11×#484—21no—
12C11×#477—21no—
13C11×#462—21no—
14C11×#451—21no—
15C4×C11×Q16—22no—
16C11×#431C2211yescharacteristic
17#10622842—21no—
18#10622707—21no—
19#10622704—21no—
20#10622676—22no—
21#10622617—21no—
22#10622608—21no—
23#10622595—21no—
24#10622591—22no—
25#10622549C2211yescharacteristic
26#10622542—21no—
27#10622541—21no—
28#10622538C2211yescharacteristic
29#10622537C2211yescharacteristic
30#10622176—22no—
31Q8⋊(C11⋊C8)—22no—
32#10622094—22no—
33C22×Q8×C11D411yescharacteristic
34C22×Dic22D411yescharacteristic
35C2×C11×Q16—22no—
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D411yescharacteristic
38C11×#125—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C4×Q8×C11—21no—
44C4×Q8×C11—21no—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C11×#117—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C42×C11—21no—
51C2×C42×C11C2311yescharacteristic
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11D411yescharacteristic
54C2×Dic11⋊C4—22no—
55C2×Dic11⋊C4—21no—
56C2×C4×Dic11—21no—
57C2×#4318—21no—
58C4×Dic22—21no—
59C4×Dic22—21no—
60C4×Dic22—21no—
61C4×Dic22—21no—
62C11×#107—22no—
63C11×C4⋊C8—21no—
64C11×#103—22no—
65C11×#103—22no—
66C11×C22⋊C8—21no—
67C4×C8×C11D412yes—
68C11⋊#95—22no—
69C11⋊#95—22no—
70C11⋊#95—22no—
71C11⋊#95—21no—
72C11⋊#95D412yes—
73C22⋊(C11⋊C8)—21no—
74#66874—22no—
75#66874—22no—
76#66872—22no—
77#66871—22no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)D412yes—
81C4×C11⋊C8—21no—
82#10003—111nomaximal, Sylow
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—42no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×Dic11—21no—
94C22×Dic11—22no—
95C22×Dic11—21no—
96C2×Dic22—21no—
97C2×Dic22—21no—
98C2×Dic22—21no—
99C2×Dic22—21no—
100C2×Dic22—21no—
101C2×Dic22Q1612yescomplemented
102C11×Q16—44no—
103C2×C8×C11—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C22⋊C4—41no—
115C42×C11—41no—
116C42×C11—41no—
117C42×C11—41no—
118C42×C11C2×D411yescharacteristic
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11#4111yescharacteristic
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—41no—
125C4⋊Dic11—41no—
126Dic11⋊C4—44no—
127Dic11⋊C4—41no—
128Dic11⋊C4—41no—
129C4×Dic11—41no—
130C4×Dic11—41no—
131#4318—41no—
132#4318—41no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—41no—
135#3104D1111yescharacteristic
136#3078—111no—
137#2581—111no—
138#1518—111no—
139#1487—111no—
140#1479—111no—
141#1286—111no—
142C23×C11#12011yescharacteristic
143Q8×C11—22no—
144Q8×C11—22no—
145Q8×C11—41no—
146Q8×C11—41no—
147Q8×C11—42no—
148Q8×C11—81no—
149C2×C4×C11—22no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12711yescharacteristic
164C2×C4×C11C2×Q1611yescharacteristic
165C2×C4×C11#13511yescharacteristic
166C2×C4×C11#13711yescharacteristic
167C2×C4×C11#13711yescharacteristic
168C2×Dic11—22no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—42no—
174C2×Dic11—41no—
175C2×Dic11—42no—
176Dic22—22no—
177Dic22—22no—
178Dic22—41no—
179Dic22—41no—
180C8×C11—42no—
181C11⋊C8—42no—
182C11⋊C8—81no—
183#533C2×D1111yescharacteristic
184C2×C4×Q8—111no—
185C2×C4×Q8C2×D1111yescharacteristic
186#484—21no—
187#479—222no—
188#477—21no—
189#477—221no—
190#475—221no—
191#462—21no—
192#451—21no—
193C4×Q16—22no—
194#431—111no—
195#431C2×D1111yescharacteristic
196#428—221no—
197#423—111no—
198#419—221no—
199#400—221no—
200#395—221no—
201#391—221no—
202#389—221no—
203#387—222no—
204#382—111no—
205#328—222no—
206Q8⋊C8—222no—
207Q8⋊C8—222no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11#39211yescharacteristic
211C22×C11#45111yescharacteristic
212C22×C11#45211yescharacteristic
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—42no—
218C4×C11—81no—
219C4×C11—81no—
220C4×C11—81no—
221C4×C11#45111yescharacteristic
222C4×C11#45211yescharacteristic
223C4×C11#46711yescharacteristic
224C4×C11#47011yescharacteristic
225Dic11—42no—
226Dic11—82no—
227Dic11—81no—
228C22×Q8—111no—
229C22×Q8C22⋊D1111yescharacteristic
230C2×Q16—22no—
231C2×M16—221no—
232C4⋊Q8C22⋊D1111yescharacteristic
233C4⋊Q8C22⋊D1111yescharacteristic
234#125—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8—21no—
242C4×Q8—21no—
243C4×Q8—221no—
244C4×Q8—221no—
245C4×Q8—221no—
246C4×Q8—221no—
247#117—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—111no—
250C2×C4⋊C4—222no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4—221no—
253C2×C4⋊C4C22⋊D1111yescharacteristic
254C2×C42—21no—
255C2×C42—221no—
256C2×C42C22×D1111yescharacteristic
257#107—22no—
258#107—222no—
259#106—222no—
260C4⋊C8—21no—
261C4⋊C8—112no—
262C4⋊C8—221no—
263C4⋊C8—221no—
264#103—22no—
265#103—22no—
266#103—222no—
267#103—222no—
268C22⋊C8—21no—
269C22⋊C8—221no—
270C4×C8—221no—
271C4×C8C22⋊D1112yes—
272#95—112no—
273#95—222no—
274#95—222no—
275#95—222no—
276#95—221no—
277C2×C11—21no—
278C2×C11—21no—
279C2×C11#200111yescharacteristic
280C2×C11#200911yescharacteristic
281C2×C11#201011yescharacteristic
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—42no—
287C2×Q8—112no—
288C2×Q8—221no—
289C2×Q8—221no—
290C2×Q8—221no—
291C2×Q8—221no—
292C2×Q8—221no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—221no—
296C22×C4—222no—
297C22×C4—221no—
298C22×C4D4×D1111yescharacteristic
299C22×C4D4×D1111yescharacteristic
300C22×C4C2×C22⋊D1111yescharacteristic
301Q16—44no—
302M16—441no—
303M16—441no—
304C2×C8—22no—
305C2×C8—222no—
306C2×C8—441no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—221no—
318C4⋊C4—221no—
319C4⋊C4—444no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C4⋊C4—441no—
323C4⋊C4—441no—
324C22⋊C4—41no—
325C42—41no—
326C42—41no—
327C42—41no—
328C42—441no—
329C42—441no—
330C42D4×D1111yescharacteristic
331C42#434111yescharacteristic
332C42C2×C22⋊D1111yescharacteristic
333C42C2×C22⋊D1111yescharacteristic
334C11#1000311yescharacteristic, complemented, Sylow
335C23#6699011yescharacteristic
336Q8—22no—
337Q8—22no—
338Q8—41no—
339Q8—41no—
340Q8—42no—
341Q8—81no—
342Q8—222no—
343Q8—222no—
344Q8—441no—
345Q8—441no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—222no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—442no—
359C2×C4—442no—
360C2×C4—442no—
361C2×C4—442no—
362C2×C4—441no—
363C2×C4Q16×D1111yescharacteristic
364C2×C4#6697111yescharacteristic
365C2×C4#6697111yescharacteristic
366C2×C4#6697211yescharacteristic
367C2×C4#6699011yescharacteristic
368C2×C4#6699111yescharacteristic
369C2×C4#6699211yescharacteristic
370C2×C4#6699211yescharacteristic
371C2×C4#6699311yescharacteristic
372C2×C4#6700611yescharacteristic
373C8—42no—
374C8—442no—
375C8—881no—
376C22—21no—
377C22—21no—
378C22#1062279911yescharacteristic
379C22#1062280011yescharacteristic
380C22#1062283611yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—42no—
386C4—81no—
387C4—81no—
388C4—81no—
389C4—442no—
390C4—882no—
391C4—881no—
392C4#1062279911yescharacteristic
393C4#1062280011yescharacteristic
394C4#1062280111yescharacteristic
395C4#1062280211yescharacteristic
396C2—21no—
397C2—21no—
398C2#1306962311yescharacteristic
399C2#1306967311yescharacteristic
400C2#1306968111yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3104C2
socleC22×C11#392
prime radicalC23×C11#120
hypercenter#3104D11
hypocenterC11#10003
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
101. C2×Dic22Q16semidirect
334. C11#10003semidirect

Maximal subgroups

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

subgroupindex
#130784172
#130739822
#130671802
#130670452
#130670122
#130664752
C11×#31042
#1000311