Finite Group Databasebeta

← #14654284

Subgroups — #14654284

Order 2816.

568 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079388C211yesmaximal, characteristic
2C2×#10622583C211yesmaximal, characteristic
3#13069601C211yesmaximal, characteristic
4#13068706C211yesmaximal, characteristic
5#13067188C211yesmaximal, characteristic
6#13066464C211yesmaximal, characteristic
7C11×#2502C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C2×#66977C2211yescharacteristic
11C11×#398—22no—
12C11×#391—21no—
13C11×#385—22no—
14C11×#384—21no—
15C4×C11×C22⋊C4C2211yescharacteristic
16#10622841—21no—
17#10622825C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×C22⋊(C11⋊C8)C2211yescharacteristic
20#10622664—22no—
21#10622663—21no—
22#10622657—21no—
23#10622583—21no—
24#10622583—22no—
25#10622583—22no—
26C2×#66874—21no—
27C2×#66871—21no—
28#10622176—22no—
29#10622167—22no—
30#10622165—22no—
31C22×Q8×C11D411yescharacteristic
32C23×C4×C11—21no—
33C23×C4×C11C2311yescharacteristic
34C22×Dic22D411yescharacteristic
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—24no—
46C2×C11×C4⋊C4D412yes—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4D412yes—
50C2×C42×C11—21no—
51C2×C22⋊Dic11—21no—
52C2×C22⋊Dic11—21no—
53C2×#4326—22no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11D411yescharacteristic
56#66977—21no—
57#66977—21no—
58#66977—21no—
59#66977—21no—
60C2×Dic11⋊C4—21no—
61C22×C11⋊C8—21no—
62C22×C11⋊C8D412yes—
63C11×#95—24no—
64C11×#95—21no—
65#66899—22no—
66C11⋊#95—21no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)D412yes—
71#66874—24no—
72#66874—22no—
73#66871—24no—
74#66871—22no—
75#9959—111nomaximal, Sylow
76C24×C11C2×D411yescharacteristic
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—42no—
80C22×C4×C11—22no—
81C22×C4×C11—21no—
82C22×C4×C11—22no—
83C22×C4×C11—21no—
84C22×C4×C11—42no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—82no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—41no—
97C2×Dic22—21no—
98C2×Dic22—21no—
99C2×Dic22—42no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—84no—
109C11×C22⋊C4—22no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4Q1614yescomplemented
113C42×C11—42no—
114C22⋊Dic11—41no—
115C22⋊Dic11—41no—
116C22⋊Dic11—42no—
117#4326—82no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—42no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—42no—
126C2×C11⋊C8—42no—
127#3189—111no—
128C2×#484—111no—
129#2502D1111yescharacteristic
130#1996—111no—
131#1824—111no—
132#1520—111no—
133#1282—111no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11#12011yescharacteristic
137C23×C11#12111yescharacteristic
138C23×C11#12711yescharacteristic
139C23×C11C2×Q1612yes—
140C23×C11#13712yes—
141Q8×C11—42no—
142Q8×C11—81no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—24no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—42no—
152C2×C4×C11—42no—
153C2×C4×C11—44no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—82no—
159C2×C4×C11—82no—
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12011yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—81no—
167C2×Dic11—81no—
168C2×Dic11—81no—
169C2×Dic11—81no—
170C2×Dic11—81no—
171Dic22—42no—
172Dic22—42no—
173C11⋊C8—42no—
174C11⋊C8—42no—
175C2×C22⋊Q8—111no—
176C2×C22⋊Q8C2×D1111yescharacteristic
177C22×C4⋊C4C2×D1111yescharacteristic
178#484—222no—
179#484—221no—
180#484—222no—
181#484—221no—
182#467—222no—
183#451—221no—
184#451—221no—
185C2×#107—221no—
186C2×#103—221no—
187C2×C22⋊C8—111no—
188C2×C22⋊C8—111no—
189#398—22no—
190#391—21no—
191#385—22no—
192#384—21no—
193#380—111no—
194C4×C22⋊C4C2×D1111yescharacteristic
195#342—222no—
196#340—222no—
197#328—222no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—42no—
205C22×C11—42no—
206C22×C11#39211yescharacteristic
207C22×C11#45112yes—
208C22×C11#46212yes—
209C22×C11#49411yescharacteristic
210C22×C11#49711yescharacteristic
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—44no—
215C4×C11—81no—
216C4×C11—82no—
217C4×C11—81no—
218C4×C11#45812yes—
219Dic11—81no—
220Dic11—81no—
221Dic11—161no—
222C22×Q8—111no—
223C22×Q8C22⋊D1111yescharacteristic
224C23×C4—21no—
225C23×C4C22×D1111yescharacteristic
226C2×Q16—222no—
227C22×C8—112no—
228C22×C8—221no—
229C22⋊Q8—21no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C22⋊Q8—221no—
234C22⋊Q8—221no—
235C22⋊Q8—221no—
236C22⋊Q8—221no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—111no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4C22⋊D1112yes—
248C2×C4⋊C4C22⋊D1111yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4—221no—
252C2×C22⋊C4C22⋊D1112yes—
253C2×C42—21no—
254#107—224no—
255#107—222no—
256#103—224no—
257#103—222no—
258#103—222no—
259C22⋊C8—112no—
260C22⋊C8—221no—
261C22⋊C8—221no—
262C22⋊C8—221no—
263#95—24no—
264#95—21no—
265#95—221no—
266C2×C11—21no—
267C2×C11—22no—
268C2×C11—22no—
269C2×C11—21no—
270C2×C11#200811yescharacteristic
271C2×C11#201611yescharacteristic
272C2×C11#202211yescharacteristic
273C24C2×C22⋊D1111yescharacteristic
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—42no—
277C2×Q8—221no—
278C2×Q8—221no—
279C2×Q8—442no—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—21no—
284C22×C4—42no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—82no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—441no—
291C22×C4D4×D1111yescharacteristic
292C22×C4D4×D1111yescharacteristic
293C22×C4D4×D1111yescharacteristic
294C22×C4#434111yescharacteristic
295C22×C4C2×C22⋊D1111yescharacteristic
296C22×C4C2×C22⋊D1111yescharacteristic
297Q16—882no—
298C2×C8—222no—
299C2×C8—222no—
300C2×C8—442no—
301C2×C8—442no—
302C4⋊C4—22no—
303C4⋊C4—21no—
304C4⋊C4—22no—
305C4⋊C4—21no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—84no—
311C4⋊C4—221no—
312C4⋊C4—221no—
313C4⋊C4—442no—
314C4⋊C4—441no—
315C4⋊C4—441no—
316C22⋊C4—22no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—441no—
320C22⋊C4—441no—
321C22⋊C4—442no—
322C22⋊C4#432614yescomplemented
323C42—42no—
324C11#995911yescharacteristic, complemented, Sylow
325C23—41no—
326C23—41no—
327C23#6699111yescharacteristic
328C23#6699311yescharacteristic
329C23#6699512yes—
330C23C2×#432612yes—
331C23#6700611yescharacteristic
332Q8—42no—
333Q8—81no—
334Q8—442no—
335Q8—442no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—24no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—44no—
347C2×C4—42no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—82no—
352C2×C4—82no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—881no—
356C2×C4—881no—
357C2×C4—881no—
358C2×C4—881no—
359C2×C4—881no—
360C2×C4#6699011yescharacteristic
361C2×C4#6699011yescharacteristic
362C2×C4#6699211yescharacteristic
363C2×C4#6699211yescharacteristic
364C8—442no—
365C8—442no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—42no—
374C22#1062269911yescharacteristic
375C22#1062270312yes—
376C22#1062270511yescharacteristic
377C22#1062283611yescharacteristic
378C22#1062284112yes—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—44no—
383C4—82no—
384C4—81no—
385C4—81no—
386C4—881no—
387C4—881no—
388C4—1761no—
389C4#1062266612yes—
390C2—22no—
391C2—21no—
392C2—22no—
393C2—21no—
394C2#1306966911yescharacteristic
395C2#1306971611yescharacteristic
396C2#1306974411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2502C2
socleC22×C11#392
prime radicalC24×C11C2×D4
hypercenter#2502D11
hypocenterC11#9959
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2502

Complements

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

NH ≅ G/Ntype
112. C11×C22⋊C4Q16semidirect
322. C22⋊C4#4326semidirect
324. C11#9959semidirect

Maximal subgroups

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

subgroupindex
#130793882
C2×#106225832
#130696012
#130687062
#130671882
#130664642
C11×#25022
#995911