Finite Group Databasebeta

← #14654300

Subgroups — #14654300

Order 2816.

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

normal subgroups only

This group has 552 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#13079388C211yesmaximal, characteristic
2C2×#10622334C211yesmaximal, characteristic
3#13073102C211yesmaximal, characteristic
4#13069600C211yesmaximal, characteristic
5#13068700C211yesmaximal, characteristic
6#13066462C211yesmaximal, characteristic
7C11×#1520C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×C4⋊Dic11C2211yescharacteristic
10C2×#66977C2211yescharacteristic
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13#10622843—21no—
14#10622841—21no—
15C4×C22⋊Dic11C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17C2×#66881—21no—
18C2×#66880—21no—
19#10622664—22no—
20#10622663—21no—
21#10622657—21no—
22#10622599—22no—
23#10622590—21no—
24#10622583—21no—
25#10622556—22no—
26#10622334—22no—
27#10622334—22no—
28C11×#328—22no—
29#10622167—22no—
30#10622165—22no—
31C22×Q8×C11D411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C23×Dic11—21no—
34C22×Dic22D411yescharacteristic
35C22×C8×C11—21no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11D412yes—
47C2×#4326—22no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11D411yescharacteristic
54C2×C4⋊Dic11D412yes—
55#66977—21no—
56#66977—21no—
57#66977—21no—
58#66977—21no—
59C2×Dic11⋊C4—21no—
60C2×C4×Dic11—21no—
61C22×C11⋊C8D412yes—
62C11×C22⋊C8—21no—
63C11×C22⋊C8D412yes—
64C11×#95—21no—
65#66899—22no—
66C11⋊#95—24no—
67C11⋊#95—24no—
68C11⋊#95—21no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71#66881—24no—
72#66880—24no—
73#66874—22no—
74#66871—22no—
75#9961—111nomaximal, Sylow
76C24×C11C2×D411yescharacteristic
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—42no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—42no—
83C22×C4×C11—41no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×Dic11—22no—
91C22×Dic11—22no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—41no—
95C22×Dic11—41no—
96C22×Dic11—42no—
97C22×Dic11—42no—
98C2×Dic22—21no—
99C2×Dic22—21no—
100C2×Dic22—42no—
101C2×C8×C11—22no—
102C2×C8×C11—42no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—42no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—42no—
111C22⋊Dic11—22no—
112C22⋊Dic11—22no—
113C22⋊Dic11—41no—
114C22⋊Dic11—41no—
115#4326—82no—
116C4⋊Dic11—21no—
117C4⋊Dic11—22no—
118C4⋊Dic11—21no—
119C4⋊Dic11—22no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122Dic11⋊C4—41no—
123Dic11⋊C4—41no—
124C4×Dic11—42no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—42no—
127#3189—111no—
128C2×#483—111no—
129#2503—111no—
130#1996—111no—
131#1823—111no—
132#1520D1111yescharacteristic
133#1282—111no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11#12011yescharacteristic
137C23×C11#12111yescharacteristic
138C23×C11#12711yescharacteristic
139C23×C11#13512yes—
140C23×C11#13712yes—
141Q8×C11—42no—
142Q8×C11—81no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—81no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×Dic11—42no—
161C2×Dic11—42no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—44no—
167C2×Dic11—82no—
168C2×Dic11—81no—
169C2×Dic11—81no—
170C2×Dic11—81no—
171C2×Dic11—81no—
172Dic22—42no—
173Dic22—42no—
174C8×C11—42no—
175C11⋊C8—42no—
176C2×C22⋊Q8—111no—
177C2×C22⋊Q8C2×D1111yescharacteristic
178C22×C4⋊C4—111no—
179#484—221no—
180#484—221no—
181#483—222no—
182#483—222no—
183#467—222no—
184#451—221no—
185#451—221no—
186C2×#106—221no—
187C2×#103—221no—
188C2×C22⋊C8—111no—
189C2×C22⋊C8C2×D1111yescharacteristic
190#400—222no—
191#391—221no—
192#382—221no—
193#381—222no—
194#380C2×D1111yescharacteristic
195C4×C22⋊C4—111no—
196#342—222no—
197#340—222no—
198#328—22no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—42no—
206C22×C11—42no—
207C22×C11#39211yescharacteristic
208C22×C11#45212yes—
209C22×C11#46412yes—
210C22×C11#49511yescharacteristic
211C22×C11#49711yescharacteristic
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—81no—
216C4×C11—81no—
217C4×C11—161no—
218C4×C11#45812yes—
219Dic11—82no—
220Dic11—81no—
221Dic11—82no—
222Dic11—81no—
223C22×Q8—111no—
224C22×Q8D4411yescharacteristic
225C23×C4—221no—
226C23×C4C22×D1111yescharacteristic
227C2×Q16—222no—
228C22×C8—21no—
229C22×C8—112no—
230C22⋊Q8—21no—
231C22⋊Q8—21no—
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234C22⋊Q8—221no—
235C22⋊Q8—221no—
236C22⋊Q8—221no—
237C22⋊Q8—221no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—112no—
241C2×C4⋊C4—111no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4D4411yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—112no—
252C2×C22⋊C4—221no—
253C2×C42—221no—
254#107—222no—
255#106—224no—
256#103—222no—
257#103—224no—
258#103—222no—
259C22⋊C8—21no—
260C22⋊C8—221no—
261C22⋊C8—221no—
262C22⋊C8C22⋊D1112yes—
263#95—21no—
264#95—224no—
265#95—224no—
266#95—221no—
267C2×C11—22no—
268C2×C11—21no—
269C2×C11—22no—
270C2×C11—21no—
271C2×C11#200911yescharacteristic
272C2×C11#201511yescharacteristic
273C2×C11#202211yescharacteristic
274C24D4×D1111yescharacteristic
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—42no—
278C2×Q8—221no—
279C2×Q8—221no—
280C2×Q8—442no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—42no—
284C22×C4—41no—
285C22×C4—222no—
286C22×C4—222no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—441no—
290C22×C4—442no—
291C22×C4—442no—
292C22×C4—441no—
293C22×C4C2×D4411yescharacteristic
294C22×C4#433911yescharacteristic
295C22×C4D4×D1111yescharacteristic
296C22×C4D4×D1111yescharacteristic
297C22×C4D4×D1111yescharacteristic
298C22×C4C2×C22⋊D1111yescharacteristic
299Q16—882no—
300C2×C8—22no—
301C2×C8—42no—
302C2×C8—222no—
303C2×C8—442no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—42no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—221no—
310C4⋊C4—222no—
311C4⋊C4—222no—
312C4⋊C4—221no—
313C4⋊C4—441no—
314C4⋊C4—441no—
315C4⋊C4—441no—
316C4⋊C4—441no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—42no—
320C22⋊C4—222no—
321C22⋊C4—222no—
322C22⋊C4—441no—
323C22⋊C4—441no—
324C42—442no—
325C11#996111yescharacteristic, complemented, Sylow
326C23—41no—
327C23—41no—
328C23#6693511yescharacteristic
329C23#6693711yescharacteristic
330C23#6696912yes—
331C23#6697112yes—
332C23#6699311yescharacteristic
333Q8—42no—
334Q8—81no—
335Q8—442no—
336Q8—442no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—442no—
351C2×C4—442no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—442no—
355C2×C4—442no—
356C2×C4—444no—
357C2×C4—881no—
358C2×C4—881no—
359C2×C4—882no—
360C2×C4—881no—
361C2×C4—881no—
362C2×C4#6693511yescharacteristic
363C2×C4#6693711yescharacteristic
364C2×C4#6698311yescharacteristic
365C2×C4#6699011yescharacteristic
366C8—42no—
367C8—442no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—42no—
375C22—42no—
376C22#1062241112yes—
377C22#1062242312yes—
378C22#1062257311yescharacteristic
379C22#1062278111yescharacteristic
380C22#1062280311yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—81no—
385C4—81no—
386C4—161no—
387C4—882no—
388C4—881no—
389C4—882no—
390C4—881no—
391C4#1062235512yes—
392C2—21no—
393C2—22no—
394C2—21no—
395C2—22no—
396C2#1306967711yescharacteristic
397C2#1306971111yescharacteristic
398C2#1306974611yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1520C2
socleC22×C11#392
prime radicalC24×C11C2×D4
hypercenter#1520D11
hypocenterC11#9961
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
325. C11#9961semidirect

Maximal subgroups

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

subgroupindex
#130793882
C2×#106223342
#130731022
#130696002
#130687002
#130664622
C11×#15202
#996111