Finite Group Databasebeta

← #14727699

Subgroups — #14727699

Order 2816.

940 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 940 conjugacy classes of subgroups — too many to draw. Only its 187 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
1C2×#10623031C211yesmaximal, characteristic
2#13079391C212yesmaximal
3#13074429C211yesmaximal, characteristic
4#13067660C214yesmaximal, complemented
5#13067592C214yesmaximal, complemented
6#13067189C212yesmaximal
7C2×C11×#324C211yesmaximal, characteristic
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×#66979—21no—
10C2×#66977—21no—
11C2×#66977C2211yescharacteristic
12C2×#66977C2212yes—
13#10623031—22no—
14#10623031—24no—
15#10623031C2214yes—
16C2×#66943—22no—
17C2×#66941—22no—
18C2×C11×C22⋊C8C2212yes—
19#10622825C2211yescharacteristic
20#10622824—21no—
21#10622823—21no—
22#10622729—24no—
23#10622599C2212yes—
24#10622597—22no—
25#10622592C2212yes—
26#10622352—22no—
27#10622352C2214yes—
28#10622335—22no—
29#10622335C2214yes—
30C11×#324C2214yes—
31#10622105C2218yes—
32C23×C4×C11D411yescharacteristic
33C23×C4×C11D411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C22×Dic22—21no—
36C22×Dic22D412yes—
37C22×Dic22C2311yescharacteristic
38C22×C8×C11—22no—
39C2×C11×C4⋊C4—22no—
40C2×C11×C4⋊C4—22no—
41C2×C11×C4⋊C4D412yes—
42C2×C11×C4⋊C4C2312yes—
43C2×C22⋊Dic11—22no—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11—21no—
46#66979—24no—
47#66979—24no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11D412yes—
53C2×C4⋊Dic11C2311yescharacteristic
54#66977—24no—
55#66977—22no—
56#66977—22no—
57#66977—24no—
58#66977—22no—
59#66977—22no—
60#66977D414yes—
61#66977C2314yes—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—22no—
66C2×C4×Dic11—22no—
67C2×Dic44—24no—
68#66943—28no—
69#66943—28no—
70#66941—28no—
71#66941—28no—
72C11×C22⋊C8—22no—
73C11×C22⋊C8C2314yes—
74C11⋊#95—22no—
75C11⋊#95—22no—
76C11⋊#95—22no—
77C11⋊#95C2312yes—
78#66882—24no—
79#66880—24no—
80#66880—24no—
81#18295—111nomaximal, Sylow
82C24×C11C2×D411yescharacteristic
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—22no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—81no—
89C22×C4×C11—81no—
90C22×C4×C11Q1614yescomplemented
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2411yescharacteristic
97C22×Dic11—22no—
98C22×Dic11—22no—
99C22×Dic11—21no—
100C22×Dic11—22no—
101C22×Dic11—21no—
102C2×Dic22—24no—
103C2×Dic22—22no—
104C2×Dic22—22no—
105C2×Dic22—81no—
106C2×Dic22—82no—
107C2×Dic22—82no—
108C2×Dic22C2×D414yes—
109C2×C8×C11—24no—
110C2×C8×C11—82no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—24no—
113C22⋊Dic11—24no—
114C22⋊Dic11—24no—
115C22⋊Dic11—41no—
116C22⋊Dic11—41no—
117C22⋊Dic11—42no—
118C4⋊Dic11—24no—
119C4⋊Dic11—24no—
120C4⋊Dic11—24no—
121C4⋊Dic11—22no—
122C4⋊Dic11—22no—
123C4⋊Dic11—81no—
124C4⋊Dic11C2×D414yes—
125Dic11⋊C4—28no—
126Dic11⋊C4—24no—
127Dic11⋊C4—24no—
128Dic11⋊C4—42no—
129Dic11⋊C4—82no—
130C4×Dic11—28no—
131Dic44—84no—
132C2×#544—111no—
133#3189—112no—
134#2627—111no—
135#1617—114no—
136#1605—114no—
137#1520—112no—
138C2×#324D1111yescharacteristic
139C23×C11—41no—
140C23×C11—41no—
141C23×C11#12011yescharacteristic
142C23×C11#12011yescharacteristic
143C23×C11C2×Q1612yes—
144C23×C11#13712yes—
145C23×C11C22×D411yescharacteristic
146C2×C4×C11—22no—
147C2×C4×C11—22no—
148C2×C4×C11—24no—
149C2×C4×C11—24no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—41no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—81no—
158C2×C4×C11#12012yes—
159C2×C4×C11C2×Q1614yes—
160C2×C4×C11C22×D412yes—
161C2×Dic11—24no—
162C2×Dic11—24no—
163C2×Dic11—44no—
164C2×Dic11—44no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—42no—
172Dic22—44no—
173Dic22—44no—
174Dic22—82no—
175Dic22—84no—
176C8×C11—44no—
177#544—114no—
178#544—224no—
179#544—222no—
180C2×C4⋊Q8—222no—
181C2×#125—222no—
182C2×C22⋊Q8—112no—
183C2×C22⋊Q8—111no—
184C2×C22⋊Q8—221no—
185C2×#117—221no—
186C22×C4⋊C4C2×D1111yescharacteristic
187#484—114no—
188#484—222no—
189#467—224no—
190#451—114no—
191#451—222no—
192C2×C22⋊C8C2×D1112yes—
193#400—112no—
194#398—222no—
195#395—112no—
196#385—221no—
197#381—221no—
198#380—111no—
199#328—118no—
200#324C2×D1114yes—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—42no—
208C22×C11—42no—
209C22×C11#45112yes—
210C22×C11#45112yes—
211C22×C11C2×#12011yescharacteristic
212C22×C11C22×Q1611yescharacteristic
213C22×C11C2×#13711yescharacteristic
214C4×C11—24no—
215C4×C11—22no—
216C4×C11—22no—
217C4×C11—42no—
218Dic11—44no—
219Dic11—44no—
220Dic11—82no—
221Dic11—81no—
222Dic11—81no—
223C22×Q8—112no—
224C22×Q8—111no—
225C22×Q8—221no—
226C23×C4D4411yescharacteristic
227C23×C4D4411yescharacteristic
228C23×C4C22×D1111yescharacteristic
229C2×Q16—224no—
230C22×C8—22no—
231C4⋊Q8—228no—
232C4⋊Q8—228no—
233#125—228no—
234#125—228no—
235C22⋊Q8—114no—
236C22⋊Q8—114no—
237C22⋊Q8—224no—
238C22⋊Q8—222no—
239C22⋊Q8—224no—
240C22⋊Q8—222no—
241C22⋊Q8—222no—
242C22⋊Q8—222no—
243#117—224no—
244#117—224no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—112no—
248C2×C4⋊C4—111no—
249C2×C4⋊C4—221no—
250C2×C4⋊C4—221no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4—222no—
253C2×C4⋊C4—222no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4—221no—
256C2×C4⋊C4—222no—
257C2×C4⋊C4D4412yes—
258C2×C4⋊C4C22×D1112yes—
259C2×C22⋊C4—222no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4—221no—
262C2×C42—222no—
263#107—224no—
264#103—224no—
265#103—224no—
266C22⋊C8—22no—
267C22⋊C8C22×D1114yes—
268#95—112no—
269#95—222no—
270#95—222no—
271#95—222no—
272C2×C11—21no—
273C2×C11—21no—
274C2×C11—22no—
275C2×C11—22no—
276C2×C11C2×#45111yescharacteristic
277C2×C11#302011yescharacteristic
278C2×C11#302611yescharacteristic
279C24C2×D4411yescharacteristic
280C2×Q8—114no—
281C2×Q8—224no—
282C2×Q8—222no—
283C2×Q8—222no—
284C2×Q8—881no—
285C2×Q8—882no—
286C2×Q8—882no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—22no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—81no—
293C22×C4—81no—
294C22×C4—222no—
295C22×C4—222no—
296C22×C4—222no—
297C22×C4—221no—
298C22×C4—221no—
299C22×C4Dic4414yescomplemented
300C22×C4C2×D4412yes—
301C22×C4C2×D4412yes—
302C22×C4C2×D4411yescharacteristic
303C22×C4D4×D1112yes—
304C22×C4D4×D1112yes—
305C22×C4C23×D1111yescharacteristic
306Q16—884no—
307C2×C8—24no—
308C2×C8—82no—
309C4⋊C4—24no—
310C4⋊C4—24no—
311C4⋊C4—114no—
312C4⋊C4—224no—
313C4⋊C4—224no—
314C4⋊C4—224no—
315C4⋊C4—228no—
316C4⋊C4—222no—
317C4⋊C4—224no—
318C4⋊C4—224no—
319C4⋊C4—222no—
320C4⋊C4—442no—
321C4⋊C4—882no—
322C4⋊C4—881no—
323C22⋊C4—224no—
324C22⋊C4—224no—
325C22⋊C4—441no—
326C22⋊C4—441no—
327C22⋊C4—442no—
328C42—228no—
329C11#1829511yescharacteristic, complemented, Sylow
330C23—41no—
331C23—41no—
332C23#6693511yescharacteristic
333C23#6693511yescharacteristic
334C23C2×Dic4412yes—
335C23#6696212yes—
336C23C22×D4411yescharacteristic
337Q8—444no—
338Q8—444no—
339Q8—882no—
340Q8—884no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—22no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—81no—
353C2×C4—224no—
354C2×C4—224no—
355C2×C4—444no—
356C2×C4—444no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4—442no—
360C2×C4—442no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—442no—
364C2×C4#6693512yes—
365C2×C4C2×Dic4414yes—
366C2×C4C2×D4×D1112yes—
367C8—44no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—42no—
375C22—42no—
376C22#1062235212yes—
377C22#1062235212yes—
378C22C2×#6693511yescharacteristic
379C22C22×Dic4411yescharacteristic
380C22C2×#6696211yescharacteristic
381C4—24no—
382C4—22no—
383C4—22no—
384C4—42no—
385C4—444no—
386C4—444no—
387C4—882no—
388C4—881no—
389C4—881no—
390C2—21no—
391C2—21no—
392C2—22no—
393C2—22no—
394C2C2×#1062235211yescharacteristic
395C2#1307798311yescharacteristic
396C2#1307801511yescharacteristic
subgroupG/H
centerC22C2×#66935
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#324C2
socleC22×C11C2×#120
prime radicalC24×C11C2×D4
hypercenterC2×#324D11
hypocenterC11#18295
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
4. #13067660C2semidirect
5. #13067592C2semidirect
90. C22×C4×C11Q16semidirect
299. C22×C4Dic44semidirect
329. C11#18295semidirect

Maximal subgroups

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

subgroupindex
C2×#106230312
#130793912
#130744292
#130676602
#130675922
#130671892
C2×C11×#3242
#1829511