Finite Group Databasebeta

← #14727696

Subgroups — #14727696

Order 2816.

940 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079388C212yesmaximal
2#13074429C211yesmaximal, characteristic
3#13067658C214yesmaximal, complemented
4#13067590C214yesmaximal, complemented
5#13067188C212yesmaximal
6C2×#10622166C211yesmaximal, characteristic
7C2×C11×#544C211yesmaximal, characteristic
8C11×#544—24no—
9C11×#544—22no—
10C11×#544C2214yes—
11C2×C11×C4⋊Q8—22no—
12C2×C11×#125—22no—
13C2×C11×C22⋊Q8—21no—
14C2×C11×C22⋊Q8C2212yes—
15C2×C11×#117—21no—
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×#66977C2211yescharacteristic
18#10622841—22no—
19#10622825C2211yescharacteristic
20#10622824—21no—
21#10622823—21no—
22C2×C22⋊(C11⋊C8)C2212yes—
23#10622664—24no—
24#10622663C2214yes—
25#10622657C2214yes—
26#10622599C2212yes—
27#10622597—22no—
28#10622592C2212yes—
29#10622583—22no—
30#10622176C2218yes—
31#10622166C2214yes—
32C22×Q8×C11—21no—
33C22×Q8×C11D412yes—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C22×Dic22C2311yescharacteristic
38C11×C4⋊Q8—28no—
39C11×C4⋊Q8—28no—
40C11×#125—28no—
41C11×#125—28no—
42C11×C22⋊Q8—24no—
43C11×C22⋊Q8—24no—
44C11×C22⋊Q8—22no—
45C11×C22⋊Q8—22no—
46C11×C22⋊Q8D414yes—
47C11×C22⋊Q8C2314yes—
48C11×#117—24no—
49C11×#117—24no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4D412yes—
58C2×C11×C4⋊C4D412yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C22⋊C4—22no—
61C2×C42×C11—22no—
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—21no—
64C2×#4326—24no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11C2311yescharacteristic
67#66977—22no—
68#66977—22no—
69C2×Dic11⋊C4—21no—
70C2×Dic11⋊C4—22no—
71C22×C11⋊C8—22no—
72#66899—24no—
73C11⋊#95—22no—
74C11⋊#95—22no—
75C11⋊#95—22no—
76C11⋊#95C2312yes—
77C22⋊(C11⋊C8)—22no—
78C22⋊(C11⋊C8)C2314yes—
79#66874—24no—
80#66871—24no—
81#18295—111nomaximal, Sylow
82C24×C11C2×D411yescharacteristic
83C2×Q8×C11—24no—
84C2×Q8×C11—22no—
85C2×Q8×C11—82no—
86C2×Q8×C11—82no—
87C2×Q8×C11C2×D414yes—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—81no—
96C22×C4×C11—81no—
97C22×C4×C11Q1614yescomplemented
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—21no—
105C22×Dic11—22no—
106C22×Dic11—21no—
107C2×Dic22—22no—
108C2×Dic22—81no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—28no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—24no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4C2×D414yes—
119C11×C22⋊C4—24no—
120C11×C22⋊C4—24no—
121C42×C11—28no—
122C22⋊Dic11—41no—
123C22⋊Dic11—41no—
124C22⋊Dic11—42no—
125#4326—84no—
126C4⋊Dic11—22no—
127C4⋊Dic11—81no—
128Dic11⋊C4—42no—
129Dic11⋊C4—82no—
130C2×C11⋊C8—24no—
131C2×C11⋊C8—82no—
132C2×#544D1111yescharacteristic
133#3189—112no—
134#2627—111no—
135#1617—114no—
136#1605—114no—
137#1520—112no—
138C2×#324—111no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11#12011yescharacteristic
142C23×C11#12011yescharacteristic
143C23×C11C2×Q1612yes—
144C23×C11#13712yes—
145C23×C11C22×D411yescharacteristic
146Q8×C11—44no—
147Q8×C11—82no—
148Q8×C11—84no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—24no—
152C2×C4×C11—24no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—22no—
156C2×C4×C11—42no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—44no—
161C2×C4×C11—42no—
162C2×C4×C11—44no—
163C2×C4×C11—42no—
164C2×C4×C11—81no—
165C2×C4×C11#12012yes—
166C2×C4×C11C2×Q1614yes—
167C2×C4×C11C22×D412yes—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—42no—
175Dic22—44no—
176C11⋊C8—44no—
177#544—24no—
178#544—22no—
179#544C2×D1114yes—
180C2×C4⋊Q8—22no—
181C2×#125—22no—
182C2×C22⋊Q8—21no—
183C2×C22⋊Q8—111no—
184C2×C22⋊Q8C2×D1112yes—
185C2×#117—21no—
186C22×C4⋊C4C2×D1111yescharacteristic
187#484—114no—
188#484—222no—
189#467—224no—
190#451—114no—
191#451—222no—
192C2×C22⋊C8—112no—
193#400—112no—
194#398—222no—
195#395—112no—
196#385—221no—
197#381—221no—
198#380—111no—
199#328—118no—
200#324—114no—
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—44no—
218C4×C11—42no—
219C4×C11—44no—
220Dic11—82no—
221Dic11—81no—
222Dic11—81no—
223C22×Q8—21no—
224C22×Q8—111no—
225C22×Q8C22⋊D1112yes—
226C23×C4C22⋊D1111yescharacteristic
227C23×C4C22⋊D1111yescharacteristic
228C23×C4C22×D1111yescharacteristic
229C2×Q16—224no—
230C22×C8—222no—
231C4⋊Q8—28no—
232C4⋊Q8—28no—
233#125—28no—
234#125—28no—
235C22⋊Q8—24no—
236C22⋊Q8—24no—
237C22⋊Q8—22no—
238C22⋊Q8—22no—
239C22⋊Q8—222no—
240C22⋊Q8—222no—
241C22⋊Q8C22⋊D1114yes—
242C22⋊Q8C22×D1114yes—
243#117—24no—
244#117—24no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4—221no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4—222no—
256C2×C4⋊C4C22⋊D1112yes—
257C2×C4⋊C4C22⋊D1112yes—
258C2×C4⋊C4C22×D1112yes—
259C2×C22⋊C4—22no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4—221no—
262C2×C42—22no—
263#107—224no—
264#103—224no—
265#103—224no—
266C22⋊C8—114no—
267C22⋊C8—222no—
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×C22⋊D1111yescharacteristic
280C2×Q8—24no—
281C2×Q8—22no—
282C2×Q8—82no—
283C2×Q8—82no—
284C2×Q8—222no—
285C2×Q8—881no—
286C2×Q8C2×C22⋊D1114yes—
287C22×C4—22no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—81no—
295C22×C4—81no—
296C22×C4—222no—
297C22×C4—221no—
298C22×C4—221no—
299C22×C4#432614yescomplemented
300C22×C4C2×C22⋊D1112yes—
301C22×C4C2×C22⋊D1112yes—
302C22×C4C2×C22⋊D1111yescharacteristic
303C22×C4C2×C22⋊D1112yes—
304C22×C4C2×C22⋊D1112yes—
305C22×C4C23×D1111yescharacteristic
306Q16—884no—
307C2×C8—224no—
308C2×C8—882no—
309C4⋊C4—24no—
310C4⋊C4—24no—
311C4⋊C4—24no—
312C4⋊C4—28no—
313C4⋊C4—24no—
314C4⋊C4—24no—
315C4⋊C4—22no—
316C4⋊C4—24no—
317C4⋊C4—24no—
318C4⋊C4—222no—
319C4⋊C4—442no—
320C4⋊C4—882no—
321C4⋊C4—881no—
322C4⋊C4C2×C22⋊D1114yes—
323C22⋊C4—24no—
324C22⋊C4—24no—
325C22⋊C4—442no—
326C22⋊C4—441no—
327C22⋊C4—441no—
328C42—28no—
329C11#1829511yescharacteristic, complemented, Sylow
330C23—41no—
331C23—41no—
332C23#6699512yes—
333C23C2×#432612yes—
334C23#6700611yescharacteristic
335C23#6700611yescharacteristic
336C23C22×C22⋊D1111yescharacteristic
337Q8—44no—
338Q8—82no—
339Q8—84no—
340Q8—444no—
341C2×C4—22no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—22no—
345C2×C4—24no—
346C2×C4—24no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—44no—
353C2×C4—42no—
354C2×C4—44no—
355C2×C4—42no—
356C2×C4—81no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4—442no—
360C2×C4—442no—
361C2×C4—442no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4C2×#432614yes—
365C2×C4#6700612yes—
366C2×C4C22×C22⋊D1112yes—
367C8—444no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—42no—
375C22—42no—
376C22#1062284112yes—
377C22#1062284112yes—
378C22C2×#6699511yescharacteristic
379C22C22×#432611yescharacteristic
380C22C2×#6700611yescharacteristic
381C4—24no—
382C4—22no—
383C4—22no—
384C4—44no—
385C4—42no—
386C4—44no—
387C4—882no—
388C4—881no—
389C4—881no—
390C2—21no—
391C2—21no—
392C2—22no—
393C2—22no—
394C2C2×#1062284111yescharacteristic
395C2#1307798011yescharacteristic
396C2#1307801311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#544C2
socleC22×C11C2×#120
prime radicalC24×C11C2×D4
hypercenterC2×#544D11
hypocenterC11#18295
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
3. #13067658C2semidirect
4. #13067590C2semidirect
97. C22×C4×C11Q16semidirect
299. C22×C4#4326semidirect
329. C11#18295semidirect

Maximal subgroups

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

subgroupindex
#130793882
#130744292
#130676582
#130675902
#130671882
C2×#106221662
C2×C11×#5442
#1829511