Finite Group Databasebeta

← #14758041

Subgroups — #14758041

Order 2816.

766 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4326C211yesmaximal, characteristic
2#13071268C211yesmaximal, characteristic
3#13069476C212yesmaximal
4#13069346C212yesmaximal
5#13069309C212yesmaximal
6#13069305C212yesmaximal
7C4×#66871C211yesmaximal, characteristic
8#13068449C211yesmaximal, characteristic
9#13068446C211yesmaximal, characteristic
10#13068303C211yesmaximal, characteristic
11C11×#2320C211yesmaximal, characteristic
12C2×C4×Q8×C11C2211yescharacteristic
13C22×#4326C2211yescharacteristic
14C2×C4×Dic22C2211yescharacteristic
15C11×#391C2212yes—
16C11×#389C2212yes—
17C11×#387—22no—
18C11×#383—21no—
19C11×#382—21no—
20C4×C11×C4⋊C4C2211yescharacteristic
21C11×#376C2211yescharacteristic
22C2×#66899C2212yes—
23C2×#66899C2211yescharacteristic
24C4×#4326C418yescomplemented
25C2×#66874C2212yes—
26C2×#66874C2211yescharacteristic
27C2×#66871C2212yes—
28C2×#66871C2211yescharacteristic
29C4×C4⋊Dic11C2211yescharacteristic
30#10622542C2212yes—
31#10622541C2212yes—
32C2×#66867C2211yescharacteristic
33C2×#66867C2212yes—
34C2×C4×C11⋊C8C2212yes—
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622265—22no—
37#10622264—21no—
38#10622263—21no—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×Q8×C11C2311yescharacteristic
43C22×Dic22C2311yescharacteristic
44C4×Q8×C11—22no—
45C4×Q8×C11C2×C414yes—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C42×C11—21no—
51C2×C42×C11—21no—
52C2×C42×C11C2312yes—
53C2×C42×C11C2311yescharacteristic
54C2×#4326—24no—
55C2×#4326C2×C414yes—
56C2×C4⋊Dic11C2312yes—
57C2×C4⋊Dic11C2311yescharacteristic
58C2×Dic11⋊C4—21no—
59C2×Dic11⋊C4—22no—
60C2×C4×Dic11—21no—
61C2×C4×Dic11—21no—
62C22×C11⋊C8C2311yescharacteristic
63C22×C11⋊C8C2312yes—
64C22×C11⋊C8C2311yescharacteristic
65C4×Dic22—22no—
66C4×Dic22C2×C414yes—
67C11×#95—21no—
68C11×#95—22no—
69C11×#95—22no—
70C11×#95—22no—
71C11×#95D411yescharacteristic
72C11×#95D411yescharacteristic
73C11×#95D412yes—
74#66899—24no—
75#66899C2×C414yes—
76C11⋊#95—21no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80#66874—24no—
81#66874C2×C414yes—
82#66871—24no—
83#66871C2×C414yes—
84#66867—22no—
85#66867—24no—
86C4×C11⋊C8—24no—
87C4×C11⋊C8C2×C414yes—
88#21281—111nomaximal, Sylow
89C2×Q8×C11—21no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11C22×C412yes—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—22no—
104C2×Dic22—22no—
105C2×Dic22—22no—
106C2×Dic22—21no—
107C2×Dic22C22×C412yes—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—82no—
113C11×C4⋊C4C22×C412yes—
114C42×C11—24no—
115C42×C11—22no—
116C42×C11—22no—
117C42×C11—81no—
118C42×C11C22×C412yes—
119C42×C11#4112yes—
120#4326—28no—
121C4⋊Dic11—21no—
122C4⋊Dic11—22no—
123C4⋊Dic11—22no—
124C4⋊Dic11C22×C412yes—
125Dic11⋊C4—24no—
126Dic11⋊C4—82no—
127C4×Dic11—24no—
128C4×Dic11—81no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8C22×C412yes—
133C2×C11⋊C8C22×C412yes—
134C2×C11⋊C8#4114yes—
135C2×C11⋊C8#4114yes—
136C2×C4×Q16—111no—
137#2320—111no—
138#2320D1111yescharacteristic
139#1969—112no—
140#1942—112no—
141#1935—112no—
142#1935—112no—
143C4×#107—111no—
144#1763—111no—
145#1763—111no—
146#1726—111no—
147C23×C11C22×D411yescharacteristic
148Q8×C11—22no—
149Q8×C11—22no—
150Q8×C11—42no—
151C2×C4×C11—21no—
152C2×C4×C11—22no—
153C2×C4×C11—21no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—42no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11C4×D412yes—
169C2×C4×C11C4×D412yes—
170C2×C4×C11C23×C411yescharacteristic
171C2×C4×C11C2×#4111yescharacteristic
172C2×C4×C11C2×#4112yes—
173C2×C4×C11C2×#4112yes—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—42no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182Dic22—22no—
183Dic22—22no—
184Dic22—42no—
185C11⋊C8—22no—
186C11⋊C8—24no—
187C11⋊C8#11714yes—
188C22×Q16—111no—
189C2×C4×Q8—111no—
190C2×C4×Q8C2×D1111yescharacteristic
191C4×Q16—118no—
192C2×#107—111no—
193C2×#107—112no—
194C2×#103—111no—
195C2×#103—111no—
196C2×#103—112no—
197C2×#103—112no—
198C2×#97—112no—
199C2×#97—111no—
200C2×C4×C8—111no—
201C2×C4×C8—112no—
202#391—112no—
203#391C2×D1112yes—
204#389—112no—
205#389C2×D1112yes—
206#387—22no—
207#387—222no—
208#383—21no—
209#383—221no—
210#382—21no—
211#382—221no—
212C4×C4⋊C4—111no—
213C4×C4⋊C4C2×D1111yescharacteristic
214#376C2×D1111yescharacteristic
215#340—112no—
216#340—112no—
217#340—112no—
218C22×C11C2×C4×D411yescharacteristic
219C22×C11#53212yes—
220C22×C11#57611yescharacteristic
221C22×C11#57812yes—
222C22×C11#57811yescharacteristic
223C4×C11—22no—
224C4×C11—22no—
225C4×C11—42no—
226C4×C11—42no—
227C4×C11—42no—
228C4×C11—42no—
229C4×C11—82no—
230C4×C11C2×#11711yescharacteristic
231C4×C11C4×#4111yescharacteristic
232C4×C11#52912yes—
233Dic11—42no—
234Dic11—42no—
235Dic11—82no—
236C22×Q8—111no—
237C22×Q8C22×D1111yescharacteristic
238C2×Q16—114no—
239C2×Q16—224no—
240C22×C8—111no—
241C22×C8—111no—
242C22×C8—112no—
243C4×Q8—22no—
244C4×Q8—114no—
245C4×Q8—222no—
246C4×Q8C4×D1114yes—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—111no—
250C2×C4⋊C4—112no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4—222no—
253C2×C4⋊C4C22×D1112yes—
254C2×C4⋊C4C22×D1111yescharacteristic
255C2×C42—21no—
256C2×C42—21no—
257C2×C42—221no—
258C2×C42—221no—
259C2×C42C22×D1112yes—
260C2×C42C22×D1111yescharacteristic
261#107—114no—
262#107—224no—
263#103—114no—
264#103—114no—
265#103—224no—
266#103—224no—
267#97—224no—
268#97—222no—
269C4×C8—114no—
270C4×C8—224no—
271#95—21no—
272#95—22no—
273#95—22no—
274#95—22no—
275#95—221no—
276#95—222no—
277#95—222no—
278#95—222no—
279#95C22⋊D1111yescharacteristic
280#95C22⋊D1111yescharacteristic
281#95C22⋊D1112yes—
282C2×C11#229311yescharacteristic
283C2×C11#295011yescharacteristic
284C2×C11#295111yescharacteristic
285C2×C11#317512yes—
286C2×C11#317712yes—
287C2×Q8—21no—
288C2×Q8—22no—
289C2×Q8—22no—
290C2×Q8—112no—
291C2×Q8—221no—
292C2×Q8—222no—
293C2×Q8—222no—
294C2×Q8C2×C4×D1112yes—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—221no—
299C22×C4—221no—
300C22×C4—222no—
301C22×C4C2×C22⋊D1112yes—
302C22×C4C2×C22⋊D1112yes—
303C22×C4C2×C22⋊D1111yescharacteristic
304C22×C4C2×C22⋊D1111yescharacteristic
305C22×C4C23×D1111yescharacteristic
306Q16—228no—
307C2×C8—112no—
308C2×C8—114no—
309C2×C8—112no—
310C2×C8—114no—
311C2×C8—222no—
312C2×C8—222no—
313C2×C8—222no—
314C4⋊C4—24no—
315C4⋊C4—21no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—82no—
319C4⋊C4—112no—
320C4⋊C4—224no—
321C4⋊C4—221no—
322C4⋊C4—222no—
323C4⋊C4—222no—
324C4⋊C4—882no—
325C4⋊C4C2×C4×D1112yes—
326C42—24no—
327C42—22no—
328C42—22no—
329C42—81no—
330C42—224no—
331C42—881no—
332C42C2×C4×D1112yes—
333C42#433912yes—
334C11#2128111yescharacteristic, complemented, Sylow
335C23C22×C22⋊D1111yescharacteristic
336Q8—22no—
337Q8—22no—
338Q8—42no—
339Q8—222no—
340Q8—222no—
341Q8—442no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—222no—
360C2×C4—222no—
361C2×C4—442no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4C4×C22⋊D1112yes—
368C2×C4C4×C22⋊D1112yes—
369C2×C4C22×C4×D1111yescharacteristic
370C2×C4C2×#433911yescharacteristic
371C2×C4#41×D1112yes—
372C2×C4#41×D1112yes—
373C8—114no—
374C8—222no—
375C8—224no—
376C22C2×C4×C22⋊D1111yescharacteristic
377C22#1062336312yes—
378C22#1062336611yescharacteristic
379C22#1062336912yes—
380C22#1062336911yescharacteristic
381C4—22no—
382C4—22no—
383C4—42no—
384C4—42no—
385C4—42no—
386C4—42no—
387C4—82no—
388C4—442no—
389C4—442no—
390C4—882no—
391C4D11×#11711yescharacteristic
392C4#1062305311yescharacteristic
393C4#1062305912yes—
394C2#1307107511yescharacteristic
395C2#1307748211yescharacteristic
396C2#1307748911yescharacteristic
397C2#1307924912yes—
398C2#1307926912yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2320C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#2320D11
hypocenterC11#21281
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2320

Complements

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

NH ≅ G/Ntype
24. C4×#4326C4semidirect
334. C11#21281semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43262
#130712682
#130694762
#130693462
#130693092
#130693052
C4×#668712
#130684492
#130684462
#130683032
C11×#23202
#2128111