Finite Group Databasebeta

← #14771591

Subgroups — #14771591

Order 2816.

724 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071023C211yesmaximal, characteristic
2#13069339C212yesmaximal, complemented
3#13069179C212yesmaximal, complemented
4#13069172C212yesmaximal, complemented
5#13068598C212yesmaximal
6#13068596C211yesmaximal, characteristic
7#13068488C212yesmaximal, complemented
8#13068384C212yesmaximal
9C11×#1749C211yesmaximal, characteristic
10C22×C42×C11C2211yescharacteristic
11C2×#66979C2212yes—
12C2×C11×C22⋊C8C2211yescharacteristic
13C2×C11×C22⋊C8C2211yescharacteristic
14C2×C11×#97C2212yes—
15#10622825C412yes—
16#10622825C411yescharacteristic
17#10622825C411yescharacteristic
18C2×C22⋊(C11⋊C8)C2212yes—
19C2×#66879C2212yes—
20C2×Dic11⋊C8C2212yes—
21C2×Dic11⋊C8C2212yes—
22C2×C8×Dic11C2212yes—
23#10622549C412yes—
24#10622548C411yescharacteristic
25#10622548C411yescharacteristic
26C4×C4⋊Dic11C2211yescharacteristic
27C4×C4⋊Dic11C2212yes—
28C4×C4⋊Dic11C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2212yes—
30C11×#336C2212yes—
31#10622188C2212yes—
32#10622188C2212yes—
33#10622188C2212yes—
34#10622188C2212yes—
35#10622162C2211yescharacteristic
36#10622162C2211yescharacteristic
37C23×C4×C11C2×C411yescharacteristic
38C23×C4×C11C2×C411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C22×C8×C11C2312yes—
41C22×C8×C11C2312yes—
42C2×C42×C11—24no—
43C2×C42×C11C2×C411yescharacteristic
44C2×C42×C11C2×C411yescharacteristic
45C2×C42×C11C2311yescharacteristic
46C2×C42×C11C2311yescharacteristic
47C2×C22⋊Dic11C2×C412yes—
48C2×C22⋊Dic11C2×C412yes—
49#66979—42no—
50#66979—42no—
51C2×C4⋊Dic11C2×C412yes—
52C2×C4⋊Dic11C2×C411yescharacteristic
53C2×C4⋊Dic11C2×C411yescharacteristic
54C2×C4⋊Dic11C2×C411yescharacteristic
55C2×C4⋊Dic11C2×C411yescharacteristic
56C2×C4⋊Dic11C2×C412yes—
57C2×C4⋊Dic11C2×C412yes—
58C2×C4⋊Dic11C2×C412yes—
59C2×C4×Dic11C2312yes—
60C2×C4×Dic11C2312yes—
61C22×C11⋊C8C2312yes—
62C22×C11⋊C8C2312yes—
63C11×C22⋊C8—22no—
64C11×C22⋊C8Q814yes—
65C11×#97—24no—
66C11⋊#95C2×C412yes—
67C11⋊#95C2×C412yes—
68C11⋊#95C2×C412yes—
69C11⋊#95C2×C412yes—
70C22⋊(C11⋊C8)—24no—
71#66879—42no—
72Dic11⋊C8—42no—
73Dic11⋊C8—42no—
74C8×Dic11—42no—
75C4⋊(C11⋊C8)—24no—
76#22628—111nomaximal, Sylow
77C24×C11C22×C411yescharacteristic
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C2×Q812yes—
92C22×C4×C11#4112yes—
93C22×C4×C11C2411yescharacteristic
94C22×Dic11C22×C412yes—
95C22×Dic11C22×C412yes—
96C22×Dic11C22×C412yes—
97C22×Dic11C22×C412yes—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11C2×Q814yes—
104C42×C11—22no—
105C42×C11—22no—
106C42×C11—22no—
107C42×C11#4114yes—
108C22⋊Dic11—42no—
109C22⋊Dic11—42no—
110C4⋊Dic11—24no—
111C4⋊Dic11—41no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115C4⋊Dic11—42no—
116C4⋊Dic11—42no—
117C4⋊Dic11—42no—
118C4×Dic11—22no—
119C4×Dic11—22no—
120C4×Dic11—22no—
121C4×Dic11—22no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128#2285—111no—
129#1940—112no—
130#1917—112no—
131#1916—112no—
132#1798—112no—
133#1797—111no—
134#1771—112no—
135#1750—112no—
136#1749D1111yescharacteristic
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11C4×Q812yes—
144C23×C11C23×C411yescharacteristic
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—24no—
154C2×C4×C11—24no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—44no—
159C2×C4×C11—44no—
160C2×C4×C11#11712yes—
161C2×C4×C11#11712yes—
162C2×C4×C11C4×Q812yes—
163C2×C4×C11#13112yes—
164C2×C4×C11C22×Q811yescharacteristic
165C2×C4×C11C2×#4111yescharacteristic
166C2×C4×C11C2×#4112yes—
167C2×C4×C11H(5,𝔽2)12yes—
168C2×Dic11—22no—
169C2×Dic11—22no—
170C2×Dic11—22no—
171C2×Dic11—22no—
172C2×Dic11—22no—
173C2×Dic11—22no—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—22no—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C8×C11—24no—
181C8×C11—42no—
182C11⋊C8—42no—
183C11⋊C8—42no—
184C2×#117—112no—
185C22×C42C2×D1111yescharacteristic
186C2×C4⋊C8—112no—
187C2×C4⋊C8—112no—
188C2×C4⋊C8—112no—
189C2×C22⋊C8—112no—
190C2×C22⋊C8C2×D1111yescharacteristic
191C2×C22⋊C8C2×D1111yescharacteristic
192C2×#97—112no—
193C2×#97C2×D1112yes—
194C2×C4×C8—112no—
195#384—111no—
196#384—111no—
197#382—112no—
198#380—112no—
199#380—111no—
200#380—111no—
201C4×C4⋊C4—112no—
202C4×C4⋊C4—111no—
203C4×C4⋊C4—111no—
204#336—112no—
205#336—112no—
206#336—112no—
207#336—112no—
208#336—111no—
209#336—111no—
210#336C2×D1112yes—
211C22×C11—22no—
212C22×C11—22no—
213C22×C11—22no—
214C22×C11—41no—
215C22×C11—41no—
216C22×C11—41no—
217C22×C11—41no—
218C22×C11C2×#11711yescharacteristic
219C22×C11C2×C4×Q811yescharacteristic
220C22×C11#51811yescharacteristic
221C22×C11C2×#13111yescharacteristic
222C22×C11#56811yescharacteristic
223C22×C11#56811yescharacteristic
224C22×C11#56811yescharacteristic
225C4×C11—22no—
226C4×C11—22no—
227C4×C11—22no—
228C4×C11—22no—
229C4×C11—41no—
230C4×C11#55312yes—
231C4×C11#55412yes—
232Dic11—42no—
233Dic11—42no—
234Dic11—42no—
235Dic11—42no—
236C23×C4C4×D1111yescharacteristic
237C23×C4C4×D1111yescharacteristic
238C23×C4C22×D1111yescharacteristic
239C22×C8—112no—
240C22×C8—112no—
241C22×C8C22×D1112yes—
242C22×C8C22×D1112yes—
243#117—442no—
244#117—442no—
245C2×C4⋊C4—112no—
246C2×C4⋊C4—112no—
247C2×C4⋊C4—112no—
248C2×C4⋊C4—111no—
249C2×C4⋊C4—111no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—111no—
252C2×C4⋊C4—112no—
253C2×C22⋊C4—112no—
254C2×C22⋊C4—112no—
255C2×C42—24no—
256C2×C42—112no—
257C2×C42—112no—
258C2×C42C4×D1111yescharacteristic
259C2×C42C4×D1111yescharacteristic
260C2×C42C22×D1111yescharacteristic
261C2×C42C22×D1111yescharacteristic
262C4⋊C8—224no—
263C4⋊C8—442no—
264C4⋊C8—442no—
265C22⋊C8—22no—
266C22⋊C8—224no—
267C22⋊C8Dic2214yes—
268#97—24no—
269#97—442no—
270C4×C8—442no—
271#95—112no—
272#95—112no—
273#95—112no—
274#95—112no—
275C2×C11—42no—
276C2×C11#234511yescharacteristic
277C2×C11#292111yescharacteristic
278C2×C11#292411yescharacteristic
279C2×C11#296111yescharacteristic
280C2×C11#296211yescharacteristic
281C2×C11#298011yescharacteristic
282C2×C11#298111yescharacteristic
283C24C2×C4×D1111yescharacteristic
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—112no—
293C22×C4—112no—
294C22×C4—112no—
295C22×C4—112no—
296C22×C4C2×Dic2212yes—
297C22×C4C2×C4×D1111yescharacteristic
298C22×C4C2×C4×D1111yescharacteristic
299C22×C4C2×C4×D1111yescharacteristic
300C22×C4C2×C4×D1111yescharacteristic
301C22×C4C2×C4×D1111yescharacteristic
302C22×C4#433912yes—
303C22×C4C23×D1111yescharacteristic
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—222no—
310C2×C8—222no—
311C2×C8—222no—
312C2×C8—222no—
313C2×C8—222no—
314C2×C8—222no—
315C2×C8C2×Dic2214yes—
316C4⋊C4—224no—
317C4⋊C4—442no—
318C4⋊C4—442no—
319C4⋊C4—441no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C4⋊C4—441no—
323C4⋊C4—442no—
324C22⋊C4—442no—
325C22⋊C4—442no—
326C42—22no—
327C42—22no—
328C42—22no—
329C42—222no—
330C42—222no—
331C42—222no—
332C42—222no—
333C42#434114yes—
334C11#2262811yescharacteristic, complemented, Sylow
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23C4×Dic2212yes—
342C23C22×C4×D1111yescharacteristic
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—24no—
352C2×C4—24no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—44no—
357C2×C4—44no—
358C2×C4—222no—
359C2×C4—222no—
360C2×C4—222no—
361C2×C4—222no—
362C2×C4—222no—
363C2×C4—222no—
364C2×C4—222no—
365C2×C4—222no—
366C2×C4—222no—
367C2×C4—222no—
368C2×C4—222no—
369C2×C4—222no—
370C2×C4C4×Dic2212yes—
371C2×C4#6693012yes—
372C2×C4#6693012yes—
373C2×C4#6696012yes—
374C2×C4C22×Dic2211yescharacteristic
375C2×C4C2×#433911yescharacteristic
376C2×C4C2×#434112yes—
377C2×C4#6704212yes—
378C8—24no—
379C8—42no—
380C8—442no—
381C8—442no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22C2×C4×Dic2211yescharacteristic
390C22C2×#6693011yescharacteristic
391C22#1062305211yescharacteristic
392C22C2×#6696011yescharacteristic
393C22#1062327611yescharacteristic
394C22#1062327611yescharacteristic
395C22#1062327611yescharacteristic
396C4—22no—
397C4—22no—
398C4—22no—
399C4—22no—
400C4—41no—
401C4—442no—
402C4—442no—
403C4—442no—
404C4—442no—
405C4#1062307412yes—
406C4#1062309612yes—
407C2—42no—
408C2#1307149111yescharacteristic
409C2#1307725111yescharacteristic
410C2#1307727611yescharacteristic
411C2#1307755611yescharacteristic
412C2#1307756311yescharacteristic
413C2#1307768611yescharacteristic
414C2#1307769411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1749C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1749D11
hypocenterC11#22628
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. #13069339C2semidirect
3. #13069179C2semidirect
4. #13069172C2semidirect
7. #13068488C2semidirect
334. C11#22628semidirect

Maximal subgroups

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

subgroupindex
#130710232
#130693392
#130691792
#130691722
#130685982
#130685962
#130684882
#130683842
C11×#17492
#2262811