Finite Group Databasebeta

← #14664825

Subgroups — #14664825

Order 2816.

476 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 79 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#13073614C211yesmaximal, characteristic
2#13068611C211yesmaximal, characteristic, complemented
3#13066938C211yesmaximal, characteristic, complemented
4#13066620C211yesmaximal, characteristic, complemented
5#13066619C211yesmaximal, characteristic, complemented
6#13066618C211yesmaximal, characteristic, complemented
7C11×#1345C211yesmaximal, characteristic, complemented
8C2×#66993C411yescharacteristic
9C2×#66940C2211yescharacteristic
10C2×#66938—21no—
11C11×#394C2211yescharacteristic
12#10622835C411yescharacteristic
13C2×#66888—21no—
14#10622731—21no—
15#10622604C2211yescharacteristic
16#10622570—21no—
17#10622570—21no—
18#10622570—21no—
19#10622331—21no—
20#10622285C411yescharacteristic
21#10622262C411yescharacteristic
22C11×#343C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622166C2211yescharacteristic
26#10622107—21no—
27C22×D4×C11C2×C411yescharacteristic
28C22×C22⋊D11—21no—
29C22×C22⋊D11—21no—
30C22×D44C2×C411yescharacteristic
31C22×Dic22D411yescharacteristic
32C2×C11×M16—21no—
33C2×C11×C4⋊C4C2311yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38#66993—41no—
39#66993—41no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4C2×C411yescharacteristic
46C2×Dic11⋊C4D411yescharacteristic
47C2×C4×Dic11—21no—
48C2×C4×Dic11C2×C411yescharacteristic
49C2×C4×Dic11D411yescharacteristic
50C2×C4×Dic11D411yescharacteristic
51C2×#4318—21no—
52#66940—41no—
53#66940—41no—
54#66938—42no—
55#66938—42no—
56C11×C22⋊C8—21no—
57C11×#95C2×C411yescharacteristic
58C11⋊#95C2×C411yescharacteristic
59C22⋊(C11⋊C8)—21no—
60#66888—42no—
61Dic11⋊C8—41no—
62Dic11⋊C8—41no—
63Dic11⋊C8—41no—
64C8×Dic11—41no—
65#11882—111nomaximal, Sylow
66C24×C11—21no—
67C23×D11—21no—
68C2×D4×C11—41no—
69C2×D4×C11—81no—
70C22×C4×C11—21no—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C2×C22⋊D11—42no—
75C2×C22⋊D11—42no—
76C2×C22⋊D11—42no—
77C2×C22⋊D11—42no—
78C2×C22⋊D11—41no—
79C2×C22⋊D11—41no—
80C2×C22⋊D11—42no—
81C22×Dic11—21no—
82C22×Dic11C22⋊C411yescharacteristic
83C22×Dic11C22⋊C411yescharacteristic
84C22×Dic11C22⋊C411yescharacteristic
85C22×Dic11C22⋊C411yescharacteristic
86C2×D44—41no—
87C2×D44—81no—
88C2×Dic22—41no—
89C2×Dic22—41no—
90C2×Dic22D812yes—
91C2×Dic22SD1612yes—
92C11×M16—41no—
93C11×M16—41no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C11×C4⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—81no—
100C22⋊Dic11—42no—
101C22⋊Dic11—81no—
102(C2×D11)⋊C4—42no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—81no—
106(C2×D11)⋊C4—81no—
107Dic11⋊C4—41no—
108Dic11⋊C4—41no—
109Dic11⋊C4—42no—
110C4×Dic11—21no—
111C4×Dic11—21no—
112C4×Dic11—21no—
113C4×Dic11—21no—
114C4×Dic11—21no—
115C4×Dic11—21no—
116C4×Dic11—42no—
117#4318—41no—
118#4318—41no—
119C2×C11⋊C8—41no—
120C2×C11⋊C8—41no—
121#2548—111no—
122#1801—111no—
123#1461—111no—
124#1345—111no—
125#1345—111no—
126#1345—111no—
127#1345D1111yescharacteristic, complemented
128C23×C11—41no—
129C23×C11—41no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11C2×C22⋊C411yescharacteristic
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143D4×C11—82no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11C2×D811yescharacteristic
154C2×C4×C11C2×SD1611yescharacteristic
155C22⋊D11—82no—
156C22⋊D11—84no—
157C22⋊D11—82no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—22no—
163C2×Dic11—21no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11#9911yescharacteristic
169C2×Dic11#9911yescharacteristic
170C2×Dic11#10212yes—
171C2×Dic11#10212yes—
172D44—82no—
173Dic22—42no—
174Dic22—42no—
175C8×C11—81no—
176C8×C11—81no—
177C11⋊C8—81no—
178C11⋊C8—81no—
179C2×#127—111no—
180C2×#124—221no—
181C2×C4×Q8—111no—
182#431—221no—
183#423—221no—
184C2×#101—221no—
185#394—111no—
186#394—111no—
187#394—111no—
188#394C2×D1111yescharacteristic
189#390—221no—
190#390—221no—
191#390—221no—
192C4×C4⋊C4—111no—
193#343—111no—
194#343C2×D1111yescharacteristic
195#324—111no—
196#324—221no—
197#324C2×D1111yescharacteristic
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11C2×#9911yescharacteristic
208C22×C11C2×#10211yescharacteristic
209C22×C11#42111yescharacteristic
210C2×D11—81no—
211C2×D11—81no—
212C2×D11—81no—
213C2×D11—81no—
214C2×D11—81no—
215C2×D11—81no—
216C2×D11—81no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—41no—
220C4×C11—41no—
221C4×C11—81no—
222Dic11—21no—
223Dic11—22no—
224Dic11—22no—
225Dic11—41no—
226Dic11—81no—
227Dic11#35512yes—
228C22×Q8—111no—
229C22×D4—111no—
230C22×D4—221no—
231C22×D4—221no—
232C22×D4C4×D1111yescharacteristic
233C2×M16—21no—
234C2×M16—221no—
235#127—441no—
236#127—441no—
237#124—442no—
238#124—442no—
239C4×Q8—441no—
240C4×Q8—441no—
241C2×C4⋊C4—111no—
242C2×C4⋊C4—111no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4C22×D1111yescharacteristic
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—221no—
248C2×C22⋊C4—221no—
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4—221no—
252C2×C22⋊C4—221no—
253C2×C42—111no—
254C2×C42—111no—
255C2×C42—111no—
256C2×C42—221no—
257C4⋊C8—441no—
258C4⋊C8—441no—
259C4⋊C8—441no—
260#101—442no—
261C22⋊C8—21no—
262C22⋊C8—221no—
263C4×C8—441no—
264#95—111no—
265#95C4×D1111yescharacteristic
266C2×C11—21no—
267C2×C11—21no—
268C2×C11—161no—
269C2×C11#151911yescharacteristic
270C2×C11#212211yescharacteristic
271C2×C11C2×#35511yescharacteristic
272D11—161no—
273C24—21no—
274C24—221no—
275C2×Q8—112no—
276C2×Q8—112no—
277C2×Q8—441no—
278C2×Q8—441no—
279C2×D4—41no—
280C2×D4—81no—
281C2×D4—441no—
282C2×D4—442no—
283C2×D4—441no—
284C2×D4—441no—
285C2×D4—442no—
286C2×D4—442no—
287C2×D4—442no—
288C2×D4—442no—
289C2×D4—881no—
290C22×C4—21no—
291C22×C4—111no—
292C22×C4—111no—
293C22×C4—111no—
294C22×C4—111no—
295C22×C4—221no—
296C22×C4C2×C4×D1111yescharacteristic
297C22×C4D4×D1111yescharacteristic
298C22×C4D4×D1111yescharacteristic
299M16—41no—
300M16—41no—
301M16—441no—
302M16—441no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—441no—
306C2×C8—441no—
307C4⋊C4—41no—
308C4⋊C4—441no—
309C4⋊C4—441no—
310C4⋊C4—442no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—81no—
314C22⋊C4—442no—
315C22⋊C4—442no—
316C22⋊C4—441no—
317C22⋊C4—441no—
318C22⋊C4—881no—
319C22⋊C4—881no—
320C22⋊C4—881no—
321C42—221no—
322C42—221no—
323C42—221no—
324C42—221no—
325C42—221no—
326C42—221no—
327C42—442no—
328C11#1188211yescharacteristic, complemented, Sylow
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—441no—
337C23—441no—
338C23—441no—
339C23—441no—
340C23—441no—
341C23—441no—
342C23—441no—
343C23C22⋊C4×D1111yescharacteristic
344Q8—442no—
345Q8—442no—
346D4—82no—
347D4—882no—
348D4—882no—
349D4—884no—
350D4—882no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—111no—
361C2×C4—111no—
362C2×C4—112no—
363C2×C4—112no—
364C2×C4—222no—
365C2×C4—221no—
366C2×C4—221no—
367C2×C4—221no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4D8×D1111yescharacteristic
375C2×C4SD16×D1111yescharacteristic
376C8—81no—
377C8—81no—
378C8—881no—
379C8—881no—
380C22—21no—
381C22—21no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22—881no—
390C22—881no—
391C22—881no—
392C22—881no—
393C22—881no—
394C22—881no—
395C22—881no—
396C22D11×#9911yescharacteristic
397C22D11×#10211yescharacteristic
398C22#1062243411yescharacteristic
399C4—21no—
400C4—21no—
401C4—41no—
402C4—41no—
403C4—81no—
404C4—112no—
405C4—222no—
406C4—222no—
407C4—221no—
408C4—441no—
409C4—881no—
410C2—21no—
411C2—21no—
412C2—161no—
413C2—1761no—
414C2#1306718211yescharacteristic
415C2#1307026411yescharacteristic
416C2D11×#35511yescharacteristic
subgroupG/H
centerC22D11×#99
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1345C2
socleC22×C11C2×#99
prime radicalC2×#66993C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1345D11
hypocenterC11#11882
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1345

Complements

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

NH ≅ G/Ntype
2. #13068611C2semidirect
3. #13066938C2semidirect
4. #13066620C2semidirect
5. #13066619C2semidirect
6. #13066618C2semidirect
7. C11×#1345C2semidirect
127. #1345D11semidirect
328. C11#11882semidirect

Maximal subgroups

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

subgroupindex
#130736142
#130686112
#130669382
#130666202
#130666192
#130666182
C11×#13452
#1188211