Finite Group Databasebeta

← #14655907

Subgroups — #14655907

Order 2816.

528 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 107 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#13079932C211yesmaximal, characteristic
2#13079741C211yesmaximal, characteristic
3#13079162C211yesmaximal, characteristic, complemented
4#13069539C211yesmaximal, characteristic, complemented
5#13067114C211yesmaximal, characteristic, complemented
6#13066467C211yesmaximal, characteristic, complemented
7C11×#1980C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C2×C11×#104—22no—
12C4×C11×M16C2211yescharacteristic
13C4×C11×C4⋊C4C2211yescharacteristic
14#10622734—22no—
15#10622707—21no—
16#10622692—21no—
17#10622688—21no—
18#10622683—21no—
19#10622654—22no—
20#10622647—22no—
21#10622632—21no—
22#10622621—21no—
23#10622621—22no—
24C2×#66874—22no—
25#10622538C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27#10622315—22no—
28#10622295—21no—
29#10622293—21no—
30#10622090—22no—
31C2×C11×#41—21no—
32C22×Dic22—21no—
33C2×C11×M16D412yes—
34C11×C4⋊Q8D411yescharacteristic
35C11×#127D411yescharacteristic
36C11×#124—21no—
37C11×#121—21no—
38C11×#121—21no—
39C4×D4×C11—21no—
40C4×D4×C11—21no—
41C2×C11×C4⋊C4—21no—
42C2×C42×C11—21no—
43C2×C42×C11C2311yescharacteristic
44C2×#4324—22no—
45#66979—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48#66977—21no—
49#66977—21no—
50C22×C11⋊C8D412yes—
51#66923—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922D412yes—
56#66922D411yescharacteristic
57#66922D411yescharacteristic
58C4×Dic22—21no—
59C4×Dic22—21no—
60C11×#104—44no—
61C11×#97—21no—
62C4×C8×C11—21no—
63C11×#95—21no—
64#66896—24no—
65#66896—22no—
66C22⋊(C11⋊C8)D412yes—
67#66882—24no—
68#66881—24no—
69#66874—22no—
70#66874—44no—
71#66872—24no—
72#66872—22no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76C4×C11⋊C8—21no—
77#10201—111nomaximal, Sylow
78C11×#41—42no—
79C11×#41—42no—
80C2×Q8×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×Dic11—41no—
91C2×Dic22—21no—
92C2×Dic22—22no—
93C2×Dic22—21no—
94C2×Dic22—42no—
95C2×Dic22—42no—
96C2×Dic22—41no—
97C11×M16—22no—
98C11×M16SD1614yescomplemented
99C2×C8×C11—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C42×C11—42no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11#4111yescharacteristic
111C22⋊Dic11—41no—
112#4324—82no—
113C4⋊Dic11—21no—
114C4⋊Dic11—22no—
115C4⋊Dic11—21no—
116C4⋊Dic11—22no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123C4×Dic11—41no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—42no—
127#3246—111no—
128#3227—111no—
129#3165—111no—
130#1981—111no—
131#1980D1111yescharacteristic
132#1503—111no—
133#1283—111no—
134C23×C11—41no—
135C23×C11#12711yescharacteristic
136Q8×C11—42no—
137D4×C11—42no—
138D4×C11—41no—
139D4×C11—41no—
140D4×C11—42no—
141D4×C11—81no—
142D4×C11—81no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—41no—
148C2×C4×C11—81no—
149C2×C4×C11—81no—
150C2×C4×C11—82no—
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11C2×SD1612yes—
158C2×C4×C11#13712yes—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—42no—
162C2×Dic11—82no—
163Dic22—44no—
164Dic22—41no—
165Dic22—41no—
166Dic22—81no—
167Dic22—81no—
168Dic22—81no—
169C8×C11—24no—
170C11⋊C8—42no—
171C11⋊C8—42no—
172#533—111no—
173#532C2×D1111yescharacteristic
174C2×C4⋊Q8—111no—
175#501—222no—
176#500—221no—
177#498—221no—
178#498—221no—
179#486—221no—
180#481—222no—
181#476—222no—
182#476—221no—
183#475—221no—
184#465—222no—
185#461—221no—
186#460—221no—
187#431—111no—
188#428—222no—
189C2×C4⋊C8—111no—
190C2×#104—22no—
191C2×#103—222no—
192C4×M16C2×D1111yescharacteristic
193C4×C4⋊C4C2×D1111yescharacteristic
194#328—222no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11#39211yescharacteristic
201C22×C11#49211yescharacteristic
202C22×C11#49711yescharacteristic
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—82no—
207C4×C11—81no—
208C4×C11#44812yes—
209C4×C11#45311yescharacteristic
210C4×C11#45411yescharacteristic
211C4×C11#46112yes—
212Dic11—82no—
213Dic11—81no—
214Dic11—81no—
215C2×#41—21no—
216C22×Q8—221no—
217C2×SD16—222no—
218C2×M16C22⋊D1112yes—
219C22×C8—112no—
220C4⋊Q8—112no—
221C4⋊Q8—111no—
222C4⋊Q8—111no—
223C4⋊Q8—221no—
224C4⋊Q8—221no—
225C4⋊Q8—221no—
226C4⋊Q8D4411yescharacteristic
227#127D4411yescharacteristic
228#125—221no—
229#124—21no—
230C22⋊Q8—221no—
231C22⋊Q8—221no—
232#121—21no—
233#121—21no—
234C4×Q8—221no—
235C4×Q8—221no—
236C4×D4—21no—
237C4×D4—21no—
238#117—221no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—221no—
242C2×C42—21no—
243C2×C42C22×D1111yescharacteristic
244#107—224no—
245#106—222no—
246#106—224no—
247#106—224no—
248C4⋊C8—221no—
249C4⋊C8—221no—
250C4⋊C8—221no—
251#104—44no—
252#103—222no—
253#103—444no—
254#102—222no—
255#102—224no—
256C22⋊C8—112no—
257#97—21no—
258C4×C8—21no—
259C4×C8—221no—
260#95—21no—
261C2×C11—21no—
262C2×C11—21no—
263C2×C11—161no—
264C2×C11#200611yescharacteristic
265C2×C11#200911yescharacteristic
266C2×C11#201311yescharacteristic
267#41—42no—
268#41—42no—
269C2×Q8—21no—
270C2×Q8—221no—
271C2×Q8—222no—
272C2×Q8—221no—
273C2×Q8—442no—
274C2×Q8—442no—
275C2×Q8—441no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—441no—
283C22×C4D4×D1111yescharacteristic
284C22×C4D4×D1111yescharacteristic
285C22×C4C2×C22⋊D1111yescharacteristic
286SD16—882no—
287M16—22no—
288M16#432414yescomplemented
289C2×C8—22no—
290C2×C8—222no—
291C2×C8—222no—
292C2×C8—442no—
293C4⋊C4—22no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—222no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—222no—
302C4⋊C4—221no—
303C4⋊C4—441no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C4⋊C4—441no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—441no—
310C42—42no—
311C42—441no—
312C42C2×D4411yescharacteristic
313C42#433911yescharacteristic
314C42D4×D1111yescharacteristic
315C42D4×D1111yescharacteristic
316C11#1020111yescharacteristic, complemented, Sylow
317C23—41no—
318C23#6699311yescharacteristic
319Q8—42no—
320Q8—444no—
321Q8—441no—
322Q8—441no—
323Q8—881no—
324Q8—881no—
325Q8—881no—
326D4—42no—
327D4—42no—
328D4—41no—
329D4—41no—
330D4—81no—
331D4—81no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—82no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—442no—
343C2×C4—882no—
344C2×C4#6693511yescharacteristic
345C2×C4#6693511yescharacteristic
346C2×C4#6693711yescharacteristic
347C2×C4#6693711yescharacteristic
348C2×C4#6698311yescharacteristic
349C2×C4C2×#432412yes—
350C2×C4#6699011yescharacteristic
351C2×C4#6700412yes—
352C8—24no—
353C8—442no—
354C8—442no—
355C22—21no—
356C22—21no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22#1062257311yescharacteristic
361C22#1062267311yescharacteristic
362C22#1062268911yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—81no—
368C4—882no—
369C4—881no—
370C4—881no—
371C4#1062243511yescharacteristic
372C4#1062244011yescharacteristic
373C4#1062263212yes—
374C4#1062265312yes—
375C2—21no—
376C2—21no—
377C2—161no—
378C2#1306965911yescharacteristic
379C2#1306967711yescharacteristic
380C2#1306969811yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1980C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#1980D11
hypocenterC11#10201
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
3. #13079162C2semidirect
4. #13069539C2semidirect
5. #13067114C2semidirect
6. #13066467C2semidirect
98. C11×M16SD16semidirect
288. M16#4324semidirect
316. C11#10201semidirect

Maximal subgroups

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

subgroupindex
#130799322
#130797412
#130791622
#130695392
#130671142
#130664672
C11×#19802
#1020111