Finite Group Databasebeta

← #14655887

Subgroups — #14655887

Order 2816.

508 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 99 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#13079566C211yesmaximal, characteristic, complemented
3#13079009C211yesmaximal, characteristic
4#13069564C211yesmaximal, characteristic, complemented
5#13069559C211yesmaximal, characteristic, complemented
6#13066465C211yesmaximal, characteristic, complemented
7C11×#1502C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13#10622845—22no—
14#10622707—21no—
15#10622694—21no—
16#10622688—21no—
17#10622683—21no—
18#10622668—22no—
19#10622654—22no—
20#10622632—21no—
21#10622621—21no—
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23C4×#4318C2211yescharacteristic
24#10622462—22no—
25#10622352—22no—
26#10622312—21no—
27#10622294—21no—
28C11×#327—22no—
29#10622167—22no—
30#10622161—22no—
31C2×C11×#41—21no—
32C22×Dic22—21no—
33C11×C4⋊Q8D411yescharacteristic
34C11×#127D411yescharacteristic
35C11×#124—21no—
36C11×#121—21no—
37C11×#121—21no—
38C4×D4×C11—21no—
39C4×D4×C11—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11—21no—
42C2×C42×C11C2311yescharacteristic
43C2×#4324—22no—
44#66979—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47#66977—21no—
48#66977—21no—
49C2×#4318D412yes—
50C22×C11⋊C8D412yes—
51C2×Dic44—24no—
52#66923—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56#66922D412yes—
57#66922D411yescharacteristic
58#66922D411yescharacteristic
59C4×Dic22—21no—
60C4×Dic22—21no—
61C11×C4⋊C8—21no—
62C11×C22⋊C8D412yes—
63C4×C8×C11—21no—
64C11×#95—21no—
65#66899—24no—
66#66896—24no—
67#66896—22no—
68#66880—24no—
69#66874—22no—
70#66872—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73#66867—21no—
74C4×C11⋊C8—21no—
75#10198—111nomaximal, Sylow
76C11×#41—42no—
77C11×#41—42no—
78C2×Q8×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×Dic11—41no—
89C2×Dic22—21no—
90C2×Dic22—22no—
91C2×Dic22—21no—
92C2×Dic22—41no—
93C2×Dic22—82no—
94C2×C8×C11—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C22⋊C4—41no—
100C11×C22⋊C4—41no—
101C42×C11—42no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11#4111yescharacteristic
106C22⋊Dic11—41no—
107#4324—82no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—41no—
115C4⋊Dic11—41no—
116Dic11⋊C4—41no—
117Dic11⋊C4—41no—
118C4×Dic11—41no—
119#4318—22no—
120#4318—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—42no—
124Dic44—84no—
125#3246—111no—
126#3209—111no—
127#3141—111no—
128#1987—111no—
129#1986—111no—
130#1502D1111yescharacteristic
131#1283—111no—
132C23×C11—41no—
133C23×C11#12711yescharacteristic
134Q8×C11—42no—
135D4×C11—42no—
136D4×C11—41no—
137D4×C11—41no—
138D4×C11—81no—
139D4×C11—81no—
140D4×C11—81no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—41no—
144C2×C4×C11—42no—
145C2×C4×C11—41no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C2×C4×C11—82no—
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#13512yes—
156C2×C4×C11#13712yes—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—42no—
160C2×Dic11—82no—
161Dic22—42no—
162Dic22—44no—
163Dic22—41no—
164Dic22—41no—
165Dic22—82no—
166C8×C11—42no—
167C11⋊C8—42no—
168C11⋊C8—42no—
169#533—111no—
170#532C2×D1111yescharacteristic
171C2×C4⋊Q8—111no—
172#494—221no—
173#489—222no—
174#487—221no—
175#487—221no—
176#486—221no—
177#476—221no—
178#475—221no—
179#465—222no—
180#462—222no—
181#461—221no—
182#460—221no—
183#451—222no—
184#431C2×D1111yescharacteristic
185C2×C4⋊C8—111no—
186#417—222no—
187C4×M16—111no—
188C4×C4⋊C4C2×D1111yescharacteristic
189#340—222no—
190#339—222no—
191#327—22no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11#39211yescharacteristic
198C22×C11#49511yescharacteristic
199C22×C11#49711yescharacteristic
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—82no—
204C4×C11—81no—
205C4×C11#45212yes—
206C4×C11#45511yescharacteristic
207C4×C11#45611yescharacteristic
208C4×C11#46412yes—
209Dic11—81no—
210Dic11—82no—
211Dic11—81no—
212C2×#41—21no—
213C22×Q8—221no—
214C2×Q16—224no—
215C2×SD16—222no—
216C2×M16—112no—
217C22×C8—112no—
218C4⋊Q8—112no—
219C4⋊Q8—111no—
220C4⋊Q8—111no—
221C4⋊Q8—221no—
222C4⋊Q8—221no—
223C4⋊Q8—221no—
224C4⋊Q8D4411yescharacteristic
225#127D4411yescharacteristic
226#125—221no—
227#124—21no—
228C22⋊Q8—221no—
229C22⋊Q8—221no—
230#121—21no—
231#121—21no—
232C4×Q8—221no—
233C4×Q8—221no—
234C4×D4—21no—
235C4×D4—21no—
236#117—221no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4—221no—
240C2×C42—21no—
241C2×C42C22×D1111yescharacteristic
242#106—222no—
243C4⋊C8—21no—
244C4⋊C8—221no—
245C4⋊C8—221no—
246#103—222no—
247#103—224no—
248#103—224no—
249#102—224no—
250#102—222no—
251C22⋊C8C22⋊D1112yes—
252#97—221no—
253C4×C8—21no—
254C4×C8—221no—
255#95—21no—
256C2×C11—21no—
257C2×C11—21no—
258C2×C11—161no—
259C2×C11#200711yescharacteristic
260C2×C11#200811yescharacteristic
261C2×C11#201511yescharacteristic
262#41—42no—
263#41—42no—
264C2×Q8—21no—
265C2×Q8—221no—
266C2×Q8—222no—
267C2×Q8—221no—
268C2×Q8—441no—
269C2×Q8—882no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—441no—
277C22×C4D4×D1111yescharacteristic
278C22×C4D4×D1111yescharacteristic
279C22×C4C2×C22⋊D1111yescharacteristic
280Q16—884no—
281SD16—882no—
282M16—222no—
283M16—222no—
284C2×C8—22no—
285C2×C8—222no—
286C2×C8—222no—
287C2×C8—442no—
288C4⋊C4—22no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—41no—
292C4⋊C4—222no—
293C4⋊C4—221no—
294C4⋊C4—222no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—441no—
299C4⋊C4—441no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—441no—
305C42—42no—
306C42—441no—
307C42C2×D4411yescharacteristic
308C42#433911yescharacteristic
309C42D4×D1111yescharacteristic
310C42D4×D1111yescharacteristic
311C11#1019811yescharacteristic, complemented, Sylow
312C23—41no—
313C23#6699311yescharacteristic
314Q8—42no—
315Q8—442no—
316Q8—444no—
317Q8—441no—
318Q8—441no—
319Q8—882no—
320D4—42no—
321D4—41no—
322D4—41no—
323D4—81no—
324D4—81no—
325D4—81no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—82no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—442no—
337C2×C4—882no—
338C2×C4#6693511yescharacteristic
339C2×C4#6693511yescharacteristic
340C2×C4#6693711yescharacteristic
341C2×C4#6693711yescharacteristic
342C2×C4#6696512yes—
343C2×C4#6696812yes—
344C2×C4#6698311yescharacteristic
345C2×C4#6699011yescharacteristic
346C8—42no—
347C8—442no—
348C8—442no—
349C22—21no—
350C22—21no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22#1062257311yescharacteristic
355C22#1062276811yescharacteristic
356C22#1062278011yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—82no—
361C4—81no—
362C4—881no—
363C4—882no—
364C4—881no—
365C4#1062238012yes—
366C4#1062239612yes—
367C4#1062243811yescharacteristic
368C4#1062243911yescharacteristic
369C2—21no—
370C2—21no—
371C2—161no—
372C2#1306966411yescharacteristic
373C2#1306966811yescharacteristic
374C2#1306971211yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1502C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#1502D11
hypocenterC11#10198
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1502

Complements

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

NH ≅ G/Ntype
2. #13079566C2semidirect
4. #13069564C2semidirect
5. #13069559C2semidirect
6. #13066465C2semidirect
311. C11#10198semidirect

Maximal subgroups

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

subgroupindex
#130799322
#130795662
#130790092
#130695642
#130695592
#130664652
C11×#15022
#1019811