Finite Group Databasebeta

← #14655883

Subgroups — #14655883

Order 2816.

508 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 101 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#13079564C211yesmaximal, characteristic, complemented
3#13069565C211yesmaximal, characteristic, complemented
4#13069560C211yesmaximal, characteristic, complemented
5#13067111C211yesmaximal, characteristic
6#13066467C211yesmaximal, characteristic, complemented
7C11×#3141C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#489—22no—
12C11×#487—21no—
13C11×#486—21no—
14C11×#417—22no—
15C4×C11×M16C2211yescharacteristic
16#10622841—22no—
17#10622707—21no—
18#10622705—21no—
19#10622703—22no—
20#10622694—21no—
21#10622688—21no—
22#10622654—22no—
23#10622632—21no—
24#10622621—21no—
25C4×C4⋊Dic11C2211yescharacteristic
26#10622538C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28#10622193—22no—
29#10622175—22no—
30#10622167—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C2×C11×M16D412yes—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8D412yes—
38C11×C4⋊Q8D411yescharacteristic
39C11×#127D411yescharacteristic
40C11×#124—21no—
41C11×#121—21no—
42C11×#121—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C42×C11C2311yescharacteristic
48C2×#4326—24no—
49C2×#4324—22no—
50#66979—21no—
51C2×C4⋊Dic11—21no—
52#66977—21no—
53#66977—21no—
54C2×C4×Dic11—21no—
55C22×C11⋊C8D412yes—
56#66923—21no—
57#66922D411yescharacteristic
58#66922D411yescharacteristic
59C4×Dic22—21no—
60C4×Dic22—21no—
61C11×#103—24no—
62C11×#102—24no—
63C11×#97—21no—
64C4×C8×C11—21no—
65#66899—24no—
66#66896—22no—
67C11⋊#95—21no—
68C22⋊(C11⋊C8)D412yes—
69#66874—22no—
70#66872—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)—21no—
74C4×C11⋊C8—21no—
75#10198—111nomaximal, Sylow
76C11×#41—42no—
77C11×#41—42no—
78C2×Q8×C11—22no—
79C2×Q8×C11—21no—
80C2×Q8×C11—41no—
81C2×Q8×C11—82no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×Dic11—41no—
92C2×Dic22—21no—
93C2×Dic22—21no—
94C11×M16—22no—
95C11×M16—22no—
96C2×C8×C11—22no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11#4111yescharacteristic
109C22⋊Dic11—41no—
110#4326—84no—
111#4324—82no—
112C4⋊Dic11—22no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—41no—
118Dic11⋊C4—41no—
119Dic11⋊C4—41no—
120C4×Dic11—41no—
121C4×Dic11—42no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—42no—
125#3246—111no—
126#3209—111no—
127#3141D1111yescharacteristic
128#1987—111no—
129#1986—111no—
130#1502—111no—
131#1283—111no—
132C23×C11—41no—
133C23×C11#12711yescharacteristic
134Q8×C11—44no—
135Q8×C11—42no—
136Q8×C11—82no—
137D4×C11—42no—
138D4×C11—41no—
139D4×C11—41no—
140D4×C11—81no—
141D4×C11—81no—
142D4×C11—81no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—42no—
148C2×C4×C11—82no—
149C2×C4×C11—82no—
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#13512yes—
157C2×C4×C11#13712yes—
158C2×Dic11—42no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—81no—
162C2×Dic11—81no—
163Dic22—42no—
164Dic22—41no—
165Dic22—41no—
166C8×C11—42no—
167C11⋊C8—42no—
168C11⋊C8—42no—
169#533—111no—
170#532C2×D1111yescharacteristic
171C2×C4⋊Q8C2×D1111yescharacteristic
172#494—221no—
173#489—22no—
174#487—21no—
175#487—221no—
176#486—21no—
177#476—221no—
178#475—221no—
179#465—222no—
180#462—222no—
181#461—221no—
182#460—221no—
183#451—222no—
184#431—111no—
185C2×C4⋊C8—111no—
186#417—22no—
187C4×M16C2×D1111yescharacteristic
188C4×C4⋊C4—111no—
189#340—222no—
190#339—222no—
191#327—222no—
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—82no—
210Dic11—81no—
211Dic11—81no—
212C2×#41—21no—
213C22×Q8—21no—
214C2×Q16—224no—
215C2×SD16—222no—
216C2×M16C22⋊D1112yes—
217C22×C8—112no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—111no—
222C4⋊Q8—111no—
223C4⋊Q8C22⋊D1112yes—
224C4⋊Q8C22⋊D1111yescharacteristic
225#127C22⋊D1111yescharacteristic
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—21no—
239C2×C4⋊C4—221no—
240C2×C42—221no—
241C2×C42C22×D1111yescharacteristic
242#106—222no—
243C4⋊C8—221no—
244C4⋊C8—221no—
245C4⋊C8—221no—
246#103—24no—
247#103—222no—
248#103—224no—
249#102—24no—
250#102—222no—
251C22⋊C8—112no—
252#97—21no—
253C4×C8—21no—
254C4×C8—221no—
255#95—221no—
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—22no—
265C2×Q8—21no—
266C2×Q8—41no—
267C2×Q8—82no—
268C2×Q8—221no—
269C2×Q8—221no—
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—22no—
283M16—22no—
284C2×C8—22no—
285C2×C8—222no—
286C2×C8—222no—
287C2×C8—442no—
288C4⋊C4—21no—
289C4⋊C4—22no—
290C4⋊C4—21no—
291C4⋊C4—22no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—222no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—441no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—441no—
305C42—441no—
306C42—442no—
307C42D4×D1111yescharacteristic
308C42#434111yescharacteristic
309C42C2×C22⋊D1111yescharacteristic
310C42C2×C22⋊D1111yescharacteristic
311C11#1019811yescharacteristic, complemented, Sylow
312C23—41no—
313C23#6699311yescharacteristic
314Q8—44no—
315Q8—42no—
316Q8—82no—
317Q8—442no—
318Q8—441no—
319Q8—441no—
320D4—41no—
321D4—41no—
322D4—42no—
323D4—81no—
324D4—81no—
325D4—81no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—82no—
332C2×C4—82no—
333C2×C4—442no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—881no—
337C2×C4—881no—
338C2×C4#6699011yescharacteristic
339C2×C4#6699011yescharacteristic
340C2×C4#6699111yescharacteristic
341C2×C4#6699211yescharacteristic
342C2×C4#6699211yescharacteristic
343C2×C4#6700312yes—
344C2×C4#6700412yes—
345C2×C4#6700611yescharacteristic
346C8—42no—
347C8—442no—
348C8—442no—
349C22—21no—
350C22—21no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22#1062267211yescharacteristic
355C22#1062267311yescharacteristic
356C22#1062283611yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—82no—
361C4—81no—
362C4—882no—
363C4—881no—
364C4—881no—
365C4#1062266712yes—
366C4#1062281511yescharacteristic
367C4#1062281811yescharacteristic
368C4#1062285212yes—
369C2—21no—
370C2—21no—
371C2—161no—
372C2#1306966111yescharacteristic
373C2#1306966711yescharacteristic
374C2#1306971011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3141C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#3141D11
hypocenterC11#10198
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
2. #13079564C2semidirect
3. #13069565C2semidirect
4. #13069560C2semidirect
6. #13066467C2semidirect
311. C11#10198semidirect

Maximal subgroups

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

subgroupindex
#130799322
#130795642
#130695652
#130695602
#130671112
#130664672
C11×#31412
#1019811