Finite Group Databasebeta

← #14655700

Subgroups — #14655700

Order 2816.

562 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 109 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#13079744C211yesmaximal, characteristic
2#13079073C211yesmaximal, characteristic
3#13069606C211yesmaximal, characteristic, complemented
4#13067288C211yesmaximal, characteristic, complemented
5#13067068C211yesmaximal, characteristic
6#13066453C211yesmaximal, characteristic, complemented
7C2×C11×#498C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66995—22no—
11#10623008C2211yescharacteristic
12C11×#498—22no—
13C11×#498—22no—
14C2×C11×#106—22no—
15C2×C4×C8×C11C2211yescharacteristic
16#10622705—21no—
17#10622701—21no—
18#10622699—22no—
19#10622698—21no—
20#10622697—22no—
21#10622692—21no—
22#10622581—22no—
23#10622538C2211yescharacteristic
24#10622537C2211yescharacteristic
25C4×#4318C2211yescharacteristic
26#10622185—22no—
27#10622168—22no—
28#10622097—22no—
29C22×Q8×C11—21no—
30C22×Q8×C11—21no—
31C2×#4339—21no—
32C22×C8×C11—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8D412yes—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4D412yes—
45C2×C42×C11C2311yescharacteristic
46C2×#4326—24no—
47#66995—44no—
48#66995—44no—
49C2×#4325—24no—
50#66983—21no—
51#66983—21no—
52C2×#4318—21no—
53C2×#4318D412yes—
54#66928—21no—
55#66927D411yescharacteristic
56C4×D44—21no—
57C4×D44—21no—
58#66922D411yescharacteristic
59C11×#106—28no—
60C4×C8×C11—21no—
61C4×C8×C11D412yes—
62C22⋊(C11⋊C8)—21no—
63#66873—24no—
64#66872—24no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)D412yes—
68#66867—21no—
69C4×C11⋊C8—21no—
70C4×C11⋊C8—21no—
71#10172—111nomaximal, Sylow
72C2×Q8×C11—22no—
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C2×Q8×C11—41no—
76C2×Q8×C11—42no—
77C2×Q8×C11—42no—
78C2×Q8×C11—82no—
79C22×C4×C11—22no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C2×C22⋊D11—41no—
85#4339—42no—
86#4339—42no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×C4×D11—41no—
91C2×Dic22—21no—
92C2×C8×C11—24no—
93C2×C8×C11—22no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—22no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106#4326—48no—
107#4325—48no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112#4318—22no—
113#4318—42no—
114#4318SD1614yes—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—41no—
118#3227—111no—
119C2×#498D1111yescharacteristic, complemented
120#3152—111no—
121#1997—111no—
122#1546—111no—
123#1492—111no—
124#1278—111no—
125C23×C11#12111yescharacteristic
126C22×D11—41no—
127Q8×C11—44no—
128Q8×C11—82no—
129Q8×C11—82no—
130Q8×C11—81no—
131Q8×C11—81no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—82no—
137C2×C4×C11—82no—
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12711yescharacteristic
144C2×C4×C11C2×SD1612yes—
145C2×C4×C11AGL(1,ℤ/8)12yes—
146C22⋊D11—82no—
147C2×Dic11—41no—
148D44—42no—
149D44—42no—
150D44—42no—
151C4×D11—81no—
152C4×D11—81no—
153Dic22—42no—
154C8×C11—24no—
155C11⋊C8—24no—
156C11⋊C8—42no—
157C11⋊C8—81no—
158C2×#137—222no—
159#532—111no—
160C2×C4⋊Q8C2×D1111yescharacteristic
161C2×C4⋊Q8C2×D1111yescharacteristic
162#498—22no—
163#498—22no—
164#498—221no—
165#497—222no—
166#494—221no—
167#492—221no—
168#486—221no—
169#481—222no—
170#476—222no—
171#431—111no—
172C2×#106—22no—
173#423—111no—
174C4×M16—111no—
175C2×C4×C8C2×D1111yescharacteristic
176#343—222no—
177#332—222no—
178D4⋊C8—222no—
179C22×C11—21no—
180C22×C11—21no—
181C22×C11#39211yescharacteristic
182C22×C11#46012yes—
183C2×D11—81no—
184C2×D11—81no—
185C2×D11—81no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—82no—
189C4×C11—82no—
190C4×C11#45012yes—
191C4×C11#45612yes—
192C4×C11#47112yes—
193C4×C11#49211yescharacteristic
194C4×C11#49611yescharacteristic
195Dic11—81no—
196C2×#41—221no—
197C22×Q8—21no—
198C22×Q8—21no—
199#137—444no—
200#137—444no—
201C2×Q16—224no—
202C2×SD16—224no—
203C2×M16—112no—
204C2×M16—221no—
205C22×C8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—111no—
214C4⋊Q8C22⋊D1112yes—
215#127—111no—
216#124—221no—
217#121—221no—
218#121—221no—
219C4×D4—221no—
220C4×D4—221no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4C22⋊D1112yes—
225C2×C42C22×D1111yescharacteristic
226#106—28no—
227#106—224no—
228C4⋊C8—112no—
229C4⋊C8—221no—
230C4⋊C8—221no—
231#102—224no—
232C22⋊C8—221no—
233#97—221no—
234C4×C8—21no—
235C4×C8—221no—
236C4×C8—221no—
237C4×C8C22⋊D1112yes—
238C2×C11—22no—
239C2×C11#200511yescharacteristic
240C2×C11#201411yescharacteristic
241C2×C11#201911yescharacteristic
242D11—161no—
243#41—442no—
244#41—442no—
245C2×Q8—22no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—42no—
250C2×Q8—42no—
251C2×Q8—82no—
252C2×Q8—221no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4—441no—
257C22×C4—22no—
258C22×C4—41no—
259C22×C4—441no—
260C22×C4D4×D1111yescharacteristic
261C22×C4#434111yescharacteristic
262C22×C4C2×C22⋊D1111yescharacteristic
263Q16—448no—
264SD16—448no—
265M16—114no—
266M16—222no—
267M16—442no—
268C2×C8—24no—
269C2×C8—22no—
270C2×C8—222no—
271C2×C8—222no—
272C2×C8—441no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C22⋊C4—441no—
284C22⋊C4—441no—
285C42D4×D1111yescharacteristic
286C42D4×D1111yescharacteristic
287C42C2×C22⋊D1111yescharacteristic
288C42C2×C22⋊D1111yescharacteristic
289C11#1017211yescharacteristic, complemented, Sylow
290C23—441no—
291C23#6699211yescharacteristic
292Q8—44no—
293Q8—82no—
294Q8—81no—
295Q8—81no—
296Q8—82no—
297Q8—442no—
298D4—442no—
299D4—442no—
300D4—442no—
301D4—882no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—82no—
307C2×C4—82no—
308C2×C4—441no—
309C2×C4—881no—
310C2×C4—881no—
311C2×C4SD16×D1112yes—
312C2×C4#6696712yes—
313C2×C4#6699011yescharacteristic
314C2×C4#6699011yescharacteristic
315C2×C4#6699111yescharacteristic
316C2×C4#6699211yescharacteristic
317C2×C4#6699311yescharacteristic
318C2×C4#6700611yescharacteristic
319C8—24no—
320C8—224no—
321C8—442no—
322C8—881no—
323C22—21no—
324C22—21no—
325C22—881no—
326C22—881no—
327C22—881no—
328C22#1062277612yes—
329C22#1062283611yescharacteristic
330C4—21no—
331C4—21no—
332C4—82no—
333C4—82no—
334C4—881no—
335C4#1062270812yes—
336C4#1062278212yes—
337C4#1062278811yescharacteristic
338C4#1062278911yescharacteristic
339C4#1062279012yes—
340C2—22no—
341C2—1761no—
342C2#1306965211yescharacteristic
343C2#1306970211yescharacteristic
344C2#1306972811yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#498C2
socleC22×C11#392
prime radical#10623008C22
hypercenterC2×#498D11
hypocenterC11#10172
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
3. #13069606C2semidirect
4. #13067288C2semidirect
6. #13066453C2semidirect
7. C2×C11×#498C2semidirect
119. C2×#498D11semidirect
289. C11#10172semidirect

Maximal subgroups

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

subgroupindex
#130797442
#130790732
#130696062
#130672882
#130670682
#130664532
C2×C11×#4982
#1017211