Finite Group Databasebeta

← #14655421

Subgroups — #14655421

Order 2816.

558 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079599C211yesmaximal, characteristic
2C2×#10622699C211yesmaximal, characteristic, complemented
3#13067333C211yesmaximal, characteristic, complemented
4#13067227C211yesmaximal, characteristic, complemented
5#13066967C211yesmaximal, characteristic, complemented
6#13066516C211yesmaximal, characteristic, complemented
7C11×#3227C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C22×#4326—21no—
11C22×#4325—21no—
12C2×#66928C2211yescharacteristic
13C11×#498—21no—
14C11×#486—21no—
15C11×#481—22no—
16C11×#476—22no—
17C11×#431C2211yescharacteristic
18#10622702—21no—
19#10622699—22no—
20#10622699—22no—
21#10622687—21no—
22#10622653—21no—
23#10622649—21no—
24#10622629—22no—
25#10622539C2211yescharacteristic
26#10622539C2211yescharacteristic
27C2×#66867C2211yescharacteristic
28#10622185—22no—
29#10622178—22no—
30#10622106—22no—
31C2×C11×#41—21no—
32C22×Q8×C11—21no—
33C22×D44D411yescharacteristic
34C22×Dic22D411yescharacteristic
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D411yescharacteristic
39C11×C4⋊Q8D412yes—
40C11×#127D411yescharacteristic
41C11×#124—21no—
42C11×#121—21no—
43C11×#121—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4326—24no—
50C2×#4326—44no—
51C2×#4325—24no—
52C2×#4325—44no—
53C2×#4324—22no—
54C2×#4323—22no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—21no—
57C22×C11⋊C8—21no—
58#66928—21no—
59#66928—21no—
60#66928—21no—
61#66928—21no—
62C11×#106—24no—
63C11×C4⋊C8—21no—
64C11×#102—24no—
65C11×C22⋊C8D412yes—
66C4×C8×C11—21no—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69#66874—22no—
70#66873—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)D412yes—
73#66867—21no—
74#66867—21no—
75#66867—21no—
76#66867D412yes—
77#10132—111nomaximal, Sylow
78C23×D11—21no—
79C11×#41—82no—
80C2×Q8×C11—22no—
81C2×Q8×C11—21no—
82C2×Q8×C11—42no—
83C2×Q8×C11—42no—
84C2×Q8×C11—41no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×Dic11—21no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—42no—
98C2×Dic22—21no—
99C2×Dic22—21no—
100C2×Dic22—42no—
101C2×C8×C11—22no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114#4326—48no—
115#4325—48no—
116#4324—82no—
117#4323—82no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—41no—
120(C2×D11)⋊C4—41no—
121(C2×D11)⋊C4—41no—
122C2×C11⋊C8—24no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—41no—
126#3227D1111yescharacteristic, complemented
127#3213—111no—
128C2×#497—111no—
129#1556—111no—
130#1530—111no—
131#1469—111no—
132#1302—111no—
133C23×C11—41no—
134C23×C11#12111yescharacteristic
135C22×D11—41no—
136C22×D11—42no—
137C22×D11—81no—
138C22×D11—81no—
139Q8×C11—42no—
140Q8×C11—42no—
141Q8×C11—81no—
142Q8×C11—82no—
143D4×C11—42no—
144D4×C11—42no—
145D4×C11—81no—
146D4×C11—82no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—42no—
152C2×C4×C11—82no—
153C2×C4×C11—82no—
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12711yescharacteristic
160C2×Dic11—41no—
161C2×Dic11—81no—
162D44—42no—
163D44—42no—
164Dic22—42no—
165Dic22—42no—
166C8×C11—42no—
167C11⋊C8—24no—
168C11⋊C8—42no—
169C11⋊C8—81no—
170C22×Q16—221no—
171C22×SD16—221no—
172#532C2×D1111yescharacteristic
173C2×C4⋊Q8C2×D1111yescharacteristic
174C2×#124—111no—
175#498—21no—
176#497—222no—
177#497—222no—
178#496—221no—
179#489—221no—
180#486—21no—
181#481—22no—
182#476—22no—
183#463—222no—
184#448—221no—
185#447—221no—
186#432—111no—
187#432—111no—
188#431C2×D1111yescharacteristic
189C2×#97—111no—
190#332—222no—
191#329—222no—
192#323—222no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11#39211yescharacteristic
199C22×C11#47112yes—
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C2×D11—162no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—82no—
210C4×C11—81no—
211C4×C11#45312yes—
212Dic11—81no—
213C2×#41—21no—
214C22×Q8—21no—
215C22×Q8—111no—
216C22×D4—111no—
217C2×Q16—224no—
218C2×Q16—444no—
219C2×SD16—224no—
220C2×SD16—222no—
221C2×SD16—444no—
222C2×D8—222no—
223C22×C8—221no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8C22⋊D1112yes—
228C4⋊Q8C22⋊D1111yescharacteristic
229#127C22⋊D1111yescharacteristic
230#124—21no—
231#124—221no—
232#124—221no—
233#124—221no—
234#124—221no—
235#121—21no—
236#121—21no—
237C4×D4—21no—
238C4×D4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C22⋊C4—221no—
242C2×C22⋊C4—221no—
243C2×C42C22×D1111yescharacteristic
244#106—24no—
245C4⋊C8—21no—
246C4⋊C8—112no—
247C4⋊C8—221no—
248#103—222no—
249#102—24no—
250#102—222no—
251C22⋊C8—221no—
252C22⋊C8—221no—
253C22⋊C8C22⋊D1112yes—
254#97—112no—
255#97—221no—
256#97—221no—
257#97—221no—
258C4×C8—21no—
259C2×C11—22no—
260C2×C11—161no—
261C2×C11#200211yescharacteristic
262C2×C11#200911yescharacteristic
263C2×C11#201911yescharacteristic
264D11—161no—
265C24—221no—
266#41—82no—
267C2×Q8—22no—
268C2×Q8—21no—
269C2×Q8—42no—
270C2×Q8—42no—
271C2×Q8—41no—
272C2×Q8—221no—
273C2×Q8—221no—
274C2×Q8—442no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—41no—
279C2×D4—221no—
280C2×D4—221no—
281C2×D4—442no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—221no—
285C22×C4D4×D1111yescharacteristic
286C22×C4#434111yescharacteristic
287C22×C4C2×C22⋊D1111yescharacteristic
288Q16—448no—
289SD16—448no—
290SD16—882no—
291D8—882no—
292C2×C8—22no—
293C2×C8—224no—
294C2×C8—222no—
295C2×C8—222no—
296C2×C8—441no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C22⋊C4—441no—
309C42D4×D1111yescharacteristic
310C42D4×D1111yescharacteristic
311C42C2×C22⋊D1111yescharacteristic
312C42C2×C22⋊D1111yescharacteristic
313C11#1013211yescharacteristic, complemented, Sylow
314C23—41no—
315C23—441no—
316C23—442no—
317C23—881no—
318C23—881no—
319C23#6699111yescharacteristic
320Q8—42no—
321Q8—42no—
322Q8—81no—
323Q8—82no—
324Q8—442no—
325Q8—442no—
326D4—42no—
327D4—42no—
328D4—81no—
329D4—82no—
330D4—442no—
331D4—442no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—441no—
340C2×C4—881no—
341C2×C4#6699011yescharacteristic
342C2×C4#6699011yescharacteristic
343C2×C4#6699211yescharacteristic
344C2×C4#6699211yescharacteristic
345C2×C4#6699311yescharacteristic
346C2×C4#6700611yescharacteristic
347C8—42no—
348C8—224no—
349C8—442no—
350C8—881no—
351C22—21no—
352C22—21no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—881no—
357C22—881no—
358C22—881no—
359C22—1762no—
360C22#1062279012yes—
361C22#1062283611yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—82no—
368C4—81no—
369C4—881no—
370C4#1062281112yes—
371C2—22no—
372C2—161no—
373C2—1761no—
374C2#1306962811yescharacteristic
375C2#1306967611yescharacteristic
376C2#1306972811yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3227C2
socleC22×C11#392
prime radical#13079599C2
hypercenter#3227D11
hypocenterC11#10132
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
2. C2×#10622699C2semidirect
3. #13067333C2semidirect
4. #13067227C2semidirect
5. #13066967C2semidirect
6. #13066516C2semidirect
7. C11×#3227C2semidirect
126. #3227D11semidirect
313. C11#10132semidirect

Maximal subgroups

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

subgroupindex
#130795992
C2×#106226992
#130673332
#130672272
#130669672
#130665162
C11×#32272
#1013211