Finite Group Databasebeta

← #14655423

Subgroups — #14655423

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#13079741C211yesmaximal, characteristic, complemented
2C2×#10622673C211yesmaximal, characteristic, complemented
3#13067334C211yesmaximal, characteristic, complemented
4#13067227C211yesmaximal, characteristic, complemented
5#13066968C211yesmaximal, characteristic, complemented
6#13066514C211yesmaximal, characteristic, complemented
7C11×#3213C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×#124C2211yescharacteristic
10C22×#4326—21no—
11C22×#4324—21no—
12C2×#66922C2211yescharacteristic
13C11×#496—21no—
14C11×#489—21no—
15C11×#463—22no—
16C11×#448—21no—
17C11×#447—21no—
18C11×#432C2211yescharacteristic
19#10622692—21no—
20#10622683—21no—
21#10622673—22no—
22#10622673—22no—
23#10622647—22no—
24#10622621—22no—
25#10622539C2211yescharacteristic
26#10622538C2211yescharacteristic
27C2×#66867C2211yescharacteristic
28#10622178—22no—
29#10622163—22no—
30#10622120—22no—
31C2×C11×#41—21no—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11D411yescharacteristic
34C22×Dic22—21no—
35C2×C11×SD16—22no—
36C2×C11×D8—22no—
37C11×C4⋊Q8D411yescharacteristic
38C11×#127D411yescharacteristic
39C11×#124—21no—
40C11×#124—21no—
41C11×#124—21no—
42C11×#124—21no—
43C11×#124—21no—
44C11×#121—21no—
45C11×#121—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C42×C11C2311yescharacteristic
51C2×#4326—24no—
52C2×#4326—44no—
53C2×#4324—24no—
54C2×#4324—44no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C22×C11⋊C8—21no—
58#66922—21no—
59#66922—21no—
60#66922—21no—
61#66922D412yes—
62C11×C4⋊C8D412yes—
63C11×#103—22no—
64C11×#102—22no—
65C11×C22⋊C8—21no—
66C11×#97—21no—
67#66896—24no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)D412yes—
70#66872—24no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73#66867—21no—
74#66867—21no—
75#66867D412yes—
76C4×C11⋊C8—21no—
77#10132—111nomaximal, Sylow
78C24×C11—21no—
79C11×#41—82no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—42no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—42no—
90C2×D4×C11—41no—
91C22×C4×C11—21no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C22×Dic11—41no—
97C2×Dic22—22no—
98C2×Dic22—42no—
99C2×Dic22—42no—
100C2×Dic22—41no—
101C11×SD16—82no—
102C11×D8—82no—
103C2×C8×C11—22no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116#4326—48no—
117#4324—48no—
118C4⋊Dic11—22no—
119C4⋊Dic11—22no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122C2×C11⋊C8—24no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—41no—
126#3227—111no—
127#3213D1111yescharacteristic
128C2×#497—111no—
129#1556—111no—
130#1530—111no—
131#1469—111no—
132#1302—111no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—42no—
136C23×C11—81no—
137C23×C11—81no—
138C23×C11#12111yescharacteristic
139Q8×C11—42no—
140Q8×C11—42no—
141Q8×C11—81no—
142D4×C11—42no—
143D4×C11—42no—
144D4×C11—42no—
145D4×C11—42no—
146D4×C11—81no—
147D4×C11—82no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—82no—
154C2×C4×C11—81no—
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12711yescharacteristic
161C2×Dic11—42no—
162C2×Dic11—82no—
163Dic22—42no—
164Dic22—42no—
165Dic22—82no—
166C8×C11—42no—
167C11⋊C8—24no—
168C11⋊C8—42no—
169C11⋊C8—81no—
170C22×Q16—221no—
171C22×SD16—221no—
172#532C2×D1111yescharacteristic
173C2×C4⋊Q8—111no—
174C2×#124C2×D1111yescharacteristic
175#498—221no—
176#497—222no—
177#497—222no—
178#496—21no—
179#489—21no—
180#486—221no—
181#481—222no—
182#476—222no—
183#463—22no—
184#448—21no—
185#447—21no—
186#432—111no—
187#432C2×D1111yescharacteristic
188#431—111no—
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—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—162no—
202C22×C11#39211yescharacteristic
203C22×C11#47112yes—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—81no—
210C4×C11—81no—
211C4×C11#45312yes—
212Dic11—82no—
213C2×#41—21no—
214C22×Q8—221no—
215C22×Q8C22⋊D1111yescharacteristic
216C22×D4C22⋊D1111yescharacteristic
217C2×Q16—224no—
218C2×Q16—444no—
219C2×SD16—22no—
220C2×SD16—224no—
221C2×SD16—444no—
222C2×D8—22no—
223C22×C8—221no—
224C4⋊Q8—112no—
225C4⋊Q8—221no—
226C4⋊Q8—221no—
227C4⋊Q8—221no—
228C4⋊Q8C22⋊D1111yescharacteristic
229#127C22⋊D1111yescharacteristic
230#124—21no—
231#124—21no—
232#124—21no—
233#124—21no—
234#124—21no—
235#121—21no—
236#121—21no—
237C4×D4—21no—
238C4×D4—21no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4—221no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C42C22×D1111yescharacteristic
244#106—224no—
245C4⋊C8—221no—
246C4⋊C8—221no—
247C4⋊C8C22⋊D1112yes—
248#103—22no—
249#102—22no—
250#102—224no—
251C22⋊C8—21no—
252C22⋊C8—112no—
253C22⋊C8—221no—
254#97—21no—
255#97—112no—
256#97—221no—
257#97—221no—
258C4×C8—221no—
259C2×C11—22no—
260C2×C11—161no—
261C2×C11—161no—
262C2×C11#200211yescharacteristic
263C2×C11#200911yescharacteristic
264C2×C11#201911yescharacteristic
265C24—21no—
266#41—82no—
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—42no—
271C2×Q8—222no—
272C2×Q8—442no—
273C2×Q8—442no—
274C2×Q8—441no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—42no—
281C2×D4—41no—
282C22×C4—21no—
283C22×C4—41no—
284C22×C4—441no—
285C22×C4D4×D1111yescharacteristic
286C22×C4#434111yescharacteristic
287C22×C4C2×C22⋊D1111yescharacteristic
288Q16—448no—
289SD16—82no—
290SD16—448no—
291D8—82no—
292C2×C8—22no—
293C2×C8—224no—
294C2×C8—222no—
295C2×C8—222no—
296C2×C8—441no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—222no—
300C4⋊C4—222no—
301C4⋊C4—441no—
302C4⋊C4—441no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C42D4×D1111yescharacteristic
310C42D4×D1111yescharacteristic
311C42C2×C22⋊D1111yescharacteristic
312C42C2×C22⋊D1111yescharacteristic
313C11#1013211yescharacteristic, complemented, Sylow
314C23—41no—
315C23—41no—
316C23—42no—
317C23—81no—
318C23—81no—
319C23#6699211yescharacteristic
320Q8—42no—
321Q8—42no—
322Q8—81no—
323Q8—442no—
324Q8—442no—
325Q8—882no—
326D4—42no—
327D4—42no—
328D4—42no—
329D4—42no—
330D4—81no—
331D4—82no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—82no—
338C2×C4—81no—
339C2×C4—442no—
340C2×C4—882no—
341C2×C4#6699011yescharacteristic
342C2×C4#6699011yescharacteristic
343C2×C4#6699111yescharacteristic
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—81no—
357C22—81no—
358C22—81no—
359C22—162no—
360C22#1062281312yes—
361C22#1062283611yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—81no—
368C4—81no—
369C4—882no—
370C4#1062285412yes—
371C2—22no—
372C2—161no—
373C2—161no—
374C2#1306962911yescharacteristic
375C2#1306967311yescharacteristic
376C2#1306973011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3213C2
socleC22×C11#392
hypercenter#3213D11
hypocenterC11#10132
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3213

Complements

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

NH ≅ G/Ntype
1. #13079741C2semidirect
2. C2×#10622673C2semidirect
3. #13067334C2semidirect
4. #13067227C2semidirect
5. #13066968C2semidirect
6. #13066514C2semidirect
313. C11#10132semidirect

Maximal subgroups

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

subgroupindex
#130797412
C2×#106226732
#130673342
#130672272
#130669682
#130665142
C11×#32132
#1013211