Finite Group Databasebeta

← #14648496

Subgroups — #14648496

Order 2816.

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

normal subgroups only

This group has 476 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#13078681C211yesmaximal, characteristic
2#13077746C211yesmaximal, characteristic
3C4×#66869C211yesmaximal, characteristic
4#13067037C211yesmaximal, characteristic, complemented
5#13066505C211yesmaximal, characteristic, complemented
6#13066449C211yesmaximal, characteristic, complemented
7C11×#1994C211yesmaximal, characteristic, complemented
8C11×#533C2211yescharacteristic
9C4×#4339C2211yescharacteristic
10C11×#423C2211yescharacteristic
11C43×C11C2211yescharacteristic
12#10622741—22no—
13#10622707C411yescharacteristic, complemented
14#10622703C411yescharacteristic, complemented
15#10622700C411yescharacteristic, complemented
16#10622696C411yescharacteristic, complemented
17#10622660—21no—
18#10622658—21no—
19C4×#4326—21no—
20C4×#4325—21no—
21C2×#66869—21no—
22#10622538C2211yescharacteristic
23#10622538C2211yescharacteristic
24C4×#4318C2211yescharacteristic
25#10622451—21no—
26#10622450—21no—
27#10622446—21no—
28#10622443—21no—
29C11×#339—22no—
30Q8⋊(C11⋊C8)—21no—
31Q8⋊(C11⋊C8)—21no—
32#10622161—21no—
33C2×#4339D411yescharacteristic
34C2×C11×M16D412yes—
35C11×C4⋊Q8C2×C411yescharacteristic
36C11×C4⋊Q8C2×C411yescharacteristic
37C11×#125—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C11×#117—21no—
43C2×C42×C11—21no—
44C2×C42×C11—21no—
45C2×C42×C11—21no—
46C2×C42×C11C2311yescharacteristic
47C2×#4326—21no—
48C2×#4325—21no—
49C4×C22⋊D11—21no—
50C4×C22⋊D11—21no—
51#66979D411yescharacteristic
52C2×#4318—21no—
53C2×#4313—22no—
54C4×D44C2×C411yescharacteristic
55C4×D44D411yescharacteristic
56#66925—21no—
57C42×D11—21no—
58C4×Dic22C2×C411yescharacteristic
59C4×Dic22D411yescharacteristic
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62#66899—21no—
63#66899—21no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66(C2×D11)⋊C8—22no—
67Dic11⋊C8—22no—
68C8×Dic11—22no—
69#66874—21no—
70#66873—21no—
71#66872—21no—
72#66871—21no—
73#66869—24no—
74C4⋊(C11⋊C8)C2×C411yescharacteristic
75C4⋊(C11⋊C8)C2×C411yescharacteristic
76C4⋊(C11⋊C8)D411yescharacteristic
77C4⋊(C11⋊C8)D411yescharacteristic
78#66867—21no—
79C4×C11⋊C8—21no—
80C4×C11⋊C8—21no—
81C4×C11⋊C8—21no—
82#8972—111nomaximal, Sylow
83C2×Q8×C11—21no—
84C2×Q8×C11—21no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C2×C22⋊D11—21no—
90#4339—22no—
91#4339—41no—
92C2×D44C22⋊C411yescharacteristic
93C2×C4×D11—21no—
94C2×C4×D11—21no—
95C2×C4×D11—21no—
96C2×Dic22C22⋊C411yescharacteristic
97C11×M16—42no—
98C2×C8×C11—22no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C22⋊C4—41no—
106C42×C11—22no—
107C42×C11—22no—
108C42×C11—22no—
109C42×C11—41no—
110C42×C11—41no—
111C42×C11—41no—
112C42×C11—41no—
113C42×C11C22×C411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117C22⋊Dic11—21no—
118#4326—42no—
119#4325—42no—
120(C2×D11)⋊C4—21no—
121(C2×D11)⋊C4—21no—
122C4⋊Dic11C22⋊C411yescharacteristic
123C4⋊Dic11C22⋊C411yescharacteristic
124Dic11⋊C4—21no—
125Dic11⋊C4—21no—
126C4×Dic11—21no—
127C4×Dic11—21no—
128C4×Dic11—21no—
129#4318—22no—
130#4318—41no—
131C2×C11⋊C8—21no—
132C2×C11⋊C8—21no—
133C2×C11⋊C8—21no—
134C2×C11⋊C8—21no—
135C2×C11⋊C8—41no—
136#4313—82no—
137#3107—111no—
138#2991—111no—
139#1994D1111yescharacteristic, complemented
140C4×#104—111no—
141#1485—111no—
142#1299—111no—
143#1276—111no—
144C23×C11#12111yescharacteristic
145C22×D11—21no—
146Q8×C11—41no—
147Q8×C11—41no—
148Q8×C11—41no—
149Q8×C11—41no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11C2×C22⋊C411yescharacteristic
162C2×C4×C11C4×D411yescharacteristic
163C2×C4×C11C4×D411yescharacteristic
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12311yescharacteristic
167C22⋊D11—42no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171D44—21no—
172D44—21no—
173C4×D11—42no—
174C4×D11—41no—
175C4×D11—41no—
176C4×D11—41no—
177C4×D11—41no—
178Dic22—21no—
179Dic22#10412yes—
180C8×C11—42no—
181C11⋊C8—42no—
182C11⋊C8—41no—
183C11⋊C8—41no—
184C11⋊C8—41no—
185C11⋊C8—41no—
186#533C2×D1111yescharacteristic
187C4×#41—111no—
188#485—221no—
189#475—111no—
190#474—111no—
191#462—111no—
192#461—111no—
193#452—221no—
194C8×Q8—221no—
195C4×Q16—221no—
196C4×SD16—221no—
197#436—221no—
198#436—222no—
199#431—111no—
200#431—111no—
201#431—221no—
202#423—221no—
203#423C2×D1111yescharacteristic
204C2×#104—221no—
205C4×M16—111no—
206C43C2×D1111yescharacteristic
207#339—22no—
208#339—221no—
209Q8⋊C8—221no—
210Q8⋊C8—221no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11#38611yescharacteristic
215C2×D11—41no—
216C2×D11—41no—
217C2×D11—41no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—44no—
222C4×C11—81no—
223C4×C11—81no—
224C4×C11C2×#10411yescharacteristic
225C4×C11#42111yescharacteristic
226C4×C11#44311yescharacteristic
227C4×C11#44411yescharacteristic
228C4×C11#45511yescharacteristic
229C4×C11#45611yescharacteristic
230Dic11—22no—
231Dic11—41no—
232Dic11—41no—
233C2×#41—111no—
234C2×Q16—221no—
235C2×SD16—221no—
236C2×M16—222no—
237C2×M16—221no—
238C2×M16C22⋊D1112yes—
239C4⋊Q8C4×D1111yescharacteristic
240C4⋊Q8C4×D1111yescharacteristic
241#125—21no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—111no—
247C4×Q8—111no—
248C4×D4—111no—
249C4×D4—111no—
250C4×D4—221no—
251C4×D4—221no—
252#117—21no—
253#117—111no—
254#117—221no—
255C2×C42—21no—
256C2×C42—21no—
257C2×C42—21no—
258C2×C42—221no—
259C2×C42C22×D1111yescharacteristic
260#107—221no—
261#106—221no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—111no—
265C4⋊C8—111no—
266C4⋊C8—111no—
267C4⋊C8—111no—
268C4⋊C8—222no—
269#104—224no—
270#103—221no—
271#103—221no—
272#103—221no—
273#102—221no—
274C22⋊C8—222no—
275C22⋊C8—221no—
276C22⋊C8—221no—
277#97—221no—
278C4×C8—222no—
279C4×C8—221no—
280C4×C8—221no—
281C4×C8—221no—
282C2×C11—41no—
283C2×C11#187111yescharacteristic
284C2×C11#187611yescharacteristic
285C2×C11#188211yescharacteristic
286D11—81no—
287#41—222no—
288#41—441no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—111no—
292C2×D4—111no—
293C2×D4—221no—
294C22×C4—41no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—221no—
298C22×C4D4×D1111yescharacteristic
299C22×C4#434111yescharacteristic
300C22×C4C2×C22⋊D1111yescharacteristic
301Q16—442no—
302SD16—442no—
303M16—42no—
304M16—222no—
305M16—441no—
306M16—882no—
307C2×C8—22no—
308C2×C8—221no—
309C2×C8—221no—
310C2×C8—221no—
311C2×C8—221no—
312C2×C8—441no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—111no—
320C4⋊C4—111no—
321C4⋊C4—221no—
322C4⋊C4—221no—
323C22⋊C4—41no—
324C22⋊C4—221no—
325C22⋊C4—221no—
326C22⋊C4—221no—
327C42—22no—
328C42—22no—
329C42—22no—
330C42—41no—
331C42—41no—
332C42—41no—
333C42—41no—
334C42—221no—
335C42—221no—
336C42—221no—
337C42C2×C4×D1111yescharacteristic
338C42#433911yescharacteristic
339C42D4×D1111yescharacteristic
340C42D4×D1111yescharacteristic
341C11#897211yescharacteristic, complemented, Sylow
342C23—221no—
343C23#6699111yescharacteristic
344Q8—41no—
345Q8—41no—
346Q8—41no—
347Q8—41no—
348Q8—112no—
349Q8—221no—
350D4—221no—
351D4—221no—
352D4—442no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—221no—
365C2×C4—221no—
366C2×C4—221no—
367C2×C4—442no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4C22⋊C4×D1111yescharacteristic
373C2×C4(C22⋊D11)⋊C411yescharacteristic
374C2×C4#6693611yescharacteristic
375C2×C4#6693711yescharacteristic
376C2×C4C4×C22⋊D1111yescharacteristic
377C2×C4#6699011yescharacteristic
378C8—42no—
379C8—442no—
380C8—441no—
381C8—441no—
382C8—441no—
383C8—441no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—441no—
388C22—441no—
389C22—441no—
390C22#1062256911yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—44no—
395C4—81no—
396C4—81no—
397C4—222no—
398C4—441no—
399C4—441no—
400C4D11×#10411yescharacteristic
401C4#1062243411yescharacteristic
402C4#1062243611yescharacteristic
403C4#1062243711yescharacteristic
404C4#1062267411yescharacteristic
405C4#1062270811yescharacteristic
406C2—41no—
407C2—881no—
408C2#1306891511yescharacteristic
409C2#1306894011yescharacteristic
410C2#1306898811yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1994C2
socleC22×C11#386
prime radicalC2×#4339D4
cosocleC2×C42×C11C23
hypercenter#1994D11
hypocenterC11#8972
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
4. #13067037C2semidirect
5. #13066505C2semidirect
6. #13066449C2semidirect
7. C11×#1994C2semidirect
13. #10622707C4semidirect
14. #10622703C4semidirect
15. #10622700C4semidirect
16. #10622696C4semidirect
139. #1994D11semidirect
341. C11#8972semidirect

Maximal subgroups

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

subgroupindex
#130786812
#130777462
C4×#668692
#130670372
#130665052
#130664492
C11×#19942
#897211