Finite Group Databasebeta

← #14645239

Subgroups — #14645239

Order 2816.

1170 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C22×#66928C211yesmaximal, characteristic
2#13068378C211yesmaximal, characteristic, complemented
3C2×#10622102C214yesmaximal, complemented
4C11×#1749C211yesmaximal, characteristic, complemented
5C23×D44C411yescharacteristic
6C23×Dic22C411yescharacteristic
7C22×C42×C11C2211yescharacteristic
8C22×(C2×D11)⋊C4—21no—
9C22×(C2×D11)⋊C4—21no—
10C2×#66928—21no—
11C2×#66928—21no—
12C2×#66928—28no—
13C2×#66928C412yes—
14C2×#66928C2212yes—
15C2×C11×C22⋊C8—21no—
16C2×C11×#97C2212yescomplemented
17C2×C22⋊(C11⋊C8)—21no—
18C2×#66867C2212yescomplemented
19C11×#336—21no—
20#10622162—21no—
21#10622102—28no—
22C24×D11—21no—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×Dic11—21no—
27C22×D44—21no—
28C22×D44—24no—
29C22×D44—42no—
30C22×D44—42no—
31C22×D44C2×C412yes—
32C22×Dic22—21no—
33C22×Dic22—24no—
34C22×Dic22—42no—
35C22×Dic22—42no—
36C22×Dic22C2×C412yes—
37C22×C8×C11—22no—
38C2×C42×C11—24no—
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×C42×C11C2311yescharacteristic
43C2×(C2×D11)⋊C4—28no—
44C2×(C2×D11)⋊C4—28no—
45C2×(C2×D11)⋊C4—22no—
46C2×(C2×D11)⋊C4—22no—
47C2×(C2×D11)⋊C4—22no—
48C2×(C2×D11)⋊C4—22no—
49C22×C11⋊C8—22no—
50#66928—28no—
51#66928—28no—
52#66928—24no—
53#66928—24no—
54#66928—24no—
55#66928D418yes—
56C11×C22⋊C8—24no—
57C11×#97—24no—
58C22⋊(C11⋊C8)—24no—
59#66867—24no—
60#8334—111nomaximal, Sylow
61C24×C11C22⋊C411yescharacteristic
62C23×D11—24no—
63C23×D11—22no—
64C23×D11—42no—
65C23×D11—42no—
66C23×D11—42no—
67C23×D11—42no—
68C23×D11—42no—
69C23×D11—42no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—24no—
86C22×Dic11—22no—
87C22×Dic11—42no—
88C22×Dic11—42no—
89C2×D44—24no—
90C2×D44—22no—
91C2×D44—416no—
92C2×D44—42no—
93C2×D44—42no—
94C2×D44—42no—
95C2×D44—42no—
96C2×D44C22⋊C414yes—
97C2×Dic22—24no—
98C2×Dic22—22no—
99C2×Dic22—42no—
100C2×Dic22—42no—
101C2×Dic22—416no—
102C2×Dic22—42no—
103C2×Dic22—42no—
104C2×Dic22C22⋊C414yes—
105C2×C8×C11—24no—
106C2×C8×C11—42no—
107C2×C8×C11—42no—
108C42×C11—22no—
109C42×C11—22no—
110C42×C11—22no—
111C42×C11C2×D414yes—
112(C2×D11)⋊C4—28no—
113(C2×D11)⋊C4—28no—
114(C2×D11)⋊C4—28no—
115(C2×D11)⋊C4—28no—
116C2×C11⋊C8—24no—
117C2×C11⋊C8—42no—
118C2×C11⋊C8—42no—
119C22×#124—111no—
120#1749—111no—
121#1749D1111yescharacteristic, complemented
122C2×#329—114no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11#10012yes—
128C23×C11#10412yes—
129C23×C11#10412yes—
130C23×C11C2×C22⋊C411yescharacteristic
131C22×D11—24no—
132C22×D11—48no—
133C22×D11—48no—
134C22×D11—48no—
135C22×D11—42no—
136C22×D11—42no—
137C22×D11—42no—
138C22×D11—42no—
139C22×D11—42no—
140C22×D11—42no—
141C22×D11—84no—
142C22×D11—84no—
143C22×D11—84no—
144C22×D11—84no—
145C2×C4×C11—28no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
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—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—44no—
161C2×C4×C11—44no—
162C2×C4×C11#10012yes—
163C2×C4×C11C2×C22⋊C412yes—
164C2×C4×C11#12012yes—
165C2×C4×C11#12012yes—
166C2×Dic11—24no—
167C2×Dic11—48no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170D44—44no—
171D44—48no—
172D44—44no—
173Dic22—48no—
174Dic22—44no—
175Dic22—44no—
176C8×C11—44no—
177C11⋊C8—44no—
178C23×Q8—111no—
179C23×D4—111no—
180C2×#124—112no—
181C2×#124—112no—
182C2×#124—228no—
183C2×#124—221no—
184C2×#124—221no—
185C22×C22⋊C4—221no—
186C22×C22⋊C4—221no—
187C22×C42C2×D1111yescharacteristic
188C2×C22⋊C8—21no—
189C2×C22⋊C8—221no—
190C2×#97—112no—
191C2×#97C2×D1112yescomplemented
192#336—21no—
193#336—221no—
194#329—228no—
195C22×C11—22no—
196C22×C11—22no—
197C22×C11—22no—
198C22×C11—22no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11#32914yescomplemented
202C22×C11#37911yescharacteristic
203C22×C11C2×#10011yescharacteristic
204C22×C11C2×#10011yescharacteristic
205C22×C11C2×#10411yescharacteristic
206C22×C11C2×#10411yescharacteristic
207C22×C11#42111yescharacteristic
208C22×C11#42111yescharacteristic
209C2×D11—44no—
210C2×D11—44no—
211C2×D11—44no—
212C2×D11—816no—
213C2×D11—82no—
214C2×D11—82no—
215C2×D11—82no—
216C2×D11—82no—
217C4×C11—22no—
218C4×C11—22no—
219C4×C11—22no—
220C4×C11—22no—
221C4×C11—41no—
222C4×C11—41no—
223Dic11—44no—
224C25—221no—
225C22×Q8—112no—
226C22×Q8—224no—
227C22×Q8—221no—
228C22×Q8—442no—
229C22×Q8—442no—
230C22×D4—112no—
231C22×D4—224no—
232C22×D4—221no—
233C22×D4—442no—
234C22×D4—442no—
235C23×C4—221no—
236C23×C4C4×D1111yescharacteristic
237C23×C4D4411yescharacteristic
238C23×C4C22⋊D1111yescharacteristic
239C22×C8—22no—
240C22×C8—222no—
241#124—118no—
242#124—224no—
243#124—224no—
244#124—228no—
245#124—228no—
246#124—224no—
247C2×C22⋊C4—228no—
248C2×C22⋊C4—228no—
249C2×C22⋊C4—222no—
250C2×C22⋊C4—222no—
251C2×C22⋊C4—222no—
252C2×C22⋊C4—222no—
253C2×C42—24no—
254C2×C42C4×D1111yescharacteristic
255C2×C42D4411yescharacteristic
256C2×C42C22⋊D1111yescharacteristic
257C2×C42C22×D1111yescharacteristic
258C22⋊C8—24no—
259C22⋊C8—224no—
260#97—24no—
261#97—224no—
262C2×C11—24no—
263C2×C11C2×#32911yescharacteristic
264C2×C11#152711yescharacteristic
265C2×C11#152711yescharacteristic
266C2×C11#153311yescharacteristic
267C2×C11#178311yescharacteristic
268C2×C11#178911yescharacteristic
269C2×C11#178911yescharacteristic
270D11—84no—
271C24—224no—
272C24—222no—
273C24—442no—
274C24—442no—
275C24—442no—
276C24—442no—
277C24—442no—
278C24—442no—
279C24(C2×D11)⋊C411yescharacteristic
280C2×Q8—114no—
281C2×Q8—224no—
282C2×Q8—222no—
283C2×Q8—4416no—
284C2×Q8—442no—
285C2×Q8—442no—
286C2×Q8—442no—
287C2×Q8—442no—
288C2×D4—114no—
289C2×D4—224no—
290C2×D4—222no—
291C2×D4—442no—
292C2×D4—442no—
293C2×D4—4416no—
294C2×D4—442no—
295C2×D4—442no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—224no—
306C22×C4—222no—
307C22×C4—442no—
308C22×C4—442no—
309C22×C4(C2×D11)⋊C411yescharacteristic
310C22×C4(C2×D11)⋊C411yescharacteristic
311C22×C4(C2×D11)⋊C411yescharacteristic
312C22×C4C2×C4×D1111yescharacteristic
313C22×C4C2×D4411yescharacteristic
314C22×C4C2×C22⋊D1111yescharacteristic
315C2×C8—24no—
316C2×C8—42no—
317C2×C8—42no—
318C2×C8—224no—
319C2×C8—442no—
320C2×C8—442no—
321C22⋊C4—228no—
322C22⋊C4—228no—
323C22⋊C4—228no—
324C22⋊C4—228no—
325C42—22no—
326C42—22no—
327C42—22no—
328C42D4×D1114yes—
329C11#833411yescharacteristic, complemented, Sylow
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—224no—
335C23—448no—
336C23—448no—
337C23—448no—
338C23—442no—
339C23—442no—
340C23—442no—
341C23—442no—
342C23—442no—
343C23—442no—
344C23—884no—
345C23—884no—
346C23—884no—
347C23—884no—
348C23#6686912yes—
349C23#6688712yes—
350C23#6688912yes—
351C23C2×(C2×D11)⋊C411yescharacteristic
352Q8—444no—
353Q8—448no—
354Q8—444no—
355D4—444no—
356D4—448no—
357D4—444no—
358C2×C4—28no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—44no—
374C2×C4—44no—
375C2×C4—224no—
376C2×C4—448no—
377C2×C4—442no—
378C2×C4—442no—
379C2×C4#6688712yes—
380C2×C4C22⋊C4×D1112yes—
381C2×C4#6693512yes—
382C2×C4#6699012yes—
383C8—44no—
384C8—444no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—444no—
392C22—444no—
393C22—444no—
394C22—8816no—
395C22—882no—
396C22—882no—
397C22—882no—
398C22—882no—
399C22#1062210214yescomplemented
400C22C2×#6686911yescharacteristic
401C22#1062256811yescharacteristic
402C22#1062261811yescharacteristic
403C22C2×#6688711yescharacteristic
404C22C2×#6688711yescharacteristic
405C22C2×#6688911yescharacteristic
406C22#1062275211yescharacteristic
407C4—22no—
408C4—22no—
409C4—22no—
410C4—22no—
411C4—41no—
412C4—41no—
413C4—444no—
414C2—24no—
415C2—884no—
416C2C2×#1062210211yescharacteristic
417C2#1306721311yescharacteristic
418C2#1306721511yescharacteristic
419C2#1306723911yescharacteristic
420C2#1306853611yescharacteristic
421C2#1306855911yescharacteristic
422C2#1306856111yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1749C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D44C4
cosocleC2×C42×C11C23
hypercenter#1749D11
hypocenterC11#8334
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. #13068378C2semidirect
3. C2×#10622102C2semidirect
4. C11×#1749C2semidirect
16. C2×C11×#97C22semidirect
18. C2×#66867C22semidirect
121. #1749D11semidirect
191. C2×#97C2×D11semidirect
201. C22×C11#329semidirect
329. C11#8334semidirect
399. C22#10622102semidirect

Maximal subgroups

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

subgroupindex
C22×#669282
#130683782
C2×#106221022
C11×#17492
#833411