Finite Group Databasebeta

← #14657580

Subgroups — #14657580

Order 2816.

522 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622461C211yesmaximal, characteristic
2#13069551C211yesmaximal, characteristic, complemented
3#13069421C211yesmaximal, characteristic
4#13068618C211yesmaximal, characteristic, complemented
5C2×#10622117C211yesmaximal, characteristic, complemented
6C2×#10622123C211yesmaximal, characteristic
7C11×#1296C211yesmaximal, characteristic, complemented
8C22×#4314—21no—
9C2×#66927C2211yescharacteristic
10C2×C4×Dic22C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C11×#384C2211yescharacteristic
14C2×#66885—21no—
15C2×#66874—21no—
16C2×#66873—21no—
17C2×#66873—21no—
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19C2×C4×C11⋊C8C2211yescharacteristic
20#10622461—22no—
21#10622461—22no—
22#10622188—21no—
23#10622188—21no—
24#10622167—21no—
25#10622123—22no—
26#10622117—22no—
27C22×D44—21no—
28C22×D44—21no—
29C22×D44—21no—
30C22×Dic22D411yescharacteristic
31C22×C8×C11—21no—
32C22×C8×C11—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C42×C11C2311yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×C4×Dic11—21no—
40C22×C11⋊C8—21no—
41C22×C11⋊C8D411yescharacteristic
42C22×C11⋊C8D411yescharacteristic
43C2×#4314—24no—
44C2×#4314—42no—
45C2×#4314—42no—
46#66927—21no—
47#66927—21no—
48#66927—21no—
49#66927D412yes—
50C4×Dic22—21no—
51C4×Dic22—21no—
52C4×Dic22—21no—
53C4×Dic22—21no—
54C11×C4⋊C8—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8D412yes—
58#66885—24no—
59#66874—42no—
60#66873—42no—
61#66873—42no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4×C11⋊C8—21no—
65C4×C11⋊C8—21no—
66#10474—111nomaximal, Sylow
67C23×D11—41no—
68C22×C4×C11—41no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11#4111yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C2×D44—22no—
75C2×D44—22no—
76C2×D44—22no—
77C2×D44—41no—
78C2×D44—41no—
79C2×D44—41no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—41no—
86C2×D44—41no—
87C2×D44—41no—
88C2×D44—81no—
89C2×D44—81no—
90C2×Dic22—21no—
91C2×Dic22—21no—
92C2×Dic22—21no—
93C2×Dic22—21no—
94C2×Dic22—21no—
95C2×Dic22D812yes—
96C2×C8×C11—22no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—81no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11#4111yescharacteristic
110C42×C11#4111yescharacteristic
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113Dic11⋊C4—41no—
114Dic11⋊C4—41no—
115C4×Dic11—41no—
116C4×Dic11—41no—
117C2×C11⋊C8—21no—
118C2×C11⋊C8—21no—
119C2×C11⋊C8—21no—
120C2×C11⋊C8—21no—
121C2×C11⋊C8—21no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125C2×C11⋊C8SD1612yescomplemented
126#4314—48no—
127C2×#460—111no—
128#1984—111no—
129#1957—111no—
130#1803—111no—
131C2×#335—111no—
132C2×#331—111no—
133#1296D1111yescharacteristic, complemented
134C23×C11#12111yescharacteristic
135C22×D11—42no—
136C22×D11—81no—
137C22×D11—81no—
138C22×D11—81no—
139C22×D11—81no—
140C22×D11—81no—
141C22×D11—81no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12311yescharacteristic
151C2×C4×C11#12311yescharacteristic
152C2×C4×C11#12411yescharacteristic
153C2×C4×C11C2×D811yescharacteristic
154C2×C4×C11C2×SD1611yescharacteristic
155C2×C4×C11#13511yescharacteristic
156C2×C4×C11#13511yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C11#13711yescharacteristic
160C2×C4×C11#13711yescharacteristic
161C2×Dic11—22no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167D44—42no—
168D44—42no—
169D44—42no—
170D44—42no—
171D44—82no—
172D44—82no—
173D44—81no—
174D44—81no—
175D44—81no—
176D44—81no—
177Dic22—22no—
178Dic22—22no—
179Dic22—41no—
180Dic22—41no—
181C8×C11—42no—
182C8×C11—81no—
183C11⋊C8—22no—
184C11⋊C8—41no—
185C11⋊C8—81no—
186C22×SD16—221no—
187C2×#127—111no—
188C2×C4×Q8—111no—
189#460—222no—
190#460—222no—
191C2×C4⋊C8—111no—
192C2×C4⋊C8C2×D1111yescharacteristic
193C2×C4⋊C8C2×D1111yescharacteristic
194C2×#103—221no—
195C2×#102—221no—
196C2×#102—221no—
197C2×#102—221no—
198C2×C4×C8—111no—
199#384C2×D1111yescharacteristic
200#340—221no—
201#336—221no—
202#336—221no—
203#335—222no—
204#331—222no—
205C22×C11#39411yescharacteristic
206C22×C11#46011yescharacteristic
207C22×C11#46411yescharacteristic
208C22×C11#46611yescharacteristic
209C22×C11#46811yescharacteristic
210C22×C11#47111yescharacteristic
211C22×C11#47211yescharacteristic
212C2×D11—82no—
213C2×D11—82no—
214C2×D11—82no—
215C2×D11—161no—
216C2×D11—161no—
217C2×D11—161no—
218C2×D11—161no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—161no—
222C4×C11#44711yescharacteristic
223C4×C11#45211yescharacteristic
224C4×C11#46111yescharacteristic
225C4×C11#46311yescharacteristic
226C4×C11#46511yescharacteristic
227C4×C11#46811yescharacteristic
228C4×C11#48011yescharacteristic
229C4×C11#48211yescharacteristic
230Dic11—42no—
231Dic11—81no—
232C22×Q8—111no—
233C22×D4—221no—
234C22×D4—221no—
235C22×D4—221no—
236C2×SD16—224no—
237C2×SD16—442no—
238C2×SD16—442no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—111no—
242C22×C8—111no—
243C22×C8—221no—
244#127—112no—
245#127—221no—
246#127—221no—
247#127—221no—
248C4×Q8—221no—
249C4×Q8—221no—
250C4×Q8—221no—
251C4×Q8—221no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—221no—
257C2×C42—221no—
258C2×C42C22×D1111yescharacteristic
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262C4⋊C8—221no—
263C4⋊C8—221no—
264C4⋊C8D4412yes—
265#103—442no—
266#102—224no—
267#102—442no—
268#102—442no—
269C4×C8—221no—
270C4×C8—221no—
271C2×C11#166811yescharacteristic
272C2×C11#168211yescharacteristic
273C2×C11#168611yescharacteristic
274C2×C11#169811yescharacteristic
275C2×C11#203311yescharacteristic
276C2×C11#205111yescharacteristic
277C2×C11#205511yescharacteristic
278D11—162no—
279C24—441no—
280C2×Q8—112no—
281C2×Q8—221no—
282C2×Q8—221no—
283C2×Q8—221no—
284C2×Q8—221no—
285C2×Q8—221no—
286C2×D4—222no—
287C2×D4—222no—
288C2×D4—222no—
289C2×D4—441no—
290C2×D4—441no—
291C2×D4—441no—
292C2×D4—441no—
293C2×D4—441no—
294C2×D4—441no—
295C2×D4—441no—
296C2×D4—441no—
297C2×D4—441no—
298C2×D4—441no—
299C2×D4—441no—
300C2×D4—881no—
301C2×D4—881no—
302C22×C4—41no—
303C22×C4—221no—
304C22×C4—221no—
305C22×C4#433911yescharacteristic
306C22×C4D4×D1111yescharacteristic
307C22×C4D4×D1111yescharacteristic
308SD16—448no—
309C2×C8—22no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—112no—
316C2×C8—221no—
317C2×C8—221no—
318C2×C8—221no—
319C2×C8—221no—
320C2×C8—221no—
321C2×C8—441no—
322C2×C8—441no—
323C2×C8—441no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—81no—
329C4⋊C4—221no—
330C4⋊C4—221no—
331C4⋊C4—441no—
332C4⋊C4—441no—
333C42—441no—
334C42—441no—
335C42C2×D4411yescharacteristic
336C42#433911yescharacteristic
337C42D4×D1111yescharacteristic
338C42#434311yescharacteristic
339C11#1047411yescharacteristic, complemented, Sylow
340C23—442no—
341C23—881no—
342C23—881no—
343C23—881no—
344C23—881no—
345C23—881no—
346C23—881no—
347C23#6693711yescharacteristic
348Q8—222no—
349Q8—222no—
350Q8—441no—
351Q8—441no—
352D4—442no—
353D4—442no—
354D4—442no—
355D4—442no—
356D4—882no—
357D4—882no—
358D4—881no—
359D4—881no—
360D4—881no—
361D4—881no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—222no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4#6692811yescharacteristic
374C2×C4#6693511yescharacteristic
375C2×C4#6693711yescharacteristic
376C2×C4#6694711yescharacteristic
377C2×C4#6694711yescharacteristic
378C2×C4#6694811yescharacteristic
379C2×C4D8×D1111yescharacteristic
380C2×C4#6696411yescharacteristic
381C2×C4SD16×D1111yescharacteristic
382C2×C4#6696711yescharacteristic
383C2×C4#6696911yescharacteristic
384C2×C4#6696911yescharacteristic
385C2×C4#6697111yescharacteristic
386C2×C4#6697111yescharacteristic
387C8—42no—
388C8—81no—
389C8—222no—
390C8—441no—
391C8—881no—
392C22—882no—
393C22—882no—
394C22—882no—
395C22—1761no—
396C22—1761no—
397C22—1761no—
398C22—1761no—
399C22#1062228511yescharacteristic
400C22#1062236211yescharacteristic
401C22#1062236711yescharacteristic
402C22#1062237511yescharacteristic
403C22#1062238811yescharacteristic
404C22#1062241111yescharacteristic
405C22#1062242511yescharacteristic
406C4—21no—
407C4—21no—
408C4—161no—
409C4—442no—
410C4—881no—
411C4#1062238611yescharacteristic
412C4#1062240011yescharacteristic
413C4#1062242311yescharacteristic
414C4#1062243111yescharacteristic
415C4#1062247711yescharacteristic
416C4#1062247911yescharacteristic
417C4#1062249511yescharacteristic
418C4#1062249911yescharacteristic
419C2—1762no—
420C2#1306797511yescharacteristic
421C2#1306806311yescharacteristic
422C2#1306809111yescharacteristic
423C2#1306815911yescharacteristic
424C2#1306980111yescharacteristic
425C2#1306991111yescharacteristic
426C2#1306993511yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1296C2
socleC23×C11#121
prime radicalC2×#66927C22
hypercenter#1296D11
hypocenterC11#10474
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #13069551C2semidirect
4. #13068618C2semidirect
5. C2×#10622117C2semidirect
7. C11×#1296C2semidirect
125. C2×C11⋊C8SD16semidirect
133. #1296D11semidirect
339. C11#10474semidirect

Maximal subgroups

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

subgroupindex
C2×#106224612
#130695512
#130694212
#130686182
C2×#106221172
C2×#106221232
C11×#12962
#1047411