Finite Group Databasebeta

← #14908868

Subgroups — #14908868

Order 2816.

548 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079186C211yesmaximal, characteristic
2#13070818C211yesmaximal, characteristic, complemented
3#13070801C211yesmaximal, characteristic
4#13070780C212yesmaximal, complemented
5#13070678C212yesmaximal, complemented
6#13070550C211yesmaximal, characteristic, complemented
7#13070533C211yesmaximal, characteristic
8#13070485C212yesmaximal, complemented
9#13070478C212yesmaximal, complemented
10#13070419C211yesmaximal, characteristic, complemented
11C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C2×C4×Q8×C11—21no—
14#10623010—21no—
15C4×C11×Q16—21no—
16C4×C11×Q16—21no—
17C4×C11×Q16C2212yes—
18C4×C11×Q16C2212yes—
19C2×C11×#107C2211yescharacteristic
20C2×C11×#103—21no—
21C2×C4×C8×C11C2211yescharacteristic
22C2×#66893C2212yes—
23C2×#66892C2212yes—
24#10622729C2211yescharacteristic
25#10622728C2211yescharacteristic
26#10622727—21no—
27C4×Dic44C2211yescharacteristic
28#10622310—21no—
29#10622309C2211yescharacteristic
30C4×D88C2211yescharacteristic
31C4×#4314—21no—
32#10622296C2211yescharacteristic
33#10622202C2212yes—
34#10622202C2212yes—
35C22⋊(C11⋊C16)C2211yescharacteristic
36C22⋊(C11⋊C16)C2211yescharacteristic
37#10622130C2212yes—
38#10622129C2212yes—
39#10622128C2212yes—
40#10622127C2212yes—
41C4⋊(C11⋊C16)C2212yes—
42#10622099C2212yes—
43C22×Q8×C11—21no—
44C2×C11×Q16—24no—
45C2×C11×Q16—21no—
46C2×C11×Q16C2312yes—
47C22×C8×C11D411yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C4×Q8×C11—22no—
50C4×Q8×C11—22no—
51C4×Q8×C11—41no—
52C4×Q8×C11—41no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—41no—
55C2×C42×C11—41no—
56C2×C42×C11D411yescharacteristic
57#66983—21no—
58#66982—41no—
59C4×C22⋊D11—41no—
60#66977—21no—
61C2×Dic44C2311yescharacteristic
62C2×D88C2311yescharacteristic
63C2×#4314—21no—
64#66929—41no—
65#66928—21no—
66C4×D44—21no—
67#66925—41no—
68#66923—21no—
69C4×Dic22—21no—
70C11×#107—21no—
71C11×#107C2312yes—
72C11×#103—22no—
73C11×#103—22no—
74C4×C8×C11D411yescharacteristic
75C4×C8×C11D411yescharacteristic
76C4×C8×C11C2311yescharacteristic
77C4×C8×C11C2311yescharacteristic
78#66893—24no—
79#66892—24no—
80#66885—21no—
81#66885—21no—
82#66882C2311yescharacteristic
83#66882C2311yescharacteristic
84#66881—21no—
85#66880—21no—
86#66880—21no—
87C2×C11⋊C16C2312yes—
88C2×C11⋊C16C2312yes—
89#33677—111nomaximal, Sylow
90C2×Q8×C11—24no—
91C2×Q8×C11—22no—
92C2×Q8×C11—42no—
93C2×Q8×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11D811yescharacteristic
97C22×C4×C11D811yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C2×C22⋊D11—41no—
100C2×D44—21no—
101C2×C4×D11—41no—
102C2×Dic22—21no—
103C11×Q16—24no—
104C11×Q16—22no—
105C11×Q16#4114yes—
106C2×C8×C11—22no—
107C2×C8×C11—41no—
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2411yescharacteristic
112C11×C4⋊C4—22no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—42no—
115C11×C4⋊C4—42no—
116C42×C11—42no—
117C42×C11—42no—
118C42×C11D811yescharacteristic
119C42×C11D811yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C22⋊Dic11—41no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127C4⋊Dic11—21no—
128C4⋊Dic11—21no—
129Dic11⋊C4—41no—
130Dic11⋊C4—41no—
131Dic11⋊C4—41no—
132Dic11⋊C4—41no—
133C4×Dic11—41no—
134Dic44—22no—
135D88—22no—
136#4314—42no—
137C11⋊C16—22no—
138C11⋊C16—22no—
139#3168—111no—
140C2×C4×Q16D1111yescharacteristic, complemented
141#2236—111no—
142#2233—111no—
143#2229—112no—
144#2211—112no—
145#2188—111no—
146#2185—111no—
147#2176—112no—
148#2175—112no—
149#2163—111no—
150C23×C11C2×D811yescharacteristic
151C22×D11—41no—
152Q8×C11—24no—
153Q8×C11—44no—
154Q8×C11—42no—
155C2×C4×C11—22no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—41no—
159C2×C4×C11—44no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—82no—
163C2×C4×C11C2×D811yescharacteristic
164C2×C4×C11C2×D811yescharacteristic
165C2×C4×C11C2×D811yescharacteristic
166C2×C4×C11C2×D811yescharacteristic
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11C22×D411yescharacteristic
169C22⋊D11—82no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173D44—41no—
174D44—41no—
175C4×D11—82no—
176Dic22—41no—
177Dic22—41no—
178C8×C11—21no—
179C8×C11—21no—
180C8×C11—21no—
181C8×C11C2×#4112yes—
182C22×Q16C2×D1111yescharacteristic
183#529—221no—
184C2×C4×Q8—21no—
185C2×Q32—112no—
186C2×SD32—112no—
187#499—111no—
188#495—111no—
189#488—221no—
190#467—111no—
191#466—111no—
192#465—221no—
193C4×Q16—21no—
194C4×Q16—21no—
195C4×Q16—111no—
196C4×Q16C2×D1112yes—
197C4×Q16C2×D1112yes—
198C4×SD16—221no—
199C4×D8—111no—
200C2×#107C2×D1111yescharacteristic
201C2×#103—21no—
202C2×C4×C8C2×D1111yescharacteristic
203#367—112no—
204#366—112no—
205C4⋊C16—112no—
206#358—112no—
207#358—112no—
208#358—112no—
209#357—112no—
210C22⋊C16—111no—
211C22⋊C16—111no—
212#346—112no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11#51012yes—
216C22×C11C22×D811yescharacteristic
217C2×D11—81no—
218C2×D11—81no—
219C2×D11—81no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—44no—
226C4×C11—82no—
227C4×C11#52511yescharacteristic
228C4×C11#57511yescharacteristic
229Dic11—81no—
230Dic11—81no—
231Dic11—81no—
232C22×Q8—21no—
233C2×Q16—24no—
234C2×Q16—21no—
235C2×Q16—111no—
236C2×Q16C22×D1112yes—
237C2×SD16—221no—
238C2×D8—111no—
239C22×C8C22⋊D1111yescharacteristic
240C22×C8C22×D1111yescharacteristic
241#126—441no—
242#125—221no—
243#124—221no—
244#123—441no—
245C22⋊Q8—221no—
246#121—221no—
247C4×Q8—22no—
248C4×Q8—22no—
249C4×Q8—41no—
250C4×Q8—41no—
251C4×Q8—221no—
252C4×D4—221no—
253C4×D4—441no—
254#117—441no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—41no—
257C2×C42—41no—
258C2×C42C22⋊D1111yescharacteristic
259Q32—224no—
260SD32—224no—
261C2×C16—112no—
262C2×C16—112no—
263#107—21no—
264#107—111no—
265#107—111no—
266#107C22×D1112yes—
267#106—221no—
268#103—22no—
269#103—22no—
270#103—221no—
271#103—221no—
272#102—221no—
273#102—221no—
274C4×C8C22⋊D1111yescharacteristic
275C4×C8C22⋊D1111yescharacteristic
276C4×C8C22×D1111yescharacteristic
277C4×C8C22×D1111yescharacteristic
278C2×C11—22no—
279C2×C11#310011yescharacteristic
280C2×C11C2×#51011yescharacteristic
281C2×C11#341411yescharacteristic
282D11—161no—
283C2×Q8—24no—
284C2×Q8—22no—
285C2×Q8—42no—
286C2×Q8—41no—
287C2×Q8—221no—
288C2×D4—221no—
289C2×D4—441no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—441no—
293C22×C4#432311yescharacteristic
294C22×C4#432311yescharacteristic
295C22×C4C2×C22⋊D1111yescharacteristic
296Q16—24no—
297Q16—22no—
298Q16—222no—
299Q16#433914yes—
300SD16—442no—
301D8—222no—
302C2×C8—22no—
303C2×C8—41no—
304C2×C8C2×C22⋊D1111yescharacteristic
305C2×C8C2×C22⋊D1111yescharacteristic
306C2×C8C2×C22⋊D1111yescharacteristic
307C2×C8C23×D1111yescharacteristic
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—42no—
311C4⋊C4—42no—
312C4⋊C4—221no—
313C4⋊C4—221no—
314C4⋊C4—441no—
315C4⋊C4—441no—
316C4⋊C4—441no—
317C4⋊C4—441no—
318C22⋊C4—441no—
319C22⋊C4—441no—
320C22⋊C4—441no—
321C22⋊C4—441no—
322C22⋊C4—441no—
323C42—42no—
324C42—42no—
325C42—441no—
326C42#432311yescharacteristic
327C42#432311yescharacteristic
328C42C2×C22⋊D1111yescharacteristic
329C42C2×C22⋊D1111yescharacteristic
330C16—222no—
331C16—222no—
332C11#3367711yescharacteristic, complemented, Sylow
333C23—441no—
334C23C2×#432311yescharacteristic
335Q8—24no—
336Q8—44no—
337Q8—42no—
338Q8—441no—
339Q8—441no—
340D4—441no—
341D4—441no—
342D4—882no—
343C2×C4—22no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—44no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—82no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—882no—
355C2×C4C2×#432311yescharacteristic
356C2×C4C2×#432311yescharacteristic
357C2×C4C2×#432311yescharacteristic
358C2×C4C2×#432311yescharacteristic
359C2×C4C2×#432311yescharacteristic
360C2×C4C22×C22⋊D1111yescharacteristic
361C8—21no—
362C8—21no—
363C8—21no—
364C8C2×#433912yes—
365C22—21no—
366C22—21no—
367C22—881no—
368C22—881no—
369C22—881no—
370C22#1062279212yes—
371C22C22×#432311yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—44no—
378C4—82no—
379C4—881no—
380C4—881no—
381C4—881no—
382C4#1062332211yescharacteristic
383C4#1062335311yescharacteristic
384C2—22no—
385C2—1761no—
386C2#1307861611yescharacteristic
387C2C2×#1062279211yescharacteristic
388C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C4×C11×Q16C2
socleC22×C11C22×D8
prime radical#10622728C22
hypercenterC2×C4×Q16D11
hypocenterC11#33677
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
2. #13070818C2semidirect
4. #13070780C2semidirect
5. #13070678C2semidirect
6. #13070550C2semidirect
8. #13070485C2semidirect
9. #13070478C2semidirect
10. #13070419C2semidirect
11. C2×C4×C11×Q16C2semidirect
140. C2×C4×Q16D11semidirect
332. C11#33677semidirect

Maximal subgroups

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

subgroupindex
#130791862
#130708182
#130708012
#130707802
#130706782
#130705502
#130705332
#130704852
#130704782
#130704192
C2×C4×C11×Q162
#3367711