Finite Group Databasebeta

← #15756089

Subgroups — #15756089

Order 3328.

454 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#6127C211yesmaximal, characteristic
2#13114857C212yesmaximal
3#13113595C211yesmaximal, characteristic, complemented
4#13112739C212yesmaximal, complemented
5C4×C13×#107C211yesmaximal, characteristic, complemented
6C4×#6127C2211yescharacteristic
7C2×C13×#107—21no—
8C2×C4×C8×C13C2211yescharacteristic
9C4×C13×C4⋊C4C2212yes—
10C8×C22⋊D13—21no—
11C8×C22⋊D13—21no—
12C2×#88045—22no—
13#11718586C2211yescharacteristic
14#11718585C2212yes—
15C8×D52C411yescharacteristic, complemented
16C8×D52C411yescharacteristic, complemented
17#11718346—21no—
18C4×C8×D13—21no—
19C8×Dic26C411yescharacteristic, complemented
20C8×Dic26C411yescharacteristic, complemented
21C13×#340—21no—
22#11718115—22no—
23#11718050—21no—
24#11718050—21no—
25C2×#6127D411yescharacteristic
26C22×C8×C13D411yescharacteristic
27C22×C8×C13D411yescharacteristic
28C2×C13×C4⋊C4—22no—
29C2×C42×C13—22no—
30C2×C42×C13C2311yescharacteristic
31C4×C22⋊D13—21no—
32C4×C22⋊D13—21no—
33#88180D411yescharacteristic
34C2×#6099—22no—
35C2×C8×D13—21no—
36C2×C8×D13—21no—
37C4×D52C2×C411yescharacteristic
38C4×D52Q811yescharacteristic
39#88126—21no—
40C42×D13—21no—
41C4×Dic26C2×C411yescharacteristic
42C4×Dic26Q811yescharacteristic
43C13×#107—24no—
44C4×C8×C13C2×C411yescharacteristic
45C4×C8×C13C2×C411yescharacteristic
46C4×C8×C13D411yescharacteristic
47C4×C8×C13D411yescharacteristic
48C13×#95—22no—
49C22⋊#1055—21no—
50#88060—21no—
51#88060—21no—
52#88054—21no—
53#88054—21no—
54C8×Dic13—21no—
55C8×Dic13—21no—
56#88045—44no—
57C4⋊#1055—22no—
58C4⋊#1055—22no—
59C4⋊#1055C2×C411yescharacteristic
60C4⋊#1055C2×C411yescharacteristic
61C4×#1055—21no—
62#8667—131nomaximal, Sylow
63C22×C4×C13—42no—
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13#4111yescharacteristic
67C2×C22⋊D13—21no—
68#6127—21no—
69#6127—21no—
70#6127D812yes—
71#6127Q1612yes—
72C2×D52C4⋊C411yescharacteristic
73C2×C4×D13—21no—
74C2×C4×D13—21no—
75C2×C4×D13—21no—
76C2×Dic26C4⋊C411yescharacteristic
77C2×C8×C13—22no—
78C2×C8×C13—41no—
79C2×C8×C13C22⋊C411yescharacteristic
80C2×C8×C13C22⋊C411yescharacteristic
81C2×C8×C13C22⋊C411yescharacteristic
82C2×C8×C13C22⋊C411yescharacteristic
83C13×C4⋊C4—24no—
84C13×C4⋊C4—42no—
85C42×C13—42no—
86C42×C13—42no—
87C42×C13C22×C411yescharacteristic
88C42×C13C2×D411yescharacteristic
89C42×C13C2×Q811yescharacteristic
90C42×C13#4111yescharacteristic
91C22⋊Dic13—21no—
92#6103—21no—
93#6103—21no—
94C4⋊Dic13C4⋊C411yescharacteristic
95C4⋊Dic13C4⋊C411yescharacteristic
96#6101—21no—
97#6101—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101#6099—42no—
102#6099—42no—
103C2×#1055—21no—
104C2×#1055—21no—
105C2×#1055—42no—
106C8×D13—42no—
107C8×D13—42no—
108C8×#41—131no—
109#1806—132no—
110C4×#107D1311yescharacteristic, complemented
111#1567—131no—
112#1303—132no—
113C23×C13#12111yescharacteristic
114C22×D13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—41no—
118C2×C4×C13—44no—
119C2×C4×C13—82no—
120C2×C4×C13—82no—
121C2×C4×C13C2×C22⋊C411yescharacteristic
122C2×C4×C13C2×C4⋊C411yescharacteristic
123C2×C4×C13#11711yescharacteristic
124C2×C4×C13#12111yescharacteristic
125C2×C4×C13C22⋊Q811yescharacteristic
126C2×C4×C13C22⋊Q811yescharacteristic
127C2×C4×C13C2×D811yescharacteristic
128C2×C4×C13C2×Q1611yescharacteristic
129C2×C4×C13#13511yescharacteristic
130C2×C4×C13#13511yescharacteristic
131C22⋊D13—22no—
132C22⋊D13—22no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136D52—21no—
137D52#10712yescomplemented
138C4×D13—22no—
139C4×D13—22no—
140C4×D13—42no—
141C4×D13—41no—
142C4×D13—41no—
143Dic26—21no—
144Dic26#10712yescomplemented
145C8×C13—21no—
146C8×C13—21no—
147C8×C13—21no—
148C8×C13#10412yescomplemented
149#1055—41no—
150#1055—41no—
151#1055—82no—
152C4×#41—131no—
153C8×Q8—131no—
154C8×Q8—131no—
155C8×D4—131no—
156C8×D4—131no—
157C8×D4—261no—
158C8×D4—261no—
159#431—131no—
160#431—261no—
161C2×#107—21no—
162#423—132no—
163C2×#104—262no—
164C2×C4×C8—261no—
165C2×C4×C8C2×D1311yescharacteristic
166C4×C4⋊C4C2×D1312yes—
167#340—21no—
168#339—262no—
169#335—261no—
170#335—261no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13#38011yescharacteristic
174C22×C13#46611yescharacteristic
175C22×C13#46711yescharacteristic
176C2×D13—22no—
177C2×D13—41no—
178C2×D13—41no—
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—84no—
183C4×C13C2×#10411yescharacteristic
184C4×C13#42111yescharacteristic
185C4×C13C2×#10711yescharacteristic
186C4×C13#42711yescharacteristic
187C4×C13#46611yescharacteristic
188C4×C13#46711yescharacteristic
189Dic13—22no—
190Dic13—41no—
191Dic13—41no—
192C2×#41—131no—
193C2×M16—262no—
194C22×C8—261no—
195C22×C8—261no—
196C22×C8C22⋊D1311yescharacteristic
197C22×C8C22⋊D1311yescharacteristic
198C4×Q8—131no—
199C4×Q8—131no—
200C4×D4—131no—
201C4×D4—131no—
202C4×D4—261no—
203C4×D4—261no—
204#117—131no—
205#117—261no—
206C2×C4⋊C4—22no—
207C2×C42—22no—
208C2×C42—261no—
209C2×C42C22×D1311yescharacteristic
210#107—24no—
211C4⋊C8—131no—
212C4⋊C8—131no—
213C4⋊C8—261no—
214C4⋊C8—261no—
215C4⋊C8—262no—
216C4⋊C8—262no—
217#104—524no—
218C22⋊C8—261no—
219C22⋊C8—261no—
220C22⋊C8—261no—
221C4×C8—261no—
222C4×C8—261no—
223C4×C8—261no—
224C4×C8C4×D1311yescharacteristic
225C4×C8C4×D1311yescharacteristic
226C4×C8D5211yescharacteristic
227C4×C8D5211yescharacteristic
228#95—22no—
229C2×C13—21no—
230C2×C13—21no—
231C2×C13#180611yescharacteristic
232C2×C13#180811yescharacteristic
233C2×C13#181411yescharacteristic
234D13—42no—
235#41—132no—
236#41—132no—
237#41—261no—
238#41—261no—
239C2×Q8—131no—
240C2×D4—131no—
241C2×D4—261no—
242C22×C4—42no—
243C22×C4—261no—
244C22×C4—261no—
245C22×C4—261no—
246C22×C4D4×D1311yescharacteristic
247C22×C4#612911yescharacteristic
248C22×C4C2×C22⋊D1311yescharacteristic
249M16—522no—
250M16—522no—
251C2×C8—22no—
252C2×C8—41no—
253C2×C8—261no—
254C2×C8—261no—
255C2×C8—522no—
256C2×C8—522no—
257C2×C8—522no—
258C2×C8#610311yescharacteristic
259C2×C8#610311yescharacteristic
260C2×C8#610311yescharacteristic
261C2×C8#610311yescharacteristic
262C4⋊C4—24no—
263C4⋊C4—42no—
264C4⋊C4—131no—
265C4⋊C4—131no—
266C4⋊C4—261no—
267C4⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C42—42no—
272C42—42no—
273C42—261no—
274C42—261no—
275C42—261no—
276C42C2×C4×D1311yescharacteristic
277C42C2×D5211yescharacteristic
278C42Q8×D1311yescharacteristic
279C42#613111yescharacteristic
280C13#866711yescharacteristic, complemented, Sylow
281C23—261no—
282C23#8819211yescharacteristic
283Q8—132no—
284Q8—261no—
285D4—132no—
286D4—262no—
287D4—262no—
288D4—261no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—44no—
293C2×C4—82no—
294C2×C4—82no—
295C2×C4—261no—
296C2×C4—262no—
297C2×C4—262no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—522no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4C4⋊C4×D1311yescharacteristic
304C2×C4#8814611yescharacteristic
305C2×C4#8814911yescharacteristic
306C2×C4#8815111yescharacteristic
307C2×C4D8×D1311yescharacteristic
308C2×C4#8816611yescharacteristic
309C2×C4Q16×D1311yescharacteristic
310C2×C4#8817311yescharacteristic
311C2×C4C2×#610311yescharacteristic
312C2×C4#8820011yescharacteristic
313C8—21no—
314C8—21no—
315C8—21no—
316C8—521no—
317C8—521no—
318C8—1042no—
319C8#8804512yescomplemented
320C22—21no—
321C22—21no—
322C22—262no—
323C22—521no—
324C22—521no—
325C22#1171864811yescharacteristic
326C22#1171881811yescharacteristic
327C22#1171884911yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—84no—
332C4—262no—
333C4—521no—
334C4—521no—
335C4D13×#10711yescharacteristic
336C4#1171854111yescharacteristic
337C4#1171854411yescharacteristic
338C4#1171854811yescharacteristic
339C4C2×#8804511yescharacteristic
340C4#1171866611yescharacteristic
341C2—21no—
342C2—21no—
343C2—522no—
344C2#1311485711yescharacteristic
345C2#1311486211yescharacteristic
346C2#1311488711yescharacteristic
subgroupG/H
centerC2×C4#88149
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC4×C13×#107C2
socleC22×C13#380
prime radicalC2×#6127D4
cosocleC2×C42×C13C23
hypercenterC4×#107D13
hypocenterC13#8667
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
3. #13113595C2semidirect
4. #13112739C2semidirect
5. C4×C13×#107C2semidirect
15. C8×D52C4semidirect
16. C8×D52C4semidirect
19. C8×Dic26C4semidirect
20. C8×Dic26C4semidirect
110. C4×#107D13semidirect
137. D52#107semidirect
144. Dic26#107semidirect
148. C8×C13#104semidirect
280. C13#8667semidirect
319. C8#88045semidirect

Maximal subgroups

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

subgroupindex
C8×#61272
#131148572
#131135952
#131127392
C4×C13×#1072
#866713