Finite Group Databasebeta

← #15755777

Subgroups — #15755777

Order 3328.

462 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718350C211yesmaximal, characteristic
2#13113584C211yesmaximal, characteristic, complemented
3#13113148C212yesmaximal
4#13112666C212yesmaximal, complemented
5C13×#1564C211yesmaximal, characteristic, complemented
6C22×#6094C411yescharacteristic
7C22×C8×D13C411yescharacteristic
8C2×#88126C2211yescharacteristic
9C13×#431C2212yes—
10C2×C4×C8×C13C2211yescharacteristic
11C2×#88055C411yescharacteristic
12C2×C8×Dic13C411yescharacteristic
13#11718586C2212yes—
14C2×#88043C2211yescharacteristic
15#11718350—21no—
16#11718350—21no—
17#11718350—21no—
18#11718350—21no—
19C13×#335—21no—
20C13×#334—21no—
21#11718061—22no—
22#11718060—22no—
23#11718050—21no—
24#11718049—21no—
25C22×C4×D13C2×C411yescharacteristic
26C22×C8×C13C2×C411yescharacteristic
27C22×C8×C13C2×C411yescharacteristic
28C2×C42×C13C2311yescharacteristic
29C2×#6103D411yescharacteristic
30C2×#6103Q811yescharacteristic
31C2×#6101D411yescharacteristic
32C2×#6101Q811yescharacteristic
33C2×C4×Dic13C2×C411yescharacteristic
34C22×#1055C2×C411yescharacteristic
35C22×#1055C2×C411yescharacteristic
36C2×#6094—22no—
37C2×#6094—21no—
38C2×#6094—21no—
39C2×#6094—22no—
40C2×C8×D13—21no—
41C2×C8×D13—21no—
42C2×C8×D13—22no—
43C2×C8×D13C814yescomplemented
44#88126—21no—
45#88126—21no—
46#88126—21no—
47#88126—21no—
48C13×C4⋊C8—22no—
49C13×C22⋊C8—22no—
50C4×C8×C13—22no—
51C4×C8×C13D411yescharacteristic
52C4×C8×C13D411yescharacteristic
53C4×C8×C13D411yescharacteristic
54C4×C8×C13D411yescharacteristic
55C22⋊#1055—22no—
56#88055—21no—
57#88055—21no—
58C8×Dic13—21no—
59C8×Dic13—21no—
60C4⋊#1055—22no—
61#88043—21no—
62#88043—21no—
63C4×#1055—22no—
64#8601—131nomaximal, Sylow
65C23×D13C4⋊C411yescharacteristic
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×Q811yescharacteristic
69C22×Dic13C4⋊C411yescharacteristic
70C22×Dic13C4⋊C411yescharacteristic
71C22×Dic13C4⋊C411yescharacteristic
72C2×C4×D13—21no—
73C2×C4×D13—21no—
74C2×C4×D13—21no—
75C2×C4×D13—21no—
76C2×C4×D13C2×C812yes—
77C2×C4×D13M1612yes—
78C2×C8×C13—21no—
79C2×C8×C13—21no—
80C2×C8×C13—42no—
81C2×C8×C13C22⋊C411yescharacteristic
82C2×C8×C13C22⋊C411yescharacteristic
83C2×C8×C13C22⋊C411yescharacteristic
84C2×C8×C13C22⋊C411yescharacteristic
85C2×C8×C13C2×C812yes—
86C2×C8×C13M1612yes—
87C42×C13C2×D411yescharacteristic
88C42×C13C2×D411yescharacteristic
89C42×C13#4111yescharacteristic
90C42×C13#4111yescharacteristic
91#6103—21no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C2×#1055—21no—
102C2×#1055—21no—
103C2×#1055—21no—
104C2×#1055—21no—
105C2×#1055—42no—
106C2×#1055C2×C812yes—
107C2×#1055M1612yes—
108#6094—24no—
109#6094—24no—
110C8×D13—24no—
111C8×D13—24no—
112C2×#405—131no—
113#1564—131no—
114#1564D1311yescharacteristic, complemented
115#1458—132no—
116#1275—132no—
117C23×C13C2×C4⋊C411yescharacteristic
118C22×D13—21no—
119C22×D13—21no—
120C22×D13—41no—
121C22×D13—41no—
122C22×D13C4⋊C812yes—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13C2×C22⋊C411yescharacteristic
126C2×C4×C13#11711yescharacteristic
127C2×C4×C13#12111yescharacteristic
128C2×C4×C13#12111yescharacteristic
129C2×C4×C13C22⋊Q811yescharacteristic
130C2×C4×C13C22⋊Q811yescharacteristic
131C2×C4×C13C22×C811yescharacteristic
132C2×C4×C13C2×M1611yescharacteristic
133C2×C4×C13C2×M1611yescharacteristic
134C2×C4×C13C2×M1611yescharacteristic
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13C4⋊C812yes—
142C4×D13—22no—
143C4×D13—22no—
144C4×D13—22no—
145C4×D13—22no—
146C8×C13—21no—
147C8×C13—21no—
148C8×C13—82no—
149C8×C13C22⋊C812yes—
150C8×C13C22⋊C812yes—
151#1055—22no—
152#1055—22no—
153#1055—82no—
154C22×M16—131no—
155C23×C8—131no—
156C2×#117—131no—
157#431—132no—
158#431C2×D1312yes—
159#405—261no—
160#405—261no—
161#405—261no—
162#405—261no—
163C2×#97—131no—
164C2×#97—131no—
165C2×C4×C8—131no—
166C2×C4×C8C2×D1311yescharacteristic
167#335—21no—
168#335—261no—
169#334—21no—
170#334—261no—
171#324—262no—
172#323—262no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13#38011yescharacteristic
176C22×C13C2×C4⋊C811yescharacteristic
177C22×C13#42311yescharacteristic
178C2×D13—22no—
179C2×D13—42no—
180C2×D13—41no—
181C2×D13—41no—
182C2×D13—42no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13C2×C22⋊C811yescharacteristic
188C4×C13#40711yescharacteristic
189C4×C13#43111yescharacteristic
190C4×C13#43211yescharacteristic
191Dic13—22no—
192Dic13—41no—
193Dic13—41no—
194C23×C4—131no—
195C2×M16—262no—
196C2×M16—262no—
197C2×M16—261no—
198C2×M16—261no—
199C22×C8—131no—
200C22×C8—131no—
201C22×C8—134no—
202C22×C8—262no—
203C22×C8—261no—
204C22×C8—261no—
205C22×C8C4×D1311yescharacteristic
206C22×C8C4×D1311yescharacteristic
207#117—261no—
208#117—261no—
209#117—261no—
210#117—261no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—131no—
213C2×C22⋊C4—131no—
214C2×C22⋊C4—131no—
215C2×C42—131no—
216C2×C42C22×D1311yescharacteristic
217C4⋊C8—22no—
218C4⋊C8—262no—
219C22⋊C8—22no—
220C22⋊C8—262no—
221#97—261no—
222#97—261no—
223#97—261no—
224#97—261no—
225C4×C8—22no—
226C4×C8—261no—
227C4×C8—261no—
228C4×C8—262no—
229C4×C8D5211yescharacteristic
230C4×C8D5211yescharacteristic
231C4×C8C22⋊D1311yescharacteristic
232C4×C8C22⋊D1311yescharacteristic
233C2×C13—21no—
234C2×C13—21no—
235C2×C13#179711yescharacteristic
236C2×C13#181211yescharacteristic
237C2×C13#181311yescharacteristic
238D13—42no—
239C24—131no—
240C22×C4—131no—
241C22×C4—132no—
242C22×C4—132no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4—261no—
248C22×C4—261no—
249C22×C4C2×C4×D1311yescharacteristic
250C22×C4D4×D1311yescharacteristic
251C22×C4Q8×D1311yescharacteristic
252M16—264no—
253M16—264no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—42no—
257C2×C8—132no—
258C2×C8—132no—
259C2×C8—261no—
260C2×C8—261no—
261C2×C8—261no—
262C2×C8—261no—
263C2×C8—264no—
264C2×C8—264no—
265C2×C8—522no—
266C2×C8C8×D1312yes—
267C2×C8#609412yes—
268C2×C8#610311yescharacteristic
269C2×C8#610311yescharacteristic
270C2×C8#610311yescharacteristic
271C2×C8#610311yescharacteristic
272C4⋊C4—261no—
273C4⋊C4—261no—
274C4⋊C4—261no—
275C4⋊C4—261no—
276C22⋊C4—261no—
277C22⋊C4—261no—
278C22⋊C4—261no—
279C22⋊C4—261no—
280C42—261no—
281C42—261no—
282C42C2×D5211yescharacteristic
283C42#612911yescharacteristic
284C42#613111yescharacteristic
285C42C2×C22⋊D1311yescharacteristic
286C13#860111yescharacteristic, complemented, Sylow
287C23—132no—
288C23—261no—
289C23—261no—
290C23—521no—
291C23—521no—
292C23C4⋊C4×D1311yescharacteristic
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—132no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—262no—
299C2×C4—262no—
300C2×C4—262no—
301C2×C4—262no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4#8814611yescharacteristic
307C2×C4#8814911yescharacteristic
308C2×C4#8815111yescharacteristic
309C2×C4C2×C8×D1311yescharacteristic
310C2×C4C2×#609411yescharacteristic
311C2×C4M16×D1311yescharacteristic
312C2×C4M16×D1311yescharacteristic
313C2×C4C2×#610311yescharacteristic
314C2×C4#8819211yescharacteristic
315C2×C4#8820011yescharacteristic
316C8—21no—
317C8—21no—
318C8—82no—
319C8—262no—
320C8—262no—
321C8—1042no—
322C8#8806012yes—
323C8#8806012yes—
324C22—21no—
325C22—21no—
326C22—262no—
327C22—522no—
328C22—522no—
329C22—521no—
330C22—521no—
331C22D13×C4⋊C811yescharacteristic
332C22#1171849811yescharacteristic
333C22#1171864811yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—262no—
339C4—521no—
340C4—521no—
341C4#1171849411yescharacteristic
342C4#1171849611yescharacteristic
343C4C2×#8806011yescharacteristic
344C4#1171878711yescharacteristic
345C2—21no—
346C2—21no—
347C2—522no—
348C2#1311481311yescharacteristic
349C2#1311487911yescharacteristic
350C2#1311488311yescharacteristic
subgroupG/H
centerC2×C4#88146
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1564C2
socleC22×C13#380
prime radicalC23×D13C4⋊C4
cosocleC2×C42×C13C23
hypercenter#1564D13
hypocenterC13#8601
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1564

Complements

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

NH ≅ G/Ntype
2. #13113584C2semidirect
4. #13112666C2semidirect
5. C13×#1564C2semidirect
43. C2×C8×D13C8semidirect
114. #1564D13semidirect
286. C13#8601semidirect

Maximal subgroups

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

subgroupindex
C2×#117183502
#131135842
#131131482
#131126662
C13×#15642
#860113