Finite Group Databasebeta

← #15755795

Subgroups — #15755795

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
1C4×#88155C211yesmaximal, characteristic
2C2×#11718050C211yesmaximal, characteristic, complemented
3#13113224C212yesmaximal
4#13112685C212yesmaximal, complemented
5C13×#1564C211yesmaximal, characteristic, complemented
6C2×#88155C411yescharacteristic
7C2×#88155C411yescharacteristic
8C4×#6127C2211yescharacteristic
9C13×#431C2212yes—
10C2×C4×C8×C13C2211yescharacteristic
11#11718762C411yescharacteristic
12#11718762C411yescharacteristic
13C2×C4⋊#1055C2212yes—
14C4×#6099C2211yescharacteristic
15#11718350—21no—
16#11718350—21no—
17C4×#6094—21no—
18C4×C8×D13—21no—
19C13×#335—21no—
20C13×#334—21no—
21#11718051—22no—
22#11718050—21no—
23#11718050—21no—
24#11718048—22no—
25C2×#6127C2×C411yescharacteristic
26C22×C8×C13C2×C411yescharacteristic
27C22×C8×C13C2×C411yescharacteristic
28C2×C42×C13C2311yescharacteristic
29C4×C22⋊D13—21no—
30C4×C22⋊D13—21no—
31#88180C2×C411yescharacteristic
32C2×#6099C2×C411yescharacteristic
33C2×#6099C2×C411yescharacteristic
34C22×#1055—22no—
35#88155—22no—
36#88155—22no—
37#88155—22no—
38#88155C814yescomplemented
39C2×#6094—21no—
40C2×#6094—21no—
41C2×C8×D13—21no—
42C2×C8×D13—21no—
43C4×D52D411yescharacteristic
44C4×D52Q811yescharacteristic
45#88126—21no—
46C42×D13—21no—
47C4×Dic26D411yescharacteristic
48C4×Dic26Q811yescharacteristic
49C13×C4⋊C8—22no—
50C13×C22⋊C8—22no—
51C4×C8×C13—22no—
52C4×C8×C13D411yescharacteristic
53C4×C8×C13D411yescharacteristic
54C4×C8×C13D411yescharacteristic
55C4×C8×C13D411yescharacteristic
56#88055—21no—
57#88055—21no—
58C8×Dic13—21no—
59C8×Dic13—21no—
60C4⋊#1055—22no—
61C4⋊#1055—22no—
62#88043—21no—
63C4×#1055—21no—
64#8605—131nomaximal, Sylow
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13#4111yescharacteristic
67C22×C4×C13#4111yescharacteristic
68C2×C22⋊D13—21no—
69#6127—21no—
70#6127—21no—
71#6127C2×C812yes—
72#6127M1612yes—
73C2×D52C4⋊C411yescharacteristic
74C2×C4×D13—21no—
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C2×Dic26C4⋊C411yescharacteristic
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×C13C2×D411yescharacteristic
90C42×C13C2×Q811yescharacteristic
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—21no—
102#6099—21no—
103#6099C2×C812yes—
104#6099M1612yes—
105C2×#1055—21no—
106C2×#1055—21no—
107C2×#1055—42no—
108C2×#1055—82no—
109#6094—24no—
110#6094—24no—
111C8×D13—24no—
112C8×D13—24no—
113C4×#131—131no—
114#1564D1311yescharacteristic, complemented
115C2×#335—131no—
116#1477—132no—
117#1283—132no—
118C23×C13#11711yescharacteristic
119C22×D13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—41no—
123C2×C4×C13C2×C22⋊C411yescharacteristic
124C2×C4×C13C2×C4⋊C411yescharacteristic
125C2×C4×C13#12111yescharacteristic
126C2×C4×C13#12111yescharacteristic
127C2×C4×C13C22⋊Q811yescharacteristic
128C2×C4×C13C22⋊Q811yescharacteristic
129C2×C4×C13C22×C811yescharacteristic
130C2×C4×C13C2×M1611yescharacteristic
131C2×C4×C13C2×M1611yescharacteristic
132C2×C4×C13C2×M1611yescharacteristic
133C22⋊D13—22no—
134C22⋊D13—22no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138D52—21no—
139D52C4⋊C812yes—
140C4×D13—22no—
141C4×D13—22no—
142C4×D13—42no—
143C4×D13—41no—
144C4×D13—41no—
145Dic26—21no—
146Dic26C4⋊C812yes—
147C8×C13—21no—
148C8×C13—21no—
149C8×C13—82no—
150C8×C13C22⋊C812yes—
151C8×C13C22⋊C812yes—
152#1055—22no—
153#1055—22no—
154#1055—82no—
155C2×#131—131no—
156C2×#131—131no—
157C4×#41—131no—
158#431C2×D1312yes—
159C2×C4⋊C8—132no—
160#405—131no—
161#405—131no—
162#405—261no—
163#405—261no—
164C4×M16—131no—
165C4×M16—261no—
166C2×C4×C8—261no—
167C2×C4×C8C2×D1311yescharacteristic
168#335—21no—
169#335—261no—
170#335—261no—
171#334—21no—
172Q8⋊C8—262no—
173D4⋊C8—262no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13#38011yescharacteristic
177C22×C13#43111yescharacteristic
178C22×C13#43211yescharacteristic
179C2×D13—22no—
180C2×D13—41no—
181C2×D13—41no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13C2×C22⋊C811yescharacteristic
186C4×C13#40711yescharacteristic
187C4×C13C2×C4⋊C811yescharacteristic
188C4×C13#42311yescharacteristic
189C4×C13#47211yescharacteristic
190C4×C13#47311yescharacteristic
191Dic13—22no—
192Dic13—41no—
193Dic13—41no—
194C2×#41—131no—
195#131—134no—
196#131—262no—
197#131—262no—
198#131—262no—
199C2×M16—131no—
200C2×M16—131no—
201C2×M16—261no—
202C2×M16—261no—
203C22×C8—261no—
204C22×C8—261no—
205C22×C8—262no—
206C22×C8C4×D1311yescharacteristic
207C22×C8C4×D1311yescharacteristic
208C4×Q8—131no—
209C4×Q8—131no—
210C4×D4—131no—
211C4×D4—131no—
212C4×D4—261no—
213C4×D4—261no—
214#117—131no—
215#117—261no—
216C2×C42—261no—
217C2×C42C22×D1311yescharacteristic
218C4⋊C8—22no—
219C4⋊C8—262no—
220C4⋊C8—262no—
221C22⋊C8—22no—
222#97—261no—
223#97—261no—
224#97—261no—
225C4×C8—22no—
226C4×C8—261no—
227C4×C8—261no—
228C4×C8—261no—
229C4×C8D5211yescharacteristic
230C4×C8D5211yescharacteristic
231C4×C8C22⋊D1311yescharacteristic
232C4×C8C22⋊D1311yescharacteristic
233C2×C13—21no—
234C2×C13—21no—
235C2×C13#179711yescharacteristic
236C2×C13#181411yescharacteristic
237C2×C13#181611yescharacteristic
238D13—42no—
239#41—132no—
240#41—132no—
241#41—261no—
242#41—261no—
243C2×Q8—131no—
244C2×D4—131no—
245C2×D4—261no—
246C22×C4—261no—
247C22×C4—261no—
248C22×C4—261no—
249C22×C4C2×C4×D1311yescharacteristic
250C22×C4#612911yescharacteristic
251C22×C4#613111yescharacteristic
252M16—132no—
253M16—132no—
254M16—264no—
255M16—261no—
256M16—261no—
257M16—264no—
258C2×C8—21no—
259C2×C8—21no—
260C2×C8—42no—
261C2×C8—264no—
262C2×C8—261no—
263C2×C8—261no—
264C2×C8—264no—
265C2×C8—522no—
266C2×C8—1042no—
267C2×C8C8×D1312yes—
268C2×C8#609412yes—
269C2×C8#610311yescharacteristic
270C2×C8#610311yescharacteristic
271C2×C8#610311yescharacteristic
272C2×C8#610311yescharacteristic
273C4⋊C4—131no—
274C4⋊C4—131no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C22⋊C4—261no—
278C22⋊C4—261no—
279C22⋊C4—261no—
280C42—261no—
281C42—261no—
282C42—261no—
283C42C2×D5211yescharacteristic
284C42D4×D1311yescharacteristic
285C42Q8×D1311yescharacteristic
286C42C2×C22⋊D1311yescharacteristic
287C13#860511yescharacteristic, complemented, Sylow
288C23—261no—
289C23#8814611yescharacteristic
290Q8—132no—
291Q8—261no—
292D4—132no—
293D4—262no—
294D4—262no—
295D4—261no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—261no—
300C2×C4—262no—
301C2×C4—262no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—522no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4C4⋊C4×D1311yescharacteristic
308C2×C4#8814911yescharacteristic
309C2×C4#8815111yescharacteristic
310C2×C4C2×C8×D1311yescharacteristic
311C2×C4C2×#609411yescharacteristic
312C2×C4M16×D1311yescharacteristic
313C2×C4M16×D1311yescharacteristic
314C2×C4C2×#610311yescharacteristic
315C2×C4#8819211yescharacteristic
316C2×C4#8820011yescharacteristic
317C8—21no—
318C8—21no—
319C8—82no—
320C8—262no—
321C8—262no—
322C8—1042no—
323C8#8806012yes—
324C8#8806012yes—
325C22—21no—
326C22—21no—
327C22—262no—
328C22—521no—
329C22—521no—
330C22#1171849411yescharacteristic
331C22#1171849611yescharacteristic
332C22#1171864811yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—262no—
337C4—521no—
338C4—521no—
339C4D13×C4⋊C811yescharacteristic
340C4#1171849811yescharacteristic
341C4#1171855711yescharacteristic
342C4#1171855811yescharacteristic
343C4C2×#8806011yescharacteristic
344C4#1171878711yescharacteristic
345C2—21no—
346C2—21no—
347C2—522no—
348C2#1311481311yescharacteristic
349C2#1311488711yescharacteristic
350C2#1311489711yescharacteristic
subgroupG/H
centerC2×C4#88149
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1564C2
socleC22×C13#380
prime radicalC2×#6127C2×C4
cosocleC2×C42×C13C23
hypercenter#1564D13
hypocenterC13#8605
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. C2×#11718050C2semidirect
4. #13112685C2semidirect
5. C13×#1564C2semidirect
38. #88155C8semidirect
114. #1564D13semidirect
287. C13#8605semidirect

Maximal subgroups

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

subgroupindex
C4×#881552
C2×#117180502
#131132242
#131126852
C13×#15642
#860513