Finite Group Databasebeta

← #16807103

Subgroups — #16807103

Order 3328.

520 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131211C212yesmaximal, complemented
2#13131209C212yesmaximal, complemented
3#13131208C212yesmaximal, complemented
4#13131206C212yesmaximal, complemented
5#13131178C212yesmaximal, complemented
6#13131073C212yesmaximal
7#13131053C212yesmaximal, complemented
8#13123263C211yesmaximal, characteristic
9C2×#88161C411yescharacteristic
10C2×#88155C2211yescharacteristic
11#11719227C411yescharacteristic
12D13⋊M32C2214yes—
13C13×#405C411yescharacteristic
14M16×Dic13C2211yescharacteristic
15C2×#88055C411yescharacteristic
16#11718658C2211yescharacteristic
17#11718369C411yescharacteristic
18#11718369C2211yescharacteristic
19D13×#97C411yescharacteristic
20D13×#97C2211yescharacteristic
21#11718350C411yescharacteristic
22#11718350C2211yescharacteristic
23C4×#6094C411yescharacteristic
24C4×#6094C2211yescharacteristic
25#11718284C2214yes—
26#11718263C2214yes—
27#11718262C2214yes—
28#11718261C2214yes—
29#11718233C2214yes—
30#11718232C2214yes—
31C2×#6127C2×C411yescharacteristic
32C2×C13×M16C2×C411yescharacteristic
33C22×C8×C13C2×C411yescharacteristic
34C13×#117C2×C411yescharacteristic
35C2×C4×Dic13C2×C411yescharacteristic
36C2×#6099C2311yescharacteristic
37C22×#1055C2×C411yescharacteristic
38#88161—24no—
39#88155—24no—
40C2×#6094C2×C411yescharacteristic
41C2×#6094C2×C411yescharacteristic
42C2×#6094C2×C411yescharacteristic
43C2×#6094C2311yescharacteristic
44C2×C8×D13C2×C411yescharacteristic
45C2×C8×D13C2×C411yescharacteristic
46C2×C8×D13C2×C411yescharacteristic
47C2×C8×D13C2311yescharacteristic
48#88147—21no—
49#88141—21no—
50#88135—21no—
51#88135—21no—
52#88126C2×C411yescharacteristic
53#88126C2×C411yescharacteristic
54C42×D13C2×C411yescharacteristic
55C42×D13C2×C411yescharacteristic
56#88106C2318yes—
57#88098—24no—
58D13⋊C16—24no—
59C13×#97C2×C411yescharacteristic
60C13×#97C2×C411yescharacteristic
61C4×C8×C13C2×C411yescharacteristic
62C4×C8×C13C2×C411yescharacteristic
63#88055C2×C411yescharacteristic
64#88055C2×C411yescharacteristic
65#88055C2×C411yescharacteristic
66#88055C2×C411yescharacteristic
67#88055C2×C411yescharacteristic
68#88055C2311yescharacteristic
69C8×Dic13C2×C411yescharacteristic
70C8×Dic13C2311yescharacteristic
71#88043C2×C411yescharacteristic
72#88043C2311yescharacteristic
73C4×#1055C2×C411yescharacteristic
74C4×#1055C2311yescharacteristic
75#33426—131nomaximal, Sylow
76C22×C4×C13C22×C411yescharacteristic
77C2×C22⋊D13M1611yescharacteristic
78C2×C22⋊D13M1611yescharacteristic
79C22×Dic13—21no—
80#6127—22no—
81#6127—22no—
82C2×D52M1611yescharacteristic
83C2×C4×D13—21no—
84C2×C4×D13—21no—
85C2×C4×D13C22×C411yescharacteristic
86C2×C4×D13C22×C411yescharacteristic
87C2×Dic26M1611yescharacteristic
88C13×M16—22no—
89C2×C8×C13—22no—
90C2×C8×C13C22×C411yescharacteristic
91C2×C8×C13C22×C411yescharacteristic
92C2×C8×C13C22×C411yescharacteristic
93C2×C8×C13C22×C411yescharacteristic
94C13×C4⋊C4—21no—
95C13×C22⋊C4—21no—
96C42×C13C22×C411yescharacteristic
97C42×C13C22×C411yescharacteristic
98#6103—21no—
99#6103—21no—
100#6101—21no—
101#6101—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104C4×Dic13—21no—
105C4×Dic13C22×C411yescharacteristic
106C4×Dic13C22×C411yescharacteristic
107#6099—22no—
108C2×#1055—22no—
109C2×#1055C22×C411yescharacteristic
110C2×#1055C22×C411yescharacteristic
111C2×#1055C22×C411yescharacteristic
112C2×#1055C2411yescharacteristic
113#6094—22no—
114#6094—22no—
115#6094—22no—
116#6094M1614yes—
117C8×D13—22no—
118C8×D13—22no—
119C8×D13—22no—
120C8×D13#4114yes—
121#6092—28no—
122#2875—131no—
123#2166—132no—
124#2166—132no—
125#2165—132no—
126#2165—132no—
127#2153—132no—
128#2115—132no—
129C2×#347—132no—
130C23×C13C2×M1611yescharacteristic
131C22×D13C2×M1611yescharacteristic
132C22×D13C2×M1611yescharacteristic
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13C2×M1611yescharacteristic
138C2×C4×C13C23×C411yescharacteristic
139C22⋊D13—22no—
140C22⋊D13—22no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—81no—
144C2×Dic13C2×M1611yescharacteristic
145C2×Dic13C2×M1611yescharacteristic
146D52—22no—
147C4×D13—21no—
148C4×D13—21no—
149C4×D13—81no—
150C4×D13—81no—
151C4×D13#11712yes—
152C4×D13C2×M1612yes—
153Dic26—22no—
154C8×C13—21no—
155C8×C13—21no—
156C8×C13#11712yes—
157C8×C13C2×M1612yes—
158#1055—21no—
159#1055—21no—
160#1055C2×M1612yes—
161#1055C2×#4112yes—
162C2×#131—131no—
163C2×#131—131no—
164C4×#41—131no—
165C2×M32—134no—
166#405—131no—
167#405—131no—
168#405—131no—
169#405—131no—
170#405—131no—
171#405#26111yescharacteristic
172C4×M16—131no—
173C4×M16—131no—
174C4×M16—131no—
175C2×#97—131no—
176C2×#97—131no—
177C2×#97—131no—
178#364—134no—
179#364—134no—
180#349—134no—
181#349—134no—
182#347—134no—
183#347—134no—
184C22×C13—21no—
185C22×C13—41no—
186C22×C13C22×M1611yescharacteristic
187C2×D13—21no—
188C2×D13—41no—
189C2×D13—41no—
190C2×D13#43212yes—
191C4×C13—21no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13C2×#11711yescharacteristic
195C4×C13C22×M1611yescharacteristic
196Dic13—21no—
197Dic13—41no—
198Dic13—41no—
199Dic13#43212yes—
200C2×#41—131no—
201#131—264no—
202#131—264no—
203C2×M16—131no—
204C2×M16—131no—
205C2×M16—131no—
206C2×M16—131no—
207C2×M16—131no—
208C2×M16C2×#26111yescharacteristic
209C22×C8—131no—
210C22×C8—131no—
211C22×C8—131no—
212C22×C8—131no—
213C22×C8—131no—
214C22×C8C2×#26111yescharacteristic
215C4×Q8—261no—
216C4×D4—261no—
217C4×D4—261no—
218C4×D4—261no—
219#117—131no—
220#117—131no—
221#117C2×#26111yescharacteristic
222C2×C42—131no—
223C2×C42—131no—
224C2×C42—131no—
225M32—138no—
226M32—264no—
227C2×C16—264no—
228#97—131no—
229#97—131no—
230#97—131no—
231#97—131no—
232#97—131no—
233#97—131no—
234#97—131no—
235#97—131no—
236#97C2×#26111yescharacteristic
237#97C2×#26111yescharacteristic
238C4×C8—131no—
239C4×C8—131no—
240C4×C8—131no—
241C4×C8—131no—
242C4×C8C2×#26111yescharacteristic
243C4×C8C2×#26111yescharacteristic
244C2×C13—21no—
245C2×C13—41no—
246C2×C13C2×#43211yescharacteristic
247D13—22no—
248D13—41no—
249#41—262no—
250#41—262no—
251C2×Q8—131no—
252C2×D4—131no—
253C2×D4—131no—
254C2×D4—131no—
255C22×C4—131no—
256C22×C4—131no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4C22×#26111yescharacteristic
261M16—22no—
262M16—134no—
263M16—262no—
264M16—262no—
265M16—262no—
266M16—262no—
267C2×C8—22no—
268C2×C8—131no—
269C2×C8—131no—
270C2×C8—134no—
271C2×C8—131no—
272C2×C8—131no—
273C2×C8—262no—
274C2×C8—262no—
275C2×C8—262no—
276C2×C8—262no—
277C2×C8C22×#26111yescharacteristic
278C2×C8C22×#26111yescharacteristic
279C2×C8C22×#26111yescharacteristic
280C2×C8C22×#26111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—261no—
283C4⋊C4—261no—
284C22⋊C4—21no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C42—131no—
288C42—131no—
289C42—261no—
290C42—261no—
291C42—261no—
292C42C22×#26111yescharacteristic
293C42C22×#26111yescharacteristic
294C16—268no—
295C13#3342611yescharacteristic, complemented, Sylow
296C23—131no—
297C23—131no—
298C23D13⋊M1611yescharacteristic
299Q8—262no—
300D4—262no—
301D4—262no—
302D4—262no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—131no—
308C2×C4—132no—
309C2×C4—132no—
310C2×C4—131no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—1041no—
316C2×C4—1041no—
317C2×C4—1041no—
318C2×C4D13⋊M1611yescharacteristic
319C2×C4C23×#26111yescharacteristic
320C8—21no—
321C8—21no—
322C8—132no—
323C8—132no—
324C8—261no—
325C8—261no—
326C8D13⋊M1612yes—
327C8#8823712yes—
328C22—21no—
329C22—41no—
330C22—132no—
331C22—261no—
332C22—521no—
333C22—521no—
334C22C2×D13⋊M1611yescharacteristic
335C4—21no—
336C4—41no—
337C4—41no—
338C4—132no—
339C4—261no—
340C4—521no—
341C4—521no—
342C4C2×D13⋊M1611yescharacteristic
343C4C2×#8823711yescharacteristic
344C2—21no—
345C2—41no—
346C2—262no—
347C2—521no—
348C2D13⋊#43211yescharacteristic
subgroupG/H
centerC4C2×#88237
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#405C4
socleC2×C13C2×#432
prime radicalC2×#6127C2×C4
cosocleC2×#1055C24
hypercenter#405#261
hypocenterC13#33426
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ #97 ◁ #405

Complements

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

NH ≅ G/Ntype
1. #13131211C2semidirect
2. #13131209C2semidirect
3. #13131208C2semidirect
4. #13131206C2semidirect
5. #13131178C2semidirect
7. #13131053C2semidirect
295. C13#33426semidirect

Maximal subgroups

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

subgroupindex
#131312112
#131312092
#131312082
#131312062
#131311782
#131310732
#131310532
#131232632
#3342613