Finite Group Databasebeta

← #15758908

Subgroups — #15758908

Order 3328.

478 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123921C211yesmaximal, characteristic, complemented
2C4×#88076C211yesmaximal, characteristic, complemented
3#13113434C212yesmaximal
4#13112700C212yesmaximal, complemented
5C13×#2632C211yesmaximal, characteristic
6C2×C13×#124C2211yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#399—21no—
9C13×#395C411yescharacteristic
10C13×#395C411yescharacteristic
11C13×#394C411yescharacteristic
12C13×#394C411yescharacteristic
13C13×#393—21no—
14C13×#388—21no—
15C13×#388—21no—
16C13×#383C2211yescharacteristic
17C2×#88076—21no—
18#11718685—24no—
19#11718587—21no—
20#11718587C2212yes—
21#11718586—21no—
22C4×#6099C2212yes—
23#11718132—24no—
24#11718122—21no—
25C22×Q8×C13C2×C411yescharacteristic
26C22×Q8×C13D411yescharacteristic
27C22×D4×C13C2×C411yescharacteristic
28C13×#124—22no—
29C13×#124—22no—
30C4×Q8×C13—22no—
31C4×Q8×C13—22no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C42×C13D411yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C42×C13C2311yescharacteristic
46C2×#6099—22no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95C2×C411yescharacteristic
52C13×#95C2×C411yescharacteristic
53#88076—24no—
54C22⋊#1055—22no—
55C4⋊#1055—22no—
56C4⋊#1055—22no—
57C4⋊#1055—22no—
58#88043—22no—
59#88043—22no—
60#88043D414yes—
61C4×#1055—22no—
62C4×#1055—22no—
63#9188—131nomaximal, Sylow
64C24×C13—21no—
65C2×Q8×C13—22no—
66C2×Q8×C13—22no—
67C2×Q8×C13—22no—
68C2×Q8×C13—41no—
69C2×Q8×C13—81no—
70C2×D4×C13—22no—
71C2×D4×C13—81no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22×C411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C13×C4⋊C4—22no—
83C13×C4⋊C4—22no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4—81no—
86C13×C4⋊C4—81no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—42no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—42no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—81no—
93C13×C22⋊C4—81no—
94C42×C13—21no—
95C42×C13—21no—
96C42×C13—21no—
97C42×C13—21no—
98C42×C13C2×D412yes—
99C42×C13#4112yes—
100#6099—24no—
101#6099—42no—
102C2×#1055—24no—
103C2×#1055—42no—
104#2983—131no—
105#2632D1311yescharacteristic
106C4×#101—131no—
107#1527—132no—
108#1288—132no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13C2×C22⋊C411yescharacteristic
117Q8×C13—44no—
118Q8×C13—82no—
119D4×C13—82no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13#10412yes—
143C2×C4×C13C4×D412yes—
144C2×C4×C13#12011yescharacteristic
145C2×C4×C13#12112yes—
146C2×C4×C13#12311yescharacteristic
147#1055—44no—
148#1055—44no—
149C2×#124C2×D1311yescharacteristic
150C2×C4×Q8C2×D1311yescharacteristic
151#446—264no—
152#432—132no—
153#432—261no—
154#431—261no—
155C2×#101—261no—
156C4×M16—132no—
157#399—21no—
158#395Dic1311yescharacteristic
159#395Dic1311yescharacteristic
160#394Dic1311yescharacteristic
161#394Dic1311yescharacteristic
162#393—21no—
163#388—21no—
164#388—21no—
165#383C2×D1311yescharacteristic
166#343—261no—
167#329—264no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—81no—
171C22×C13—81no—
172C22×C13—81no—
173C22×C13—81no—
174C22×C13—81no—
175C22×C13—81no—
176C22×C13—81no—
177C22×C13#38611yescharacteristic
178C22×C13C2×#10411yescharacteristic
179C22×C13#42111yescharacteristic
180C4×C13—22no—
181C4×C13—22no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—22no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—81no—
189C4×C13—81no—
190C4×C13—81no—
191C22×Q8C2×Dic1311yescharacteristic
192C22×Q8C22⋊D1311yescharacteristic
193C22×D4C2×Dic1311yescharacteristic
194C2×M16—262no—
195#124—22no—
196#124—22no—
197C4×Q8—22no—
198C4×Q8—22no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C2×Dic1311yescharacteristic
202C2×C4⋊C4C2×Dic1311yescharacteristic
203C2×C4⋊C4C22⋊D1311yescharacteristic
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C42C22⋊D1311yescharacteristic
211C2×C42C22⋊D1311yescharacteristic
212C2×C42C22×D1311yescharacteristic
213C4⋊C8—262no—
214C4⋊C8—262no—
215C4⋊C8—262no—
216#101—264no—
217C22⋊C8—262no—
218#97—134no—
219#97—262no—
220#97—262no—
221C4×C8—262no—
222C4×C8—262no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95C2×Dic1311yescharacteristic
228#95C2×Dic1311yescharacteristic
229C2×C13—21no—
230C2×C13—21no—
231C2×C13—161no—
232C2×C13#187111yescharacteristic
233C2×C13#191211yescharacteristic
234C2×C13#191411yescharacteristic
235C24—21no—
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—81no—
241C2×D4—22no—
242C2×D4—81no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4C22⋊Dic1311yescharacteristic
247C22×C4C22⋊Dic1311yescharacteristic
248C22×C4C22⋊Dic1311yescharacteristic
249C22×C4C22⋊Dic1311yescharacteristic
250C22×C4C22×Dic1311yescharacteristic
251C22×C4C2×C22⋊D1311yescharacteristic
252C22×C4C2×C22⋊D1311yescharacteristic
253M16—264no—
254M16—522no—
255C2×C8—264no—
256C2×C8—522no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—81no—
261C4⋊C4—81no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—42no—
267C22⋊C4—81no—
268C22⋊C4—81no—
269C42—21no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42D4×D1312yes—
274C42#612912yes—
275C13#918811yescharacteristic, complemented, Sylow
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23C2×C22⋊Dic1311yescharacteristic
284Q8—44no—
285Q8—82no—
286D4—82no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4#8807712yes—
310C2×C4D4×Dic1312yes—
311C2×C4#8818911yescharacteristic
312C2×C4#8819111yescharacteristic
313C2×C4#8819312yes—
314C8—524no—
315C8—524no—
316C22—21no—
317C22—21no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22—81no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22#1171888111yescharacteristic
326C22C2×#8807711yescharacteristic
327C22#1171889711yescharacteristic
328C4—22no—
329C4—22no—
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C2—21no—
340C2—21no—
341C2—161no—
342C2#1311513911yescharacteristic
343C2#1311537411yescharacteristic
344C2#1311538411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2632C2
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenter#2632D13
hypocenterC13#9188
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2632

Complements

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

NH ≅ G/Ntype
1. #13123921C2semidirect
2. C4×#88076C2semidirect
4. #13112700C2semidirect
275. C13#9188semidirect

Maximal subgroups

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

subgroupindex
#131239212
C4×#880762
#131134342
#131127002
C13×#26322
#918813