Finite Group Databasebeta

← #16790860

Subgroups — #16790860

Order 3328.

522 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 132 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
1C2×#11718260C211yesmaximal, characteristic, complemented
2C2×#11718259C212yesmaximal, complemented
3C2×C22⋊#6092C212yesmaximal, complemented
4C2×#11718258C211yesmaximal, characteristic, complemented
5C2×#11718386C211yesmaximal, characteristic
6C2×C4×C22⋊D13C411yescharacteristic
7C23×#1055C2211yescharacteristic
8C22×C8×D13C2211yescharacteristic
9C22×#6092C2212yes—
10C22×#6092C2212yes—
11C2×C13×C22⋊C8C411yescharacteristic
12C2×#88060C411yescharacteristic
13C2×#88054C411yescharacteristic
14C2×C8×Dic13C2211yescharacteristic
15#11718386—22no—
16#11718386—22no—
17C22⋊#6092—24no—
18#11718260—22no—
19#11718259—24no—
20#11718258—22no—
21C23×C4×C13C2×C411yescharacteristic
22C22×C22⋊D13C811yescharacteristic
23C22×C4×D13C2×C411yescharacteristic
24C22×C8×C13C2×C411yescharacteristic
25C22×C8×C13C2×C411yescharacteristic
26C2×C22⋊Dic13C811yescharacteristic
27C4×C22⋊D13—22no—
28C4×C22⋊D13—22no—
29C2×#6103C811yescharacteristic
30C2×#6101C811yescharacteristic
31C2×C4×Dic13C2×C411yescharacteristic
32C22×#1055—22no—
33C22×#1055—21no—
34C22×#1055—21no—
35C22×#1055—22no—
36C22×#1055C2×C411yescharacteristic
37C22×#1055C2311yescharacteristic
38C2×C8×D13—22no—
39C2×C8×D13—21no—
40C2×C8×D13—21no—
41C2×C8×D13—22no—
42C2×#6092—22no—
43C2×#6092—22no—
44C2×#6092—22no—
45C2×#6092—22no—
46C2×#6092—22no—
47C2×#6092D414yescomplemented
48C13×C22⋊C8—22no—
49#88060—22no—
50#88054—22no—
51C8×Dic13D412yes—
52C8×Dic13D412yes—
53#13190—131nomaximal, Sylow
54C24×C13C2×C811yescharacteristic
55C23×D13C2×C811yescharacteristic
56C22×C4×C13—21no—
57C22×C4×C13—22no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13C2×C811yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C2×C22⋊D13—22no—
63C2×C22⋊D13—22no—
64C2×C22⋊D13—22no—
65C22×Dic13C2×C811yescharacteristic
66C22×Dic13C2×C811yescharacteristic
67C22×Dic13C2×C811yescharacteristic
68C2×C4×D13—21no—
69C2×C4×D13—22no—
70C2×C4×D13—21no—
71C2×C4×D13—22no—
72C2×C8×C13—22no—
73C2×C8×C13—21no—
74C2×C8×C13—22no—
75C2×C8×C13C22⋊C412yes—
76C22⋊Dic13—22no—
77#6103—22no—
78#6101—22no—
79C4×Dic13C22⋊C412yes—
80C4×Dic13M1612yes—
81C2×#1055—21no—
82C2×#1055—22no—
83C2×#1055—42no—
84C2×#1055—41no—
85C2×#1055—41no—
86C2×#1055C2×D411yescharacteristic
87C2×#1055C2×D412yes—
88C2×#1055C2×D411yescharacteristic
89C2×#1055#4112yes—
90C8×D13—42no—
91C8×D13—41no—
92C8×D13—41no—
93#6092—24no—
94#6092—42no—
95C2×C8×D4—131no—
96C2×C4⋊C16—131no—
97C2×C22⋊C16—132no—
98C2×C22⋊C16—132no—
99C2×#346—131no—
100C23×C13—21no—
101C23×C13—22no—
102C23×C13—21no—
103C23×C13—22no—
104C23×C13M3212yes—
105C23×C13C22×C811yescharacteristic
106C22×D13—21no—
107C22×D13—22no—
108C22×D13—21no—
109C22×D13—22no—
110C22×D13M3212yes—
111C2×C4×C13—21no—
112C2×C4×C13—22no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—42no—
116C2×C4×C13C2×C22⋊C411yescharacteristic
117C2×C4×C13C4×D412yes—
118C2×C4×C13C2×M1611yescharacteristic
119C2×C4×C13#13112yes—
120C22⋊D13—28no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—22no—
124C2×Dic13—21no—
125C2×Dic13—22no—
126C2×Dic13C22⋊C812yes—
127C2×Dic13C22⋊C812yes—
128C4×D13—41no—
129C4×D13—41no—
130C4×D13—42no—
131C8×C13—22no—
132C8×C13—41no—
133#1055—41no—
134#1055#12112yes—
135#1055#12411yescharacteristic
136#1055#12711yescharacteristic
137C23×C8—131no—
138C23×C8—131no—
139C2×C4×D4—131no—
140C22×C16—132no—
141C22×C16—132no—
142C8×D4—262no—
143C8×D4—262no—
144C2×C4⋊C8—131no—
145C2×C22⋊C8—131no—
146C2×C22⋊C8#26111yescharacteristic
147C2×C4×C8—131no—
148C4⋊C16—262no—
149C22⋊C16—264no—
150C22⋊C16—264no—
151#346—262no—
152C22×C13—22no—
153C22×C13—24no—
154C22×C13—41no—
155C22×C13—42no—
156C22×C13—41no—
157C22×C13C2×C22⋊C811yescharacteristic
158C22×C13C8×D412yes—
159C22×C13C2×M3211yescharacteristic
160C22×C13C2×M3211yescharacteristic
161C22×C13#50412yes—
162C2×D13—22no—
163C2×D13—24no—
164C2×D13—41no—
165C2×D13—42no—
166C2×D13—41no—
167C4×C13—41no—
168C4×C13#39011yescharacteristic
169C4×C13#40811yescharacteristic
170C4×C13#43612yes—
171Dic13—22no—
172Dic13—22no—
173Dic13—41no—
174C22×D4—131no—
175C23×C4—131no—
176C23×C4C2×#26111yescharacteristic
177C22×C8—131no—
178C22×C8—131no—
179C22×C8—262no—
180C22×C8—262no—
181C22×C8—261no—
182C22×C8—261no—
183C22×C8—262no—
184C22×C8—262no—
185C22×C8—261no—
186C22×C8—261no—
187C22×C8C2×#26111yescharacteristic
188C22×C8C2×#26111yescharacteristic
189C4×D4—262no—
190C4×D4—262no—
191C2×C4⋊C4—131no—
192C2×C22⋊C4—131no—
193C2×C22⋊C4—131no—
194C2×C42—131no—
195C2×C16—134no—
196C2×C16—262no—
197C2×C16—262no—
198C2×C16—262no—
199C2×C16—262no—
200C2×C16—262no—
201C4⋊C8—262no—
202C22⋊C8—22no—
203C22⋊C8—262no—
204C4×C8—132no—
205C4×C8—132no—
206C2×C13—42no—
207C2×C13#195411yescharacteristic
208C2×C13#211211yescharacteristic
209C2×C13#211311yescharacteristic
210C2×C13#216812yes—
211C2×C13#216812yes—
212D13—42no—
213C24—131no—
214C24D13⋊C811yescharacteristic
215C2×D4—262no—
216C2×D4—262no—
217C2×D4—262no—
218C22×C4—21no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—21no—
222C22×C4—131no—
223C22×C4—131no—
224C22×C4—131no—
225C22×C4—261no—
226C22×C4—262no—
227C22×C4—262no—
228C22×C4—261no—
229C22×C4D13⋊C811yescharacteristic
230C22×C4C22×#26111yescharacteristic
231C2×C8—22no—
232C2×C8—22no—
233C2×C8—21no—
234C2×C8—132no—
235C2×C8—132no—
236C2×C8—131no—
237C2×C8—131no—
238C2×C8—262no—
239C2×C8—261no—
240C2×C8—522no—
241C2×C8—521no—
242C2×C8—521no—
243C2×C8—522no—
244C2×C8—521no—
245C2×C8—521no—
246C2×C8C22⋊#26112yes—
247C4⋊C4—262no—
248C22⋊C4—262no—
249C22⋊C4—262no—
250C42—132no—
251C42—132no—
252C16—264no—
253C16—522no—
254C13#1319011yescharacteristic, complemented, Sylow
255C23—22no—
256C23—21no—
257C23—22no—
258C23—21no—
259C23—132no—
260C23—262no—
261C23—261no—
262C23—262no—
263C23—261no—
264C23#8809812yes—
265C23C2×D13⋊C811yescharacteristic
266D4—268no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—132no—
273C2×C4—132no—
274C2×C4—261no—
275C2×C4—261no—
276C2×C4—262no—
277C2×C4—262no—
278C2×C4—261no—
279C2×C4—522no—
280C2×C4—521no—
281C2×C4—521no—
282C2×C4D13⋊M1611yescharacteristic
283C2×C4#8823812yes—
284C2×C4D4×#26112yes—
285C2×C4C2×C22⋊#26111yescharacteristic
286C8—22no—
287C8—41no—
288C8—132no—
289C8—131no—
290C8—131no—
291C8—521no—
292C22—22no—
293C22—24no—
294C22—41no—
295C22—41no—
296C22—42no—
297C22—262no—
298C22—264no—
299C22—521no—
300C22—521no—
301C22—522no—
302C22#1171906312yes—
303C22C2×#8809811yescharacteristic
304C22D13⋊M3211yescharacteristic
305C22#1171909612yes—
306C22D13⋊(C22⋊C8)11yescharacteristic
307C4—41no—
308C4—262no—
309C4—262no—
310C4—521no—
311C4#1171906612yes—
312C4#1171914611yescharacteristic
313C4#1171915111yescharacteristic
314C2—42no—
315C2—522no—
316C2#1313095911yescharacteristic
317C2#1313106411yescharacteristic
318C2#1313106711yescharacteristic
319C2#1313121712yes—
320C2#1313121812yes—
subgroupG/H
center, FrattiniC22×C4C22×#261
commutator, socleC23×C13C22×C8
FittingC2×C13×C22⋊C8C4
prime radicalC22×C22⋊D13C8
cosocleC22×#1055C23
hypercenterC2×C22⋊C8#261
hypocenterC13#13190
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#11718260C2semidirect
2. C2×#11718259C2semidirect
3. C2×C22⋊#6092C2semidirect
4. C2×#11718258C2semidirect
47. C2×#6092D4semidirect
254. C13#13190semidirect

Maximal subgroups

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

subgroupindex
C2×#117182602
C2×#117182592
C2×C22⋊#60922
C2×#117182582
C2×#117183862
#1319013