Finite Group Databasebeta

← #16807084

Subgroups — #16807084

Order 3328.

590 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131201C214yesmaximal, complemented
2#13131197C212yesmaximal, complemented
3#13131193C212yesmaximal, complemented
4#13131168C211yesmaximal, characteristic, complemented
5C2×C4⋊#6092C211yesmaximal, characteristic, complemented
6#13131066C212yesmaximal
7#13131045C212yesmaximal, complemented
8C4×#88202C211yesmaximal, characteristic
9C4×C13×#41C411yescharacteristic
10C2×#88202C411yescharacteristic
11C2×#88202C2211yescharacteristic
12C2×#88106C2212yes—
13C22×#6092C2212yes—
14#11718658C411yescharacteristic
15#11718658C412yes—
16#11718658C2211yescharacteristic
17#11718658C2212yes—
18C4×#6099C412yes—
19C4×#6099C411yescharacteristic
20C2×C4×#1055C2211yescharacteristic
21C2×C4×#1055C2212yes—
22C22⋊#6092C2214yes—
23C22⋊#6092C2214yes—
24#11718231C2214yes—
25C4⋊#6092C2211yescharacteristic
26C4⋊#6092C2211yescharacteristic
27C4⋊#6092C2212yes—
28C4⋊#6092C2212yes—
29C4⋊#6092C2212yes—
30C4×#6092C2214yes—
31C2×C13×#41C2×C411yescharacteristic
32C4×Q8×C13C811yescharacteristic
33C4×Q8×C13C811yescharacteristic
34C4×D4×C13C812yes—
35C4×D4×C13C811yescharacteristic
36C4×D4×C13C812yes—
37C4×D4×C13C811yescharacteristic
38C13×#117C2×C412yes—
39C13×#117C2×C411yescharacteristic
40C2×C42×C13C2×C412yes—
41C2×C42×C13C2×C411yescharacteristic
42#88202—24no—
43#88202—22no—
44#88202—22no—
45C2×#6099C2×C411yescharacteristic
46C2×#6099C2×C412yes—
47C2×#6099C2×C412yes—
48C2×#6099C2×C411yescharacteristic
49C22×#1055C2×C411yescharacteristic
50C22×#1055C2×C412yes—
51C22×#1055C2312yes—
52C22×#1055C2311yescharacteristic
53#88106—24no—
54C2×#6092—24no—
55C2×#6092C2312yes—
56C2×#6092C2314yes—
57C2×#6092C2312yes—
58#88043C2×C412yes—
59#88043C2×C412yes—
60#88043C2×C412yes—
61C4×#1055C2×C412yes—
62C4×#1055C2×C411yescharacteristic
63C4×#1055C2×C411yescharacteristic
64C4×#1055C2×C412yes—
65C4×#1055C2312yes—
66C4×#1055C2311yescharacteristic
67C4×#1055C2311yescharacteristic
68#33423—131nomaximal, Sylow
69C13×#41—22no—
70C13×#41—22no—
71C2×Q8×C13C2×C811yescharacteristic
72C2×D4×C13C2×C812yes—
73C2×D4×C13C2×C811yescharacteristic
74C22×C4×C13C2×C812yes—
75C22×C4×C13C2×C811yescharacteristic
76C22×C4×C13C2×C812yes—
77C22×C4×C13C2×C811yescharacteristic
78C22×C4×C13C22×C412yes—
79C22×C4×C13C22×C411yescharacteristic
80C13×C4⋊C4C2×C812yes—
81C13×C4⋊C4C2×C812yes—
82C13×C4⋊C4C2×C811yescharacteristic
83C13×C4⋊C4C2×C811yescharacteristic
84C13×C22⋊C4C2×C812yes—
85C13×C22⋊C4C2×C812yes—
86C13×C22⋊C4C2×C812yes—
87C42×C13C2×C812yes—
88C42×C13C2×C811yescharacteristic
89C42×C13C2×C812yes—
90C42×C13C2×C811yescharacteristic
91C42×C13C22×C411yescharacteristic
92C42×C13C22×C412yes—
93C42×C13C22×C411yescharacteristic
94#6099—22no—
95#6099—24no—
96#6099—24no—
97#6099M1614yes—
98C2×#1055—22no—
99C2×#1055—24no—
100C2×#1055—22no—
101C2×#1055—22no—
102C2×#1055C22×C411yescharacteristic
103C2×#1055C22×C411yescharacteristic
104C2×#1055C22×C412yes—
105C2×#1055C22×C411yescharacteristic
106C2×#1055C22×C412yes—
107C2×#1055#4112yes—
108C2×#1055#4112yes—
109C2×#1055C2411yescharacteristic
110#6092—22no—
111#6092—22no—
112#6092—24no—
113C4×#131—131no—
114#2164—134no—
115#2163—132no—
116#2162—132no—
117#2150—131no—
118C2×C4⋊C16—131no—
119#2113—132no—
120#2108—132no—
121C23×C13C22×C812yes—
122C23×C13C22×C811yescharacteristic
123Q8×C13—22no—
124D4×C13—24no—
125D4×C13—22no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—24no—
130C2×C4×C13—41no—
131C2×C4×C13—42no—
132C2×C4×C13#11712yes—
133C2×C4×C13C22×C811yescharacteristic
134C2×C4×C13C22×C812yes—
135C2×C4×C13C22×C812yes—
136C2×C4×C13C22×C811yescharacteristic
137C2×C4×C13C22×C812yes—
138C2×C4×C13C22×C811yescharacteristic
139C2×C4×C13C22×C811yescharacteristic
140C2×C4×C13C22×C811yescharacteristic
141C2×C4×C13C2×M1612yes—
142C2×C4×C13C23×C411yescharacteristic
143#1055—22no—
144#1055—21no—
145#1055—21no—
146#1055#11712yes—
147#1055C2×M1614yes—
148#1055C2×#4111yescharacteristic
149#1055C2×#4111yescharacteristic
150C2×#131—131no—
151C2×#131—131no—
152C4×#41#26111yescharacteristic
153C2×M32—132no—
154C22×C16—132no—
155#405—132no—
156#405—131no—
157#405—131no—
158#405—132no—
159C4×M16—131no—
160C4×M16—132no—
161C2×C4×C8—131no—
162C2×C4×C8—132no—
163C4⋊C16—131no—
164C4⋊C16—131no—
165C4⋊C16—132no—
166C4⋊C16—132no—
167C4⋊C16—132no—
168C22⋊C16—134no—
169C22⋊C16—134no—
170#346—134no—
171C4×C16—134no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—22no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13#43112yes—
178C22×C13C23×C811yescharacteristic
179C4×C13—21no—
180C4×C13—22no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—22no—
184C4×C13—22no—
185C4×C13#43112yes—
186C4×C13#50412yes—
187C4×C13C2×#11711yescharacteristic
188C4×C13C22×M1611yescharacteristic
189C2×#41C2×#26111yescharacteristic
190#131—262no—
191#131—262no—
192#131—264no—
193C2×M16—131no—
194C2×M16—132no—
195C2×M16—132no—
196C2×M16—131no—
197C22×C8—131no—
198C22×C8—132no—
199C22×C8—132no—
200C22×C8—131no—
201C4×Q8#105711yescharacteristic
202C4×Q8#105711yescharacteristic
203C4×D4#105712yes—
204C4×D4#105711yescharacteristic
205C4×D4#105712yes—
206C4×D4#105711yescharacteristic
207#117C2×#26112yes—
208#117C2×#26111yescharacteristic
209C2×C42C2×#26112yes—
210C2×C42C2×#26111yescharacteristic
211M32—264no—
212C2×C16—132no—
213C2×C16—134no—
214C2×C16—132no—
215C2×C16—264no—
216#97—132no—
217#97—132no—
218#97—132no—
219C4×C8—132no—
220C4×C8—131no—
221C4×C8—131no—
222C4×C8—131no—
223C4×C8—132no—
224C4×C8—131no—
225C4×C8—132no—
226C2×C13—22no—
227C2×C13—42no—
228C2×C13C2×#43111yescharacteristic
229C2×C13C2×#50411yescharacteristic
230C2×C13#340711yescharacteristic
231#41—22no—
232#41—22no—
233C2×Q8C2×#105711yescharacteristic
234C2×D4C2×#105712yes—
235C2×D4C2×#105711yescharacteristic
236C22×C4C2×#105712yes—
237C22×C4C2×#105711yescharacteristic
238C22×C4C2×#105712yes—
239C22×C4C2×#105711yescharacteristic
240C22×C4C22×#26112yes—
241C22×C4C22×#26111yescharacteristic
242M16—134no—
243M16—264no—
244M16—264no—
245M16—262no—
246C2×C8—132no—
247C2×C8—132no—
248C2×C8—131no—
249C2×C8—132no—
250C2×C8—131no—
251C2×C8—131no—
252C2×C8—131no—
253C2×C8—132no—
254C2×C8—264no—
255C2×C8—262no—
256C2×C8—262no—
257C2×C8—262no—
258C4⋊C4C2×#105712yes—
259C4⋊C4C2×#105712yes—
260C4⋊C4C2×#105711yescharacteristic
261C4⋊C4C2×#105711yescharacteristic
262C22⋊C4C2×#105712yes—
263C22⋊C4C2×#105712yes—
264C22⋊C4C2×#105712yes—
265C42C2×#105712yes—
266C42C2×#105711yescharacteristic
267C42C2×#105712yes—
268C42C2×#105711yescharacteristic
269C42C22×#26111yescharacteristic
270C42C22×#26112yes—
271C42C22×#26111yescharacteristic
272C16—262no—
273C16—262no—
274C16—264no—
275C13#3342311yescharacteristic, complemented, Sylow
276C23C22×#105712yes—
277C23C22×#105711yescharacteristic
278Q8—22no—
279D4—24no—
280D4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—24no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4D13⋊M1612yes—
288C2×C4#8823712yes—
289C2×C4C22×#105711yescharacteristic
290C2×C4C22×#105712yes—
291C2×C4C22×#105712yes—
292C2×C4C22×#105711yescharacteristic
293C2×C4C22×#105712yes—
294C2×C4C22×#105711yescharacteristic
295C2×C4C22×#105711yescharacteristic
296C2×C4C22×#105711yescharacteristic
297C2×C4C23×#26111yescharacteristic
298C8—134no—
299C8—131no—
300C8—131no—
301C8—132no—
302C8—261no—
303C8—261no—
304C8—262no—
305C22—21no—
306C22—21no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22#1171911912yes—
311C22C23×#105711yescharacteristic
312C4—21no—
313C4—22no—
314C4—21no—
315C4—21no—
316C4—22no—
317C4—22no—
318C4#1171911912yes—
319C4#1171916212yes—
320C4C2×D13⋊M1611yescharacteristic
321C4C2×#8823711yescharacteristic
322C2—22no—
323C2—42no—
324C2C2×#1171911911yescharacteristic
325C2C2×#1171916211yescharacteristic
326C2#1313180311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×#261
commutator, socleC22×C13C23×C8
FittingC4×C13×#41C4
prime radicalC2×C13×#41C2×C4
cosocleC2×#1055C24
hypercenterC4×#41#261
hypocenterC13#33423
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. #13131201C2semidirect
2. #13131197C2semidirect
3. #13131193C2semidirect
4. #13131168C2semidirect
5. C2×C4⋊#6092C2semidirect
7. #13131045C2semidirect
275. C13#33423semidirect

Maximal subgroups

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

subgroupindex
#131312012
#131311972
#131311932
#131311682
C2×C4⋊#60922
#131310662
#131310452
C4×#882022
#3342313