Finite Group Databasebeta

← #16853972

Subgroups — #16853972

Order 3968.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14520990C211yesmaximal, characteristic, complemented
2#14520987C211yesmaximal, characteristic, complemented
3#14520985C211yesmaximal, characteristic
4#14520982C211yesmaximal, characteristic, complemented
5#14520980C211yesmaximal, characteristic, complemented
6#14520980C211yesmaximal, characteristic, complemented
7#14520979C211yesmaximal, characteristic, complemented
8#14520972C211yesmaximal, characteristic
9#14520970C211yesmaximal, characteristic, complemented
10#14520969C211yesmaximal, characteristic, complemented
11#14520961C211yesmaximal, characteristic
12#14520910C211yesmaximal, characteristic
13#14520907C211yesmaximal, characteristic
14#14520907C211yesmaximal, characteristic
15C31×#396C211yesmaximal, characteristic
16C23×Dic31C2211yescharacteristic
17C22×Dic62C2211yescharacteristic
18C2×C4⋊C4×C31C2211yescharacteristic
19C2×C4⋊C4×C31C2211yescharacteristic
20C2×C4⋊C4×C31C2211yescharacteristic
21C2×C22⋊C4×C31C2211yescharacteristic
22C2×C22⋊C4×C31C2211yescharacteristic
23C2×C22⋊C4×C31C2211yescharacteristic
24C2×C22⋊Dic31C2211yescharacteristic
25C2×C22⋊Dic31C2211yescharacteristic
26C2×C22⋊Dic31C2211yescharacteristic
27C2×C4⋊Dic31C2211yescharacteristic
28C2×C4⋊Dic31C2211yescharacteristic
29C2×Dic31⋊C4C2211yescharacteristic
30C2×Dic31⋊C4C2211yescharacteristic
31C2×Dic31⋊C4C2211yescharacteristic
32C2×Dic31⋊C4C2211yescharacteristic
33C2×Dic31⋊C4C2211yescharacteristic
34C2×Dic31⋊C4C2211yescharacteristic
35C2×Dic31⋊C4C2211yescharacteristic
36C2×Dic31⋊C4C2211yescharacteristic
37C31×#95C2211yescharacteristic
38C31⋊#95C2211yescharacteristic
39C31⋊#95C2211yescharacteristic
40C31⋊#95C2211yescharacteristic
41C31⋊#95C2211yescharacteristic
42C31⋊#95C2211yescharacteristic
43C31⋊#95C2211yescharacteristic
44C31⋊#95C2211yescharacteristic
45C31⋊#95C2211yescharacteristic
46C31⋊#95C2211yescharacteristic
47C31⋊#95C2211yescharacteristic
48C31⋊#95C2211yescharacteristic
49C31⋊#95C2211yescharacteristic
50C31⋊#95C2211yescharacteristic
51C24×C31C2311yescharacteristic
52C22×C4×C31C2311yescharacteristic
53C22×C4×C31C2311yescharacteristic
54C22×C4×C31C2311yescharacteristic
55C22×C4×C31C2311yescharacteristic
56C22×C4×C31C2311yescharacteristic
57C22×C4×C31C2311yescharacteristic
58C22×Dic31—41no—
59C22×Dic31—41no—
60C22×Dic31Q814yescomplemented
61C22×Dic31C2311yescharacteristic
62C22×Dic31C2311yescharacteristic
63C22×Dic31C2311yescharacteristic
64C22×Dic31C2311yescharacteristic
65C22×Dic31C2311yescharacteristic
66C22×Dic31C2311yescharacteristic
67C22×Dic31C2311yescharacteristic
68C22×Dic31C2311yescharacteristic
69C2×Dic62—41no—
70C2×Dic62—41no—
71C2×Dic62—41no—
72C4⋊C4×C31—41no—
73C4⋊C4×C31—41no—
74C4⋊C4×C31—41no—
75C22⋊C4×C31—41no—
76C22⋊C4×C31—41no—
77C22⋊C4×C31—41no—
78C22⋊Dic31—41no—
79C22⋊Dic31—41no—
80C22⋊Dic31—41no—
81C4⋊Dic31—41no—
82C4⋊Dic31—41no—
83Dic31⋊C4—41no—
84Dic31⋊C4—41no—
85Dic31⋊C4—41no—
86Dic31⋊C4—41no—
87Dic31⋊C4—41no—
88Dic31⋊C4—41no—
89Dic31⋊C4—41no—
90Dic31⋊C4—41no—
91C23×C31—21no—
92C23×C31—21no—
93C23×C31—21no—
94C23×C31—21no—
95C23×C31—21no—
96C23×C31—21no—
97C23×C31C2×Q812yes—
98C23×C31C2411yescharacteristic
99C2×C4×C31—21no—
100C2×C4×C31—21no—
101C2×C4×C31—21no—
102C2×C4×C31—21no—
103C2×C4×C31—21no—
104C2×C4×C31—21no—
105C2×C4×C31—21no—
106C2×C4×C31—21no—
107C2×C4×C31—21no—
108C2×C4×C31—21no—
109C2×C4×C31—21no—
110C2×C4×C31—21no—
111C2×C4×C31—21no—
112C2×C4×C31—21no—
113C2×C4×C31—21no—
114C2×C4×C31—21no—
115C2×C4×C31—21no—
116C2×C4×C31—21no—
117C2×Dic31—21no—
118C2×Dic31—21no—
119C2×Dic31—21no—
120C2×Dic31—21no—
121C2×Dic31—21no—
122C2×Dic31—21no—
123C2×Dic31—21no—
124C2×Dic31—21no—
125C2×Dic31—21no—
126C2×Dic31—21no—
127C2×Dic31—21no—
128C2×Dic31—21no—
129C2×Dic31—21no—
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31—21no—
133C2×Dic31—21no—
134C2×Dic31—21no—
135C2×Dic31—21no—
136C2×Dic31—21no—
137C2×Dic31—21no—
138C2×Dic31—21no—
139C2×Dic31—44no—
140C2×Dic31C2×Q812yes—
141C2×Dic31C2×Q812yes—
142Dic62—44no—
143#2841—311nomaximal, Sylow
144C22×C31—22no—
145C22×C31—22no—
146C22×C31—22no—
147C22×C31—41no—
148C22×C31—41no—
149C22×C31—41no—
150C22×C31—41no—
151C22×C31C22×Q811yescharacteristic
152C22×C31H(5,𝔽2)11yescharacteristic
153C22×C31H(5,𝔽2)11yescharacteristic
154C22×C31H(5,𝔽2)11yescharacteristic
155C22×C31H(5,𝔽2)11yescharacteristic
156C22×C312−1+411yescharacteristic
157C22×C312−1+411yescharacteristic
158C4×C31—41no—
159C4×C31—41no—
160C4×C31—41no—
161C4×C31—41no—
162C4×C31—41no—
163C4×C31—41no—
164Dic31—22no—
165Dic31—22no—
166Dic31—41no—
167Dic31—41no—
168Dic31—41no—
169Dic31—41no—
170Dic31—41no—
171Dic31—41no—
172#400—311no—
173#400—311no—
174#399—311no—
175#398—311no—
176#398—311no—
177#398—311no—
178#398—311no—
179#396—311no—
180#396D3111yescharacteristic
181#395—311no—
182#395—311no—
183#393—311no—
184#381—311no—
185#380—311no—
186#380—311no—
187C2×C31—42no—
188C2×C31#54311yescharacteristic
189C2×C31#54411yescharacteristic
190C2×C31#54411yescharacteristic
191C2×C31#56011yescharacteristic
192C2×C31#56211yescharacteristic
193C2×C31#56211yescharacteristic
194C2×C31#56311yescharacteristic
195C22×Q8—311no—
196C23×C4—311no—
197C2×C4⋊C4—311no—
198C2×C4⋊C4—311no—
199C2×C4⋊C4—311no—
200C2×C4⋊C4—311no—
201C2×C4⋊C4—311no—
202C2×C4⋊C4—311no—
203C2×C4⋊C4—311no—
204C2×C4⋊C4—311no—
205C2×C4⋊C4—311no—
206C2×C4⋊C4—311no—
207C2×C4⋊C4C2×D3111yescharacteristic
208C2×C4⋊C4C2×D3111yescharacteristic
209C2×C4⋊C4C2×D3111yescharacteristic
210C2×C22⋊C4—311no—
211C2×C22⋊C4—311no—
212C2×C22⋊C4—311no—
213C2×C22⋊C4C2×D3111yescharacteristic
214C2×C22⋊C4C2×D3111yescharacteristic
215C2×C22⋊C4C2×D3111yescharacteristic
216#95—311no—
217#95—311no—
218#95—311no—
219#95—311no—
220#95—311no—
221#95—311no—
222#95—311no—
223#95—311no—
224#95—311no—
225#95—311no—
226#95—311no—
227#95—311no—
228#95—311no—
229#95C2×D3111yescharacteristic
230C31#284111yescharacteristic, complemented, Sylow
231C24C22×D3111yescharacteristic
232C2×Q8—1241no—
233C2×Q8—1241no—
234C2×Q8—1241no—
235C22×C4—311no—
236C22×C4—311no—
237C22×C4—314no—
238C22×C4—311no—
239C22×C4—311no—
240C22×C4—311no—
241C22×C4—311no—
242C22×C4—311no—
243C22×C4—311no—
244C22×C4—1241no—
245C22×C4—1241no—
246C22×C4C22×D3111yescharacteristic
247C22×C4C22×D3111yescharacteristic
248C22×C4C22×D3111yescharacteristic
249C22×C4C22×D3111yescharacteristic
250C22×C4C22×D3111yescharacteristic
251C22×C4C22×D3111yescharacteristic
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—1241no—
256C4⋊C4—1241no—
257C4⋊C4—1241no—
258C4⋊C4—1241no—
259C4⋊C4—1241no—
260C4⋊C4—1241no—
261C4⋊C4—1241no—
262C4⋊C4—1241no—
263C4⋊C4—1241no—
264C4⋊C4—1241no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—1241no—
269C22⋊C4—1241no—
270C22⋊C4—1241no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23Q8×D3112yes—
278C23C23×D3111yescharacteristic
279Q8—1244no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
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—21no—
297C2×C4—21no—
298C2×C4—312no—
299C2×C4—312no—
300C2×C4—621no—
301C2×C4—621no—
302C2×C4—621no—
303C2×C4—621no—
304C2×C4—621no—
305C2×C4—621no—
306C2×C4—621no—
307C2×C4—621no—
308C2×C4—621no—
309C2×C4—621no—
310C2×C4—621no—
311C2×C4—621no—
312C2×C4—621no—
313C2×C4—621no—
314C2×C4—621no—
315C2×C4—621no—
316C2×C4—621no—
317C2×C4—621no—
318C2×C4—621no—
319C2×C4—621no—
320C2×C4—621no—
321C2×C4—621no—
322C2×C4—1244no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22#1175856111yescharacteristic
331C22#1175856111yescharacteristic
332C22#1175856111yescharacteristic
333C22C2×Q8×D3111yescharacteristic
334C22#1175856611yescharacteristic
335C22#1175856711yescharacteristic
336C22#1175856711yescharacteristic
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—622no—
344C4—622no—
345C4—1241no—
346C4—1241no—
347C4—1241no—
348C4—1241no—
349C4—1241no—
350C4—1241no—
351C2—42no—
352C2#1452167411yescharacteristic
353C2#1452167811yescharacteristic
354C2#1452167811yescharacteristic
355C2#1452178711yescharacteristic
356C2#1452179411yescharacteristic
357C2#1452179411yescharacteristic
358C2#1452180111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutator, socle, cosocleC23×C31C24
FittingC31×#396C2
prime radicalC24×C31C23
hypercenter#396D31
hypocenterC31#2841
LCSG ▷ C23×C31 ▷ C31
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. #14520990C2semidirect
2. #14520987C2semidirect
4. #14520982C2semidirect
5. #14520980C2semidirect
6. #14520980C2semidirect
7. #14520979C2semidirect
9. #14520970C2semidirect
10. #14520969C2semidirect
60. C22×Dic31Q8semidirect
230. C31#2841semidirect

Maximal subgroups

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

subgroupindex
#145209902
#145209872
#145209852
#145209822
#145209802
#145209792
#145209722
#145209702
#145209692
#145209612
#145209102
#145209072
C31×#3962
#284131