Finite Group Databasebeta

← #16857777

Subgroups — #16857777

Order 3968.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521769C211yesmaximal, characteristic, complemented
2#14521408C211yesmaximal, characteristic, complemented
3#14521387C211yesmaximal, characteristic, complemented
4#14521370C211yesmaximal, characteristic, complemented
5#14521344C211yesmaximal, characteristic, complemented
6#14521293C211yesmaximal, characteristic, complemented
7#14521288C211yesmaximal, characteristic, complemented
8#14521268C211yesmaximal, characteristic, complemented
9#14521211C211yesmaximal, characteristic, complemented
10#14521205C211yesmaximal, characteristic, complemented
11#14521154C211yesmaximal, characteristic, complemented
12#14521121C211yesmaximal, characteristic, complemented
13#14521058C211yesmaximal, characteristic, complemented
14#14521045C211yesmaximal, characteristic, complemented
15C31×#548C211yesmaximal, characteristic
16C2×#41×C31C2211yescharacteristic
17C22×Q8×C31C2211yescharacteristic
18C31×#124—21no—
19C31×#124C2211yescharacteristic
20C31×C22⋊Q8—21no—
21C31×C22⋊Q8C2211yescharacteristic
22C31×#121—21no—
23C31×#121C2211yescharacteristic
24C4×Q8×C31C2211yescharacteristic
25C4×D4×C31—21no—
26C4×D4×C31C2211yescharacteristic
27C2×#92482C2211yescharacteristic
28C2×#92482C2211yescharacteristic
29#11758513—21no—
30C2×#92480C2211yescharacteristic
31#11758503C2211yescharacteristic
32#11758503C2211yescharacteristic
33#11758501C2211yescharacteristic
34#11758501C2211yescharacteristic
35C2×#92474C2211yescharacteristic
36C22×C31⋊C8C2211yescharacteristic
37#11758464—21no—
38#11758456—21no—
39#11758456—21no—
40#11758446C2211yescharacteristic
41C4×Dic62C2211yescharacteristic
42#11758423C2211yescharacteristic
43#11758423C2211yescharacteristic
44#11758423C2211yescharacteristic
45#11758423C2211yescharacteristic
46#11758423C2211yescharacteristic
47#11758423C2211yescharacteristic
48#11758420C2211yescharacteristic
49#11758420C2211yescharacteristic
50#11758420C2211yescharacteristic
51C22⋊(C31⋊C8)C2211yescharacteristic
52C22⋊(C31⋊C8)C2211yescharacteristic
53#11758398C2211yescharacteristic
54#11758396C2211yescharacteristic
55#11758395C2211yescharacteristic
56#11758395C2211yescharacteristic
57C4⋊(C31⋊C8)C2211yescharacteristic
58#11758391C2211yescharacteristic
59#41×C31—22no—
60#41×C31—41no—
61C2×Q8×C31—21no—
62C2×Q8×C31—22no—
63C2×Q8×C31—41no—
64C2×Q8×C31C2311yescharacteristic
65C2×Q8×C31C2311yescharacteristic
66C2×D4×C31—21no—
67C2×D4×C31—21no—
68C2×D4×C31D411yescharacteristic
69C2×D4×C31C2311yescharacteristic
70C22×C4×C31—21no—
71C22×C4×C31—21no—
72C22×C4×C31C2311yescharacteristic
73C22×C4×C31C2311yescharacteristic
74C2×Dic62—21no—
75C2×Dic62C2311yescharacteristic
76C4⋊C4×C31—21no—
77C4⋊C4×C31—21no—
78C4⋊C4×C31D411yescharacteristic
79C4⋊C4×C31C2311yescharacteristic
80C22⋊C4×C31—21no—
81C22⋊C4×C31—21no—
82C22⋊C4×C31—21no—
83C22⋊C4×C31—21no—
84C22⋊C4×C31D411yescharacteristic
85C22⋊C4×C31D411yescharacteristic
86C42×C31—21no—
87C42×C31C2311yescharacteristic
88C22⋊Dic31—21no—
89C22⋊Dic31—21no—
90C22⋊Dic31—21no—
91C22⋊Dic31—21no—
92#92482—22no—
93#92482—41no—
94#92480—41no—
95C4⋊Dic31—21no—
96C4⋊Dic31C2311yescharacteristic
97C4⋊Dic31C2311yescharacteristic
98C4⋊Dic31C2311yescharacteristic
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4—21no—
102C4×Dic31—21no—
103C4×Dic31—21no—
104C4×Dic31—21no—
105#92474—41no—
106C2×C31⋊C8—41no—
107C2×C31⋊C8C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110C2×C31⋊C8C2311yescharacteristic
111C23×C31—21no—
112C23×C31C2×D411yescharacteristic
113C23×C31C2×D411yescharacteristic
114Q8×C31—21no—
115Q8×C31—21no—
116Q8×C31—21no—
117Q8×C31—42no—
118Q8×C31#4112yes—
119D4×C31—21no—
120D4×C31—21no—
121D4×C31—41no—
122D4×C31—42no—
123D4×C31—42no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—21no—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—42no—
132C2×C4×C31—42no—
133C2×C4×C31C2×D411yescharacteristic
134C2×C4×C31C2×D411yescharacteristic
135C2×C4×C31C2×D411yescharacteristic
136C2×C4×C31C2×D411yescharacteristic
137C2×C4×C31C2411yescharacteristic
138C2×Dic31—21no—
139C2×Dic31—21no—
140C2×Dic31—21no—
141C2×Dic31—21no—
142Dic62—21no—
143Dic62—21no—
144Dic62—42no—
145C31⋊C8—21no—
146C31⋊C8—21no—
147C31⋊C8—21no—
148C31⋊C8—21no—
149#3313—311nomaximal, Sylow
150C22×C31—21no—
151C22×C31—21no—
152C22×C31—21no—
153C22×C31—21no—
154C22×C31—21no—
155C22×C31—21no—
156C22×C31—41no—
157C22×C31—41no—
158C22×C31—41no—
159C22×C31C22×D411yescharacteristic
160C4×C31—21no—
161C4×C31—21no—
162C4×C31—22no—
163C4×C31—21no—
164C4×C31—21no—
165C4×C31—41no—
166C4×C31—41no—
167C4×C31C2×#4111yescharacteristic
168C4×C31H(5,𝔽2)11yescharacteristic
169Dic31—41no—
170Dic31—41no—
171Dic31—41no—
172Dic31—41no—
173#556—311no—
174#548D3111yescharacteristic
175#489—311no—
176#485—311no—
177#482—311no—
178#477—311no—
179#468—311no—
180#467—311no—
181#464—311no—
182#452—311no—
183#451—311no—
184#441—311no—
185#435—311no—
186#419—311no—
187#416—311no—
188C2×C31—41no—
189C2×C31—41no—
190C2×C31—81no—
191C2×C31#54611yescharacteristic
192C2×C31#57511yescharacteristic
193C2×C31#57811yescharacteristic
194C2×#41C2×D3111yescharacteristic
195C22×Q8C2×D3111yescharacteristic
196C2×Q16—311no—
197C2×Q16—311no—
198C2×SD16—311no—
199C2×M16—311no—
200C22×C8—311no—
201C4⋊Q8—311no—
202#126—621no—
203#126—621no—
204#124—21no—
205#124—621no—
206#124C2×D3111yescharacteristic
207C22⋊Q8—21no—
208C22⋊Q8—311no—
209C22⋊Q8—311no—
210C22⋊Q8C2×D3111yescharacteristic
211#121—21no—
212#121C2×D3111yescharacteristic
213C4×Q8—311no—
214C4×Q8—621no—
215C4×Q8C2×D3111yescharacteristic
216C4×D4—21no—
217C4×D4C2×D3111yescharacteristic
218#117—311no—
219#117—311no—
220#107—311no—
221#107—311no—
222#106—311no—
223C4⋊C8—311no—
224#103—311no—
225#103—311no—
226#103—311no—
227#103—311no—
228#103—311no—
229#103—311no—
230#103—311no—
231#102—311no—
232#102—311no—
233#102—311no—
234C22⋊C8—311no—
235C22⋊C8—311no—
236#97—311no—
237C31#331311yescharacteristic, complemented, Sylow
238#41—22no—
239#41—41no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—311no—
244C2×Q8—621no—
245C2×Q8C22×D3111yescharacteristic
246C2×Q8C22×D3111yescharacteristic
247C2×D4—21no—
248C2×D4—21no—
249C2×D4C22⋊D3111yescharacteristic
250C2×D4C22×D3111yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4C22×D3111yescharacteristic
254C22×C4C22×D3111yescharacteristic
255Q16—622no—
256Q16—1241no—
257SD16—1241no—
258M16—1241no—
259C2×C8—311no—
260C2×C8—311no—
261C2×C8—311no—
262C2×C8—311no—
263C2×C8—1241no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—311no—
267C4⋊C4—311no—
268C4⋊C4—311no—
269C4⋊C4—621no—
270C4⋊C4—621no—
271C4⋊C4—621no—
272C4⋊C4—621no—
273C4⋊C4C22⋊D3111yescharacteristic
274C4⋊C4C22×D3111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—621no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4C22⋊D3111yescharacteristic
284C22⋊C4C22⋊D3111yescharacteristic
285C42—21no—
286C42—621no—
287C42—621no—
288C42—621no—
289C42C22×D3111yescharacteristic
290C23—21no—
291C23C2×C22⋊D3111yescharacteristic
292C23C2×C22⋊D3111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—42no—
297Q8—621no—
298Q8—621no—
299Q8—1242no—
300Q8#9249712yes—
301D4—21no—
302D4—21no—
303D4—41no—
304D4—42no—
305D4—42no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—621no—
316C2×C4—621no—
317C2×C4—621no—
318C2×C4—621no—
319C2×C4C2×C22⋊D3111yescharacteristic
320C2×C4C2×C22⋊D3111yescharacteristic
321C2×C4C2×C22⋊D3111yescharacteristic
322C2×C4C2×C22⋊D3111yescharacteristic
323C2×C4C23×D3111yescharacteristic
324C8—621no—
325C8—621no—
326C8—621no—
327C8—621no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22C22×C22⋊D3111yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—22no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—1241no—
346C4—1241no—
347C4—1241no—
348C4—1241no—
349C4C2×#9249711yescharacteristic
350C4#1175856111yescharacteristic
351C2—41no—
352C2—41no—
353C2—81no—
354C2#1452169311yescharacteristic
355C2#1452184711yescharacteristic
356C2#1452186411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
Fitting, prime radicalC31×#548C2
socleC22×C31C22×D4
hypercenter#548D31
hypocenterC31#3313
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #14521769C2semidirect
2. #14521408C2semidirect
3. #14521387C2semidirect
4. #14521370C2semidirect
5. #14521344C2semidirect
6. #14521293C2semidirect
7. #14521288C2semidirect
8. #14521268C2semidirect
9. #14521211C2semidirect
10. #14521205C2semidirect
11. #14521154C2semidirect
12. #14521121C2semidirect
13. #14521058C2semidirect
14. #14521045C2semidirect
237. C31#3313semidirect

Maximal subgroups

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

subgroupindex
#145217692
#145214082
#145213872
#145213702
#145213442
#145212932
#145212882
#145212682
#145212112
#145212052
#145211542
#145211212
#145210582
#145210452
C31×#5482
#331331