Finite Group Databasebeta

← #16857756

Subgroups — #16857756

Order 3968.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Dic62C211yesmaximal, characteristic
2#14521419C211yesmaximal, characteristic, complemented
3#14521390C211yesmaximal, characteristic, complemented
4#14521379C211yesmaximal, characteristic, complemented
5#14521353C211yesmaximal, characteristic, complemented
6#14521305C211yesmaximal, characteristic, complemented
7#14521288C211yesmaximal, characteristic, complemented
8#14521259C211yesmaximal, characteristic, complemented
9#14521204C211yesmaximal, characteristic, complemented
10#14521204C211yesmaximal, characteristic, complemented
11#14521154C211yesmaximal, characteristic, complemented
12#14521121C211yesmaximal, characteristic
13#14521057C211yesmaximal, characteristic, complemented
14C2×#11758398C211yesmaximal, characteristic, complemented
15C31×#552C211yesmaximal, characteristic
16C22×Dic62C2211yescharacteristic
17C22×Dic62C2211yescharacteristic
18C31×#126—21no—
19C31×#125—21no—
20C31×#125C2211yescharacteristic
21C31×#123—21no—
22C31×C22⋊Q8C2211yescharacteristic
23C31×C22⋊Q8C2211yescharacteristic
24C4×Q8×C31C2211yescharacteristic
25C4×D4×C31C2211yescharacteristic
26C31×#117—21no—
27C31×#117C2211yescharacteristic
28C2×C4⋊C4×C31C2211yescharacteristic
29C2×#92482C2211yescharacteristic
30C2×#92482C2211yescharacteristic
31C2×#92482C2211yescharacteristic
32D4×Dic31—21no—
33#11758501C2211yescharacteristic
34#11758501C2211yescharacteristic
35C2×#92474C2211yescharacteristic
36C22×C31⋊C8C2211yescharacteristic
37#11758465—21no—
38#11758455—21no—
39#11758455—21no—
40#11758446C2211yescharacteristic
41C4×Dic62C2211yescharacteristic
42#11758423C2211yescharacteristic
43C22⋊(C31⋊C8)C2211yescharacteristic
44C22⋊(C31⋊C8)C2211yescharacteristic
45#11758398C2211yescharacteristic
46#11758398C2211yescharacteristic
47#11758398C2211yescharacteristic
48#11758398C2211yescharacteristic
49#11758398C2211yescharacteristic
50#11758398C2211yescharacteristic
51#11758398C2211yescharacteristic
52#11758398C2211yescharacteristic
53#11758398C2211yescharacteristic
54#11758396C2211yescharacteristic
55#11758396C2211yescharacteristic
56#11758395C2211yescharacteristic
57C4⋊(C31⋊C8)C2211yescharacteristic
58#11758391C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C2×D4×C31D411yescharacteristic
61C22×C4×C31—21no—
62C22×C4×C31C2311yescharacteristic
63C22×C4×C31C2311yescharacteristic
64C22×Dic31—21no—
65C22×Dic31—21no—
66C2×Dic62—22no—
67C2×Dic62—22no—
68C2×Dic62—21no—
69C2×Dic62—21no—
70C2×Dic62—41no—
71C2×Dic62—41no—
72C2×Dic62C2311yescharacteristic
73C2×Dic62C2311yescharacteristic
74C2×Dic62C2311yescharacteristic
75C4⋊C4×C31—21no—
76C4⋊C4×C31—21no—
77C4⋊C4×C31—21no—
78C4⋊C4×C31—21no—
79C4⋊C4×C31—21no—
80C4⋊C4×C31—21no—
81C4⋊C4×C31D411yescharacteristic
82C4⋊C4×C31C2311yescharacteristic
83C4⋊C4×C31C2311yescharacteristic
84C4⋊C4×C31C2311yescharacteristic
85C22⋊C4×C31—21no—
86C22⋊C4×C31—21no—
87C22⋊C4×C31—21no—
88C22⋊C4×C31D411yescharacteristic
89C22⋊C4×C31D411yescharacteristic
90C42×C31—21no—
91C42×C31—21no—
92C42×C31C2311yescharacteristic
93C22⋊Dic31—21no—
94C22⋊Dic31—21no—
95#92482—22no—
96#92482—41no—
97#92482—41no—
98C4⋊Dic31—21no—
99C4⋊Dic31—21no—
100C4⋊Dic31C2311yescharacteristic
101Dic31⋊C4—21no—
102Dic31⋊C4—21no—
103Dic31⋊C4—21no—
104C4×Dic31—21no—
105#92474—41no—
106C2×C31⋊C8—41no—
107C2×C31⋊C8C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110C2×C31⋊C8C2311yescharacteristic
111C23×C31C2×D411yescharacteristic
112C23×C31C2×D411yescharacteristic
113Q8×C31—21no—
114Q8×C31—21no—
115D4×C31—22no—
116C2×C4×C31—21no—
117C2×C4×C31—21no—
118C2×C4×C31—21no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—42no—
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2×D411yescharacteristic
128C2×C4×C31C2×D411yescharacteristic
129C2×C4×C31C2411yescharacteristic
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31—21no—
133C2×Dic31—21no—
134C2×Dic31—42no—
135C2×Dic31—42no—
136Dic62—21no—
137Dic62—21no—
138Dic62—21no—
139Dic62—21no—
140Dic62—21no—
141Dic62—42no—
142Dic62—42no—
143Dic62#4112yes—
144C31⋊C8—21no—
145C31⋊C8—21no—
146C31⋊C8—21no—
147C31⋊C8—21no—
148#3312—311nomaximal, Sylow
149C22×C31—21no—
150C22×C31—21no—
151C22×C31—21no—
152C22×C31—21no—
153C22×C31—21no—
154C22×C31#13712yes—
155C22×C31C22×D411yescharacteristic
156C4×C31—21no—
157C4×C31—21no—
158C4×C31—21no—
159C4×C31—21no—
160C4×C31—41no—
161C4×C31—41no—
162C4×C31—41no—
163C4×C31—41no—
164C4×C31C2×#4111yescharacteristic
165C4×C31H(5,𝔽2)11yescharacteristic
166Dic31—22no—
167Dic31—41no—
168Dic31—41no—
169Dic31—41no—
170#552D3111yescharacteristic
171D4×Q8—311no—
172#491—311no—
173#485—311no—
174#483—311no—
175#479—311no—
176#470—311no—
177#467—311no—
178#462—311no—
179#451—311no—
180#451—311no—
181#441—311no—
182#435—311no—
183#419—311no—
184C2×#103—311no—
185C2×C31—22no—
186C2×C31—41no—
187C2×C31#54611yescharacteristic
188C2×C31C2×#13711yescharacteristic
189C2×C31#57811yescharacteristic
190C22×Q8—311no—
191C22×Q8—311no—
192C2×Q16—311no—
193C2×Q16—311no—
194C2×Q16—311no—
195C2×M16—311no—
196C22×C8—311no—
197C4⋊Q8—311no—
198C4⋊Q8—621no—
199#126—21no—
200#125—21no—
201#125C2×D3111yescharacteristic
202#123—21no—
203C22⋊Q8—311no—
204C22⋊Q8—311no—
205C22⋊Q8—621no—
206C22⋊Q8—621no—
207C22⋊Q8C2×D3111yescharacteristic
208C22⋊Q8C2×D3111yescharacteristic
209C4×Q8—311no—
210C4×Q8C2×D3111yescharacteristic
211C4×D4—621no—
212C4×D4C2×D3111yescharacteristic
213#117—21no—
214#117C2×D3111yescharacteristic
215C2×C4⋊C4C2×D3111yescharacteristic
216#107—311no—
217#106—311no—
218#106—311no—
219C4⋊C8—311no—
220#103—311no—
221#103—311no—
222#103—311no—
223#103—311no—
224#103—311no—
225#103—311no—
226#103—311no—
227#103—311no—
228#103—311no—
229#103—311no—
230C22⋊C8—311no—
231C22⋊C8—311no—
232#97—311no—
233C31#331211yescharacteristic, complemented, Sylow
234C2×Q8—311no—
235C2×Q8—311no—
236C2×Q8—311no—
237C2×Q8—622no—
238C2×Q8—622no—
239C2×Q8—621no—
240C2×Q8—621no—
241C2×Q8—1241no—
242C2×Q8—1241no—
243C2×Q8C22×D3111yescharacteristic
244C2×D4C22⋊D3111yescharacteristic
245C22×C4—21no—
246C22×C4—621no—
247C22×C4—621no—
248C22×C4C22×D3111yescharacteristic
249C22×C4C22×D3111yescharacteristic
250Q16—622no—
251Q16—1241no—
252Q16—1241no—
253M16—1241no—
254C2×C8—311no—
255C2×C8—311no—
256C2×C8—311no—
257C2×C8—311no—
258C2×C8—1241no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—311no—
266C4⋊C4—621no—
267C4⋊C4—621no—
268C4⋊C4—621no—
269C4⋊C4—621no—
270C4⋊C4—621no—
271C4⋊C4C22⋊D3111yescharacteristic
272C4⋊C4C22×D3111yescharacteristic
273C4⋊C4C22×D3111yescharacteristic
274C4⋊C4C22×D3111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—621no—
279C22⋊C4—621no—
280C22⋊C4C22⋊D3111yescharacteristic
281C22⋊C4C22⋊D3111yescharacteristic
282C42—21no—
283C42—21no—
284C42—621no—
285C42C22×D3111yescharacteristic
286C23C2×C22⋊D3111yescharacteristic
287C23C2×C22⋊D3111yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—312no—
291Q8—621no—
292Q8—621no—
293Q8—621no—
294Q8—621no—
295Q8—621no—
296Q8—1242no—
297Q8—1242no—
298D4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—621no—
309C2×C4—621no—
310C2×C4—621no—
311C2×C4—621no—
312C2×C4—1242no—
313C2×C4—1242no—
314C2×C4C2×C22⋊D3111yescharacteristic
315C2×C4C2×C22⋊D3111yescharacteristic
316C2×C4C2×C22⋊D3111yescharacteristic
317C2×C4C2×C22⋊D3111yescharacteristic
318C2×C4C23×D3111yescharacteristic
319C8—621no—
320C8—621no—
321C8—621no—
322C8—621no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22#1175852812yes—
329C22C22×C22⋊D3111yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—622no—
339C4—1241no—
340C4—1241no—
341C4—1241no—
342C4#41×D3111yescharacteristic
343C4#1175856611yescharacteristic
344C2—22no—
345C2—41no—
346C2#1452168711yescharacteristic
347C2C2×#1175852811yescharacteristic
348C2#1452186411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#552C2
socleC22×C31C22×D4
prime radicalC2×D4×C31D4
hypercenter#552D31
hypocenterC31#3312
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #14521419C2semidirect
3. #14521390C2semidirect
4. #14521379C2semidirect
5. #14521353C2semidirect
6. #14521305C2semidirect
7. #14521288C2semidirect
8. #14521259C2semidirect
9. #14521204C2semidirect
10. #14521204C2semidirect
11. #14521154C2semidirect
13. #14521057C2semidirect
14. C2×#11758398C2semidirect
233. C31#3312semidirect

Maximal subgroups

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

subgroupindex
D4×Dic622
#145214192
#145213902
#145213792
#145213532
#145213052
#145212882
#145212592
#145212042
#145211542
#145211212
#145210572
C2×#117583982
C31×#5522
#331231