Finite Group Databasebeta

← #16857762

Subgroups — #16857762

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
1#14521739C211yesmaximal, characteristic
2#14521417C211yesmaximal, characteristic, complemented
3#14521387C211yesmaximal, characteristic, complemented
4#14521377C211yesmaximal, characteristic, complemented
5#14521356C211yesmaximal, characteristic, complemented
6#14521305C211yesmaximal, characteristic, complemented
7#14521288C211yesmaximal, characteristic, complemented
8#14521256C211yesmaximal, characteristic, complemented
9#14521205C211yesmaximal, characteristic, complemented
10#14521205C211yesmaximal, characteristic, complemented
11#14521154C211yesmaximal, characteristic, complemented
12#14521121C211yesmaximal, characteristic
13#14521058C211yesmaximal, characteristic, complemented
14C2×#11758423C211yesmaximal, characteristic, complemented
15D4×Q8×C31C211yesmaximal, characteristic
16C22×Q8×C31C2211yescharacteristic
17C22×Q8×C31C2211yescharacteristic
18C31×C4⋊Q8—21no—
19C31×C4⋊Q8C2211yescharacteristic
20C31×C22⋊Q8—21no—
21C31×C22⋊Q8—21no—
22C31×C22⋊Q8C2211yescharacteristic
23C31×C22⋊Q8C2211yescharacteristic
24C4×Q8×C31C2211yescharacteristic
25C4×D4×C31—21no—
26C4×D4×C31C2211yescharacteristic
27C2×#92482C2211yescharacteristic
28C2×#92482C2211yescharacteristic
29C2×#92482C2211yescharacteristic
30#11758512—21no—
31#11758503C2211yescharacteristic
32C2×C4⋊Dic31C2211yescharacteristic
33#11758501C2211yescharacteristic
34#11758501C2211yescharacteristic
35C2×#92474C2211yescharacteristic
36C22×C31⋊C8C2211yescharacteristic
37#11758466—21no—
38#11758456—21no—
39#11758454—21no—
40#11758447C2211yescharacteristic
41C4×Dic62C2211yescharacteristic
42#11758423C2211yescharacteristic
43#11758423C2211yescharacteristic
44#11758423C2211yescharacteristic
45#11758423C2211yescharacteristic
46#11758423C2211yescharacteristic
47#11758423C2211yescharacteristic
48#11758423C2211yescharacteristic
49#11758423C2211yescharacteristic
50#11758423C2211yescharacteristic
51C22⋊(C31⋊C8)C2211yescharacteristic
52C22⋊(C31⋊C8)C2211yescharacteristic
53#11758398C2211yescharacteristic
54#11758396C2211yescharacteristic
55#11758396C2211yescharacteristic
56#11758395C2211yescharacteristic
57C4⋊(C31⋊C8)C2211yescharacteristic
58#11758391C2211yescharacteristic
59C2×Q8×C31—21no—
60C2×Q8×C31—21no—
61C2×Q8×C31—22no—
62C2×Q8×C31—22no—
63C2×Q8×C31—41no—
64C2×Q8×C31—41no—
65C2×Q8×C31C2311yescharacteristic
66C2×Q8×C31C2311yescharacteristic
67C2×Q8×C31C2311yescharacteristic
68C2×D4×C31D411yescharacteristic
69C22×C4×C31—21no—
70C22×C4×C31—21no—
71C22×C4×C31C2311yescharacteristic
72C22×C4×C31C2311yescharacteristic
73C22×Dic31—21no—
74C2×Dic62C2311yescharacteristic
75C4⋊C4×C31—21no—
76C4⋊C4×C31—21no—
77C4⋊C4×C31—21no—
78C4⋊C4×C31—21no—
79C4⋊C4×C31—21no—
80C4⋊C4×C31D411yescharacteristic
81C4⋊C4×C31C2311yescharacteristic
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—
91#92482—22no—
92#92482—41no—
93#92482—41no—
94C4⋊Dic31—21no—
95C4⋊Dic31C2311yescharacteristic
96C4⋊Dic31C2311yescharacteristic
97C4⋊Dic31C2311yescharacteristic
98Dic31⋊C4—21no—
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4—21no—
102Dic31⋊C4—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×C31C2×D411yescharacteristic
112C23×C31C2×D411yescharacteristic
113Q8×C31—21no—
114Q8×C31—21no—
115Q8×C31—21no—
116Q8×C31—21no—
117Q8×C31—21no—
118Q8×C31—42no—
119Q8×C31—42no—
120Q8×C31#4112yes—
121D4×C31—22no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
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—42no—
131C2×C4×C31—42no—
132C2×C4×C31C2×D411yescharacteristic
133C2×C4×C31C2×D411yescharacteristic
134C2×C4×C31C2×D411yescharacteristic
135C2×C4×C31C2×D411yescharacteristic
136C2×C4×C31C2411yescharacteristic
137C2×Dic31—21no—
138C2×Dic31—21no—
139C2×Dic31—21no—
140C2×Dic31—21no—
141C2×Dic31—42no—
142Dic62—21no—
143Dic62—21no—
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—22no—
159C4×C31—21no—
160C4×C31—21no—
161C4×C31—41no—
162C4×C31—41no—
163C4×C31—41no—
164C4×C31C2×#4111yescharacteristic
165C4×C31H(5,𝔽2)11yescharacteristic
166Dic31—41no—
167Dic31—41no—
168Dic31—41no—
169Dic31—41no—
170#552—311no—
171D4×Q8D3111yescharacteristic
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×Q8C2×D3111yescharacteristic
191C22×Q8C2×D3111yescharacteristic
192C2×Q16—311no—
193C2×Q16—311no—
194C2×Q16—311no—
195C2×M16—311no—
196C22×C8—311no—
197C4⋊Q8—21no—
198C4⋊Q8C2×D3111yescharacteristic
199#126—621no—
200#125—311no—
201#125—621no—
202#123—621no—
203C22⋊Q8—21no—
204C22⋊Q8—21no—
205C22⋊Q8—311no—
206C22⋊Q8—311no—
207C22⋊Q8C2×D3111yescharacteristic
208C22⋊Q8C2×D3111yescharacteristic
209C4×Q8—311no—
210C4×Q8C2×D3111yescharacteristic
211C4×D4—21no—
212C4×D4C2×D3111yescharacteristic
213#117—311no—
214#117—621no—
215C2×C4⋊C4—311no—
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—21no—
235C2×Q8—21no—
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—311no—
241C2×Q8C22×D3111yescharacteristic
242C2×Q8C22×D3111yescharacteristic
243C2×Q8C22×D3111yescharacteristic
244C2×D4C22⋊D3111yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
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—311no—
265C4⋊C4—311no—
266C4⋊C4—311no—
267C4⋊C4—621no—
268C4⋊C4—621no—
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—621no—
278C22⋊C4—621no—
279C22⋊C4—621no—
280C22⋊C4C22⋊D3111yescharacteristic
281C22⋊C4C22⋊D3111yescharacteristic
282C42—21no—
283C42—621no—
284C42—621no—
285C42C22×D3111yescharacteristic
286C23C2×C22⋊D3111yescharacteristic
287C23C2×C22⋊D3111yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—42no—
294Q8—42no—
295Q8—621no—
296Q8—621no—
297Q8#9249712yes—
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—42no—
309C2×C4—621no—
310C2×C4—621no—
311C2×C4—621no—
312C2×C4—621no—
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#1175851912yes—
329C22C22×C22⋊D3111yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—22no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—1241no—
339C4—1241no—
340C4—1241no—
341C4—1241no—
342C4C2×#9249711yescharacteristic
343C4#1175856111yescharacteristic
344C2—22no—
345C2—41no—
346C2#1452169311yescharacteristic
347C2C2×#1175851911yescharacteristic
348C2#1452186411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingD4×Q8×C31C2
socleC22×C31C22×D4
prime radicalC2×D4×C31D4
hypercenterD4×Q8D31
hypocenterC31#3312
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
2. #14521417C2semidirect
3. #14521387C2semidirect
4. #14521377C2semidirect
5. #14521356C2semidirect
6. #14521305C2semidirect
7. #14521288C2semidirect
8. #14521256C2semidirect
9. #14521205C2semidirect
10. #14521205C2semidirect
11. #14521154C2semidirect
13. #14521058C2semidirect
14. C2×#11758423C2semidirect
233. C31#3312semidirect

Maximal subgroups

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

subgroupindex
#145217392
#145214172
#145213872
#145213772
#145213562
#145213052
#145212882
#145212562
#145212052
#145211542
#145211212
#145210582
C2×#117584232
D4×Q8×C312
#331231