Finite Group Databasebeta

← #16857792

Subgroups — #16857792

Order 3968.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521756C211yesmaximal, characteristic, complemented
2#14521408C211yesmaximal, characteristic, complemented
3#14521382C211yesmaximal, characteristic, complemented
4#14521360C211yesmaximal, characteristic, complemented
5#14521329C211yesmaximal, characteristic, complemented
6#14521293C211yesmaximal, characteristic, complemented
7#14521288C211yesmaximal, characteristic, complemented
8#14521268C211yesmaximal, characteristic, complemented
9#14521211C211yesmaximal, characteristic, complemented
10#14521200C211yesmaximal, characteristic, complemented
11#14521149C211yesmaximal, characteristic, complemented
12#14521121C211yesmaximal, characteristic, complemented
13#14521050C211yesmaximal, characteristic, complemented
14C2×#11758420C211yesmaximal, characteristic, complemented
15C31×#546C211yesmaximal, characteristic
16C2×#41×C31C2211yescharacteristic
17C22×D4×C31C2211yescharacteristic
18C31×#124C2211yescharacteristic
19C31×#123—21no—
20C31×C22⋊Q8C2211yescharacteristic
21C31×#121—21no—
22C31×#121C2211yescharacteristic
23C31×#120—21no—
24C4×D4×C31C2211yescharacteristic
25C4×D4×C31C2211yescharacteristic
26C2×C22⋊C4×C31—21no—
27C2×#92482C2211yescharacteristic, complemented
28D4×Dic31—21no—
29C2×#92480C2211yescharacteristic
30C2×#92480C2211yescharacteristic
31C2×C4⋊Dic31C2211yescharacteristic
32C2×C4⋊Dic31C2211yescharacteristic, complemented
33#11758501C2211yescharacteristic
34#11758501C2211yescharacteristic, complemented
35C2×#92474C2211yescharacteristic, complemented
36C22×C31⋊C8C2211yescharacteristic
37#11758467—21no—
38#11758455—21no—
39#11758455—21no—
40#11758446C2211yescharacteristic, complemented
41C4×Dic62C2211yescharacteristic, complemented
42#11758423C2211yescharacteristic, complemented
43#11758423C2211yescharacteristic, complemented
44#11758423C2211yescharacteristic, complemented
45#11758420C2211yescharacteristic
46#11758420C2211yescharacteristic
47#11758420C2211yescharacteristic
48#11758420C2211yescharacteristic
49#11758420C2211yescharacteristic
50#11758420C2211yescharacteristic
51C22⋊(C31⋊C8)C2211yescharacteristic
52C22⋊(C31⋊C8)C2211yescharacteristic, complemented
53#11758398C2211yescharacteristic, complemented
54#11758395C2211yescharacteristic, complemented
55#11758395C2211yescharacteristic, complemented
56#11758395C2211yescharacteristic, complemented
57C4⋊(C31⋊C8)C2211yescharacteristic, complemented
58#11758391C2211yescharacteristic, complemented
59C24×C31—21no—
60#41×C31—22no—
61#41×C31—41no—
62C2×Q8×C31C2311yescharacteristic
63C2×D4×C31—22no—
64C2×D4×C31—21no—
65C2×D4×C31—21no—
66C2×D4×C31—21no—
67C2×D4×C31—41no—
68C2×D4×C31D411yescharacteristic
69C2×D4×C31C2311yescharacteristic
70C2×D4×C31C2311yescharacteristic
71C22×C4×C31—21no—
72C22×C4×C31—21no—
73C22×C4×C31C2311yescharacteristic
74C22×C4×C31C2311yescharacteristic
75C22×Dic31—21no—
76C22×Dic31—21no—
77C2×Dic62—21no—
78C2×Dic62C2311yescharacteristic
79C4⋊C4×C31—21no—
80C4⋊C4×C31D411yescharacteristic
81C4⋊C4×C31C2311yescharacteristic
82C22⋊C4×C31—21no—
83C22⋊C4×C31—21no—
84C22⋊C4×C31—21no—
85C22⋊C4×C31—21no—
86C22⋊C4×C31—21no—
87C22⋊C4×C31D411yescharacteristic
88C22⋊C4×C31D411yescharacteristic
89C42×C31C2311yescharacteristic
90C22⋊Dic31—21no—
91C22⋊Dic31—21no—
92#92482—41no—
93#92480—22no—
94#92480—41no—
95C4⋊Dic31—21no—
96C4⋊Dic31—21no—
97C4⋊Dic31—21no—
98C4⋊Dic31C2311yescharacteristic
99C4⋊Dic31C2311yescharacteristic
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×C31—21no—
112C23×C31—21no—
113C23×C31—42no—
114C23×C31—42no—
115C23×C31—81no—
116C23×C31C2×D411yescharacteristic
117C23×C31C2×D411yescharacteristic
118Q8×C31—21no—
119Q8×C31—21no—
120D4×C31—22no—
121D4×C31—21no—
122D4×C31—21no—
123D4×C31—21no—
124D4×C31—42no—
125D4×C31—42no—
126D4×C31—81no—
127D4×C31#4112yes—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—21no—
132C2×C4×C31—21no—
133C2×C4×C31—21no—
134C2×C4×C31—42no—
135C2×C4×C31—81no—
136C2×C4×C31C2×D411yescharacteristic
137C2×C4×C31C2×D411yescharacteristic
138C2×C4×C31C2×D411yescharacteristic
139C2×C4×C31C2×D411yescharacteristic
140C2×C4×C31C2411yescharacteristic
141C2×Dic31—21no—
142C2×Dic31—21no—
143C2×Dic31—21no—
144C2×Dic31—21no—
145C2×Dic31—81no—
146C2×Dic31—81no—
147Dic62—21no—
148Dic62—21no—
149Dic62—81no—
150C31⋊C8—21no—
151C31⋊C8—21no—
152C31⋊C8—21no—
153C31⋊C8—21no—
154#3314—311nomaximal, Sylow
155C22×C31—21no—
156C22×C31—21no—
157C22×C31—21no—
158C22×C31—22no—
159C22×C31—21no—
160C22×C31—21no—
161C22×C31—41no—
162C22×C31—41no—
163C22×C31—41no—
164C22×C31—41no—
165C22×C31—41no—
166C22×C31—84no—
167C22×C31#13712yes—
168C22×C31C22×D411yescharacteristic
169C4×C31—21no—
170C4×C31—21no—
171C4×C31—21no—
172C4×C31—21no—
173C4×C31—41no—
174C4×C31—41no—
175C4×C31C2×#4111yescharacteristic
176C4×C31H(5,𝔽2)11yescharacteristic
177Dic31—41no—
178Dic31—41no—
179Dic31—41no—
180Dic31—41no—
181#554—311no—
182#546D3111yescharacteristic
183#489—311no—
184#484—311no—
185#480—311no—
186#474—311no—
187#468—311no—
188#467—311no—
189#464—311no—
190#452—311no—
191#450—311no—
192#440—311no—
193#435—311no—
194#417—311no—
195C2×#102—311no—
196C2×C31—22no—
197C2×C31—41no—
198C2×C31—42no—
199C2×C31—81no—
200C2×C31#54611yescharacteristic
201C2×C31C2×#13711yescharacteristic
202C2×C31#57611yescharacteristic
203C2×#41C2×D3111yescharacteristic
204C22×D4C2×D3111yescharacteristic
205C2×Q16—311no—
206C2×SD16—311no—
207C2×SD16—311no—
208C2×M16—311no—
209C22×C8—311no—
210C4⋊Q8—311no—
211#125—621no—
212#124C2×D3111yescharacteristic
213#123—21no—
214C22⋊Q8—311no—
215C22⋊Q8—311no—
216C22⋊Q8—621no—
217C22⋊Q8—621no—
218C22⋊Q8C2×D3111yescharacteristic
219#121—21no—
220#121C2×D3111yescharacteristic
221#120—21no—
222C4×Q8—311no—
223C4×D4—621no—
224C4×D4C2×D3111yescharacteristic
225C4×D4C2×D3111yescharacteristic
226C2×C4⋊C4—311no—
227C2×C4⋊C4—311no—
228C2×C22⋊C4—21no—
229#107—311no—
230#107—311no—
231#107—311no—
232C4⋊C8—311no—
233#103—311no—
234#103—311no—
235#103—311no—
236#103—311no—
237#102—311no—
238#102—311no—
239#102—311no—
240#102—311no—
241#102—311no—
242#102—311no—
243C22⋊C8—311no—
244C22⋊C8—311no—
245#97—311no—
246C31#331411yescharacteristic, complemented, Sylow
247C24—21no—
248#41—22no—
249#41—41no—
250C2×Q8—311no—
251C2×Q8—621no—
252C2×Q8C22×D3111yescharacteristic
253C2×D4—22no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4C22⋊D3111yescharacteristic
259C2×D4C22×D3111yescharacteristic
260C2×D4C22×D3111yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—621no—
264C22×C4—621no—
265C22×C4C22×D3111yescharacteristic
266C22×C4C22×D3111yescharacteristic
267Q16—1241no—
268SD16—622no—
269SD16—1241no—
270M16—1241no—
271C2×C8—311no—
272C2×C8—311no—
273C2×C8—311no—
274C2×C8—311no—
275C2×C8—1241no—
276C4⋊C4—21no—
277C4⋊C4—311no—
278C4⋊C4—311no—
279C4⋊C4—311no—
280C4⋊C4—621no—
281C4⋊C4—621no—
282C4⋊C4—621no—
283C4⋊C4—621no—
284C4⋊C4—621no—
285C4⋊C4—621no—
286C4⋊C4C22⋊D3111yescharacteristic
287C4⋊C4C22×D3111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—621no—
294C22⋊C4—621no—
295C22⋊C4C22⋊D3111yescharacteristic
296C22⋊C4C22⋊D3111yescharacteristic
297C42—621no—
298C42C22×D3111yescharacteristic
299C23—21no—
300C23—21no—
301C23—42no—
302C23—42no—
303C23—81no—
304C23C2×C22⋊D3111yescharacteristic
305C23C2×C22⋊D3111yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—621no—
309Q8—621no—
310Q8—2481no—
311D4—22no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4#9249712yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—81no—
327C2×C4—621no—
328C2×C4—621no—
329C2×C4—621no—
330C2×C4—621no—
331C2×C4—2481no—
332C2×C4—2481no—
333C2×C4C2×C22⋊D3111yescharacteristic
334C2×C4C2×C22⋊D3111yescharacteristic
335C2×C4C2×C22⋊D3111yescharacteristic
336C2×C4C2×C22⋊D3111yescharacteristic
337C2×C4C23×D3111yescharacteristic
338C8—621no—
339C8—621no—
340C8—621no—
341C8—621no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—84no—
354C22#1175852812yes—
355C22C22×C22⋊D3111yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—1241no—
363C4—1241no—
364C4—1241no—
365C4—1241no—
366C4C2×#9249711yescharacteristic
367C4#1175856111yescharacteristic
368C2—22no—
369C2—41no—
370C2—42no—
371C2—81no—
372C2#1452169311yescharacteristic
373C2C2×#1175852811yescharacteristic
374C2#1452185211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
Fitting, prime radicalC31×#546C2
socleC22×C31C22×D4
hypercenter#546D31
hypocenterC31#3314
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #14521756C2semidirect
2. #14521408C2semidirect
3. #14521382C2semidirect
4. #14521360C2semidirect
5. #14521329C2semidirect
6. #14521293C2semidirect
7. #14521288C2semidirect
8. #14521268C2semidirect
9. #14521211C2semidirect
10. #14521200C2semidirect
11. #14521149C2semidirect
12. #14521121C2semidirect
13. #14521050C2semidirect
14. C2×#11758420C2semidirect
27. C2×#92482C22semidirect
32. C2×C4⋊Dic31C22semidirect
34. #11758501C22semidirect
35. C2×#92474C22semidirect
40. #11758446C22semidirect
41. C4×Dic62C22semidirect
42. #11758423C22semidirect
43. #11758423C22semidirect
44. #11758423C22semidirect
52. C22⋊(C31⋊C8)C22semidirect
53. #11758398C22semidirect
54. #11758395C22semidirect
55. #11758395C22semidirect
56. #11758395C22semidirect
57. C4⋊(C31⋊C8)C22semidirect
58. #11758391C22semidirect
246. C31#3314semidirect

Maximal subgroups

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

subgroupindex
#145217562
#145214082
#145213822
#145213602
#145213292
#145212932
#145212882
#145212682
#145212112
#145212002
#145211492
#145211212
#145210502
C2×#117584202
C31×#5462
#331431