Finite Group Databasebeta

← #31903066

Subgroups — #31903066

Order 18176.

918 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C71⋊C8C211yesmaximal, characteristic
2C2×#17985754C212yesmaximal
3C2×#17985754C212yesmaximal
4C2×#17985754C211yesmaximal, characteristic
5C4×#95×C71C211yesmaximal, characteristic
6C23×C71⋊C8C2212yes—
7C23×C71⋊C8C2211yescharacteristic
8C23×C71⋊C8C2211yescharacteristic
9C2×C4×C71⋊C8—24no—
10C2×C4×C71⋊C8C414yescomplemented
11#17985754—24no—
12#17985754—24no—
13#17985754C414yescomplemented
14C22×C42×C71C2212yes—
15C22×C42×C71C2211yescharacteristic
16C2×#95×C71C412yes—
17C2×#95×C71C412yes—
18C22×C71⋊C8—22no—
19C22×C71⋊C8—22no—
20C22×C71⋊C8—22no—
21C22×C71⋊C8—21no—
22C22×C71⋊C8—22no—
23C22×C71⋊C8—22no—
24C22×C71⋊C8—21no—
25C22×C71⋊C8—22no—
26C22×C71⋊C8—22no—
27C22×C71⋊C8—22no—
28C22×C71⋊C8—22no—
29C22×C71⋊C8C2×C414yes—
30C22×C71⋊C8C2×C412yes—
31C22×C71⋊C8C2×C412yes—
32C22×C71⋊C8D414yes—
33C22×C71⋊C8D412yes—
34C22×C71⋊C8Q812yes—
35C4×C71⋊C8—28no—
36C23×C4×C71C2×C414yes—
37C23×C4×C71C2×C411yescharacteristic
38C23×C4×C71C2×C411yescharacteristic
39C23×C4×C71C2311yescharacteristic
40C2×C42×C71—22no—
41C2×C42×C71—22no—
42C2×C42×C71—22no—
43C2×C42×C71—22no—
44C2×C42×C71—22no—
45C2×C42×C71—22no—
46C2×C42×C71—22no—
47C2×C42×C71—22no—
48C2×C42×C71C2×C412yes—
49C2×C42×C71C2×C412yes—
50#95×C71—24no—
51#95×C71C818yescomplemented
52C2×C71⋊C8—22no—
53C2×C71⋊C8—22no—
54C2×C71⋊C8—22no—
55C2×C71⋊C8—22no—
56C2×C71⋊C8—24no—
57C2×C71⋊C8—24no—
58C2×C71⋊C8—24no—
59C2×C71⋊C8—24no—
60C2×C71⋊C8—24no—
61C2×C71⋊C8—24no—
62C2×C71⋊C8—24no—
63C2×C71⋊C8—42no—
64C2×C71⋊C8—42no—
65C2×C71⋊C8—42no—
66C2×C71⋊C8—42no—
67C2×C71⋊C8C22⋊C414yes—
68C2×C71⋊C8C4⋊C414yes—
69C24×C71C22×C411yescharacteristic
70C22×C4×C71—22no—
71C22×C4×C71—22no—
72C22×C4×C71—22no—
73C22×C4×C71—22no—
74C22×C4×C71—24no—
75C22×C4×C71—24no—
76C22×C4×C71—24no—
77C22×C4×C71—24no—
78C22×C4×C71—24no—
79C22×C4×C71—24no—
80C22×C4×C71C4212yes—
81C22×C4×C71C4212yes—
82C22×C4×C71C2×C818yes—
83C22×C4×C71C2×C814yes—
84C22×C4×C71M1614yes—
85C22×C4×C71C22×C411yescharacteristic
86C22×C4×C71C22×C411yescharacteristic
87C22×C4×C71C2×D412yes—
88C22×C4×C71C2×D411yescharacteristic
89C22×C4×C71C2×Q811yescharacteristic
90C22×C4×C71#4112yes—
91C22×C4×C71#4111yescharacteristic
92C22×C4×C71#4112yes—
93C22×C4×C71#4112yes—
94C22×C4×C71#4111yescharacteristic
95C42×C71—22no—
96C42×C71—22no—
97C42×C71—24no—
98C42×C71—42no—
99C42×C71—42no—
100C42×C71—42no—
101C42×C71—42no—
102C23×C71C2×C4211yescharacteristic
103C23×C71#11712yes—
104C23×C71C4×D412yes—
105C23×C71C4×D411yescharacteristic
106C23×C71C4×Q811yescharacteristic
107C23×C71C22×C812yes—
108C23×C71C2×M1612yes—
109C23×C71#13112yes—
110C23×C71#13112yes—
111C2×C4×C71—22no—
112C2×C4×C71—22no—
113C2×C4×C71—22no—
114C2×C4×C71—22no—
115C2×C4×C71—28no—
116C2×C4×C71—28no—
117C2×C4×C71—28no—
118C2×C4×C71—28no—
119C2×C4×C71—28no—
120C2×C4×C71—44no—
121C2×C4×C71—44no—
122C2×C4×C71—44no—
123C2×C4×C71—44no—
124C2×C4×C71C4×C814yes—
125C2×C4×C71#9714yes—
126C2×C4×C71C2×C22⋊C411yescharacteristic
127C2×C4×C71C2×C4⋊C411yescharacteristic
128C2×C4×C71#11711yescharacteristic
129C2×C4×C71#11711yescharacteristic
130C2×C4×C71#11711yescharacteristic
131C2×C4×C71#11712yes—
132C2×C4×C71#11711yescharacteristic
133C2×C4×C71C4×D412yes—
134C2×C4×C71C4×D411yescharacteristic
135C2×C4×C71C4×Q811yescharacteristic
136C2×C4×C71#12112yes—
137C2×C4×C71C22⋊Q812yes—
138C2×C4×C71#12312yes—
139C2×C4×C71#12312yes—
140C2×C4×C71#12412yes—
141C2×C4×C71#12512yes—
142C2×C4×C71#12612yes—
143C2×C4×C71#12612yes—
144C71⋊C8—24no—
145C71⋊C8—24no—
146C71⋊C8—44no—
147C22×C71#37611yescharacteristic
148C22×C71C4×C22⋊C411yescharacteristic
149C22×C71C4×C4⋊C411yescharacteristic
150C22×C71#38712yes—
151C22×C71#38812yes—
152C22×C71C2×C4×C811yescharacteristic
153C22×C71C2×#9711yescharacteristic
154C22×C71#40511yescharacteristic
155C22×C71#40511yescharacteristic
156C22×C71#43114yes—
157C22×C71#43314yes—
158C22×C71C8×D414yes—
159C22×C71C8×D412yes—
160C22×C71#43514yes—
161C22×C71#43612yes—
162C22×C71C8×Q812yes—
163C22×C71#44612yes—
164C4×C71—24no—
165C4×C71—24no—
166C4×C71—48no—
167C4×C71#38011yescharacteristic
168C4×C71#38111yescharacteristic
169C4×C71#38211yescharacteristic
170C4×C71#38311yescharacteristic
171C4×C71#38712yes—
172C4×C71#38812yes—
173#10797—711nomaximal, Sylow
174C2×C71#143411yescharacteristic
175C2×C71#174411yescharacteristic
176C2×C71#174611yescharacteristic
177C2×C71C8×C22⋊C411yescharacteristic
178C2×C71#175211yescharacteristic
179C2×C71C8×C4⋊C411yescharacteristic
180C2×C71#177011yescharacteristic
181C2×C71#191614yes—
182C2×C71#192314yes—
183C22×C4×C8—711no—
184C2×#336—711no—
185C2×#336—712no—
186C2×#336—712no—
187C4×#95D7111yescharacteristic
188C71#1079711yescharacteristic, complemented, Sylow
189C23×C8—711no—
190C23×C8—711no—
191C23×C8—712no—
192C22×C42C2×D7112yes—
193C22×C42C2×D7111yescharacteristic
194C2×C4×C8—714no—
195C2×C4×C8—1424no—
196C2×#95Dic7112yes—
197C2×#95Dic7112yes—
198#336—714no—
199#336—1424no—
200#336—1424no—
201C23×C4C2×Dic7114yes—
202C23×C4C2×Dic7111yescharacteristic
203C23×C4C2×Dic7111yescharacteristic
204C23×C4C22×D7111yescharacteristic
205C22×C8—712no—
206C22×C8—712no—
207C22×C8—712no—
208C22×C8—714no—
209C22×C8—712no—
210C22×C8—714no—
211C22×C8—1422no—
212C22×C8—1422no—
213C22×C8—1422no—
214C22×C8—1422no—
215C22×C8—1422no—
216C22×C8—1422no—
217C22×C8—1422no—
218C22×C8—1421no—
219C22×C8—1422no—
220C22×C8—1422no—
221C22×C8—1421no—
222C2×C42—22no—
223C2×C42—22no—
224C2×C42—22no—
225C2×C42—22no—
226C2×C42—22no—
227C2×C42—22no—
228C2×C42—22no—
229C2×C42—22no—
230C2×C42C4×D7112yes—
231C2×C42C4×D7112yes—
232C4×C8—1428no—
233#95—24no—
234#95C71⋊C818yescomplemented
235C24C22×Dic7111yescharacteristic
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—24no—
241C22×C4—24no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—24no—
246C22×C4C4×Dic7112yes—
247C22×C4C4×Dic7112yes—
248C22×C4C2×C71⋊C818yes—
249C22×C4C2×C71⋊C814yes—
250C22×C4#1176584914yes—
251C22×C4C2×C4×D7111yescharacteristic
252C22×C4C2×C4×D7111yescharacteristic
253C22×C4D4×D7112yes—
254C22×C4D4×D7111yescharacteristic
255C22×C4Q8×D7111yescharacteristic
256C22×C4#1176586412yes—
257C22×C4#1176586411yescharacteristic
258C22×C4#1176586512yes—
259C22×C4#1176586512yes—
260C22×C4#1176586611yescharacteristic
261C2×C8—2842no—
262C2×C8—2842no—
263C2×C8—2842no—
264C2×C8—2842no—
265C2×C8—714no—
266C2×C8—714no—
267C2×C8—1424no—
268C2×C8—1424no—
269C2×C8—1424no—
270C2×C8—1422no—
271C2×C8—1422no—
272C2×C8—1422no—
273C2×C8—1422no—
274C2×C8—1424no—
275C2×C8—1424no—
276C2×C8—1424no—
277C2×C8—1424no—
278C42—22no—
279C42—22no—
280C42—24no—
281C42—42no—
282C42—42no—
283C42—42no—
284C42—42no—
285C23C2×C4×Dic7111yescharacteristic
286C23#1455608712yes—
287C23D4×Dic7112yes—
288C23D4×Dic7111yescharacteristic
289C23Q8×Dic7111yescharacteristic
290C23C22×C71⋊C812yes—
291C23C2×#1176584912yes—
292C23#1455613512yes—
293C23#1455613512yes—
294C2×C4—28no—
295C2×C4—28no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—28no—
301C2×C4—28no—
302C2×C4—28no—
303C2×C4—44no—
304C2×C4—44no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4C4×C71⋊C814yes—
308C2×C4#1455603914yes—
309C2×C4C22⋊C4×D7111yescharacteristic
310C2×C4C4⋊C4×D7111yescharacteristic
311C2×C4#1455608411yescharacteristic
312C2×C4#1455608511yescharacteristic
313C2×C4#1455608511yescharacteristic
314C2×C4#1455608512yes—
315C2×C4#1455608611yescharacteristic
316C2×C4(C22⋊D71)⋊C412yes—
317C2×C4#1455609011yescharacteristic
318C2×C4#1455609311yescharacteristic
319C2×C4#1455610112yes—
320C2×C4#1455610612yes—
321C2×C4#1455611012yes—
322C2×C4#1455611312yes—
323C2×C4#1455611412yes—
324C2×C4#1455611812yes—
325C2×C4#1455612112yes—
326C2×C4#1455612312yes—
327C8—2844no—
328C8—1424no—
329C8—1424no—
330C22#1798584511yescharacteristic
331C22C22⋊C4×Dic7111yescharacteristic
332C22C4⋊C4×Dic7111yescharacteristic
333C22#1798588512yes—
334C22#1798589212yes—
335C22C2×C4×C71⋊C811yescharacteristic
336C22C2×#1455603911yescharacteristic
337C22#1798595511yescharacteristic
338C22#1798595511yescharacteristic
339C22#1798605214yes—
340C22#1798606014yes—
341C22D4×C71⋊C812yes—
342C22D4×C71⋊C814yes—
343C22#1798607114yes—
344C22#1798607712yes—
345C22Q8×C71⋊C812yes—
346C22#1798613012yes—
347C4—24no—
348C4—24no—
349C4—48no—
350C4#1798585811yescharacteristic
351C4#1798586111yescharacteristic
352C4#1798586311yescharacteristic
353C4#1798586611yescharacteristic
354C4#1798588112yes—
355C4#1798588812yes—
356C2#2258656511yescharacteristic
357C2#2258808611yescharacteristic
358C2#2258809211yescharacteristic
359C2C22⋊C4×C71⋊C811yescharacteristic
360C2#2258811811yescharacteristic
361C2C4⋊C4×C71⋊C811yescharacteristic
362C2#2258820911yescharacteristic
363C2#2258889914yes—
364C2#2258894814yes—
subgroupG/H
center, FrattiniC23×C4C22×D71
commutatorC22×C71C2×C4×C8
FittingC4×#95×C71C2
socle, prime radicalC24×C71C22×C4
cosocleC23×C4×C71C23
hypercenterC4×#95D71
hypocenterC71#10797
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
10. C2×C4×C71⋊C8C4semidirect
13. #17985754C4semidirect
51. #95×C71C8semidirect
188. C71#10797semidirect
234. #95C71⋊C8semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C71⋊C82
C2×#179857542
C4×#95×C712
#1079771