Finite Group Databasebeta

← #22593726

Subgroups — #22593726

Order 9088.

468 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556118C211yesmaximal, characteristic
2C2×#14556093C211yesmaximal, characteristic
3#17985933C211yesmaximal, characteristic
4#17985932C211yesmaximal, characteristic
5#17985920C211yesmaximal, characteristic
6#17985919C211yesmaximal, characteristic
7#17985897C211yesmaximal, characteristic
8#17985896C211yesmaximal, characteristic
9#17985896C211yesmaximal, characteristic
10#17985894C211yesmaximal, characteristic
11#17985894C211yesmaximal, characteristic
12#17985894C211yesmaximal, characteristic
13#17985894C211yesmaximal, characteristic
14C4×Dic71⋊C4C211yesmaximal, characteristic
15#389×C71C211yesmaximal, characteristic
16C22×Dic142C2211yescharacteristic
17#14556118—24no—
18#14556093—24no—
19C2×C4⋊Dic71C2211yescharacteristic
20C2×C4⋊Dic71C2211yescharacteristic
21C2×C4⋊Dic71C2211yescharacteristic
22C2×Dic71⋊C4C2211yescharacteristic
23C2×Dic71⋊C4C2211yescharacteristic
24C2×Dic71⋊C4C2211yescharacteristic
25C2×Dic71⋊C4C2211yescharacteristic
26C2×Dic71⋊C4C2211yescharacteristic
27C2×Dic71⋊C4C2211yescharacteristic
28C2×Dic71⋊C4C2211yescharacteristic
29C2×Dic71⋊C4C2211yescharacteristic
30C2×Dic71⋊C4C2211yescharacteristic
31C2×Dic71⋊C4C2211yescharacteristic
32C2×Dic71⋊C4C2211yescharacteristic
33C2×Dic71⋊C4C2211yescharacteristic
34C2×C4×Dic71C2211yescharacteristic
35C2×C4×Dic71C2211yescharacteristic
36C2×C4×Dic71C2211yescharacteristic
37C2×C4×Dic71C2211yescharacteristic
38C71⋊#95C2211yescharacteristic
39C71⋊#95C2211yescharacteristic
40C71⋊#95C2211yescharacteristic
41C71⋊#95C2211yescharacteristic
42C71⋊#95C2211yescharacteristic
43C71⋊#95C2211yescharacteristic
44C71⋊#95C2211yescharacteristic
45C71⋊#95C2211yescharacteristic
46C2×C4⋊C4×C71C2211yescharacteristic
47C2×C4⋊C4×C71C2211yescharacteristic
48C2×C4⋊C4×C71C2211yescharacteristic
49C2×C4⋊C4×C71C2211yescharacteristic
50C2×C42×C71C2211yescharacteristic
51#95×C71C2211yescharacteristic
52#95×C71C2211yescharacteristic
53C2×Dic142—22no—
54C2×Dic142—22no—
55C2×Dic142—22no—
56C22×Dic71C2311yescharacteristic
57C22×Dic71C2311yescharacteristic
58C22×Dic71C2311yescharacteristic
59C22×Dic71C2311yescharacteristic
60C22×Dic71C2311yescharacteristic
61C22×Dic71C2311yescharacteristic
62C22×Dic71C2311yescharacteristic
63C22×Dic71C2311yescharacteristic
64C4⋊Dic71—22no—
65C4⋊Dic71—22no—
66C4⋊Dic71—41no—
67Dic71⋊C4—22no—
68Dic71⋊C4—22no—
69Dic71⋊C4—22no—
70Dic71⋊C4—22no—
71Dic71⋊C4—22no—
72Dic71⋊C4—22no—
73Dic71⋊C4—22no—
74Dic71⋊C4—22no—
75Dic71⋊C4—41no—
76Dic71⋊C4—41no—
77Dic71⋊C4Q814yescomplemented
78Dic71⋊C4Q814yescomplemented
79C4×Dic71—22no—
80C4×Dic71—22no—
81C4×Dic71—41no—
82C4×Dic71D414yes—
83C22×C4×C71C2311yescharacteristic
84C22×C4×C71C2311yescharacteristic
85C22×C4×C71C2311yescharacteristic
86C22×C4×C71C2311yescharacteristic
87C22×C4×C71C2311yescharacteristic
88C22×C4×C71C2311yescharacteristic
89C22×C4×C71C2311yescharacteristic
90C4⋊C4×C71—22no—
91C4⋊C4×C71—22no—
92C4⋊C4×C71—22no—
93C4⋊C4×C71—41no—
94C42×C71—41no—
95C23×C71C2411yescharacteristic
96C2×C4×C71—21no—
97C2×C4×C71—21no—
98C2×C4×C71—21no—
99C2×C4×C71—21no—
100C2×C4×C71—21no—
101C2×C4×C71—21no—
102C2×C4×C71—21no—
103C2×C4×C71—21no—
104C2×C4×C71—21no—
105C2×C4×C71—21no—
106C2×C4×C71—21no—
107C2×C4×C71—21no—
108C2×C4×C71—21no—
109C2×C4×C71—21no—
110C2×C4×C71—21no—
111C2×C4×C71—21no—
112C2×C4×C71—21no—
113C2×C4×C71C2×D412yes—
114C2×C4×C71C2×Q812yes—
115C2×C4×C71C2×Q812yes—
116C2×C4×C71#4112yes—
117C2×Dic71—21no—
118C2×Dic71—21no—
119C2×Dic71—21no—
120C2×Dic71—21no—
121C2×Dic71—21no—
122C2×Dic71—21no—
123C2×Dic71—21no—
124C2×Dic71—21no—
125C2×Dic71—21no—
126C2×Dic71—21no—
127C2×Dic71—21no—
128C2×Dic71—21no—
129C2×Dic71—21no—
130C2×Dic71—21no—
131C2×Dic71—21no—
132C2×Dic71—21no—
133C2×Dic71—21no—
134C2×Dic71C2×D412yes—
135C2×Dic71C2×D412yes—
136C2×Dic71C2×Q812yes—
137C2×Dic71C2×Q812yes—
138C2×Dic71C2×Q812yes—
139C2×Dic71C2×Q812yes—
140C2×Dic71#4112yes—
141Dic142—28no—
142C22×C71C22×D411yescharacteristic
143C22×C71C22×Q811yescharacteristic
144C22×C71C22×Q811yescharacteristic
145C22×C71C2×#4111yescharacteristic
146C22×C71C2×#4111yescharacteristic
147C22×C71H(5,𝔽2)11yescharacteristic
148C22×C712−1+411yescharacteristic
149C4×C71—22no—
150C4×C71—22no—
151C4×C71—22no—
152C4×C71—22no—
153C4×C71—41no—
154C4×C71—41no—
155C4×C71—41no—
156Dic71—22no—
157Dic71—22no—
158Dic71—22no—
159Dic71—22no—
160Dic71—41no—
161Dic71—41no—
162Dic71—41no—
163Dic71C4⋊Q814yes—
164C2×C71#52511yescharacteristic
165C2×C71C2×C4⋊Q811yescharacteristic
166C2×C71#53711yescharacteristic
167C2×C71#55411yescharacteristic
168C2×C71#55411yescharacteristic
169C2×C71#55711yescharacteristic
170C2×C71#55711yescharacteristic
171#2584—711nomaximal, Sylow
172C71#258411yescharacteristic, complemented, Sylow
173C2×#125—711no—
174C2×C4×Q8—711no—
175#398—711no—
176#398—711no—
177#395—711no—
178#395—711no—
179#389—711no—
180#389—711no—
181#389—711no—
182#389—711no—
183#389—711no—
184#389—711no—
185#389—711no—
186#389D7111yescharacteristic
187C4×C4⋊C4—711no—
188C22×Q8—711no—
189#125—1424no—
190C4×Q8—1424no—
191C2×C4⋊C4—711no—
192C2×C4⋊C4—711no—
193C2×C4⋊C4—711no—
194C2×C4⋊C4—711no—
195C2×C4⋊C4—711no—
196C2×C4⋊C4—711no—
197C2×C4⋊C4—711no—
198C2×C4⋊C4—711no—
199C2×C4⋊C4—711no—
200C2×C4⋊C4—711no—
201C2×C4⋊C4—711no—
202C2×C4⋊C4—711no—
203C2×C4⋊C4—711no—
204C2×C4⋊C4—711no—
205C2×C4⋊C4—711no—
206C2×C4⋊C4C2×D7111yescharacteristic
207C2×C4⋊C4C2×D7111yescharacteristic
208C2×C4⋊C4C2×D7111yescharacteristic
209C2×C4⋊C4C2×D7111yescharacteristic
210C2×C42—711no—
211C2×C42—711no—
212C2×C42—711no—
213C2×C42—711no—
214C2×C42C2×D7111yescharacteristic
215#95—711no—
216#95—711no—
217#95—711no—
218#95—711no—
219#95—711no—
220#95—711no—
221#95—711no—
222#95—711no—
223#95C2×D7111yescharacteristic
224#95C2×D7111yescharacteristic
225C2×Q8—1422no—
226C2×Q8—1422no—
227C2×Q8—1422no—
228C22×C4—711no—
229C22×C4—711no—
230C22×C4—711no—
231C22×C4—711no—
232C22×C4—711no—
233C22×C4—711no—
234C22×C4—711no—
235C22×C4—711no—
236C22×C4C22×D7111yescharacteristic
237C22×C4C22×D7111yescharacteristic
238C22×C4C22×D7111yescharacteristic
239C22×C4C22×D7111yescharacteristic
240C22×C4C22×D7111yescharacteristic
241C22×C4C22×D7111yescharacteristic
242C22×C4C22×D7111yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—41no—
247C4⋊C4—2841no—
248C4⋊C4—2841no—
249C4⋊C4—2841no—
250C4⋊C4—714no—
251C4⋊C4—714no—
252C4⋊C4—1422no—
253C4⋊C4—1422no—
254C4⋊C4—1422no—
255C4⋊C4—1422no—
256C4⋊C4—1422no—
257C4⋊C4—1422no—
258C4⋊C4—1422no—
259C4⋊C4—1422no—
260C4⋊C4—1422no—
261C4⋊C4—1422no—
262C42—41no—
263C42—2841no—
264C42—714no—
265C42—1422no—
266C42—1422no—
267C23C23×D7111yescharacteristic
268Q8—1428no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—712no—
287C2×C4—712no—
288C2×C4—712no—
289C2×C4—712no—
290C2×C4—712no—
291C2×C4—712no—
292C2×C4—712no—
293C2×C4—1421no—
294C2×C4—1421no—
295C2×C4—1421no—
296C2×C4—1421no—
297C2×C4—1421no—
298C2×C4—1421no—
299C2×C4—1421no—
300C2×C4—1421no—
301C2×C4—1421no—
302C2×C4—1421no—
303C2×C4—1421no—
304C2×C4—1421no—
305C2×C4—1421no—
306C2×C4—1421no—
307C2×C4—1421no—
308C2×C4—1421no—
309C2×C4—1421no—
310C2×C4D4×D7112yes—
311C2×C4Q8×D7112yes—
312C2×C4Q8×D7112yes—
313C2×C4#1176586512yes—
314C22C2×D4×D7111yescharacteristic
315C22C2×Q8×D7111yescharacteristic
316C22C2×Q8×D7111yescharacteristic
317C22#41×D7111yescharacteristic
318C22C2×#1176586511yescharacteristic
319C22#1455617311yescharacteristic
320C22#1455617511yescharacteristic
321C4—22no—
322C4—22no—
323C4—22no—
324C4—22no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—2841no—
329C4—2841no—
330C4—2841no—
331C4—714no—
332C4—1422no—
333C4—1422no—
334C4—1422no—
335C4—1422no—
336C2#1798650811yescharacteristic
337C2C4⋊Q8×D7111yescharacteristic
338C2#1798657611yescharacteristic
339C2#1798670311yescharacteristic
340C2#1798670411yescharacteristic
341C2#1798672611yescharacteristic
342C2#1798672711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#389×C71C2
hypercenter#389D71
hypocenterC71#2584
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
77. Dic71⋊C4Q8semidirect
78. Dic71⋊C4Q8semidirect
172. C71#2584semidirect