Finite Group Databasebeta

← #31896018

Subgroups — #31896018

Order 18176.

378 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22589059C211yesmaximal, characteristic
2#22589056C211yesmaximal, characteristic
3C4×#14556061C211yesmaximal, characteristic
4C2×#17985749C211yesmaximal, characteristic
5C2×#17985720C211yesmaximal, characteristic
6#22586180C211yesmaximal, characteristic
7C71×#1279C211yesmaximal, characteristic
8C2×#14556061C411yescharacteristic
9C2×#14556061C411yescharacteristic
10C2×C4⋊(C71⋊C8)—21no—
11C2×C4⋊(C71⋊C8)C2211yescharacteristic
12C2×Dic71⋊C8—21no—
13C2×C4×C71⋊C8C2211yescharacteristic
14C2×C4×C71⋊C8C2211yescharacteristic
15C4×C4⋊Dic71C2211yescharacteristic
16#17985761C411yescharacteristic
17#17985761C411yescharacteristic
18#17985754—21no—
19#17985753—21no—
20#17985749—22no—
21#17985720—22no—
22C2×C4⋊C8×C71C2211yescharacteristic
23C2×C4×C8×C71C2211yescharacteristic
24C4×C4⋊C4×C71C2211yescharacteristic
25C22×C71⋊C8—21no—
26C22×C71⋊C8C2×C411yescharacteristic
27C22×C71⋊C8C2×C411yescharacteristic
28C22×C71⋊C8D411yescharacteristic
29C22×C71⋊C8D411yescharacteristic
30C2×C4⋊Dic71C2×C411yescharacteristic
31C2×C4⋊Dic71C2×C411yescharacteristic
32C2×C4×Dic71—21no—
33#14556061—22no—
34#14556061—22no—
35C4⋊(C71⋊C8)—21no—
36C4⋊(C71⋊C8)—21no—
37C4⋊(C71⋊C8)—42no—
38Dic71⋊C8—42no—
39C4×C71⋊C8—21no—
40C4×C71⋊C8—21no—
41C4×C71⋊C8D412yes—
42C4×C71⋊C8Q812yes—
43C71⋊#95—21no—
44C22×C8×C71—21no—
45C22×C8×C71—21no—
46C2×C4⋊C4×C71C2×C411yescharacteristic
47C2×C4⋊C4×C71C2×C411yescharacteristic
48C2×C42×C71—21no—
49C2×C42×C71C2311yescharacteristic
50C4⋊C8×C71—21no—
51C4⋊C8×C71—21no—
52C4×C8×C71—21no—
53C4×C8×C71Q812yes—
54#95×C71—21no—
55C22×Dic71—21no—
56C22×Dic71—21no—
57C2×C71⋊C8—21no—
58C2×C71⋊C8—21no—
59C2×C71⋊C8—21no—
60C2×C71⋊C8—21no—
61C2×C71⋊C8—21no—
62C2×C71⋊C8—21no—
63C2×C71⋊C8—21no—
64C2×C71⋊C8—21no—
65C2×C71⋊C8—21no—
66C2×C71⋊C8—21no—
67C2×C71⋊C8—41no—
68C2×C71⋊C8—41no—
69C2×C71⋊C8—41no—
70C2×C71⋊C8C4⋊C412yes—
71C2×C71⋊C8C4⋊C412yes—
72C4⋊Dic71—21no—
73C4⋊Dic71—21no—
74C4⋊Dic71—21no—
75C4⋊Dic71M1612yes—
76C4×Dic71—41no—
77C4×Dic71—41no—
78C22×C4×C71—21no—
79C22×C4×C71—21no—
80C22×C4×C71C22×C411yescharacteristic
81C22×C4×C71C2×D411yescharacteristic
82C22×C4×C71#4111yescharacteristic
83C2×C8×C71—22no—
84C2×C8×C71—22no—
85C2×C8×C71—22no—
86C2×C8×C71—41no—
87C2×C8×C71—41no—
88C2×C8×C71—41no—
89C4⋊C4×C71—21no—
90C4⋊C4×C71—21no—
91C4⋊C4×C71—21no—
92C4⋊C4×C71M1612yes—
93C42×C71—41no—
94C42×C71—41no—
95C42×C71C2×D411yescharacteristic
96C42×C71C2×Q811yescharacteristic
97C42×C71C2×Q811yescharacteristic
98C42×C71#4111yescharacteristic
99C23×C71C4×D411yescharacteristic
100C2×C4×C71—21no—
101C2×C4×C71—21no—
102C2×C4×C71—22no—
103C2×C4×C71—41no—
104C2×C4×C71—41no—
105C2×C4×C71—41no—
106C2×C4×C71—41no—
107C2×C4×C71—41no—
108C2×C4×C71C2×C4⋊C411yescharacteristic
109C2×C4×C71C4×Q811yescharacteristic
110C2×C4×C71#12111yescharacteristic
111C2×C4×C71C22⋊Q811yescharacteristic
112C2×C4×C71#12511yescharacteristic
113C2×C4×C71C4⋊Q811yescharacteristic
114C2×C4×C71C2×M1611yescharacteristic
115C2×C4×C71C2×M1611yescharacteristic
116C2×C4×C71#13111yescharacteristic
117C2×C4×C71#13111yescharacteristic
118C2×C4×C71AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C71AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C71#13711yescharacteristic
121C2×C4×C71#13711yescharacteristic
122C2×Dic71—22no—
123C2×Dic71—41no—
124C2×Dic71—41no—
125C2×Dic71—41no—
126C2×Dic71—41no—
127C2×Dic71—41no—
128C8×C71—24no—
129C8×C71—81no—
130C71⋊C8—22no—
131C71⋊C8—22no—
132C71⋊C8—41no—
133C71⋊C8—41no—
134C71⋊C8—81no—
135C22×C71#38911yescharacteristic
136C22×C71#43511yescharacteristic
137C22×C71#43511yescharacteristic
138C22×C71#44111yescharacteristic
139C22×C71#44211yescharacteristic
140C22×C71#44311yescharacteristic
141C22×C71#44311yescharacteristic
142C4×C71—21no—
143C4×C71—21no—
144C4×C71—42no—
145C4×C71—81no—
146C4×C71#42311yescharacteristic
147C4×C71#42411yescharacteristic
148C4×C71#44611yescharacteristic
149C4×C71#44611yescharacteristic
150C4×C71#46811yescharacteristic
151C4×C71#46811yescharacteristic
152C4×C71#50111yescharacteristic
153C4×C71#50111yescharacteristic
154Dic71—42no—
155Dic71—81no—
156#9599—711nomaximal, Sylow
157C2×C71#158611yescharacteristic
158C2×C71#158611yescharacteristic
159C2×C71#158711yescharacteristic
160C2×C71#158711yescharacteristic
161C2×C71#194011yescharacteristic
162C2×C71#194311yescharacteristic
163C2×C71#194511yescharacteristic
164#1939—711no—
165#1939—711no—
166C4×#107—711no—
167C2×#334—711no—
168C2×#322—711no—
169#1279—711no—
170#1279D7111yescharacteristic
171C71#959911yescharacteristic, complemented, Sylow
172C2×#107—711no—
173C2×#107—711no—
174C2×C4⋊C8—711no—
175C2×C4⋊C8—1421no—
176C2×C4⋊C8—1421no—
177C2×C4⋊C8C2×D7111yescharacteristic
178C2×C4×C8—711no—
179C2×C4×C8—711no—
180C2×C4×C8C2×D7111yescharacteristic
181C4×C4⋊C4—711no—
182C4×C4⋊C4C2×D7111yescharacteristic
183#340—711no—
184#340—711no—
185#336—1421no—
186#336—1421no—
187#334—1422no—
188#322—1422no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—711no—
192C22×C8—711no—
193C22×C8—711no—
194C22×C8—711no—
195C22×C8—1421no—
196C2×C4⋊C4—711no—
197C2×C4⋊C4—711no—
198C2×C4⋊C4C4×D7111yescharacteristic
199C2×C4⋊C4C4×D7111yescharacteristic
200C2×C42—21no—
201C2×C42—1421no—
202C2×C42C22×D7111yescharacteristic
203#107—1422no—
204#107—1422no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—2842no—
208C4⋊C8—2842no—
209C4⋊C8—1421no—
210C4⋊C8—1421no—
211C4×C8—21no—
212C4×C8—712no—
213C4×C8—712no—
214C4×C8—1421no—
215C4×C8—1421no—
216C4×C8Dic14212yes—
217#95—21no—
218#95—1421no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—1421no—
222C22×C4—1421no—
223C22×C4C2×C4×D7111yescharacteristic
224C22×C4D4×D7111yescharacteristic
225C22×C4#1176586411yescharacteristic
226C2×C8—22no—
227C2×C8—22no—
228C2×C8—22no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—2841no—
233C2×C8—2841no—
234C2×C8—2841no—
235C2×C8—712no—
236C2×C8—712no—
237C2×C8—1421no—
238C2×C8—1421no—
239C2×C8—1421no—
240C2×C8—1421no—
241C2×C8—1421no—
242C2×C8—1421no—
243C2×C8—1421no—
244C2×C8—1421no—
245C2×C8—1421no—
246C2×C8—1421no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—712no—
251C4⋊C4—1421no—
252C4⋊C4—1421no—
253C4⋊C4—1421no—
254C4⋊C4#1176584812yes—
255C42—41no—
256C42—41no—
257C42—2841no—
258C42—2841no—
259C42D4×D7111yescharacteristic
260C42Q8×D7111yescharacteristic
261C42C2×Dic14211yescharacteristic
262C42#1176586511yescharacteristic
263C23(C22⋊D71)⋊C411yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—2841no—
273C2×C4—2841no—
274C2×C4—2841no—
275C2×C4—2841no—
276C2×C4—2841no—
277C2×C4—1422no—
278C2×C4C4⋊C4×D7111yescharacteristic
279C2×C4C4×Dic14211yescharacteristic
280C2×C4#1455610111yescharacteristic
281C2×C4#1455610511yescharacteristic
282C2×C4#1455611811yescharacteristic
283C2×C4#1455612711yescharacteristic
284C2×C4M16×D7111yescharacteristic
285C2×C4C2×#1176584811yescharacteristic
286C2×C4#1455613411yescharacteristic
287C2×C4#1455613611yescharacteristic
288C2×C4#1455615211yescharacteristic
289C2×C4#1455615511yescharacteristic
290C2×C4#1455615711yescharacteristic
291C2×C4#1455616011yescharacteristic
292C8—24no—
293C8—81no—
294C8—2841no—
295C8—2841no—
296C8—5681no—
297C8—1422no—
298C8—1422no—
299C22#1798589611yescharacteristic
300C22#1798606711yescharacteristic
301C22#1798607311yescharacteristic
302C22#1798610311yescharacteristic
303C22#1798610811yescharacteristic
304C22#1798611311yescharacteristic
305C22#1798611311yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—81no—
310C4—2842no—
311C4—5681no—
312C4#1798602111yescharacteristic
313C4#1798602411yescharacteristic
314C4#1798612711yescharacteristic
315C4#1798612911yescharacteristic
316C4#1798624411yescharacteristic
317C4#1798624811yescharacteristic
318C4#1798640611yescharacteristic
319C4#1798640711yescharacteristic
320C2#2258720111yescharacteristic
321C2#2258720711yescharacteristic
322C2#2258720811yescharacteristic
323C2#2258721411yescharacteristic
324C2#2258906211yescharacteristic
325C2#2258907711yescharacteristic
326C2#2258908711yescharacteristic
subgroupG/H
centerC22×C4D4×D71
commutatorC22×C4×C71C22×C4
FrattiniC2×C42C22×D71
FittingC71×#1279C2
socle, prime radicalC23×C71C4×D4
cosocleC2×C42×C71C23
hypercenter#1279D71
hypocenterC71#9599
LCSG ▷ C22×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
171. C71#9599semidirect

Maximal subgroups

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

subgroupindex
#225890592
#225890562
C4×#145560612
C2×#179857492
C2×#179857202
#225861802
C71×#12792
#959971