Finite Group Databasebeta

← #31885864

Subgroups — #31885864

Order 18176.

438 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22596707C211yesmaximal, characteristic
2#22588483C211yesmaximal, characteristic, complemented
3#22586164C212yesmaximal, complemented
4#22586160C212yesmaximal
5C4×C4⋊C8×C71C211yesmaximal, characteristic, complemented
6C2×#14556122—21no—
7#17985901C411yescharacteristic
8#17985901C411yescharacteristic
9#17985901C2211yescharacteristic
10#17985897C411yescharacteristic
11#17985897C411yescharacteristic
12#17985897C2211yescharacteristic
13#17985890—21no—
14#17985890—21no—
15#17985890—21no—
16#17985754—21no—
17#17985754—21no—
18#17985754C2212yes—
19C2×C4⋊C8×C71—21no—
20C2×C4×C8×C71—21no—
21C43×C71C2211yescharacteristic
22#336×C71C2212yes—
23C22×D284C2×C411yescharacteristic
24C22×C71⋊C8—22no—
25#14556122—42no—
26#14556122—42no—
27C2×C4⋊Dic71C2×C411yescharacteristic
28C2×C4⋊Dic71C2×C411yescharacteristic
29C2×C4⋊Dic71C2×C411yescharacteristic
30C2×Dic71⋊C4—21no—
31C2×Dic71⋊C4—21no—
32C2×Dic71⋊C4—21no—
33C2×(C2×D71)⋊C4—21no—
34C2×(C2×D71)⋊C4—21no—
35C2×(C2×D71)⋊C4—21no—
36C2×(C2×D71)⋊C4—21no—
37C2×(C2×D71)⋊C4—21no—
38C2×(C2×D71)⋊C4—21no—
39C71⋊#95—21no—
40C71⋊#95—21no—
41C71⋊#95—21no—
42C22×C8×C71—22no—
43C2×C42×C71C2×C411yescharacteristic
44C2×C42×C71C2×C411yescharacteristic
45C2×C42×C71D411yescharacteristic
46C2×C42×C71D411yescharacteristic
47C2×C42×C71D411yescharacteristic
48C2×C42×C71D411yescharacteristic
49C2×C42×C71C2311yescharacteristic
50C4⋊C8×C71—24no—
51C4×C8×C71—42no—
52C23×D71—21no—
53C2×D284—22no—
54C2×D284—41no—
55C2×D284—41no—
56C22×Dic71—21no—
57C22×Dic71—21no—
58C22×Dic71—21no—
59C2×C71⋊C8—42no—
60C2×C71⋊C8—42no—
61C2×C71⋊C8—42no—
62C4⋊Dic71—22no—
63C4⋊Dic71—41no—
64C4⋊Dic71—41no—
65Dic71⋊C4—42no—
66Dic71⋊C4—42no—
67Dic71⋊C4—41no—
68Dic71⋊C4—41no—
69(C2×D71)⋊C4—42no—
70(C2×D71)⋊C4—42no—
71(C2×D71)⋊C4—42no—
72(C2×D71)⋊C4—42no—
73(C2×D71)⋊C4—41no—
74(C2×D71)⋊C4—41no—
75(C2×D71)⋊C4—42no—
76C22×C4×C71C22⋊C411yescharacteristic
77C22×C4×C71C22⋊C411yescharacteristic
78C22×C4×C71C22⋊C411yescharacteristic
79C22×C4×C71C22⋊C411yescharacteristic
80C22×C4×C71C22×C411yescharacteristic
81C22×C4×C71C2×D411yescharacteristic
82C22×C4×C71C2×D411yescharacteristic
83C2×C8×C71—24no—
84C2×C8×C71—42no—
85C2×C8×C71—42no—
86C42×C71—22no—
87C42×C71—22no—
88C42×C71—22no—
89C42×C71—41no—
90C42×C71—41no—
91C42×C71—41no—
92C42×C71D812yes—
93C42×C71SD1612yes—
94C23×C71C2×C22⋊C411yescharacteristic
95C22×D71—41no—
96C22×D71—41no—
97C22×D71—41no—
98C22×D71—41no—
99C22×D71—41no—
100C22×D71—41no—
101C22×D71—41no—
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×C71—21no—
114C2×C4×C71—21no—
115C2×C4×C71—21no—
116C2×C4×C71—21no—
117C2×C4×C71#10212yes—
118C2×C4×C71#10212yes—
119C2×C4×C71#10412yes—
120C2×C4×C71#13112yes—
121C2×C4×C71C2×D811yescharacteristic
122C2×C4×C71C2×SD1611yescharacteristic
123C2×C4×C71#13512yes—
124C2×Dic71—41no—
125C2×Dic71—41no—
126C2×Dic71—41no—
127C2×Dic71—41no—
128C2×Dic71—41no—
129C2×Dic71—41no—
130C2×Dic71—41no—
131C2×Dic71—41no—
132C2×Dic71—41no—
133D284—82no—
134C8×C71—44no—
135C71⋊C8—82no—
136C22×C71#40811yescharacteristic
137C22×C71#41011yescharacteristic
138C22×C71#41311yescharacteristic
139C22×C71C2×#10211yescharacteristic
140C22×C71#41611yescharacteristic
141C22×C71C2×#10411yescharacteristic
142C22×C71#42111yescharacteristic
143C2×D71—81no—
144C2×D71—81no—
145C2×D71—81no—
146C2×D71—81no—
147C2×D71—81no—
148C2×D71—81no—
149C2×D71—81no—
150C4×C71—22no—
151C4×C71—22no—
152C4×C71—22no—
153C4×C71—22no—
154C4×C71—21no—
155C4×C71—21no—
156C4×C71—22no—
157C4×C71—41no—
158Dic71—81no—
159Dic71—81no—
160Dic71—81no—
161#7672—711nomaximal, Sylow
162C2×C71#147311yescharacteristic
163C2×C71#148011yescharacteristic
164C2×C71#149411yescharacteristic
165C2×C71#150211yescharacteristic
166C2×C71#152111yescharacteristic
167C2×C71#152911yescharacteristic
168C2×C71#154011yescharacteristic
169D71—161no—
170#2860—711no—
171#1839—711no—
172C4×C4⋊C8D7111yescharacteristic, complemented
173#1271—712no—
174#1270—712no—
175C71#767211yescharacteristic, complemented, Sylow
176C2×#126—1421no—
177C2×C4⋊C8—21no—
178C2×C4×C8—21no—
179#390—711no—
180#390—711no—
181#390—711no—
182#389—711no—
183#389—711no—
184#389—711no—
185#388—1421no—
186#388—1421no—
187#388—1421no—
188C43C2×D7111yescharacteristic
189#336—712no—
190#336—1421no—
191#336—1421no—
192#336C2×D7112yes—
193C22×D4—711no—
194C22×C8—22no—
195C22×C8—1422no—
196#126—2842no—
197#126—2842no—
198C2×C4⋊C4—711no—
199C2×C4⋊C4—711no—
200C2×C4⋊C4—711no—
201C2×C4⋊C4—1421no—
202C2×C4⋊C4—1421no—
203C2×C4⋊C4—1421no—
204C2×C22⋊C4—1421no—
205C2×C22⋊C4—1421no—
206C2×C22⋊C4—1421no—
207C2×C22⋊C4—1421no—
208C2×C22⋊C4—1421no—
209C2×C22⋊C4—1421no—
210C2×C42C4×D7111yescharacteristic
211C2×C42C4×D7111yescharacteristic
212C2×C42D28411yescharacteristic
213C2×C42D28411yescharacteristic
214C2×C42C22⋊D7111yescharacteristic
215C2×C42C22⋊D7111yescharacteristic
216C2×C42C22×D7111yescharacteristic
217C4⋊C8—24no—
218C4×C8—42no—
219#95—1421no—
220#95—1421no—
221#95—1421no—
222C24—1421no—
223C2×D4—2841no—
224C2×D4—2841no—
225C2×D4—1422no—
226C22×C4—1421no—
227C22×C4—1421no—
228C22×C4—1421no—
229C22×C4(C2×D71)⋊C411yescharacteristic
230C22×C4(C2×D71)⋊C411yescharacteristic
231C22×C4(C2×D71)⋊C411yescharacteristic
232C22×C4(C2×D71)⋊C411yescharacteristic
233C22×C4C2×C4×D7111yescharacteristic
234C22×C4C2×C22⋊D7111yescharacteristic
235C22×C4C2×D28411yescharacteristic
236C2×C8—24no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—2842no—
240C2×C8—2842no—
241C2×C8—2842no—
242C4⋊C4—2841no—
243C4⋊C4—2841no—
244C4⋊C4—2842no—
245C4⋊C4—2842no—
246C4⋊C4—2841no—
247C4⋊C4—2841no—
248C4⋊C4—1422no—
249C22⋊C4—2842no—
250C22⋊C4—2842no—
251C22⋊C4—2842no—
252C22⋊C4—2842no—
253C22⋊C4—2841no—
254C22⋊C4—2841no—
255C22⋊C4—2842no—
256C42—22no—
257C42—22no—
258C42—22no—
259C42—41no—
260C42—41no—
261C42—41no—
262C42#1176585012yes—
263C42#1176585212yes—
264C23—2841no—
265C23—2841no—
266C23—2841no—
267C23—2841no—
268C23—2841no—
269C23—2841no—
270C23—2841no—
271C23C2×(C2×D71)⋊C411yescharacteristic
272D4—5682no—
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—21no—
287C2×C4—21no—
288C2×C4—2841no—
289C2×C4—2841no—
290C2×C4—2841no—
291C2×C4—2841no—
292C2×C4—2841no—
293C2×C4—2841no—
294C2×C4—2841no—
295C2×C4—2841no—
296C2×C4—2841no—
297C2×C4#1455604812yes—
298C2×C4#1455604812yes—
299C2×C4#1455605612yes—
300C2×C4#1455613412yes—
301C2×C4C2×#1176585011yescharacteristic
302C2×C4C2×#1176585211yescharacteristic
303C2×C4#1455615012yes—
304C8—44no—
305C8—5682no—
306C22—5681no—
307C22—5681no—
308C22—5681no—
309C22—5681no—
310C22—5681no—
311C22—5681no—
312C22—5681no—
313C22#1798596511yescharacteristic
314C22#1798597211yescharacteristic
315C22#1798598111yescharacteristic
316C22C2×#1455604811yescharacteristic
317C22#1798599611yescharacteristic
318C22C2×#1455605611yescharacteristic
319C22#1798601511yescharacteristic
320C4—22no—
321C4—22no—
322C4—22no—
323C4—22no—
324C4—22no—
325C4—21no—
326C4—21no—
327C4—41no—
328C4—5681no—
329C4—5681no—
330C4—5681no—
331C2—11361no—
332C2#2258670711yescharacteristic
333C2#2258673811yescharacteristic
334C2#2258680111yescharacteristic
335C2#2258683411yescharacteristic
336C2#2258691811yescharacteristic
337C2#2258694511yescharacteristic
338C2#2258699011yescharacteristic
subgroupG/H
centerC23C2×(C2×D71)⋊C4
commutatorC22×C4×C71C22×C4
FrattiniC2×C42C22×D71
FittingC4×C4⋊C8×C71C2
socleC23×C71C2×C22⋊C4
prime radicalC22×D284C2×C4
cosocleC2×C42×C71C23
hypercenterC4×C4⋊C8D71
hypocenterC71#7672
LCSG ▷ C22×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #22588483C2semidirect
3. #22586164C2semidirect
5. C4×C4⋊C8×C71C2semidirect
172. C4×C4⋊C8D71semidirect
175. C71#7672semidirect

Maximal subgroups

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

subgroupindex
#225967072
#225884832
#225861642
#225861602
C4×C4⋊C8×C712
#767271