Finite Group Databasebeta

← #31887633

Subgroups — #31887633

Order 18176.

606 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22596973C211yesmaximal, characteristic
2C2×C4×#11765849C211yesmaximal, characteristic
3#22586231C214yesmaximal, complemented
4C71×#2920C211yesmaximal, characteristic
5C22×#11765849—21no—
6#17986056—21no—
7#17986056—21no—
8#17986052—21no—
9#17986052—21no—
10#17986023C2212yes—
11#17985963C412yes—
12C4×#11765849—21no—
13C4×#11765849—21no—
14C4×#11765849C412yes—
15C4×#11765849C412yes—
16C4×#11765849C2212yes—
17C2×#14556039C412yes—
18C2×C4×C71⋊C8—21no—
19C22×C42×C71C2211yescharacteristic
20#432×C71—21no—
21#432×C71C412yes—
22#431×C71—21no—
23#431×C71C2212yes—
24#423×C71C412yes—
25#407×C71—21no—
26C4×M16×C71—21no—
27C2×#11765849—28no—
28C2×#11765849—22no—
29C2×#11765849—22no—
30C2×#11765849C2×C414yes—
31C22×C71⋊C8—22no—
32C4⋊(C71⋊C8)—22no—
33C4⋊(C71⋊C8)—22no—
34C22⋊(C71⋊C8)—22no—
35C22⋊(C71⋊C8)—22no—
36#14556039—22no—
37#14556039—22no—
38#14556039C2×C414yes—
39C4×C71⋊C8—22no—
40C4×C71⋊C8—22no—
41C4×C71⋊C8—22no—
42C23×C4×C71C2×C411yescharacteristic
43C23×C4×C71D411yescharacteristic
44C23×C4×C71Q811yescharacteristic
45C2×M16×C71—22no—
46C2×C42×C71C2×C411yescharacteristic
47C2×C42×C71C2×C411yescharacteristic
48C2×C42×C71C2×C411yescharacteristic
49C2×C42×C71C2×C411yescharacteristic
50C2×C42×C71C2×C411yescharacteristic
51C2×C42×C71D411yescharacteristic
52C2×C42×C71D411yescharacteristic
53C2×C42×C71D411yescharacteristic
54C2×C42×C71D411yescharacteristic
55C2×C42×C71D411yescharacteristic
56C2×C42×C71Q811yescharacteristic
57C2×C42×C71C2311yescharacteristic
58C4⋊C8×C71—22no—
59C4⋊C8×C71C2×C414yes—
60C22⋊C8×C71—22no—
61C22⋊C8×C71—22no—
62#97×C71—22no—
63C4×C8×C71—22no—
64#11765849—28no—
65#11765849—28no—
66#11765849—44no—
67C2×C71⋊C8—28no—
68C2×C71⋊C8—24no—
69C2×C71⋊C8—24no—
70C24×C71C4⋊C411yescharacteristic
71C22×C4×C71—24no—
72C22×C4×C71—42no—
73C22×C4×C71—42no—
74C22×C4×C71C4211yescharacteristic
75C22×C4×C71C4211yescharacteristic
76C22×C4×C71C22⋊C411yescharacteristic
77C22×C4×C71C22⋊C411yescharacteristic
78C22×C4×C71C22⋊C411yescharacteristic
79C22×C4×C71C22⋊C411yescharacteristic
80C22×C4×C71C22⋊C411yescharacteristic
81C22×C4×C71C22⋊C411yescharacteristic
82C22×C4×C71C4⋊C411yescharacteristic
83C22×C4×C71C4⋊C411yescharacteristic
84C22×C4×C71C4⋊C411yescharacteristic
85C22×C4×C71C4⋊C411yescharacteristic
86C22×C4×C71C4⋊C411yescharacteristic
87C22×C4×C71C4⋊C411yescharacteristic
88C22×C4×C71C4⋊C411yescharacteristic
89C22×C4×C71C22×C411yescharacteristic
90C22×C4×C71C2×D411yescharacteristic
91C22×C4×C71C2×Q811yescharacteristic
92M16×C71—44no—
93C2×C8×C71—24no—
94C42×C71C4211yescharacteristic
95C42×C71C4211yescharacteristic
96C42×C71C22⋊C411yescharacteristic
97C42×C71C22⋊C411yescharacteristic
98C42×C71C22⋊C411yescharacteristic
99C42×C71C22⋊C411yescharacteristic
100C42×C71C22⋊C411yescharacteristic
101C42×C71C22⋊C411yescharacteristic
102C42×C71C4⋊C411yescharacteristic
103C42×C71C4⋊C411yescharacteristic
104C42×C71C4⋊C411yescharacteristic
105C42×C71C4⋊C411yescharacteristic
106C42×C71C22×C411yescharacteristic
107C42×C71C22×C411yescharacteristic
108C42×C71C2×D411yescharacteristic
109C42×C71C2×D411yescharacteristic
110C23×C71—22no—
111C23×C71—41no—
112C23×C71—41no—
113C23×C71#9511yescharacteristic
114C23×C71#9511yescharacteristic
115C23×C71C2×C4⋊C411yescharacteristic
116C2×C4×C71—22no—
117C2×C4×C71—22no—
118C2×C4×C71—22no—
119C2×C4×C71—22no—
120C2×C4×C71—22no—
121C2×C4×C71—22no—
122C2×C4×C71—22no—
123C2×C4×C71—22no—
124C2×C4×C71—22no—
125C2×C4×C71—22no—
126C2×C4×C71—22no—
127C2×C4×C71—41no—
128C2×C4×C71—41no—
129C2×C4×C71—41no—
130C2×C4×C71—41no—
131C2×C4×C71—41no—
132C2×C4×C71—41no—
133C2×C4×C71#9511yescharacteristic
134C2×C4×C71#9511yescharacteristic
135C2×C4×C71#9511yescharacteristic
136C2×C4×C71#9511yescharacteristic
137C2×C4×C71#9511yescharacteristic
138C2×C4×C71#9511yescharacteristic
139C2×C4×C71#10414yes—
140C2×C4×C71C2×C4211yescharacteristic
141C2×C4×C71C2×C22⋊C411yescharacteristic
142C2×C4×C71C2×C22⋊C411yescharacteristic
143C2×C4×C71C2×C22⋊C411yescharacteristic
144C2×C4×C71C2×C4⋊C411yescharacteristic
145C2×C4×C71C2×C4⋊C411yescharacteristic
146C8×C71—44no—
147C71⋊C8—28no—
148C71⋊C8—44no—
149C22×C71—21no—
150C22×C71—21no—
151C22×C71—21no—
152C22×C71—21no—
153C22×C71—21no—
154C22×C71—21no—
155C22×C71—21no—
156C22×C71—21no—
157C22×C71—44no—
158C22×C71#33912yes—
159C22×C71C2×#9511yescharacteristic
160C4×C71—21no—
161C4×C71—21no—
162C4×C71—21no—
163C4×C71—21no—
164C4×C71—21no—
165C4×C71—21no—
166C4×C71—21no—
167C4×C71—21no—
168C4×C71#33912yes—
169C4×C71#41312yes—
170C4×C71C2×#10412yes—
171C4×C71#43012yes—
172#8064—711nomaximal, Sylow
173C2×C71—22no—
174C2×C71—41no—
175C2×C71—41no—
176C2×C71C2×#33911yescharacteristic
177C2×C71#173811yescharacteristic
178C2×C71#174211yescharacteristic
179#2920—711no—
180#2920D7111yescharacteristic
181C2×C4×M16—711no—
182#1299—714no—
183C71#806411yescharacteristic, complemented, Sylow
184C22×M16—1421no—
185C22×C42C2×D7111yescharacteristic
186#432—21no—
187#432—1421no—
188#432—1421no—
189#432Dic7112yes—
190#431—21no—
191#431—1421no—
192#431—1421no—
193#431C2×D7112yes—
194#423—712no—
195#423Dic7112yes—
196#407—21no—
197#407—712no—
198C4×M16—21no—
199C4×M16—712no—
200C4×M16—712no—
201C4×M16—712no—
202C4×M16—1421no—
203C4×M16—1421no—
204C2×#97—712no—
205C2×C4×C8—1421no—
206C23×C4Dic14211yescharacteristic
207C23×C4C4×D7111yescharacteristic
208C23×C4C22⋊D7111yescharacteristic
209C2×M16—22no—
210C2×M16—714no—
211C2×M16—1428no—
212C2×M16—1422no—
213C2×M16—1422no—
214C22×C8—1422no—
215C2×C42Dic14211yescharacteristic
216C2×C42C4×D7111yescharacteristic
217C2×C42C4×D7111yescharacteristic
218C2×C42C4×D7111yescharacteristic
219C2×C42D28411yescharacteristic
220C2×C42D28411yescharacteristic
221C2×C42C2×Dic7111yescharacteristic
222C2×C42C2×Dic7111yescharacteristic
223C2×C42C22⋊D7111yescharacteristic
224C2×C42C22⋊D7111yescharacteristic
225C2×C42C22⋊D7111yescharacteristic
226C2×C42C22×D7111yescharacteristic
227C4⋊C8—22no—
228C4⋊C8—1422no—
229C4⋊C8—1422no—
230C4⋊C8C2×Dic7114yes—
231C22⋊C8—22no—
232C22⋊C8—22no—
233C22⋊C8—1422no—
234C22⋊C8—1422no—
235#97—22no—
236#97—714no—
237#97—1422no—
238#97—1422no—
239C4×C8—22no—
240C4×C8—1422no—
241C4×C8—1422no—
242C4×C8—1422no—
243C24Dic71⋊C411yescharacteristic
244C22×C4—24no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4C4×Dic7111yescharacteristic
248C22×C4C4×Dic7111yescharacteristic
249C22×C4(C2×D71)⋊C411yescharacteristic
250C22×C4(C2×D71)⋊C411yescharacteristic
251C22×C4(C2×D71)⋊C411yescharacteristic
252C22×C4(C2×D71)⋊C411yescharacteristic
253C22×C4C22⋊Dic7111yescharacteristic
254C22×C4C22⋊Dic7111yescharacteristic
255C22×C4Dic71⋊C411yescharacteristic
256C22×C4Dic71⋊C411yescharacteristic
257C22×C4Dic71⋊C411yescharacteristic
258C22×C4Dic71⋊C411yescharacteristic
259C22×C4Dic71⋊C411yescharacteristic
260C22×C4C4⋊Dic7111yescharacteristic
261C22×C4C4⋊Dic7111yescharacteristic
262C22×C4C2×C4×D7111yescharacteristic
263C22×C4C2×C22⋊D7111yescharacteristic
264C22×C4C2×Dic14211yescharacteristic
265M16—44no—
266M16—2844no—
267M16—1428no—
268M16—1428no—
269C2×C8—24no—
270C2×C8—1424no—
271C2×C8—1428no—
272C2×C8—1424no—
273C42C4×Dic7111yescharacteristic
274C42C4×Dic7111yescharacteristic
275C42(C2×D71)⋊C411yescharacteristic
276C42(C2×D71)⋊C411yescharacteristic
277C42(C2×D71)⋊C411yescharacteristic
278C42(C2×D71)⋊C411yescharacteristic
279C42C22⋊Dic7111yescharacteristic
280C42C22⋊Dic7111yescharacteristic
281C42Dic71⋊C411yescharacteristic
282C42Dic71⋊C411yescharacteristic
283C42C4⋊Dic7111yescharacteristic
284C42C4⋊Dic7111yescharacteristic
285C42C2×C4×D7111yescharacteristic
286C42C22×Dic7111yescharacteristic
287C42C2×C22⋊D7111yescharacteristic
288C42C2×D28411yescharacteristic
289C23—22no—
290C23—41no—
291C23—41no—
292C23C71⋊#9511yescharacteristic
293C23C71⋊#9511yescharacteristic
294C23C2×Dic71⋊C411yescharacteristic
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4C71⋊#9511yescharacteristic
313C2×C4C71⋊#9511yescharacteristic
314C2×C4C71⋊#9511yescharacteristic
315C2×C4C71⋊#9511yescharacteristic
316C2×C4C71⋊#9511yescharacteristic
317C2×C4C71⋊#9511yescharacteristic
318C2×C4#1455605514yes—
319C2×C4C2×C4×Dic7111yescharacteristic
320C2×C4C2×(C2×D71)⋊C411yescharacteristic
321C2×C4C2×(C2×D71)⋊C411yescharacteristic
322C2×C4C2×C22⋊Dic7111yescharacteristic
323C2×C4C2×Dic71⋊C411yescharacteristic
324C2×C4C2×C4⋊Dic7111yescharacteristic
325C8—44no—
326C8—2844no—
327C8—1428no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—44no—
337C22#1798575812yes—
338C22C2×C71⋊#9511yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4#1798575812yes—
348C4#1798598112yes—
349C4C2×#1455605512yes—
350C4#1798604812yes—
351C2—22no—
352C2—41no—
353C2—41no—
354C2C2×#1798575811yescharacteristic
355C2#2258806711yescharacteristic
356C2#2258807811yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D71)⋊C4
commutatorC2×C4×C71C2×C42
FrattiniC2×C42C22×D71
FittingC71×#2920C2
socleC22×C71C2×#95
prime radicalC24×C71C4⋊C4
cosocleC2×C42×C71C23
hypercenter#2920D71
hypocenterC71#8064
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
3. #22586231C2semidirect
183. C71#8064semidirect

Maximal subgroups

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

subgroupindex
#225969732
C2×C4×#117658492
#225862312
C71×#29202
#806471