Finite Group Databasebeta

← #35294665

Subgroups — #35294665

Order 21248.

628 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#24916096C211yesmaximal, characteristic
2C2×C4×#13050574C211yesmaximal, characteristic
3#24905363C214yesmaximal, complemented
4C2×#431×C83C211yesmaximal, characteristic
5C22×#13050574—21no—
6#19127758—21no—
7#19127758C2212yes—
8#19127754—21no—
9#19127754C412yes—
10#19127725C412yes—
11#19127665—21no—
12C4×#13050574—21no—
13C4×#13050574—21no—
14C4×#13050574—21no—
15C4×#13050574C412yes—
16C4×#13050574C412yes—
17C2×#14581703C2212yes—
18C2×C4×C83⋊C8—21no—
19C22×C42×C83C2211yescharacteristic
20#431×C83—21no—
21#431×C83—21no—
22#431×C83C412yes—
23#431×C83C2212yes—
24C2×C4⋊C8×C83—21no—
25C2×C22⋊C8×C83C412yes—
26C2×C4×C8×C83—21no—
27C2×#13050574—28no—
28C2×#13050574—22no—
29C2×#13050574—22no—
30C2×#13050574—22no—
31C22×C83⋊C8—22no—
32C4⋊(C83⋊C8)—22no—
33C4⋊(C83⋊C8)C2×C414yes—
34C22⋊(C83⋊C8)—22no—
35C22⋊(C83⋊C8)—22no—
36#14581703—22no—
37#14581703—22no—
38#14581703C2×C414yes—
39C4×C83⋊C8—22no—
40C4×C83⋊C8—22no—
41C4×C83⋊C8—22no—
42C23×C4×C83C2×C411yescharacteristic
43C23×C4×C83D411yescharacteristic
44C23×C4×C83Q811yescharacteristic
45C22×C8×C83—22no—
46C2×C42×C83C2×C411yescharacteristic
47C2×C42×C83C2×C411yescharacteristic
48C2×C42×C83C2×C411yescharacteristic
49C2×C42×C83C2×C411yescharacteristic
50C2×C42×C83C2×C411yescharacteristic
51C2×C42×C83D411yescharacteristic
52C2×C42×C83D411yescharacteristic
53C2×C42×C83D411yescharacteristic
54C2×C42×C83D411yescharacteristic
55C2×C42×C83D411yescharacteristic
56C2×C42×C83Q811yescharacteristic
57C2×C42×C83C2311yescharacteristic
58C4⋊C8×C83—22no—
59C4⋊C8×C83—22no—
60C22⋊C8×C83—22no—
61C22⋊C8×C83C2×C414yes—
62C4×C8×C83—22no—
63C4×C8×C83—22no—
64#13050574—28no—
65#13050574—28no—
66#13050574—44no—
67C2×C83⋊C8—28no—
68C2×C83⋊C8—24no—
69C2×C83⋊C8—24no—
70C24×C83C4⋊C411yescharacteristic
71C22×C4×C83—24no—
72C22×C4×C83—24no—
73C22×C4×C83—42no—
74C22×C4×C83C4211yescharacteristic
75C22×C4×C83C4211yescharacteristic
76C22×C4×C83C22⋊C411yescharacteristic
77C22×C4×C83C22⋊C411yescharacteristic
78C22×C4×C83C22⋊C411yescharacteristic
79C22×C4×C83C22⋊C411yescharacteristic
80C22×C4×C83C22⋊C411yescharacteristic
81C22×C4×C83C22⋊C411yescharacteristic
82C22×C4×C83C4⋊C411yescharacteristic
83C22×C4×C83C4⋊C411yescharacteristic
84C22×C4×C83C4⋊C411yescharacteristic
85C22×C4×C83C4⋊C411yescharacteristic
86C22×C4×C83C4⋊C411yescharacteristic
87C22×C4×C83C4⋊C411yescharacteristic
88C22×C4×C83C4⋊C411yescharacteristic
89C22×C4×C83C22×C411yescharacteristic
90C22×C4×C83C2×D411yescharacteristic
91C22×C4×C83C2×Q811yescharacteristic
92C2×C8×C83—24no—
93C2×C8×C83—44no—
94C42×C83C4211yescharacteristic
95C42×C83C4211yescharacteristic
96C42×C83C22⋊C411yescharacteristic
97C42×C83C22⋊C411yescharacteristic
98C42×C83C22⋊C411yescharacteristic
99C42×C83C22⋊C411yescharacteristic
100C42×C83C22⋊C411yescharacteristic
101C42×C83C22⋊C411yescharacteristic
102C42×C83C4⋊C411yescharacteristic
103C42×C83C4⋊C411yescharacteristic
104C42×C83C4⋊C411yescharacteristic
105C42×C83C4⋊C411yescharacteristic
106C42×C83C22×C411yescharacteristic
107C42×C83C22×C411yescharacteristic
108C42×C83C2×D411yescharacteristic
109C42×C83C2×D411yescharacteristic
110C23×C83—22no—
111C23×C83—22no—
112C23×C83—41no—
113C23×C83#9511yescharacteristic
114C23×C83#9511yescharacteristic
115C23×C83C2×C4⋊C411yescharacteristic
116C2×C4×C83—22no—
117C2×C4×C83—22no—
118C2×C4×C83—22no—
119C2×C4×C83—22no—
120C2×C4×C83—22no—
121C2×C4×C83—22no—
122C2×C4×C83—22no—
123C2×C4×C83—22no—
124C2×C4×C83—22no—
125C2×C4×C83—22no—
126C2×C4×C83—22no—
127C2×C4×C83—22no—
128C2×C4×C83—22no—
129C2×C4×C83—41no—
130C2×C4×C83—41no—
131C2×C4×C83—41no—
132C2×C4×C83#9511yescharacteristic
133C2×C4×C83#9511yescharacteristic
134C2×C4×C83#9511yescharacteristic
135C2×C4×C83#9511yescharacteristic
136C2×C4×C83#9511yescharacteristic
137C2×C4×C83#9511yescharacteristic
138C2×C4×C83#10414yes—
139C2×C4×C83#10814yes—
140C2×C4×C83C2×C4211yescharacteristic
141C2×C4×C83C2×C22⋊C411yescharacteristic
142C2×C4×C83C2×C22⋊C411yescharacteristic
143C2×C4×C83C2×C22⋊C411yescharacteristic
144C2×C4×C83C2×C4⋊C411yescharacteristic
145C2×C4×C83C2×C4⋊C411yescharacteristic
146C8×C83—44no—
147C83⋊C8—28no—
148C83⋊C8—44no—
149C22×C83—21no—
150C22×C83—21no—
151C22×C83—21no—
152C22×C83—21no—
153C22×C83—21no—
154C22×C83—21no—
155C22×C83—21no—
156C22×C83—44no—
157C22×C83#33912yes—
158C22×C83C2×#9511yescharacteristic
159C22×C83C2×#10812yes—
160C4×C83—21no—
161C4×C83—21no—
162C4×C83—21no—
163C4×C83—21no—
164C4×C83—21no—
165C4×C83—21no—
166C4×C83—21no—
167C4×C83#33912yes—
168C4×C83#34112yes—
169C4×C83#34112yes—
170C4×C83#34412yes—
171C4×C83C2×#10412yes—
172#8084—831nomaximal, Sylow
173C2×C83—22no—
174C2×C83—22no—
175C2×C83—41no—
176C2×C83C2×#33911yescharacteristic
177C2×C83C2×#34111yescharacteristic
178C2×C83C2×#34411yescharacteristic
179#2920—831no—
180C2×#431D8311yescharacteristic
181C2×C4×M16—831no—
182#1302—834no—
183C83#808411yescharacteristic, complemented, Sylow
184C22×M16—1661no—
185C22×C42C2×D8311yescharacteristic
186#432—832no—
187#432—1661no—
188#431—21no—
189#431—21no—
190#431—832no—
191#431—1661no—
192#431Dic8312yes—
193#431C2×D8312yes—
194#423—832no—
195C2×C4⋊C8—21no—
196#407—1661no—
197C2×C22⋊C8Dic8312yes—
198C4×M16—832no—
199C4×M16—832no—
200C4×M16—1661no—
201C4×M16—1661no—
202C4×M16—1661no—
203C2×#97—832no—
204C2×C4×C8—21no—
205C2×C4×C8—1661no—
206C23×C4Dic16611yescharacteristic
207C23×C4D33211yescharacteristic
208C23×C4C2×Dic8311yescharacteristic
209C2×M16—1662no—
210C2×M16—1668no—
211C2×M16—1662no—
212C2×M16—1662no—
213C22×C8—22no—
214C22×C8—1662no—
215C2×C42Dic16611yescharacteristic
216C2×C42C4×D8311yescharacteristic
217C2×C42C4×D8311yescharacteristic
218C2×C42C4×D8311yescharacteristic
219C2×C42C4×D8311yescharacteristic
220C2×C42D33211yescharacteristic
221C2×C42C2×Dic8311yescharacteristic
222C2×C42C22⋊D8311yescharacteristic
223C2×C42C22⋊D8311yescharacteristic
224C2×C42C22⋊D8311yescharacteristic
225C2×C42C22⋊D8311yescharacteristic
226C2×C42C22×D8311yescharacteristic
227C4⋊C8—22no—
228C4⋊C8—22no—
229C4⋊C8—834no—
230C4⋊C8—1662no—
231C22⋊C8—22no—
232C22⋊C8—1662no—
233C22⋊C8—1662no—
234C22⋊C8C2×Dic8314yes—
235#97—834no—
236#97—1662no—
237#97—1662no—
238C4×C8—22no—
239C4×C8—22no—
240C4×C8—1662no—
241C4×C8—1662no—
242C4×C8—1662no—
243C24C4⋊Dic8311yescharacteristic
244C22×C4—24no—
245C22×C4—24no—
246C22×C4—42no—
247C22×C4C4×Dic8311yescharacteristic
248C22×C4C4×Dic8311yescharacteristic
249C22×C4(C2×D83)⋊C411yescharacteristic
250C22×C4(C2×D83)⋊C411yescharacteristic
251C22×C4(C2×D83)⋊C411yescharacteristic
252C22×C4(C2×D83)⋊C411yescharacteristic
253C22×C4C22⋊Dic8311yescharacteristic
254C22×C4C22⋊Dic8311yescharacteristic
255C22×C4Dic83⋊C411yescharacteristic
256C22×C4Dic83⋊C411yescharacteristic
257C22×C4Dic83⋊C411yescharacteristic
258C22×C4Dic83⋊C411yescharacteristic
259C22×C4C4⋊Dic8311yescharacteristic
260C22×C4C4⋊Dic8311yescharacteristic
261C22×C4C4⋊Dic8311yescharacteristic
262C22×C4C22×Dic8311yescharacteristic
263C22×C4C2×D33211yescharacteristic
264C22×C4C2×Dic16611yescharacteristic
265M16—3324no—
266M16—1668no—
267M16—1668no—
268C2×C8—24no—
269C2×C8—44no—
270C2×C8—1664no—
271C2×C8—1668no—
272C2×C8—1664no—
273C42C4×Dic8311yescharacteristic
274C42C4×Dic8311yescharacteristic
275C42(C2×D83)⋊C411yescharacteristic
276C42(C2×D83)⋊C411yescharacteristic
277C42(C2×D83)⋊C411yescharacteristic
278C42(C2×D83)⋊C411yescharacteristic
279C42C22⋊Dic8311yescharacteristic
280C42C22⋊Dic8311yescharacteristic
281C42Dic83⋊C411yescharacteristic
282C42Dic83⋊C411yescharacteristic
283C42Dic83⋊C411yescharacteristic
284C42Dic83⋊C411yescharacteristic
285C42C2×C4×D8311yescharacteristic
286C42C2×C4×D8311yescharacteristic
287C42C2×C22⋊D8311yescharacteristic
288C42C2×C22⋊D8311yescharacteristic
289C23—22no—
290C23—22no—
291C23—41no—
292C23C83⋊#9511yescharacteristic
293C23C83⋊#9511yescharacteristic
294C23C2×C4⋊Dic8311yescharacteristic
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—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4C83⋊#9511yescharacteristic
312C2×C4C83⋊#9511yescharacteristic
313C2×C4C83⋊#9511yescharacteristic
314C2×C4C83⋊#9511yescharacteristic
315C2×C4C83⋊#9511yescharacteristic
316C2×C4C83⋊#9511yescharacteristic
317C2×C4#1458171814yes—
318C2×C4#1458172814yes—
319C2×C4C2×C4×Dic8311yescharacteristic
320C2×C4C2×(C2×D83)⋊C411yescharacteristic
321C2×C4C2×(C2×D83)⋊C411yescharacteristic
322C2×C4C2×C22⋊Dic8311yescharacteristic
323C2×C4C2×Dic83⋊C411yescharacteristic
324C2×C4C2×Dic83⋊C411yescharacteristic
325C8—44no—
326C8—3324no—
327C8—1668no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—44no—
336C22#1912746212yes—
337C22C2×C83⋊#9511yescharacteristic
338C22C2×#1458172812yes—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4#1912746212yes—
347C4#1912746612yes—
348C4#1912746612yes—
349C4#1912747112yes—
350C4C2×#1458171812yes—
351C2—22no—
352C2—22no—
353C2—41no—
354C2C2×#1912746211yescharacteristic
355C2C2×#1912746611yescharacteristic
356C2C2×#1912747111yescharacteristic
subgroupG/H
centerC42(C2×D83)⋊C4
commutatorC2×C4×C83C2×C42
FrattiniC2×C42C22×D83
FittingC2×#431×C83C2
socleC22×C83C2×#95
prime radicalC24×C83C4⋊C4
cosocleC2×C42×C83C23
hypercenterC2×#431D83
hypocenterC83#8084
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C42 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
3. #24905363C2semidirect
183. C83#8084semidirect

Maximal subgroups

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

subgroupindex
#249160962
C2×C4×#130505742
#249053632
C2×#431×C832
#808483