Finite Group Databasebeta

← C83×#9654 #35237478

Subgroups — C83×#9654 #35237478

Order 21248.

640 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C83C211yesmaximal, characteristic
2C83×#1797C211yesmaximal, characteristic
3C83×#1749C211yesmaximal, characteristic
4C2×#324×C83C214yesmaximal
5C22×C4⋊C4×C83C411yescharacteristic
6C22×C4⋊C4×C83C411yescharacteristic
7C22×C4⋊C4×C83C2212yes—
8C22×C42×C83C2211yescharacteristic
9C2×C4⋊C8×C83—21no—
10C2×C22⋊C8×C83C2212yes—
11C2×C22⋊C8×C83C2212yes—
12C2×#97×C83—21no—
13#389×C83—21no—
14#389×C83—21no—
15#389×C83—21no—
16#389×C83—21no—
17C2×#95×C83C412yes—
18#336×C83—21no—
19#336×C83—21no—
20#324×C83—28no—
21C23×C4×C83C2×C411yescharacteristic
22C23×C4×C83C2×C412yes—
23C23×C4×C83C2×C411yescharacteristic
24C23×C4×C83C2×C412yes—
25C23×C4×C83C2311yescharacteristic
26C22×C8×C83—22no—
27C22×C8×C83—22no—
28C2×C4⋊C4×C83—21no—
29C2×C4⋊C4×C83—21no—
30C2×C4⋊C4×C83—24no—
31C2×C4⋊C4×C83—21no—
32C2×C4⋊C4×C83—21no—
33C2×C4⋊C4×C83—24no—
34C2×C4⋊C4×C83—22no—
35C2×C4⋊C4×C83—22no—
36C2×C4⋊C4×C83—24no—
37C2×C4⋊C4×C83—42no—
38C2×C42×C83—42no—
39C2×C42×C83D411yescharacteristic
40C2×C42×C83D411yescharacteristic
41C2×C42×C83D411yescharacteristic
42C2×C42×C83D411yescharacteristic
43C4⋊C8×C83—42no—
44C22⋊C8×C83—22no—
45C22⋊C8×C83—24no—
46C22⋊C8×C83D414yes—
47#97×C83—42no—
48#95×C83—22no—
49#95×C83—22no—
50C24×C83C22×C411yescharacteristic
51C22×C4×C83—22no—
52C22×C4×C83—22no—
53C22×C4×C83—22no—
54C22×C4×C83—22no—
55C22×C4×C83—24no—
56C22×C4×C83—22no—
57C22×C4×C83—22no—
58C22×C4×C83—24no—
59C22×C4×C83—22no—
60C22×C4×C83—22no—
61C22×C4×C83—24no—
62C22×C4×C83—41no—
63C22×C4×C83—41no—
64C22×C4×C83—41no—
65C22×C4×C83—42no—
66C22×C4×C83—42no—
67C22×C4×C83C22⋊C411yescharacteristic
68C22×C4×C83C22⋊C411yescharacteristic
69C22×C4×C83C22⋊C411yescharacteristic
70C22×C4×C83C22⋊C411yescharacteristic
71C22×C4×C83M1614yes—
72C22×C4×C83C2×D411yescharacteristic
73C22×C4×C83C2×D411yescharacteristic
74C22×C4×C83C2×D412yes—
75C22×C4×C83#4112yes—
76C2×C8×C83—24no—
77C2×C8×C83—42no—
78C2×C8×C83—42no—
79C2×C8×C83—42no—
80C2×C8×C83—42no—
81C2×C8×C83—42no—
82C4⋊C4×C83—24no—
83C4⋊C4×C83—24no—
84C4⋊C4×C83—42no—
85C4⋊C4×C83—42no—
86C4⋊C4×C83—44no—
87C4⋊C4×C83—42no—
88C4⋊C4×C83—42no—
89C42×C83—22no—
90C42×C83—22no—
91C42×C83—41no—
92C42×C83—41no—
93C23×C83—21no—
94C23×C83—21no—
95C23×C83—21no—
96C23×C83—21no—
97C23×C83C2×C22⋊C411yescharacteristic
98C23×C83C4×D412yes—
99C23×C83C2×M1612yes—
100C23×C83#13112yes—
101C2×C4×C83—28no—
102C2×C4×C83—21no—
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—21no—
107C2×C4×C83—21no—
108C2×C4×C83—21no—
109C2×C4×C83—21no—
110C2×C4×C83—21no—
111C2×C4×C83—21no—
112C2×C4×C83—24no—
113C2×C4×C83—21no—
114C2×C4×C83—21no—
115C2×C4×C83—21no—
116C2×C4×C83—28no—
117C2×C4×C83—42no—
118C2×C4×C83—42no—
119C2×C4×C83—44no—
120C2×C4×C83—42no—
121C2×C4×C83—42no—
122C2×C4×C83—44no—
123C2×C4×C83—42no—
124C2×C4×C83—42no—
125C2×C4×C83—42no—
126C2×C4×C83—84no—
127C2×C4×C83#9912yes—
128C2×C4×C83#10112yes—
129C2×C4×C83#10112yes—
130C2×C4×C83#12112yes—
131C2×C4×C83#12411yescharacteristic
132C2×C4×C83#12711yescharacteristic
133C8×C83—44no—
134C8×C83—82no—
135C22×C83—22no—
136C22×C83—22no—
137C22×C83—22no—
138C22×C83—22no—
139C22×C83—22no—
140C22×C83—22no—
141C22×C83#39011yescharacteristic
142C22×C83#40711yescharacteristic
143C22×C83#40811yescharacteristic
144C22×C83C2×#9911yescharacteristic
145C22×C83#41011yescharacteristic
146C22×C83C2×#10111yescharacteristic
147C22×C83C2×#10111yescharacteristic
148C22×C83#43514yes—
149C4×C83—22no—
150C4×C83—21no—
151C4×C83—21no—
152C4×C83—22no—
153C4×C83—22no—
154C4×C83—22no—
155C4×C83—44no—
156C4×C83—41no—
157C4×C83—82no—
158#9654C8311yesmaximal, characteristic, direct product factor, Sylow
159C2×C83—24no—
160C2×C83#146311yescharacteristic
161C2×C83#146711yescharacteristic
162C2×C83#147011yescharacteristic
163C2×C83#147211yescharacteristic
164C2×C83#195511yescharacteristic
165C2×C83#196411yescharacteristic
166C2×C83#196611yescharacteristic
167C2×#389C2×C8311yescharacteristic
168#1797C2×C8311yescharacteristic
169#1749C2×C8311yescharacteristic
170C2×#324C2×C8314yes—
171C83#965411yescharacteristic, direct product factor, Sylow
172C22×C4⋊C4C4×C8311yescharacteristic
173C22×C4⋊C4C4×C8311yescharacteristic
174C22×C4⋊C4C22×C8312yes—
175C22×C42C22×C8311yescharacteristic
176C2×C4⋊C8—21no—
177C2×C22⋊C8C22×C8312yes—
178C2×C22⋊C8C22×C8312yes—
179C2×#97—21no—
180#389—21no—
181#389—21no—
182#389—21no—
183#389—21no—
184C2×#95C4×C8312yes—
185#336—21no—
186#336—21no—
187#324—28no—
188C23×C4C2×C4×C8311yescharacteristic
189C23×C4C2×C4×C8312yes—
190C23×C4C2×C4×C8311yescharacteristic
191C23×C4C2×C4×C8312yes—
192C23×C4C23×C8311yescharacteristic
193C22×C8—22no—
194C22×C8—22no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—24no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—24no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—24no—
204C2×C4⋊C4—42no—
205C2×C42—42no—
206C2×C42D4×C8311yescharacteristic
207C2×C42D4×C8311yescharacteristic
208C2×C42D4×C8311yescharacteristic
209C2×C42D4×C8311yescharacteristic
210C4⋊C8—42no—
211C22⋊C8—22no—
212C22⋊C8—24no—
213C22⋊C8D4×C8314yes—
214#97—42no—
215#95—22no—
216#95—22no—
217C24C22×C4×C8311yescharacteristic
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—24no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—24no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—24no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4C22⋊C4×C8311yescharacteristic
235C22×C4C22⋊C4×C8311yescharacteristic
236C22×C4C22⋊C4×C8311yescharacteristic
237C22×C4C22⋊C4×C8311yescharacteristic
238C22×C4M16×C8314yes—
239C22×C4C2×D4×C8311yescharacteristic
240C22×C4C2×D4×C8311yescharacteristic
241C22×C4C2×D4×C8312yes—
242C22×C4#41×C8312yes—
243C2×C8—24no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C4⋊C4—24no—
250C4⋊C4—24no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—44no—
254C4⋊C4—42no—
255C4⋊C4—42no—
256C42—22no—
257C42—22no—
258C42—41no—
259C42—41no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23C2×C22⋊C4×C8311yescharacteristic
265C23C4×D4×C8312yes—
266C23C2×M16×C8312yes—
267C23#131×C8312yes—
268C2×C4—28no—
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—24no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—28no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—44no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—44no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—84no—
294C2×C4#99×C8312yes—
295C2×C4#101×C8312yes—
296C2×C4#101×C8312yes—
297C2×C4#121×C8312yes—
298C2×C4#124×C8311yescharacteristic
299C2×C4#127×C8311yescharacteristic
300C8—44no—
301C8—82no—
302C22—22no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22#390×C8311yescharacteristic
309C22#407×C8311yescharacteristic
310C22#408×C8311yescharacteristic
311C22C2×#99×C8311yescharacteristic
312C22#410×C8311yescharacteristic
313C22C2×#101×C8311yescharacteristic
314C22C2×#101×C8311yescharacteristic
315C22#435×C8314yes—
316C4—22no—
317C4—21no—
318C4—21no—
319C4—22no—
320C4—22no—
321C4—22no—
322C4—44no—
323C4—41no—
324C4—82no—
325C2—24no—
326C2C83×#146311yescharacteristic
327C2C83×#146711yescharacteristic
328C2C83×#147011yescharacteristic
329C2C83×#147211yescharacteristic
330C2C83×#195511yescharacteristic
331C2C83×#196411yescharacteristic
332C2C83×#196611yescharacteristic
subgroupG/H
center, socleC23×C83C2×C22⋊C4
commutatorC24C22×C4×C83
Frattini, cosocleC23×C4C23×C83
prime radicalC24×C83C22×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C22×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
158. #9654C83direct (N × H)
171. C83#9654direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#389×C832
C83×#17972
C83×#17492
C2×#324×C832
#965483