Finite Group Databasebeta

← C83×#9330 #35237154

Subgroups — C83×#9330 #35237154

Order 21248.

482 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3112C211yesmaximal, characteristic
2C83×#2320C211yesmaximal, characteristic, complemented
3C83×#1980C211yesmaximal, characteristic
4C83×#1505C211yesmaximal, characteristic
5C83×#1491C211yesmaximal, characteristic, complemented
6C83×#1300C211yesmaximal, characteristic, complemented
7C83×#1285C211yesmaximal, characteristic, complemented
8#532×C83C2211yescharacteristic
9C2×C4×Q8×C83C2211yescharacteristic
10#480×C83—21no—
11#477×C83C412yescomplemented
12#460×C83C412yescomplemented
13#448×C83—21no—
14#440×C83—22no—
15#432×C83C2211yescharacteristic
16#432×C83C2211yescharacteristic
17C2×#104×C83—22no—
18C4×M16×C83C2211yescharacteristic
19#391×C83—21no—
20#389×C83—21no—
21#387×C83—22no—
22#383×C83—21no—
23#382×C83—21no—
24C4×C4⋊C4×C83C2211yescharacteristic
25#376×C83C2211yescharacteristic
26#327×C83—21no—
27#327×C83—21no—
28Q8⋊C8×C83—22no—
29C2×#41×C83—21no—
30C22×Q8×C83D411yescharacteristic
31C2×SD16×C83—22no—
32C2×M16×C83—21no—
33C4⋊Q8×C83C2×C411yescharacteristic
34#127×C83C2×C411yescharacteristic
35#124×C83—21no—
36#121×C83—21no—
37#121×C83—21no—
38C4×Q8×C83—21no—
39C4×Q8×C83—21no—
40C4×Q8×C83C2×C412yes—
41C4×Q8×C83D412yes—
42C4×D4×C83—21no—
43C4×D4×C83—21no—
44C2×C4⋊C4×C83—21no—
45C2×C4⋊C4×C83—21no—
46C2×C4⋊C4×C83—22no—
47C2×C4⋊C4×C83D411yescharacteristic
48C2×C42×C83—21no—
49C2×C42×C83—21no—
50C2×C42×C83D412yes—
51C2×C42×C83C2311yescharacteristic
52#107×C83—22no—
53C4⋊C8×C83—21no—
54C4⋊C8×C83C2×C412yes—
55#104×C83—44no—
56#103×C83—22no—
57#102×C83—22no—
58C22⋊C8×C83—21no—
59C22⋊C8×C83—21no—
60#97×C83—21no—
61#97×C83—21no—
62#97×C83—21no—
63C4×C8×C83—21no—
64#95×C83—22no—
65#95×C83—22no—
66#95×C83—22no—
67#95×C83—21no—
68#95×C83—21no—
69#95×C83D411yescharacteristic
70#95×C83D411yescharacteristic
71#41×C83—42no—
72#41×C83—42no—
73C2×Q8×C83—21no—
74C2×Q8×C83—21no—
75C2×Q8×C83—42no—
76C2×Q8×C83C22⋊C412yes—
77C2×D4×C83—21no—
78C2×D4×C83—21no—
79C2×D4×C83—21no—
80C2×D4×C83—41no—
81C22×C4×C83—21no—
82C22×C4×C83—21no—
83C22×C4×C83—21no—
84C22×C4×C83—22no—
85C22×C4×C83—21no—
86C22×C4×C83—41no—
87C22×C4×C83C2×D411yescharacteristic
88C22×C4×C83C2×D411yescharacteristic
89C22×C4×C83C2×D411yescharacteristic
90SD16×C83—44no—
91M16×C83—22no—
92M16×C83—41no—
93C2×C8×C83—22no—
94C2×C8×C83—41no—
95C2×C8×C83—41no—
96C4⋊C4×C83—22no—
97C4⋊C4×C83—22no—
98C4⋊C4×C83—21no—
99C4⋊C4×C83—21no—
100C4⋊C4×C83—21no—
101C4⋊C4×C83—42no—
102C4⋊C4×C83—82no—
103C4⋊C4×C83C22⋊C412yes—
104C22⋊C4×C83—41no—
105C22⋊C4×C83—41no—
106C42×C83—22no—
107C42×C83—22no—
108C42×C83—42no—
109C42×C83—42no—
110C42×C83C22×C411yescharacteristic
111C42×C83C2×D411yescharacteristic
112C42×C83#4111yescharacteristic
113C42×C83#4111yescharacteristic
114C23×C83—41no—
115C23×C83#12011yescharacteristic
116Q8×C83—22no—
117Q8×C83—22no—
118Q8×C83—42no—
119Q8×C83—42no—
120D4×C83—42no—
121D4×C83—42no—
122D4×C83—81no—
123D4×C83—81no—
124D4×C83—81no—
125C2×C4×C83—21no—
126C2×C4×C83—21no—
127C2×C4×C83—22no—
128C2×C4×C83—22no—
129C2×C4×C83—22no—
130C2×C4×C83—41no—
131C2×C4×C83—42no—
132C2×C4×C83—41no—
133C2×C4×C83—41no—
134C2×C4×C83—41no—
135C2×C4×C83—41no—
136C2×C4×C83—42no—
137C2×C4×C83—41no—
138C2×C4×C83—42no—
139C2×C4×C83—41no—
140C2×C4×C83—41no—
141C2×C4×C83—42no—
142C2×C4×C83—41no—
143C2×C4×C83—41no—
144C2×C4×C83—82no—
145C2×C4×C83C2×C22⋊C411yescharacteristic
146C2×C4×C83C4×D411yescharacteristic
147C2×C4×C83C4×D411yescharacteristic
148C2×C4×C83#12111yescharacteristic
149C2×C4×C83#12111yescharacteristic
150C2×C4×C83#12311yescharacteristic
151C8×C83—42no—
152C8×C83—42no—
153C8×C83—81no—
154C22×C83—21no—
155C22×C83—21no—
156C22×C83—81no—
157C22×C83—81no—
158C22×C83—81no—
159C22×C83#38611yescharacteristic
160C22×C83#45311yescharacteristic
161C22×C83#45411yescharacteristic
162C4×C83—21no—
163C4×C83—21no—
164C4×C83—21no—
165C4×C83—21no—
166C4×C83—21no—
167C4×C83—42no—
168C4×C83—42no—
169C4×C83—81no—
170C4×C83—82no—
171C4×C83—81no—
172C4×C83—81no—
173C4×C83#42112yes—
174#9330C8311yesmaximal, characteristic, direct product factor, Sylow
175C2×C83—21no—
176C2×C83—21no—
177C2×C83—161no—
178C2×C83#188311yescharacteristic
179C2×C83#189711yescharacteristic
180C2×C83#190511yescharacteristic
181#3112C2×C8311yescharacteristic
182#2320C2×C8311yescharacteristic, complemented
183#1980C2×C8311yescharacteristic
184#1505C2×C8311yescharacteristic
185#1491C2×C8311yescharacteristic, complemented
186#1300C2×C8311yescharacteristic, complemented
187#1285C2×C8311yescharacteristic, complemented
188C83#933011yescharacteristic, direct product factor, Sylow
189#532C22×C8311yescharacteristic
190C2×C4×Q8C22×C8311yescharacteristic
191#480—21no—
192#477C4×C8312yescomplemented
193#460C4×C8312yescomplemented
194#448—21no—
195#440—22no—
196#432C22×C8311yescharacteristic
197#432C22×C8311yescharacteristic
198C2×#104—22no—
199C4×M16C22×C8311yescharacteristic
200#391—21no—
201#389—21no—
202#387—22no—
203#383—21no—
204#382—21no—
205C4×C4⋊C4C22×C8311yescharacteristic
206#376C22×C8311yescharacteristic
207#327—21no—
208#327—21no—
209Q8⋊C8—22no—
210C2×#41—21no—
211C22×Q8D4×C8311yescharacteristic
212C2×SD16—22no—
213C2×M16—21no—
214C4⋊Q8C2×C4×C8311yescharacteristic
215#127C2×C4×C8311yescharacteristic
216#124—21no—
217#121—21no—
218#121—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8C2×C4×C8312yes—
222C4×Q8D4×C8312yes—
223C4×D4—21no—
224C4×D4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4D4×C8311yescharacteristic
229C2×C42—21no—
230C2×C42—21no—
231C2×C42D4×C8312yes—
232C2×C42C23×C8311yescharacteristic
233#107—22no—
234C4⋊C8—21no—
235C4⋊C8C2×C4×C8312yes—
236#104—44no—
237#103—22no—
238#102—22no—
239C22⋊C8—21no—
240C22⋊C8—21no—
241#97—21no—
242#97—21no—
243#97—21no—
244C4×C8—21no—
245#95—22no—
246#95—22no—
247#95—22no—
248#95—21no—
249#95—21no—
250#95D4×C8311yescharacteristic
251#95D4×C8311yescharacteristic
252#41—42no—
253#41—42no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—42no—
257C2×Q8C22⋊C4×C8312yes—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—41no—
268C22×C4C2×D4×C8311yescharacteristic
269C22×C4C2×D4×C8311yescharacteristic
270C22×C4C2×D4×C8311yescharacteristic
271SD16—44no—
272M16—22no—
273M16—41no—
274C2×C8—22no—
275C2×C8—41no—
276C2×C8—41no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—42no—
283C4⋊C4—82no—
284C4⋊C4C22⋊C4×C8312yes—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C42—22no—
288C42—22no—
289C42—42no—
290C42—42no—
291C42C22×C4×C8311yescharacteristic
292C42C2×D4×C8311yescharacteristic
293C42#41×C8311yescharacteristic
294C42#41×C8311yescharacteristic
295C23—41no—
296C23#120×C8311yescharacteristic
297Q8—22no—
298Q8—22no—
299Q8—42no—
300Q8—42no—
301D4—42no—
302D4—42no—
303D4—81no—
304D4—81no—
305D4—81no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—82no—
326C2×C4C2×C22⋊C4×C8311yescharacteristic
327C2×C4C4×D4×C8311yescharacteristic
328C2×C4C4×D4×C8311yescharacteristic
329C2×C4#121×C8311yescharacteristic
330C2×C4#121×C8311yescharacteristic
331C2×C4#123×C8311yescharacteristic
332C8—42no—
333C8—42no—
334C8—81no—
335C22—21no—
336C22—21no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22#386×C8311yescharacteristic
341C22#453×C8311yescharacteristic
342C22#454×C8311yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—42no—
350C4—81no—
351C4—82no—
352C4—81no—
353C4—81no—
354C4#421×C8312yes—
355C2—21no—
356C2—21no—
357C2—161no—
358C2C83×#188311yescharacteristic
359C2C83×#189711yescharacteristic
360C2C83×#190511yescharacteristic
subgroupG/H
center, socleC22×C83#386
commutatorC42C22×C4×C83
Frattini, cosocleC2×C42C23×C83
prime radical#532×C83C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C2×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C83×#2320C2semidirect
5. C83×#1491C2semidirect
6. C83×#1300C2semidirect
7. C83×#1285C2semidirect
11. #477×C83C4semidirect
12. #460×C83C4semidirect
174. #9330C83direct (N × H)
182. #2320C2×C83semidirect
185. #1491C2×C83semidirect
186. #1300C2×C83semidirect
187. #1285C2×C83semidirect
188. C83#9330direct (N × H)
192. #477C4×C83semidirect
193. #460C4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#31122
C83×#23202
C83×#19802
C83×#15052
C83×#14912
C83×#13002
C83×#12852
#933083