Finite Group Databasebeta

← C83×#9310 #35237134

Subgroups — C83×#9310 #35237134

Order 21248.

470 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3037C211yesmaximal, characteristic
2C83×#2983C211yesmaximal, characteristic, complemented
3C83×#1805C211yesmaximal, characteristic, complemented
4C83×#1517C211yesmaximal, characteristic
5C83×#1480C211yesmaximal, characteristic
6C83×#1301C211yesmaximal, characteristic, complemented
7C83×#1286C211yesmaximal, characteristic, complemented
8C2×#137×C83—21no—
9#532×C83C2211yescharacteristic
10C2×C4×Q8×C83C2211yescharacteristic
11#464×C83—22no—
12#462×C83C412yescomplemented
13#460×C83C412yescomplemented
14#446×C83—22no—
15#446×C83—22no—
16#432×C83—22no—
17#431×C83C2211yescharacteristic
18#431×C83C2211yescharacteristic
19#423×C83C2211yescharacteristic
20C2×C4⋊C8×C83C2211yescharacteristic
21#417×C83—21no—
22C2×#103×C83—21no—
23#382×C83C2211yescharacteristic
24#340×C83—21no—
25#327×C83—22no—
26D4⋊C8×C83—22no—
27C2×#41×C83—21no—
28C22×Q8×C83D411yescharacteristic
29#137×C83—42no—
30#137×C83—42no—
31C2×Q16×C83—22no—
32C2×SD16×C83—22no—
33C2×M16×C83—21no—
34C22×C8×C83—21no—
35C4⋊Q8×C83C2×C411yescharacteristic
36#127×C83C2×C411yescharacteristic
37#124×C83—21no—
38#121×C83—21no—
39#121×C83—21no—
40C4×Q8×C83—21no—
41C4×Q8×C83—21no—
42C4×Q8×C83C2×C412yes—
43C4×Q8×C83D412yes—
44C4×D4×C83—21no—
45C4×D4×C83—21no—
46C2×C4⋊C4×C83—21no—
47C2×C4⋊C4×C83—21no—
48C2×C4⋊C4×C83D411yescharacteristic
49C2×C42×C83—21no—
50C2×C42×C83C2311yescharacteristic
51C4⋊C8×C83—24no—
52C4⋊C8×C83—21no—
53C4⋊C8×C83—21no—
54C4⋊C8×C83—21no—
55C4⋊C8×C83—21no—
56C4⋊C8×C83—21no—
57C4⋊C8×C83C2×C412yes—
58#103×C83—22no—
59#103×C83—42no—
60#102×C83—22no—
61C22⋊C8×C83—21no—
62C22⋊C8×C83D412yes—
63#97×C83—24no—
64C4×C8×C83—21no—
65C4×C8×C83D412yes—
66#95×C83—21no—
67#95×C83—21no—
68#41×C83—41no—
69#41×C83—41no—
70#41×C83—41no—
71#41×C83—41no—
72C2×Q8×C83—21no—
73C2×Q8×C83—21no—
74C2×Q8×C83—21no—
75C2×Q8×C83—21no—
76C2×Q8×C83—21no—
77C2×Q8×C83—21no—
78C2×Q8×C83C22⋊C412yes—
79C2×D4×C83—21no—
80C2×D4×C83—21no—
81C2×D4×C83—21no—
82C2×D4×C83—41no—
83C22×C4×C83—21no—
84C22×C4×C83—21no—
85C22×C4×C83—41no—
86C22×C4×C83—41no—
87C22×C4×C83C2×D411yescharacteristic
88C22×C4×C83C2×D411yescharacteristic
89C22×C4×C83#4111yescharacteristic
90Q16×C83—44no—
91SD16×C83—44no—
92M16×C83—41no—
93M16×C83—41no—
94C2×C8×C83—22no—
95C2×C8×C83—22no—
96C2×C8×C83—22no—
97C2×C8×C83—41no—
98C2×C8×C83—41no—
99C2×C8×C83—41no—
100C4⋊C4×C83—22no—
101C4⋊C4×C83—21no—
102C4⋊C4×C83—22no—
103C4⋊C4×C83—21no—
104C4⋊C4×C83—21no—
105C4⋊C4×C83—41no—
106C4⋊C4×C83—41no—
107C4⋊C4×C83C22⋊C412yes—
108C22⋊C4×C83—41no—
109C22⋊C4×C83—41no—
110C42×C83—22no—
111C42×C83—22no—
112C42×C83C22×C411yescharacteristic
113C42×C83C2×D411yescharacteristic
114C42×C83C2×D411yescharacteristic
115C42×C83#4111yescharacteristic
116C23×C83—41no—
117C23×C83#12111yescharacteristic
118Q8×C83—22no—
119Q8×C83—22no—
120Q8×C83—41no—
121Q8×C83—41no—
122Q8×C83—41no—
123Q8×C83—41no—
124D4×C83—42no—
125D4×C83—41no—
126D4×C83—41no—
127D4×C83—81no—
128D4×C83—81no—
129D4×C83—81no—
130C2×C4×C83—22no—
131C2×C4×C83—22no—
132C2×C4×C83—41no—
133C2×C4×C83—41no—
134C2×C4×C83—41no—
135C2×C4×C83—41no—
136C2×C4×C83—41no—
137C2×C4×C83—81no—
138C2×C4×C83—81no—
139C2×C4×C83—81no—
140C2×C4×C83—81no—
141C2×C4×C83—81no—
142C2×C4×C83—81no—
143C2×C4×C83C2×C22⋊C411yescharacteristic
144C2×C4×C83C4×D411yescharacteristic
145C2×C4×C83C4×D411yescharacteristic
146C2×C4×C83#12011yescharacteristic
147C2×C4×C83#12111yescharacteristic
148C2×C4×C83#12311yescharacteristic
149C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C83#13711yescharacteristic
153C8×C83—42no—
154C8×C83—42no—
155C8×C83—42no—
156C8×C83—81no—
157C22×C83—21no—
158C22×C83—21no—
159C22×C83—81no—
160C22×C83—81no—
161C22×C83—81no—
162C22×C83#38611yescharacteristic
163C22×C83#46811yescharacteristic
164C22×C83#46911yescharacteristic
165C4×C83—21no—
166C4×C83—21no—
167C4×C83—21no—
168C4×C83—21no—
169C4×C83—42no—
170C4×C83—42no—
171C4×C83—81no—
172C4×C83—161no—
173C4×C83#41711yescharacteristic
174C4×C83#41811yescharacteristic
175C4×C83#46811yescharacteristic
176C4×C83#46911yescharacteristic
177#9310C8311yesmaximal, characteristic, direct product factor, Sylow
178C2×C83—21no—
179C2×C83—21no—
180C2×C83—161no—
181C2×C83#188111yescharacteristic
182C2×C83#189511yescharacteristic
183C2×C83#190511yescharacteristic
184#3037C2×C8311yescharacteristic
185#2983C2×C8311yescharacteristic, complemented
186#1805C2×C8311yescharacteristic, complemented
187#1517C2×C8311yescharacteristic
188#1480C2×C8311yescharacteristic
189#1301C2×C8311yescharacteristic, complemented
190#1286C2×C8311yescharacteristic, complemented
191C83#931011yescharacteristic, direct product factor, Sylow
192C2×#137—21no—
193#532C22×C8311yescharacteristic
194C2×C4×Q8C22×C8311yescharacteristic
195#464—22no—
196#462C4×C8312yescomplemented
197#460C4×C8312yescomplemented
198#446—22no—
199#446—22no—
200#432—22no—
201#431C22×C8311yescharacteristic
202#431C22×C8311yescharacteristic
203#423C22×C8311yescharacteristic
204C2×C4⋊C8C22×C8311yescharacteristic
205#417—21no—
206C2×#103—21no—
207#382C22×C8311yescharacteristic
208#340—21no—
209#327—22no—
210D4⋊C8—22no—
211C2×#41—21no—
212C22×Q8D4×C8311yescharacteristic
213#137—42no—
214#137—42no—
215C2×Q16—22no—
216C2×SD16—22no—
217C2×M16—21no—
218C22×C8—21no—
219C4⋊Q8C2×C4×C8311yescharacteristic
220#127C2×C4×C8311yescharacteristic
221#124—21no—
222#121—21no—
223#121—21no—
224C4×Q8—21no—
225C4×Q8—21no—
226C4×Q8C2×C4×C8312yes—
227C4×Q8D4×C8312yes—
228C4×D4—21no—
229C4×D4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4D4×C8311yescharacteristic
233C2×C42—21no—
234C2×C42C23×C8311yescharacteristic
235C4⋊C8—24no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8C2×C4×C8312yes—
242#103—22no—
243#103—42no—
244#102—22no—
245C22⋊C8—21no—
246C22⋊C8D4×C8312yes—
247#97—24no—
248C4×C8—21no—
249C4×C8D4×C8312yes—
250#95—21no—
251#95—21no—
252#41—41no—
253#41—41no—
254#41—41no—
255#41—41no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8C22⋊C4×C8312yes—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4C2×D4×C8311yescharacteristic
272C22×C4C2×D4×C8311yescharacteristic
273C22×C4#41×C8311yescharacteristic
274Q16—44no—
275SD16—44no—
276M16—41no—
277M16—41no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C4⋊C4—22no—
285C4⋊C4—21no—
286C4⋊C4—22no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4C22⋊C4×C8312yes—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C42—22no—
295C42—22no—
296C42C22×C4×C8311yescharacteristic
297C42C2×D4×C8311yescharacteristic
298C42C2×D4×C8311yescharacteristic
299C42#41×C8311yescharacteristic
300C23—41no—
301C23#121×C8311yescharacteristic
302Q8—22no—
303Q8—22no—
304Q8—41no—
305Q8—41no—
306Q8—41no—
307Q8—41no—
308D4—42no—
309D4—41no—
310D4—41no—
311D4—81no—
312D4—81no—
313D4—81no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4C2×C22⋊C4×C8311yescharacteristic
328C2×C4C4×D4×C8311yescharacteristic
329C2×C4C4×D4×C8311yescharacteristic
330C2×C4#120×C8311yescharacteristic
331C2×C4#121×C8311yescharacteristic
332C2×C4#123×C8311yescharacteristic
333C2×C4AGL(1,ℤ/8)×C8311yescharacteristic
334C2×C4AGL(1,ℤ/8)×C8311yescharacteristic
335C2×C4AGL(1,ℤ/8)×C8311yescharacteristic
336C2×C4#137×C8311yescharacteristic
337C8—42no—
338C8—42no—
339C8—42no—
340C8—81no—
341C22—21no—
342C22—21no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22#386×C8311yescharacteristic
347C22#468×C8311yescharacteristic
348C22#469×C8311yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—42no—
354C4—42no—
355C4—81no—
356C4—161no—
357C4#417×C8311yescharacteristic
358C4#418×C8311yescharacteristic
359C4#468×C8311yescharacteristic
360C4#469×C8311yescharacteristic
361C2—21no—
362C2—21no—
363C2—161no—
364C2C83×#188111yescharacteristic
365C2C83×#189511yescharacteristic
366C2C83×#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×#2983C2semidirect
3. C83×#1805C2semidirect
6. C83×#1301C2semidirect
7. C83×#1286C2semidirect
12. #462×C83C4semidirect
13. #460×C83C4semidirect
177. #9310C83direct (N × H)
185. #2983C2×C83semidirect
186. #1805C2×C83semidirect
189. #1301C2×C83semidirect
190. #1286C2×C83semidirect
191. C83#9310direct (N × H)
196. #462C4×C83semidirect
197. #460C4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#30372
C83×#29832
C83×#18052
C83×#15172
C83×#14802
C83×#13012
C83×#12862
#931083