Finite Group Databasebeta

← C83×#9512 #35237336

Subgroups — C83×#9512 #35237336

Order 21248.

558 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#2921C211yesmaximal, characteristic, complemented
2C83×#2482C211yesmaximal, characteristic
3C83×#1822C211yesmaximal, characteristic, complemented
4C83×#1462C212yesmaximal
5C83×#1306C212yesmaximal, complemented
6C2×#117×C83C2211yescharacteristic
7C22×C22⋊C4×C83C2211yescharacteristic
8#433×C83—24no—
9#423×C83—21no—
10#407×C83C2212yes—
11#407×C83C2212yes—
12C4×M16×C83—21no—
13#399×C83—21no—
14#397×C83—21no—
15#388×C83—21no—
16#388×C83—21no—
17#385×C83C411yescharacteristic
18#385×C83C411yescharacteristic
19#381×C83C2211yescharacteristic
20#379×C83C411yescharacteristic
21#379×C83C411yescharacteristic
22#343×C83—21no—
23#343×C83—21no—
24#323×C83—24no—
25C25×C83C2×C411yescharacteristic
26C23×C4×C83C2×C411yescharacteristic
27C23×C4×C83C2311yescharacteristic
28C2×M16×C83—22no—
29C2×M16×C83—22no—
30#117×C83—22no—
31#117×C83—22no—
32C2×C4⋊C4×C83—21no—
33C2×C4⋊C4×C83—21no—
34C2×C4⋊C4×C83D411yescharacteristic
35C2×C4⋊C4×C83D411yescharacteristic
36C2×C22⋊C4×C83—21no—
37C2×C22⋊C4×C83—21no—
38C2×C22⋊C4×C83—22no—
39C2×C22⋊C4×C83—21no—
40C2×C22⋊C4×C83—21no—
41C2×C22⋊C4×C83—22no—
42C2×C22⋊C4×C83—21no—
43C2×C22⋊C4×C83—21no—
44C2×C22⋊C4×C83C2×C411yescharacteristic
45C2×C22⋊C4×C83C2×C411yescharacteristic
46C2×C22⋊C4×C83C2×C411yescharacteristic
47C2×C22⋊C4×C83C2×C411yescharacteristic
48C2×C42×C83D411yescharacteristic
49C2×C42×C83D411yescharacteristic
50C4⋊C8×C83—24no—
51C22⋊C8×C83—22no—
52C22⋊C8×C83—22no—
53C22⋊C8×C83—22no—
54C22⋊C8×C83D414yes—
55#97×C83—22no—
56C4×C8×C83—22no—
57#95×C83—21no—
58#95×C83—21no—
59#95×C83—21no—
60#95×C83—21no—
61C24×C83—21no—
62C24×C83—22no—
63C24×C83—42no—
64C24×C83—41no—
65C24×C83—41no—
66C24×C83—81no—
67C24×C83C22×C411yescharacteristic
68C22×C4×C83—21no—
69C22×C4×C83—21no—
70C22×C4×C83—21no—
71C22×C4×C83—22no—
72C22×C4×C83—41no—
73C22×C4×C83—41no—
74C22×C4×C83—81no—
75C22×C4×C83C22⋊C411yescharacteristic
76C22×C4×C83C22⋊C411yescharacteristic
77C22×C4×C83C22⋊C411yescharacteristic
78C22×C4×C83C22⋊C411yescharacteristic
79C22×C4×C83C2×D411yescharacteristic
80C22×C4×C83C2×D411yescharacteristic
81C22×C4×C83C2×D412yes—
82C22×C4×C83#4112yes—
83M16×C83—42no—
84M16×C83—42no—
85M16×C83—42no—
86M16×C83—42no—
87C2×C8×C83—24no—
88C2×C8×C83—42no—
89C4⋊C4×C83—22no—
90C4⋊C4×C83—22no—
91C4⋊C4×C83—81no—
92C4⋊C4×C83—81no—
93C22⋊C4×C83—22no—
94C22⋊C4×C83—22no—
95C22⋊C4×C83—42no—
96C22⋊C4×C83—42no—
97C22⋊C4×C83—41no—
98C22⋊C4×C83—42no—
99C22⋊C4×C83—41no—
100C22⋊C4×C83—41no—
101C22⋊C4×C83—41no—
102C22⋊C4×C83—81no—
103C22⋊C4×C83—81no—
104C42×C83—21no—
105C42×C83—21no—
106C42×C83—21no—
107C42×C83—21no—
108C23×C83—21no—
109C23×C83—21no—
110C23×C83—22no—
111C23×C83—24no—
112C23×C83—41no—
113C23×C83—41no—
114C23×C83—41no—
115C23×C83—41no—
116C23×C83—41no—
117C23×C83—42no—
118C23×C83—41no—
119C23×C83—41no—
120C23×C83—41no—
121C23×C83—82no—
122C23×C83—82no—
123C23×C83—84no—
124C23×C83—84no—
125C23×C83C2×C22⋊C411yescharacteristic
126C23×C83C4×D412yes—
127C2×C4×C83—21no—
128C2×C4×C83—21no—
129C2×C4×C83—21no—
130C2×C4×C83—21no—
131C2×C4×C83—21no—
132C2×C4×C83—21no—
133C2×C4×C83—21no—
134C2×C4×C83—21no—
135C2×C4×C83—42no—
136C2×C4×C83—42no—
137C2×C4×C83—41no—
138C2×C4×C83—41no—
139C2×C4×C83—41no—
140C2×C4×C83—41no—
141C2×C4×C83—41no—
142C2×C4×C83—41no—
143C2×C4×C83—41no—
144C2×C4×C83—41no—
145C2×C4×C83—41no—
146C2×C4×C83—41no—
147C2×C4×C83—41no—
148C2×C4×C83—41no—
149C2×C4×C83—41no—
150C2×C4×C83—82no—
151C2×C4×C83#12011yescharacteristic
152C2×C4×C83#12112yes—
153C2×C4×C83#12311yescharacteristic
154C8×C83—44no—
155C8×C83—82no—
156C22×C83—21no—
157C22×C83—21no—
158C22×C83—22no—
159C22×C83—22no—
160C22×C83—22no—
161C22×C83—42no—
162C22×C83—42no—
163C22×C83—42no—
164C22×C83—42no—
165C22×C83—42no—
166C22×C83—81no—
167C22×C83—81no—
168C22×C83—84no—
169C22×C83—84no—
170C22×C83—81no—
171C22×C83—81no—
172C22×C83#38611yescharacteristic
173C22×C83#41011yescharacteristic
174C22×C83#41011yescharacteristic
175C4×C83—21no—
176C4×C83—22no—
177C4×C83—21no—
178C4×C83—41no—
179C4×C83—41no—
180C4×C83—41no—
181C4×C83—41no—
182C4×C83—81no—
183C4×C83—81no—
184C4×C83—81no—
185#9512C8311yesmaximal, characteristic, direct product factor, Sylow
186C2×C83—21no—
187C2×C83—21no—
188C2×C83—42no—
189C2×C83—82no—
190C2×C83#189111yescharacteristic
191C2×C83#189911yescharacteristic
192C2×C83#191411yescharacteristic
193#2921C2×C8311yescharacteristic, complemented
194#2482C2×C8311yescharacteristic
195#1822C2×C8311yescharacteristic, complemented
196#1462C2×C8312yes—
197#1306C2×C8312yescomplemented
198C83#951211yescharacteristic, direct product factor, Sylow
199C2×#117C22×C8311yescharacteristic
200C22×C22⋊C4C22×C8311yescharacteristic
201#433—24no—
202#423—21no—
203#407C22×C8312yes—
204#407C22×C8312yes—
205C4×M16—21no—
206#399—21no—
207#397—21no—
208#388—21no—
209#388—21no—
210#385C4×C8311yescharacteristic
211#385C4×C8311yescharacteristic
212#381C22×C8311yescharacteristic
213#379C4×C8311yescharacteristic
214#379C4×C8311yescharacteristic
215#343—21no—
216#343—21no—
217#323—24no—
218C25C2×C4×C8311yescharacteristic
219C23×C4C2×C4×C8311yescharacteristic
220C23×C4C23×C8311yescharacteristic
221C2×M16—22no—
222C2×M16—22no—
223#117—22no—
224#117—22no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4D4×C8311yescharacteristic
228C2×C4⋊C4D4×C8311yescharacteristic
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4C2×C4×C8311yescharacteristic
238C2×C22⋊C4C2×C4×C8311yescharacteristic
239C2×C22⋊C4C2×C4×C8311yescharacteristic
240C2×C22⋊C4C2×C4×C8311yescharacteristic
241C2×C42D4×C8311yescharacteristic
242C2×C42D4×C8311yescharacteristic
243C4⋊C8—24no—
244C22⋊C8—22no—
245C22⋊C8—22no—
246C22⋊C8—22no—
247C22⋊C8D4×C8314yes—
248#97—22no—
249C4×C8—22no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254C24—21no—
255C24—22no—
256C24—42no—
257C24—41no—
258C24—41no—
259C24—81no—
260C24C22×C4×C8311yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—22no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—81no—
268C22×C4C22⋊C4×C8311yescharacteristic
269C22×C4C22⋊C4×C8311yescharacteristic
270C22×C4C22⋊C4×C8311yescharacteristic
271C22×C4C22⋊C4×C8311yescharacteristic
272C22×C4C2×D4×C8311yescharacteristic
273C22×C4C2×D4×C8311yescharacteristic
274C22×C4C2×D4×C8312yes—
275C22×C4#41×C8312yes—
276M16—42no—
277M16—42no—
278M16—42no—
279M16—42no—
280C2×C8—24no—
281C2×C8—42no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—81no—
285C4⋊C4—81no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—42no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—81no—
296C22⋊C4—81no—
297C42—21no—
298C42—21no—
299C42—21no—
300C42—21no—
301C23—21no—
302C23—21no—
303C23—22no—
304C23—24no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—42no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—82no—
315C23—82no—
316C23—84no—
317C23—84no—
318C23C2×C22⋊C4×C8311yescharacteristic
319C23C4×D4×C8312yes—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—82no—
344C2×C4#120×C8311yescharacteristic
345C2×C4#121×C8312yes—
346C2×C4#123×C8311yescharacteristic
347C8—44no—
348C8—82no—
349C22—21no—
350C22—21no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—42no—
355C22—42no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—81no—
360C22—81no—
361C22—84no—
362C22—84no—
363C22—81no—
364C22—81no—
365C22#386×C8311yescharacteristic
366C22#410×C8311yescharacteristic
367C22#410×C8311yescharacteristic
368C4—21no—
369C4—22no—
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—81no—
376C4—81no—
377C4—81no—
378C2—21no—
379C2—21no—
380C2—42no—
381C2—82no—
382C2C83×#189111yescharacteristic
383C2C83×#189911yescharacteristic
384C2C83×#191411yescharacteristic
subgroupG/H
center, socleC22×C83#386
commutatorC24C22×C4×C83
Frattini, cosocleC23×C4C23×C83
prime radicalC25×C83C2×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C23×C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#2921C2semidirect
3. C83×#1822C2semidirect
5. C83×#1306C2semidirect
185. #9512C83direct (N × H)
193. #2921C2×C83semidirect
195. #1822C2×C83semidirect
197. #1306C2×C83semidirect
198. C83#9512direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#29212
C83×#24822
C83×#18222
C83×#14622
C83×#13062
#951283