Finite Group Databasebeta

← C83×#9189 #35237013

Subgroups — C83×#9189 #35237013

Order 21248.

502 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 502 conjugacy classes of subgroups — too many to draw. Only its 122 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×#2973C211yesmaximal, characteristic
2C83×#2633C211yesmaximal, characteristic
3C4×#100×C83C211yesmaximal, characteristic
4C83×#1528C212yesmaximal, complemented
5C83×#1288C212yesmaximal, complemented
6C2×#125×C83C2211yescharacteristic
7C2×C4×D4×C83C2211yescharacteristic
8#435×C83—24no—
9#432×C83C2212yes—
10C2×#100×C83—21no—
11#407×C83—21no—
12C2×C22⋊C8×C83—21no—
13C4×M16×C83C2212yes—
14#399×C83C411yescharacteristic
15#399×C83C411yescharacteristic
16#398×C83—21no—
17#397×C83C411yescharacteristic
18#397×C83C411yescharacteristic
19#394×C83—21no—
20#385×C83—21no—
21#385×C83—21no—
22#383×C83C2211yescharacteristic
23#343×C83—21no—
24#330×C83—24no—
25C22×D4×C83D411yescharacteristic
26C23×C4×C83D411yescharacteristic
27C23×C4×C83D411yescharacteristic
28C2×M16×C83—22no—
29C2×M16×C83—22no—
30C22×C8×C83—22no—
31#125×C83—22no—
32#125×C83—22no—
33C4×D4×C83—22no—
34C4×D4×C83—22no—
35C2×C4⋊C4×C83—21no—
36C2×C4⋊C4×C83—21no—
37C2×C4⋊C4×C83—21no—
38C2×C4⋊C4×C83—21no—
39C2×C4⋊C4×C83C2×C411yescharacteristic
40C2×C4⋊C4×C83C2×C411yescharacteristic
41C2×C4⋊C4×C83D411yescharacteristic
42C2×C22⋊C4×C83—21no—
43C2×C22⋊C4×C83—21no—
44C2×C22⋊C4×C83—21no—
45C2×C22⋊C4×C83—21no—
46C2×C22⋊C4×C83C2×C411yescharacteristic
47C2×C22⋊C4×C83C2×C411yescharacteristic
48C2×C42×C83C2311yescharacteristic
49C4⋊C8×C83—22no—
50#100×C83—24no—
51C22⋊C8×C83—22no—
52C22⋊C8×C83—22no—
53C22⋊C8×C83—22no—
54#97×C83—22no—
55#97×C83D414yes—
56C4×C8×C83—22no—
57#95×C83—21no—
58#95×C83—21no—
59#95×C83—21no—
60#95×C83—21no—
61#95×C83C2×C411yescharacteristic
62#95×C83C2×C411yescharacteristic
63C24×C83C22⋊C411yescharacteristic
64C24×C83C22⋊C411yescharacteristic
65C2×D4×C83—22no—
66C2×D4×C83—22no—
67C2×D4×C83—41no—
68C22×C4×C83—21no—
69C22×C4×C83—21no—
70C22×C4×C83—21no—
71C22×C4×C83—21no—
72C22×C4×C83—21no—
73C22×C4×C83—21no—
74C22×C4×C83—21no—
75C22×C4×C83—21no—
76C22×C4×C83—81no—
77C22×C4×C83—81no—
78C22×C4×C83C22⋊C411yescharacteristic
79C22×C4×C83C22⋊C411yescharacteristic
80C22×C4×C83C22×C411yescharacteristic
81C22×C4×C83C2×D411yescharacteristic
82C22×C4×C83C2×D411yescharacteristic
83M16×C83—24no—
84M16×C83—42no—
85M16×C83—82no—
86C2×C8×C83—24no—
87C2×C8×C83—42no—
88C2×C8×C83—82no—
89C4⋊C4×C83—22no—
90C4⋊C4×C83—22no—
91C4⋊C4×C83—22no—
92C4⋊C4×C83—41no—
93C4⋊C4×C83—42no—
94C4⋊C4×C83—41no—
95C4⋊C4×C83—81no—
96C4⋊C4×C83—81no—
97C22⋊C4×C83—22no—
98C22⋊C4×C83—22no—
99C22⋊C4×C83—42no—
100C22⋊C4×C83—42no—
101C22⋊C4×C83—81no—
102C22⋊C4×C83—81no—
103C42×C83C2×D412yes—
104C42×C83#4112yes—
105C23×C83—21no—
106C23×C83—21no—
107C23×C83—21no—
108C23×C83—21no—
109C23×C83—21no—
110C23×C83—41no—
111C23×C83—41no—
112C23×C83—41no—
113C23×C83—41no—
114C23×C83#10412yes—
115C23×C83C2×C22⋊C411yescharacteristic
116D4×C83—44no—
117C2×C4×C83—21no—
118C2×C4×C83—21no—
119C2×C4×C83—21no—
120C2×C4×C83—21no—
121C2×C4×C83—41no—
122C2×C4×C83—41no—
123C2×C4×C83—42no—
124C2×C4×C83—42no—
125C2×C4×C83—41no—
126C2×C4×C83—41no—
127C2×C4×C83—41no—
128C2×C4×C83—41no—
129C2×C4×C83—41no—
130C2×C4×C83—41no—
131C2×C4×C83—41no—
132C2×C4×C83—41no—
133C2×C4×C83—41no—
134C2×C4×C83—41no—
135C2×C4×C83—41no—
136C2×C4×C83—41no—
137C2×C4×C83—41no—
138C2×C4×C83—41no—
139C2×C4×C83—81no—
140C2×C4×C83—81no—
141C2×C4×C83C4×D412yes—
142C2×C4×C83#12011yescharacteristic
143C2×C4×C83#12112yes—
144C2×C4×C83#12311yescharacteristic
145C8×C83—44no—
146C8×C83—44no—
147C22×C83—21no—
148C22×C83—21no—
149C22×C83—22no—
150C22×C83—42no—
151C22×C83—42no—
152C22×C83—41no—
153C22×C83—41no—
154C22×C83—41no—
155C22×C83—41no—
156C22×C83—41no—
157C22×C83—81no—
158C22×C83—81no—
159C22×C83#38611yescharacteristic
160C22×C83C2×#10411yescharacteristic
161C22×C83#42111yescharacteristic
162C4×C83—22no—
163C4×C83—21no—
164C4×C83—21no—
165C4×C83—22no—
166C4×C83—41no—
167C4×C83—41no—
168C4×C83—81no—
169C4×C83—81no—
170C4×C83—81no—
171C4×C83—81no—
172#9189C8311yesmaximal, characteristic, direct product factor, Sylow
173C2×C83—21no—
174C2×C83—21no—
175C2×C83—42no—
176C2×C83—81no—
177C2×C83#187111yescharacteristic
178C2×C83#191111yescharacteristic
179C2×C83#191511yescharacteristic
180#2973C2×C8311yescharacteristic
181#2633C2×C8311yescharacteristic
182C4×#100C2×C8311yescharacteristic
183#1528C2×C8312yescomplemented
184#1288C2×C8312yescomplemented
185C83#918911yescharacteristic, direct product factor, Sylow
186C2×#125C22×C8311yescharacteristic
187C2×C4×D4C22×C8311yescharacteristic
188#435—24no—
189#432C22×C8312yes—
190C2×#100—21no—
191#407—21no—
192C2×C22⋊C8—21no—
193C4×M16C22×C8312yes—
194#399C4×C8311yescharacteristic
195#399C4×C8311yescharacteristic
196#398—21no—
197#397C4×C8311yescharacteristic
198#397C4×C8311yescharacteristic
199#394—21no—
200#385—21no—
201#385—21no—
202#383C22×C8311yescharacteristic
203#343—21no—
204#330—24no—
205C22×D4D4×C8311yescharacteristic
206C23×C4D4×C8311yescharacteristic
207C23×C4D4×C8311yescharacteristic
208C2×M16—22no—
209C2×M16—22no—
210C22×C8—22no—
211#125—22no—
212#125—22no—
213C4×D4—22no—
214C4×D4—22no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4C2×C4×C8311yescharacteristic
220C2×C4⋊C4C2×C4×C8311yescharacteristic
221C2×C4⋊C4D4×C8311yescharacteristic
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4C2×C4×C8311yescharacteristic
227C2×C22⋊C4C2×C4×C8311yescharacteristic
228C2×C42C23×C8311yescharacteristic
229C4⋊C8—22no—
230#100—24no—
231C22⋊C8—22no—
232C22⋊C8—22no—
233C22⋊C8—22no—
234#97—22no—
235#97D4×C8314yes—
236C4×C8—22no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95C2×C4×C8311yescharacteristic
242#95C2×C4×C8311yescharacteristic
243C24C22⋊C4×C8311yescharacteristic
244C24C22⋊C4×C8311yescharacteristic
245C2×D4—22no—
246C2×D4—22no—
247C2×D4—41no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—81no—
257C22×C4—81no—
258C22×C4C22⋊C4×C8311yescharacteristic
259C22×C4C22⋊C4×C8311yescharacteristic
260C22×C4C22×C4×C8311yescharacteristic
261C22×C4C2×D4×C8311yescharacteristic
262C22×C4C2×D4×C8311yescharacteristic
263M16—24no—
264M16—42no—
265M16—82no—
266C2×C8—24no—
267C2×C8—42no—
268C2×C8—82no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—41no—
273C4⋊C4—42no—
274C4⋊C4—41no—
275C4⋊C4—81no—
276C4⋊C4—81no—
277C22⋊C4—22no—
278C22⋊C4—22no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—81no—
282C22⋊C4—81no—
283C42C2×D4×C8312yes—
284C42#41×C8312yes—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23#104×C8312yes—
295C23C2×C22⋊C4×C8311yescharacteristic
296D4—44no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4C4×D4×C8312yes—
322C2×C4#120×C8311yescharacteristic
323C2×C4#121×C8312yes—
324C2×C4#123×C8311yescharacteristic
325C8—44no—
326C8—44no—
327C22—21no—
328C22—21no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22#386×C8311yescharacteristic
340C22C2×#104×C8311yescharacteristic
341C22#421×C8311yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—22no—
346C4—41no—
347C4—41no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4—81no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—81no—
356C2C83×#187111yescharacteristic
357C2C83×#191111yescharacteristic
358C2C83×#191511yescharacteristic
subgroupG/H
center, socleC22×C83#386
commutatorC22×C4C22×C4×C83
Frattini, cosocleC2×C42C23×C83
prime radicalC22×D4×C83D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C2×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
4. C83×#1528C2semidirect
5. C83×#1288C2semidirect
172. #9189C83direct (N × H)
183. #1528C2×C83semidirect
184. #1288C2×C83semidirect
185. C83#9189direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#29732
C83×#26332
C4×#100×C832
C83×#15282
C83×#12882
#918983