Finite Group Databasebeta

← C83×#11549 #35239373

Subgroups — C83×#11549 #35239373

Order 21248.

496 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2501C211yesmaximal, characteristic
2C83×#1463C211yesmaximal, characteristic, complemented
3C2×#324×C83C211yesmaximal, characteristic, complemented
4C83×#1325C212yesmaximal, complemented
5C83×#1318C212yesmaximal, complemented
6C2×#123×C83—21no—
7C2×#123×C83—21no—
8C2×#121×C83C411yescharacteristic
9C22×C4⋊C4×C83C2211yescharacteristic
10#407×C83—21no—
11C2×C22⋊C8×C83—21no—
12#399×C83—21no—
13#399×C83—21no—
14#390×C83C411yescharacteristic
15#390×C83C2211yescharacteristic
16#384×C83C411yescharacteristic
17#384×C83C2211yescharacteristic
18C4×C22⋊C4×C83C411yescharacteristic
19#324×C83—21no—
20#324×C83—21no—
21#324×C83C2212yes—
22#324×C83C2212yes—
23C22×D4×C83—21no—
24C22×D4×C83C2×C411yescharacteristic
25C23×C4×C83C2×C411yescharacteristic
26C23×C4×C83D411yescharacteristic
27C23×C4×C83D411yescharacteristic
28C2×M16×C83—41no—
29C22×C8×C83—41no—
30#123×C83—44no—
31#123×C83—44no—
32#121×C83—41no—
33#121×C83—41no—
34C2×C4⋊C4×C83—21no—
35C2×C4⋊C4×C83—21no—
36C2×C4⋊C4×C83—21no—
37C2×C4⋊C4×C83—21no—
38C2×C4⋊C4×C83—41no—
39C2×C4⋊C4×C83—41no—
40C2×C4⋊C4×C83C2×C411yescharacteristic
41C2×C4⋊C4×C83C2×C411yescharacteristic
42C2×C4⋊C4×C83D411yescharacteristic
43C2×C4⋊C4×C83D411yescharacteristic
44C2×C4⋊C4×C83C2311yescharacteristic
45C2×C22⋊C4×C83—21no—
46C2×C22⋊C4×C83—21no—
47C2×C22⋊C4×C83—21no—
48C2×C22⋊C4×C83—21no—
49C2×C22⋊C4×C83—21no—
50C2×C22⋊C4×C83—21no—
51C2×C42×C83C2×C411yescharacteristic
52C2×C42×C83C2×C411yescharacteristic
53C22⋊C8×C83—22no—
54C22⋊C8×C83—22no—
55C22⋊C8×C83—41no—
56C22⋊C8×C83—41no—
57#95×C83—21no—
58C24×C83—21no—
59C24×C83C22⋊C411yescharacteristic
60C2×D4×C83—22no—
61C2×D4×C83—41no—
62C2×D4×C83—41no—
63C2×D4×C83—42no—
64C2×D4×C83—42no—
65C2×D4×C83—41no—
66C2×D4×C83—41no—
67C22×C4×C83—21no—
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—22no—
76C22×C4×C83—21no—
77C22×C4×C83—41no—
78C22×C4×C83—42no—
79C22×C4×C83—42no—
80C22×C4×C83C22⋊C411yescharacteristic
81C22×C4×C83C22⋊C411yescharacteristic
82C22×C4×C83C22⋊C411yescharacteristic
83C22×C4×C83C22×C411yescharacteristic
84C22×C4×C83C2×D411yescharacteristic
85C22×C4×C83C2×D411yescharacteristic
86M16×C83—82no—
87C2×C8×C83—42no—
88C2×C8×C83—42no—
89C2×C8×C83—82no—
90C4⋊C4×C83—41no—
91C4⋊C4×C83—41no—
92C4⋊C4×C83—41no—
93C4⋊C4×C83—41no—
94C4⋊C4×C83—41no—
95C4⋊C4×C83—42no—
96C4⋊C4×C83—42no—
97C4⋊C4×C83—42no—
98C4⋊C4×C83—42no—
99C22⋊C4×C83—24no—
100C22⋊C4×C83—42no—
101C22⋊C4×C83—42no—
102C22⋊C4×C83—42no—
103C22⋊C4×C83—42no—
104C22⋊C4×C83—42no—
105C42×C83—22no—
106C42×C83—41no—
107C23×C83—22no—
108C23×C83—21no—
109C23×C83—21no—
110C23×C83—41no—
111C23×C83—41no—
112C23×C83—41no—
113C23×C83—41no—
114C23×C83—41no—
115C23×C83—41no—
116C23×C83—41no—
117C23×C83—41no—
118C23×C83#9911yescharacteristic
119C23×C83#9911yescharacteristic
120C23×C83C2×C22⋊C411yescharacteristic
121D4×C83—82no—
122D4×C83—82no—
123D4×C83—82no—
124C2×C4×C83—21no—
125C2×C4×C83—21no—
126C2×C4×C83—22no—
127C2×C4×C83—22no—
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—42no—
140C2×C4×C83—42no—
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—81no—
151C2×C4×C83—81no—
152C2×C4×C83#13112yes—
153C8×C83—82no—
154C8×C83—82no—
155C22×C83—21no—
156C22×C83—21no—
157C22×C83—21no—
158C22×C83—21no—
159C22×C83—21no—
160C22×C83—21no—
161C22×C83—21no—
162C22×C83—42no—
163C22×C83—42no—
164C22×C83—81no—
165C22×C83—81no—
166C22×C83—81no—
167C22×C83—81no—
168C22×C83—81no—
169C22×C83—81no—
170C22×C83—81no—
171C22×C83#35312yes—
172C22×C83#40811yescharacteristic
173C22×C83C2×#9911yescharacteristic
174C22×C83#41311yescharacteristic
175C4×C83—22no—
176C4×C83—42no—
177C4×C83—42no—
178C4×C83—41no—
179C4×C83—41no—
180C4×C83—41no—
181C4×C83—41no—
182C4×C83—41no—
183C4×C83—81no—
184#11549C8311yesmaximal, characteristic, direct product factor, Sylow
185C2×C83—21no—
186C2×C83—21no—
187C2×C83—22no—
188C2×C83—41no—
189C2×C83—161no—
190C2×C83#146811yescharacteristic
191C2×C83C2×#35311yescharacteristic
192C2×C83#213311yescharacteristic
193#2501C2×C8311yescharacteristic
194#1463C2×C8311yescharacteristic, complemented
195C2×#324C2×C8311yescharacteristic, complemented
196#1325C2×C8312yescomplemented
197#1318C2×C8312yescomplemented
198C83#1154911yescharacteristic, direct product factor, Sylow
199C2×#123—21no—
200C2×#123—21no—
201C2×#121C4×C8311yescharacteristic
202C22×C4⋊C4C22×C8311yescharacteristic
203#407—21no—
204C2×C22⋊C8—21no—
205#399—21no—
206#399—21no—
207#390C4×C8311yescharacteristic
208#390C22×C8311yescharacteristic
209#384C4×C8311yescharacteristic
210#384C22×C8311yescharacteristic
211C4×C22⋊C4C4×C8311yescharacteristic
212#324—21no—
213#324—21no—
214#324C22×C8312yes—
215#324C22×C8312yes—
216C22×D4—21no—
217C22×D4C2×C4×C8311yescharacteristic
218C23×C4C2×C4×C8311yescharacteristic
219C23×C4D4×C8311yescharacteristic
220C23×C4D4×C8311yescharacteristic
221C2×M16—41no—
222C22×C8—41no—
223#123—44no—
224#123—44no—
225#121—41no—
226#121—41no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—41no—
232C2×C4⋊C4—41no—
233C2×C4⋊C4C2×C4×C8311yescharacteristic
234C2×C4⋊C4C2×C4×C8311yescharacteristic
235C2×C4⋊C4D4×C8311yescharacteristic
236C2×C4⋊C4D4×C8311yescharacteristic
237C2×C4⋊C4C23×C8311yescharacteristic
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C42C2×C4×C8311yescharacteristic
245C2×C42C2×C4×C8311yescharacteristic
246C22⋊C8—22no—
247C22⋊C8—22no—
248C22⋊C8—41no—
249C22⋊C8—41no—
250#95—21no—
251C24—21no—
252C24C22⋊C4×C8311yescharacteristic
253C2×D4—22no—
254C2×D4—41no—
255C2×D4—41no—
256C2×D4—42no—
257C2×D4—42no—
258C2×D4—41no—
259C2×D4—41no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—41no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4C22⋊C4×C8311yescharacteristic
274C22×C4C22⋊C4×C8311yescharacteristic
275C22×C4C22⋊C4×C8311yescharacteristic
276C22×C4C22×C4×C8311yescharacteristic
277C22×C4C2×D4×C8311yescharacteristic
278C22×C4C2×D4×C8311yescharacteristic
279M16—82no—
280C2×C8—42no—
281C2×C8—42no—
282C2×C8—82no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C22⋊C4—24no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C42—22no—
299C42—41no—
300C23—22no—
301C23—21no—
302C23—21no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23#99×C8311yescharacteristic
312C23#99×C8311yescharacteristic
313C23C2×C22⋊C4×C8311yescharacteristic
314D4—82no—
315D4—82no—
316D4—82no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—22no—
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—42no—
333C2×C4—42no—
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—81no—
344C2×C4—81no—
345C2×C4#131×C8312yes—
346C8—82no—
347C8—82no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—42no—
356C22—42no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22#353×C8312yes—
365C22#408×C8311yescharacteristic
366C22C2×#99×C8311yescharacteristic
367C22#413×C8311yescharacteristic
368C4—22no—
369C4—42no—
370C4—42no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—81no—
377C2—21no—
378C2—21no—
379C2—22no—
380C2—41no—
381C2—161no—
382C2C83×#146811yescharacteristic
383C2C2×#353×C8311yescharacteristic
384C2C83×#213311yescharacteristic
subgroupG/H
center, socleC22×C83C2×#99
commutatorC22×C4C22×C4×C83
Frattini, cosocleC2×C4⋊C4C23×C83
prime radicalC2×#121×C83C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C83 ◁ C24×C83 ◁ C22×C4⋊C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C83×#1463C2semidirect
3. C2×#324×C83C2semidirect
4. C83×#1325C2semidirect
5. C83×#1318C2semidirect
184. #11549C83direct (N × H)
194. #1463C2×C83semidirect
195. C2×#324C2×C83semidirect
196. #1325C2×C83semidirect
197. #1318C2×C83semidirect
198. C83#11549direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#25012
C83×#14632
C2×#324×C832
C83×#13252
C83×#13182
#1154983