Finite Group Databasebeta

← C83×#11547 #35239371

Subgroups — C83×#11547 #35239371

Order 21248.

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

normal subgroups only

This group has 492 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×#2483C211yesmaximal, characteristic
2C83×#1462C211yesmaximal, characteristic
3C2×#323×C83C211yesmaximal, characteristic
4C83×#1326C212yesmaximal, complemented
5C83×#1317C212yesmaximal, complemented
6C22×C22⋊C4×C83C411yescharacteristic
7C22×C22⋊C4×C83C2211yescharacteristic
8#407×C83—21no—
9C2×C22⋊C8×C83—21no—
10#397×C83—21no—
11#397×C83—21no—
12#385×C83—21no—
13#385×C83C411yescharacteristic
14#385×C83C2211yescharacteristic
15#381×C83—21no—
16#381×C83C411yescharacteristic
17#381×C83C2211yescharacteristic
18#379×C83C411yescharacteristic
19#323×C83—21no—
20#323×C83—21no—
21#323×C83C2212yes—
22#323×C83C2212yes—
23C25×C83C2×C411yescharacteristic
24C23×C4×C83C2×C411yescharacteristic
25C23×C4×C83C2×C411yescharacteristic
26C23×C4×C83D411yescharacteristic
27C23×C4×C83D411yescharacteristic
28C2×M16×C83—41no—
29C22×C8×C83—41no—
30C2×C4⋊C4×C83—21no—
31C2×C4⋊C4×C83—21no—
32C2×C22⋊C4×C83—21no—
33C2×C22⋊C4×C83—21no—
34C2×C22⋊C4×C83—21no—
35C2×C22⋊C4×C83—21no—
36C2×C22⋊C4×C83—41no—
37C2×C22⋊C4×C83—41no—
38C2×C22⋊C4×C83—41no—
39C2×C22⋊C4×C83—41no—
40C2×C22⋊C4×C83C2×C411yescharacteristic
41C2×C22⋊C4×C83C2×C411yescharacteristic
42C2×C22⋊C4×C83C2×C411yescharacteristic
43C2×C22⋊C4×C83D411yescharacteristic
44C2×C22⋊C4×C83D411yescharacteristic
45C2×C22⋊C4×C83C2311yescharacteristic
46C22⋊C8×C83—22no—
47C22⋊C8×C83—22no—
48C22⋊C8×C83—41no—
49C22⋊C8×C83—41no—
50#95×C83—21no—
51#95×C83—21no—
52#95×C83—21no—
53#95×C83—21no—
54#95×C83—21no—
55#95×C83—21no—
56C24×C83—21no—
57C24×C83—21no—
58C24×C83—22no—
59C24×C83—41no—
60C24×C83—42no—
61C24×C83—81no—
62C24×C83C22⋊C411yescharacteristic
63C24×C83C22⋊C411yescharacteristic
64C24×C83C22×C411yescharacteristic
65C22×C4×C83—21no—
66C22×C4×C83—21no—
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—22no—
74C22×C4×C83—42no—
75C22×C4×C83—41no—
76C22×C4×C83—41no—
77C22×C4×C83—41no—
78C22×C4×C83—81no—
79C22×C4×C83—81no—
80C22×C4×C83C22⋊C411yescharacteristic
81C22×C4×C83C22⋊C411yescharacteristic
82C22×C4×C83C2×D411yescharacteristic
83C22×C4×C83C2×D411yescharacteristic
84M16×C83—82no—
85C2×C8×C83—42no—
86C2×C8×C83—42no—
87C2×C8×C83—82no—
88C4⋊C4×C83—81no—
89C4⋊C4×C83—81no—
90C22⋊C4×C83—22no—
91C22⋊C4×C83—41no—
92C22⋊C4×C83—41no—
93C22⋊C4×C83—41no—
94C22⋊C4×C83—41no—
95C22⋊C4×C83—42no—
96C22⋊C4×C83—42no—
97C22⋊C4×C83—41no—
98C22⋊C4×C83—41no—
99C22⋊C4×C83—41no—
100C22⋊C4×C83—81no—
101C23×C83—22no—
102C23×C83—21no—
103C23×C83—21no—
104C23×C83—21no—
105C23×C83—21no—
106C23×C83—21no—
107C23×C83—21no—
108C23×C83—21no—
109C23×C83—41no—
110C23×C83—42no—
111C23×C83—42no—
112C23×C83—41no—
113C23×C83—41no—
114C23×C83—42no—
115C23×C83—41no—
116C23×C83—41no—
117C23×C83—42no—
118C23×C83—81no—
119C23×C83—81no—
120C23×C83—84no—
121C23×C83—84no—
122C23×C83#9911yescharacteristic
123C23×C83#9911yescharacteristic
124C23×C83C2×C22⋊C411yescharacteristic
125C23×C83#13112yes—
126C2×C4×C83—21no—
127C2×C4×C83—21no—
128C2×C4×C83—21no—
129C2×C4×C83—21no—
130C2×C4×C83—42no—
131C2×C4×C83—42no—
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—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—81no—
149C2×C4×C83—81no—
150C2×C4×C83—82no—
151C2×C4×C83—82no—
152C8×C83—82no—
153C8×C83—82no—
154C22×C83—21no—
155C22×C83—21no—
156C22×C83—21no—
157C22×C83—21no—
158C22×C83—21no—
159C22×C83—21no—
160C22×C83—22no—
161C22×C83—21no—
162C22×C83—42no—
163C22×C83—42no—
164C22×C83—42no—
165C22×C83—42no—
166C22×C83—41no—
167C22×C83—41no—
168C22×C83—41no—
169C22×C83—41no—
170C22×C83—41no—
171C22×C83—84no—
172C22×C83—81no—
173C22×C83—81no—
174C22×C83—84no—
175C22×C83#35212yes—
176C22×C83#40811yescharacteristic
177C22×C83C2×#9911yescharacteristic
178C22×C83#41311yescharacteristic
179C4×C83—41no—
180C4×C83—41no—
181C4×C83—41no—
182C4×C83—41no—
183C4×C83—81no—
184C4×C83—81no—
185C4×C83—81no—
186C4×C83—81no—
187#11547C8311yesmaximal, characteristic, direct product factor, Sylow
188C2×C83—21no—
189C2×C83—21no—
190C2×C83—22no—
191C2×C83—41no—
192C2×C83—42no—
193C2×C83—81no—
194C2×C83#146811yescharacteristic
195C2×C83C2×#35211yescharacteristic
196C2×C83#212111yescharacteristic
197#2483C2×C8311yescharacteristic
198#1462C2×C8311yescharacteristic
199C2×#323C2×C8311yescharacteristic
200#1326C2×C8312yescomplemented
201#1317C2×C8312yescomplemented
202C83#1154711yescharacteristic, direct product factor, Sylow
203C22×C22⋊C4C4×C8311yescharacteristic
204C22×C22⋊C4C22×C8311yescharacteristic
205#407—21no—
206C2×C22⋊C8—21no—
207#397—21no—
208#397—21no—
209#385—21no—
210#385C4×C8311yescharacteristic
211#385C22×C8311yescharacteristic
212#381—21no—
213#381C4×C8311yescharacteristic
214#381C22×C8311yescharacteristic
215#379C4×C8311yescharacteristic
216#323—21no—
217#323—21no—
218#323C22×C8312yes—
219#323C22×C8312yes—
220C25C2×C4×C8311yescharacteristic
221C23×C4C2×C4×C8311yescharacteristic
222C23×C4C2×C4×C8311yescharacteristic
223C23×C4D4×C8311yescharacteristic
224C23×C4D4×C8311yescharacteristic
225C2×M16—41no—
226C22×C8—41no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—41no—
234C2×C22⋊C4—41no—
235C2×C22⋊C4—41no—
236C2×C22⋊C4—41no—
237C2×C22⋊C4C2×C4×C8311yescharacteristic
238C2×C22⋊C4C2×C4×C8311yescharacteristic
239C2×C22⋊C4C2×C4×C8311yescharacteristic
240C2×C22⋊C4D4×C8311yescharacteristic
241C2×C22⋊C4D4×C8311yescharacteristic
242C2×C22⋊C4C23×C8311yescharacteristic
243C22⋊C8—22no—
244C22⋊C8—22no—
245C22⋊C8—41no—
246C22⋊C8—41no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253C24—21no—
254C24—21no—
255C24—22no—
256C24—41no—
257C24—42no—
258C24—81no—
259C24C22⋊C4×C8311yescharacteristic
260C24C22⋊C4×C8311yescharacteristic
261C24C22×C4×C8311yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—42no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—81no—
276C22×C4—81no—
277C22×C4C22⋊C4×C8311yescharacteristic
278C22×C4C22⋊C4×C8311yescharacteristic
279C22×C4C2×D4×C8311yescharacteristic
280C22×C4C2×D4×C8311yescharacteristic
281M16—82no—
282C2×C8—42no—
283C2×C8—42no—
284C2×C8—82no—
285C4⋊C4—81no—
286C4⋊C4—81no—
287C22⋊C4—22no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—42no—
293C22⋊C4—42no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—81no—
298C23—22no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—41no—
307C23—42no—
308C23—42no—
309C23—41no—
310C23—41no—
311C23—42no—
312C23—41no—
313C23—41no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—84no—
318C23—84no—
319C23#99×C8311yescharacteristic
320C23#99×C8311yescharacteristic
321C23C2×C22⋊C4×C8311yescharacteristic
322C23#131×C8312yes—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
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—41no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—82no—
348C2×C4—82no—
349C8—82no—
350C8—82no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—81no—
370C22—81no—
371C22—84no—
372C22#352×C8312yes—
373C22#408×C8311yescharacteristic
374C22C2×#99×C8311yescharacteristic
375C22#413×C8311yescharacteristic
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—81no—
381C4—81no—
382C4—81no—
383C4—81no—
384C2—21no—
385C2—21no—
386C2—22no—
387C2—41no—
388C2—42no—
389C2—81no—
390C2C83×#146811yescharacteristic
391C2C2×#352×C8311yescharacteristic
392C2C83×#212111yescharacteristic
subgroupG/H
center, socleC22×C83C2×#99
commutatorC24C22×C4×C83
Frattini, cosocleC2×C22⋊C4C23×C83
prime radicalC25×C83C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C83 ◁ C24×C83 ◁ C22×C22⋊C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
4. C83×#1326C2semidirect
5. C83×#1317C2semidirect
187. #11547C83direct (N × H)
200. #1326C2×C83semidirect
201. #1317C2×C83semidirect
202. C83#11547direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#24832
C83×#14622
C2×#323×C832
C83×#13262
C83×#13172
#1154783