Finite Group Databasebeta

← C83×#9384 #35237208

Subgroups — C83×#9384 #35237208

Order 21248.

640 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#2972C211yesmaximal, characteristic, complemented
2C83×#2543C211yesmaximal, characteristic
3C83×#1799C211yesmaximal, characteristic, complemented
4C83×#1519C212yesmaximal, complemented
5C83×#1294C212yesmaximal, complemented
6C2×#121×C83—21no—
7C2×#121×C83C2211yescharacteristic
8C2×C4×D4×C83C2211yescharacteristic
9C8×D4×C83—24no—
10#431×C83—21no—
11C2×#99×C83—21no—
12C2×C22⋊C8×C83—21no—
13C2×C22⋊C8×C83C2212yes—
14#398×C83C411yescharacteristic, complemented
15#397×C83C411yescharacteristic, complemented
16#394×C83C411yescharacteristic, complemented
17#392×C83C411yescharacteristic, complemented
18#388×C83—21no—
19#386×C83—21no—
20#386×C83—21no—
21#380×C83C2212yes—
22C2×#95×C83C2211yescharacteristic
23#342×C83—21no—
24#327×C83—24no—
25C22×D4×C83—21no—
26C22×D4×C83—21no—
27C22×D4×C83C2×C411yescharacteristic
28C22×D4×C83D411yescharacteristic
29C23×C4×C83—21no—
30C23×C4×C83D411yescharacteristic
31C23×C4×C83C2311yescharacteristic
32C22×C8×C83—22no—
33C22×C8×C83—22no—
34#121×C83—22no—
35#121×C83—22no—
36#121×C83—42no—
37#121×C83—42no—
38C4×D4×C83—22no—
39C4×D4×C83—22no—
40C2×C4⋊C4×C83—21no—
41C2×C4⋊C4×C83—22no—
42C2×C4⋊C4×C83C2×C411yescharacteristic
43C2×C4⋊C4×C83C2×C411yescharacteristic
44C2×C22⋊C4×C83—21no—
45C2×C22⋊C4×C83—21no—
46C2×C22⋊C4×C83—21no—
47C2×C22⋊C4×C83—21no—
48C2×C22⋊C4×C83—22no—
49C2×C22⋊C4×C83—21no—
50C2×C22⋊C4×C83C2×C411yescharacteristic
51C2×C22⋊C4×C83D411yescharacteristic
52C2×C42×C83D411yescharacteristic
53C4⋊C8×C83—22no—
54#99×C83—42no—
55C22⋊C8×C83—22no—
56C22⋊C8×C83—22no—
57C22⋊C8×C83D414yescomplemented
58C4×C8×C83—22no—
59#95×C83—21no—
60#95×C83—21no—
61#95×C83—21no—
62#95×C83—22no—
63#95×C83C2×C411yescharacteristic
64#95×C83C2×C411yescharacteristic
65C24×C83—21no—
66C24×C83C22⋊C411yescharacteristic
67C24×C83C2×D411yescharacteristic
68C2×D4×C83—22no—
69C2×D4×C83—22no—
70C2×D4×C83—22no—
71C2×D4×C83—42no—
72C2×D4×C83—42no—
73C2×D4×C83—42no—
74C2×D4×C83—41no—
75C2×D4×C83—41no—
76C2×D4×C83—42no—
77C2×D4×C83—81no—
78C2×D4×C83—81no—
79C2×D4×C83D812yes—
80C2×D4×C83SD1612yes—
81C22×C4×C83—21no—
82C22×C4×C83—21no—
83C22×C4×C83—21no—
84C22×C4×C83—21no—
85C22×C4×C83—21no—
86C22×C4×C83—42no—
87C22×C4×C83—41no—
88C22×C4×C83—41no—
89C22×C4×C83—42no—
90C22×C4×C83—81no—
91C22×C4×C83—81no—
92C22×C4×C83—81no—
93C22×C4×C83C22⋊C411yescharacteristic
94C22×C4×C83C22⋊C411yescharacteristic
95C22×C4×C83C22⋊C411yescharacteristic
96C22×C4×C83C22×C411yescharacteristic
97C22×C4×C83C2×D412yes—
98C22×C4×C83C2×D411yescharacteristic
99C22×C4×C83#4112yes—
100C2×C8×C83—24no—
101C2×C8×C83—82no—
102C2×C8×C83—82no—
103C4⋊C4×C83—22no—
104C4⋊C4×C83—22no—
105C4⋊C4×C83—42no—
106C4⋊C4×C83—82no—
107C22⋊C4×C83—22no—
108C22⋊C4×C83—22no—
109C22⋊C4×C83—42no—
110C22⋊C4×C83—42no—
111C22⋊C4×C83—42no—
112C22⋊C4×C83—41no—
113C22⋊C4×C83—41no—
114C22⋊C4×C83—42no—
115C22⋊C4×C83—42no—
116C22⋊C4×C83—81no—
117C42×C83—21no—
118C42×C83—21no—
119C23×C83—21no—
120C23×C83—21no—
121C23×C83—41no—
122C23×C83—41no—
123C23×C83—41no—
124C23×C83—41no—
125C23×C83—41no—
126C23×C83—41no—
127C23×C83—41no—
128C23×C83—41no—
129C23×C83—41no—
130C23×C83—41no—
131C23×C83—41no—
132C23×C83#10212yes—
133C23×C83C2×C22⋊C411yescharacteristic
134C23×C83#12112yes—
135C23×C83C2×D811yescharacteristic
136C23×C83C2×SD1611yescharacteristic
137C23×C83#13512yes—
138D4×C83—24no—
139D4×C83—24no—
140D4×C83—82no—
141D4×C83—84no—
142D4×C83—82no—
143D4×C83—82no—
144C2×C4×C83—21no—
145C2×C4×C83—21no—
146C2×C4×C83—22no—
147C2×C4×C83—21no—
148C2×C4×C83—21no—
149C2×C4×C83—42no—
150C2×C4×C83—42no—
151C2×C4×C83—41no—
152C2×C4×C83—41no—
153C2×C4×C83—42no—
154C2×C4×C83—41no—
155C2×C4×C83—41no—
156C2×C4×C83—41no—
157C2×C4×C83—41no—
158C2×C4×C83—41no—
159C2×C4×C83—41no—
160C2×C4×C83—41no—
161C2×C4×C83—41no—
162C2×C4×C83—41no—
163C2×C4×C83—41no—
164C2×C4×C83—81no—
165C2×C4×C83—82no—
166C2×C4×C83—82no—
167C2×C4×C83—82no—
168C2×C4×C83—82no—
169C2×C4×C83—82no—
170C2×C4×C83#10212yes—
171C2×C4×C83C4×D412yes—
172C2×C4×C83#12011yescharacteristic
173C2×C4×C83#12311yescharacteristic
174C8×C83—44no—
175C22×C83—21no—
176C22×C83—22no—
177C22×C83—21no—
178C22×C83—22no—
179C22×C83—22no—
180C22×C83—41no—
181C22×C83—41no—
182C22×C83—42no—
183C22×C83—42no—
184C22×C83—41no—
185C22×C83—41no—
186C22×C83—81no—
187C22×C83—81no—
188C22×C83—81no—
189C22×C83—81no—
190C22×C83—81no—
191C22×C83—81no—
192C22×C83—81no—
193C22×C83—81no—
194C22×C83#38611yescharacteristic
195C22×C83C2×#10211yescharacteristic
196C22×C83#41611yescharacteristic
197C22×C83#46512yes—
198C22×C83#46612yes—
199C4×C83—22no—
200C4×C83—21no—
201C4×C83—21no—
202C4×C83—22no—
203C4×C83—42no—
204C4×C83—41no—
205C4×C83—41no—
206C4×C83—81no—
207C4×C83—81no—
208C4×C83—162no—
209#9384C8311yesmaximal, characteristic, direct product factor, Sylow
210C2×C83—21no—
211C2×C83—22no—
212C2×C83—21no—
213C2×C83—22no—
214C2×C83—42no—
215C2×C83—161no—
216C2×C83#188411yescharacteristic
217C2×C83#189311yescharacteristic
218C2×C83#191311yescharacteristic
219#2972C2×C8311yescharacteristic, complemented
220#2543C2×C8311yescharacteristic
221#1799C2×C8311yescharacteristic, complemented
222#1519C2×C8312yescomplemented
223#1294C2×C8312yescomplemented
224C83#938411yescharacteristic, direct product factor, Sylow
225C2×#121—21no—
226C2×#121C22×C8311yescharacteristic
227C2×C4×D4C22×C8311yescharacteristic
228C8×D4—24no—
229#431—21no—
230C2×#99—21no—
231C2×C22⋊C8—21no—
232C2×C22⋊C8C22×C8312yes—
233#398C4×C8311yescharacteristic, complemented
234#397C4×C8311yescharacteristic, complemented
235#394C4×C8311yescharacteristic, complemented
236#392C4×C8311yescharacteristic, complemented
237#388—21no—
238#386—21no—
239#386—21no—
240#380C22×C8312yes—
241C2×#95C22×C8311yescharacteristic
242#342—21no—
243#327—24no—
244C22×D4—21no—
245C22×D4—21no—
246C22×D4C2×C4×C8311yescharacteristic
247C22×D4D4×C8311yescharacteristic
248C23×C4—21no—
249C23×C4D4×C8311yescharacteristic
250C23×C4C23×C8311yescharacteristic
251C22×C8—22no—
252C22×C8—22no—
253#121—22no—
254#121—22no—
255#121—42no—
256#121—42no—
257C4×D4—22no—
258C4×D4—22no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4C2×C4×C8311yescharacteristic
262C2×C4⋊C4C2×C4×C8311yescharacteristic
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4C2×C4×C8311yescharacteristic
270C2×C22⋊C4D4×C8311yescharacteristic
271C2×C42D4×C8311yescharacteristic
272C4⋊C8—22no—
273#99—42no—
274C22⋊C8—22no—
275C22⋊C8—22no—
276C22⋊C8D4×C8314yescomplemented
277C4×C8—22no—
278#95—21no—
279#95—21no—
280#95—21no—
281#95—22no—
282#95C2×C4×C8311yescharacteristic
283#95C2×C4×C8311yescharacteristic
284C24—21no—
285C24C22⋊C4×C8311yescharacteristic
286C24C2×D4×C8311yescharacteristic
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—42no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—42no—
296C2×D4—81no—
297C2×D4—81no—
298C2×D4D8×C8312yes—
299C2×D4SD16×C8312yes—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—42no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—42no—
309C22×C4—81no—
310C22×C4—81no—
311C22×C4—81no—
312C22×C4C22⋊C4×C8311yescharacteristic
313C22×C4C22⋊C4×C8311yescharacteristic
314C22×C4C22⋊C4×C8311yescharacteristic
315C22×C4C22×C4×C8311yescharacteristic
316C22×C4C2×D4×C8312yes—
317C22×C4C2×D4×C8311yescharacteristic
318C22×C4#41×C8312yes—
319C2×C8—24no—
320C2×C8—82no—
321C2×C8—82no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—42no—
325C4⋊C4—82no—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—42no—
329C22⋊C4—42no—
330C22⋊C4—42no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—42no—
334C22⋊C4—42no—
335C22⋊C4—81no—
336C42—21no—
337C42—21no—
338C23—21no—
339C23—21no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—41no—
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23#102×C8312yes—
352C23C2×C22⋊C4×C8311yescharacteristic
353C23#121×C8312yes—
354C23C2×D8×C8311yescharacteristic
355C23C2×SD16×C8311yescharacteristic
356C23#135×C8312yes—
357D4—24no—
358D4—24no—
359D4—82no—
360D4—84no—
361D4—82no—
362D4—82no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—22no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—81no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4—82no—
387C2×C4—82no—
388C2×C4—82no—
389C2×C4#102×C8312yes—
390C2×C4C4×D4×C8312yes—
391C2×C4#120×C8311yescharacteristic
392C2×C4#123×C8311yescharacteristic
393C8—44no—
394C22—21no—
395C22—22no—
396C22—21no—
397C22—22no—
398C22—22no—
399C22—41no—
400C22—41no—
401C22—42no—
402C22—42no—
403C22—41no—
404C22—41no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22#386×C8311yescharacteristic
414C22C2×#102×C8311yescharacteristic
415C22#416×C8311yescharacteristic
416C22#465×C8312yes—
417C22#466×C8312yes—
418C4—22no—
419C4—21no—
420C4—21no—
421C4—22no—
422C4—42no—
423C4—41no—
424C4—41no—
425C4—81no—
426C4—81no—
427C4—162no—
428C2—21no—
429C2—22no—
430C2—21no—
431C2—22no—
432C2—42no—
433C2—161no—
434C2C83×#188411yescharacteristic
435C2C83×#189311yescharacteristic
436C2C83×#191311yescharacteristic
subgroupG/H
center, socleC22×C83#386
commutatorC22×C4C22×C4×C83
Frattini, cosocleC23×C4C23×C83
prime radicalC83×#2543C2
LCSG ▷ C22×C4 ▷ 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×#2972C2semidirect
3. C83×#1799C2semidirect
4. C83×#1519C2semidirect
5. C83×#1294C2semidirect
14. #398×C83C4semidirect
15. #397×C83C4semidirect
16. #394×C83C4semidirect
17. #392×C83C4semidirect
57. C22⋊C8×C83D4semidirect
209. #9384C83direct (N × H)
219. #2972C2×C83semidirect
221. #1799C2×C83semidirect
222. #1519C2×C83semidirect
223. #1294C2×C83semidirect
224. C83#9384direct (N × H)
233. #398C4×C83semidirect
234. #397C4×C83semidirect
235. #394C4×C83semidirect
236. #392C4×C83semidirect
276. C22⋊C8D4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#29722
C83×#25432
C83×#17992
C83×#15192
C83×#12942
#938483