Finite Group Databasebeta

← #35294666

Subgroups — #35294666

Order 21248.

524 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24916091C211yesmaximal, characteristic
2C2×#19127756C211yesmaximal, characteristic
3#432×D83C211yesmaximal, characteristic
4#24905363C211yesmaximal, characteristic, complemented
5#24905362C211yesmaximal, characteristic, complemented
6#24905361C211yesmaximal, characteristic, complemented
7C83×#1302C211yesmaximal, characteristic, complemented
8C2×C42×D83C2211yescharacteristic
9#19127758C2211yescharacteristic
10#19127757—21no—
11#19127757C412yes—
12#19127756—21no—
13#19127756—21no—
14#19127756—21no—
15#19127756C412yes—
16#19127756C412yes—
17#19127755—21no—
18#19127755C412yes—
19#19127754C2211yescharacteristic
20#19127752—21no—
21#19127723—21no—
22C2×Dic83⋊C8—21no—
23C4⋊C8×D83C412yes—
24#19127663C412yes—
25C2×(C2×D83)⋊C8—21no—
26C22⋊C8×D83—21no—
27C4×#13050573—21no—
28C2×#14581703C2211yescharacteristic
29#97×D83—21no—
30#432×C83C2211yescharacteristic
31#431×C83C2211yescharacteristic
32C2×#97×C83C2211yescharacteristic
33C22×C4×D83C2×C411yescharacteristic
34C22×C4×D83D411yescharacteristic
35C22×C4×D83Q811yescharacteristic
36C2×#13050573—22no—
37C22×C83⋊C8—21no—
38C2×C8×D83—22no—
39C2×C4×Dic83C2×C411yescharacteristic
40C2×C4×Dic83D411yescharacteristic
41C2×C4×Dic83Q811yescharacteristic
42C42×D83C2×C411yescharacteristic
43C42×D83C2×C411yescharacteristic
44C42×D83C2×C411yescharacteristic
45C42×D83C2×C411yescharacteristic
46C42×D83D411yescharacteristic
47C42×D83D411yescharacteristic
48C42×D83D411yescharacteristic
49C42×D83D411yescharacteristic
50C4⋊(C83⋊C8)—21no—
51C4⋊(C83⋊C8)C2×C412yes—
52Dic83⋊C8—22no—
53Dic83⋊C8—22no—
54Dic83⋊C8—22no—
55Dic83⋊C8—22no—
56C22⋊(C83⋊C8)—21no—
57C22⋊(C83⋊C8)C2×C412yes—
58(C2×D83)⋊C8—22no—
59(C2×D83)⋊C8—22no—
60(C2×D83)⋊C8—22no—
61(C2×D83)⋊C8—22no—
62#14581703—21no—
63#14581703—21no—
64#14581703C2×C412yes—
65#14581702—22no—
66#14581702—22no—
67C4×C83⋊C8—21no—
68C22×C8×C83—21no—
69C2×C42×C83C2311yescharacteristic
70C4⋊C8×C83—21no—
71C4⋊C8×C83C2×C412yes—
72C22⋊C8×C83—21no—
73C22⋊C8×C83C2×C412yes—
74#97×C83—21no—
75#97×C83—21no—
76#97×C83C2×C412yes—
77C4×C8×C83—21no—
78C23×D83C4⋊C411yescharacteristic
79C22×Dic83C4⋊C411yescharacteristic
80C22×Dic83C4⋊C411yescharacteristic
81C22×Dic83C4⋊C411yescharacteristic
82C2×C4×D83—42no—
83C2×C4×D83—42no—
84C2×C4×D83—42no—
85C2×C4×D83C4211yescharacteristic
86C2×C4×D83C4211yescharacteristic
87C2×C4×D83C22⋊C411yescharacteristic
88C2×C4×D83C22⋊C411yescharacteristic
89C2×C4×D83C22⋊C411yescharacteristic
90C2×C4×D83C22⋊C411yescharacteristic
91C2×C4×D83C22⋊C411yescharacteristic
92C2×C4×D83C22⋊C411yescharacteristic
93C2×C4×D83C4⋊C411yescharacteristic
94C2×C4×D83C4⋊C411yescharacteristic
95C2×C4×D83C4⋊C411yescharacteristic
96C2×C4×D83C4⋊C411yescharacteristic
97#13050573—44no—
98C2×C83⋊C8—22no—
99C2×C83⋊C8—22no—
100C2×C83⋊C8—22no—
101C2×C83⋊C8—42no—
102C8×D83—44no—
103C4×Dic83C4211yescharacteristic
104C4×Dic83C4211yescharacteristic
105C4×Dic83C22⋊C411yescharacteristic
106C4×Dic83C22⋊C411yescharacteristic
107C4×Dic83C22⋊C411yescharacteristic
108C4×Dic83C22⋊C411yescharacteristic
109C4×Dic83C22⋊C411yescharacteristic
110C4×Dic83C22⋊C411yescharacteristic
111C4×Dic83C4⋊C411yescharacteristic
112C4×Dic83C4⋊C411yescharacteristic
113C4×Dic83C4⋊C411yescharacteristic
114C4×Dic83C4⋊C411yescharacteristic
115C22×C4×C83C22×C411yescharacteristic
116C22×C4×C83C2×D411yescharacteristic
117C22×C4×C83C2×Q811yescharacteristic
118C2×C8×C83—22no—
119C2×C8×C83—22no—
120C2×C8×C83—22no—
121C2×C8×C83—42no—
122C42×C83C22×C411yescharacteristic
123C42×C83C22×C411yescharacteristic
124C42×C83C2×D411yescharacteristic
125C42×C83C2×D411yescharacteristic
126C23×C83C2×C4⋊C411yescharacteristic
127C22×D83—22no—
128C22×D83—22no—
129C22×D83—41no—
130C22×D83#9511yescharacteristic
131C22×D83#9511yescharacteristic
132C2×C4×C83—22no—
133C2×C4×C83—22no—
134C2×C4×C83—41no—
135C2×C4×C83C2×C4211yescharacteristic
136C2×C4×C83C2×C22⋊C411yescharacteristic
137C2×C4×C83C2×C22⋊C411yescharacteristic
138C2×C4×C83C2×C22⋊C411yescharacteristic
139C2×C4×C83C2×C4⋊C411yescharacteristic
140C2×C4×C83C2×C4⋊C411yescharacteristic
141C2×Dic83—22no—
142C2×Dic83—41no—
143C2×Dic83—41no—
144C2×Dic83#9511yescharacteristic
145C2×Dic83#9511yescharacteristic
146C2×Dic83#9511yescharacteristic
147C2×Dic83#9511yescharacteristic
148C2×Dic83#9511yescharacteristic
149C2×Dic83#9511yescharacteristic
150C4×D83—22no—
151C4×D83—22no—
152C4×D83—22no—
153C4×D83—22no—
154C4×D83—41no—
155C4×D83—41no—
156C4×D83—41no—
157C4×D83—41no—
158C4×D83—41no—
159C4×D83—41no—
160C4×D83—41no—
161C4×D83—41no—
162C8×C83—42no—
163C8×C83—42no—
164C8×C83—42no—
165C83⋊C8—42no—
166C83⋊C8—42no—
167C83⋊C8—42no—
168C22×C83—21no—
169C22×C83—21no—
170C22×C83C2×#9511yescharacteristic
171C22×C83#43012yes—
172C2×D83—21no—
173C2×D83—21no—
174C2×D83—21no—
175C2×D83—21no—
176C2×D83—21no—
177C2×D83—44no—
178C2×D83#34412yes—
179C4×C83—21no—
180C4×C83—21no—
181C4×C83—21no—
182C4×C83—21no—
183C4×C83—21no—
184C4×C83#42112yes—
185Dic83—21no—
186Dic83—21no—
187Dic83—21no—
188Dic83—21no—
189Dic83—21no—
190Dic83—21no—
191#8085—831nomaximal, Sylow
192C2×C83—22no—
193C2×C83#173311yescharacteristic
194C2×C83#173811yescharacteristic
195C2×C83C2×#34411yescharacteristic
196D83—22no—
197D83—41no—
198#2920—831no—
199C2×#432—831no—
200C2×#432—831no—
201#1302—831no—
202#1302—831no—
203#1302—831no—
204#1302D8311yescharacteristic, complemented
205C83#808511yescharacteristic, complemented, Sylow
206C22×C42—831no—
207#432—832no—
208#432—832no—
209#432—832no—
210#432—831no—
211#432—832no—
212#432—1661no—
213#432—1661no—
214#432—1661no—
215#432—1661no—
216#432—1661no—
217#432C2×D8311yescharacteristic
218#431—831no—
219#431—1661no—
220#431C2×D8311yescharacteristic
221#423—1661no—
222C2×C4⋊C8—832no—
223C2×C4⋊C8—1661no—
224#407—832no—
225C2×C22⋊C8—1661no—
226C2×C22⋊C8—1661no—
227C4×M16—1661no—
228C2×#97—831no—
229C2×#97—1661no—
230C2×#97C2×D8311yescharacteristic
231C23×C4—831no—
232C23×C4—831no—
233C23×C4—831no—
234C2×M16—1662no—
235C22×C8—21no—
236C22×C8—1662no—
237C22×C8—1661no—
238C2×C42—831no—
239C2×C42—831no—
240C2×C42—831no—
241C2×C42—831no—
242C2×C42—831no—
243C2×C42—831no—
244C2×C42—831no—
245C2×C42—831no—
246C2×C42—831no—
247C2×C42—831no—
248C2×C42—831no—
249C2×C42C22×D8311yescharacteristic
250C4⋊C8—21no—
251C4⋊C8—832no—
252C4⋊C8—1662no—
253C4⋊C8—1662no—
254C4⋊C8—1662no—
255C4⋊C8—1662no—
256C4⋊C8—1661no—
257C4⋊C8C4×D8312yes—
258C22⋊C8—21no—
259C22⋊C8—832no—
260C22⋊C8—1662no—
261C22⋊C8—1662no—
262C22⋊C8—1662no—
263C22⋊C8—1662no—
264C22⋊C8—1661no—
265C22⋊C8C4×D8312yes—
266#97—21no—
267#97—21no—
268#97—832no—
269#97—1662no—
270#97—1662no—
271#97—1661no—
272#97—1661no—
273#97C4×D8312yes—
274C4×C8—21no—
275C4×C8—1661no—
276C24—831no—
277C22×C4—3322no—
278C22×C4—3322no—
279C22×C4—3322no—
280C22×C4—831no—
281C22×C4—831no—
282C22×C4—831no—
283C22×C4—831no—
284C22×C4—831no—
285C22×C4—831no—
286C22×C4—831no—
287C22×C4—831no—
288C22×C4—831no—
289C22×C4—831no—
290C22×C4—831no—
291C22×C4—831no—
292C22×C4—831no—
293C22×C4—831no—
294C22×C4—831no—
295C22×C4C2×C4×D8311yescharacteristic
296C22×C4D4×D8311yescharacteristic
297C22×C4Q8×D8311yescharacteristic
298M16—3324no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—42no—
303C2×C8—3324no—
304C2×C8—3322no—
305C2×C8—1662no—
306C2×C8—1662no—
307C2×C8—1662no—
308C42—831no—
309C42—831no—
310C42—831no—
311C42—831no—
312C42—831no—
313C42—831no—
314C42—831no—
315C42—831no—
316C42—831no—
317C42—831no—
318C42—831no—
319C42—831no—
320C42C2×C4×D8311yescharacteristic
321C42C2×C4×D8311yescharacteristic
322C42D4×D8311yescharacteristic
323C42D4×D8311yescharacteristic
324C23—3321no—
325C23—831no—
326C23—831no—
327C23—1662no—
328C23—1662no—
329C23C4⋊C4×D8311yescharacteristic
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—3321no—
334C2×C4—3321no—
335C2×C4—3321no—
336C2×C4—3321no—
337C2×C4—3321no—
338C2×C4—3321no—
339C2×C4—3321no—
340C2×C4—3321no—
341C2×C4—3321no—
342C2×C4—3321no—
343C2×C4—831no—
344C2×C4—831no—
345C2×C4—831no—
346C2×C4—831no—
347C2×C4—831no—
348C2×C4—831no—
349C2×C4—1662no—
350C2×C4—1662no—
351C2×C4—1662no—
352C2×C4—1662no—
353C2×C4—1662no—
354C2×C4C42×D8311yescharacteristic
355C2×C4C22⋊C4×D8311yescharacteristic
356C2×C4C22⋊C4×D8311yescharacteristic
357C2×C4C22⋊C4×D8311yescharacteristic
358C2×C4C4⋊C4×D8311yescharacteristic
359C2×C4C4⋊C4×D8311yescharacteristic
360C8—42no—
361C8—42no—
362C8—42no—
363C8—3322no—
364C8—3322no—
365C8—3322no—
366C22—21no—
367C22—21no—
368C22—3324no—
369C22—832no—
370C22—1661no—
371C22—1661no—
372C22—1661no—
373C22—1661no—
374C22—1661no—
375C22#95×D8311yescharacteristic
376C22#1912774812yes—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—1661no—
383C4—1661no—
384C4—1661no—
385C4—1661no—
386C4—1661no—
387C4—1661no—
388C4#1912771612yes—
389C2—22no—
390C2—3321no—
391C2—1662no—
392C2#2490717111yescharacteristic
393C2#2490718811yescharacteristic
394C2#344×D8311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D83
commutatorC2×C4×C83C2×C42
FrattiniC2×C42C22×D83
FittingC83×#1302C2
socleC22×C83C2×#95
prime radicalC23×D83C4⋊C4
cosocleC2×C42×C83C23
hypercenter#1302D83
hypocenterC83#8085
LCSG ▷ C2×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1302

Complements

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

NH ≅ G/Ntype
4. #24905363C2semidirect
5. #24905362C2semidirect
6. #24905361C2semidirect
7. C83×#1302C2semidirect
204. #1302D83semidirect
205. C83#8085semidirect

Maximal subgroups

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

subgroupindex
#249160912
C2×#191277562
#432×D832
#249053632
#249053622
#249053612
C83×#13022
#808583