Finite Group Databasebeta

← #35298666

Subgroups — #35298666

Order 21248.

530 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24910414C211yesmaximal, characteristic
2#24908219C211yesmaximal, characteristic, complemented
3#24907460C211yesmaximal, characteristic
4C2×#19127430C211yesmaximal, characteristic
5#24905346C211yesmaximal, characteristic, complemented
6#24905303C211yesmaximal, characteristic, complemented
7C83×#1834C211yesmaximal, characteristic, complemented
8C2×C4×D332C2211yescharacteristic
9C2×#14581750—21no—
10C2×#14581725—21no—
11C2×C4⋊(C83⋊C8)C2211yescharacteristic
12C2×C4⋊(C83⋊C8)C2211yescharacteristic
13C2×#14581712—21no—
14#19127602—21no—
15#19127591—22no—
16#19127558—21no—
17C4⋊C4×Dic83—21no—
18C4×C4⋊Dic83C2211yescharacteristic
19#19127463—21no—
20#19127463—21no—
21#19127430C414yescomplemented
22C2×C4×C8×C83C2211yescharacteristic
23#384×C83C2211yescharacteristic
24#384×C83C2211yescharacteristic
25#340×C83—22no—
26C22×D332D411yescharacteristic
27C22×C4×D83—21no—
28C22×C83⋊C8—21no—
29C22×C83⋊C8—21no—
30C4×D332—21no—
31C4×D332—21no—
32C4×D332C2×C412yes—
33C4×D332Q812yes—
34#14581750—42no—
35#14581750—42no—
36C2×C4⋊Dic83D411yescharacteristic
37C2×C4⋊Dic83D411yescharacteristic
38C2×C4⋊Dic83D411yescharacteristic
39C2×(C2×D83)⋊C4—22no—
40C2×(C2×D83)⋊C4—22no—
41C2×(C2×D83)⋊C4—21no—
42C2×C4×Dic83—22no—
43C2×C4×Dic83—21no—
44#14581725—42no—
45C4⋊(C83⋊C8)—21no—
46C4⋊(C83⋊C8)—21no—
47C4⋊(C83⋊C8)—21no—
48C4⋊(C83⋊C8)C2×C412yes—
49#14581712—42no—
50C83⋊#95—22no—
51C83⋊#95—21no—
52C22×C8×C83—21no—
53C2×C4⋊C4×C83—21no—
54C2×C4⋊C4×C83—21no—
55C2×C4⋊C4×C83—21no—
56C2×C4⋊C4×C83—21no—
57C2×C4⋊C4×C83—21no—
58C2×C4⋊C4×C83D412yes—
59C2×C42×C83C2311yescharacteristic
60C4×C8×C83—21no—
61C4×C8×C83C2×C412yes—
62C23×D83—21no—
63C2×D332—21no—
64C2×D332—21no—
65C2×D332—21no—
66C2×D332—21no—
67C2×D332—21no—
68C2×D332C4⋊C412yes—
69C22×Dic83—21no—
70C22×Dic83—21no—
71C22×Dic83—21no—
72C2×C4×D83—22no—
73C2×C4×D83—22no—
74C2×C4×D83—41no—
75C2×C4×D83—41no—
76C2×C4×D83—41no—
77C2×C4×D83—41no—
78C2×C83⋊C8—22no—
79C2×C83⋊C8—41no—
80C2×C83⋊C8—41no—
81C2×C83⋊C8—41no—
82C2×C83⋊C8—41no—
83C2×C83⋊C8—41no—
84C4⋊Dic83—21no—
85C4⋊Dic83—21no—
86C4⋊Dic83—21no—
87C4⋊Dic83—21no—
88C4⋊Dic83C4⋊C412yes—
89C4⋊Dic83D812yes—
90(C2×D83)⋊C4—22no—
91(C2×D83)⋊C4—22no—
92(C2×D83)⋊C4—44no—
93(C2×D83)⋊C4—82no—
94C4×Dic83—44no—
95C4×Dic83—41no—
96C4×Dic83—41no—
97C22×C4×C83—22no—
98C22×C4×C83—41no—
99C22×C4×C83C2×D411yescharacteristic
100C22×C4×C83C2×D411yescharacteristic
101C22×C4×C83C2×D411yescharacteristic
102C2×C8×C83—22no—
103C2×C8×C83—41no—
104C2×C8×C83—41no—
105C4⋊C4×C83—42no—
106C4⋊C4×C83—42no—
107C4⋊C4×C83—41no—
108C4⋊C4×C83—41no—
109C4⋊C4×C83—41no—
110C4⋊C4×C83—41no—
111C4⋊C4×C83—41no—
112C4⋊C4×C83—41no—
113C4⋊C4×C83—41no—
114C4⋊C4×C83—41no—
115C42×C83C22×C411yescharacteristic
116C42×C83C2×Q811yescharacteristic
117C42×C83#4111yescharacteristic
118C42×C83#4111yescharacteristic
119C23×C83#12011yescharacteristic
120C22×D83—22no—
121C22×D83—41no—
122C22×D83—41no—
123C22×D83—41no—
124C22×D83—41no—
125C22×D83—41no—
126C22×D83—41no—
127C2×C4×C83—21no—
128C2×C4×C83—21no—
129C2×C4×C83—42no—
130C2×C4×C83—42no—
131C2×C4×C83—42no—
132C2×C4×C83—81no—
133C2×C4×C83—81no—
134C2×C4×C83—81no—
135C2×C4×C83C2×C4⋊C411yescharacteristic
136C2×C4×C83C4×D411yescharacteristic
137C2×C4×C83C4×D411yescharacteristic
138C2×C4×C83C22⋊Q811yescharacteristic
139C2×C4×C83C22⋊Q811yescharacteristic
140C2×C4×C83#12311yescharacteristic
141C2×C4×C83C2×D811yescharacteristic
142C2×C4×C83#13511yescharacteristic
143C2×C4×C83#13511yescharacteristic
144C2×C4×C83#13511yescharacteristic
145C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C83#13711yescharacteristic
148C2×C4×C83#13711yescharacteristic
149C2×Dic83—22no—
150C2×Dic83—22no—
151C2×Dic83—41no—
152C2×Dic83—41no—
153C2×Dic83—41no—
154C2×Dic83—41no—
155C2×Dic83—41no—
156C2×Dic83—41no—
157C2×Dic83—41no—
158D332—22no—
159D332—22no—
160D332—41no—
161D332—41no—
162C4×D83—42no—
163C4×D83—42no—
164C4×D83—42no—
165C4×D83—42no—
166C8×C83—42no—
167C83⋊C8—42no—
168C83⋊C8—81no—
169C22×C83#38511yescharacteristic
170C22×C83#44711yescharacteristic
171C22×C83#44911yescharacteristic
172C22×C83#45211yescharacteristic
173C22×C83#45211yescharacteristic
174C22×C83#45411yescharacteristic
175C22×C83#45511yescharacteristic
176C2×D83—42no—
177C2×D83—42no—
178C2×D83—42no—
179C2×D83—81no—
180C2×D83—81no—
181C2×D83—81no—
182C2×D83—81no—
183C4×C83—21no—
184C4×C83—21no—
185C4×C83—82no—
186C4×C83—161no—
187C4×C83#42711yescharacteristic
188C4×C83#42811yescharacteristic
189C4×C83C4×D811yescharacteristic
190C4×C83#44011yescharacteristic
191C4×C83#47411yescharacteristic
192C4×C83#47811yescharacteristic
193C4×C83#48211yescharacteristic
194C4×C83#48511yescharacteristic
195Dic83—42no—
196Dic83—42no—
197Dic83—81no—
198#8897—831nomaximal, Sylow
199C2×C83#162511yescharacteristic
200C2×C83#163811yescharacteristic
201C2×C83#164111yescharacteristic
202C2×C83#164611yescharacteristic
203C2×C83#185411yescharacteristic
204C2×C83#186011yescharacteristic
205C2×C83#186211yescharacteristic
206D83—82no—
207#2354—831no—
208#1947—831no—
209#1834D8311yescharacteristic, complemented
210#1802—831no—
211C2×D4⋊C8—831no—
212#1296—831no—
213#1279—831no—
214C83#889711yescharacteristic, complemented, Sylow
215C2×C4×D4—831no—
216C2×#117—1661no—
217C2×#107—1661no—
218C2×C4⋊C8—831no—
219C2×C4⋊C8—831no—
220C2×#102—1661no—
221C2×C4×C8C2×D8311yescharacteristic
222#390—1661no—
223#388—1662no—
224#384C2×D8311yescharacteristic
225#384C2×D8311yescharacteristic
226#380—1661no—
227C4×C4⋊C4—831no—
228C4×C4⋊C4—1661no—
229#340—22no—
230#340—1661no—
231#340—1661no—
232D4⋊C8—834no—
233C22×D4—831no—
234C23×C4—1661no—
235C22×C8—21no—
236C22×C8—1661no—
237C22×C8—1661no—
238C4×D4—832no—
239C4×D4—832no—
240C4×D4—1661no—
241C4×D4—1661no—
242#117—3322no—
243#117—3322no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—831no—
250C2×C4⋊C4—831no—
251C2×C4⋊C4—831no—
252C2×C4⋊C4C22⋊D8312yes—
253C2×C22⋊C4—1662no—
254C2×C22⋊C4—1662no—
255C2×C22⋊C4—1661no—
256C2×C42—1662no—
257C2×C42—1661no—
258C2×C42C22×D8311yescharacteristic
259#107—3322no—
260C4⋊C8—832no—
261C4⋊C8—1661no—
262C4⋊C8—1661no—
263C4⋊C8—1661no—
264#102—3322no—
265C4×C8—21no—
266C4×C8C4×D8312yes—
267#95—1662no—
268#95—1661no—
269C24—1661no—
270C2×D4—832no—
271C2×D4—1661no—
272C2×D4—1661no—
273C2×D4—1661no—
274C2×D4—1661no—
275C2×D4—1661no—
276C22×C4—22no—
277C22×C4—41no—
278C22×C4—3321no—
279C22×C4—3321no—
280C22×C4—3321no—
281C22×C4—3321no—
282C22×C4—1661no—
283C22×C4—1661no—
284C22×C4—1661no—
285C22×C4—1662no—
286C22×C4—1662no—
287C22×C4D4×D8311yescharacteristic
288C22×C4D4×D8311yescharacteristic
289C22×C4C2×C22⋊D8311yescharacteristic
290C2×C8—22no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—3321no—
294C2×C8—3321no—
295C2×C8—3321no—
296C2×C8—3321no—
297C2×C8—3321no—
298C2×C8—1662no—
299C4⋊C4—42no—
300C4⋊C4—42no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—832no—
310C4⋊C4—832no—
311C4⋊C4—1661no—
312C4⋊C4—1661no—
313C4⋊C4—1661no—
314C4⋊C4—1661no—
315C22⋊C4—3324no—
316C22⋊C4—6642no—
317C22⋊C4—1662no—
318C22⋊C4—1662no—
319C42—3324no—
320C42—3321no—
321C42—3321no—
322C42C2×C4×D8311yescharacteristic
323C42Q8×D8311yescharacteristic
324C42#1305059011yescharacteristic
325C42#1305059111yescharacteristic
326C23—3321no—
327C23—3321no—
328C23—3321no—
329C23—3321no—
330C23—3321no—
331C23—3321no—
332C23—1662no—
333C23#1458176011yescharacteristic
334D4—3321no—
335D4—3321no—
336D4—1662no—
337D4—1662no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—3321no—
347C2×C4—3321no—
348C2×C4—3321no—
349C2×C4—3321no—
350C2×C4—3322no—
351C2×C4—3322no—
352C2×C4—3322no—
353C2×C4—3322no—
354C2×C4—3321no—
355C2×C4—3321no—
356C2×C4—3321no—
357C2×C4—1662no—
358C2×C4—1662no—
359C2×C4C4⋊C4×D8311yescharacteristic
360C2×C4C4×C22⋊D8311yescharacteristic
361C2×C4#1458175411yescharacteristic
362C2×C4#1458176811yescharacteristic
363C2×C4#1458177011yescharacteristic
364C2×C4#1458177711yescharacteristic
365C2×C4D8×D8311yescharacteristic
366C2×C4#1458181311yescharacteristic
367C2×C4#1458181311yescharacteristic
368C2×C4#1458181511yescharacteristic
369C2×C4#1458181611yescharacteristic
370C2×C4#1458181911yescharacteristic
371C2×C4#1458182111yescharacteristic
372C2×C4#1458182411yescharacteristic
373C8—42no—
374C8—3322no—
375C8—6641no—
376C22—3322no—
377C22—3322no—
378C22—3322no—
379C22—6641no—
380C22—6641no—
381C22—6641no—
382C22—6641no—
383C22#1912757211yescharacteristic
384C22#1912783311yescharacteristic
385C22#1912784511yescharacteristic
386C22#1912786011yescharacteristic
387C22#1912786211yescharacteristic
388C22#1912787311yescharacteristic
389C22#1912787811yescharacteristic
390C4—21no—
391C4—21no—
392C4—82no—
393C4—161no—
394C4—3322no—
395C4—3322no—
396C4—6641no—
397C4#1912773611yescharacteristic
398C4#1912774011yescharacteristic
399C4#1912778311yescharacteristic
400C4#1912780011yescharacteristic
401C4#1912798011yescharacteristic
402C4#1912800411yescharacteristic
403C4#1912802711yescharacteristic
404C4#1912804511yescharacteristic
405C2—6642no—
406C2#2490654911yescharacteristic
407C2#2490663211yescharacteristic
408C2#2490665311yescharacteristic
409C2#2490668811yescharacteristic
410C2#2490766111yescharacteristic
411C2#2490769511yescharacteristic
412C2#2490770711yescharacteristic
subgroupG/H
centerC23#14581760
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1834C2
socleC23×C83#120
prime radicalC22×D332D4
cosocleC2×C42×C83C23
hypercenter#1834D83
hypocenterC83#8897
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
2. #24908219C2semidirect
5. #24905346C2semidirect
6. #24905303C2semidirect
7. C83×#1834C2semidirect
21. #19127430C4semidirect
209. #1834D83semidirect
214. C83#8897semidirect

Maximal subgroups

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

subgroupindex
#249104142
#249082192
#249074602
C2×#191274302
#249053462
#249053032
C83×#18342
#889783