Finite Group Databasebeta

← #35299474

Subgroups — #35299474

Order 21248.

534 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 111 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
1#24916492C211yesmaximal, characteristic
2C4×#14581709C211yesmaximal, characteristic
3#24905910C212yesmaximal, complemented
4#24905356C212yesmaximal, complemented
5C83×#2398C211yesmaximal, characteristic
6#19127773—24no—
7#19127758C2212yes—
8C2×#14581709—21no—
9#19127665—21no—
10C2×C22⋊(C83⋊C8)—21no—
11C4×#13050574C2212yes—
12#19127470—21no—
13Q8⋊(C83⋊C8)—24no—
14C2×C4×Q8×C83C2211yescharacteristic
15C2×C4×D4×C83C2211yescharacteristic
16#400×C83—21no—
17#397×C83C411yescharacteristic
18#397×C83C411yescharacteristic
19#394×C83—21no—
20#393×C83C411yescharacteristic
21#393×C83C411yescharacteristic
22C4×C22⋊C4×C83—21no—
23C4×C22⋊C4×C83—21no—
24#376×C83C2211yescharacteristic
25C2×#13050574—22no—
26C2×#13050574—22no—
27C22×C83⋊C8—22no—
28C4⋊(C83⋊C8)D414yes—
29#14581709—24no—
30C22⋊(C83⋊C8)—22no—
31C22⋊(C83⋊C8)—22no—
32C22⋊(C83⋊C8)—22no—
33#14581703—22no—
34#14581703—22no—
35C4×C83⋊C8—22no—
36C22×Q8×C83C2×C411yescharacteristic
37C22×D4×C83D411yescharacteristic
38C23×C4×C83D411yescharacteristic
39C23×C4×C83D411yescharacteristic
40C4×Q8×C83—22no—
41C4×Q8×C83—22no—
42C4×D4×C83—22no—
43C4×D4×C83—22no—
44C2×C4⋊C4×C83—21no—
45C2×C4⋊C4×C83C2×C411yescharacteristic
46C2×C4⋊C4×C83D411yescharacteristic
47C2×C22⋊C4×C83—21no—
48C2×C22⋊C4×C83—21no—
49C2×C22⋊C4×C83—21no—
50C2×C22⋊C4×C83—21no—
51C2×C22⋊C4×C83C2×C411yescharacteristic
52C2×C22⋊C4×C83C2×C411yescharacteristic
53C2×C42×C83—21no—
54C2×C42×C83—21no—
55C2×C42×C83C2311yescharacteristic
56#95×C83—21no—
57#95×C83—21no—
58#95×C83—21no—
59#95×C83—21no—
60#95×C83—21no—
61#95×C83C2×C411yescharacteristic
62#95×C83C2×C411yescharacteristic
63#13050574—24no—
64#13050574—42no—
65#13050574—82no—
66C2×C83⋊C8—24no—
67C2×C83⋊C8—42no—
68C2×C83⋊C8—82no—
69C24×C83C22⋊C411yescharacteristic
70C24×C83C22⋊C411yescharacteristic
71C2×Q8×C83—22no—
72C2×Q8×C83—42no—
73C2×D4×C83—22no—
74C2×D4×C83—22no—
75C2×D4×C83—41no—
76C22×C4×C83—21no—
77C22×C4×C83—21no—
78C22×C4×C83—21no—
79C22×C4×C83—21no—
80C22×C4×C83—21no—
81C22×C4×C83—21no—
82C22×C4×C83—21no—
83C22×C4×C83—21no—
84C22×C4×C83—42no—
85C22×C4×C83—42no—
86C22×C4×C83C22⋊C411yescharacteristic
87C22×C4×C83C22⋊C411yescharacteristic
88C22×C4×C83C22×C411yescharacteristic
89C22×C4×C83C2×D411yescharacteristic
90C22×C4×C83C2×D411yescharacteristic
91C4⋊C4×C83—22no—
92C4⋊C4×C83—22no—
93C4⋊C4×C83—42no—
94C22⋊C4×C83—22no—
95C22⋊C4×C83—22no—
96C22⋊C4×C83—42no—
97C22⋊C4×C83—42no—
98C22⋊C4×C83—42no—
99C22⋊C4×C83—42no—
100C42×C83—42no—
101C42×C83—41no—
102C42×C83—41no—
103C42×C83C2×D412yes—
104C42×C83#4112yes—
105C23×C83—21no—
106C23×C83—21no—
107C23×C83—21no—
108C23×C83—21no—
109C23×C83—21no—
110C23×C83—41no—
111C23×C83—41no—
112C23×C83—41no—
113C23×C83—41no—
114C23×C83#10412yes—
115C23×C83C2×C22⋊C411yescharacteristic
116Q8×C83—24no—
117Q8×C83—42no—
118D4×C83—44no—
119C2×C4×C83—21no—
120C2×C4×C83—21no—
121C2×C4×C83—22no—
122C2×C4×C83—22no—
123C2×C4×C83—21no—
124C2×C4×C83—21no—
125C2×C4×C83—41no—
126C2×C4×C83—41no—
127C2×C4×C83—41no—
128C2×C4×C83—42no—
129C2×C4×C83—42no—
130C2×C4×C83—41no—
131C2×C4×C83—41no—
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—81no—
142C2×C4×C83—81no—
143C2×C4×C83C4×D412yes—
144C2×C4×C83#12011yescharacteristic
145C2×C4×C83#12112yes—
146C2×C4×C83#12311yescharacteristic
147C83⋊C8—44no—
148C83⋊C8—44no—
149C22×C83—21no—
150C22×C83—21no—
151C22×C83—22no—
152C22×C83—42no—
153C22×C83—42no—
154C22×C83—41no—
155C22×C83—41no—
156C22×C83—41no—
157C22×C83—41no—
158C22×C83—41no—
159C22×C83—81no—
160C22×C83—81no—
161C22×C83#38611yescharacteristic
162C22×C83C2×#10411yescharacteristic
163C22×C83#42111yescharacteristic
164C4×C83—22no—
165C4×C83—21no—
166C4×C83—22no—
167C4×C83—41no—
168C4×C83—41no—
169C4×C83—42no—
170C4×C83—81no—
171C4×C83—81no—
172C4×C83—81no—
173C4×C83#45512yes—
174#9029—831nomaximal, Sylow
175C2×C83—21no—
176C2×C83—21no—
177C2×C83—42no—
178C2×C83—81no—
179C2×C83#187111yescharacteristic
180C2×C83#188511yescharacteristic
181C2×C83#189111yescharacteristic
182#2973—831no—
183#2398D8311yescharacteristic
184C4×#100—831no—
185#1491—832no—
186#1300—832no—
187C83#902911yescharacteristic, complemented, Sylow
188C2×C4×Q8C2×D8311yescharacteristic
189C2×C4×D4C2×D8311yescharacteristic
190#435—1664no—
191#432—832no—
192C2×#100—1661no—
193#407—1661no—
194C2×C22⋊C8—1661no—
195C4×M16—832no—
196#400—21no—
197#397Dic8311yescharacteristic
198#397Dic8311yescharacteristic
199#394—21no—
200#393Dic8311yescharacteristic
201#393Dic8311yescharacteristic
202C4×C22⋊C4—21no—
203C4×C22⋊C4—21no—
204#376C2×D8311yescharacteristic
205#343—1661no—
206Q8⋊C8—1664no—
207C22×Q8C2×Dic8311yescharacteristic
208C22×D4C22⋊D8311yescharacteristic
209C23×C4C22⋊D8311yescharacteristic
210C23×C4C22⋊D8311yescharacteristic
211C2×M16—1662no—
212C2×M16—1662no—
213C22×C8—1662no—
214C4×Q8—22no—
215C4×Q8—22no—
216C4×D4—22no—
217C4×D4—22no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4C2×Dic8311yescharacteristic
220C2×C4⋊C4C22⋊D8311yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4C2×Dic8311yescharacteristic
226C2×C22⋊C4C2×Dic8311yescharacteristic
227C2×C42—21no—
228C2×C42—21no—
229C2×C42C22×D8311yescharacteristic
230C4⋊C8—834no—
231#100—1664no—
232C22⋊C8—1662no—
233C22⋊C8—1662no—
234C22⋊C8—1662no—
235#97—1662no—
236#97—1662no—
237C4×C8—1662no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95C2×Dic8311yescharacteristic
244#95C2×Dic8311yescharacteristic
245C24C22⋊Dic8311yescharacteristic
246C24C22⋊Dic8311yescharacteristic
247C2×Q8—22no—
248C2×Q8—42no—
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4C22⋊Dic8311yescharacteristic
263C22×C4C22⋊Dic8311yescharacteristic
264C22×C4C22×Dic8311yescharacteristic
265C22×C4C2×C22⋊D8311yescharacteristic
266C22×C4C2×C22⋊D8311yescharacteristic
267M16—3322no—
268M16—6642no—
269M16—1664no—
270C2×C8—3322no—
271C2×C8—6642no—
272C2×C8—1664no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—42no—
276C22⋊C4—22no—
277C22⋊C4—22no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C42—42no—
283C42—41no—
284C42—41no—
285C42D4×D8312yes—
286C42#1305058912yes—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23#1458171912yes—
297C23C2×C22⋊Dic8311yescharacteristic
298Q8—24no—
299Q8—42no—
300D4—44no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4D4×Dic8312yes—
326C2×C4#1458176011yescharacteristic
327C2×C4#1458176412yes—
328C2×C4#1458177311yescharacteristic
329C8—3324no—
330C8—3324no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—81no—
342C22—81no—
343C22#1912758111yescharacteristic
344C22C2×#1458171911yescharacteristic
345C22#1912771811yescharacteristic
346C4—21no—
347C4—22no—
348C4—22no—
349C4—41no—
350C4—41no—
351C4—42no—
352C4—81no—
353C4—81no—
354C4—81no—
355C4#1912787812yes—
356C2—21no—
357C2—21no—
358C2—42no—
359C2—81no—
360C2#2490776611yescharacteristic
361C2#2490785211yescharacteristic
362C2#2490788211yescharacteristic
subgroupG/H
centerC2×C4#14581760
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#2398C2
socleC22×C83#386
prime radicalC22×D4×C83D4
cosocleC2×C42×C83C23
hypercenter#2398D83
hypocenterC83#9029
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2398

Complements

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

NH ≅ G/Ntype
3. #24905910C2semidirect
4. #24905356C2semidirect
187. C83#9029semidirect

Maximal subgroups

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

subgroupindex
#249164922
C4×#145817092
#249059102
#249053562
C83×#23982
#902983