Finite Group Databasebeta

← #35320552

Subgroups — #35320552

Order 21248.

396 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D83C211yesmaximal, characteristic
2C2×#19127524C211yesmaximal, characteristic, complemented
3#24907498C211yesmaximal, characteristic
4#24907485C211yesmaximal, characteristic
5#24905563C211yesmaximal, characteristic, complemented
6#24905561C211yesmaximal, characteristic, complemented
7C2×#365×C83C211yesmaximal, characteristic, complemented
8C22×C8×D83C2211yescharacteristic
9C2×#14581732C2211yescharacteristic
10C2×#14581731C412yescomplemented
11M32×D83—22no—
12M32×D83—22no—
13C2×C16×D83C412yescomplemented
14C2×#14581728C2211yescharacteristic
15C2×#14581724C2211yescharacteristic
16#19127664—21no—
17#19127558—21no—
18#19127524—22no—
19#19127465—21no—
20#19127463—21no—
21C2×M32×C83C2211yescharacteristic
22C2×#108×C83C2211yescharacteristic
23C2×#106×C83C2211yescharacteristic
24#365×C83—22no—
25C22×C4×D83D411yescharacteristic
26C2×#13050574—21no—
27C22×C83⋊C8D411yescharacteristic
28C2×C8×D83—21no—
29C2×C8×D83—21no—
30C2×C8×D83—21no—
31C2×C8×D83—21no—
32C2×C8×D83C2×C411yescharacteristic
33C2×C8×D83C2×C411yescharacteristic
34C2×C8×D83Q811yescharacteristic
35C2×C8×D83Q811yescharacteristic
36C2×C4⋊Dic83—21no—
37C2×(C2×D83)⋊C4—41no—
38#14581732—21no—
39#14581732—21no—
40#14581731—24no—
41C2×C83⋊C16C2×C412yes—
42C16×D83—24no—
43#14581728—21no—
44#14581728—21no—
45#14581724—21no—
46#14581724—21no—
47(C2×D83)⋊C8—41no—
48(C2×D83)⋊C8—41no—
49C83⋊#95—41no—
50C2×M16×C83—21no—
51C22×C8×C83C2311yescharacteristic
52C2×C4⋊C4×C83—21no—
53M32×C83D412yes—
54M32×C83D412yes—
55C2×C16×C83C2×C412yes—
56#108×C83—21no—
57#108×C83—21no—
58#106×C83—21no—
59#106×C83—21no—
60C23×D83SD1611yescharacteristic
61C22×Dic83—41no—
62C22×Dic83SD1611yescharacteristic
63C2×C4×D83—21no—
64C2×C4×D83—21no—
65C2×C4×D83—21no—
66C2×C4×D83—21no—
67C2×C4×D83C4⋊C411yescharacteristic
68C2×C4×D83C4⋊C411yescharacteristic
69C2×C4×D83SD1611yescharacteristic
70C2×C4×D83SD1611yescharacteristic
71#13050574—41no—
72#13050574—41no—
73C2×C83⋊C8—21no—
74C2×C83⋊C8—21no—
75C2×C83⋊C8—41no—
76C2×C83⋊C8C4⋊C411yescharacteristic
77C2×C83⋊C8C4⋊C411yescharacteristic
78C8×D83—21no—
79C8×D83—21no—
80C8×D83—21no—
81C8×D83—21no—
82C8×D83—21no—
83C8×D83—21no—
84C8×D83—21no—
85C8×D83—21no—
86C4⋊Dic83—41no—
87C4⋊Dic83—41no—
88(C2×D83)⋊C4—82no—
89C83⋊C16—22no—
90C22×C4×C83—41no—
91C22×C4×C83C2×D411yescharacteristic
92M16×C83—41no—
93M16×C83—41no—
94C2×C8×C83—41no—
95C2×C8×C83C22×C411yescharacteristic
96C2×C8×C83C2×D411yescharacteristic
97C2×C8×C83C2×D411yescharacteristic
98C2×C8×C83C2×Q811yescharacteristic
99C2×C8×C83#4111yescharacteristic
100C2×C8×C83#4111yescharacteristic
101C4⋊C4×C83—41no—
102C4⋊C4×C83—41no—
103C16×C83C22⋊C414yescomplemented
104C23×C83C2×SD1611yescharacteristic
105C22×D83—21no—
106C22×D83—21no—
107C22×D83—22no—
108C22×D83—41no—
109C22×D83#10611yescharacteristic
110C22×D83#10611yescharacteristic
111C2×C4×C83—81no—
112C2×C4×C83—81no—
113C2×C4×C83—81no—
114C2×C4×C83C2×C4⋊C411yescharacteristic
115C2×C4×C83#12111yescharacteristic
116C2×C4×C83#12111yescharacteristic
117C2×C4×C83C2×SD1611yescharacteristic
118C2×C4×C83#13511yescharacteristic
119C2×C4×C83#13511yescharacteristic
120C2×Dic83—21no—
121C2×Dic83—21no—
122C2×Dic83—81no—
123C2×Dic83—81no—
124C2×Dic83—81no—
125C2×Dic83#10611yescharacteristic
126C2×Dic83#10611yescharacteristic
127C4×D83—21no—
128C4×D83—21no—
129C4×D83—21no—
130C4×D83—21no—
131C4×D83—21no—
132C4×D83—21no—
133C4×D83—21no—
134C4×D83—21no—
135C8×C83—81no—
136C8×C83C2×C22⋊C411yescharacteristic
137C8×C83#11711yescharacteristic
138C8×C83C22⋊Q811yescharacteristic
139C8×C83C22⋊Q811yescharacteristic
140C83⋊C8—21no—
141C83⋊C8—21no—
142C83⋊C8—81no—
143C22×C83—21no—
144C22×C83—21no—
145C22×C83C2×#10611yescharacteristic
146C22×C83#46511yescharacteristic
147C22×C83#46511yescharacteristic
148C2×D83—21no—
149C2×D83—21no—
150C2×D83—21no—
151C2×D83—21no—
152C2×D83—21no—
153C2×D83—42no—
154C2×D83—42no—
155C2×D83#36512yescomplemented
156C4×C83—161no—
157C4×C83#38011yescharacteristic
158C4×C83#42711yescharacteristic
159C4×C83#46511yescharacteristic
160C4×C83#46511yescharacteristic
161Dic83—21no—
162Dic83—21no—
163Dic83—161no—
164#12831—831nomaximal, Sylow
165C2×C83—21no—
166C2×C83—21no—
167C2×C83#180711yescharacteristic
168C2×C83C2×#36511yescharacteristic
169C2×C83#215511yescharacteristic
170D83—22no—
171D83—41no—
172C22×M32—831no—
173C2×#365—831no—
174C2×#365D8311yescharacteristic, complemented
175#1810—831no—
176#1807—831no—
177#1383—831no—
178#1383—831no—
179C83#1283111yescharacteristic, complemented, Sylow
180C23×C8—831no—
181C2×M32—831no—
182C2×M32—832no—
183C2×M32—1662no—
184C2×M32—1662no—
185C2×M32C2×D8311yescharacteristic
186C22×C16—832no—
187C2×#108—831no—
188C2×#108C2×D8311yescharacteristic
189C2×#106—831no—
190C2×#106C2×D8311yescharacteristic
191#407—1661no—
192#380—1661no—
193#365—22no—
194#365—1662no—
195#341—1661no—
196#340—1661no—
197C23×C4—831no—
198C2×M16—21no—
199C2×M16—1661no—
200C22×C8—831no—
201C22×C8—831no—
202C22×C8—831no—
203C22×C8—831no—
204C22×C8—831no—
205C22×C8—1661no—
206C22×C8—1661no—
207C22×C8—1661no—
208C22×C8—1661no—
209C22×C8C22×D8311yescharacteristic
210C2×C4⋊C4—21no—
211C2×C4⋊C4—1661no—
212C2×C22⋊C4—3321no—
213M32—1661no—
214M32—1661no—
215M32—1664no—
216M32D33212yes—
217M32C22⋊D8312yes—
218C2×C16—832no—
219C2×C16—1664no—
220C2×C16C4×D8312yes—
221#108—21no—
222#108—21no—
223#108—1661no—
224#108—1661no—
225#106—21no—
226#106—21no—
227#106—1661no—
228#106—1661no—
229C22⋊C8—3321no—
230C22⋊C8—3321no—
231#95—3321no—
232C24—831no—
233C22×C4—41no—
234C22×C4—3321no—
235C22×C4—831no—
236C22×C4—831no—
237C22×C4—831no—
238C22×C4—831no—
239C22×C4—831no—
240C22×C4—1661no—
241C22×C4—1661no—
242C22×C4—1661no—
243C22×C4—1661no—
244C22×C4D4×D8311yescharacteristic
245M16—41no—
246M16—41no—
247M16—3321no—
248M16—3321no—
249C2×C8—41no—
250C2×C8—3321no—
251C2×C8—831no—
252C2×C8—831no—
253C2×C8—1661no—
254C2×C8—1661no—
255C2×C8—1661no—
256C2×C8—1661no—
257C2×C8—1661no—
258C2×C8—1661no—
259C2×C8—1661no—
260C2×C8—1661no—
261C2×C8—1661no—
262C2×C8—1661no—
263C2×C8C2×C4×D8311yescharacteristic
264C2×C8C2×C22⋊D8311yescharacteristic
265C2×C8C2×D33211yescharacteristic
266C2×C8Q8×D8311yescharacteristic
267C2×C8#1305058911yescharacteristic
268C2×C8#1305059111yescharacteristic
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—3321no—
272C4⋊C4—3321no—
273C22⋊C4—6642no—
274C16—1662no—
275C16(C2×D83)⋊C414yescomplemented
276C23—3321no—
277C23—831no—
278C23—831no—
279C23—1662no—
280C23—1661no—
281C23—1661no—
282C23SD16×D8311yescharacteristic
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—831no—
287C2×C4—831no—
288C2×C4—6641no—
289C2×C4—6641no—
290C2×C4—6641no—
291C2×C4—1661no—
292C2×C4—1661no—
293C2×C4—1661no—
294C2×C4—1661no—
295C2×C4—1661no—
296C2×C4—1661no—
297C2×C4—1661no—
298C2×C4—1661no—
299C2×C4—1661no—
300C2×C4—1661no—
301C2×C4C4⋊C4×D8311yescharacteristic
302C2×C4#1458176311yescharacteristic
303C2×C4#1458176711yescharacteristic
304C2×C4SD16×D8311yescharacteristic
305C2×C4#1458181311yescharacteristic
306C2×C4#1458181311yescharacteristic
307C8—81no—
308C8—6641no—
309C8—1661no—
310C8—1661no—
311C8C2×(C2×D83)⋊C411yescharacteristic
312C8#1458175011yescharacteristic
313C8#1458176811yescharacteristic
314C8#1458177211yescharacteristic
315C22—21no—
316C22—21no—
317C22—3322no—
318C22—3322no—
319C22—832no—
320C22—1661no—
321C22—1661no—
322C22—1661no—
323C22—1661no—
324C22—1661no—
325C22#106×D8311yescharacteristic
326C22#1912792711yescharacteristic
327C22#1912793111yescharacteristic
328C4—161no—
329C4—13281no—
330C4—1661no—
331C4—1661no—
332C4#1912755811yescharacteristic
333C4#1912773611yescharacteristic
334C4#1912792711yescharacteristic
335C4#1912793111yescharacteristic
336C2—21no—
337C2—21no—
338C2—3321no—
339C2—1662no—
340C2#2490748511yescharacteristic
341C2#365×D8311yescharacteristic
342C2#2490923411yescharacteristic
subgroupG/H
centerC22#106×D83
commutatorC2×C8×C83C22×C4
FrattiniC22×C8C22×D83
FittingC2×#365×C83C2
socleC22×C83C2×#106
prime radicalC23×D83SD16
cosocleC22×C8×C83C23
hypercenterC2×#365D83
hypocenterC83#12831
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

Complements

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

NH ≅ G/Ntype
2. C2×#19127524C2semidirect
5. #24905563C2semidirect
6. #24905561C2semidirect
7. C2×#365×C83C2semidirect
10. C2×#14581731C4semidirect
13. C2×C16×D83C4semidirect
103. C16×C83C22⋊C4semidirect
155. C2×D83#365semidirect
174. C2×#365D83semidirect
179. C83#12831semidirect
275. C16(C2×D83)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D832
C2×#191275242
#249074982
#249074852
#249055632
#249055612
C2×#365×C832
#1283183