Finite Group Databasebeta

← #35303511

Subgroups — #35303511

Order 21248.

486 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24915840C211yesmaximal, characteristic
2#24907614C211yesmaximal, characteristic
3#24907318C211yesmaximal, characteristic
4C2×#19127448C211yesmaximal, characteristic
5C2×#19127447C211yesmaximal, characteristic
6C2×#19127446C211yesmaximal, characteristic
7C2×#332×C83C211yesmaximal, characteristic
8C2×#14581792C2211yescharacteristic
9C2×C4⋊(C83⋊C8)C2211yescharacteristic
10C2×C4⋊(C83⋊C8)C2211yescharacteristic
11C2×Dic83⋊C8—22no—
12C2×#14581702—21no—
13#19127608—21no—
14#19127608—21no—
15#19127606—22no—
16#19127566C414yes—
17C42×Dic83C2211yescharacteristic
18#19127455—21no—
19#19127448—22no—
20#19127447—22no—
21#19127446—22no—
22C2×C4⋊Q8×C83C2211yescharacteristic
23C2×C4⋊C8×C83C2211yescharacteristic
24C2×C4⋊C8×C83C2211yescharacteristic
25#332×C83—22no—
26C22×Dic166—21no—
27C22×C83⋊C8—21no—
28C22×C83⋊C8—21no—
29#14581792—21no—
30#14581792—21no—
31#14581792—21no—
32#14581792—21no—
33C2×C4⋊Dic83—21no—
34C2×C4⋊Dic83C2×C412yes—
35C2×C4×Dic83C2×C412yes—
36C2×C4×Dic83D412yes—
37C2×C4×Dic83D411yescharacteristic
38C2×C4×Dic83D411yescharacteristic
39C4⋊(C83⋊C8)—21no—
40C4⋊(C83⋊C8)—21no—
41C4⋊(C83⋊C8)—21no—
42C4⋊(C83⋊C8)D412yes—
43Dic83⋊C8—44no—
44#14581702—42no—
45C83⋊#95—24no—
46C83⋊#95—24no—
47C22×Q8×C83—21no—
48C22×C8×C83—21no—
49C22×C8×C83—21no—
50C4⋊Q8×C83—21no—
51C4⋊Q8×C83—21no—
52C4⋊Q8×C83—21no—
53C4⋊Q8×C83—21no—
54C2×C4⋊C4×C83—21no—
55C2×C4⋊C4×C83C2×C412yes—
56C2×C42×C83C2311yescharacteristic
57C4⋊C8×C83—21no—
58C4⋊C8×C83—21no—
59C4⋊C8×C83—21no—
60C4⋊C8×C83D412yes—
61C2×Dic166—41no—
62C2×Dic166—41no—
63C2×Dic166—42no—
64C2×Dic166—42no—
65C22×Dic83—22no—
66C22×Dic83C22⋊C412yes—
67C22×Dic83C22⋊C412yes—
68C2×C83⋊C8—22no—
69C2×C83⋊C8—41no—
70C2×C83⋊C8—41no—
71C2×C83⋊C8—41no—
72C2×C83⋊C8—42no—
73C4⋊Dic83—22no—
74C4⋊Dic83—22no—
75C4⋊Dic83—41no—
76C4⋊Dic83—41no—
77C4×Dic83—21no—
78C4×Dic83—21no—
79C4×Dic83—21no—
80C4×Dic83—22no—
81C4×Dic83—21no—
82C4×Dic83—22no—
83C4×Dic83—24no—
84C2×Q8×C83—41no—
85C2×Q8×C83—41no—
86C2×Q8×C83—41no—
87C2×Q8×C83—41no—
88C2×Q8×C83—41no—
89C2×Q8×C83—41no—
90C22×C4×C83—22no—
91C22×C4×C83C22×C411yescharacteristic
92C22×C4×C83C2×D411yescharacteristic
93C22×C4×C83C2×D411yescharacteristic
94C2×C8×C83—22no—
95C2×C8×C83—41no—
96C2×C8×C83—41no—
97C2×C8×C83—41no—
98C2×C8×C83—42no—
99C4⋊C4×C83—22no—
100C4⋊C4×C83—22no—
101C4⋊C4×C83—41no—
102C4⋊C4×C83—41no—
103C42×C83C2×D411yescharacteristic
104C42×C83C2×D411yescharacteristic
105C42×C83#4111yescharacteristic
106C42×C83#4111yescharacteristic
107C23×C83C2×C22⋊C411yescharacteristic
108Q8×C83—81no—
109Q8×C83—81no—
110Q8×C83—81no—
111Q8×C83—81no—
112C2×C4×C83—22no—
113C2×C4×C83—42no—
114C2×C4×C83—42no—
115C2×C4×C83—42no—
116C2×C4×C83C4×D411yescharacteristic
117C2×C4×C83C4×D411yescharacteristic
118C2×C4×C83#12111yescharacteristic
119C2×C4×C83#12111yescharacteristic
120C2×C4×C83#12411yescharacteristic
121C2×C4×C83#12711yescharacteristic
122C2×C4×C83#13511yescharacteristic
123C2×C4×C83#13511yescharacteristic
124C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C83AGL(1,ℤ/8)12yes—
126C2×C4×C83#13711yescharacteristic
127C2×C4×C83#13712yes—
128C2×Dic83—22no—
129C2×Dic83—22no—
130C2×Dic83—22no—
131C2×Dic83—22no—
132C2×Dic83—22no—
133C2×Dic83—42no—
134C2×Dic83—44no—
135C2×Dic83#10114yes—
136Dic166—82no—
137Dic166—81no—
138Dic166—81no—
139C8×C83—42no—
140C8×C83—81no—
141C83⋊C8—42no—
142C83⋊C8—81no—
143C22×C83#39011yescharacteristic
144C22×C83C2×#10112yes—
145C22×C83#41611yescharacteristic
146C22×C83#41711yescharacteristic
147C22×C83#41712yes—
148C4×C83—21no—
149C4×C83—21no—
150C4×C83—82no—
151C4×C83#46311yescharacteristic
152C4×C83#46311yescharacteristic
153C4×C83#46411yescharacteristic
154C4×C83#46411yescharacteristic
155C4×C83#48912yes—
156C4×C83#49611yescharacteristic
157C4×C83#49711yescharacteristic
158Dic83—24no—
159Dic83—42no—
160Dic83—82no—
161#9708—831nomaximal, Sylow
162C2×C83#155212yes—
163C2×C83#156112yes—
164C2×C83#195911yescharacteristic
165C2×C83#196611yescharacteristic
166C2×C83#198311yescharacteristic
167#2862—831no—
168#1842—831no—
169#1767—831no—
170C2×#332—831no—
171C2×#332—831no—
172C2×#332—831no—
173C2×#332D8311yescharacteristic
174C83#970811yescharacteristic, complemented, Sylow
175C2×C4⋊Q8—831no—
176C2×C4⋊Q8C2×D8311yescharacteristic
177C2×C4⋊C8—831no—
178C2×C4⋊C8—831no—
179C2×C4⋊C8—1662no—
180C2×C4⋊C8C2×D8311yescharacteristic
181C2×C4⋊C8C2×D8311yescharacteristic
182C2×#97—1661no—
183#391—1662no—
184#391—1661no—
185#391—1661no—
186#382—834no—
187C43—831no—
188#336—1661no—
189#332—22no—
190#332—1662no—
191#332—1662no—
192#332—1662no—
193C22×Q8—21no—
194C22×Q8—1661no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—1661no—
198C22×C8—1661no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—1661no—
204C4⋊Q8—1661no—
205C4⋊Q8—1661no—
206C4⋊Q8—1661no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—832no—
209C2×C4⋊C4—1661no—
210C2×C4⋊C4C4×D8312yes—
211C2×C42—832no—
212C2×C42—831no—
213C2×C42—831no—
214C2×C42—832no—
215C2×C42C22×D8311yescharacteristic
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—3324no—
220C4⋊C8—832no—
221C4⋊C8—1661no—
222C4⋊C8—1661no—
223C4⋊C8—1661no—
224C4⋊C8C22⋊D8312yes—
225#97—3322no—
226#95—1664no—
227#95—1664no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—3321no—
235C2×Q8—3321no—
236C2×Q8—3322no—
237C2×Q8—3322no—
238C22×C4—22no—
239C22×C4—832no—
240C22×C4—832no—
241C22×C4—1662no—
242C22×C4C2×C4×D8311yescharacteristic
243C22×C4D4×D8311yescharacteristic
244C22×C4D4×D8311yescharacteristic
245C2×C8—22no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—42no—
250C2×C8—3321no—
251C2×C8—3321no—
252C2×C8—3321no—
253C2×C8—3322no—
254C2×C8—1662no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—3321no—
260C4⋊C4—3321no—
261C4⋊C4—1662no—
262C4⋊C4—1662no—
263C42—1664no—
264C42—1661no—
265C42—1661no—
266C42—1661no—
267C42—1662no—
268C42—1661no—
269C42—1662no—
270C42D4×D8311yescharacteristic
271C42C2×C22⋊D8311yescharacteristic
272C42#1305058911yescharacteristic
273C42#1305059011yescharacteristic
274C23C22⋊C4×D8311yescharacteristic
275Q8—81no—
276Q8—81no—
277Q8—81no—
278Q8—81no—
279Q8—6641no—
280Q8—6641no—
281Q8—6642no—
282C2×C4—22no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—3322no—
287C2×C4—3324no—
288C2×C4—834no—
289C2×C4—1662no—
290C2×C4—1662no—
291C2×C4—1662no—
292C2×C4—1662no—
293C2×C4—1662no—
294C2×C4(C22⋊D83)⋊C411yescharacteristic
295C2×C4C4×C22⋊D8311yescharacteristic
296C2×C4#1458176411yescharacteristic
297C2×C4#1458176511yescharacteristic
298C2×C4#1458177811yescharacteristic
299C2×C4#1458178811yescharacteristic
300C2×C4#1458181111yescharacteristic
301C2×C4#1458181311yescharacteristic
302C2×C4#1458181611yescharacteristic
303C2×C4#1458181912yes—
304C2×C4#1458182111yescharacteristic
305C2×C4#1458182412yes—
306C8—42no—
307C8—81no—
308C8—3322no—
309C8—6641no—
310C22#1912760111yescharacteristic
311C22#101×D8312yes—
312C22#1912769411yescharacteristic
313C22#1912769911yescharacteristic
314C22#1912770112yes—
315C4—21no—
316C4—21no—
317C4—82no—
318C4—3322no—
319C4—6642no—
320C4—1664no—
321C4#1912791411yescharacteristic
322C4#1912791511yescharacteristic
323C4#1912792111yescharacteristic
324C4#1912792211yescharacteristic
325C4#1912806212yes—
326C4#1912808711yescharacteristic
327C4#1912809411yescharacteristic
328C2#2490616012yes—
329C2#2490619912yes—
330C2#2490827611yescharacteristic
331C2#2490830511yescharacteristic
332C2#2490839411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D83
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC2×#332×C83C2
socle, prime radicalC23×C83C2×C22⋊C4
cosocleC2×C42×C83C23
hypercenterC2×#332D83
hypocenterC83#9708
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
174. C83#9708semidirect

Maximal subgroups

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

subgroupindex
#249158402
#249076142
#249073182
C2×#191274482
C2×#191274472
C2×#191274462
C2×#332×C832
#970883