Finite Group Databasebeta

← #35298752

Subgroups — #35298752

Order 21248.

376 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1M16×Dic166C211yesmaximal, characteristic
2#24906218C211yesmaximal, characteristic
3#24905891C211yesmaximal, characteristic
4C2×#19127431C211yesmaximal, characteristic
5#24905360C211yesmaximal, characteristic
6#24905301C211yesmaximal, characteristic
7C83×#1950C211yesmaximal, characteristic
8C2×C4×Dic166C2211yescharacteristic
9#19127831—21no—
10#19127829—22no—
11C8×Dic166—21no—
12#19127754C2211yescharacteristic
13#19127725C2211yescharacteristic
14#19127724—21no—
15M16×Dic83—21no—
16C2×C4×C83⋊C8C2211yescharacteristic
17#19127451—22no—
18#19127431—21no—
19#19127431—21no—
20#19127431C411yescharacteristic
21#19127431C411yescharacteristic
22#19127431C411yescharacteristic
23#19127431C411yescharacteristic
24C2×#108×C83—21no—
25#423×C83C2211yescharacteristic
26C2×C4⋊C8×C83C2211yescharacteristic
27C4×M16×C83C2211yescharacteristic
28#341×C83—21no—
29C22×Dic166Q811yescharacteristic
30C2×#13050574—21no—
31C22×C83⋊C8—21no—
32C4×Dic166—21no—
33C4×Dic166—21no—
34C4×Dic166C2×C411yescharacteristic
35C4×Dic166C2×C411yescharacteristic
36C4×Dic166D411yescharacteristic
37C4×Dic166D411yescharacteristic
38C2×C4⋊Dic83Q811yescharacteristic
39C2×Dic83⋊C4—21no—
40C2×C4×Dic83—21no—
41C4⋊(C83⋊C8)—21no—
42C4⋊(C83⋊C8)—21no—
43C4⋊(C83⋊C8)D412yes—
44Dic83⋊C8—22no—
45Dic83⋊C8—22no—
46C22⋊(C83⋊C8)—21no—
47#14581702—22no—
48C4×C83⋊C8—21no—
49C4×C83⋊C8—21no—
50C4×C83⋊C8C2×C411yescharacteristic
51C4×C83⋊C8C2×C411yescharacteristic
52C8×Dic83—22no—
53C2×M16×C83—21no—
54C2×M16×C83D411yescharacteristic
55C2×M16×C83D411yescharacteristic
56C22×C8×C83—21no—
57C2×C42×C83C2311yescharacteristic
58#108×C83—42no—
59C4⋊C8×C83—21no—
60C4⋊C8×C83—21no—
61C4⋊C8×C83—21no—
62C4⋊C8×C83C2×C411yescharacteristic
63C4⋊C8×C83C2×C411yescharacteristic
64#97×C83—21no—
65C4×C8×C83—21no—
66C2×Dic166—22no—
67C2×Dic166—21no—
68C2×Dic166—41no—
69C2×Dic166C4⋊C411yescharacteristic
70C2×Dic166C4⋊C411yescharacteristic
71C22×Dic83—21no—
72C22×Dic83—21no—
73#13050574—41no—
74#13050574—41no—
75C2×C83⋊C8—21no—
76C2×C83⋊C8—21no—
77C2×C83⋊C8—22no—
78C2×C83⋊C8—42no—
79C2×C83⋊C8—41no—
80C4⋊Dic83—21no—
81C4⋊Dic83C4⋊C411yescharacteristic
82C4⋊Dic83C4⋊C411yescharacteristic
83Dic83⋊C4—21no—
84Dic83⋊C4—21no—
85Dic83⋊C4—21no—
86Dic83⋊C4—21no—
87C4×Dic83—21no—
88C4×Dic83—21no—
89C4×Dic83—21no—
90C4×Dic83—21no—
91C22×C4×C83C2×D411yescharacteristic
92C22×C4×C83C2×Q811yescharacteristic
93C22×C4×C83#4111yescharacteristic
94M16×C83—21no—
95M16×C83—21no—
96M16×C83—21no—
97M16×C83—41no—
98M16×C83—41no—
99M16×C83SD1612yes—
100C2×C8×C83—21no—
101C2×C8×C83—21no—
102C2×C8×C83—21no—
103C2×C8×C83—21no—
104C2×C8×C83—41no—
105C2×C8×C83—41no—
106C2×C8×C83—41no—
107C42×C83C22×C411yescharacteristic
108C42×C83C2×D411yescharacteristic
109C42×C83C2×D411yescharacteristic
110C42×C83#4111yescharacteristic
111C23×C83C22⋊Q811yescharacteristic
112C2×C4×C83—21no—
113C2×C4×C83—21no—
114C2×C4×C83—41no—
115C2×C4×C83C2×C4⋊C411yescharacteristic
116C2×C4×C83C4×D411yescharacteristic
117C2×C4×C83C4×D411yescharacteristic
118C2×C4×C83#12011yescharacteristic
119C2×C4×C83C22⋊Q811yescharacteristic
120C2×C4×C83#12311yescharacteristic
121C2×C4×C83C2×SD1611yescharacteristic
122C2×C4×C83#13511yescharacteristic
123C2×C4×C83#13711yescharacteristic
124C2×C4×C83#13711yescharacteristic
125C2×Dic83—21no—
126C2×Dic83—21no—
127C2×Dic83—21no—
128C2×Dic83—21no—
129C2×Dic83—42no—
130C2×Dic83—81no—
131Dic166—21no—
132Dic166—21no—
133Dic166—21no—
134Dic166—42no—
135Dic166#10812yescomplemented
136C8×C83—22no—
137C8×C83—41no—
138C8×C83—41no—
139C8×C83—41no—
140C8×C83—81no—
141C83⋊C8—22no—
142C83⋊C8—41no—
143C83⋊C8—42no—
144C83⋊C8—81no—
145C22×C83—21no—
146C22×C83—21no—
147C22×C83#38511yescharacteristic
148C22×C83#47511yescharacteristic
149C22×C83#47911yescharacteristic
150C4×C83—21no—
151C4×C83—21no—
152C4×C83—21no—
153C4×C83C2×#10811yescharacteristic
154C4×C83#43011yescharacteristic
155C4×C83C4×SD1611yescharacteristic
156C4×C83#44111yescharacteristic
157C4×C83#44811yescharacteristic
158C4×C83#45211yescharacteristic
159Dic83—22no—
160Dic83—41no—
161Dic83—41no—
162Dic83—41no—
163#8909—831nomaximal, Sylow
164C2×C83—21no—
165C2×C83—21no—
166C2×C83#185511yescharacteristic
167C2×C83#186111yescharacteristic
168C2×C83#186511yescharacteristic
169Q8×M16—831no—
170#1950D8311yescharacteristic
171#1566—831no—
172#1487—831no—
173C2×Q8⋊C8—831no—
174#1301—831no—
175#1278—831no—
176C83#890911yescharacteristic, complemented, Sylow
177C2×C4×Q8—831no—
178#446—1661no—
179#446—1662no—
180C8×Q8—1661no—
181#431—831no—
182C2×#108—21no—
183#423—831no—
184#423—1661no—
185#423C2×D8311yescharacteristic
186C2×C4⋊C8C2×D8311yescharacteristic
187C4×M16—1661no—
188C4×M16C2×D8311yescharacteristic
189C2×C4×C8—831no—
190#341—21no—
191#334—1662no—
192Q8⋊C8—831no—
193Q8⋊C8—831no—
194Q8⋊C8—831no—
195Q8⋊C8—831no—
196Q8⋊C8—1661no—
197Q8⋊C8—1661no—
198C22×Q8—831no—
199C2×M16—21no—
200C2×M16—1661no—
201C2×M16C22⋊D8311yescharacteristic
202C2×M16C22⋊D8311yescharacteristic
203C22×C8—21no—
204C22×C8—1661no—
205C4×Q8—831no—
206C4×Q8—831no—
207C4×Q8—831no—
208C4×Q8—831no—
209C4×Q8—1661no—
210C4×Q8—1661no—
211C2×C4⋊C4—831no—
212C2×C4⋊C4—1661no—
213C2×C42—1661no—
214C2×C42C22×D8311yescharacteristic
215#108—42no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—832no—
220C4⋊C8—1662no—
221C4⋊C8—1662no—
222C4⋊C8—1661no—
223C4⋊C8—1661no—
224C4⋊C8C4×D8311yescharacteristic
225C4⋊C8C4×D8311yescharacteristic
226C22⋊C8—1661no—
227#97—21no—
228#97—1662no—
229C4×C8—21no—
230C4×C8—831no—
231C4×C8—831no—
232C4×C8—1662no—
233C4×C8—1661no—
234C4×C8—1661no—
235C2×Q8—3321no—
236C2×Q8—831no—
237C2×Q8—831no—
238C2×Q8—1662no—
239C2×Q8—1661no—
240C22×C4—1661no—
241C22×C4—1661no—
242C22×C4C2×C22⋊D8311yescharacteristic
243C22×C4Q8×D8311yescharacteristic
244C22×C4#1305059111yescharacteristic
245M16—21no—
246M16—21no—
247M16—21no—
248M16—41no—
249M16—41no—
250M16—3321no—
251M16—3321no—
252M16#1305057812yes—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—3322no—
261C2×C8—3321no—
262C2×C8—1662no—
263C2×C8—1661no—
264C2×C8—1661no—
265C4⋊C4—831no—
266C4⋊C4—831no—
267C4⋊C4—1661no—
268C4⋊C4—1661no—
269C4⋊C4—1661no—
270C4⋊C4—1661no—
271C4⋊C4—1661no—
272C42—1661no—
273C42—1661no—
274C42—1661no—
275C42—1661no—
276C42C2×C4×D8311yescharacteristic
277C42D4×D8311yescharacteristic
278C42D4×D8311yescharacteristic
279C42#1305059011yescharacteristic
280C23#1458176811yescharacteristic
281Q8—3322no—
282Q8—832no—
283Q8—1661no—
284Q8—1661no—
285Q8—1661no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—3322no—
290C2×C4—6641no—
291C2×C4—1661no—
292C2×C4—1661no—
293C2×C4—1661no—
294C2×C4—1661no—
295C2×C4C4⋊C4×D8311yescharacteristic
296C2×C4C4×C22⋊D8311yescharacteristic
297C2×C4#1458175411yescharacteristic
298C2×C4#1458176011yescharacteristic
299C2×C4#1458177011yescharacteristic
300C2×C4#1458177711yescharacteristic
301C2×C4C2×#1305057811yescharacteristic
302C2×C4#1458181211yescharacteristic
303C2×C4#1458182211yescharacteristic
304C2×C4#1458182311yescharacteristic
305C8—22no—
306C8—41no—
307C8—41no—
308C8—41no—
309C8—81no—
310C8—3321no—
311C8—3322no—
312C8—6641no—
313C8—1662no—
314C22—21no—
315C22—21no—
316C22#1912757211yescharacteristic
317C22#1912798311yescharacteristic
318C22#1912800511yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—3321no—
323C4—3321no—
324C4—3321no—
325C4—1662no—
326C4#108×D8311yescharacteristic
327C4#1912774811yescharacteristic
328C4C4×#1305057811yescharacteristic
329C4#1912780611yescharacteristic
330C4#1912783911yescharacteristic
331C4#1912786111yescharacteristic
332C2—21no—
333C2—21no—
334C2#2490766611yescharacteristic
335C2#2490770011yescharacteristic
336C2#2490773011yescharacteristic
subgroupG/H
centerC2×C4#14581760
commutatorC42×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1950C2
socleC22×C83#385
prime radicalC23×C83C22⋊Q8
cosocleC2×C42×C83C23
hypercenter#1950D83
hypocenterC83#8909
LCSG ▷ C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
135. Dic166#108semidirect
176. C83#8909semidirect

Maximal subgroups

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

subgroupindex
M16×Dic1662
#249062182
#249058912
C2×#191274312
#249053602
#249053012
C83×#19502
#890983