Finite Group Databasebeta

← #32995880

Subgroups — #32995880

Order 18688.

328 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 93 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#22618896C211yesmaximal, characteristic
2#22611732C211yesmaximal, characteristic, complemented
3C4⋊C16×D73C211yesmaximal, characteristic, complemented
4#22607913C211yesmaximal, characteristic, complemented
5#22607890C211yesmaximal, characteristic, complemented
6#22607888C211yesmaximal, characteristic, complemented
7C73×#1338C211yesmaximal, characteristic, complemented
8C4×#11924029C411yescharacteristic
9C2×C16×D73—21no—
10#17988718C411yescharacteristic
11#17988666C2211yescharacteristic
12#17988664C411yescharacteristic
13#17988660—21no—
14#17988657—21no—
15#17988639—21no—
16#17988639C411yescharacteristic
17#17988539—21no—
18C4×C8×D73C2211yescharacteristic
19C4⋊#11924003C2211yescharacteristic
20#17988405—21no—
21#17988405—21no—
22#17988366—21no—
23#17988363C2211yescharacteristic
24#446×C73C2211yescharacteristic
25C4⋊C16×C73C2211yescharacteristic
26#346×C73C2211yescharacteristic
27C2×#11924029C811yescharacteristic
28C2×#11924011—21no—
29C2×#11924011—21no—
30C2×C8×D73D411yescharacteristic
31C2×C8×D73D411yescharacteristic
32Q8×Dic73C811yescharacteristic
33C4×D292—21no—
34C4×D292C2×C411yescharacteristic
35#14556553—21no—
36#14556553C811yescharacteristic
37#14556549—21no—
38#14556549C811yescharacteristic
39C42×D73—21no—
40C42×D73C2×C411yescharacteristic
41C2×#11924003—21no—
42C2×#11924003—21no—
43C16×D73—42no—
44C4⋊#10596831—21no—
45C4⋊#10596831C2×C411yescharacteristic
46#14556503—21no—
47#14556503—21no—
48#14556503—21no—
49#14556502—21no—
50C4×#10596831C2×C411yescharacteristic
51C8×Dic73—21no—
52C8×Dic73D411yescharacteristic
53C8×Dic73D411yescharacteristic
54C4×Q8×C73C2×C411yescharacteristic
55C2×C16×C73—21no—
56C2×C16×C73—21no—
57C4⋊C8×C73—21no—
58C4⋊C8×C73C2×C411yescharacteristic
59#97×C73—21no—
60C4×C8×C73C2311yescharacteristic
61#11924029—42no—
62C2×D292—21no—
63C2×D292C2×C811yescharacteristic
64C2×C4×D73—21no—
65C2×C4×D73—21no—
66C2×C4×D73—21no—
67C2×C4×D73C22⋊C411yescharacteristic
68C2×C4×D73C2×C811yescharacteristic
69C2×C4×D73M1611yescharacteristic
70#11924011—42no—
71#11924011—41no—
72#11924011—41no—
73C2×#10596831—21no—
74C2×#10596831C22⋊C411yescharacteristic
75C2×#10596831C22⋊C411yescharacteristic
76C8×D73—21no—
77C8×D73—21no—
78C8×D73—41no—
79C4⋊Dic73—21no—
80C4⋊Dic73C2×C811yescharacteristic
81#11924005—21no—
82#11924005—21no—
83#11924005—21no—
84C4×Dic73—21no—
85C4×Dic73—21no—
86C4×Dic73C22⋊C411yescharacteristic
87C4×Dic73C2×C811yescharacteristic
88C4×Dic73M1611yescharacteristic
89#11924003—41no—
90#11924003—41no—
91C2×Q8×C73C2×C811yescharacteristic
92C2×C8×C73—21no—
93C2×C8×C73C2×D411yescharacteristic
94C2×C8×C73C2×D411yescharacteristic
95C4⋊C4×C73—21no—
96C4⋊C4×C73C2×C811yescharacteristic
97C42×C73—21no—
98C42×C73C22×C411yescharacteristic
99C16×C73—41no—
100C16×C73—41no—
101C22×D73—21no—
102C22×D73C22⋊C811yescharacteristic
103Q8×C73—41no—
104C2×C4×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73C2×C22⋊C411yescharacteristic
107C2×C4×C73C22×C811yescharacteristic
108C2×C4×C73C2×M1611yescharacteristic
109C2×Dic73—21no—
110C2×Dic73C22⋊C811yescharacteristic
111C2×Dic73C22⋊C811yescharacteristic
112C2×Dic73C22⋊C811yescharacteristic
113D292—41no—
114D292—42no—
115C4×D73—22no—
116C4×D73—21no—
117C4×D73—21no—
118C4×D73—22no—
119C4×D73—42no—
120C4×D73—41no—
121C4×D73—41no—
122C4×D73—42no—
123C8×C73—21no—
124C8×C73—41no—
125C8×C73AGL(1,ℤ/8)11yescharacteristic
126C8×C73#13711yescharacteristic
127#10596831—21no—
128#10596831—21no—
129#10596831—41no—
130C22×C73C2×C22⋊C811yescharacteristic
131C2×D73—21no—
132C2×D73—21no—
133C2×D73—41no—
134C2×D73—41no—
135C2×D73—41no—
136C2×D73#34912yes—
137C4×C73—21no—
138C4×C73—21no—
139C4×C73—41no—
140C4×C73—41no—
141C4×C73#41711yescharacteristic
142C4×C73#42111yescharacteristic
143Dic73—21no—
144Dic73—21no—
145Dic73—41no—
146Dic73#35012yes—
147#11626—731nomaximal, Sylow
148C2×C73#147711yescharacteristic
149C2×C73C2×#34911yescharacteristic
150C2×C73C2×#35011yescharacteristic
151D73—22no—
152D73—81no—
153#2965—731no—
154#2163—731no—
155C2×C4⋊C16—731no—
156#1338—731no—
157#1338D7311yescharacteristic, complemented
158#1330—731no—
159#1330—731no—
160C73#1162611yescharacteristic, complemented, Sylow
161C4×#41—731no—
162C22×C16—1461no—
163#446—731no—
164#446C2×D7311yescharacteristic
165#436—731no—
166#436—731no—
167#435—1461no—
168#435—1461no—
169#431—731no—
170#431—1461no—
171C4×M16—1461no—
172C2×C4×C8—731no—
173C4⋊C16—731no—
174C4⋊C16—1461no—
175C4⋊C16—1461no—
176C4⋊C16C2×D7311yescharacteristic
177C22⋊C16—1461no—
178#346—731no—
179#346C2×D7311yescharacteristic
180C2×#41—731no—
181C2×M16—1461no—
182C2×M16—1461no—
183C22×C8—731no—
184C22×C8—731no—
185C4×Q8—731no—
186C4×Q8C4×D7311yescharacteristic
187C4×D4—731no—
188C4×D4—731no—
189C4×D4—1461no—
190C4×D4—1461no—
191#117—731no—
192#117—1461no—
193C2×C42—731no—
194C2×C42—1461no—
195C2×C16—21no—
196C2×C16—21no—
197C2×C16—2922no—
198C2×C16—1461no—
199C2×C16—1461no—
200C4⋊C8—21no—
201C4⋊C8—731no—
202C4⋊C8—1461no—
203C4⋊C8C4×D7311yescharacteristic
204C22⋊C8—1461no—
205C22⋊C8—1461no—
206C22⋊C8—1461no—
207#97—21no—
208#97—1461no—
209C4×C8—731no—
210C4×C8—731no—
211C4×C8—731no—
212C4×C8—1461no—
213C4×C8C22×D7311yescharacteristic
214#41—2922no—
215C2×Q8C8×D7311yescharacteristic
216C2×D4—731no—
217C2×D4—1461no—
218C22×C4—731no—
219C22×C4—731no—
220C22×C4—731no—
221C22×C4—1461no—
222C22×C4—1461no—
223C22×C4—1461no—
224M16—2922no—
225M16—2921no—
226M16—2921no—
227C2×C8—21no—
228C2×C8—2921no—
229C2×C8—731no—
230C2×C8—731no—
231C2×C8—1461no—
232C2×C8—1461no—
233C2×C8—1461no—
234C2×C8D4×D7311yescharacteristic
235C2×C8D4×D7311yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—731no—
238C4⋊C4—1461no—
239C4⋊C4C8×D7311yescharacteristic
240C22⋊C4—1461no—
241C22⋊C4—1461no—
242C22⋊C4—1461no—
243C42—21no—
244C42—731no—
245C42—731no—
246C42—731no—
247C42—1461no—
248C42—1461no—
249C42C2×C4×D7311yescharacteristic
250C16—41no—
251C16—41no—
252C16—2921no—
253C16—2921no—
254C23—731no—
255C23—1461no—
256Q8—41no—
257D4—2921no—
258D4—2922no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—2922no—
262C2×C4—2922no—
263C2×C4—2921no—
264C2×C4—2921no—
265C2×C4—731no—
266C2×C4—731no—
267C2×C4—731no—
268C2×C4—1462no—
269C2×C4—1462no—
270C2×C4—1461no—
271C2×C4—1461no—
272C2×C4—1461no—
273C2×C4C22⋊C4×D7311yescharacteristic
274C2×C4C2×C8×D7311yescharacteristic
275C2×C4M16×D7311yescharacteristic
276C8—21no—
277C8—41no—
278C8—2921no—
279C8—1461no—
280C8—1461no—
281C8#1455661811yescharacteristic
282C8#1455662311yescharacteristic
283C22—2921no—
284C22—2921no—
285C22—2921no—
286C22—732no—
287C22—1461no—
288C22—1461no—
289C22C22⋊C8×D7311yescharacteristic
290C4—21no—
291C4—21no—
292C4—41no—
293C4—41no—
294C4—2921no—
295C4—732no—
296C4—1461no—
297C4—1461no—
298C4#1798858711yescharacteristic
299C4#1798860211yescharacteristic
300C2—5841no—
301C2—1462no—
302C2#2260831711yescharacteristic
303C2#349×D7311yescharacteristic
304C2#350×D7311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D73
commutatorC2×C4×C73C22×C8
FrattiniC4×C8C22×D73
FittingC73×#1338C2
socleC22×C73C2×C22⋊C8
prime radicalC2×#11924029C8
cosocleC4×C8×C73C23
hypercenter#1338D73
hypocenterC73#11626
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1338

Complements

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

NH ≅ G/Ntype
2. #22611732C2semidirect
3. C4⋊C16×D73C2semidirect
4. #22607913C2semidirect
5. #22607890C2semidirect
6. #22607888C2semidirect
7. C73×#1338C2semidirect
157. #1338D73semidirect
160. C73#11626semidirect

Maximal subgroups

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

subgroupindex
#226188962
#226117322
C4⋊C16×D732
#226079132
#226078902
#226078882
C73×#13382
#1162673