Finite Group Databasebeta

← #32995888

Subgroups — #32995888

Order 18688.

322 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 91 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#22618894C211yesmaximal, characteristic
2#22611732C211yesmaximal, characteristic, complemented
3#22611685C211yesmaximal, characteristic, complemented
4#22607914C211yesmaximal, characteristic, complemented
5#22607912C211yesmaximal, characteristic, complemented
6#22607889C211yesmaximal, characteristic, complemented
7C73×#1330C211yesmaximal, characteristic, complemented
8C4×#11924027C411yescharacteristic
9C2×#14556530—21no—
10#17988717C2211yescharacteristic
11#17988714C411yescharacteristic
12#17988665C411yescharacteristic
13#17988661—21no—
14#17988656—21no—
15#17988639C411yescharacteristic
16#17988637—21no—
17M16×Dic73—21no—
18C4×C8×D73C2211yescharacteristic
19C4⋊#11924003C2211yescharacteristic
20#17988405—21no—
21#17988405—21no—
22#17988366—21no—
23#17988363C2211yescharacteristic
24#436×C73C2211yescharacteristic
25C4⋊C16×C73C2211yescharacteristic
26#346×C73C2211yescharacteristic
27C2×#11924027C811yescharacteristic
28C2×#11924012—21no—
29C2×C8×D73D411yescharacteristic
30C2×C8×D73D411yescharacteristic
31C4×Dic146C2×C411yescharacteristic
32#14556556C811yescharacteristic
33D4×Dic73C811yescharacteristic
34C4×C22⋊D73—21no—
35#14556551—21no—
36#14556549C811yescharacteristic
37#14556547—21no—
38C2×C4×Dic73—21no—
39C42×D73C2×C411yescharacteristic
40#14556530—42no—
41C2×#11924003—21no—
42C2×#11924003—21no—
43C4⋊#10596831C2×C411yescharacteristic
44#14556520—21no—
45#14556520—21no—
46C22⋊#10596831—21no—
47#14556503—21no—
48#14556501—21no—
49#14556501—21no—
50C4×#10596831C2×C411yescharacteristic
51C8×Dic73—21no—
52C8×Dic73D411yescharacteristic
53C8×Dic73D411yescharacteristic
54C2×M16×C73—21no—
55C4×D4×C73C2×C411yescharacteristic
56C2×C16×C73—21no—
57C2×C16×C73—21no—
58C4⋊C8×C73C2×C411yescharacteristic
59C22⋊C8×C73—21no—
60C4×C8×C73C2311yescharacteristic
61#11924027—42no—
62C2×Dic146C2×C811yescharacteristic
63C2×C22⋊D73—21no—
64C22×Dic73—21no—
65C22×Dic73—21no—
66C2×C4×D73C22⋊C411yescharacteristic
67C2×C4×D73C2×C811yescharacteristic
68C2×C4×D73M1611yescharacteristic
69#11924012—42no—
70C2×#10596831—21no—
71C2×#10596831C22⋊C411yescharacteristic
72C2×#10596831C22⋊C411yescharacteristic
73C8×D73—21no—
74C8×D73—21no—
75C8×D73—41no—
76C4⋊Dic73C2×C811yescharacteristic
77#11924007—21no—
78#11924007—21no—
79C22⋊Dic73—21no—
80#11924005—21no—
81C4×Dic73—21no—
82C4×Dic73—21no—
83C4×Dic73—21no—
84C4×Dic73C22⋊C411yescharacteristic
85C4×Dic73C2×C811yescharacteristic
86C4×Dic73M1611yescharacteristic
87#11924003—41no—
88#11924003—41no—
89C2×D4×C73C2×C811yescharacteristic
90C22×C4×C73—21no—
91M16×C73—41no—
92M16×C73—41no—
93C2×C8×C73—21no—
94C2×C8×C73C2×D411yescharacteristic
95C2×C8×C73C2×D411yescharacteristic
96C4⋊C4×C73C2×C811yescharacteristic
97C22⋊C4×C73—21no—
98C42×C73C22×C411yescharacteristic
99C16×C73—41no—
100C16×C73—41no—
101C23×C73—21no—
102C22×D73C22⋊C811yescharacteristic
103D4×C73—41no—
104C2×C4×C73—21no—
105C2×C4×C73—41no—
106C2×C4×C73—41no—
107C2×C4×C73C2×C22⋊C411yescharacteristic
108C2×C4×C73C22×C811yescharacteristic
109C2×C4×C73C2×M1611yescharacteristic
110C22⋊D73—42no—
111C2×Dic73—21no—
112C2×Dic73—21no—
113C2×Dic73—42no—
114C2×Dic73—42no—
115C2×Dic73C22⋊C811yescharacteristic
116C2×Dic73C22⋊C811yescharacteristic
117C2×Dic73C22⋊C811yescharacteristic
118C4×D73—21no—
119C4×D73—21no—
120C4×D73—22no—
121C4×D73—41no—
122Dic146—41no—
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×C73—41no—
131C22×C73—41no—
132C22×C73—41no—
133C22×C73C2×C22⋊C811yescharacteristic
134C2×D73—21no—
135C2×D73—21no—
136C2×D73—21no—
137C4×C73—21no—
138C4×C73—21no—
139C4×C73—41no—
140C4×C73#41711yescharacteristic
141C4×C73#42111yescharacteristic
142Dic73—21no—
143Dic73—21no—
144Dic73—41no—
145Dic73—41no—
146Dic73#34912yes—
147#11628—731nomaximal, Sylow
148C2×C73—81no—
149C2×C73#147711yescharacteristic
150C2×C73C2×#34911yescharacteristic
151C2×C73#211711yescharacteristic
152D73—41no—
153#2965—731no—
154#2163—731no—
155#2150—731no—
156#1338—731no—
157#1338—731no—
158#1330—731no—
159#1330D7311yescharacteristic, complemented
160C73#1162811yescharacteristic, complemented, Sylow
161C4×#41—731no—
162C2×M32—1461no—
163#446—731no—
164#446—731no—
165#436—731no—
166#436C2×D7311yescharacteristic
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—21no—
182C2×M16—1461no—
183C22×C8—731no—
184C22×C8—731no—
185C4×Q8—731no—
186C4×Q8—731no—
187C4×D4—731no—
188C4×D4—1461no—
189C4×D4—1461no—
190C4×D4C4×D7311yescharacteristic
191#117—731no—
192#117—1461no—
193C2×C42—731no—
194C2×C42—1461no—
195M32—2922no—
196C2×C16—21no—
197C2×C16—21no—
198C2×C16—1461no—
199C2×C16—1461no—
200C4⋊C8—731no—
201C4⋊C8—1461no—
202C4⋊C8—1461no—
203C4⋊C8C4×D7311yescharacteristic
204C22⋊C8—21no—
205C22⋊C8—1461no—
206C22⋊C8—1461no—
207#97—1461no—
208#97—1461no—
209C4×C8—731no—
210C4×C8—731no—
211C4×C8—731no—
212C4×C8—1461no—
213C4×C8C22×D7311yescharacteristic
214#41—2922no—
215C2×Q8—731no—
216C2×D4—1461no—
217C2×D4C8×D7311yescharacteristic
218C22×C4—21no—
219C22×C4—731no—
220C22×C4—731no—
221C22×C4—731no—
222C22×C4—1461no—
223C22×C4—1461no—
224M16—41no—
225M16—41no—
226M16—2922no—
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—731no—
237C4⋊C4—1461no—
238C4⋊C4—1461no—
239C4⋊C4C8×D7311yescharacteristic
240C22⋊C4—21no—
241C22⋊C4—1461no—
242C22⋊C4—1461no—
243C42—731no—
244C42—731no—
245C42—731no—
246C42—1461no—
247C42—1461no—
248C42—1461no—
249C42C2×C4×D7311yescharacteristic
250C16—41no—
251C16—41no—
252C16—2921no—
253C16—2921no—
254C23—21no—
255C23—731no—
256Q8—2921no—
257D4—41no—
258D4—2922no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—2921no—
263C2×C4—2922no—
264C2×C4—2922no—
265C2×C4—731no—
266C2×C4—731no—
267C2×C4—731no—
268C2×C4—1462no—
269C2×C4—1461no—
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#1455661511yescharacteristic
282C8#1455662011yescharacteristic
283C22—41no—
284C22—41no—
285C22—41no—
286C22—1461no—
287C22—1461no—
288C22—1461no—
289C22C22⋊C8×D7311yescharacteristic
290C4—21no—
291C4—21no—
292C4—41no—
293C4—2921no—
294C4—2921no—
295C4—732no—
296C4—1461no—
297C4—1461no—
298C4#1798858511yescharacteristic
299C4#1798860211yescharacteristic
300C2—81no—
301C2—2921no—
302C2#2260831511yescharacteristic
303C2#349×D7311yescharacteristic
304C2#2261155711yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D73
commutatorC2×C4×C73C22×C8
FrattiniC4×C8C22×D73
FittingC73×#1330C2
socleC22×C73C2×C22⋊C8
prime radicalC2×#11924027C8
cosocleC4×C8×C73C23
hypercenter#1330D73
hypocenterC73#11628
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1330

Complements

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

NH ≅ G/Ntype
2. #22611732C2semidirect
3. #22611685C2semidirect
4. #22607914C2semidirect
5. #22607912C2semidirect
6. #22607889C2semidirect
7. C73×#1330C2semidirect
159. #1330D73semidirect
160. C73#11628semidirect

Maximal subgroups

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

subgroupindex
#226188942
#226117322
#226116852
#226079142
#226079122
#226078892
C73×#13302
#1162873