Finite Group Databasebeta

← #34001455

Subgroups — #34001455

Order 18688.

608 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 106 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#22625859C212yesmaximal, complemented
2#22624748C212yesmaximal, complemented
3#22624747C212yesmaximal, complemented
4C4×#14556587C211yesmaximal, characteristic
5#17989453—22no—
6#17989453—22no—
7#17989453C2214yes—
8C2×#14556587C411yescharacteristic
9C2×C4×D292C411yescharacteristic
10C2×C4×C22⋊D73—22no—
11#17988490C2211yescharacteristic
12#17988488C2211yescharacteristic
13#17988487—22no—
14#17988456C411yescharacteristic
15C42×Dic73C2211yescharacteristic
16C2×C4×D4×C73C411yescharacteristic
17C22×#10596833—24no—
18C22×D292C2×C411yescharacteristic
19C22×C22⋊D73—22no—
20C22×C4×D73—21no—
21#14556587—22no—
22#14556587C814yescomplemented
23C4×D292—42no—
24C4×C22⋊D73—48no—
25C2×C4⋊Dic73C2×C411yescharacteristic
26C2×#11924007—22no—
27C2×C22⋊Dic73—22no—
28C2×#11924005—22no—
29C2×#11924005—21no—
30C2×C4×Dic73C2×C411yescharacteristic
31C2×C4×Dic73D412yes—
32C2×C4×Dic73D412yes—
33C2×C4×Dic73C2311yescharacteristic
34C22×D4×C73C2×C411yescharacteristic
35C23×C4×C73—21no—
36C4×D4×C73—42no—
37C2×C4⋊C4×C73C2×C411yescharacteristic
38C2×C22⋊C4×C73—21no—
39C2×C42×C73C2×C411yescharacteristic
40C2×#10596833—44no—
41C2×#10596833—44no—
42C2×#10596833—44no—
43C23×D73—21no—
44C2×D292—21no—
45C2×D292—41no—
46C2×D292—41no—
47C2×D292C2×C812yes—
48C2×C22⋊D73—28no—
49C2×C22⋊D73—44no—
50C2×C22⋊D73—44no—
51C22×Dic73—21no—
52C22×Dic73C22⋊C412yes—
53C22×Dic73C2×D412yes—
54C2×C4×D73—44no—
55C2×C4×D73—42no—
56C4⋊Dic73—41no—
57#11924007—44no—
58C22⋊Dic73—44no—
59#11924005—42no—
60#11924005—44no—
61C4×Dic73—24no—
62C4×Dic73—42no—
63C4×Dic73—41no—
64C4×Dic73C2×C812yes—
65C4×Dic73M1612yes—
66C24×C73—21no—
67C2×D4×C73—21no—
68C2×D4×C73—41no—
69C2×D4×C73—41no—
70C2×D4×C73C2×C812yes—
71C22×C4×C73—21no—
72C22×C4×C73—44no—
73C22×C4×C73—42no—
74C22×C4×C73C22⋊C411yescharacteristic
75C22×C4×C73C22⋊C411yescharacteristic
76C22×C4×C73C22×C411yescharacteristic
77C4⋊C4×C73—41no—
78C22⋊C4×C73—42no—
79C42×C73—22no—
80C23×C73—22no—
81C23×C73—41no—
82C23×C73—41no—
83C23×C73—42no—
84C23×C73—42no—
85C23×C73C2×C22⋊C411yescharacteristic
86C22×D73—22no—
87C22×D73—41no—
88C22×D73—41no—
89C22×D73—42no—
90C22×D73—42no—
91D4×C73—42no—
92D4×C73—42no—
93C2×C4×C73—21no—
94C2×C4×C73—21no—
95C2×C4×C73—22no—
96C2×C4×C73—21no—
97C2×C4×C73—22no—
98C2×C4×C73—41no—
99C2×C4×C73—42no—
100C2×C4×C73—84no—
101C2×C4×C73#10012yes—
102C2×C4×C73C22×C811yescharacteristic
103C2×C4×C73C2×M1611yescharacteristic
104C22⋊D73—416no—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73—22no—
108C2×Dic73—22no—
109C2×Dic73—41no—
110C2×Dic73—42no—
111C2×Dic73C22⋊C814yes—
112C2×Dic73AGL(1,ℤ/8)14yes—
113D292—42no—
114D292—42no—
115C4×D73—84no—
116#10596833—84no—
117C22×C73—42no—
118C22×C73—44no—
119C22×C73—81no—
120C22×C73—81no—
121C22×C73—82no—
122C22×C73C2×C22⋊C811yescharacteristic
123C22×C73#41011yescharacteristic
124C22×C73C2×#10011yescharacteristic
125C22×C73#41812yes—
126C22×C73#42112yes—
127C2×D73—42no—
128C2×D73—44no—
129C2×D73—81no—
130C2×D73—81no—
131C2×D73—82no—
132C4×C73—22no—
133C4×C73—21no—
134C4×C73—21no—
135C4×C73—41no—
136C4×C73—81no—
137Dic73—24no—
138Dic73—24no—
139Dic73—81no—
140#7603—731nomaximal, Sylow
141C2×C73—82no—
142C2×C73#146011yescharacteristic
143C2×C73#147812yes—
144C2×C73#151412yes—
145C2×C73#153611yescharacteristic
146C2×C73#155511yescharacteristic
147D73—82no—
148C4×#127—731no—
149#1839—732no—
150#1270—732no—
151#1270—732no—
152C73#760311yescharacteristic, complemented, Sylow
153C2×#127—731no—
154C2×C4×D4—731no—
155C2×C4×D4—1462no—
156C2×C4×D4#6440811yescharacteristic
157#390—731no—
158#390—731no—
159#390—1462no—
160#384—731no—
161C43—731no—
162#336—734no—
163#336—1462no—
164#336—1462no—
165C22×D4—731no—
166C22×D4—1462no—
167C22×D4C2×#6440811yescharacteristic
168C23×C4—21no—
169C23×C4—1461no—
170C22×C8—1464no—
171#127—734no—
172#127—1462no—
173C4×D4—42no—
174C4×D4—2922no—
175C4×D4—2928no—
176C2×C4⋊C4—731no—
177C2×C4⋊C4—1462no—
178C2×C4⋊C4C2×#6440811yescharacteristic
179C2×C22⋊C4—21no—
180C2×C22⋊C4—1462no—
181C2×C22⋊C4—1462no—
182C2×C22⋊C4—1461no—
183C2×C42—732no—
184C2×C42—731no—
185C2×C42—731no—
186C2×C42—732no—
187C2×C42C2×#6440811yescharacteristic
188C24—21no—
189C24—1461no—
190C2×D4—21no—
191C2×D4—41no—
192C2×D4—41no—
193C2×D4—2921no—
194C2×D4—2921no—
195C2×D4—2924no—
196C2×D4—2924no—
197C2×D4—732no—
198C2×D4—1468no—
199C2×D4—1461no—
200C2×D4#1192403612yes—
201C22×C4—21no—
202C22×C4—44no—
203C22×C4—42no—
204C22×C4—2924no—
205C22×C4—2922no—
206C22×C4—732no—
207C22×C4—732no—
208C22×C4—1461no—
209C22×C4C22⋊#6440811yescharacteristic
210C22×C4C22⋊#6440811yescharacteristic
211C22×C4C22×#6440811yescharacteristic
212C2×C8—2924no—
213C2×C8—2924no—
214C2×C8—2924no—
215C4⋊C4—41no—
216C4⋊C4—2921no—
217C4⋊C4—2924no—
218C22⋊C4—42no—
219C22⋊C4—2922no—
220C22⋊C4—2924no—
221C22⋊C4—2924no—
222C42—22no—
223C42—2921no—
224C42—2922no—
225C42—732no—
226C42—732no—
227C42—1464no—
228C23—22no—
229C23—41no—
230C23—41no—
231C23—42no—
232C23—42no—
233C23—2921no—
234C23—2921no—
235C23—2922no—
236C23—2922no—
237C23—1462no—
238C23C2×C22⋊#6440811yescharacteristic
239D4—42no—
240D4—42no—
241D4—2922no—
242D4—2922no—
243D4—29216no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—84no—
252C2×C4—2921no—
253C2×C4—2922no—
254C2×C4—5844no—
255C2×C4—734no—
256C2×C4—734no—
257C2×C4—1462no—
258C2×C4—1462no—
259C2×C4—1462no—
260C2×C4—1462no—
261C2×C4#1455665112yes—
262C2×C4C2×#1192403611yescharacteristic
263C2×C4D73⋊M1611yescharacteristic
264C8—5844no—
265C22—42no—
266C22—44no—
267C22—82no—
268C22—81no—
269C22—81no—
270C22—2922no—
271C22—2924no—
272C22—5842no—
273C22—5841no—
274C22—5841no—
275C22#1798955511yescharacteristic
276C22#1798956611yescharacteristic
277C22C2×#1455665111yescharacteristic
278C22#1798957912yes—
279C22#1798958412yes—
280C4—21no—
281C4—21no—
282C4—22no—
283C4—41no—
284C4—81no—
285C4—5841no—
286C4—1464no—
287C4—1464no—
288C2—82no—
289C2—5842no—
290C2#2262517011yescharacteristic
291C2#2262523112yes—
292C2#2262535012yes—
293C2#2262541911yescharacteristic
294C2#2262545811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
FittingC2×C4×D4×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC2×#14556587C4
cosocleC2×C4×Dic73C23
hypercenterC2×C4×D4#64408
hypocenterC73#7603
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #22625859C2semidirect
2. #22624748C2semidirect
3. #22624747C2semidirect
22. #14556587C8semidirect
152. C73#7603semidirect

Maximal subgroups

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

subgroupindex
#226258592
#226247482
#226247472
C4×#145565872
#760373