Finite Group Databasebeta

← #34033623

Subgroups — #34033623

Order 18688.

438 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 87 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#22627099C212yesmaximal, complemented
2#22626965C212yesmaximal, complemented
3#22626952C212yesmaximal, complemented
4C2×#17989614C211yesmaximal, characteristic
5C2×#14556688—22no—
6#17989684—22no—
7C22⋊#11924040C2214yes—
8C22×#11924036C2211yescharacteristic
9C23×#10596833C411yescharacteristic
10#17989614—22no—
11#17989614—22no—
12C2×#14556658C2211yescharacteristic
13C2×#14556648C411yescharacteristic
14C2×C22⋊#10596833C2211yescharacteristic
15C2×C4×#10596833C411yescharacteristic
16C2×#14556551C411yescharacteristic
17#14556688—44no—
18C2×#11924040—24no—
19C2×#11924036—42no—
20C2×#11924036D412yes—
21C2×#11924036D412yes—
22C22×#10596833—21no—
23C22×#10596833—21no—
24C22×#10596833—42no—
25C22×#10596833C2×C411yescharacteristic
26C22×#10596833C2×C411yescharacteristic
27C22×#10596833C2×C411yescharacteristic
28C22×#10596833C2311yescharacteristic
29#14556658—22no—
30#14556648—22no—
31C22⋊#10596833—22no—
32C4×#10596833—21no—
33C4×#10596833—21no—
34C22×C22⋊D73C811yescharacteristic
35C23×Dic73C2×C411yescharacteristic
36C22×C4×D73C2×C411yescharacteristic
37#14556551—22no—
38#14556551—22no—
39C2×#11924007C811yescharacteristic
40C2×#11924005C811yescharacteristic
41C2×C4×Dic73C2×C411yescharacteristic
42C2×C22⋊C4×C73C811yescharacteristic
43#11924040—44no—
44#11924036—24no—
45#11924036—42no—
46C2×#10596833—22no—
47C2×#10596833—21no—
48C2×#10596833—21no—
49C2×#10596833—41no—
50C2×#10596833—42no—
51C2×#10596833—42no—
52C2×#10596833—41no—
53C2×#10596833—41no—
54C2×#10596833C22⋊C411yescharacteristic
55C2×#10596833C22⋊C411yescharacteristic
56C2×#10596833C2×D412yes—
57C23×D73C2×C811yescharacteristic
58C2×C22⋊D73—22no—
59C2×C22⋊D73—22no—
60C2×C22⋊D73—22no—
61C22×Dic73—21no—
62C22×Dic73—21no—
63C22×Dic73—41no—
64C22×Dic73—41no—
65C22×Dic73C2×C811yescharacteristic
66C22×Dic73C2×C811yescharacteristic
67C22×Dic73C22×C411yescharacteristic
68C2×C4×D73—41no—
69C2×C4×D73—41no—
70C2×C4×D73C22⋊C412yes—
71C2×C4×D73M1612yes—
72#11924007—22no—
73#11924005—22no—
74C4×Dic73—21no—
75C4×Dic73—21no—
76C24×C73C2×C811yescharacteristic
77C22×C4×C73C2×C811yescharacteristic
78C22×C4×C73C2×C811yescharacteristic
79C22⋊C4×C73—22no—
80C23×C73—21no—
81C23×C73—21no—
82C23×C73—41no—
83C23×C73—41no—
84C23×C73M3212yescomplemented
85C23×C73C22×C811yescharacteristic
86C22×D73—21no—
87C22×D73—21no—
88C22×D73—41no—
89C22×D73—41no—
90C22×D73C22⋊C812yes—
91C2×C4×C73—21no—
92C2×C4×C73—41no—
93C2×C4×C73—41no—
94C2×C4×C73C22⋊C812yes—
95C22⋊D73—28no—
96C2×Dic73—21no—
97C2×Dic73—21no—
98C2×Dic73—21no—
99C2×Dic73—21no—
100C2×Dic73—21no—
101C2×Dic73—42no—
102C2×Dic73—41no—
103C2×Dic73—41no—
104C2×Dic73—41no—
105C2×Dic73M3212yescomplemented
106C2×Dic73C2×C22⋊C411yescharacteristic
107C2×Dic73C2×M1611yescharacteristic
108C4×D73—22no—
109C4×D73—22no—
110C4×D73—42no—
111#10596833—21no—
112#10596833—22no—
113#10596833—41no—
114#10596833—41no—
115#10596833#9912yes—
116C22×C73—21no—
117C22×C73—21no—
118C22×C73—22no—
119C22×C73—42no—
120C22×C73—42no—
121C22×C73—41no—
122C22×C73—41no—
123C22×C73C2×C22⋊C811yescharacteristic
124C22×C73C2×M3211yescharacteristic
125C22×C73C2×M3211yescharacteristic
126C2×D73—22no—
127C2×D73—22no—
128C2×D73—22no—
129C2×D73—42no—
130C2×D73—42no—
131C4×C73—22no—
132C4×C73—41no—
133Dic73—22no—
134Dic73—21no—
135Dic73—41no—
136Dic73C2×#9911yescharacteristic
137Dic73#41311yescharacteristic
138#11466—731nomaximal, Sylow
139C2×C73—21no—
140C2×C73—21no—
141C2×C73—42no—
142C2×C73#145911yescharacteristic
143C2×C73#211211yescharacteristic
144C2×C73#211511yescharacteristic
145D73—42no—
146C2×C8×D4—731no—
147#2112—732no—
148#1322—732no—
149#1314—732no—
150C73#1146611yescharacteristic, complemented, Sylow
151C23×C8—731no—
152C23×C8—731no—
153C2×C4×D4—731no—
154C2×M32—1462no—
155C8×D4—1462no—
156C8×D4—1462no—
157C2×C4⋊C8—731no—
158C2×C22⋊C8—731no—
159C2×C22⋊C8—731no—
160C2×C4×C8—731no—
161C22⋊C16—734no—
162C22⋊C16—1462no—
163C22×D4—731no—
164C23×C4—731no—
165C23×C4—731no—
166C22×C8—2922no—
167C22×C8—2922no—
168C22×C8—731no—
169C22×C8—732no—
170C22×C8—731no—
171C22×C8—731no—
172C22×C8—731no—
173C22×C8—732no—
174C22×C8—1461no—
175C22×C8—1461no—
176C4×D4—1462no—
177C4×D4—1462no—
178C2×C4⋊C4—731no—
179C2×C22⋊C4—731no—
180C2×C22⋊C4#1059684211yescharacteristic
181C2×C42—731no—
182M32—2924no—
183C2×C16—1464no—
184C4⋊C8—1462no—
185C22⋊C8—1462no—
186C22⋊C8—1462no—
187C4×C8—1461no—
188C4×C8—1461no—
189C24—731no—
190C24C2×#1059684211yescharacteristic
191C2×D4—1462no—
192C2×D4—1462no—
193C2×D4—1462no—
194C22×C4—2921no—
195C22×C4—2921no—
196C22×C4—2921no—
197C22×C4—2921no—
198C22×C4—732no—
199C22×C4—731no—
200C22×C4—731no—
201C22×C4—731no—
202C22×C4—732no—
203C22×C4—1461no—
204C22×C4—1461no—
205C22×C4C2×#1059684211yescharacteristic
206C22×C4C2×#1059684211yescharacteristic
207C2×C8—2922no—
208C2×C8—2922no—
209C2×C8—2921no—
210C2×C8—2921no—
211C2×C8—2921no—
212C2×C8—2922no—
213C2×C8—731no—
214C2×C8—731no—
215C2×C8—732no—
216C2×C8—1461no—
217C2×C8—1461no—
218C2×C8—1462no—
219C2×C8—1464no—
220C4⋊C4—1462no—
221C22⋊C4—22no—
222C22⋊C4—1462no—
223C42—1461no—
224C42—1461no—
225C16—2924no—
226C23—21no—
227C23—21no—
228C23—41no—
229C23—41no—
230C23—2921no—
231C23—2921no—
232C23—732no—
233C23—1461no—
234C23—1461no—
235C23#1455668812yescomplemented
236C23C22×#1059684211yescharacteristic
237D4—1468no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—2922no—
242C2×C4—2921no—
243C2×C4—2921no—
244C2×C4—2922no—
245C2×C4—2921no—
246C2×C4—731no—
247C2×C4—731no—
248C2×C4—732no—
249C2×C4—1462no—
250C2×C4—1462no—
251C2×C4—1461no—
252C2×C4—1461no—
253C2×C4—1461no—
254C2×C4—1461no—
255C2×C4—1461no—
256C2×C4C22⋊#1059684212yes—
257C8—2921no—
258C8—2921no—
259C8—732no—
260C8—1462no—
261C8—1461no—
262C22—21no—
263C22—21no—
264C22—22no—
265C22—42no—
266C22—42no—
267C22—41no—
268C22—41no—
269C22—2922no—
270C22—2922no—
271C22—1462no—
272C22—1462no—
273C22—1462no—
274C22C2×C22⋊#1059684211yescharacteristic
275C22#1798970611yescharacteristic
276C22C2×#1455668811yescharacteristic
277C4—22no—
278C4—41no—
279C4—2921no—
280C4—731no—
281C4—731no—
282C4—1462no—
283C4—1461no—
284C2—21no—
285C2—21no—
286C2—42no—
287C2—2922no—
288C2#2262704411yescharacteristic
289C2#2262709911yescharacteristic
290C2#2262710811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10596842
commutatorC23×C73C22×C8
FrattiniC23C22×#10596842
FittingC2×C22⋊C4×C73C8
socleC22×C73C2×C22⋊C8
prime radicalC22×C22⋊D73C8
cosocleC22×#10596833C23
hypercenterC2×C22⋊C4#10596842
hypocenterC73#11466
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #22627099C2semidirect
2. #22626965C2semidirect
3. #22626952C2semidirect
84. C23×C73M32semidirect
105. C2×Dic73M32semidirect
150. C73#11466semidirect
235. C23#14556688semidirect

Maximal subgroups

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

subgroupindex
#226270992
#226269652
#226269522
C2×#179896142
#1146673