Finite Group Databasebeta

← #34029666

Subgroups — #34029666

Order 18688.

636 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 198 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#22626104C212yesmaximal
2#22626100C212yesmaximal
3#22625989C214yesmaximal
4#22625985C214yesmaximal
5#22625859C212yesmaximal
6#22612500C211yesmaximal, characteristic
7C2×C4⋊#10596833C2212yes—
8C2×C4⋊#10596833C2212yes—
9C2×#14556646C2212yes—
10C2×C4×#10596833C2212yes—
11#17989453C2214yes—
12#17989453C2214yes—
13#17989453C2214yes—
14#17989453C2212yes—
15#17989453C2214yes—
16#17989453C2212yes—
17C2×#14556589C411yescharacteristic
18C2×Q8×Dic73C2211yescharacteristic
19C2×#14556556C2211yescharacteristic
20#17988493C411yescharacteristic
21#17988484C414yes—
22#17988456C411yescharacteristic
23#17988438C2214yes—
24C42×Dic73C2211yescharacteristic
25#391×C73C411yescharacteristic
26C22×#10596833C2314yes—
27C22×#10596833C2314yes—
28C4⋊#10596833—42no—
29C4⋊#10596833—42no—
30#14556646—42no—
31C4×#10596833—42no—
32C22×Dic146C2×C411yescharacteristic
33#14556589—24no—
34Q8×Dic73—41no—
35Q8×Dic73—41no—
36#14556556—41no—
37#14556556—41no—
38C2×C4⋊Dic73C2×C411yescharacteristic
39C2×C4⋊Dic73C2×C412yes—
40C2×#11924007C2×C414yes—
41C2×#11924007C2×C414yes—
42C2×#11924007C2×C412yes—
43C2×C4×Dic73C2×C411yescharacteristic
44C2×C4×Dic73C2×C412yes—
45C2×C4×Dic73C2312yes—
46C2×C4×Dic73C2311yescharacteristic
47C2×C4×Dic73C2312yes—
48C2×C4×Dic73C2312yes—
49#14556498C2×C414yes—
50C22×Q8×C73C2×C411yescharacteristic
51C2×C4⋊C4×C73C2×C411yescharacteristic
52C2×C42×C73C2×C411yescharacteristic
53#95×C73C2×C414yes—
54C2×#10596833—24no—
55C2×#10596833—24no—
56C2×#10596833—28no—
57C2×#10596833—28no—
58C2×Dic146—22no—
59C2×Dic146—41no—
60C2×Dic146—41no—
61C22×Dic73C22×C412yes—
62C22×Dic73C22×C412yes—
63C22×Dic73C22×C411yescharacteristic
64C22×Dic73C22×C412yes—
65C22×Dic73C2411yescharacteristic
66C4⋊Dic73—42no—
67C4⋊Dic73—41no—
68#11924007—28no—
69#11924007—28no—
70#11924007—42no—
71C4×Dic73—22no—
72C4×Dic73—24no—
73C4×Dic73—21no—
74C4×Dic73—21no—
75C4×Dic73—22no—
76C4×Dic73—22no—
77C4×Dic73—22no—
78C4×Dic73—22no—
79C4×Dic73—24no—
80C2×Q8×C73—41no—
81C2×Q8×C73—41no—
82C2×Q8×C73M1614yes—
83C22×C4×C73C22×C412yes—
84C22×C4×C73C22×C412yes—
85C22×C4×C73C22×C412yes—
86C22×C4×C73C22×C411yescharacteristic
87C4⋊C4×C73—41no—
88C42×C73—41no—
89C23×C73C23×C411yescharacteristic
90Q8×C73—44no—
91C2×C4×C73—21no—
92C2×C4×C73—22no—
93C2×C4×C73—21no—
94C2×C4×C73—22no—
95C2×C4×C73—22no—
96C2×C4×C73—22no—
97C2×C4×C73—22no—
98C2×C4×C73—24no—
99C2×C4×C73—22no—
100C2×C4×C73C2×M1612yes—
101C2×C4×C73C2×M1614yes—
102C2×Dic73—22no—
103C2×Dic73—22no—
104C2×Dic73—21no—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73—22no—
108C2×Dic73—22no—
109C2×Dic73—24no—
110C2×Dic73—22no—
111C2×Dic73#13114yes—
112C2×Dic73H(5,𝔽2)11yescharacteristic
113C2×Dic73H(5,𝔽2)11yescharacteristic
114C2×Dic732−1+414yes—
115Dic146—44no—
116#10596833—44no—
117#10596833—44no—
118C22×C73#51811yescharacteristic
119C22×C73#51912yes—
120C22×C73C22×M1611yescharacteristic
121C22×C73C2×#13112yes—
122C22×C73#56811yescharacteristic
123C4×C73—22no—
124C4×C73—24no—
125C4×C73—42no—
126C4×C73—42no—
127Dic73—24no—
128Dic73—42no—
129Dic73—41no—
130Dic73—42no—
131Dic73#56312yes—
132Dic73#56312yes—
133#23365—731nomaximal, Sylow
134C2×C73#238111yescharacteristic
135C2×C73#297311yescharacteristic
136C2×C73#297911yescharacteristic
137C2×C73#298412yes—
138C2×C73#298512yes—
139C4×C4⋊Q8—731no—
140#1985—732no—
141#1984—732no—
142#1917—734no—
143#1916—734no—
144#1839—732no—
145C73#2336511yescharacteristic, complemented, Sylow
146C2×C4⋊Q8—731no—
147C2×C4×Q8—731no—
148C2×C4×Q8—731no—
149C2×C4⋊C8—732no—
150C2×C4⋊C8—732no—
151C2×#97—732no—
152C2×C4×C8—732no—
153#391—731no—
154#391#6440811yescharacteristic
155#389—734no—
156#384—731no—
157C4×C4⋊C4—734no—
158C43—731no—
159#336—732no—
160#336—734no—
161#336—732no—
162#336—734no—
163#336—734no—
164#336—734no—
165C22×Q8—731no—
166C22×Q8C2×#6440811yescharacteristic
167C22×C8—734no—
168C22×C8—734no—
169C4⋊Q8—1464no—
170C4×Q8—2921no—
171C4×Q8—2921no—
172C4×Q8—2921no—
173C4×Q8—2921no—
174C2×C4⋊C4—731no—
175C2×C4⋊C4—732no—
176C2×C4⋊C4—732no—
177C2×C4⋊C4—734no—
178C2×C4⋊C4—734no—
179C2×C4⋊C4C2×#6440811yescharacteristic
180C2×C42—731no—
181C2×C42—732no—
182C2×C42—732no—
183C2×C42—731no—
184C2×C42—732no—
185C2×C42—732no—
186C2×C42C2×#6440811yescharacteristic
187C4⋊C8—2922no—
188C4⋊C8—2922no—
189#97—2922no—
190C4×C8—2922no—
191#95—734no—
192#95C2×#6440814yes—
193C2×Q8—41no—
194C2×Q8—41no—
195C2×Q8—2921no—
196C2×Q8—2921no—
197C2×Q8—1462no—
198C2×Q8#1192403814yes—
199C22×C4—731no—
200C22×C4—732no—
201C22×C4—732no—
202C22×C4—732no—
203C22×C4—731no—
204C22×C4C22×#6440812yes—
205C22×C4C22×#6440812yes—
206C22×C4C22×#6440812yes—
207C22×C4C22×#6440811yescharacteristic
208C2×C8—1464no—
209C2×C8—1464no—
210C2×C8—1468no—
211C2×C8—1468no—
212C4⋊C4—41no—
213C4⋊C4—2922no—
214C4⋊C4—2921no—
215C4⋊C4—2922no—
216C4⋊C4—1468no—
217C4⋊C4—1468no—
218C42—41no—
219C42—1462no—
220C42—1462no—
221C42—1462no—
222C42—1462no—
223C42—1464no—
224C42—1464no—
225C42—1461no—
226C42—1461no—
227C42—1462no—
228C23C23×#6440811yescharacteristic
229Q8—44no—
230Q8—2924no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—24no—
239C2×C4—22no—
240C2×C4—731no—
241C2×C4—731no—
242C2×C4—734no—
243C2×C4—734no—
244C2×C4—1461no—
245C2×C4—1462no—
246C2×C4—1462no—
247C2×C4—1462no—
248C2×C4—1462no—
249C2×C4—1464no—
250C2×C4—1462no—
251C2×C4—1462no—
252C2×C4—1462no—
253C2×C4C2×#1192403812yes—
254C2×C4C2×#1192403814yes—
255C8—2924no—
256C8—2924no—
257C22#1798965411yescharacteristic
258C22#1798965512yes—
259C22C22×#1192403811yescharacteristic
260C22D73⋊#13112yes—
261C22#1798966511yescharacteristic
262C4—22no—
263C4—24no—
264C4—42no—
265C4—42no—
266C4—2922no—
267C4—2921no—
268C4—2922no—
269C4—732no—
270C4—732no—
271C4—1464no—
272C2#2262647611yescharacteristic
273C2#2262678411yescharacteristic
274C2#2262681311yescharacteristic
275C2#2262683312yes—
276C2#2262683712yes—
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socle, prime radicalC23×C73C23×C4
Fitting#391×C73C4
cosocleC22×Dic73C24
hypercenter#391#64408
hypocenterC73#23365
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
145. C73#23365semidirect

Maximal subgroups

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

subgroupindex
#226261042
#226261002
#226259892
#226259852
#226258592
#226125002
#2336573