Finite Group Databasebeta

← #34010298

Subgroups — #34010298

Order 18688.

394 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 74 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#22625193C211yesmaximal, characteristic
2#22625173C211yesmaximal, characteristic
3#22624862C214yesmaximal
4#22614919C211yesmaximal, characteristic
5#17989608—21no—
6#17989604—21no—
7#17989433—21no—
8#17989433—21no—
9#17989432C2212yes—
10#17989432C2212yes—
11C2×#14556591C412yes—
12C2×#14556591C411yescharacteristic
13C2×C4×Dic146C2211yescharacteristic
14#17988519—21no—
15#17988519—21no—
16#17988493C2212yes—
17#17988486—21no—
18#17988486—21no—
19C4×C4⋊C4×C73C411yescharacteristic
20#14556658—41no—
21C4⋊#10596833—41no—
22C22⋊#10596833—22no—
23C22⋊#10596833—22no—
24#14556646—41no—
25C4×#10596833—41no—
26C22×Dic146C2×C412yes—
27C22×Dic146C2×C411yescharacteristic
28#14556591—41no—
29#14556591—41no—
30#14556591—44no—
31C4×Dic146—41no—
32C4×Dic146—41no—
33C2×C4⋊Dic73—22no—
34C2×C4⋊Dic73—22no—
35C2×C4⋊Dic73—21no—
36C2×C4⋊Dic73—21no—
37C2×C4⋊Dic73C2311yescharacteristic
38C2×#11924007D411yescharacteristic
39C2×#11924007D411yescharacteristic
40C2×C4×Dic73D411yescharacteristic
41C2×C4×Dic73D411yescharacteristic
42#14556498—22no—
43#14556498—22no—
44C2×C4⋊C4×C73—21no—
45C2×C42×C73C2×C411yescharacteristic
46C2×C42×C73C2×C412yes—
47#95×C73—21no—
48C2×#10596833—42no—
49C2×#10596833—42no—
50C2×Dic146—22no—
51C2×Dic146—22no—
52C2×Dic146—24no—
53C2×Dic146—41no—
54C2×Dic146—42no—
55C2×Dic146—42no—
56C22×Dic73—22no—
57C22×Dic73C22⋊C411yescharacteristic
58C22×Dic73C22⋊C411yescharacteristic
59C22×Dic73C2×D411yescharacteristic
60C22×Dic73C2×D411yescharacteristic
61C4⋊Dic73—41no—
62C4⋊Dic73—44no—
63C4⋊Dic73—42no—
64C4⋊Dic73—41no—
65C4⋊Dic73—41no—
66C4⋊Dic73—44no—
67#11924007—41no—
68#11924007—41no—
69C4×Dic73—21no—
70C4×Dic73—21no—
71C4×Dic73—21no—
72C4×Dic73—21no—
73C22×C4×C73—22no—
74C22×C4×C73C22⋊C411yescharacteristic
75C22×C4×C73C22⋊C411yescharacteristic
76C22×C4×C73C22×C411yescharacteristic
77C4⋊C4×C73—24no—
78C42×C73—21no—
79C42×C73—21no—
80C42×C73—42no—
81C23×C73C2×C22⋊C411yescharacteristic
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—22no—
85C2×C4×C73—24no—
86C2×C4×C73—21no—
87C2×C4×C73—42no—
88C2×C4×C73—42no—
89C2×C4×C73—41no—
90C2×C4×C73#9911yescharacteristic
91C2×C4×C73#9911yescharacteristic
92C2×C4×C73#13112yes—
93C2×Dic73—21no—
94C2×Dic73—21no—
95C2×Dic73—21no—
96C2×Dic73—21no—
97C2×Dic73—21no—
98C2×Dic73—21no—
99C2×Dic73—21no—
100C2×Dic73—41no—
101C2×Dic73—41no—
102C2×Dic73—42no—
103C2×Dic73—42no—
104C2×Dic73—42no—
105C2×Dic73#10012yes—
106Dic146—44no—
107Dic146—84no—
108#10596833—82no—
109#10596833—82no—
110C22×C73—21no—
111C22×C73—21no—
112C22×C73#40811yescharacteristic
113C22×C73C2×#9911yescharacteristic
114C22×C73C2×#10011yescharacteristic
115C4×C73—21no—
116C4×C73—22no—
117C4×C73—44no—
118C4×C73—41no—
119C4×C73#35612yes—
120Dic73—22no—
121Dic73—41no—
122Dic73—41no—
123Dic73—41no—
124Dic73—82no—
125#11568—731nomaximal, Sylow
126C2×C73—21no—
127C2×C73—21no—
128C2×C73#147111yescharacteristic
129C2×C73#212911yescharacteristic
130C2×C73C2×#35611yescharacteristic
131#2546—731no—
132#1467—731no—
133#1461—731no—
134#1319—734no—
135C73#1156811yescharacteristic, complemented, Sylow
136C2×C4⋊Q8—732no—
137C2×C4⋊Q8—731no—
138C2×C4×Q8—731no—
139#432—1461no—
140#431—1461no—
141#398—1461no—
142#398—1461no—
143#391—732no—
144#389—1461no—
145#389—1461no—
146C4×C4⋊C4#6440811yescharacteristic
147#324—732no—
148#324—732no—
149#324—1461no—
150#324—1461no—
151C22×Q8—731no—
152C22×Q8—732no—
153C4⋊Q8—2921no—
154C4⋊Q8—2921no—
155C4⋊Q8—2924no—
156C4×Q8—2921no—
157C4×Q8—2921no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—731no—
160C2×C4⋊C4—731no—
161C2×C4⋊C4—731no—
162C2×C4⋊C4—1462no—
163C2×C4⋊C4—1462no—
164C2×C4⋊C4—1461no—
165C2×C4⋊C4—1461no—
166C2×C42—731no—
167C2×C42—731no—
168C2×C42C2×#6440812yes—
169C2×C42C2×#6440811yescharacteristic
170C4⋊C8—2921no—
171C4⋊C8—2921no—
172C22⋊C8—1462no—
173C22⋊C8—1462no—
174#97—2921no—
175C4×C8—2921no—
176#95—21no—
177#95—1462no—
178#95—1462no—
179C2×Q8—2922no—
180C2×Q8—2922no—
181C2×Q8—2921no—
182C2×Q8—1462no—
183C2×Q8—1464no—
184C2×Q8—1462no—
185C22×C4—22no—
186C22×C4—731no—
187C22×C4—731no—
188C22×C4—731no—
189C22×C4—731no—
190C22×C4—1462no—
191C22×C4C22⋊#6440811yescharacteristic
192C22×C4C22⋊#6440811yescharacteristic
193C22×C4C22×#6440811yescharacteristic
194C2×C8—2922no—
195C2×C8—2922no—
196C4⋊C4—24no—
197C4⋊C4—2922no—
198C4⋊C4—2921no—
199C4⋊C4—2921no—
200C4⋊C4—2921no—
201C4⋊C4—2924no—
202C4⋊C4—2924no—
203C4⋊C4—2921no—
204C4⋊C4—2921no—
205C42—21no—
206C42—21no—
207C42—42no—
208C42—1461no—
209C42—1461no—
210C42—1461no—
211C42—1461no—
212C23C2×C22⋊#6440811yescharacteristic
213Q8—2924no—
214Q8—5844no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—24no—
219C2×C4—21no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—2921no—
224C2×C4—2921no—
225C2×C4—2922no—
226C2×C4—2922no—
227C2×C4—2922no—
228C2×C4—732no—
229C2×C4—1461no—
230C2×C4—1461no—
231C2×C4—1461no—
232C2×C4—1461no—
233C2×C4—1461no—
234C2×C4—1461no—
235C2×C4—1461no—
236C2×C4#1455665011yescharacteristic
237C2×C4#1455665011yescharacteristic
238C2×C4#1455667912yes—
239C8—5842no—
240C8—5842no—
241C22—21no—
242C22—21no—
243C22#1798956211yescharacteristic
244C22C2×#1455665011yescharacteristic
245C22D73⋊#10011yescharacteristic
246C4—21no—
247C4—22no—
248C4—44no—
249C4—41no—
250C4—2921no—
251C4—2921no—
252C4—2921no—
253C4—5842no—
254C4—1462no—
255C4#1798949812yes—
256C2—21no—
257C2—21no—
258C2#2262520811yescharacteristic
259C2#2262621511yescharacteristic
260C2C2×#1798949811yescharacteristic
subgroupG/H
centerC22C2×#14556650
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC4×C4⋊C4×C73C4
socleC22×C73C2×#99
prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4⋊Dic73C23
hypercenterC4×C4⋊C4#64408
hypocenterC73#11568
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
135. C73#11568semidirect

Maximal subgroups

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

subgroupindex
#226251932
#226251732
#226248622
#226149192
#1156873