Finite Group Databasebeta

← #34013099

Subgroups — #34013099

Order 18688.

432 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 86 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
1C2×#17989498C212yesmaximal
2#22625797C212yesmaximal
3#22625028C212yesmaximal
4#22612650C211yesmaximal, characteristic
5#17989590—22no—
6C2×#14556652C2214yes—
7#17989498—24no—
8#17989467—22no—
9C2×#14556591C2211yescharacteristic
10C2×C4×Dic146C411yescharacteristic
11C2×C4×Dic146C2211yescharacteristic
12#17988493C411yescharacteristic
13#17988493C2211yescharacteristic
14#17988472—22no—
15#17988472—22no—
16#17988453C411yescharacteristic
17#376×C73C411yescharacteristic
18C2×#11924037—24no—
19#14556658—42no—
20C4⋊#10596833—42no—
21#14556652—24no—
22#14556652—24no—
23C22×Dic146C2×C411yescharacteristic
24C22×Dic146C2311yescharacteristic
25#14556591—22no—
26#14556591D412yes—
27#14556591Q812yes—
28C4×Dic146—42no—
29C4×Dic146—42no—
30C2×C4⋊Dic73—22no—
31C2×C4⋊Dic73C2×C411yescharacteristic
32C2×C4⋊Dic73C2×C411yescharacteristic
33C2×#11924007—21no—
34C2×#11924007D412yes—
35C2×C4×Dic73—21no—
36C2×C4×Dic73D412yes—
37#14556498—22no—
38#14556498—22no—
39#14556498—22no—
40C2×C42×C73C2×C411yescharacteristic
41C2×C42×C73C2×C411yescharacteristic
42C2×C42×C73C2×C411yescharacteristic
43#95×C73—21no—
44#95×C73—21no—
45#11924037—44no—
46#11924037—44no—
47C2×#10596833—44no—
48C2×Dic146—21no—
49C2×Dic146—41no—
50C2×Dic146—41no—
51C2×Dic146—41no—
52C2×Dic146—41no—
53C2×Dic146C4⋊C412yes—
54C2×Dic146C2×D411yescharacteristic
55C2×Dic146C2×Q811yescharacteristic
56C2×Dic146#4112yes—
57C22×Dic73—21no—
58C22×Dic73—21no—
59C22×Dic73C22⋊C412yes—
60C22×Dic73C2×D412yes—
61C4⋊Dic73—24no—
62C4⋊Dic73—24no—
63C4⋊Dic73—41no—
64C4⋊Dic73—41no—
65#11924007—42no—
66#11924007—42no—
67C4×Dic73—22no—
68C4×Dic73—22no—
69C4×Dic73—42no—
70C22×C4×C73—21no—
71C22×C4×C73—21no—
72C22×C4×C73C22⋊C411yescharacteristic
73C22×C4×C73C22⋊C411yescharacteristic
74C22×C4×C73C22×C411yescharacteristic
75C42×C73—22no—
76C42×C73—21no—
77C42×C73—41no—
78C42×C73C4⋊C412yes—
79C23×C73C2×C22⋊C411yescharacteristic
80C2×C4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—22no—
83C2×C4×C73—21no—
84C2×C4×C73—41no—
85C2×C4×C73—41no—
86C2×C4×C73—41no—
87C2×C4×C73—41no—
88C2×C4×C73—41no—
89C2×C4×C73—41no—
90C2×C4×C73—41no—
91C2×C4×C73#9912yes—
92C2×C4×C73C2×C4⋊C411yescharacteristic
93C2×C4×C73#11711yescharacteristic
94C2×Dic73—22no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—22no—
98C2×Dic73—41no—
99C2×Dic73—41no—
100C2×Dic73—42no—
101C2×Dic73—42no—
102C2×Dic73—41no—
103C2×Dic73#12112yes—
104C2×Dic73C22⋊Q812yes—
105Dic146—41no—
106Dic146—41no—
107Dic146—42no—
108Dic146—42no—
109Dic146—42no—
110#10596833—84no—
111C22×C73—21no—
112C22×C73—21no—
113C22×C73#38011yescharacteristic
114C22×C73C2×#9911yescharacteristic
115C22×C73#41011yescharacteristic
116C4×C73—21no—
117C4×C73—21no—
118C4×C73—22no—
119C4×C73—42no—
120C4×C73—41no—
121C4×C73—81no—
122Dic73—22no—
123Dic73—22no—
124Dic73—42no—
125Dic73—42no—
126Dic73—81no—
127#12804—731nomaximal, Sylow
128C2×C73—21no—
129C2×C73—21no—
130C2×C73#179911yescharacteristic
131C2×C73#213311yescharacteristic
132C2×C73#213511yescharacteristic
133#2327—731no—
134C2×#356—732no—
135#1801—732no—
136#1394—732no—
137C73#1280411yescharacteristic, complemented, Sylow
138C2×C4⋊Q8—731no—
139C2×C4×Q8—731no—
140C2×C4×Q8—731no—
141#423—1462no—
142C2×#101—734no—
143#391—731no—
144#391—731no—
145#387—1462no—
146#387—1462no—
147#382—731no—
148#376#6440811yescharacteristic
149#356—1464no—
150#343—1462no—
151C22×Q8—731no—
152C22×Q8—731no—
153C2×M16—1464no—
154C4⋊Q8—732no—
155C4⋊Q8—732no—
156C4⋊Q8—1462no—
157C4×Q8—2922no—
158C4×Q8—2922no—
159C2×C4⋊C4—732no—
160C2×C4⋊C4—731no—
161C2×C4⋊C4—731no—
162C2×C4⋊C4—1461no—
163C2×C4⋊C4—1462no—
164C2×C42—732no—
165C2×C42—1461no—
166C2×C42C2×#6440811yescharacteristic
167C2×C42C2×#6440811yescharacteristic
168C2×C42C2×#6440811yescharacteristic
169C4⋊C8—2922no—
170C4⋊C8—2922no—
171#101—1464no—
172#101—1464no—
173#95—21no—
174#95—21no—
175#95—1462no—
176#95—1462no—
177#95—1462no—
178C2×Q8—2921no—
179C2×Q8—2921no—
180C2×Q8—2921no—
181C2×Q8—2921no—
182C2×Q8—731no—
183C2×Q8—731no—
184C2×Q8—732no—
185C2×Q8—732no—
186C2×Q8—1461no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—732no—
190C22×C4—732no—
191C22×C4—1461no—
192C22×C4—1461no—
193C22×C4C22⋊#6440811yescharacteristic
194C22×C4C22⋊#6440811yescharacteristic
195C22×C4C22×#6440811yescharacteristic
196M16—2924no—
197M16—2924no—
198C2×C8—2924no—
199C4⋊C4—2921no—
200C4⋊C4—2922no—
201C4⋊C4—2921no—
202C4⋊C4—2922no—
203C4⋊C4—1464no—
204C4⋊C4—1464no—
205C42—22no—
206C42—21no—
207C42—41no—
208C42—2922no—
209C42—1462no—
210C42—1462no—
211C42C4⋊#6440812yes—
212C23C2×C22⋊#6440811yescharacteristic
213Q8—2922no—
214Q8—2922no—
215Q8—2921no—
216Q8—2921no—
217Q8—2922no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—2921no—
230C2×C4—2921no—
231C2×C4—2922no—
232C2×C4—2922no—
233C2×C4—2921no—
234C2×C4—732no—
235C2×C4—732no—
236C2×C4—1462no—
237C2×C4—1462no—
238C2×C4—1462no—
239C2×C4—1462no—
240C2×C4#1455665012yes—
241C2×C4C2×C4⋊#6440811yescharacteristic
242C2×C4#1455667011yescharacteristic
243C8—5844no—
244C22—21no—
245C22—21no—
246C22#1798952911yescharacteristic
247C22C2×#1455665011yescharacteristic
248C22#1798956611yescharacteristic
249C4—21no—
250C4—21no—
251C4—22no—
252C4—42no—
253C4—41no—
254C4—81no—
255C4—2922no—
256C4—2922no—
257C4—5841no—
258C4—1462no—
259C4—1462no—
260C2—21no—
261C2—21no—
262C2#2262579211yescharacteristic
263C2#2262622811yescharacteristic
264C2#2262623511yescharacteristic
subgroupG/H
centerC22C2×#14556650
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
Fitting#376×C73C4
socleC22×C73C2×#99
prime radicalC23×C73C2×C22⋊C4
cosocleC22×Dic146C23
hypercenter#376#64408
hypocenterC73#12804
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
137. C73#12804semidirect

Maximal subgroups

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

subgroupindex
C2×#179894982
#226257972
#226250282
#226126502
#1280473