Finite Group Databasebeta

← #34010307

Subgroups — #34010307

Order 18688.

350 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 70 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#22624874C212yesmaximal
4#22624872C212yesmaximal
5#22615123C211yesmaximal, characteristic
6#17989608—21no—
7#17989604—21no—
8#17989433—21no—
9#17989433—21no—
10#17989432C2212yes—
11#17989432C2212yes—
12C2×C4×Dic146C2211yescharacteristic
13#17988520—21no—
14#17988520—21no—
15#17988492C411yescharacteristic
16#17988492C411yescharacteristic
17#17988468—21no—
18#17988468—21no—
19#17988456C2211yescharacteristic
20#17988452C2211yescharacteristic
21C4×C4⋊Dic73C411yescharacteristic
22C2×#125×C73C411yescharacteristic
23#14556658—41no—
24C4⋊#10596833—41no—
25C22⋊#10596833—22no—
26C22⋊#10596833—22no—
27#14556646—41no—
28C4×#10596833—41no—
29C22×Dic146C2×C411yescharacteristic
30C4×Dic146—41no—
31C4×Dic146—41no—
32C2×C4⋊Dic73—21no—
33C2×C4⋊Dic73C2311yescharacteristic
34C2×#11924007—21no—
35C2×#11924007—21no—
36C2×#11924007D411yescharacteristic
37C2×#11924007D411yescharacteristic
38C2×C4×Dic73C2×C411yescharacteristic
39C2×C4×Dic73C2×C411yescharacteristic
40C2×C4×Dic73D411yescharacteristic
41C2×C4×Dic73D411yescharacteristic
42#14556498—21no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48#14556498—21no—
49#125×C73—41no—
50#125×C73—41no—
51C2×C4⋊C4×C73—21no—
52C2×C4⋊C4×C73—21no—
53C2×C4⋊C4×C73C2×C411yescharacteristic
54C2×C4⋊C4×C73C2×C411yescharacteristic
55C2×C42×C73C2×C411yescharacteristic
56C2×#10596833—42no—
57C2×#10596833—42no—
58C2×Dic146—22no—
59C2×Dic146—22no—
60C2×Dic146—41no—
61C22×Dic73—21no—
62C22×Dic73—21no—
63C22×Dic73C22⋊C411yescharacteristic
64C22×Dic73C22⋊C411yescharacteristic
65C22×Dic73C2×D411yescharacteristic
66C22×Dic73C2×D411yescharacteristic
67C4⋊Dic73—41no—
68C4⋊Dic73—42no—
69#11924007—41no—
70#11924007—41no—
71#11924007—42no—
72#11924007—42no—
73C4×Dic73—21no—
74C4×Dic73—21no—
75C4×Dic73—21no—
76C4×Dic73—21no—
77C4×Dic73—22no—
78C4×Dic73—22no—
79C22×C4×C73—21no—
80C22×C4×C73—21no—
81C22×C4×C73C22⋊C411yescharacteristic
82C22×C4×C73C22⋊C411yescharacteristic
83C22×C4×C73C22×C411yescharacteristic
84C4⋊C4×C73—41no—
85C4⋊C4×C73—41no—
86C4⋊C4×C73—42no—
87C4⋊C4×C73—41no—
88C4⋊C4×C73—41no—
89C42×C73—21no—
90C42×C73—21no—
91C23×C73C2×C22⋊C411yescharacteristic
92C2×C4×C73—21no—
93C2×C4×C73—21no—
94C2×C4×C73—21no—
95C2×C4×C73—41no—
96C2×C4×C73—41no—
97C2×C4×C73—42no—
98C2×C4×C73—41no—
99C2×C4×C73—41no—
100C2×C4×C73—41no—
101C2×C4×C73—41no—
102C2×C4×C73#9911yescharacteristic
103C2×C4×C73#9911yescharacteristic
104C2×C4×C73#13112yes—
105C2×Dic73—21no—
106C2×Dic73—21no—
107C2×Dic73—22no—
108C2×Dic73—21no—
109C2×Dic73—21no—
110C2×Dic73—21no—
111C2×Dic73—21no—
112C2×Dic73—21no—
113C2×Dic73—41no—
114C2×Dic73—41no—
115C2×Dic73—41no—
116C2×Dic73—41no—
117C2×Dic73—41no—
118C2×Dic73—41no—
119C2×Dic73—41no—
120C2×Dic73#10112yes—
121Dic146—44no—
122#10596833—82no—
123#10596833—82no—
124C22×C73—21no—
125C22×C73—21no—
126C22×C73#40811yescharacteristic
127C22×C73C2×#9911yescharacteristic
128C22×C73C2×#10111yescharacteristic
129C4×C73—21no—
130C4×C73—21no—
131C4×C73—22no—
132C4×C73—41no—
133C4×C73—81no—
134C4×C73—81no—
135Dic73—22no—
136Dic73—42no—
137Dic73—41no—
138Dic73—41no—
139Dic73—41no—
140Dic73—81no—
141#11571—731nomaximal, Sylow
142C2×C73—21no—
143C2×C73—21no—
144C2×C73#147211yescharacteristic
145C2×C73#212611yescharacteristic
146C2×C73#213311yescharacteristic
147#2565—731no—
148#1467—731no—
149#1461—731no—
150#1325—732no—
151#1324—732no—
152C73#1157111yescharacteristic, complemented, Sylow
153C2×#125#6440811yescharacteristic
154C2×C4×Q8—731no—
155#432—1461no—
156#431—1461no—
157#398—1461no—
158#398—1461no—
159#391—731no—
160#391—731no—
161#387—1461no—
162#387—1461no—
163#384—731no—
164#382—731no—
165C4×C4⋊C4—731no—
166#324—732no—
167#324—732no—
168#324—1461no—
169#324—1461no—
170C22×Q8—731no—
171#125—41no—
172#125—41no—
173C4×Q8—2921no—
174C4×Q8—2921no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—731no—
178C2×C4⋊C4—731no—
179C2×C4⋊C4—731no—
180C2×C4⋊C4—1461no—
181C2×C4⋊C4—1461no—
182C2×C4⋊C4—1461no—
183C2×C4⋊C4C2×#6440811yescharacteristic
184C2×C4⋊C4C2×#6440811yescharacteristic
185C2×C42—731no—
186C2×C42—731no—
187C2×C42—731no—
188C2×C42—731no—
189C2×C42C2×#6440811yescharacteristic
190C4⋊C8—2921no—
191C4⋊C8—2921no—
192C22⋊C8—1462no—
193C22⋊C8—1462no—
194#97—2921no—
195C4×C8—2921no—
196#95—1461no—
197#95—1461no—
198#95—1461no—
199#95—1461no—
200#95—1461no—
201#95—1461no—
202#95—1461no—
203C2×Q8—2921no—
204C2×Q8—1462no—
205C2×Q8—1462no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—731no—
209C22×C4—731no—
210C22×C4—731no—
211C22×C4—731no—
212C22×C4—1461no—
213C22×C4—1461no—
214C22×C4C22⋊#6440811yescharacteristic
215C22×C4C22⋊#6440811yescharacteristic
216C22×C4C22×#6440811yescharacteristic
217C2×C8—2922no—
218C2×C8—2922no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—42no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—2921no—
225C4⋊C4—2921no—
226C4⋊C4—2921no—
227C4⋊C4—2922no—
228C4⋊C4—2922no—
229C4⋊C4—2922no—
230C42—21no—
231C42—21no—
232C42—1462no—
233C42—1462no—
234C42—1461no—
235C42—1461no—
236C42—1461no—
237C42—1461no—
238C23C2×C22⋊#6440811yescharacteristic
239Q8—2924no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—2921no—
251C2×C4—2921no—
252C2×C4—2921no—
253C2×C4—2921no—
254C2×C4—2921no—
255C2×C4—2921no—
256C2×C4—2921no—
257C2×C4—732no—
258C2×C4—1462no—
259C2×C4—1461no—
260C2×C4—1461no—
261C2×C4—1461no—
262C2×C4—1461no—
263C2×C4—1461no—
264C2×C4—1461no—
265C2×C4—1461no—
266C2×C4#1455664911yescharacteristic
267C2×C4#1455664911yescharacteristic
268C2×C4#1455667912yes—
269C8—5842no—
270C8—5842no—
271C22—21no—
272C22—21no—
273C22#1798956211yescharacteristic
274C22C2×#1455664911yescharacteristic
275C22D73⋊#10111yescharacteristic
276C4—21no—
277C4—21no—
278C4—22no—
279C4—41no—
280C4—81no—
281C4—81no—
282C4—2922no—
283C4—2921no—
284C4—2921no—
285C4—2921no—
286C4—5841no—
287C4—1462no—
288C2—21no—
289C2—21no—
290C2#2262521111yescharacteristic
291C2#2262620211yescharacteristic
292C2#2262622611yescharacteristic
subgroupG/H
centerC22C2×#14556649
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC2×#125×C73C4
socleC22×C73C2×#99
prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4⋊Dic73C23
hypercenterC2×#125#64408
hypocenterC73#11571
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
152. C73#11571semidirect

Maximal subgroups

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

subgroupindex
#226251932
#226251732
#226248742
#226248722
#226151232
#1157173