Finite Group Databasebeta

← #34005251

Subgroups — #34005251

Order 18688.

526 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 100 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#22625658C211yesmaximal, characteristic
2#22625658C211yesmaximal, characteristic
3#22624807C214yesmaximal, complemented
4#22612336C211yesmaximal, characteristic
5C2×#14556648—21no—
6C2×#14556648—21no—
7C2×#14556646C2212yes—
8C2×#14556646C2212yes—
9#17989453—21no—
10#17989453—21no—
11C2×#14556549C412yes—
12C2×C42×D73C2211yescharacteristic
13#17988457C411yescharacteristic
14#17988452C2212yes—
15#17988444—21no—
16#17988444—21no—
17C4⋊C4×Dic73—21no—
18C4⋊C4×Dic73—21no—
19#384×C73C411yescharacteristic
20C22×#10596833—22no—
21C22×#10596833—22no—
22#14556648—24no—
23#14556648—24no—
24#14556646—24no—
25#14556646—24no—
26C22×C4×D73C2×C411yescharacteristic
27C22×C4×D73D411yescharacteristic
28C22×C4×D73D411yescharacteristic
29#14556549—44no—
30C2×C4⋊Dic73—21no—
31C2×C4⋊Dic73—21no—
32C2×C4⋊Dic73C2×C412yes—
33C2×#11924005—22no—
34C2×C4×Dic73—22no—
35C2×C4×Dic73D411yescharacteristic
36C2×C4×Dic73D411yescharacteristic
37C2×C4×Dic73C2311yescharacteristic
38C42×D73—24no—
39#14556498—22no—
40#14556498—22no—
41C2×C4⋊C4×C73—21no—
42C2×C4⋊C4×C73—21no—
43C2×C4⋊C4×C73C2×C412yes—
44C2×C42×C73C2×C411yescharacteristic
45C2×#10596833—24no—
46C2×#10596833—24no—
47C2×#10596833—42no—
48C2×#10596833—42no—
49C2×#10596833—42no—
50C2×#10596833—42no—
51C23×D73C22⋊C411yescharacteristic
52C22×Dic73—22no—
53C22×Dic73C22⋊C411yescharacteristic
54C22×Dic73C2×D411yescharacteristic
55C22×Dic73C2×D411yescharacteristic
56C2×C4×D73—22no—
57C2×C4×D73—22no—
58C2×C4×D73—22no—
59C2×C4×D73—22no—
60C2×C4×D73—22no—
61C2×C4×D73—22no—
62C2×C4×D73—22no—
63C2×C4×D73—41no—
64C2×C4×D73—41no—
65C4⋊Dic73—42no—
66C4⋊Dic73—42no—
67C4⋊Dic73—42no—
68#11924005—44no—
69C4×Dic73—22no—
70C4×Dic73—22no—
71C4×Dic73—44no—
72C4×Dic73#4114yes—
73C22×C4×C73—22no—
74C22×C4×C73C22⋊C411yescharacteristic
75C22×C4×C73C22⋊C411yescharacteristic
76C22×C4×C73C22×C411yescharacteristic
77C4⋊C4×C73—42no—
78C4⋊C4×C73—42no—
79C4⋊C4×C73—42no—
80C42×C73—22no—
81C23×C73C2×C22⋊C411yescharacteristic
82C22×D73—21no—
83C22×D73—21no—
84C22×D73—21no—
85C22×D73—21no—
86C22×D73—21no—
87C22×D73—21no—
88C22×D73#10012yes—
89C2×C4×C73—21no—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—21no—
93C2×C4×C73—21no—
94C2×C4×C73—21no—
95C2×C4×C73—42no—
96C2×C4×C73—42no—
97C2×C4×C73—42no—
98C2×C4×C73#10412yes—
99C2×C4×C73#10412yes—
100C2×C4×C73#11712yes—
101C2×Dic73—21no—
102C2×Dic73—21no—
103C2×Dic73—21no—
104C2×Dic73—21no—
105C2×Dic73—21no—
106C2×Dic73—21no—
107C2×Dic73—42no—
108C2×Dic73—42no—
109C2×Dic73—42no—
110C2×Dic73#10112yes—
111C2×Dic73#12312yes—
112C2×Dic73#12312yes—
113C4×D73—28no—
114C4×D73—44no—
115C4×D73—44no—
116#10596833—44no—
117#10596833—44no—
118C22×C73#38111yescharacteristic
119C22×C73C2×#10011yescharacteristic
120C22×C73C2×#10111yescharacteristic
121C22×C73C2×#10411yescharacteristic
122C22×C73C2×#10411yescharacteristic
123C22×C73#42111yescharacteristic
124C22×C73#42111yescharacteristic
125C2×D73—22no—
126C2×D73—22no—
127C2×D73—22no—
128C2×D73—41no—
129C2×D73—41no—
130C2×D73—41no—
131C2×D73—41no—
132C4×C73—22no—
133C4×C73—22no—
134C4×C73—22no—
135C4×C73—82no—
136Dic73—22no—
137Dic73—22no—
138Dic73—22no—
139Dic73—82no—
140#8722—731nomaximal, Sylow
141C2×C73#152611yescharacteristic
142C2×C73#153011yescharacteristic
143C2×C73#153011yescharacteristic
144C2×C73#153711yescharacteristic
145C2×C73#182111yescharacteristic
146C2×C73#182611yescharacteristic
147C2×C73#182611yescharacteristic
148D73—42no—
149#2285—731no—
150#1749—731no—
151#1749—731no—
152#1295—734no—
153C73#872211yescharacteristic, complemented, Sylow
154C2×#117—732no—
155C22×C42—731no—
156C2×C22⋊C8—1461no—
157C2×C22⋊C8—1461no—
158C2×#97—732no—
159C2×#97—732no—
160#384—731no—
161#384#6440811yescharacteristic
162#382—732no—
163#380—1461no—
164#380—1461no—
165C4×C4⋊C4—1461no—
166C4×C4⋊C4—1461no—
167#336—1461no—
168#336—1461no—
169C23×C4—731no—
170C23×C4—731no—
171C23×C4—731no—
172C22×C8—1462no—
173C22×C8—1462no—
174#117—2924no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—732no—
178C2×C4⋊C4—1461no—
179C2×C4⋊C4—1461no—
180C2×C4⋊C4C2×#6440812yes—
181C2×C22⋊C4—1462no—
182C2×C42—731no—
183C2×C42—731no—
184C2×C42—731no—
185C2×C42—1464no—
186C2×C42—1462no—
187C2×C42C2×#6440811yescharacteristic
188C22⋊C8—1464no—
189C22⋊C8—1464no—
190#97—1464no—
191#97—1464no—
192#95—1462no—
193#95—1462no—
194C24—731no—
195C22×C4—22no—
196C22×C4—2921no—
197C22×C4—2921no—
198C22×C4—731no—
199C22×C4—731no—
200C22×C4—731no—
201C22×C4—1462no—
202C22×C4—1462no—
203C22×C4—1462no—
204C22×C4—1462no—
205C22×C4—1462no—
206C22×C4—1462no—
207C22×C4—1462no—
208C22×C4—1462no—
209C22×C4C22⋊#6440811yescharacteristic
210C22×C4C22⋊#6440811yescharacteristic
211C22×C4C22×#6440811yescharacteristic
212C2×C8—2922no—
213C2×C8—2922no—
214C2×C8—2922no—
215C2×C8—2922no—
216C2×C8—1464no—
217C2×C8—1464no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—2922no—
222C4⋊C4—2922no—
223C4⋊C4—2922no—
224C22⋊C4—2924no—
225C42—22no—
226C42—2924no—
227C42—734no—
228C42—1462no—
229C42—1462no—
230C23—732no—
231C23—1461no—
232C23—1461no—
233C23—1461no—
234C23—1461no—
235C23—1461no—
236C23—1461no—
237C23C2×C22⋊#6440811yescharacteristic
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—2924no—
248C2×C4—2924no—
249C2×C4—2922no—
250C2×C4—2922no—
251C2×C4—2922no—
252C2×C4—732no—
253C2×C4—732no—
254C2×C4—732no—
255C2×C4—1468no—
256C2×C4—1461no—
257C2×C4—1461no—
258C2×C4—1461no—
259C2×C4—1461no—
260C2×C4—1461no—
261C2×C4—1461no—
262C2×C4#1455665512yes—
263C2×C4#1455665612yes—
264C2×C4#1455667012yes—
265C8—2924no—
266C8—2924no—
267C22—2921no—
268C22—2921no—
269C22—2921no—
270C22—2921no—
271C22—1462no—
272C22—1462no—
273C22—1462no—
274C22#1798953011yescharacteristic
275C22D73⋊#10011yescharacteristic
276C22D73⋊#10111yescharacteristic
277C22C2×#1455665511yescharacteristic
278C22C2×#1455665611yescharacteristic
279C22#1798958511yescharacteristic
280C22#1798958611yescharacteristic
281C4—22no—
282C4—22no—
283C4—22no—
284C4—82no—
285C4—5842no—
286C4—1462no—
287C4—1462no—
288C4—1462no—
289C2—2922no—
290C2#2262538911yescharacteristic
291C2#2262540111yescharacteristic
292C2#2262540211yescharacteristic
293C2#2262542311yescharacteristic
294C2#2262583111yescharacteristic
295C2#2262583711yescharacteristic
296C2#2262583811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
Fitting#384×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC23×D73C22⋊C4
cosocleC2×C4×Dic73C23
hypercenter#384#64408
hypocenterC73#8722
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
3. #22624807C2semidirect
153. C73#8722semidirect

Maximal subgroups

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

subgroupindex
#226256582
#226248072
#226123362
#872273