Finite Group Databasebeta

← #34001469

Subgroups — #34001469

Order 18688.

612 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 118 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#22625822C211yesmaximal, characteristic
2#22625594C211yesmaximal, characteristic
3#22624750C214yesmaximal, complemented
4C2×#17988483C211yesmaximal, characteristic
5C22×#11924037—21no—
6C2×C22⋊#10596833—21no—
7#17989453—21no—
8#17989453—21no—
9#17989453C2212yes—
10#17989453C2212yes—
11C22×C4⋊Dic73C411yescharacteristic
12C22×#11924007—21no—
13C22×C4×Dic73C2211yescharacteristic
14#17988483—21no—
15#17988483—21no—
16#17988483C412yes—
17#17988483C2212yes—
18C2×#14556498—21no—
19C22×C4⋊C4×C73C411yescharacteristic
20C2×#11924037—24no—
21C2×#11924037—42no—
22C2×#11924037—42no—
23C22×#10596833—22no—
24C22×#10596833—22no—
25C22⋊#10596833—42no—
26C23×Dic73—21no—
27C23×Dic73D411yescharacteristic
28C23×Dic73D411yescharacteristic
29C2×C4⋊Dic73—24no—
30C2×C4⋊Dic73—21no—
31C2×C4⋊Dic73C2×C412yes—
32C2×#11924007—22no—
33C2×#11924007—22no—
34C2×#11924007—44no—
35C2×C4×Dic73—42no—
36C2×C4×Dic73C2×C411yescharacteristic
37C2×C4×Dic73D411yescharacteristic
38C2×C4×Dic73D411yescharacteristic
39C2×C4×Dic73C2311yescharacteristic
40#14556498—22no—
41#14556498—22no—
42C23×C4×C73—21no—
43C23×C4×C73C2×C411yescharacteristic
44C2×C4⋊C4×C73—21no—
45C2×C4⋊C4×C73—42no—
46C2×C4⋊C4×C73C2×C412yes—
47#11924037—48no—
48C2×#10596833—24no—
49C2×#10596833—42no—
50C2×#10596833—42no—
51C2×#10596833—42no—
52C2×#10596833—42no—
53C2×#10596833—42no—
54C22×Dic73—22no—
55C22×Dic73—22no—
56C22×Dic73—24no—
57C22×Dic73—22no—
58C22×Dic73—22no—
59C22×Dic73—22no—
60C22×Dic73—41no—
61C22×Dic73—42no—
62C22×Dic73—42no—
63C22×Dic73C22⋊C411yescharacteristic
64C22×Dic73C22⋊C411yescharacteristic
65C22×Dic73SD1612yes—
66C22×Dic73Q1612yes—
67C22×Dic73C2×D411yescharacteristic
68C22×Dic73C2×D411yescharacteristic
69C4⋊Dic73—24no—
70C4⋊Dic73—22no—
71C4⋊Dic73M1614yescomplemented
72#11924007—44no—
73#11924007—44no—
74C4×Dic73—41no—
75C4×Dic73—41no—
76C4×Dic73—41no—
77C4×Dic73—41no—
78C24×C73C22⋊C411yescharacteristic
79C22×C4×C73—22no—
80C22×C4×C73—22no—
81C22×C4×C73—22no—
82C22×C4×C73—22no—
83C22×C4×C73—42no—
84C22×C4×C73—42no—
85C22×C4×C73—42no—
86C22×C4×C73C22⋊C411yescharacteristic
87C22×C4×C73C22×C411yescharacteristic
88C4⋊C4×C73—42no—
89C4⋊C4×C73—42no—
90C23×C73—21no—
91C23×C73—21no—
92C23×C73—21no—
93C23×C73—21no—
94C23×C73#9912yes—
95C23×C73#10312yes—
96C23×C73#10412yes—
97C23×C73C2×C22⋊C411yescharacteristic
98C2×C4×C73—28no—
99C2×C4×C73—21no—
100C2×C4×C73—21no—
101C2×C4×C73—21no—
102C2×C4×C73—21no—
103C2×C4×C73—42no—
104C2×C4×C73—42no—
105C2×C4×C73—42no—
106C2×C4×C73—84no—
107C2×C4×C73#10112yes—
108C2×C4×C73C2×M1612yes—
109C2×Dic73—24no—
110C2×Dic73—24no—
111C2×Dic73—21no—
112C2×Dic73—21no—
113C2×Dic73—21no—
114C2×Dic73—21no—
115C2×Dic73—21no—
116C2×Dic73—21no—
117C2×Dic73—24no—
118C2×Dic73—21no—
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73—44no—
122C2×Dic73—48no—
123C2×Dic73—42no—
124C2×Dic73—42no—
125C2×Dic73#10312yes—
126C2×Dic73C2×SD1611yescharacteristic
127C2×Dic73C2×Q1611yescharacteristic
128C2×Dic73AGL(1,ℤ/8)12yes—
129#10596833—44no—
130#10596833—82no—
131C22×C73—22no—
132C22×C73—22no—
133C22×C73—22no—
134C22×C73—22no—
135C22×C73—22no—
136C22×C73—22no—
137C22×C73#32814yes—
138C22×C73#40711yescharacteristic
139C22×C73C2×#9911yescharacteristic
140C22×C73C2×#10111yescharacteristic
141C22×C73C2×#10311yescharacteristic
142C22×C73#41811yescharacteristic
143C22×C73C2×#10411yescharacteristic
144C22×C73#42111yescharacteristic
145C4×C73—22no—
146C4×C73—22no—
147C4×C73—82no—
148Dic73—21no—
149Dic73—22no—
150Dic73—21no—
151Dic73—22no—
152Dic73—44no—
153Dic73—41no—
154#7607—731nomaximal, Sylow
155C2×C73—24no—
156C2×C73#146311yescharacteristic
157C2×C73#148711yescharacteristic
158C2×C73#149011yescharacteristic
159C2×C73C2×#32811yescharacteristic
160C2×C73#151011yescharacteristic
161C2×C73#152811yescharacteristic
162C2×C73#154911yescharacteristic
163C2×#389—731no—
164#1817—731no—
165#1728—731no—
166#1271—734no—
167C73#760711yescharacteristic, complemented, Sylow
168C22×M16—1461no—
169C22×C4⋊C4—731no—
170C22×C4⋊C4—1461no—
171C22×C4⋊C4#6440811yescharacteristic
172C22×C42—731no—
173C2×C22⋊C8—1461no—
174#389—732no—
175#389—732no—
176#389—1461no—
177#389—1461no—
178C2×#95—1461no—
179#336—732no—
180#336—732no—
181#336—1461no—
182#336—1461no—
183C23×C4—21no—
184C23×C4—731no—
185C23×C4—731no—
186C23×C4—1461no—
187C23×C4C2×#6440811yescharacteristic
188C2×M16—2922no—
189C2×M16—2922no—
190C2×M16—1464no—
191C22×C8—1462no—
192C22×C8—1462no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—42no—
195C2×C4⋊C4—2924no—
196C2×C4⋊C4—732no—
197C2×C4⋊C4—1462no—
198C2×C4⋊C4—1462no—
199C2×C4⋊C4—1464no—
200C2×C4⋊C4—1461no—
201C2×C4⋊C4C2×#6440812yes—
202C2×C42—2922no—
203C2×C42—731no—
204C2×C42—731no—
205C2×C42—731no—
206C2×C42—731no—
207C22⋊C8—2922no—
208#95—1462no—
209#95—1462no—
210C24C22⋊#6440811yescharacteristic
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—2922no—
219C22×C4—2922no—
220C22×C4—2921no—
221C22×C4—732no—
222C22×C4—732no—
223C22×C4—731no—
224C22×C4—731no—
225C22×C4—731no—
226C22×C4—731no—
227C22×C4—1462no—
228C22×C4—1464no—
229C22×C4—1462no—
230C22×C4—1462no—
231C22×C4—1462no—
232C22×C4—1462no—
233C22×C4C22⋊#6440811yescharacteristic
234C22×C4C22×#6440811yescharacteristic
235M16—2928no—
236C2×C8—2922no—
237C2×C8—2922no—
238C2×C8—2922no—
239C2×C8—2922no—
240C2×C8—2922no—
241C2×C8—1464no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—2924no—
245C4⋊C4—2924no—
246C4⋊C4—734no—
247C4⋊C4—1464no—
248C4⋊C4—1462no—
249C42—2921no—
250C42—2921no—
251C42—2921no—
252C42—2921no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23#1455664912yes—
258C23#1455665412yes—
259C23#1455665612yes—
260C23C2×C22⋊#6440811yescharacteristic
261C2×C4—28no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—84no—
270C2×C4—2928no—
271C2×C4—2922no—
272C2×C4—2922no—
273C2×C4—2924no—
274C2×C4—731no—
275C2×C4—732no—
276C2×C4—731no—
277C2×C4—732no—
278C2×C4—1464no—
279C2×C4—1461no—
280C2×C4—1461no—
281C2×C4—1461no—
282C2×C4—1464no—
283C2×C4—1464no—
284C2×C4—1461no—
285C2×C4—1461no—
286C2×C4—1461no—
287C2×C4—1461no—
288C2×C4—1461no—
289C2×C4—1461no—
290C2×C4#1455665212yes—
291C2×C4D73⋊M1612yes—
292C8—2924no—
293C8—5842no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22#1798944114yes—
301C22#1798955911yescharacteristic
302C22C2×#1455664911yescharacteristic
303C22C2×#1455665211yescharacteristic
304C22C2×#1455665411yescharacteristic
305C22#1798957911yescharacteristic
306C22C2×#1455665611yescharacteristic
307C22#1798958511yescharacteristic
308C4—22no—
309C4—22no—
310C4—82no—
311C4—2921no—
312C4—2924no—
313C4—1461no—
314C4—1462no—
315C4—1461no—
316C4—1462no—
317C2—24no—
318C2#2262518111yescharacteristic
319C2#2262526111yescharacteristic
320C2#2262527211yescharacteristic
321C2C2×#1798944111yescharacteristic
322C2#2262533611yescharacteristic
323C2#2262539511yescharacteristic
324C2#2262544611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC22×C4⋊C4×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22⋊C4
cosocleC2×C4×Dic73C23
hypercenterC22×C4⋊C4#64408
hypocenterC73#7607
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #22624750C2semidirect
71. C4⋊Dic73M16semidirect
167. C73#7607semidirect

Maximal subgroups

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

subgroupindex
#226258222
#226255942
#226247502
C2×#179884832
#760773