Finite Group Databasebeta

← #34001743

Subgroups — #34001743

Order 18688.

562 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 116 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
1C4×#14556648C211yesmaximal, characteristic
2#22625595C211yesmaximal, characteristic
3#22624749C214yesmaximal, complemented
4#22618284C211yesmaximal, characteristic
5C22×#11924038—21no—
6C2×#14556648—21no—
7C2×C4×#10596833—21no—
8#17989453—21no—
9#17989453C2212yes—
10#17989453C2212yes—
11C2×#14556591C411yescharacteristic
12C2×#14556571—21no—
13C2×C42×D73C2211yescharacteristic
14#17988492—21no—
15#17988486—21no—
16#17988486C2212yes—
17#17988444—21no—
18#17988444C412yes—
19#384×C73C411yescharacteristic
20C2×#11924038—24no—
21C2×#11924038—42no—
22C2×#11924038—42no—
23C22×#10596833—22no—
24C22×#10596833—22no—
25#14556648—24no—
26C4×#10596833—42no—
27C22×Dic146—21no—
28C22×C4×D73C2×C411yescharacteristic
29C22×C4×D73D411yescharacteristic
30C22×C4×D73D411yescharacteristic
31#14556591—42no—
32#14556571—42no—
33#14556571—42no—
34C2×C4⋊Dic73—22no—
35C2×C4⋊Dic73—21no—
36C2×C4⋊Dic73C2×C412yes—
37C2×#11924005—22no—
38C2×C4×Dic73D411yescharacteristic
39C2×C4×Dic73D411yescharacteristic
40C2×C4×Dic73C2311yescharacteristic
41C42×D73—42no—
42#14556498—22no—
43#14556498—22no—
44C2×C4⋊C4×C73—21no—
45C2×C4⋊C4×C73—21no—
46C2×C4⋊C4×C73C2×C412yes—
47C2×C42×C73C2×C411yescharacteristic
48#11924038—48no—
49C2×#10596833—24no—
50C2×#10596833—24no—
51C2×#10596833—42no—
52C2×#10596833—42no—
53C2×#10596833—42no—
54C2×#10596833—42no—
55C23×D73C22⋊C411yescharacteristic
56C2×Dic146—42no—
57C2×Dic146—42no—
58C2×Dic146—42no—
59C22×Dic73—22no—
60C22×Dic73C22⋊C411yescharacteristic
61C22×Dic73C2×D411yescharacteristic
62C22×Dic73C2×D411yescharacteristic
63C2×C4×D73—22no—
64C2×C4×D73—22no—
65C2×C4×D73—22no—
66C2×C4×D73—22no—
67C2×C4×D73—22no—
68C2×C4×D73—22no—
69C2×C4×D73—41no—
70C2×C4×D73—41no—
71C2×C4×D73D812yes—
72C2×C4×D73SD1612yes—
73C4⋊Dic73—42no—
74C4⋊Dic73—42no—
75C4⋊Dic73—42no—
76C4⋊Dic73—42no—
77#11924005—44no—
78C4×Dic73—22no—
79C4×Dic73—41no—
80C4×Dic73—41no—
81C22×C4×C73—22no—
82C22×C4×C73C22⋊C411yescharacteristic
83C22×C4×C73C22⋊C411yescharacteristic
84C22×C4×C73C22×C411yescharacteristic
85C4⋊C4×C73—24no—
86C4⋊C4×C73—42no—
87C4⋊C4×C73—42no—
88C42×C73—22no—
89C23×C73C2×C22⋊C411yescharacteristic
90C22×D73—21no—
91C22×D73—21no—
92C22×D73—21no—
93C22×D73—21no—
94C22×D73—21no—
95C22×D73—21no—
96C22×D73#10212yes—
97C2×C4×C73—21no—
98C2×C4×C73—21no—
99C2×C4×C73—21no—
100C2×C4×C73—21no—
101C2×C4×C73—42no—
102C2×C4×C73—42no—
103C2×C4×C73—42no—
104C2×C4×C73#9912yes—
105C2×C4×C73#10212yes—
106C2×C4×C73#10412yes—
107C2×C4×C73#10412yes—
108C2×C4×C73#13112yes—
109C2×Dic73—21no—
110C2×Dic73—21no—
111C2×Dic73—21no—
112C2×Dic73—21no—
113C2×Dic73—21no—
114C2×Dic73—21no—
115C2×Dic73—42no—
116C2×Dic73—42no—
117C2×Dic73—42no—
118C2×Dic73#10112yes—
119C2×Dic73C2×D811yescharacteristic
120C2×Dic73C2×SD1611yescharacteristic
121C2×Dic73#13712yes—
122C4×D73—24no—
123C4×D73—24no—
124C4×D73—44no—
125C4×D73—44no—
126Dic146—84no—
127#10596833—44no—
128#10596833—44no—
129C22×C73#40811yescharacteristic
130C22×C73C2×#9911yescharacteristic
131C22×C73C2×#10111yescharacteristic
132C22×C73C2×#10211yescharacteristic
133C22×C73#41911yescharacteristic
134C22×C73C2×#10411yescharacteristic
135C22×C73C2×#10411yescharacteristic
136C2×D73—22no—
137C2×D73—22no—
138C2×D73—22no—
139C2×D73—41no—
140C2×D73—41no—
141C2×D73—41no—
142C2×D73—41no—
143C4×C73—22no—
144C4×C73—22no—
145C4×C73—82no—
146C4×C73#32714yes—
147Dic73—22no—
148Dic73—21no—
149Dic73—21no—
150Dic73—22no—
151Dic73—82no—
152#7685—731nomaximal, Sylow
153C2×C73#147211yescharacteristic
154C2×C73#148511yescharacteristic
155C2×C73#149211yescharacteristic
156C2×C73C2×#32711yescharacteristic
157C2×C73#150811yescharacteristic
158C2×C73#152611yescharacteristic
159C2×C73#154611yescharacteristic
160D73—42no—
161#2857—731no—
162C4×C22⋊C8—731no—
163#1728—731no—
164#1271—734no—
165C73#768511yescharacteristic, complemented, Sylow
166C22×M16—1461no—
167C2×C4⋊Q8—731no—
168C2×C22⋊Q8—1461no—
169C22×C42—731no—
170C2×C22⋊C8—1461no—
171C2×C4×C8—1461no—
172#391—1461no—
173#389—732no—
174#389—1461no—
175#384#6440811yescharacteristic
176#380—732no—
177#380—1461no—
178#336—732no—
179#336—732no—
180#336—1461no—
181C22×Q8—1461no—
182C23×C4—731no—
183C23×C4—731no—
184C23×C4—731no—
185C2×M16—2922no—
186C2×M16—2922no—
187C2×M16—1464no—
188C22×C8—1462no—
189C22×C8—1462no—
190C4⋊Q8—2922no—
191C22⋊Q8—2922no—
192C22⋊Q8—2922no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—732no—
196C2×C4⋊C4—1462no—
197C2×C4⋊C4—1461no—
198C2×C4⋊C4C2×#6440812yes—
199C2×C22⋊C4—1462no—
200C2×C42—2922no—
201C2×C42—731no—
202C2×C42—731no—
203C2×C42—731no—
204C2×C42C2×#6440811yescharacteristic
205C22⋊C8—1464no—
206C4×C8—2922no—
207#95—1462no—
208#95—1462no—
209C24—731no—
210C2×Q8—2922no—
211C2×Q8—2922no—
212C2×Q8—2922no—
213C22×C4—22no—
214C22×C4—2921no—
215C22×C4—2921no—
216C22×C4—731no—
217C22×C4—731no—
218C22×C4—731no—
219C22×C4—732no—
220C22×C4—732no—
221C22×C4—1462no—
222C22×C4—1462no—
223C22×C4—1462no—
224C22×C4—1462no—
225C22×C4—1462no—
226C22×C4—1462no—
227C22×C4—1462no—
228C22×C4C22⋊#6440811yescharacteristic
229C22×C4C22⋊#6440811yescharacteristic
230C22×C4C22×#6440811yescharacteristic
231M16—2928no—
232C2×C8—2922no—
233C2×C8—2922no—
234C2×C8—2922no—
235C2×C8—2922no—
236C2×C8—1464no—
237C2×C8—1464no—
238C4⋊C4—24no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C4⋊C4—2922no—
242C4⋊C4—2922no—
243C4⋊C4—2922no—
244C4⋊C4—2922no—
245C22⋊C4—2924no—
246C42—22no—
247C42—2921no—
248C42—2921no—
249C42—1462no—
250C23—732no—
251C23—1461no—
252C23—1461no—
253C23—1461no—
254C23—1461no—
255C23—1461no—
256C23—1461no—
257C23C2×C22⋊#6440811yescharacteristic
258Q8—5844no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—2924no—
267C2×C4—2924no—
268C2×C4—2922no—
269C2×C4—2922no—
270C2×C4—2922no—
271C2×C4—732no—
272C2×C4—731no—
273C2×C4—731no—
274C2×C4—732no—
275C2×C4—1461no—
276C2×C4—1461no—
277C2×C4—1461no—
278C2×C4—1461no—
279C2×C4—1461no—
280C2×C4—1461no—
281C2×C4—1464no—
282C2×C4—1464no—
283C2×C4#1455665012yes—
284C2×C4#1455665312yes—
285C2×C4#1455665512yes—
286C2×C4#1455665612yes—
287C2×C4#1455667812yes—
288C8—2924no—
289C8—2924no—
290C22—2921no—
291C22—2921no—
292C22—2921no—
293C22—2921no—
294C22—1462no—
295C22—1462no—
296C22—1462no—
297C22#1798956111yescharacteristic
298C22C2×#1455665011yescharacteristic
299C22D73⋊#10111yescharacteristic
300C22C2×#1455665311yescharacteristic
301C22#1798958011yescharacteristic
302C22C2×#1455665511yescharacteristic
303C22C2×#1455665611yescharacteristic
304C4—22no—
305C4—22no—
306C4—82no—
307C4—5842no—
308C4—1461no—
309C4—1461no—
310C4—1462no—
311C4—1462no—
312C4#1798943914yes—
313C2—2922no—
314C2#2262520911yescharacteristic
315C2#2262525411yescharacteristic
316C2#2262527711yescharacteristic
317C2C2×#1798943911yescharacteristic
318C2#2262533011yescharacteristic
319C2#2262538911yescharacteristic
320C2#2262544111yescharacteristic
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#7685
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. #22624749C2semidirect
165. C73#7685semidirect

Maximal subgroups

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

subgroupindex
C4×#145566482
#226255952
#226247492
#226182842
#768573