Finite Group Databasebeta

← #34003769

Subgroups — #34003769

Order 18688.

708 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 156 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×#14556658C212yesmaximal, complemented
2C2×#17989445C212yesmaximal
3#22624809C212yesmaximal, complemented
4#22612495C211yesmaximal, characteristic
5C2×#14556658C2214yes—
6C2×C4×#10596833—22no—
7#17989453—22no—
8#17989445C418yescomplemented
9C2×#14556587C2211yescharacteristic
10C2×D4×Dic73C411yescharacteristic
11C2×#14556553C411yescharacteristic
12C2×#14556551—22no—
13#17988489C411yescharacteristic
14#17988487—22no—
15#17988456C2211yescharacteristic
16C42×Dic73C2211yescharacteristic
17#390×C73C411yescharacteristic
18C22×#10596833—24no—
19#14556658—24no—
20#14556658C2×C418yescomplemented
21C4×#10596833—44no—
22C22×D292C2×C411yescharacteristic
23C22×C22⋊D73—22no—
24C23×Dic73—21no—
25C22×C4×D73—21no—
26#14556587—22no—
27#14556587C2×C414yes—
28D4×Dic73—42no—
29#14556553—42no—
30#14556551—44no—
31#14556551—44no—
32C2×C4⋊Dic73C2×C411yescharacteristic
33C2×#11924007—22no—
34C2×C22⋊Dic73—21no—
35C2×#11924005—21no—
36C2×#11924005—22no—
37C2×C4×Dic73C2×C411yescharacteristic
38C2×C4×Dic73D412yes—
39C2×C4×Dic73D412yes—
40C2×C4×Dic73C2311yescharacteristic
41C22×D4×C73C2×C411yescharacteristic
42C2×C4⋊C4×C73C2×C411yescharacteristic
43C2×C22⋊C4×C73—22no—
44C2×C42×C73C2×C411yescharacteristic
45C2×#10596833—28no—
46C2×#10596833—44no—
47C2×#10596833—44no—
48C23×D73—21no—
49C2×D292—21no—
50C2×D292—41no—
51C2×D292—41no—
52C2×D292C4212yes—
53C2×C22⋊D73—28no—
54C2×C22⋊D73—42no—
55C2×C22⋊D73—42no—
56C2×C22⋊D73—44no—
57C22×Dic73—21no—
58C22×Dic73—42no—
59C22×Dic73—44no—
60C22×Dic73C22⋊C411yescharacteristic
61C22×Dic73C22⋊C411yescharacteristic
62C22×Dic73C2×D412yes—
63C2×C4×D73—42no—
64C2×C4×D73—44no—
65C4⋊Dic73—41no—
66#11924007—42no—
67#11924007—42no—
68C22⋊Dic73—42no—
69#11924005—42no—
70#11924005—44no—
71C4×Dic73—22no—
72C4×Dic73—24no—
73C4×Dic73D814yes—
74C4×Dic73SD1614yes—
75C4×Dic73C22×C412yes—
76C4×Dic73#4112yes—
77C24×C73—21no—
78C2×D4×C73—21no—
79C2×D4×C73—41no—
80C2×D4×C73—41no—
81C2×D4×C73C4212yes—
82C22×C4×C73—21no—
83C22×C4×C73C22⋊C412yes—
84C22×C4×C73C22×C411yescharacteristic
85C4⋊C4×C73—41no—
86C22⋊C4×C73—44no—
87C42×C73—41no—
88C23×C73—22no—
89C23×C73—41no—
90C23×C73—41no—
91C23×C73—42no—
92C23×C73—42no—
93C23×C73C2×C22⋊C411yescharacteristic
94C22×D73—22no—
95C22×D73—41no—
96C22×D73—41no—
97C22×D73—42no—
98C22×D73—42no—
99D4×C73—42no—
100D4×C73—42no—
101C2×C4×C73—21no—
102C2×C4×C73—22no—
103C2×C4×C73—21no—
104C2×C4×C73—22no—
105C2×C4×C73—41no—
106C2×C4×C73—42no—
107C2×C4×C73#10214yes—
108C2×C4×C73C2×C4211yescharacteristic
109C2×C4×C73#11711yescharacteristic
110C22⋊D73—48no—
111C22⋊D73—48no—
112C2×Dic73—21no—
113C2×Dic73—22no—
114C2×Dic73—41no—
115C2×Dic73—42no—
116C2×Dic73—84no—
117C2×Dic73#10012yes—
118C2×Dic73#10214yes—
119C2×Dic73C4×D414yes—
120C2×Dic73C2×D812yes—
121C2×Dic73C2×SD1612yes—
122C2×Dic73#13514yes—
123D292—42no—
124D292—42no—
125C4×D73—84no—
126#10596833—48no—
127C22×C73—42no—
128C22×C73—44no—
129C22×C73—81no—
130C22×C73—82no—
131C22×C73—81no—
132C22×C73C4×C22⋊C411yescharacteristic
133C22×C73C2×#10011yescharacteristic
134C22×C73#41311yescharacteristic
135C22×C73C2×#10212yes—
136C22×C73#41612yes—
137C2×D73—42no—
138C2×D73—44no—
139C2×D73—81no—
140C2×D73—82no—
141C2×D73—81no—
142C4×C73—24no—
143C4×C73—21no—
144C4×C73—21no—
145C4×C73—81no—
146Dic73—41no—
147Dic73—81no—
148Dic73#33114yescomplemented
149Dic73C4×D814yes—
150Dic73C4×SD1614yes—
151C4×#331—731nomaximal, Sylow
152C2×C73—82no—
153C2×C73C2×#33111yescharacteristic
154C2×C73#154012yes—
155C2×C73#154311yescharacteristic
156C2×C73C4×#10011yescharacteristic
157C2×C73C4×#10212yes—
158D73—82no—
159C4×#127—731no—
160C4×C4⋊C8—732no—
161C2×#331—732no—
162#1296—732no—
163C73C4×#33111yescharacteristic, complemented, Sylow
164C2×#127—731no—
165C2×C4×D4—731no—
166C2×C4×D4—731no—
167C2×C4×D4—1462no—
168C2×C4⋊C8—734no—
169C2×C4×C8—1462no—
170#390—731no—
171#390—1462no—
172#390#6440811yescharacteristic
173#384—731no—
174C43—731no—
175#336—1462no—
176#331—738no—
177C22×D4—731no—
178C22×D4—1462no—
179C22×D4C2×#6440811yescharacteristic
180C23×C4—1461no—
181C23×C4—1461no—
182C22×C8—1464no—
183#127—734no—
184#127—1462no—
185C4×D4—2924no—
186C4×D4—2924no—
187C4×D4—2922no—
188C4×D4—2922no—
189C2×C4⋊C4—731no—
190C2×C4⋊C4—1462no—
191C2×C4⋊C4C2×#6440811yescharacteristic
192C2×C22⋊C4—22no—
193C2×C22⋊C4—1461no—
194C2×C22⋊C4—1461no—
195C2×C22⋊C4—1462no—
196C2×C42—732no—
197C2×C42—731no—
198C2×C42—732no—
199C2×C42—731no—
200C2×C42C2×#6440811yescharacteristic
201C4⋊C8—738no—
202C4⋊C8—1464no—
203C4×C8—2924no—
204C24—21no—
205C24—1461no—
206C2×D4—21no—
207C2×D4—41no—
208C2×D4—41no—
209C2×D4—2921no—
210C2×D4—2921no—
211C2×D4—2922no—
212C2×D4—2922no—
213C2×D4—2924no—
214C2×D4—732no—
215C2×D4—1468no—
216C2×D4—1461no—
217C2×D4C4×#6440812yes—
218C22×C4—21no—
219C22×C4—2924no—
220C22×C4—2922no—
221C22×C4—2924no—
222C22×C4—2922no—
223C22×C4—731no—
224C22×C4—732no—
225C22×C4—731no—
226C22×C4—1461no—
227C22×C4C22⋊#6440812yes—
228C22×C4C22×#6440811yescharacteristic
229C2×C8—2924no—
230C2×C8—2924no—
231C2×C8—1468no—
232C4⋊C4—41no—
233C4⋊C4—2921no—
234C4⋊C4—2922no—
235C4⋊C4—2922no—
236C22⋊C4—44no—
237C22⋊C4—2922no—
238C22⋊C4—2922no—
239C22⋊C4—2924no—
240C42—41no—
241C42—734no—
242C42—734no—
243C42—732no—
244C42—732no—
245C42—1464no—
246C42—1462no—
247C23—22no—
248C23—41no—
249C23—41no—
250C23—42no—
251C23—42no—
252C23—2921no—
253C23—2921no—
254C23—2922no—
255C23—2922no—
256C23—1462no—
257C23C2×C22⋊#6440811yescharacteristic
258D4—42no—
259D4—42no—
260D4—2922no—
261D4—2922no—
262D4—2928no—
263D4—2928no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—2921no—
271C2×C4—2922no—
272C2×C4—5844no—
273C2×C4—5844no—
274C2×C4—734no—
275C2×C4—732no—
276C2×C4—732no—
277C2×C4—732no—
278C2×C4—734no—
279C2×C4—734no—
280C2×C4—1461no—
281C2×C4—1462no—
282C2×C4#1455665314yes—
283C2×C4C2×C4×#6440811yescharacteristic
284C2×C4#1455667011yescharacteristic
285C8—2928no—
286C22—42no—
287C22—44no—
288C22—81no—
289C22—82no—
290C22—81no—
291C22—2922no—
292C22—2924no—
293C22—5841no—
294C22—5842no—
295C22—5841no—
296C22C4×C22⋊#6440811yescharacteristic
297C22D73⋊#10011yescharacteristic
298C22#1798957411yescharacteristic
299C22C2×#1455665312yes—
300C22#1798957712yes—
301C4—21no—
302C4—21no—
303C4—24no—
304C4—81no—
305C4—2921no—
306C4—5841no—
307C4—734no—
308C4—734no—
309C4—734no—
310C2—82no—
311C2—5842no—
312C2D73⋊#33111yescharacteristic
313C2#2262542912yes—
314C2#2262543511yescharacteristic
315C2#2262568111yescharacteristic
316C2C4×#1455665312yes—
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C2×C42
FrattiniC22×C4C22×#64408
Fitting#390×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC2×#14556587C22
cosocleC2×C4×Dic73C23
hypercenter#390#64408
hypocenterC73C4×#331
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C4×#14556658C2semidirect
3. #22624809C2semidirect
8. #17989445C4semidirect
20. #14556658C2×C4semidirect
148. Dic73#331semidirect
163. C73C4×#331semidirect

Maximal subgroups

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

subgroupindex
C4×#145566582
C2×#179894452
#226248092
#226124952
C4×#33173