Finite Group Databasebeta

← #34003777

Subgroups — #34003777

Order 18688.

684 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 134 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#22625716C212yesmaximal, complemented
2C2×#17989445C212yesmaximal
3#22624809C212yesmaximal, complemented
4C4×#14556587C211yesmaximal, characteristic
5C2×#14556658C2214yes—
6C2×#14556646—22no—
7#17989453—22no—
8#17989445C418yescomplemented
9C2×#14556587C2211yescharacteristic
10C2×C4×D292C411yescharacteristic
11C2×C4×C22⋊D73—22no—
12#17988490C411yescharacteristic
13#17988488C411yescharacteristic
14#17988487—22no—
15#17988456C2211yescharacteristic
16C42×Dic73C2211yescharacteristic
17C2×C4×D4×C73C411yescharacteristic
18C22×#10596833—24no—
19#14556658—24no—
20#14556658C2×C418yescomplemented
21#14556646—44no—
22C22×D292C2×C411yescharacteristic
23C22×C22⋊D73—22no—
24C22×C4×D73—21no—
25#14556587—22no—
26#14556587C2×C414yes—
27C4×D292—42no—
28C4×C22⋊D73—48no—
29C2×C4⋊Dic73C2×C411yescharacteristic
30C2×#11924007—22no—
31C2×C22⋊Dic73—22no—
32C2×#11924005—22no—
33C2×#11924005—21no—
34C2×C4×Dic73C2×C411yescharacteristic
35C2×C4×Dic73D412yes—
36C2×C4×Dic73D412yes—
37C2×C4×Dic73C2311yescharacteristic
38C22×D4×C73C2×C411yescharacteristic
39C23×C4×C73—21no—
40C4×D4×C73—42no—
41C2×C4⋊C4×C73C2×C411yescharacteristic
42C2×C22⋊C4×C73—21no—
43C2×C42×C73C2×C411yescharacteristic
44C2×#10596833—28no—
45C2×#10596833—44no—
46C2×#10596833—44no—
47C23×D73—21no—
48C2×D292—21no—
49C2×D292—41no—
50C2×D292—41no—
51C2×D292C4212yes—
52C2×C22⋊D73—28no—
53C2×C22⋊D73—44no—
54C2×C22⋊D73—42no—
55C2×C22⋊D73—42no—
56C22×Dic73—21no—
57C22×Dic73C22⋊C412yes—
58C22×Dic73C2×D412yes—
59C2×C4×D73—44no—
60C2×C4×D73—42no—
61C4⋊Dic73—41no—
62#11924007—44no—
63C22⋊Dic73—44no—
64#11924005—44no—
65#11924005—42no—
66C4×Dic73—24no—
67C4×Dic73—22no—
68C4×Dic73—22no—
69C4×Dic73—41no—
70C4×Dic73C22×C412yes—
71C4×Dic73#4112yes—
72C24×C73—21no—
73C2×D4×C73—21no—
74C2×D4×C73—41no—
75C2×D4×C73—41no—
76C2×D4×C73C4212yes—
77C22×C4×C73—21no—
78C22×C4×C73—44no—
79C22×C4×C73—42no—
80C22×C4×C73C22⋊C411yescharacteristic
81C22×C4×C73C22⋊C411yescharacteristic
82C22×C4×C73C22×C411yescharacteristic
83C4⋊C4×C73—41no—
84C22⋊C4×C73—42no—
85C42×C73—22no—
86C23×C73—22no—
87C23×C73—41no—
88C23×C73—41no—
89C23×C73—42no—
90C23×C73—42no—
91C23×C73C2×C22⋊C411yescharacteristic
92C22×D73—22no—
93C22×D73—41no—
94C22×D73—41no—
95C22×D73—42no—
96C22×D73—42no—
97D4×C73—42no—
98D4×C73—42no—
99C2×C4×C73—21no—
100C2×C4×C73—21no—
101C2×C4×C73—22no—
102C2×C4×C73—21no—
103C2×C4×C73—22no—
104C2×C4×C73—41no—
105C2×C4×C73—42no—
106C2×C4×C73—84no—
107C2×C4×C73#10012yes—
108C2×C4×C73C2×C4211yescharacteristic
109C2×C4×C73#11711yescharacteristic
110C22⋊D73—48no—
111C22⋊D73—48no—
112C2×Dic73—22no—
113C2×Dic73—22no—
114C2×Dic73—22no—
115C2×Dic73—41no—
116C2×Dic73—42no—
117C2×Dic73C4×D414yes—
118C2×Dic73AGL(1,ℤ/8)14yes—
119C2×Dic73AGL(1,ℤ/8)12yes—
120C2×Dic73#13712yes—
121D292—42no—
122D292—42no—
123C4×D73—84no—
124#10596833—48no—
125C22×C73—42no—
126C22×C73—44no—
127C22×C73—81no—
128C22×C73—82no—
129C22×C73—81no—
130C22×C73C4×C22⋊C411yescharacteristic
131C22×C73C2×#10011yescharacteristic
132C22×C73#41311yescharacteristic
133C22×C73#41712yes—
134C22×C73#41812yes—
135C2×D73—42no—
136C2×D73—44no—
137C2×D73—81no—
138C2×D73—82no—
139C2×D73—81no—
140C4×C73—22no—
141C4×C73—21no—
142C4×C73—21no—
143C4×C73—41no—
144C4×C73—81no—
145Dic73—42no—
146Dic73—81no—
147Dic73#44014yes—
148Dic73#44214yes—
149#8231—731nomaximal, Sylow
150C2×C73—82no—
151C2×C73#155511yescharacteristic
152C2×C73#155712yes—
153C2×C73#156011yescharacteristic
154C2×C73C4×#10011yescharacteristic
155C2×C73#176212yes—
156D73—82no—
157C4×#127—731no—
158#1767—732no—
159C2×#331—732no—
160#1296—732no—
161C73#823111yescharacteristic, complemented, Sylow
162C2×#127—731no—
163C2×C4×D4—731no—
164C2×C4×D4—1462no—
165C2×C4×D4#6440811yescharacteristic
166C2×C4⋊C8—734no—
167C2×#97—1462no—
168#390—731no—
169#390—731no—
170#390—1462no—
171#384—731no—
172C43—731no—
173#336—1462no—
174#331—738no—
175C22×D4—731no—
176C22×D4—1462no—
177C22×D4C2×#6440811yescharacteristic
178C23×C4—21no—
179C23×C4—1461no—
180C22×C8—1464no—
181#127—734no—
182#127—1462no—
183C4×D4—42no—
184C4×D4—2922no—
185C4×D4—2928no—
186C2×C4⋊C4—731no—
187C2×C4⋊C4—1462no—
188C2×C4⋊C4C2×#6440811yescharacteristic
189C2×C22⋊C4—21no—
190C2×C22⋊C4—1462no—
191C2×C22⋊C4—1462no—
192C2×C22⋊C4—1461no—
193C2×C42—731no—
194C2×C42—731no—
195C2×C42—732no—
196C2×C42—732no—
197C2×C42C2×#6440811yescharacteristic
198C4⋊C8—738no—
199C4⋊C8—1464no—
200#97—2924no—
201C24—21no—
202C24—1461no—
203C2×D4—21no—
204C2×D4—41no—
205C2×D4—41no—
206C2×D4—2921no—
207C2×D4—2921no—
208C2×D4—2924no—
209C2×D4—2922no—
210C2×D4—2922no—
211C2×D4—732no—
212C2×D4—1468no—
213C2×D4—1461no—
214C2×D4C4×#6440812yes—
215C22×C4—21no—
216C22×C4—44no—
217C22×C4—42no—
218C22×C4—2924no—
219C22×C4—2922no—
220C22×C4—732no—
221C22×C4—732no—
222C22×C4—1461no—
223C22×C4C22⋊#6440811yescharacteristic
224C22×C4C22⋊#6440811yescharacteristic
225C22×C4C22×#6440811yescharacteristic
226C2×C8—2924no—
227C2×C8—2924no—
228C2×C8—1468no—
229C4⋊C4—41no—
230C4⋊C4—2921no—
231C4⋊C4—2924no—
232C22⋊C4—42no—
233C22⋊C4—2922no—
234C22⋊C4—2924no—
235C22⋊C4—2924no—
236C42—22no—
237C42—2921no—
238C42—732no—
239C42—732no—
240C42—1462no—
241C42—1462no—
242C42—1464no—
243C23—22no—
244C23—41no—
245C23—41no—
246C23—42no—
247C23—42no—
248C23—2921no—
249C23—2921no—
250C23—2922no—
251C23—2922no—
252C23—1462no—
253C23C2×C22⋊#6440811yescharacteristic
254D4—42no—
255D4—42no—
256D4—2922no—
257D4—2922no—
258D4—2928no—
259D4—2928no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—84no—
268C2×C4—2921no—
269C2×C4—2922no—
270C2×C4—5844no—
271C2×C4—734no—
272C2×C4—732no—
273C2×C4—732no—
274C2×C4—734no—
275C2×C4—1462no—
276C2×C4—1462no—
277C2×C4—1462no—
278C2×C4#1455665112yes—
279C2×C4C2×C4×#6440811yescharacteristic
280C2×C4#1455667011yescharacteristic
281C8—2928no—
282C22—42no—
283C22—44no—
284C22—81no—
285C22—82no—
286C22—81no—
287C22—2922no—
288C22—2924no—
289C22—5841no—
290C22—5842no—
291C22—5841no—
292C22C4×C22⋊#6440811yescharacteristic
293C22C2×#1455665111yescharacteristic
294C22#1798957311yescharacteristic
295C22#1798957812yes—
296C22#1798957912yes—
297C4—21no—
298C4—21no—
299C4—22no—
300C4—41no—
301C4—81no—
302C4—2922no—
303C4—5841no—
304C4—734no—
305C4—734no—
306C2—82no—
307C2—5842no—
308C2#2262545811yescharacteristic
309C2#2262546212yes—
310C2#2262546811yescharacteristic
311C2C4×#1455665111yescharacteristic
312C2#2262570112yes—
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C2×C42
FrattiniC22×C4C22×#64408
FittingC2×C4×D4×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC2×#14556587C22
cosocleC2×C4×Dic73C23
hypercenterC2×C4×D4#64408
hypocenterC73#8231
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #22625716C2semidirect
3. #22624809C2semidirect
8. #17989445C4semidirect
20. #14556658C2×C4semidirect
161. C73#8231semidirect

Maximal subgroups

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

subgroupindex
#226257162
C2×#179894452
#226248092
C4×#145565872
#823173