Finite Group Databasebeta

← #34013094

Subgroups — #34013094

Order 18688.

480 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 86 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
1C2×#17989495C212yesmaximal
2#22625797C212yesmaximal, complemented
3#22625029C212yesmaximal, complemented
4#22612643C211yesmaximal, characteristic
5#17989590—22no—
6C2×#14556652C2214yes—
7#17989495—24no—
8#17989467—22no—
9C2×#14556578C2211yescharacteristic
10C2×C4×Dic146C2211yescharacteristic
11#17988492C2211yescharacteristic
12#17988490C411yescharacteristic
13#17988475—22no—
14#17988460—22no—
15#17988456C411yescharacteristic
16#17988433C411yescharacteristic
17C2×C4×D4×C73C411yescharacteristic
18C2×#11924037—24no—
19#14556658—42no—
20C4⋊#10596833—42no—
21#14556652—24no—
22#14556652—24no—
23C22×Dic146C2311yescharacteristic
24#14556578—22no—
25#14556578D412yes—
26#14556578Q812yes—
27C4×Dic146—42no—
28C2×C4⋊Dic73C2×C411yescharacteristic
29C2×#11924007—22no—
30C2×#11924007D412yes—
31C2×C22⋊Dic73—22no—
32C2×C22⋊Dic73—22no—
33C2×C4×Dic73C2×C411yescharacteristic
34C2×C4×Dic73C2×C411yescharacteristic
35C2×C4×Dic73D412yes—
36#14556498—22no—
37#14556498—21no—
38#14556498—21no—
39C22×D4×C73C2×C411yescharacteristic
40C23×C4×C73—21no—
41C4×D4×C73—42no—
42C2×C4⋊C4×C73C2×C411yescharacteristic
43C2×C22⋊C4×C73—21no—
44C2×C42×C73C2×C411yescharacteristic
45#11924037—44no—
46#11924037—44no—
47C2×#10596833—44no—
48C2×Dic146—41no—
49C2×Dic146—41no—
50C2×Dic146C2×D411yescharacteristic
51C2×Dic146C2×Q811yescharacteristic
52C2×Dic146#4112yes—
53C22×Dic73—21no—
54C22×Dic73—21no—
55C22×Dic73C22⋊C412yes—
56C22×Dic73C2×D412yes—
57C4⋊Dic73—41no—
58#11924007—42no—
59#11924007—82no—
60C22⋊Dic73—24no—
61C22⋊Dic73—24no—
62C22⋊Dic73—82no—
63C4×Dic73—22no—
64C4×Dic73—22no—
65C4×Dic73—21no—
66C4×Dic73—41no—
67C4×Dic73C4⋊C412yes—
68C24×C73—21no—
69C2×D4×C73—21no—
70C2×D4×C73—41no—
71C2×D4×C73—41no—
72C2×D4×C73C4⋊C412yes—
73C22×C4×C73—21no—
74C22×C4×C73—42no—
75C22×C4×C73—82no—
76C22×C4×C73C22⋊C411yescharacteristic
77C22×C4×C73C22⋊C411yescharacteristic
78C22×C4×C73C22×C411yescharacteristic
79C4⋊C4×C73—41no—
80C22⋊C4×C73—42no—
81C42×C73—22no—
82C23×C73—22no—
83C23×C73—42no—
84C23×C73—42no—
85C23×C73—41no—
86C23×C73—41no—
87C23×C73C2×C22⋊C411yescharacteristic
88D4×C73—42no—
89D4×C73—42no—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—21no—
93C2×C4×C73—41no—
94C2×C4×C73—41no—
95C2×C4×C73—42no—
96C2×C4×C73—41no—
97C2×C4×C73—84no—
98C2×C4×C73#9912yes—
99C2×C4×C73C2×C4⋊C411yescharacteristic
100C2×C4×C73#11711yescharacteristic
101C2×Dic73—22no—
102C2×Dic73—22no—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73—41no—
106C2×Dic73—41no—
107C2×Dic73—42no—
108C2×Dic73—41no—
109C2×Dic73—41no—
110C2×Dic73—41no—
111C2×Dic73#12112yes—
112C2×Dic73C22⋊Q812yes—
113Dic146—41no—
114Dic146—41no—
115Dic146—42no—
116#10596833—84no—
117C22×C73—21no—
118C22×C73—21no—
119C22×C73—44no—
120C22×C73—42no—
121C22×C73—82no—
122C22×C73—81no—
123C22×C73—81no—
124C22×C73#38011yescharacteristic
125C22×C73C2×#9911yescharacteristic
126C22×C73#41011yescharacteristic
127C4×C73—21no—
128C4×C73—21no—
129C4×C73—22no—
130C4×C73—41no—
131C4×C73—81no—
132Dic73—22no—
133Dic73—22no—
134Dic73—42no—
135Dic73—42no—
136Dic73—81no—
137#12803—731nomaximal, Sylow
138C2×C73—21no—
139C2×C73—21no—
140C2×C73—82no—
141C2×C73#179911yescharacteristic
142C2×C73#213311yescharacteristic
143C2×C73#213411yescharacteristic
144#2326—731no—
145C2×#355—732no—
146#1801—732no—
147#1394—732no—
148C73#1280311yescharacteristic, complemented, Sylow
149C2×#124—731no—
150C2×C4×Q8—731no—
151C2×C4×D4#6440811yescharacteristic
152#423—1462no—
153C2×#101—734no—
154#391—731no—
155#390—731no—
156#388—1462no—
157#385—1462no—
158#384—731no—
159#376—731no—
160#355—1464no—
161#343—1462no—
162C22×Q8—731no—
163C22×D4C2×#6440811yescharacteristic
164C23×C4—21no—
165C2×M16—1464no—
166#124—732no—
167#124—732no—
168#124—1462no—
169C4×Q8—2922no—
170C4×D4—42no—
171C2×C4⋊C4—732no—
172C2×C4⋊C4—731no—
173C2×C4⋊C4—1462no—
174C2×C4⋊C4C2×#6440811yescharacteristic
175C2×C22⋊C4—21no—
176C2×C22⋊C4—1462no—
177C2×C22⋊C4—1462no—
178C2×C42—731no—
179C2×C42—731no—
180C2×C42—732no—
181C2×C42C2×#6440811yescharacteristic
182C4⋊C8—2922no—
183C4⋊C8—2922no—
184#101—1464no—
185#101—1464no—
186#95—1462no—
187#95—1461no—
188#95—1461no—
189C24—21no—
190C2×Q8—2921no—
191C2×Q8—2921no—
192C2×Q8—731no—
193C2×Q8—731no—
194C2×Q8—732no—
195C2×D4—21no—
196C2×D4—41no—
197C2×D4—41no—
198C2×D4C4⋊#6440812yes—
199C22×C4—21no—
200C22×C4—42no—
201C22×C4—82no—
202C22×C4—732no—
203C22×C4—732no—
204C22×C4—1461no—
205C22×C4—1461no—
206C22×C4C22⋊#6440811yescharacteristic
207C22×C4C22⋊#6440811yescharacteristic
208C22×C4C22×#6440811yescharacteristic
209M16—2924no—
210M16—2924no—
211C2×C8—2924no—
212C4⋊C4—41no—
213C4⋊C4—2922no—
214C4⋊C4—2921no—
215C4⋊C4—5842no—
216C22⋊C4—42no—
217C22⋊C4—5842no—
218C22⋊C4—1464no—
219C22⋊C4—1464no—
220C42—22no—
221C42—2921no—
222C42—732no—
223C42—1462no—
224C42—1462no—
225C42—1461no—
226C23—22no—
227C23—42no—
228C23—42no—
229C23—41no—
230C23—41no—
231C23C2×C22⋊#6440811yescharacteristic
232Q8—2921no—
233Q8—2921no—
234Q8—2922no—
235D4—42no—
236D4—42no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—84no—
245C2×C4—2921no—
246C2×C4—2921no—
247C2×C4—2922no—
248C2×C4—2921no—
249C2×C4—2921no—
250C2×C4—2921no—
251C2×C4—732no—
252C2×C4—732no—
253C2×C4—1462no—
254C2×C4—1462no—
255C2×C4—1462no—
256C2×C4—1462no—
257C2×C4#1455664912yes—
258C2×C4C2×C4⋊#6440811yescharacteristic
259C2×C4#1455667011yescharacteristic
260C8—5844no—
261C22—21no—
262C22—21no—
263C22—44no—
264C22—42no—
265C22—82no—
266C22—81no—
267C22—81no—
268C22#1798952911yescharacteristic
269C22C2×#1455664911yescharacteristic
270C22#1798956611yescharacteristic
271C4—22no—
272C4—21no—
273C4—21no—
274C4—41no—
275C4—81no—
276C4—2922no—
277C4—2922no—
278C4—5841no—
279C4—1462no—
280C4—1462no—
281C2—21no—
282C2—21no—
283C2—82no—
284C2#2262579111yescharacteristic
285C2#2262622611yescharacteristic
286C2#2262623011yescharacteristic
subgroupG/H
centerC22C2×#14556649
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC2×C4×D4×C73C4
socleC22×C73C2×#99
prime radicalC22×D4×C73C2×C4
cosocleC22×Dic146C23
hypercenterC2×C4×D4#64408
hypocenterC73#12803
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. #22625797C2semidirect
3. #22625029C2semidirect
148. C73#12803semidirect

Maximal subgroups

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

subgroupindex
C2×#179894952
#226257972
#226250292
#226126432
#1280373