Finite Group Databasebeta

← #33004670

Subgroups — #33004670

Order 18688.

420 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 103 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#22615136C211yesmaximal, characteristic
2C4×#14556510C211yesmaximal, characteristic
3#22608057C214yesmaximal
4C73×#1801C211yesmaximal, characteristic
5C2×#14556591C411yescharacteristic
6C2×#14556510C2212yes—
7C4×#11924012—21no—
8#17988507—21no—
9#17988507—21no—
10#17988494C2212yes—
11#17988485—21no—
12#17988485—21no—
13#17988456C412yes—
14C4×C4⋊Dic73C411yescharacteristic
15#17988356—21no—
16C2×C4×Q8×C73C2211yescharacteristic
17#423×C73—21no—
18C2×#101×C73C2212yes—
19#343×C73—21no—
20C22×Dic146—21no—
21C2×#11924012—22no—
22#14556591—41no—
23#14556591—41no—
24C2×C4⋊Dic73—21no—
25C2×C4⋊Dic73—21no—
26C2×C4⋊Dic73C2×C412yes—
27C2×#11924007—22no—
28C2×#11924007—22no—
29C2×C4×Dic73C2×C412yes—
30#14556510—22no—
31#14556510Q814yescomplemented
32#14556502—41no—
33C4×#10596831—41no—
34#14556498—21no—
35#14556498—22no—
36#14556498—22no—
37C22×Q8×C73C2311yescharacteristic
38C2×M16×C73—22no—
39C4×Q8×C73—41no—
40C4×Q8×C73—41no—
41C2×C4⋊C4×C73C2×C411yescharacteristic
42C2×C4⋊C4×C73D411yescharacteristic
43C2×C4⋊C4×C73D411yescharacteristic
44C2×C42×C73C2×C411yescharacteristic
45C2×C42×C73D411yescharacteristic
46C2×C42×C73D411yescharacteristic
47C4⋊C8×C73—41no—
48C4⋊C8×C73—41no—
49#101×C73—24no—
50C2×Dic146—42no—
51C2×Dic146—82no—
52C22×Dic73—22no—
53C22×Dic73—22no—
54#11924012—24no—
55#11924012—42no—
56C2×#10596831—42no—
57C4⋊Dic73—24no—
58C4⋊Dic73—41no—
59C4⋊Dic73—41no—
60C4⋊Dic73—42no—
61#11924007—82no—
62#11924007—82no—
63C4×Dic73—42no—
64C2×Q8×C73—41no—
65C2×Q8×C73—41no—
66C2×Q8×C73C2×Q812yes—
67C2×Q8×C73#4112yes—
68C22×C4×C73C22⋊C411yescharacteristic
69C22×C4×C73C22⋊C411yescharacteristic
70C22×C4×C73C22⋊C411yescharacteristic
71C22×C4×C73C22⋊C411yescharacteristic
72C22×C4×C73C22×C411yescharacteristic
73C22×C4×C73C2×D411yescharacteristic
74C22×C4×C73C2×D411yescharacteristic
75M16×C73—42no—
76M16×C73—42no—
77C2×C8×C73—42no—
78C4⋊C4×C73—41no—
79C4⋊C4×C73—41no—
80C4⋊C4×C73—41no—
81C42×C73—21no—
82C42×C73—21no—
83C42×C73—21no—
84C42×C73—21no—
85C42×C73—21no—
86C42×C73—21no—
87C23×C73C2×C22⋊C411yescharacteristic
88Q8×C73—42no—
89Q8×C73—42no—
90C2×C4×C73—21no—
91C2×C4×C73—21no—
92C2×C4×C73—21no—
93C2×C4×C73—21no—
94C2×C4×C73—21no—
95C2×C4×C73—21no—
96C2×C4×C73—22no—
97C2×C4×C73—21no—
98C2×C4×C73—21no—
99C2×C4×C73—21no—
100C2×C4×C73—41no—
101C2×C4×C73—41no—
102C2×C4×C73—41no—
103C2×C4×C73#9911yescharacteristic
104C2×C4×C73#9911yescharacteristic
105C2×C4×C73C4×Q812yes—
106C2×C4×C73C22⋊Q812yes—
107C2×C4×C73#12411yescharacteristic
108C2×C4×C73C4⋊Q811yescharacteristic
109C2×Dic73—24no—
110C2×Dic73—42no—
111C2×Dic73—42no—
112C2×Dic73—42no—
113C2×Dic73—42no—
114C2×Dic73—42no—
115Dic146—84no—
116C8×C73—82no—
117#10596831—44no—
118C22×C73—21no—
119C22×C73—21no—
120C22×C73#39111yescharacteristic
121C22×C73C2×#9911yescharacteristic
122C22×C73#41011yescharacteristic
123C4×C73—21no—
124C4×C73—22no—
125C4×C73—21no—
126C4×C73—22no—
127C4×C73—21no—
128C4×C73—41no—
129C4×C73—41no—
130C4×C73—41no—
131C4×C73#35612yes—
132Dic73—44no—
133Dic73—82no—
134#13302—731nomaximal, Sylow
135C2×C73—21no—
136C2×C73—21no—
137C2×C73#199611yescharacteristic
138C2×C73C2×#35611yescharacteristic
139C2×C73#213411yescharacteristic
140#2567—731no—
141#1801D7311yescharacteristic
142C4×#101—731no—
143#1394—734no—
144C73#1330211yescharacteristic, complemented, Sylow
145C2×C4⋊Q8—731no—
146C2×C4×Q8C2×D7311yescharacteristic
147#423—21no—
148C2×#101—732no—
149C2×#101C2×D7312yes—
150C4×M16—1461no—
151#395—1461no—
152#395—1461no—
153#391—732no—
154#389—1461no—
155#389—1461no—
156#384—732no—
157C4×C4⋊C4—731no—
158#343—21no—
159#343—1461no—
160C22×Q8—1461no—
161C22×Q8C22×D7311yescharacteristic
162C2×M16—22no—
163C2×M16—1462no—
164C4⋊Q8—2921no—
165C4⋊Q8—2921no—
166C4×Q8—41no—
167C4×Q8—41no—
168C2×C4⋊C4—732no—
169C2×C4⋊C4—1461no—
170C2×C4⋊C4—1462no—
171C2×C4⋊C4—1462no—
172C2×C4⋊C4—1461no—
173C2×C4⋊C4C4×D7311yescharacteristic
174C2×C4⋊C4D29211yescharacteristic
175C2×C4⋊C4C22⋊D7311yescharacteristic
176C2×C42—732no—
177C2×C42C4×D7311yescharacteristic
178C2×C42D29211yescharacteristic
179C2×C42C22⋊D7311yescharacteristic
180C4⋊C8—41no—
181C4⋊C8—41no—
182#101—24no—
183#101—734no—
184#101—1462no—
185#97—2921no—
186C4×C8—2921no—
187#95—1461no—
188#95—1462no—
189#95—1462no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—2922no—
193C2×Q8—5842no—
194C2×Q8Q8×D7312yes—
195C2×Q8#1192402712yes—
196C22×C4—1462no—
197C22×C4—1462no—
198C22×C4#1192400511yescharacteristic
199C22×C4#1192400511yescharacteristic
200C22×C4#1192400511yescharacteristic
201C22×C4#1192400511yescharacteristic
202C22×C4C2×C4×D7311yescharacteristic
203C22×C4C2×C22⋊D7311yescharacteristic
204C22×C4C2×D29211yescharacteristic
205M16—42no—
206M16—42no—
207M16—2922no—
208M16—1464no—
209C2×C8—42no—
210C2×C8—2922no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—2922no—
215C4⋊C4—2921no—
216C4⋊C4—2921no—
217C4⋊C4—5842no—
218C4⋊C4—5842no—
219C4⋊C4—1464no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—2922no—
227C23C2×#1192400511yescharacteristic
228Q8—42no—
229Q8—42no—
230Q8—5844no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—2922no—
245C2×C4—2922no—
246C2×C4—2922no—
247C2×C4—2922no—
248C2×C4—2922no—
249C2×C4—1464no—
250C2×C4#1455650511yescharacteristic
251C2×C4#1455650511yescharacteristic
252C2×C4#1455655612yes—
253C2×C4#1455657112yes—
254C2×C4#1455657811yescharacteristic
255C2×C4#1455658911yescharacteristic
256C8—82no—
257C8—2924no—
258C22—21no—
259C22—21no—
260C22#1798849211yescharacteristic
261C22C2×#1455650511yescharacteristic
262C22#1798856011yescharacteristic
263C4—21no—
264C4—21no—
265C4—22no—
266C4—22no—
267C4—21no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—2924no—
272C4—5842no—
273C4#1798838512yes—
274C2—21no—
275C2—21no—
276C2#2261091511yescharacteristic
277C2C2×#1798838511yescharacteristic
278C2#2261162211yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC22×Q8C22×D73
FittingC73×#1801C2
socleC22×C73C2×#99
prime radicalC23×C73C2×C22⋊C4
cosocleC22×Q8×C73C23
hypercenter#1801D73
hypocenterC73#13302
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
31. #14556510Q8semidirect
144. C73#13302semidirect

Maximal subgroups

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

subgroupindex
#226151362
C4×#145565102
#226080572
C73×#18012
#1330273