Finite Group Databasebeta

← #34010313

Subgroups — #34010313

Order 18688.

358 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 74 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#22625193C211yesmaximal, characteristic
2#22625173C211yesmaximal, characteristic
3#22624871C214yesmaximal
4#22615146C211yesmaximal, characteristic
5#17989608—21no—
6#17989604—21no—
7#17989433—21no—
8#17989433—21no—
9#17989432C2212yes—
10#17989432C2212yes—
11C2×#14556591C411yescharacteristic
12C2×C4×Dic146C2211yescharacteristic
13#17988527—21no—
14#17988527—21no—
15#17988493C412yes—
16#17988492—21no—
17#17988492—21no—
18#17988453C2212yes—
19C4×C4⋊C4×C73C411yescharacteristic
20#14556658—41no—
21C4⋊#10596833—41no—
22C22⋊#10596833—22no—
23C22⋊#10596833—22no—
24#14556646—41no—
25C4×#10596833—41no—
26C22×Dic146—21no—
27C22×Dic146C2×C411yescharacteristic
28#14556591—41no—
29#14556591—41no—
30C4×Dic146—41no—
31C4×Dic146—41no—
32C2×C4⋊Dic73—21no—
33C2×C4⋊Dic73C2×C412yes—
34C2×C4⋊Dic73C2311yescharacteristic
35C2×#11924007D411yescharacteristic
36C2×#11924007D411yescharacteristic
37C2×C4×Dic73D411yescharacteristic
38C2×C4×Dic73D411yescharacteristic
39#14556498—22no—
40#14556498—22no—
41#14556498—22no—
42#14556498—22no—
43C2×C4⋊C4×C73—21no—
44C2×C42×C73C2×C412yes—
45C2×C42×C73C2×C411yescharacteristic
46#95×C73—21no—
47C2×#10596833—42no—
48C2×#10596833—42no—
49C2×Dic146—22no—
50C2×Dic146—22no—
51C2×Dic146—41no—
52C2×Dic146—44no—
53C2×Dic146—41no—
54C2×Dic146—41no—
55C22×Dic73—22no—
56C22×Dic73C22⋊C411yescharacteristic
57C22×Dic73C22⋊C411yescharacteristic
58C22×Dic73C2×D411yescharacteristic
59C22×Dic73C2×D411yescharacteristic
60C4⋊Dic73—41no—
61C4⋊Dic73—42no—
62C4⋊Dic73—42no—
63#11924007—41no—
64#11924007—41no—
65C4×Dic73—21no—
66C4×Dic73—21no—
67C4×Dic73—21no—
68C4×Dic73—21no—
69C22×C4×C73—22no—
70C22×C4×C73C22⋊C411yescharacteristic
71C22×C4×C73C22⋊C411yescharacteristic
72C22×C4×C73C22×C411yescharacteristic
73C4⋊C4×C73—42no—
74C42×C73—21no—
75C42×C73—21no—
76C42×C73—24no—
77C23×C73C2×C22⋊C411yescharacteristic
78C2×C4×C73—21no—
79C2×C4×C73—21no—
80C2×C4×C73—22no—
81C2×C4×C73—21no—
82C2×C4×C73—41no—
83C2×C4×C73—42no—
84C2×C4×C73—42no—
85C2×C4×C73—42no—
86C2×C4×C73#9911yescharacteristic
87C2×C4×C73#9911yescharacteristic
88C2×C4×C73#13112yes—
89C2×Dic73—21no—
90C2×Dic73—21no—
91C2×Dic73—21no—
92C2×Dic73—21no—
93C2×Dic73—21no—
94C2×Dic73—21no—
95C2×Dic73—21no—
96C2×Dic73—41no—
97C2×Dic73—41no—
98C2×Dic73—44no—
99C2×Dic73—42no—
100C2×Dic73#10112yes—
101Dic146—44no—
102Dic146—82no—
103Dic146—82no—
104#10596833—82no—
105#10596833—82no—
106C22×C73—21no—
107C22×C73—21no—
108C22×C73#40811yescharacteristic
109C22×C73C2×#9911yescharacteristic
110C22×C73C2×#10111yescharacteristic
111C4×C73—21no—
112C4×C73—22no—
113C4×C73—41no—
114C4×C73—82no—
115C4×C73#35512yes—
116Dic73—22no—
117Dic73—41no—
118Dic73—41no—
119Dic73—41no—
120Dic73—82no—
121#11573—731nomaximal, Sylow
122C2×C73—21no—
123C2×C73—21no—
124C2×C73#147211yescharacteristic
125C2×C73#212911yescharacteristic
126C2×C73C2×#35511yescharacteristic
127#2568—731no—
128#1467—731no—
129#1461—731no—
130#1324—734no—
131C73#1157311yescharacteristic, complemented, Sylow
132C2×C4⋊Q8—731no—
133C2×C4×Q8—731no—
134#432—1461no—
135#431—1461no—
136#400—1461no—
137#400—1461no—
138#391—732no—
139#391—1461no—
140#391—1461no—
141#382—732no—
142C4×C4⋊C4#6440811yescharacteristic
143#324—732no—
144#324—732no—
145#324—1461no—
146#324—1461no—
147C22×Q8—731no—
148C22×Q8—1461no—
149C4⋊Q8—2921no—
150C4⋊Q8—2921no—
151C4×Q8—2921no—
152C4×Q8—2921no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—731no—
155C2×C4⋊C4—731no—
156C2×C4⋊C4—731no—
157C2×C4⋊C4—732no—
158C2×C4⋊C4—1461no—
159C2×C42—731no—
160C2×C42—731no—
161C2×C42C2×#6440812yes—
162C2×C42C2×#6440811yescharacteristic
163C4⋊C8—2921no—
164C4⋊C8—2921no—
165C22⋊C8—1462no—
166C22⋊C8—1462no—
167#97—2921no—
168C4×C8—2921no—
169#95—21no—
170#95—1462no—
171#95—1462no—
172#95—1462no—
173#95—1462no—
174C2×Q8—2924no—
175C2×Q8—2921no—
176C2×Q8—2921no—
177C2×Q8—2921no—
178C2×Q8—1462no—
179C2×Q8—1462no—
180C22×C4—22no—
181C22×C4—731no—
182C22×C4—731no—
183C22×C4—731no—
184C22×C4—731no—
185C22×C4—1462no—
186C22×C4C22⋊#6440811yescharacteristic
187C22×C4C22⋊#6440811yescharacteristic
188C22×C4C22×#6440811yescharacteristic
189C2×C8—2922no—
190C2×C8—2922no—
191C4⋊C4—42no—
192C4⋊C4—2922no—
193C4⋊C4—2922no—
194C4⋊C4—2921no—
195C4⋊C4—2921no—
196C4⋊C4—2921no—
197C42—21no—
198C42—21no—
199C42—24no—
200C42—1461no—
201C42—1461no—
202C42—1461no—
203C42—1461no—
204C23C2×C22⋊#6440811yescharacteristic
205Q8—2924no—
206Q8—5842no—
207Q8—5842no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—2921no—
217C2×C4—2921no—
218C2×C4—2924no—
219C2×C4—2922no—
220C2×C4—732no—
221C2×C4—1461no—
222C2×C4—1461no—
223C2×C4—1461no—
224C2×C4—1461no—
225C2×C4—1461no—
226C2×C4—1461no—
227C2×C4—1461no—
228C2×C4#1455665011yescharacteristic
229C2×C4#1455665011yescharacteristic
230C2×C4#1455667812yes—
231C8—5842no—
232C8—5842no—
233C22—21no—
234C22—21no—
235C22#1798956111yescharacteristic
236C22C2×#1455665011yescharacteristic
237C22D73⋊#10111yescharacteristic
238C4—21no—
239C4—22no—
240C4—41no—
241C4—82no—
242C4—2921no—
243C4—2921no—
244C4—2921no—
245C4—5842no—
246C4—1462no—
247C4#1798949612yes—
248C2—21no—
249C2—21no—
250C2#2262520911yescharacteristic
251C2#2262621511yescharacteristic
252C2C2×#1798949611yescharacteristic
subgroupG/H
centerC22C2×#14556650
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC4×C4⋊C4×C73C4
socleC22×C73C2×#99
prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4⋊Dic73C23
hypercenterC4×C4⋊C4#64408
hypocenterC73#11573
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
131. C73#11573semidirect

Maximal subgroups

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

subgroupindex
#226251932
#226251732
#226248712
#226151462
#1157373