Finite Group Databasebeta

← #22626075

Subgroups — #22626075

Order 9344.

312 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 70 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#17989590C211yesmaximal, characteristic, complemented
2C2×#14556652C212yesmaximal, complemented
3C2×#14556651C212yesmaximal
4C4×#11924037C211yesmaximal, characteristic, complemented
5C2×#14556577C211yesmaximal, characteristic
6C2×#11924037C2212yes—
7C2×#11924037C2212yes—
8#14556658—21no—
9C4⋊#10596833—21no—
10#14556652—24no—
11#14556651—24no—
12#14556646—21no—
13C4×#10596833—21no—
14C22×Dic146C2211yescharacteristic
15C22×C22⋊D73C2211yescharacteristic
16#14556577—21no—
17#14556577—21no—
18#14556577—21no—
19#14556577—21no—
20C2×C22⋊Dic73C411yescharacteristic
21C2×#11924005C411yescharacteristic
22C2×#11924005C411yescharacteristic
23C2×C4×Dic73C2211yescharacteristic
24C2×C22⋊C4×C73C411yescharacteristic
25#11924037—22no—
26#11924037—22no—
27#11924037—22no—
28#11924037D414yes—
29C2×#10596833—22no—
30C2×#10596833—22no—
31C23×D73C2×C411yescharacteristic
32C2×Dic146—21no—
33C2×Dic146—21no—
34C2×Dic146—22no—
35C2×Dic146—22no—
36C2×C22⋊D73—21no—
37C2×C22⋊D73—21no—
38C2×C22⋊D73—22no—
39C2×C22⋊D73—22no—
40C22×Dic73C2×C411yescharacteristic
41C22×Dic73C2×C411yescharacteristic
42C22×Dic73C2311yescharacteristic
43C22⋊Dic73—21no—
44C22⋊Dic73—21no—
45#11924005—21no—
46#11924005—21no—
47#11924005—21no—
48#11924005—21no—
49C4×Dic73D411yescharacteristic
50C4×Dic73D411yescharacteristic
51C4×Dic73D411yescharacteristic
52C4×Dic73D411yescharacteristic
53C24×C73C2×C411yescharacteristic
54C22×C4×C73C2×C411yescharacteristic
55C22×C4×C73C2×C411yescharacteristic
56C22⋊C4×C73—21no—
57C22⋊C4×C73—21no—
58C23×C73—21no—
59C23×C73—22no—
60C23×C73—41no—
61C23×C73—41no—
62C23×C73C22×C411yescharacteristic
63C22×D73—21no—
64C22×D73—22no—
65C22×D73—41no—
66C22×D73—41no—
67C2×C4×C73—21no—
68C2×C4×C73—22no—
69C2×C4×C73—41no—
70C2×C4×C73C22⋊C411yescharacteristic
71C2×C4×C73C22⋊C411yescharacteristic
72C22⋊D73—42no—
73C22⋊D73—41no—
74C22⋊D73—41no—
75C2×Dic73—21no—
76C2×Dic73—22no—
77C2×Dic73—41no—
78C2×Dic73C22⋊C411yescharacteristic
79C2×Dic73C22⋊C411yescharacteristic
80C2×Dic73C2×D411yescharacteristic
81C2×Dic73C2×D412yes—
82C2×Dic73C2×D411yescharacteristic
83C2×Dic73#4112yes—
84Dic146—42no—
85Dic146—41no—
86Dic146—41no—
87#10596833—24no—
88#10596833—42no—
89C22×C73—21no—
90C22×C73—21no—
91C22×C73—41no—
92C22×C73—41no—
93C22×C73—41no—
94C22×C73—82no—
95C22×C73C2×C22⋊C411yescharacteristic
96C22×C73C4×D412yes—
97C2×D73—41no—
98C2×D73—41no—
99C2×D73—41no—
100C2×D73—82no—
101C4×C73—21no—
102C4×C73—21no—
103C4×C73—41no—
104Dic73—21no—
105Dic73—21no—
106Dic73—41no—
107Dic73#12112yes—
108Dic73#12411yescharacteristic
109Dic73#12711yescharacteristic
110C2×C73—22no—
111C2×C73—81no—
112C2×C73#39011yescharacteristic
113C2×C73#41311yescharacteristic
114C2×C73#41311yescharacteristic
115D73—81no—
116#1967—731nomaximal, Sylow
117C73#196711yescharacteristic, complemented, Sylow
118C2×#124—731no—
119#423—731no—
120C2×#101—732no—
121C2×#100—732no—
122C4×M16—731no—
123C22×Q8—731no—
124C22×D4—731no—
125C2×M16—732no—
126C2×M16—732no—
127#124—1461no—
128#124—1461no—
129#124—1461no—
130#124—1461no—
131C2×C22⋊C4—731no—
132C2×C22⋊C4—731no—
133C2×C22⋊C4—731no—
134C2×C22⋊C4#6440811yescharacteristic
135C2×C42—731no—
136C4⋊C8—1461no—
137C4⋊C8—1461no—
138#101—1464no—
139#100—1464no—
140#97—1461no—
141C4×C8—1461no—
142C24—731no—
143C24C2×#6440811yescharacteristic
144C2×Q8—1462no—
145C2×Q8—1461no—
146C2×Q8—1461no—
147C2×Q8—1462no—
148C2×D4—1462no—
149C2×D4—1461no—
150C2×D4—1461no—
151C2×D4—1462no—
152C22×C4—731no—
153C22×C4—731no—
154C22×C4—731no—
155C22×C4C2×#6440811yescharacteristic
156C22×C4C2×#6440811yescharacteristic
157M16—734no—
158M16—1462no—
159M16—1462no—
160M16—1462no—
161C2×C8—1462no—
162C2×C8—1462no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—1461no—
166C22⋊C4—1461no—
167C22⋊C4—1461no—
168C22⋊C4—1461no—
169C22⋊C4—1461no—
170C22⋊C4—1461no—
171C42—731no—
172C42—731no—
173C42—731no—
174C42—731no—
175C23—21no—
176C23—22no—
177C23—41no—
178C23—41no—
179C23—2921no—
180C23—2921no—
181C23—1461no—
182C23—1462no—
183C23C22×#6440811yescharacteristic
184Q8—2921no—
185Q8—2922no—
186Q8—2921no—
187D4—2921no—
188D4—2922no—
189D4—2921no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—2921no—
194C2×C4—731no—
195C2×C4—731no—
196C2×C4—732no—
197C2×C4—732no—
198C2×C4—731no—
199C2×C4—731no—
200C2×C4—1461no—
201C2×C4—1462no—
202C2×C4C22⋊#6440811yescharacteristic
203C2×C4C22⋊#6440811yescharacteristic
204C8—2922no—
205C8—1464no—
206C22—21no—
207C22—21no—
208C22—41no—
209C22—41no—
210C22—41no—
211C22—82no—
212C22—2921no—
213C22—2921no—
214C22—2921no—
215C22—5842no—
216C22C2×C22⋊#6440811yescharacteristic
217C22D4×#6440812yes—
218C4—21no—
219C4—21no—
220C4—41no—
221C4—2921no—
222C4—731no—
223C4—732no—
224C4—731no—
225C4—1461no—
226C4—1461no—
227C2—22no—
228C2—81no—
229C2—5841no—
230C2#1798953911yescharacteristic
231C2#1798957311yescharacteristic
232C2#1798957411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC2×C22⋊C4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×C22⋊C4#64408
hypocenterC73#1967
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #17989590C2semidirect
2. C2×#14556652C2semidirect
4. C4×#11924037C2semidirect
117. C73#1967semidirect