Finite Group Databasebeta

← #22626096

Subgroups — #22626096

Order 9344.

336 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 72 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×#14556656C212yesmaximal, complemented
2C2×#14556655C212yesmaximal, complemented
3C4×#11924038C211yesmaximal, characteristic, complemented
4C4×C4⋊#64408C211yesmaximal, characteristic, complemented
5#17989136C211yesmaximal, characteristic
6C2×#11924038C2212yes—
7C2×C4⋊#64408—21no—
8C2×C4×#64408C2212yes—
9#14556656—24no—
10#14556655—24no—
11#14556646—21no—
12C4×#10596833—21no—
13(C2×#64408)⋊C4—21no—
14C2×#11924029C2211yescharacteristic
15C2×#11924027C2211yescharacteristic
16#14556589C411yescharacteristic, complemented
17#14556587C411yescharacteristic, complemented
18#14556579C411yescharacteristic, complemented
19#14556564—21no—
20#14556564—21no—
21#14556551—21no—
22#14556551—21no—
23C42×D73C2211yescharacteristic
24#124×C73C411yescharacteristic, complemented
25C22×#64408—22no—
26#11924038—22no—
27#11924038D414yescomplemented
28C2×#10596833—22no—
29C4⋊#64408—24no—
30C4×#64408—22no—
31C4×#64408—22no—
32#11924029—22no—
33#11924029—22no—
34#11924027—22no—
35#11924027—22no—
36C2×Dic146C2×C411yescharacteristic
37C2×D292—21no—
38C2×D292C2×C411yescharacteristic
39C2×C22⋊D73—21no—
40C2×C22⋊D73—21no—
41C2×C22⋊D73—21no—
42C22×Dic73—21no—
43C2×C4×D73—21no—
44C2×C4×D73D411yescharacteristic
45C2×C4×D73D411yescharacteristic
46C2×C4×D73C2311yescharacteristic
47#11924007—21no—
48#11924007—21no—
49#11924005—21no—
50#11924005—21no—
51C4×Dic73C2×C411yescharacteristic
52C4×Dic73D411yescharacteristic
53C4×Dic73D411yescharacteristic
54C2×Q8×C73C2×C411yescharacteristic
55C2×D4×C73C2×C411yescharacteristic
56C22⋊C4×C73—21no—
57C22⋊C4×C73—21no—
58C42×C73C2×C411yescharacteristic
59C23×C73—21no—
60C22×D73—21no—
61C22×D73C2×D411yescharacteristic
62C2×#64408—24no—
63C2×#64408—42no—
64C2×#64408—42no—
65Q8×C73—22no—
66D4×C73—22no—
67C2×C4×C73—21no—
68C2×C4×C73C22⋊C411yescharacteristic
69C2×C4×C73C22⋊C411yescharacteristic
70C2×C4×C73C22×C411yescharacteristic
71C22⋊D73—42no—
72C22⋊D73—41no—
73C22⋊D73—41no—
74C22⋊D73—42no—
75C2×Dic73—21no—
76C2×Dic73—42no—
77C2×Dic73C22⋊C411yescharacteristic
78C2×Dic73C22⋊C411yescharacteristic
79C2×Dic73C2×D411yescharacteristic
80D292—22no—
81D292—41no—
82D292—41no—
83C4×D73—22no—
84C4×D73—41no—
85C4×D73—42no—
86C4×D73C2×D412yes—
87C4×D73#4112yes—
88Dic146—22no—
89#10596833—24no—
90C22×C73—41no—
91C22×C73—41no—
92C22×C73—41no—
93C22×C73C2×C22⋊C411yescharacteristic
94C2×D73—21no—
95C2×D73—21no—
96C2×D73—41no—
97C2×D73—41no—
98C2×D73—41no—
99C2×D73#12411yescharacteristic
100C2×D73#12711yescharacteristic
101#64408—44no—
102C4×C73—21no—
103C4×C73—21no—
104C4×C73—41no—
105C4×C73C4×D412yes—
106Dic73—21no—
107Dic73—41no—
108Dic73#10412yescomplemented
109Dic73#12112yes—
110C2×C73—81no—
111C2×C73#39011yescharacteristic
112C2×C73C2×#10411yescharacteristic
113C2×C73#42111yescharacteristic
114D73—21no—
115D73—21no—
116D73—81no—
117#1980—731nomaximal, Sylow
118C73#198011yescharacteristic, complemented, Sylow
119#532—731no—
120C2×#104—732no—
121C2×#104—732no—
122C4×M16—731no—
123C4×C4⋊C4—731no—
124C2×#41—731no—
125C2×#41—731no—
126C2×M16—732no—
127C4⋊Q8—731no—
128#127—731no—
129#124—731no—
130#124#6440811yescharacteristic, complemented
131#121—1461no—
132#121—1461no—
133C4×D4—1461no—
134C4×D4—1461no—
135C2×C4⋊C4—1461no—
136C2×C42—731no—
137C2×C42—732no—
138#104—1464no—
139#104—1464no—
140#97—1461no—
141C4×C8—1461no—
142#95—1461no—
143#41—1462no—
144#41—1462no—
145#41—1462no—
146#41—1462no—
147C2×Q8—731no—
148C2×Q8C2×#6440811yescharacteristic
149C2×D4—731no—
150C2×D4—1461no—
151C2×D4—1461no—
152C2×D4—1461no—
153C2×D4—1461no—
154C2×D4C2×#6440811yescharacteristic
155C22×C4—731no—
156C22×C4—731no—
157C22×C4—731no—
158C22×C4—1461no—
159C22×C4—1461no—
160C22×C4—1462no—
161M16—734no—
162M16—1462no—
163C2×C8—1462no—
164C4⋊C4—1461no—
165C4⋊C4—1461no—
166C4⋊C4—1464no—
167C22⋊C4—21no—
168C22⋊C4—21no—
169C22⋊C4—1461no—
170C22⋊C4—1461no—
171C42—731no—
172C42—731no—
173C42—731no—
174C42—1462no—
175C42—1462no—
176C42C2×#6440811yescharacteristic
177C23—21no—
178C23—731no—
179C23—1461no—
180Q8—22no—
181Q8—1462no—
182D4—22no—
183D4—2921no—
184D4—2921no—
185D4—2921no—
186D4—2921no—
187D4—2922no—
188D4—2922no—
189D4—1462no—
190C2×C4—21no—
191C2×C4—2921no—
192C2×C4—2922no—
193C2×C4—2922no—
194C2×C4—2922no—
195C2×C4—2922no—
196C2×C4—731no—
197C2×C4—731no—
198C2×C4—732no—
199C2×C4—732no—
200C2×C4—731no—
201C2×C4—1462no—
202C2×C4—1464no—
203C2×C4—1461no—
204C2×C4C22⋊#6440811yescharacteristic
205C2×C4C22⋊#6440811yescharacteristic
206C2×C4C22×#6440811yescharacteristic
207C8—1464no—
208C22—41no—
209C22—41no—
210C22—41no—
211C22—2921no—
212C22—2921no—
213C22—2921no—
214C22—731no—
215C22—731no—
216C22—1461no—
217C22—1461no—
218C22C2×C22⋊#6440811yescharacteristic
219C4—21no—
220C4—21no—
221C4—41no—
222C4—2924no—
223C4—2921no—
224C4—732no—
225C4—732no—
226C4—1461no—
227C4D4×#6440812yes—
228C2—81no—
229C2—5841no—
230C2—1461no—
231C2—1461no—
232C2#1798953911yescharacteristic
233C2D73⋊#10411yescharacteristic
234C2#1798958411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#124×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#124#64408
hypocenterC73#1980
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C2×#14556656C2semidirect
2. C2×#14556655C2semidirect
3. C4×#11924038C2semidirect
4. C4×C4⋊#64408C2semidirect
16. #14556589C4semidirect
17. #14556587C4semidirect
18. #14556579C4semidirect
24. #124×C73C4semidirect
27. #11924038D4semidirect
108. Dic73#104semidirect
118. C73#1980semidirect
130. #124#64408semidirect