Finite Group Databasebeta

← #22626010

Subgroups — #22626010

Order 9344.

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

normal subgroups only

This group has 254 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
1C2×#14556659C211yesmaximal, characteristic
2C2×#14556654C211yesmaximal, characteristic
3(C2×#64408)⋊Q8C211yesmaximal, characteristic
4C4⋊C4×#64408C211yesmaximal, characteristic
5#17989460C211yesmaximal, characteristic
6#17989452C211yesmaximal, characteristic
7#103×D73C211yesmaximal, characteristic
8C2×#11924036C2211yescharacteristic
9C2×C4⋊#64408C2211yescharacteristic
10C2×C4⋊#64408C2211yescharacteristic
11C2×C4×#64408—21no—
12C2×C4×#64408C2211yescharacteristic
13#14556659—22no—
14#14556654—22no—
15(C2×#64408)⋊C4—21no—
16(C2×#64408)⋊C4—21no—
17(C2×#64408)⋊C4—21no—
18C2×Q8×D73C2211yescharacteristic
19C2×C8×D73C2211yescharacteristic
20C4⋊C4×D73C2211yescharacteristic
21#14556516C411yescharacteristic, complemented
22#14556515C411yescharacteristic, complemented
23#14556514C411yescharacteristic, complemented
24#103×C73C411yescharacteristic, complemented
25C22×#64408—21no—
26C22×#64408—21no—
27C22×#64408D411yescharacteristic
28C22×#64408D411yescharacteristic
29#11924036—21no—
30#11924036—21no—
31C2×#10596833—21no—
32C4⋊#64408—21no—
33C4⋊#64408—21no—
34C4⋊#64408—21no—
35C4⋊#64408D412yes—
36C4×#64408—21no—
37C4×#64408—21no—
38C4×#64408—42no—
39C2×Dic146—21no—
40C2×Dic146C2×C411yescharacteristic
41Q8×D73—21no—
42Q8×D73—21no—
43Q8×D73—21no—
44Q8×D73—21no—
45C2×C4×D73—21no—
46C2×C4×D73—21no—
47C2×C4×D73C2311yescharacteristic
48C2×#10596831C2×C411yescharacteristic
49C8×D73—21no—
50C8×D73—21no—
51C4⋊Dic73C2×C411yescharacteristic
52#11924007—21no—
53C2×Q8×C73C2×C411yescharacteristic
54C2×C8×C73C2×C411yescharacteristic
55C4⋊C4×C73C2×C411yescharacteristic
56C22×D73C2×D411yescharacteristic
57C2×#64408—21no—
58C2×#64408—21no—
59C2×#64408—22no—
60C2×#64408—21no—
61C2×#64408—21no—
62C2×#64408—21no—
63C2×#64408—41no—
64C2×#64408—41no—
65C2×#64408—41no—
66C2×#64408—41no—
67C2×#64408—41no—
68C2×#64408SD1612yes—
69Q8×C73—21no—
70Q8×C73—21no—
71C2×C4×C73—21no—
72C2×C4×C73—21no—
73C2×C4×C73C22×C411yescharacteristic
74C2×Dic73—21no—
75C2×Dic73—21no—
76C2×Dic73#4111yescharacteristic
77C4×D73—41no—
78C4×D73—41no—
79C4×D73—41no—
80C4×D73—41no—
81C4×D73C2×D411yescharacteristic
82C4×D73#4111yescharacteristic
83C4×D73#4111yescharacteristic
84C4×D73#4111yescharacteristic
85Dic146—21no—
86Dic146—21no—
87Dic146—41no—
88Dic146—41no—
89#10596833—41no—
90C8×C73—21no—
91#10596831—21no—
92C22×C73C4×D411yescharacteristic
93C2×D73#12111yescharacteristic
94C2×D73#12311yescharacteristic
95C2×D73C2×SD1611yescharacteristic
96C2×D73#13511yescharacteristic
97C2×D73#13711yescharacteristic
98C2×D73#13711yescharacteristic
99#64408—22no—
100#64408—42no—
101#64408—41no—
102#64408—81no—
103C4×C73—41no—
104C4×C73—41no—
105C4×C73#11711yescharacteristic
106C4×C73C4×D411yescharacteristic
107Dic73—41no—
108Dic73—41no—
109Dic73#12411yescharacteristic
110Dic73#12611yescharacteristic
111C2×C73#38811yescharacteristic
112C2×C73C4×SD1611yescharacteristic
113C2×C73#44111yescharacteristic
114D73#46111yescharacteristic
115D73#46411yescharacteristic
116D73#48311yescharacteristic
117D73#48511yescharacteristic
118#1927—731nomaximal, Sylow
119C73#192711yescharacteristic, complemented, Sylow
120C2×#106—731no—
121C2×#103—731no—
122C2×#103—731no—
123#391—731no—
124C4×C4⋊C4—731no—
125#340—731no—
126#336—731no—
127C22×Q8—731no—
128C22×C8—731no—
129C22×C8—731no—
130C2×C4⋊C4—731no—
131C2×C4⋊C4—731no—
132C2×C4⋊C4—731no—
133C2×C42—731no—
134C2×C42—1461no—
135#106—1462no—
136#103—731no—
137#103—731no—
138#103—731no—
139#103—1462no—
140#103#6440811yescharacteristic, complemented
141#95—1461no—
142#95—1461no—
143#95—1461no—
144C2×Q8—731no—
145C2×Q8—1461no—
146C2×Q8—1461no—
147C2×Q8—1461no—
148C2×Q8—1461no—
149C2×Q8—1461no—
150C2×Q8C2×#6440811yescharacteristic
151C22×C4—731no—
152C22×C4—731no—
153C22×C4—731no—
154C22×C4—1461no—
155C22×C4—1461no—
156C22×C4—1461no—
157C22×C4—1461no—
158C2×C8—731no—
159C2×C8—1461no—
160C2×C8—1461no—
161C2×C8—1461no—
162C2×C8—1461no—
163C2×C8—1461no—
164C2×C8C2×#6440811yescharacteristic
165C4⋊C4—732no—
166C4⋊C4—731no—
167C4⋊C4—1461no—
168C4⋊C4—1461no—
169C4⋊C4—1461no—
170C4⋊C4—1461no—
171C4⋊C4C2×#6440811yescharacteristic
172C42—2922no—
173C42—1461no—
174C42—1461no—
175C23—731no—
176Q8—21no—
177Q8—21no—
178Q8—2921no—
179Q8—2921no—
180Q8—1461no—
181Q8—1461no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—2921no—
185C2×C4—2921no—
186C2×C4—2921no—
187C2×C4—2921no—
188C2×C4—2921no—
189C2×C4—2921no—
190C2×C4—2921no—
191C2×C4—2921no—
192C2×C4—2921no—
193C2×C4—731no—
194C2×C4—731no—
195C2×C4—731no—
196C2×C4—731no—
197C2×C4—731no—
198C2×C4—732no—
199C2×C4—1461no—
200C2×C4—1462no—
201C2×C4—1461no—
202C2×C4—1461no—
203C2×C4—1461no—
204C2×C4—1461no—
205C2×C4—1461no—
206C2×C4—1461no—
207C2×C4C22×#6440811yescharacteristic
208C8—21no—
209C8—2921no—
210C8—1461no—
211C22—731no—
212C22—731no—
213C22—731no—
214C22—731no—
215C22—731no—
216C22—731no—
217C22D4×#6440811yescharacteristic
218C4—41no—
219C4—41no—
220C4—2922no—
221C4—2921no—
222C4—2921no—
223C4—2921no—
224C4—5841no—
225C4—731no—
226C4—731no—
227C4—1462no—
228C4#1455667011yescharacteristic
229C4D4×#6440811yescharacteristic
230C2—731no—
231C2—731no—
232C2—731no—
233C2—731no—
234C2#1798953711yescharacteristic
235C2SD16×#6440811yescharacteristic
236C2#1798962711yescharacteristic
subgroupG/H
centerC22D4×#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#103×C73C4
socleC22×C73C4×D4
hypercenter#103#64408
hypocenterC73#1927
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
21. #14556516C4semidirect
22. #14556515C4semidirect
23. #14556514C4semidirect
24. #103×C73C4semidirect
119. C73#1927semidirect
140. #103#64408semidirect