Finite Group Databasebeta

← #22625349

Subgroups — #22625349

Order 9344.

286 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 58 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#17989559C211yesmaximal, characteristic, complemented
2#17989529C211yesmaximal, characteristic, complemented
3#17989441C212yesmaximal, complemented
4#17989439C212yesmaximal, complemented
5#17989100C211yesmaximal, characteristic
6C2×#11924037—21no—
7C2×C4⋊#64408—21no—
8C2×C22⋊#64408—21no—
9#14556648—21no—
10#14556648C2212yes—
11(C2×#64408)⋊C4C2212yes—
12C2×#11924029C411yescharacteristic, complemented
13C22×C4×D73C2211yescharacteristic
14#14556576—21no—
15#14556567C2211yescharacteristic
16#14556566C2211yescharacteristic
17#14556565C411yescharacteristic, complemented
18#14556561—21no—
19#14556553—21no—
20#14556551—21no—
21#14556549C411yescharacteristic, complemented
22C22⋊Q8×C73C411yescharacteristic, complemented
23C22×#64408—22no—
24#11924037—42no—
25C2×#10596833—22no—
26C4⋊#64408—42no—
27C22⋊#64408—42no—
28C23×D73D411yescharacteristic
29#11924029—42no—
30C2×D292—21no—
31C2×D292—21no—
32C2×D292C2×C411yescharacteristic
33C2×C22⋊D73—21no—
34C22×Dic73D411yescharacteristic
35C2×C4×D73—21no—
36C2×C4×D73—42no—
37C2×C4×D73C2×C411yescharacteristic
38C2×C4×D73D411yescharacteristic
39C2×C4×D73D411yescharacteristic
40C2×C4×D73C2311yescharacteristic
41C4⋊Dic73C2×C411yescharacteristic
42#11924007—21no—
43#11924005—21no—
44#11924005—21no—
45#11924005—21no—
46#11924005—21no—
47C4×Dic73—21no—
48C2×Q8×C73C2×C411yescharacteristic
49C22×C4×C73C2×C411yescharacteristic
50C4⋊C4×C73—21no—
51C4⋊C4×C73C2×C411yescharacteristic
52C22⋊C4×C73—21no—
53C23×C73C22⋊C411yescharacteristic
54C22×D73—21no—
55C22×D73—21no—
56C22×D73—21no—
57C22×D73—41no—
58C22×D73—41no—
59C22×D73C22⋊C411yescharacteristic
60C22×D73C2×D411yescharacteristic
61C2×#64408—42no—
62C2×#64408—42no—
63C2×#64408—42no—
64Q8×C73—41no—
65C2×C4×C73—21no—
66C2×C4×C73—21no—
67C2×C4×C73—41no—
68C2×C4×C73C22⋊C411yescharacteristic
69C2×C4×C73C22×C411yescharacteristic
70C22⋊D73—42no—
71C2×Dic73—22no—
72C2×Dic73—21no—
73C2×Dic73C22⋊C411yescharacteristic
74C2×Dic73C2×D411yescharacteristic
75D292—41no—
76D292—42no—
77D292—41no—
78D292—41no—
79C4×D73—22no—
80C4×D73—22no—
81C4×D73—41no—
82C4×D73—41no—
83C4×D73—42no—
84#10596833—42no—
85C22×C73—21no—
86C22×C73—21no—
87C22×C73—21no—
88C22×C73C2×C22⋊C411yescharacteristic
89C2×D73—21no—
90C2×D73—21no—
91C2×D73—21no—
92C2×D73—21no—
93C2×D73—21no—
94C2×D73—42no—
95C2×D73—42no—
96C2×D73—41no—
97C2×D73—41no—
98C2×D73—41no—
99C2×D73AGL(1,ℤ/8)11yescharacteristic
100C2×D73#13711yescharacteristic
101#64408—82no—
102C4×C73—21no—
103C4×C73—21no—
104C4×C73—41no—
105C4×C73—41no—
106Dic73—21no—
107Dic73—41no—
108Dic73#9912yes—
109C2×C73—41no—
110C2×C73C2×#9911yescharacteristic
111C2×C73#41711yescharacteristic
112C2×C73#42111yescharacteristic
113D73—21no—
114D73—21no—
115D73—41no—
116D73—81no—
117#1513—731nomaximal, Sylow
118C73#151311yescharacteristic, complemented, Sylow
119#525—731no—
120#407—731no—
121#380—731no—
122#328—732no—
123#327—732no—
124C2×#41—731no—
125C23×C4—731no—
126C2×M16—1461no—
127#123—1461no—
128C22⋊Q8—731no—
129C22⋊Q8#6440811yescharacteristic, complemented
130#121—731no—
131#121—731no—
132#120—1461no—
133C4×D4—1461no—
134C4×D4—1461no—
135#117—731no—
136C2×C4⋊C4—1461no—
137C2×C22⋊C4—1461no—
138C22⋊C8—732no—
139C22⋊C8—1461no—
140#95—732no—
141C24—731no—
142#41—2922no—
143C2×Q8C2×#6440811yescharacteristic
144C2×D4—731no—
145C2×D4—1461no—
146C2×D4—1461no—
147C2×D4—1461no—
148C22×C4—2922no—
149C22×C4—731no—
150C22×C4—731no—
151C22×C4—731no—
152C22×C4—731no—
153C22×C4—731no—
154C22×C4—1461no—
155C22×C4—1462no—
156C22×C4C2×#6440811yescharacteristic
157M16—2922no—
158C2×C8—1462no—
159C4⋊C4—21no—
160C4⋊C4—2922no—
161C4⋊C4—731no—
162C4⋊C4—1461no—
163C4⋊C4C2×#6440811yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—2922no—
166C22⋊C4—1461no—
167C22⋊C4—1461no—
168C22⋊C4—1461no—
169C22⋊C4—1461no—
170C42—1461no—
171C23—2921no—
172C23—2921no—
173C23—731no—
174C23—731no—
175C23—1461no—
176C23—1461no—
177C23—1461no—
178C23C22⋊#6440811yescharacteristic
179Q8—41no—
180D4—2921no—
181D4—2921no—
182D4—2921no—
183D4—2922no—
184D4—2922no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—2921no—
189C2×C4—2921no—
190C2×C4—2922no—
191C2×C4—2922no—
192C2×C4—2922no—
193C2×C4—2922no—
194C2×C4—731no—
195C2×C4—731no—
196C2×C4—1462no—
197C2×C4—1462no—
198C2×C4—1461no—
199C2×C4—1462no—
200C2×C4C22⋊#6440811yescharacteristic
201C2×C4C22×#6440811yescharacteristic
202C8—2922no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—2922no—
207C22—2922no—
208C22—2921no—
209C22—2921no—
210C22—2921no—
211C22—731no—
212C22—731no—
213C22—1461no—
214C22—1461no—
215C22—1461no—
216C22—1461no—
217C22—1461no—
218C22C2×C22⋊#6440811yescharacteristic
219C4—21no—
220C4—21no—
221C4—41no—
222C4—41no—
223C4—2921no—
224C4—5842no—
225C4—732no—
226C4—1461no—
227C2—41no—
228C2—2921no—
229C2—5841no—
230C2—1461no—
231C2—1461no—
232C2D73⋊#9911yescharacteristic
233C2#1798957811yescharacteristic
234C2#1798958611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC22⋊Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22⋊Q8#64408
hypocenterC73#1513
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #17989559C2semidirect
2. #17989529C2semidirect
3. #17989441C2semidirect
4. #17989439C2semidirect
12. C2×#11924029C4semidirect
17. #14556565C4semidirect
21. #14556549C4semidirect
22. C22⋊Q8×C73C4semidirect
118. C73#1513semidirect
129. C22⋊Q8#64408semidirect