Finite Group Databasebeta

← #22626017

Subgroups — #22626017

Order 9344.

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

normal subgroups only

This group has 232 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#17989598C211yesmaximal, characteristic, complemented
2#17989579C211yesmaximal, characteristic
3C2×#14556653C211yesmaximal, characteristic
4#17989553C211yesmaximal, characteristic, complemented
5#17989466C211yesmaximal, characteristic, complemented
6#17989462C211yesmaximal, characteristic, complemented
7#100×D73C211yesmaximal, characteristic
8D73⋊M16C2211yescharacteristic
9C2×#11924036C2211yescharacteristic
10#14556670C2211yescharacteristic
11C2×C4⋊#64408C2211yescharacteristic
12#14556660—21no—
13#14556659—21no—
14#14556653—21no—
15#14556653—21no—
16#14556653—21no—
17#14556653—21no—
18#14556645—21no—
19C8×#64408—21no—
20C2×D4×D73C2211yescharacteristic
21M16×D73C2211yescharacteristic
22M16×D73C2211yescharacteristic
23#14556508C411yescharacteristic, complemented
24#14556507C411yescharacteristic, complemented
25#14556507C411yescharacteristic, complemented
26#100×C73C411yescharacteristic, complemented
27C22×#64408—21no—
28#11924038—21no—
29#11924037—21no—
30#11924036—21no—
31#11924036—21no—
32#11924036D411yescharacteristic
33#11924036D411yescharacteristic
34C2×#10596833—21no—
35C4⋊#64408—21no—
36C4⋊#64408—21no—
37C4⋊#64408D411yescharacteristic
38C4⋊#64408D411yescharacteristic
39C22⋊#64408—21no—
40C4×#64408—21no—
41C23×D73—21no—
42C2×D292C2×C411yescharacteristic
43C2×C22⋊D73—21no—
44D4×D73—21no—
45D4×D73—21no—
46D4×D73—21no—
47D4×D73—21no—
48C2×C4×D73C2311yescharacteristic
49#11924012C2×C411yescharacteristic
50#11924012C2×C411yescharacteristic
51#11924011—21no—
52#11924011—21no—
53C8×D73—21no—
54C8×D73—21no—
55C2×D4×C73C2×C411yescharacteristic
56M16×C73C2×C411yescharacteristic
57M16×C73C2×C411yescharacteristic
58C23×C73—21no—
59C22×D73—21no—
60C22×D73—41no—
61C22×D73—41no—
62C22×D73—81no—
63C22×D73—81no—
64C22×D73#4111yescharacteristic
65C2×#64408—21no—
66C2×#64408—21no—
67C2×#64408—41no—
68C2×#64408—81no—
69D4×C73—21no—
70D4×C73—21no—
71C2×C4×C73C22×C411yescharacteristic
72C22⋊D73—41no—
73C22⋊D73—41no—
74C2×Dic73#4111yescharacteristic
75D292—21no—
76D292—21no—
77C4×D73C2×D411yescharacteristic
78C4×D73C2×D411yescharacteristic
79C4×D73#4111yescharacteristic
80C4×D73#4111yescharacteristic
81#10596833—21no—
82#10596833—21no—
83#10596833—41no—
84C8×C73—21no—
85C8×C73—21no—
86#10596831—21no—
87#10596831—21no—
88C22×C73—41no—
89C22×C73—81no—
90C22×C73#11711yescharacteristic
91C2×D73—21no—
92C2×D73—21no—
93C2×D73—41no—
94C2×D73—82no—
95C2×D73—81no—
96C2×D73—81no—
97C2×D73—81no—
98C2×D73#12111yescharacteristic
99C2×D73#12611yescharacteristic
100#64408—41no—
101#64408—41no—
102#64408—81no—
103C4×C73C4×D411yescharacteristic
104C4×C73C4×D411yescharacteristic
105Dic73#12311yescharacteristic
106Dic73#12411yescharacteristic
107C2×C73—21no—
108C2×C73—81no—
109C2×C73#38811yescharacteristic
110D73—21no—
111D73—81no—
112D73#47111yescharacteristic
113D73#47211yescharacteristic
114#1931—731nomaximal, Sylow
115C73#193111yescharacteristic, complemented, Sylow
116#428—731no—
117#418—731no—
118C2×#102—731no—
119C2×#100—731no—
120#405—731no—
121#343—731no—
122#341—731no—
123C22×D4—731no—
124C2×M16—731no—
125C2×M16—731no—
126C2×M16—731no—
127C22×C8—731no—
128#117—731no—
129C2×C4⋊C4—731no—
130#107—1461no—
131#106—1461no—
132#102—1461no—
133#102—1461no—
134#102—1461no—
135#102—1461no—
136#100—731no—
137#100—731no—
138#100—731no—
139#100#6440811yescharacteristic, complemented
140#97—1461no—
141C4×C8—1461no—
142C24—1461no—
143C2×D4—731no—
144C2×D4—1461no—
145C2×D4—1461no—
146C2×D4—1461no—
147C2×D4—1461no—
148C2×D4—1461no—
149C2×D4C2×#6440811yescharacteristic
150C22×C4—731no—
151C22×C4—1461no—
152M16—731no—
153M16—731no—
154M16—1461no—
155M16—1461no—
156M16—1461no—
157M16—1461no—
158M16C2×#6440811yescharacteristic
159M16C2×#6440811yescharacteristic
160C2×C8—731no—
161C2×C8—731no—
162C2×C8—1461no—
163C2×C8—1461no—
164C2×C8—1461no—
165C2×C8—1461no—
166C2×C8—1461no—
167C4⋊C4—731no—
168C4⋊C4—731no—
169C4⋊C4—1461no—
170C4⋊C4—1461no—
171C22⋊C4—1461no—
172C42—1461no—
173C23—21no—
174C23—2921no—
175C23—2921no—
176C23—5841no—
177C23—5841no—
178C23—731no—
179C23—1461no—
180D4—21no—
181D4—21no—
182D4—2921no—
183D4—2921no—
184D4—1461no—
185D4—1461no—
186C2×C4—2921no—
187C2×C4—5841no—
188C2×C4—731no—
189C2×C4—731no—
190C2×C4—731no—
191C2×C4—731no—
192C2×C4—731no—
193C2×C4—1461no—
194C2×C4—1461no—
195C2×C4C22×#6440811yescharacteristic
196C8—21no—
197C8—21no—
198C8—2921no—
199C8—1461no—
200C8—1461no—
201C8—1461no—
202C8—1461no—
203C22—41no—
204C22—81no—
205C22—2921no—
206C22—5841no—
207C22—5841no—
208C22—5841no—
209C22—5842no—
210C22—731no—
211C22—731no—
212C22—1461no—
213C22—1461no—
214C22#1455667011yescharacteristic
215C4—2921no—
216C4—2921no—
217C4—5841no—
218C4—731no—
219C4—731no—
220C4D4×#6440811yescharacteristic
221C4D4×#6440811yescharacteristic
222C2—21no—
223C2—81no—
224C2—5841no—
225C2—731no—
226C2—731no—
227C2—1461no—
228C2#1798953711yescharacteristic
subgroupG/H
centerC2#17989537
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#100×C73C4
socleC2×C73#388
hypercenter#100#64408
hypocenterC73#1931
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

Complements

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

NH ≅ G/Ntype
1. #17989598C2semidirect
4. #17989553C2semidirect
5. #17989466C2semidirect
6. #17989462C2semidirect
23. #14556508C4semidirect
24. #14556507C4semidirect
25. #14556507C4semidirect
26. #100×C73C4semidirect
115. C73#1931semidirect
139. #100#64408semidirect