Finite Group Databasebeta

← #22626258

Subgroups — #22626258

Order 9344.

220 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 62 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×#14556666C211yesmaximal, characteristic, complemented
2D73⋊#108C211yesmaximal, characteristic, complemented
3#17989506C212yesmaximal, complemented
4#17989505C212yesmaximal, complemented
5#135×D73C211yesmaximal, characteristic
6D73⋊M16—21no—
7#14556666—21no—
8#14556666C2212yes—
9C2×#11924031—21no—
10#14556662—21no—
11#14556661C2212yes—
12#41×D73—21no—
13#14556614C411yescharacteristic
14#14556613C411yescharacteristic
15#14556612—21no—
16#14556611—21no—
17#14556610C411yescharacteristic
18Q16×D73C2211yescharacteristic
19SD16×D73—21no—
20D8×D73C2211yescharacteristic
21C2×C8×D73C2211yescharacteristic
22#135×C73C411yescharacteristic
23#11924038—22no—
24#11924037—41no—
25#11924036—41no—
26#11924031—22no—
27#11924029—21no—
28#11924028—21no—
29#11924028—41no—
30#11924027—21no—
31#11924027—41no—
32Q8×D73—21no—
33D4×D73—21no—
34D4×D73—41no—
35C2×C4×D73—41no—
36C2×C4×D73D411yescharacteristic
37Dic292C2×C411yescharacteristic
38#11924018—21no—
39#11924017—21no—
40#11924016—21no—
41#11924015—21no—
42D584C2×C411yescharacteristic
43#11924013—21no—
44C2×#10596831D411yescharacteristic
45C8×D73C2×C411yescharacteristic
46C8×D73D411yescharacteristic
47C8×D73D411yescharacteristic
48C8×D73C2311yescharacteristic
49#41×C73—21no—
50Q16×C73C2×C411yescharacteristic
51SD16×C73—21no—
52D8×C73C2×C411yescharacteristic
53C2×C8×C73C2×C411yescharacteristic
54C22×D73—41no—
55C22×D73SD1611yescharacteristic
56Q8×C73—21no—
57D4×C73—21no—
58D4×C73—41no—
59C2×C4×C73—41no—
60C2×C4×C73C22⋊C411yescharacteristic
61C22⋊D73—41no—
62C22⋊D73—41no—
63C22⋊D73—41no—
64C2×Dic73—41no—
65C2×Dic73D811yescharacteristic
66D292—21no—
67D292—41no—
68C4×D73—41no—
69C4×D73—41no—
70C4×D73—41no—
71C4×D73C22⋊C411yescharacteristic
72C4×D73D811yescharacteristic
73C4×D73SD1611yescharacteristic
74C4×D73C2×D411yescharacteristic
75Dic146—21no—
76Dic146—41no—
77#10596833—42no—
78C8×C73C22⋊C411yescharacteristic
79C8×C73C22×C411yescharacteristic
80#10596831C22⋊C411yescharacteristic
81#10596831C2×D411yescharacteristic
82C22×C73—41no—
83C22×C73#10211yescharacteristic
84C2×D73—41no—
85C2×D73—41no—
86C2×D73—82no—
87C2×D73#10211yescharacteristic
88C2×D73C2×SD1611yescharacteristic
89C4×C73—41no—
90C4×C73#10211yescharacteristic
91C4×C73C2×C22⋊C411yescharacteristic
92Dic73—41no—
93Dic73#10211yescharacteristic
94Dic73C2×D811yescharacteristic
95C2×C73—21no—
96C2×C73—81no—
97C2×C73C2×#10211yescharacteristic
98D73—21no—
99D73—21no—
100D73—81no—
101#2148—731nomaximal, Sylow
102C73#214811yescharacteristic, complemented, Sylow
103C2×#135—731no—
104C2×M32—731no—
105C2×#108—731no—
106#362—732no—
107#361—732no—
108C2×#41—1461no—
109#135—731no—
110#135—731no—
111#135—731no—
112#135—1461no—
113#135—1461no—
114#135#6440811yescharacteristic
115C2×Q16—731no—
116C2×SD16—1461no—
117C2×D8—731no—
118C2×M16—1461no—
119C22×C8—731no—
120M32—732no—
121M32—1461no—
122C2×C16—1461no—
123#108—732no—
124#108—1461no—
125#41—21no—
126#41—2921no—
127#41—2921no—
128#41—1461no—
129#41—1461no—
130#41—1461no—
131C2×Q8—1461no—
132C2×D4—2921no—
133C2×D4—1461no—
134C22×C4—2921no—
135C22×C4—731no—
136Q16—731no—
137Q16—1461no—
138Q16C2×#6440811yescharacteristic
139SD16—21no—
140SD16—1461no—
141SD16—1461no—
142SD16—1461no—
143D8—731no—
144D8—1461no—
145D8C2×#6440811yescharacteristic
146M16—2921no—
147M16—1462no—
148C2×C8—2921no—
149C2×C8—731no—
150C2×C8—731no—
151C2×C8—731no—
152C2×C8—731no—
153C2×C8—731no—
154C2×C8C2×#6440811yescharacteristic
155C16—1462no—
156C23—2921no—
157C23—731no—
158Q8—21no—
159Q8—2921no—
160Q8—1461no—
161D4—21no—
162D4—41no—
163D4—2921no—
164D4—2921no—
165D4—2921no—
166D4—2921no—
167D4—1461no—
168C2×C4—41no—
169C2×C4—2921no—
170C2×C4—2921no—
171C2×C4—2921no—
172C2×C4—2921no—
173C2×C4—731no—
174C2×C4—731no—
175C2×C4—731no—
176C2×C4—731no—
177C2×C4—731no—
178C2×C4C22⋊#6440811yescharacteristic
179C8—2922no—
180C8—731no—
181C8—731no—
182C8C22⋊#6440811yescharacteristic
183C8C22×#6440811yescharacteristic
184C22—41no—
185C22—2921no—
186C22—2921no—
187C22—5842no—
188C22—731no—
189C22—731no—
190C22#1455665311yescharacteristic
191C4—41no—
192C4—2921no—
193C4—731no—
194C4—731no—
195C4#1455665311yescharacteristic
196C4C2×C22⋊#6440811yescharacteristic
197C2—21no—
198C2—81no—
199C2—5841no—
200C2—1461no—
201C2—1461no—
202C2C2×#1455665311yescharacteristic
subgroupG/H
centerC4#14556653
commutatorC8×C73C22×C4
FrattiniC8C22×#64408
Fitting#135×C73C4
socleC2×C73C2×#102
hypercenter#135#64408
hypocenterC73#2148
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
1. C2×#14556666C2semidirect
2. D73⋊#108C2semidirect
3. #17989506C2semidirect
4. #17989505C2semidirect
102. C73#2148semidirect