Finite Group Databasebeta

← #22626044

Subgroups — #22626044

Order 9344.

240 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 78 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×#14556660C211yesmaximal, characteristic
2C2×#14556659C211yesmaximal, characteristic
3#17989531C211yesmaximal, characteristic
4C4×C4⋊#64408C211yesmaximal, characteristic
5#17989461C211yesmaximal, characteristic
6#17989461C211yesmaximal, characteristic
7C4⋊C8×D73C211yesmaximal, characteristic
8C2×C4⋊#64408C2211yescharacteristic
9C2×C4⋊#64408C2211yescharacteristic
10C2×C4⋊#64408C2211yescharacteristic
11C2×C4⋊#64408C2211yescharacteristic
12C2×C4×#64408—21no—
13#14556660—22no—
14#14556659—22no—
15(C2×#64408)⋊C4—21no—
16(C2×#64408)⋊C4—21no—
17(C2×#64408)⋊C4—21no—
18C2×C8×D73C2211yescharacteristic
19C2×C8×D73C2211yescharacteristic
20C42×D73C2211yescharacteristic
21C4⋊#10596831C411yescharacteristic, complemented
22#14556520C411yescharacteristic, complemented
23#14556520C411yescharacteristic, complemented
24C4⋊C8×C73C411yescharacteristic, complemented
25C22×#64408—21no—
26C22×#64408—21no—
27C22×#64408—21no—
28C22×#64408—21no—
29C4⋊#64408—21no—
30C4⋊#64408—21no—
31C4⋊#64408—21no—
32C4⋊#64408—21no—
33C4⋊#64408—21no—
34C4⋊#64408—21no—
35C4⋊#64408D412yes—
36C4⋊#64408Q812yes—
37C4×#64408—42no—
38C2×C4×D73D411yescharacteristic
39C2×C4×D73D411yescharacteristic
40C2×C4×D73C2311yescharacteristic
41C2×#10596831C2×C411yescharacteristic
42C2×#10596831C2×C411yescharacteristic
43C8×D73—21no—
44C8×D73—21no—
45C8×D73—21no—
46C8×D73—21no—
47C4×Dic73C2×C411yescharacteristic
48C4×Dic73Q811yescharacteristic
49C4×Dic73Q811yescharacteristic
50C2×C8×C73C2×C411yescharacteristic
51C2×C8×C73C2×C411yescharacteristic
52C42×C73C2×C411yescharacteristic
53C22×D73C2×D411yescharacteristic
54C2×#64408—22no—
55C2×#64408—22no—
56C2×#64408—41no—
57C2×#64408—41no—
58C2×#64408—41no—
59C2×#64408—41no—
60C2×#64408—41no—
61C2×#64408—41no—
62C2×#64408—41no—
63C2×#64408—41no—
64C2×#64408—41no—
65C2×#64408—41no—
66C2×C4×C73C4⋊C411yescharacteristic
67C2×C4×C73C4⋊C411yescharacteristic
68C2×C4×C73C22×C411yescharacteristic
69C2×Dic73C4⋊C411yescharacteristic
70C2×Dic73C4⋊C411yescharacteristic
71C2×Dic73C2×Q811yescharacteristic
72C4×D73—21no—
73C4×D73—21no—
74C4×D73—21no—
75C4×D73—21no—
76C4×D73C2×D411yescharacteristic
77C4×D73C2×Q811yescharacteristic
78C4×D73#4111yescharacteristic
79C4×D73#4111yescharacteristic
80C8×C73—21no—
81C8×C73—21no—
82#10596831—21no—
83#10596831—21no—
84C22×C73C2×C4⋊C411yescharacteristic
85C2×D73#12111yescharacteristic
86C2×D73C22⋊Q811yescharacteristic
87C2×D73#13511yescharacteristic
88C2×D73#13511yescharacteristic
89C2×D73AGL(1,ℤ/8)11yescharacteristic
90C2×D73#13711yescharacteristic
91#64408—42no—
92#64408—42no—
93#64408—81no—
94#64408—81no—
95C4×C73—21no—
96C4×C73—21no—
97C4×C73C4×D411yescharacteristic
98C4×C73C4×Q811yescharacteristic
99Dic73—21no—
100Dic73—21no—
101Dic73#12511yescharacteristic
102Dic73C4⋊Q811yescharacteristic
103C2×C73#38911yescharacteristic
104C2×C73#42711yescharacteristic
105C2×C73#42811yescharacteristic
106D73#46311yescharacteristic
107D73#46411yescharacteristic
108D73#47811yescharacteristic
109D73#47911yescharacteristic
110#1949—731nomaximal, Sylow
111C73#194911yescharacteristic, complemented, Sylow
112C2×#107—731no—
113C2×#106—731no—
114C2×C4⋊C8—731no—
115#382—731no—
116C4×C4⋊C4—731no—
117#340—731no—
118#340—731no—
119C22×C8—731no—
120C22×C8—731no—
121C2×C4⋊C4—731no—
122C2×C4⋊C4—731no—
123C2×C4⋊C4—731no—
124C2×C4⋊C4—731no—
125C2×C42—731no—
126C2×C42—1461no—
127#107—1462no—
128#106—1462no—
129C4⋊C8—731no—
130C4⋊C8—731no—
131C4⋊C8—731no—
132C4⋊C8#6440811yescharacteristic, complemented
133#95—1461no—
134#95—1461no—
135#95—1461no—
136C22×C4—731no—
137C22×C4—731no—
138C22×C4—731no—
139C22×C4—1461no—
140C22×C4—1461no—
141C22×C4—1461no—
142C22×C4—1461no—
143C2×C8—731no—
144C2×C8—731no—
145C2×C8—1461no—
146C2×C8—1461no—
147C2×C8—1461no—
148C2×C8—1461no—
149C2×C8C2×#6440811yescharacteristic
150C2×C8C2×#6440811yescharacteristic
151C4⋊C4—732no—
152C4⋊C4—732no—
153C4⋊C4—1461no—
154C4⋊C4—1461no—
155C4⋊C4—1461no—
156C4⋊C4—1461no—
157C4⋊C4—1461no—
158C4⋊C4—1461no—
159C42—2922no—
160C42—731no—
161C42—731no—
162C42—731no—
163C42C2×#6440811yescharacteristic
164C23—731no—
165C2×C4—2921no—
166C2×C4—2921no—
167C2×C4—2921no—
168C2×C4—2921no—
169C2×C4—2921no—
170C2×C4—2921no—
171C2×C4—2921no—
172C2×C4—2921no—
173C2×C4—2921no—
174C2×C4—2921no—
175C2×C4—731no—
176C2×C4—731no—
177C2×C4—731no—
178C2×C4—731no—
179C2×C4—731no—
180C2×C4—731no—
181C2×C4—731no—
182C2×C4—1461no—
183C2×C4—1461no—
184C2×C4—1461no—
185C2×C4—1461no—
186C2×C4—1462no—
187C2×C4—1462no—
188C2×C4C4⋊#6440811yescharacteristic
189C2×C4C4⋊#6440811yescharacteristic
190C2×C4C22×#6440811yescharacteristic
191C8—21no—
192C8—21no—
193C8—1461no—
194C8—1461no—
195C22—731no—
196C22—731no—
197C22—731no—
198C22—731no—
199C22—731no—
200C22—731no—
201C22C2×C4⋊#6440811yescharacteristic
202C4—21no—
203C4—21no—
204C4—2922no—
205C4—2922no—
206C4—5841no—
207C4—5841no—
208C4—731no—
209C4—731no—
210C4—1461no—
211C4—1461no—
212C4D4×#6440811yescharacteristic
213C4Q8×#6440811yescharacteristic
214C2—731no—
215C2—731no—
216C2—731no—
217C2—731no—
218C2#1798953811yescharacteristic
219C2#1798959711yescharacteristic
220C2#1798959811yescharacteristic
subgroupG/H
centerC22C2×C4⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4⋊C8×C73C4
socleC22×C73C2×C4⋊C4
hypercenterC4⋊C8#64408
hypocenterC73#1949
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
21. C4⋊#10596831C4semidirect
22. #14556520C4semidirect
23. #14556520C4semidirect
24. C4⋊C8×C73C4semidirect
111. C73#1949semidirect
132. C4⋊C8#64408semidirect