Finite Group Databasebeta

← #22611235

Subgroups — #22611235

Order 9344.

264 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 63 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#17989385C211yesmaximal, characteristic
2#17988613C211yesmaximal, characteristic, complemented
3#17988584C211yesmaximal, characteristic, complemented
4#17988561C211yesmaximal, characteristic, complemented
5#17988560C211yesmaximal, characteristic, complemented
6#17988343C211yesmaximal, characteristic, complemented
7#416×C73C211yesmaximal, characteristic, complemented
8C2×#11924028C2211yescharacteristic
9#14556622—21no—
10#14556621—21no—
11#14556617—21no—
12#14556616—21no—
13#14556611—22no—
14C2×#11924012C2211yescharacteristic
15#14556550C2211yescharacteristic
16#14556550C2211yescharacteristic
17#14556520—22no—
18#14556516—21no—
19#14556513—21no—
20#14556506—22no—
21#14556505—22no—
22C2×#41×C73C2211yescharacteristic
23C22×C8×C73C2211yescharacteristic
24#117×C73C2211yescharacteristic
25#103×C73—21no—
26#102×C73—21no—
27#11924028—21no—
28#11924028—21no—
29#11924028—21no—
30#11924028—21no—
31C2×Dic146D411yescharacteristic
32C2×D292D411yescharacteristic
33C2×C22⋊D73—21no—
34C2×C4×D73—21no—
35#11924018—22no—
36#11924016—22no—
37#11924015—22no—
38#11924013—22no—
39#11924012—21no—
40#11924012—21no—
41C2×#10596831D412yes—
42C4⋊Dic73—21no—
43C4⋊Dic73—21no—
44C22⋊Dic73—21no—
45C22⋊Dic73D412yes—
46C4×Dic73—21no—
47C4×Dic73—21no—
48#41×C73—21no—
49#41×C73—21no—
50#41×C73—21no—
51#41×C73—21no—
52C2×Q8×C73D411yescharacteristic
53C2×D4×C73—21no—
54C2×D4×C73D411yescharacteristic
55C22×C4×C73—21no—
56C22×C4×C73C2311yescharacteristic
57C2×C8×C73—21no—
58C2×C8×C73—21no—
59C2×C8×C73—21no—
60C4⋊C4×C73—21no—
61C22⋊C4×C73—21no—
62C42×C73—21no—
63C23×C73—21no—
64C23×C73C2×D411yescharacteristic
65C22×D73—21no—
66Q8×C73—21no—
67Q8×C73—21no—
68D4×C73—21no—
69D4×C73—21no—
70D4×C73—41no—
71D4×C73—41no—
72C2×C4×C73—21no—
73C2×C4×C73—41no—
74C2×C4×C73—41no—
75C2×C4×C73—41no—
76C2×C4×C73C2×D411yescharacteristic
77C2×C4×C73C2×D411yescharacteristic
78C2×C4×C73C2×D411yescharacteristic
79C2×C4×C73#4111yescharacteristic
80C2×C4×C73#4111yescharacteristic
81C2×C4×C73#4111yescharacteristic
82C22⋊D73—41no—
83C22⋊D73—41no—
84C2×Dic73—22no—
85C2×Dic73—21no—
86C2×Dic73—41no—
87D292—21no—
88D292—21no—
89C4×D73—41no—
90C4×D73—41no—
91Dic146—21no—
92Dic146—21no—
93C8×C73—41no—
94#10596831—22no—
95C22×C73—41no—
96C22×C73—41no—
97C22×C73—81no—
98C22×C73#12111yescharacteristic
99C22×C73#12111yescharacteristic
100C22×C73#12111yescharacteristic
101C2×D73—41no—
102C2×D73—81no—
103C4×C73—41no—
104C4×C73—81no—
105C4×C73#12011yescharacteristic
106C4×C73#12311yescharacteristic
107C4×C73#12311yescharacteristic
108C4×C73#12411yescharacteristic
109Dic73—42no—
110Dic73—41no—
111Dic73—81no—
112C2×C73—21no—
113C2×C73—21no—
114C2×C73—21no—
115C2×C73—81no—
116C2×C73#39411yescharacteristic
117D73—81no—
118#2053—731nomaximal, Sylow
119C73#205311yescharacteristic, complemented, Sylow
120#575—731no—
121#424—731no—
122#416—731no—
123#416D7311yescharacteristic, complemented
124#410—731no—
125#410—731no—
126H(3,ℤ/4)—731no—
127C2×#41—731no—
128C2×#41C2×D7311yescharacteristic
129#137—1461no—
130#137—1461no—
131AGL(1,ℤ/8)—1461no—
132AGL(1,ℤ/8)—1461no—
133#135—1462no—
134C2×M16—731no—
135C22×C8C2×D7311yescharacteristic
136#117—731no—
137#117—731no—
138#117C2×D7311yescharacteristic
139C4⋊C8—1462no—
140#103—21no—
141#103—1461no—
142#102—21no—
143#102—1461no—
144#99—1462no—
145#99—1462no—
146#41—21no—
147#41—21no—
148#41—21no—
149#41—21no—
150#41—1461no—
151#41—1461no—
152#41—1461no—
153#41—1461no—
154C2×Q8—731no—
155C2×Q8C22⋊D7311yescharacteristic
156C2×D4—21no—
157C2×D4—731no—
158C2×D4—1461no—
159C2×D4C22⋊D7311yescharacteristic
160C22×C4—21no—
161C22×C4—1461no—
162C22×C4C22×D7311yescharacteristic
163Q16—1462no—
164SD16—1462no—
165SD16—1462no—
166D8—1462no—
167M16—1461no—
168M16—1461no—
169C2×C8—21no—
170C2×C8—21no—
171C2×C8—21no—
172C2×C8—732no—
173C4⋊C4—21no—
174C4⋊C4—1461no—
175C4⋊C4—1461no—
176C22⋊C4—21no—
177C22⋊C4—732no—
178C22⋊C4—1461no—
179C42—21no—
180C42—1461no—
181C42—1461no—
182C23—21no—
183C23—1461no—
184C23D4×D7311yescharacteristic
185Q8—21no—
186Q8—21no—
187Q8—1461no—
188Q8—1461no—
189D4—21no—
190D4—21no—
191D4—41no—
192D4—41no—
193D4—2921no—
194D4—2921no—
195D4—1461no—
196D4—1461no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—2921no—
202C2×C4—2921no—
203C2×C4—2921no—
204C2×C4—1462no—
205C2×C4—1461no—
206C2×C4D4×D7311yescharacteristic
207C2×C4D4×D7311yescharacteristic
208C2×C4C2×C22⋊D7311yescharacteristic
209C2×C4#1192402711yescharacteristic
210C2×C4#1192402811yescharacteristic
211C2×C4#1192402811yescharacteristic
212C8—41no—
213C8—1462no—
214C22—41no—
215C22—41no—
216C22—81no—
217C22—2921no—
218C22—5841no—
219C22#1455656311yescharacteristic
220C22#1455656411yescharacteristic
221C22#1455656411yescharacteristic
222C4—41no—
223C4—81no—
224C4—2922no—
225C4—2921no—
226C4—5841no—
227C4#1455655911yescharacteristic
228C4#1455657311yescharacteristic
229C4#1455657411yescharacteristic
230C4#1455657711yescharacteristic
231C2—21no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—5841no—
236C2#1798850211yescharacteristic
subgroupG/H
centerC4#14556577
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#416×C73C2
socleC2×C73#394
hypercenter#416D73
hypocenterC73#2053
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #17988613C2semidirect
3. #17988584C2semidirect
4. #17988561C2semidirect
5. #17988560C2semidirect
6. #17988343C2semidirect
7. #416×C73C2semidirect
119. C73#2053semidirect
123. #416D73semidirect