Finite Group Databasebeta

← #22622607

Subgroups — #22622607

Order 9344.

336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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
1Q8×Dic146C211yesmaximal, characteristic
2#17989315C211yesmaximal, characteristic
3#17988938C211yesmaximal, characteristic
4#17988936C212yesmaximal
5#17988882C211yesmaximal, characteristic
6#17988881C212yesmaximal
7#17988797C211yesmaximal, characteristic
8#17988795C212yesmaximal
9C8×Dic146C211yesmaximal, characteristic
10#17988679C212yesmaximal
11C4×Q16×C73C211yesmaximal, characteristic
12C2×#11924018C2212yes—
13#14556591—21no—
14#14556591C2211yescharacteristic
15#14556591C2211yescharacteristic
16#14556590—22no—
17#14556590C2212yes—
18#14556589C2212yes—
19#14556583—21no—
20#14556581—22no—
21Q8×Dic73C2212yes—
22C4×Dic146—21no—
23C4×Dic146—21no—
24C4×Dic146C2211yescharacteristic
25#14556556C2212yes—
26#14556524C2212yes—
27C4⋊#10596831C2211yescharacteristic
28#14556520C2212yes—
29#14556516C2212yes—
30#14556516C2212yes—
31#14556515C2212yes—
32#14556514C2212yes—
33C8×Dic73C2212yes—
34C2×Q16×C73C2211yescharacteristic
35C4×Q8×C73C2211yescharacteristic
36C4×Q8×C73C2211yescharacteristic
37#107×C73C2211yescharacteristic
38#103×C73C2211yescharacteristic
39#103×C73C2211yescharacteristic
40C4×C8×C73C2211yescharacteristic
41C2×Dic146—21no—
42C2×Dic146—22no—
43C2×Dic146D411yescharacteristic
44C2×Dic146C2312yes—
45#11924018—24no—
46C2×#10596831C2312yes—
47C4⋊Dic73—21no—
48C4⋊Dic73—21no—
49C4⋊Dic73—21no—
50C4⋊Dic73—22no—
51C4⋊Dic73D411yescharacteristic
52C4⋊Dic73C2312yes—
53#11924007—22no—
54#11924007—22no—
55#11924007—22no—
56#11924007—22no—
57#11924007D412yes—
58C4×Dic73—22no—
59C4×Dic73—22no—
60C4×Dic73C2312yes—
61C2×Q8×C73C2311yescharacteristic
62C2×Q8×C73C2311yescharacteristic
63Q16×C73—22no—
64C2×C8×C73C2311yescharacteristic
65C2×C8×C73C2311yescharacteristic
66C4⋊C4×C73—21no—
67C4⋊C4×C73—21no—
68C4⋊C4×C73C2311yescharacteristic
69C4⋊C4×C73C2311yescharacteristic
70C42×C73—21no—
71C42×C73—21no—
72C42×C73C2311yescharacteristic
73Q8×C73—21no—
74Q8×C73—21no—
75Q8×C73—21no—
76Q8×C73#4112yes—
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73C2×D411yescharacteristic
82C2×C4×C73C2×D411yescharacteristic
83C2×C4×C73C2411yescharacteristic
84C2×Dic73—22no—
85C2×Dic73—22no—
86C2×Dic73C2×D412yes—
87C2×Dic73C2×D412yes—
88Dic146—22no—
89Dic146—22no—
90Dic146—82no—
91Dic146—81no—
92Dic146Q1614yescomplemented
93C8×C73—21no—
94C8×C73—21no—
95#10596831—22no—
96C22×C73C22×D411yescharacteristic
97C4×C73—22no—
98C4×C73—21no—
99C4×C73—41no—
100C4×C73—41no—
101C4×C73—41no—
102C4×C73C2×Q1612yes—
103C4×C73C2×#4111yescharacteristic
104C4×C732−1+411yescharacteristic
105Dic73—22no—
106Dic73—42no—
107Dic73—42no—
108Dic73C2×Q1614yes—
109C2×C73#54811yescharacteristic
110C2×C73C22×Q1611yescharacteristic
111C2×C73#57711yescharacteristic
112#3363—731nomaximal, Sylow
113C73#336311yescharacteristic, complemented, Sylow
114Q82—731no—
115#557—731no—
116#487—732no—
117#487—731no—
118#477—731no—
119#477—732no—
120#462—732no—
121#462—731no—
122C8×Q8—731no—
123C4×Q16—732no—
124C4×Q16D7311yescharacteristic
125C2×Q16—732no—
126C2×Q16C2×D7311yescharacteristic
127C4⋊Q8—732no—
128C4⋊Q8—732no—
129C4⋊Q8—731no—
130C4⋊Q8—731no—
131C4⋊Q8—1461no—
132C4⋊Q8—1462no—
133#125—1461no—
134#125—1462no—
135C4×Q8—731no—
136C4×Q8—732no—
137C4×Q8—732no—
138C4×Q8—1461no—
139C4×Q8—1461no—
140C4×Q8C2×D7311yescharacteristic
141C4×Q8C2×D7311yescharacteristic
142#107—732no—
143#107C2×D7311yescharacteristic
144C4⋊C8—732no—
145C4⋊C8—731no—
146#103—732no—
147#103—732no—
148#103—732no—
149#103—732no—
150#103C2×D7311yescharacteristic
151#103C2×D7311yescharacteristic
152C4×C8—732no—
153C4×C8C2×D7311yescharacteristic
154C2×Q8—731no—
155C2×Q8—732no—
156C2×Q8—1462no—
157C2×Q8—1461no—
158C2×Q8C22×D7311yescharacteristic
159C2×Q8C22×D7311yescharacteristic
160Q16—22no—
161Q16—1464no—
162C2×C8—732no—
163C2×C8C22×D7311yescharacteristic
164C2×C8C22×D7311yescharacteristic
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—732no—
168C4⋊C4—731no—
169C4⋊C4—732no—
170C4⋊C4—1462no—
171C4⋊C4—1462no—
172C4⋊C4—1462no—
173C4⋊C4—1462no—
174C4⋊C4—1462no—
175C4⋊C4—1461no—
176C4⋊C4—1461no—
177C4⋊C4—1461no—
178C4⋊C4C22×D7311yescharacteristic
179C4⋊C4C22×D7311yescharacteristic
180C42—21no—
181C42—21no—
182C42—732no—
183C42—1462no—
184C42—1462no—
185C42C22×D7311yescharacteristic
186Q8—21no—
187Q8—21no—
188Q8—21no—
189Q8—5841no—
190Q8—5842no—
191Q8—734no—
192Q8—1462no—
193Q8—1462no—
194Q8#1192402812yes—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—732no—
200C2×C4—732no—
201C2×C4—1462no—
202C2×C4—1462no—
203C2×C4D4×D7311yescharacteristic
204C2×C4D4×D7311yescharacteristic
205C2×C4C23×D7311yescharacteristic
206C8—21no—
207C8—21no—
208C8—1462no—
209C22C2×D4×D7311yescharacteristic
210C4—21no—
211C4—22no—
212C4—41no—
213C4—41no—
214C4—41no—
215C4—2922no—
216C4—2922no—
217C4—734no—
218C4—1462no—
219C4Q16×D7312yes—
220C4C2×#1192402811yescharacteristic
221C4#1455663811yescharacteristic
222C2#1798924611yescharacteristic
223C2C2×Q16×D7311yescharacteristic
224C2#1798939411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC4×Q16×C73C2
socleC22×C73C22×D4
hypercenterC4×Q16D73
hypocenterC73#3363
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
92. Dic146Q16semidirect
113. C73#3363semidirect