Finite Group Databasebeta

← #22621809

Subgroups — #22621809

Order 9344.

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

normal subgroups only

This group has 388 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
1#17989297C211yesmaximal, characteristic
2Q8×D292C211yesmaximal, characteristic
3#17988938C211yesmaximal, characteristic, complemented
4#17988924C212yesmaximal, complemented
5#17988882C211yesmaximal, characteristic, complemented
6#17988827C212yesmaximal, complemented
7#17988797C211yesmaximal, characteristic, complemented
8#17988741C212yesmaximal, complemented
9C8×D292C211yesmaximal, characteristic
10#103×D73C212yesmaximal, complemented
11C4×Q16×C73C211yesmaximal, characteristic, complemented
12C2×Q8×D73C2212yes—
13C2×#11924018C2212yes—
14C2×C8×D73C2212yes—
15#14556591—21no—
16#14556591C2211yescharacteristic
17#14556591C2211yescharacteristic
18#14556583—21no—
19#14556571—22no—
20#14556571C2212yes—
21#14556569—22no—
22#14556567C2212yes—
23C4×D292—21no—
24C4×D292—21no—
25C4×D292C2211yescharacteristic
26C4⋊C4×D73C2212yes—
27#14556524C2212yes—
28C4⋊#10596831C2211yescharacteristic
29#14556516C2212yes—
30#14556516C2212yes—
31#14556515C2212yes—
32#14556514C2212yes—
33#14556503C2212yes—
34C2×Q16×C73C2211yescharacteristic
35C4×Q8×C73C2211yescharacteristic
36C4×Q8×C73C2211yescharacteristic
37#107×C73C2211yescharacteristic
38#103×C73C2211yescharacteristic
39#103×C73C2211yescharacteristic
40C4×C8×C73C2211yescharacteristic
41C2×Dic146—22no—
42C2×Dic146—21no—
43C2×Dic146C2312yes—
44Q8×D73—24no—
45Q8×D73—42no—
46C2×D292D411yescharacteristic
47C2×C4×D73—22no—
48C2×C4×D73—22no—
49C2×C4×D73C2312yes—
50#11924018—42no—
51C2×#10596831C2312yes—
52C8×D73—42no—
53C4⋊Dic73—21no—
54C4⋊Dic73—21no—
55C4⋊Dic73—21no—
56C4⋊Dic73—22no—
57C4⋊Dic73D411yescharacteristic
58C4⋊Dic73C2312yes—
59#11924007—22no—
60#11924007—22no—
61#11924005—22no—
62#11924005—22no—
63#11924005D412yes—
64C2×Q8×C73C2311yescharacteristic
65C2×Q8×C73C2311yescharacteristic
66Q16×C73—22no—
67C2×C8×C73C2311yescharacteristic
68C2×C8×C73C2311yescharacteristic
69C4⋊C4×C73—21no—
70C4⋊C4×C73—21no—
71C4⋊C4×C73C2311yescharacteristic
72C4⋊C4×C73C2311yescharacteristic
73C42×C73—21no—
74C42×C73—21no—
75C42×C73C2311yescharacteristic
76C22×D73C2×D412yes—
77Q8×C73—21no—
78Q8×C73—21no—
79Q8×C73—21no—
80Q8×C73#4112yes—
81C2×C4×C73—21no—
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73C2×D411yescharacteristic
86C2×C4×C73C2×D411yescharacteristic
87C2×C4×C73C2411yescharacteristic
88C2×Dic73—22no—
89C2×Dic73—22no—
90C2×Dic73C2×D412yes—
91D292Q1614yescomplemented
92C4×D73—22no—
93C4×D73—22no—
94C4×D73—44no—
95C4×D73—82no—
96Dic146—22no—
97Dic146—22no—
98Dic146—44no—
99Dic146—81no—
100C8×C73—21no—
101C8×C73—21no—
102#10596831—22no—
103C22×C73C22×D411yescharacteristic
104C2×D73—22no—
105C2×D73—22no—
106C2×D73C2×Q1614yes—
107C4×C73—22no—
108C4×C73—21no—
109C4×C73—41no—
110C4×C73—41no—
111C4×C73—41no—
112C4×C73C2×Q1612yes—
113C4×C73C2×#4111yescharacteristic
114C4×C73H(5,𝔽2)11yescharacteristic
115Dic73—22no—
116Dic73—42no—
117Dic73—42no—
118C2×C73#54611yescharacteristic
119C2×C73C22×Q1611yescharacteristic
120C2×C73#57711yescharacteristic
121D73—24no—
122#3299—731nomaximal, Sylow
123C73#329911yescharacteristic, complemented, Sylow
124#554—731no—
125D4×Q8—731no—
126#487—731no—
127#484—732no—
128#477—731no—
129#467—732no—
130#462—731no—
131#451—732no—
132C4×Q16D7311yescharacteristic, complemented
133C8×D4—731no—
134C2×#103—732no—
135C22×Q8—732no—
136C2×Q16—732no—
137C2×Q16C2×D7311yescharacteristic
138C22×C8—732no—
139C4⋊Q8—731no—
140C4⋊Q8—731no—
141C4⋊Q8—1461no—
142#125—1461no—
143C22⋊Q8—732no—
144C22⋊Q8—732no—
145C22⋊Q8—1462no—
146C22⋊Q8—1462no—
147C4×Q8C2×D7311yescharacteristic
148C4×Q8C2×D7311yescharacteristic
149C4×D4—731no—
150C4×D4—1461no—
151C4×D4—1461no—
152C2×C4⋊C4—732no—
153#107—732no—
154#107C2×D7311yescharacteristic
155C4⋊C8—731no—
156#103—732no—
157#103—732no—
158#103—732no—
159#103—732no—
160#103C2×D7311yescharacteristic
161#103C2×D7311yescharacteristic
162C22⋊C8—732no—
163C4×C8C2×D7311yescharacteristic
164C2×Q8—2922no—
165C2×Q8—732no—
166C2×Q8—1462no—
167C2×Q8—1464no—
168C2×Q8—1461no—
169C2×Q8C22×D7311yescharacteristic
170C2×Q8C22×D7311yescharacteristic
171C2×D4—731no—
172C22×C4—732no—
173C22×C4—1462no—
174C22×C4—1462no—
175Q16—22no—
176Q16—2922no—
177C2×C8—2922no—
178C2×C8—732no—
179C2×C8C22×D7311yescharacteristic
180C2×C8C22×D7311yescharacteristic
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—731no—
184C4⋊C4—732no—
185C4⋊C4—1462no—
186C4⋊C4—1462no—
187C4⋊C4—1462no—
188C4⋊C4—1461no—
189C4⋊C4—1461no—
190C4⋊C4—1461no—
191C4⋊C4C22×D7311yescharacteristic
192C4⋊C4C22×D7311yescharacteristic
193C22⋊C4—732no—
194C22⋊C4—1462no—
195C22⋊C4—1462no—
196C42—21no—
197C42—21no—
198C42C22×D7311yescharacteristic
199C23—732no—
200Q8—21no—
201Q8—21no—
202Q8—21no—
203Q8—2924no—
204Q8—5841no—
205Q8—1462no—
206Q8—1462no—
207Q8#1192402812yes—
208D4—734no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—2924no—
214C2×C4—5842no—
215C2×C4—732no—
216C2×C4—1462no—
217C2×C4—1462no—
218C2×C4—1462no—
219C2×C4—1462no—
220C2×C4D4×D7311yescharacteristic
221C2×C4D4×D7311yescharacteristic
222C2×C4C23×D7311yescharacteristic
223C8—21no—
224C8—21no—
225C8—1462no—
226C22—734no—
227C22—1462no—
228C22—1462no—
229C22C2×D4×D7311yescharacteristic
230C4—21no—
231C4—22no—
232C4—41no—
233C4—41no—
234C4—41no—
235C4—2922no—
236C4—2922no—
237C4—1462no—
238C4Q16×D7312yes—
239C4C2×#1192402811yescharacteristic
240C4#1455663711yescharacteristic
241C2—1464no—
242C2#1798923311yescharacteristic
243C2C2×Q16×D7311yescharacteristic
244C2#1798939411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC4×Q16×C73C2
socleC22×C73C22×D4
hypercenterC4×Q16D73
hypocenterC73#3299
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
3. #17988938C2semidirect
4. #17988924C2semidirect
5. #17988882C2semidirect
6. #17988827C2semidirect
7. #17988797C2semidirect
8. #17988741C2semidirect
10. #103×D73C2semidirect
11. C4×Q16×C73C2semidirect
91. D292Q16semidirect
123. C73#3299semidirect
132. C4×Q16D73semidirect