Finite Group Databasebeta

← #22611241

Subgroups — #22611241

Order 9344.

360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C22×#11924013C211yesmaximal, characteristic
2C2×C4⋊#10596831C211yesmaximal, characteristic, complemented
3C2×#14556512C211yesmaximal, characteristic, complemented
4C2×#14556511C211yesmaximal, characteristic, complemented
5#17988489C211yesmaximal, characteristic, complemented
6#17988349C211yesmaximal, characteristic, complemented
7#390×C73C211yesmaximal, characteristic, complemented
8C22×D292C2211yescharacteristic
9C2×#11924013—22no—
10C2×#11924013—22no—
11C2×#11924013—22no—
12C22×#10596831C2211yescharacteristic
13C22×#10596831C2211yescharacteristic
14C2×C4⋊Dic73C2211yescharacteristic
15C2×#11924005—21no—
16C2×#11924005—21no—
17C4⋊#10596831—22no—
18#14556512—22no—
19#14556511—22no—
20C22×D4×C73C2211yescharacteristic
21C2×C4⋊C4×C73C2211yescharacteristic
22C2×C22⋊C4×C73—21no—
23C2×C22⋊C4×C73—21no—
24C2×C42×C73C2211yescharacteristic
25C23×D73—21no—
26C2×D292—21no—
27C2×D292—21no—
28C2×D292—21no—
29C2×D292—21no—
30C2×D292—21no—
31C2×D292D412yes—
32C22×Dic73—21no—
33#11924013—28no—
34C2×#10596831—21no—
35C2×#10596831—21no—
36C2×#10596831—21no—
37C2×#10596831—21no—
38C2×#10596831—21no—
39C2×#10596831D412yes—
40C4⋊Dic73—21no—
41C4⋊Dic73—21no—
42#11924005—42no—
43#11924005—42no—
44C24×C73—21no—
45C2×D4×C73—21no—
46C2×D4×C73—21no—
47C2×D4×C73—21no—
48C2×D4×C73—21no—
49C2×D4×C73—21no—
50C2×D4×C73D412yes—
51C22×C4×C73—21no—
52C22×C4×C73D411yescharacteristic
53C22×C4×C73D411yescharacteristic
54C22×C4×C73C2311yescharacteristic
55C4⋊C4×C73—21no—
56C4⋊C4×C73—21no—
57C22⋊C4×C73—42no—
58C22⋊C4×C73—42no—
59C42×C73—21no—
60C42×C73—21no—
61C23×C73—22no—
62C23×C73—41no—
63C23×C73—41no—
64C23×C73—41no—
65C23×C73—41no—
66C23×C73—41no—
67C23×C73—41no—
68C23×C73C2×D411yescharacteristic
69C22×D73—22no—
70C22×D73—41no—
71C22×D73—41no—
72C22×D73—41no—
73C22×D73—41no—
74C22×D73—41no—
75C22×D73—41no—
76D4×C73—22no—
77D4×C73—22no—
78D4×C73—41no—
79D4×C73—41no—
80C2×C4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—41no—
86C2×C4×C73—41no—
87C2×C4×C73—41no—
88C2×C4×C73D812yescomplemented
89C2×C4×C73C2×D411yescharacteristic
90C2×C4×C73C2×D411yescharacteristic
91C2×C4×C73C2×D411yescharacteristic
92C2×C4×C73#4111yescharacteristic
93C2×C4×C73#4111yescharacteristic
94C2×C4×C73#4111yescharacteristic
95C2×Dic73—41no—
96C2×Dic73—41no—
97C2×Dic73—41no—
98D292—22no—
99D292—22no—
100D292—41no—
101D292—41no—
102#10596831—22no—
103#10596831—41no—
104C22×C73—42no—
105C22×C73—42no—
106C22×C73—42no—
107C22×C73—81no—
108C22×C73—81no—
109C22×C73—81no—
110C22×C73—81no—
111C22×C73#12111yescharacteristic
112C22×C73#12111yescharacteristic
113C22×C73#12111yescharacteristic
114C22×C73C2×D811yescharacteristic
115C22×C73#13511yescharacteristic
116C22×C73AGL(1,ℤ/8)11yescharacteristic
117C22×C73AGL(1,ℤ/8)11yescharacteristic
118C2×D73—42no—
119C2×D73—42no—
120C2×D73—42no—
121C2×D73—81no—
122C2×D73—81no—
123C2×D73—81no—
124C2×D73—81no—
125C4×C73—22no—
126C4×C73—41no—
127C4×C73—81no—
128C4×C73#12011yescharacteristic
129C4×C73#12311yescharacteristic
130C4×C73#12311yescharacteristic
131C4×C73#12411yescharacteristic
132Dic73—81no—
133C2×C73—82no—
134C2×C73#39411yescharacteristic
135C2×C73#45911yescharacteristic
136C2×C73#45911yescharacteristic
137C2×C73#46311yescharacteristic
138C2×C73#46311yescharacteristic
139C2×C73#46611yescharacteristic
140C2×C73#46911yescharacteristic
141D73—82no—
142#2054—731nomaximal, Sylow
143C73#205411yescharacteristic, complemented, Sylow
144C22×D8—731no—
145C2×C4⋊C8—731no—
146C2×#102—731no—
147C2×#102—731no—
148#390—731no—
149#390D7311yescharacteristic, complemented
150#340—731no—
151C22×D4—731no—
152C22×D4C2×D7311yescharacteristic
153C2×D8—1462no—
154C2×D8—1462no—
155C2×D8—1462no—
156C22×C8—731no—
157C22×C8—731no—
158C2×C4⋊C4—731no—
159C2×C4⋊C4C2×D7311yescharacteristic
160C2×C22⋊C4—21no—
161C2×C22⋊C4—21no—
162C2×C22⋊C4—1461no—
163C2×C22⋊C4—1461no—
164C2×C42C2×D7311yescharacteristic
165C4⋊C8—1462no—
166#102—1462no—
167#102—1462no—
168C24—21no—
169C24—1461no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—732no—
176C2×D4—1461no—
177C2×D4—1461no—
178C2×D4—1461no—
179C2×D4—1461no—
180C2×D4—1461no—
181C2×D4D29212yes—
182C22×C4—21no—
183C22×C4—1461no—
184C22×C4C22⋊D7311yescharacteristic
185C22×C4C22⋊D7311yescharacteristic
186C22×C4C22×D7311yescharacteristic
187D8—1468no—
188C2×C8—732no—
189C2×C8—1461no—
190C2×C8—1461no—
191C2×C8—1461no—
192C2×C8—1461no—
193C2×C8—1461no—
194C4⋊C4—21no—
195C4⋊C4—21no—
196C4⋊C4—1461no—
197C4⋊C4—1461no—
198C22⋊C4—42no—
199C22⋊C4—42no—
200C22⋊C4—2922no—
201C22⋊C4—2922no—
202C42—21no—
203C42—21no—
204C23—22no—
205C23—41no—
206C23—41no—
207C23—41no—
208C23—41no—
209C23—41no—
210C23—41no—
211C23—2921no—
212C23—2921no—
213C23—2921no—
214C23—2921no—
215C23—2921no—
216C23—2921no—
217C23—1462no—
218C23C2×C22⋊D7311yescharacteristic
219D4—22no—
220D4—22no—
221D4—41no—
222D4—41no—
223D4—2921no—
224D4—2921no—
225D4—1462no—
226D4—1462no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—2921no—
236C2×C4—2921no—
237C2×C4—2921no—
238C2×C4#1192401312yescomplemented
239C2×C4D4×D7311yescharacteristic
240C2×C4D4×D7311yescharacteristic
241C2×C4C2×D29211yescharacteristic
242C2×C4#1192402711yescharacteristic
243C2×C4#1192402711yescharacteristic
244C2×C4#1192402811yescharacteristic
245C8—2921no—
246C8—1462no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—81no—
251C22—81no—
252C22—81no—
253C22—81no—
254C22—2922no—
255C22—2922no—
256C22—2922no—
257C22—5841no—
258C22—5841no—
259C22—5841no—
260C22—5841no—
261C22#1455656211yescharacteristic
262C22#1455656311yescharacteristic
263C22#1455656511yescharacteristic
264C22C2×#1192401311yescharacteristic
265C22#1455661111yescharacteristic
266C22#1455661611yescharacteristic
267C22#1455661711yescharacteristic
268C4—22no—
269C4—41no—
270C4—81no—
271C4—5841no—
272C4#1455656111yescharacteristic
273C4#1455657311yescharacteristic
274C4#1455657511yescharacteristic
275C4#1455657711yescharacteristic
276C2—82no—
277C2—5842no—
278C2#1798850311yescharacteristic
279C2#1798877911yescharacteristic
280C2#1798878211yescharacteristic
281C2#1798879911yescharacteristic
282C2#1798880211yescharacteristic
283C2#1798882111yescharacteristic
284C2#1798883811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#390×C73C2
socleC23×C73C2×D4
hypercenter#390D73
hypocenterC73#2054
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊#10596831C2semidirect
3. C2×#14556512C2semidirect
4. C2×#14556511C2semidirect
5. #17988489C2semidirect
6. #17988349C2semidirect
7. #390×C73C2semidirect
88. C2×C4×C73D8semidirect
143. C73#2054semidirect
149. #390D73semidirect
238. C2×C4#11924013semidirect