Finite Group Databasebeta

← #22611113

Subgroups — #22611113

Order 9344.

368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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×#14556565C211yesmaximal, characteristic
2C2×#14556524C211yesmaximal, characteristic, complemented
3C2×#14556511C211yesmaximal, characteristic, complemented
4C2×#14556511C211yesmaximal, characteristic, complemented
5C2×C22⋊#10596831C211yesmaximal, characteristic, complemented
6#17988349C211yesmaximal, characteristic, complemented
7#380×C73C211yesmaximal, characteristic, complemented
8C22×D292C2211yescharacteristic
9C22×C22⋊D73—21no—
10C22×#10596831C2211yescharacteristic
11C22×#10596831C2211yescharacteristic
12#14556565—22no—
13#14556565—22no—
14C2×C4⋊Dic73C2211yescharacteristic
15C2×#11924005—21no—
16#14556524—22no—
17#14556511—22no—
18#14556511—22no—
19C22⋊#10596831—22no—
20C23×C4×C73C2211yescharacteristic
21C2×C4⋊C4×C73C2211yescharacteristic
22C2×C4⋊C4×C73C2211yescharacteristic
23C2×C22⋊C4×C73—21no—
24#95×C73—21no—
25C23×D73—21no—
26C2×D292—21no—
27C2×D292—21no—
28C2×D292—21no—
29C2×D292—21no—
30C2×D292—21no—
31C2×D292D412yes—
32C2×C22⋊D73—24no—
33C2×C22⋊D73—42no—
34C2×C22⋊D73—42no—
35C22×Dic73—21no—
36C2×#10596831—21no—
37C2×#10596831—21no—
38C2×#10596831—21no—
39C2×#10596831—21no—
40C2×#10596831—21no—
41C2×#10596831D412yescomplemented
42C4⋊Dic73—21no—
43C4⋊Dic73D412yes—
44#11924005—24no—
45C24×C73D411yescharacteristic
46C22×C4×C73—21no—
47C22×C4×C73—21no—
48C22×C4×C73—21no—
49C22×C4×C73—21no—
50C22×C4×C73—21no—
51C22×C4×C73—21no—
52C22×C4×C73—21no—
53C22×C4×C73—21no—
54C22×C4×C73D411yescharacteristic
55C22×C4×C73C2311yescharacteristic
56C4⋊C4×C73—21no—
57C4⋊C4×C73—21no—
58C4⋊C4×C73—21no—
59C4⋊C4×C73—21no—
60C22⋊C4×C73—42no—
61C23×C73—21no—
62C23×C73—21no—
63C23×C73—21no—
64C23×C73—21no—
65C23×C73—21no—
66C23×C73—21no—
67C23×C73D812yes—
68C23×C73C2×D411yescharacteristic
69C22×D73—22no—
70C22×D73—41no—
71C22×D73—41no—
72C22×D73—41no—
73C22×D73—41no—
74C22×D73—41no—
75C22×D73—41no—
76C2×C4×C73—21no—
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73—41no—
80C2×C4×C73—41no—
81C2×C4×C73—41no—
82C2×C4×C73—41no—
83C2×C4×C73—41no—
84C2×C4×C73—41no—
85C2×C4×C73—41no—
86C2×C4×C73—41no—
87C2×C4×C73—41no—
88C2×C4×C73—41no—
89C2×C4×C73C2×D411yescharacteristic
90C2×C4×C73C2×D411yescharacteristic
91C2×C4×C73C2×D411yescharacteristic
92C2×C4×C73#4111yescharacteristic
93C2×C4×C73#4111yescharacteristic
94C2×C4×C73#4111yescharacteristic
95C22⋊D73—48no—
96C2×Dic73—22no—
97C2×Dic73—41no—
98C2×Dic73—41no—
99D292—22no—
100D292—22no—
101D292—41no—
102D292—41no—
103#10596831—22no—
104#10596831—41no—
105C22×C73—22no—
106C22×C73—22no—
107C22×C73—22no—
108C22×C73—41no—
109C22×C73—41no—
110C22×C73—41no—
111C22×C73—41no—
112C22×C73#12011yescharacteristic
113C22×C73#12111yescharacteristic
114C22×C73#12311yescharacteristic
115C22×C73C2×D811yescharacteristic
116C22×C73#13511yescharacteristic
117C22×C73AGL(1,ℤ/8)11yescharacteristic
118C22×C73#13711yescharacteristic
119C2×D73—42no—
120C2×D73—42no—
121C2×D73—42no—
122C2×D73—81no—
123C2×D73—81no—
124C2×D73—81no—
125C2×D73—81no—
126C4×C73—41no—
127C4×C73—81no—
128C4×C73—81no—
129C4×C73#12111yescharacteristic
130C4×C73#12111yescharacteristic
131C4×C73#12311yescharacteristic
132C4×C73#12411yescharacteristic
133Dic73—42no—
134C2×C73—42no—
135C2×C73#39411yescharacteristic
136C2×C73#44711yescharacteristic
137C2×C73#45211yescharacteristic
138C2×C73#46611yescharacteristic
139C2×C73#46811yescharacteristic
140C2×C73#48011yescharacteristic
141C2×C73#48211yescharacteristic
142D73—82no—
143#2033—731nomaximal, Sylow
144C73#203311yescharacteristic, complemented, Sylow
145C2×#121—731no—
146C2×#107—731no—
147C2×#102—731no—
148C2×#102—731no—
149C2×C22⋊C8—731no—
150#380D7311yescharacteristic, complemented
151#340—731no—
152C22×D4—731no—
153C22×D4—1461no—
154C23×C4C2×D7311yescharacteristic
155C22×C8—731no—
156C22×C8—731no—
157#121—1462no—
158#121—1462no—
159C2×C4⋊C4—731no—
160C2×C4⋊C4C2×D7311yescharacteristic
161C2×C4⋊C4C2×D7311yescharacteristic
162C2×C22⋊C4—21no—
163C2×C22⋊C4—1461no—
164#107—1462no—
165#102—1462no—
166#102—1462no—
167C22⋊C8—1462no—
168#95—21no—
169C24—1461no—
170C24C22⋊D7311yescharacteristic
171C2×D4—2922no—
172C2×D4—2922no—
173C2×D4—732no—
174C2×D4—1464no—
175C2×D4—1461no—
176C2×D4—1461no—
177C2×D4—1461no—
178C2×D4—1461no—
179C2×D4—1461no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—1461no—
189C22×C4C22⋊D7311yescharacteristic
190C22×C4C22×D7311yescharacteristic
191C2×C8—732no—
192C2×C8—1461no—
193C2×C8—1461no—
194C2×C8—1461no—
195C2×C8—1461no—
196C2×C8—1461no—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4—732no—
202C4⋊C4—1461no—
203C22⋊C4—42no—
204C22⋊C4—1464no—
205C23—21no—
206C23—21no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—2921no—
212C23—2921no—
213C23—2921no—
214C23—2921no—
215C23—2921no—
216C23—2921no—
217C23—1462no—
218C23#1192401312yes—
219C23C2×C22⋊D7311yescharacteristic
220D4—2928no—
221D4—2921no—
222D4—2921no—
223D4—1462no—
224D4—1462no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—2921no—
239C2×C4—2921no—
240C2×C4—1462no—
241C2×C4D4×D7311yescharacteristic
242C2×C4D4×D7311yescharacteristic
243C2×C4D4×D7311yescharacteristic
244C2×C4#1192402711yescharacteristic
245C2×C4#1192402811yescharacteristic
246C2×C4#1192402811yescharacteristic
247C8—2921no—
248C8—1462no—
249C22—22no—
250C22—22no—
251C22—22no—
252C22—41no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—2922no—
257C22—2922no—
258C22—2922no—
259C22—5841no—
260C22—5841no—
261C22—5841no—
262C22—5841no—
263C22#1455655911yescharacteristic
264C22#1455656311yescharacteristic
265C22#1455657411yescharacteristic
266C22C2×#1192401311yescharacteristic
267C22#1455661111yescharacteristic
268C22#1455661611yescharacteristic
269C22#1455662211yescharacteristic
270C4—41no—
271C4—81no—
272C4—81no—
273C4—2922no—
274C4#1455656411yescharacteristic
275C4#1455656411yescharacteristic
276C4#1455657311yescharacteristic
277C4#1455657711yescharacteristic
278C2—42no—
279C2—5842no—
280C2#1798850211yescharacteristic
281C2#1798872011yescharacteristic
282C2#1798874711yescharacteristic
283C2#1798882111yescharacteristic
284C2#1798883511yescharacteristic
285C2#1798890011yescharacteristic
286C2#1798891111yescharacteristic
subgroupG/H
centerC23C2×C22⋊D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#380×C73C2
socleC23×C73C2×D4
hypercenter#380D73
hypocenterC73#2033
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C2×#14556524C2semidirect
3. C2×#14556511C2semidirect
4. C2×#14556511C2semidirect
5. C2×C22⋊#10596831C2semidirect
6. #17988349C2semidirect
7. #380×C73C2semidirect
41. C2×#10596831D4semidirect
144. C73#2033semidirect
150. #380D73semidirect