Finite Group Databasebeta

← #22611122

Subgroups — #22611122

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×#14556566C211yesmaximal, characteristic
2C2×#14556513C211yesmaximal, characteristic, complemented
3C2×#14556511C211yesmaximal, characteristic, complemented
4C2×#14556503C211yesmaximal, characteristic, complemented
5#17988444C211yesmaximal, characteristic, complemented
6#17988349C211yesmaximal, characteristic, complemented
7C2×#106×C73C211yesmaximal, characteristic, complemented
8C22×D292—21no—
9C22×D292C2211yescharacteristic
10C22×C4×D73C2211yescharacteristic
11C22×#10596831C2211yescharacteristic
12#14556566—22no—
13#14556566—22no—
14C2×C4⋊Dic73C2211yescharacteristic
15C2×#11924005—21no—
16C2×#11924005—21no—
17#14556513—22no—
18#14556511—22no—
19#14556503—22no—
20#14556498—21no—
21C22×C8×C73C2211yescharacteristic
22C2×C4⋊C4×C73C2211yescharacteristic
23C2×C4⋊C4×C73C2211yescharacteristic
24#106×C73—22no—
25C23×D73—21no—
26C23×D73D411yescharacteristic
27C2×D292—21no—
28C2×D292—21no—
29C2×D292—21no—
30C2×D292—21no—
31C2×D292—24no—
32C2×D292—21no—
33C2×D292—42no—
34C2×D292—42no—
35C2×D292D412yes—
36C22×Dic73—21no—
37C22×Dic73D411yescharacteristic
38C2×C4×D73—21no—
39C2×C4×D73—21no—
40C2×C4×D73—21no—
41C2×C4×D73—21no—
42C2×C4×D73—21no—
43C2×C4×D73—21no—
44C2×#10596831—21no—
45C2×#10596831—21no—
46C2×#10596831—21no—
47C4⋊Dic73—21no—
48C4⋊Dic73—21no—
49#11924005—24no—
50#11924005—42no—
51C22×C4×C73—21no—
52C22×C4×C73—21no—
53C22×C4×C73C2311yescharacteristic
54C2×C8×C73—21no—
55C2×C8×C73—21no—
56C2×C8×C73D412yescomplemented
57C4⋊C4×C73—21no—
58C4⋊C4×C73—21no—
59C4⋊C4×C73—21no—
60C4⋊C4×C73D412yes—
61C23×C73C2×D411yescharacteristic
62C22×D73—21no—
63C22×D73—21no—
64C22×D73—21no—
65C22×D73—21no—
66C22×D73—21no—
67C22×D73—21no—
68C22×D73—22no—
69C22×D73—41no—
70C22×D73—41no—
71C22×D73—41no—
72C22×D73—41no—
73C22×D73—41no—
74C22×D73—41no—
75C22×D73SD1612yes—
76C2×C4×C73—22no—
77C2×C4×C73—41no—
78C2×C4×C73—41no—
79C2×C4×C73—41no—
80C2×C4×C73—41no—
81C2×C4×C73—41no—
82C2×C4×C73C2×D411yescharacteristic
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73#4111yescharacteristic
86C2×C4×C73#4111yescharacteristic
87C2×C4×C73#4111yescharacteristic
88C2×Dic73—21no—
89C2×Dic73—21no—
90C2×Dic73—21no—
91C2×Dic73—41no—
92C2×Dic73—41no—
93C2×Dic73—41no—
94D292—22no—
95D292—22no—
96D292—48no—
97D292—41no—
98D292—41no—
99C4×D73—41no—
100C4×D73—41no—
101C4×D73—41no—
102C4×D73—41no—
103C8×C73—22no—
104#10596831—41no—
105C22×C73#12011yescharacteristic
106C22×C73#12111yescharacteristic
107C22×C73#12311yescharacteristic
108C22×C73C2×SD1611yescharacteristic
109C22×C73#13511yescharacteristic
110C22×C73AGL(1,ℤ/8)11yescharacteristic
111C22×C73AGL(1,ℤ/8)11yescharacteristic
112C2×D73—22no—
113C2×D73—22no—
114C2×D73—22no—
115C2×D73—41no—
116C2×D73—41no—
117C2×D73—41no—
118C2×D73—41no—
119C2×D73—42no—
120C2×D73—42no—
121C2×D73—42no—
122C2×D73—81no—
123C2×D73—81no—
124C2×D73—81no—
125C2×D73—81no—
126C4×C73—42no—
127C4×C73—81no—
128C4×C73#12111yescharacteristic
129C4×C73#12111yescharacteristic
130C4×C73#12311yescharacteristic
131C4×C73#12411yescharacteristic
132Dic73—41no—
133Dic73—81no—
134C2×C73#39411yescharacteristic
135C2×C73#44911yescharacteristic
136C2×C73#45011yescharacteristic
137C2×C73#46511yescharacteristic
138C2×C73#46911yescharacteristic
139C2×C73#48111yescharacteristic
140C2×C73#48211yescharacteristic
141D73—42no—
142D73—82no—
143#2034—731nomaximal, Sylow
144C73#203411yescharacteristic, complemented, Sylow
145C2×#121—731no—
146C2×#106D7311yescharacteristic, complemented
147C2×#102—731no—
148C2×#102—731no—
149C2×C22⋊C8—731no—
150#380—731no—
151#340—731no—
152C22×D4—731no—
153C22×D4—1461no—
154C23×C4—731no—
155C22×C8—731no—
156C22×C8C2×D7311yescharacteristic
157#121—1462no—
158#121—1462no—
159C2×C4⋊C4—731no—
160C2×C4⋊C4C2×D7311yescharacteristic
161C2×C4⋊C4C2×D7311yescharacteristic
162C2×C22⋊C4—1461no—
163C2×C22⋊C4—1461no—
164#106—22no—
165#102—1462no—
166#102—1462no—
167C22⋊C8—1462no—
168#95—1461no—
169C24—731no—
170C24—1461no—
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—731no—
183C22×C4—1461no—
184C22×C4—1461no—
185C22×C4—1461no—
186C22×C4—1461no—
187C22×C4—1461no—
188C22×C4—1461no—
189C22×C4—1461no—
190C22×C4C22×D7311yescharacteristic
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—1461no—
194C2×C8—1461no—
195C2×C8—1461no—
196C2×C8D29212yescomplemented
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—1461no—
201C4⋊C4—1461no—
202C4⋊C4C22⋊D7312yes—
203C22⋊C4—2922no—
204C22⋊C4—1464no—
205C23—2921no—
206C23—2921no—
207C23—2921no—
208C23—2921no—
209C23—2921no—
210C23—2921no—
211C23—732no—
212C23—1462no—
213C23—1461no—
214C23—1461no—
215C23—1461no—
216C23—1461no—
217C23—1461no—
218C23—1461no—
219C23D4×D7311yescharacteristic
220D4—2928no—
221D4—2921no—
222D4—2921no—
223D4—1462no—
224D4—1462no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—2921no—
232C2×C4—2921no—
233C2×C4—2921no—
234C2×C4—2921no—
235C2×C4—2921no—
236C2×C4—2921no—
237C2×C4—2921no—
238C2×C4—1461no—
239C2×C4—1461no—
240C2×C4—1461no—
241C2×C4D4×D7311yescharacteristic
242C2×C4C2×C22⋊D7311yescharacteristic
243C2×C4C2×D29211yescharacteristic
244C2×C4#1192402811yescharacteristic
245C2×C4#1192402911yescharacteristic
246C2×C4#1192402911yescharacteristic
247C8—22no—
248C8—2921no—
249C22—2921no—
250C22—2921no—
251C22—2921no—
252C22—2921no—
253C22—2922no—
254C22—2922no—
255C22—2922no—
256C22—5841no—
257C22—5841no—
258C22—5841no—
259C22—5841no—
260C22—1462no—
261C22—1462no—
262C22—1462no—
263C22#1455655911yescharacteristic
264C22#1455656611yescharacteristic
265C22#1455657611yescharacteristic
266C22SD16×D7311yescharacteristic
267C22#1455661211yescharacteristic
268C22#1455661811yescharacteristic
269C22#1455661811yescharacteristic
270C4—42no—
271C4—81no—
272C4—2921no—
273C4—5841no—
274C4#1455656511yescharacteristic
275C4#1455656611yescharacteristic
276C4#1455657611yescharacteristic
277C4#1455658011yescharacteristic
278C2—2922no—
279C2—5842no—
280C2#1798850411yescharacteristic
281C2#1798873111yescharacteristic
282C2#1798873611yescharacteristic
283C2#1798881711yescharacteristic
284C2#1798884111yescharacteristic
285C2#1798890711yescharacteristic
286C2#1798891311yescharacteristic
subgroupG/H
centerC23D4×D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×#106×C73C2
socleC23×C73C2×D4
hypercenterC2×#106D73
hypocenterC73#2034
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×#14556513C2semidirect
3. C2×#14556511C2semidirect
4. C2×#14556503C2semidirect
5. #17988444C2semidirect
6. #17988349C2semidirect
7. C2×#106×C73C2semidirect
56. C2×C8×C73D4semidirect
144. C73#2034semidirect
146. C2×#106D73semidirect
196. C2×C8D292semidirect