Finite Group Databasebeta

← #22611240

Subgroups — #22611240

Order 9344.

360 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14556520C211yesmaximal, characteristic, complemented
3C2×#14556513C211yesmaximal, characteristic, complemented
4#17988490C211yesmaximal, characteristic, complemented
5#17988488C211yesmaximal, characteristic, complemented
6#17988349C211yesmaximal, characteristic, complemented
7C2×#102×C73C211yesmaximal, characteristic, complemented
8C22×D292C2211yescharacteristic
9C2×#11924013—22no—
10C2×#11924013—22no—
11C2×#11924013—22no—
12C22×#10596831C2211yescharacteristic
13C2×C4⋊Dic73C2211yescharacteristic
14C2×C22⋊Dic73—21no—
15C2×C22⋊Dic73—21no—
16C2×#11924005—21no—
17C2×#11924005—21no—
18C2×C4×Dic73C2211yescharacteristic
19#14556520—22no—
20#14556513—22no—
21C22×D4×C73C2211yescharacteristic
22C22×C8×C73C2211yescharacteristic
23C2×C4⋊C4×C73C2211yescharacteristic
24#102×C73—22no—
25C23×D73—21no—
26C2×D292—21no—
27C2×D292—21no—
28C2×D292—21no—
29C2×D292—21no—
30C2×D292—21no—
31C2×D292D412yes—
32C22×Dic73—21no—
33C22×Dic73D411yescharacteristic
34C22×Dic73D411yescharacteristic
35#11924013—28no—
36C2×#10596831—21no—
37C2×#10596831—21no—
38C2×#10596831D412yes—
39C4⋊Dic73—21no—
40C4⋊Dic73—21no—
41C22⋊Dic73—42no—
42C22⋊Dic73—42no—
43#11924005—42no—
44#11924005—42no—
45C4×Dic73—21no—
46C4×Dic73—21no—
47C24×C73—21no—
48C2×D4×C73—21no—
49C2×D4×C73—21no—
50C2×D4×C73—21no—
51C2×D4×C73—21no—
52C2×D4×C73—21no—
53C2×D4×C73D412yes—
54C22×C4×C73—21no—
55C22×C4×C73C2311yescharacteristic
56C2×C8×C73—21no—
57C2×C8×C73—21no—
58C2×C8×C73—21no—
59C4⋊C4×C73—21no—
60C4⋊C4×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—41no—
81C2×C4×C73—41no—
82C2×C4×C73—41no—
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73C2×D411yescharacteristic
86C2×C4×C73#4111yescharacteristic
87C2×C4×C73#4111yescharacteristic
88C2×C4×C73#4111yescharacteristic
89C2×Dic73—21no—
90C2×Dic73—21no—
91C2×Dic73—21no—
92C2×Dic73—21no—
93C2×Dic73—21no—
94C2×Dic73—41no—
95C2×Dic73—41no—
96C2×Dic73—41no—
97C2×Dic73D812yescomplemented
98D292—22no—
99D292—22no—
100D292—41no—
101D292—41no—
102C8×C73—41no—
103#10596831—22no—
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—81no—
126C4×C73#12011yescharacteristic
127C4×C73#12311yescharacteristic
128C4×C73#12311yescharacteristic
129C4×C73#12411yescharacteristic
130Dic73—22no—
131Dic73—41no—
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×#102D7311yescharacteristic, complemented
148#390—731no—
149#390—731no—
150#340—731no—
151C22×D4—731no—
152C22×D4C2×D7311yescharacteristic
153C2×D8—1462no—
154C2×D8—1462no—
155C2×D8—1462no—
156C22×C8—731no—
157C22×C8C2×D7311yescharacteristic
158C2×C4⋊C4—731no—
159C2×C4⋊C4C2×D7311yescharacteristic
160C2×C22⋊C4—1461no—
161C2×C22⋊C4—1461no—
162C2×C22⋊C4—1461no—
163C2×C22⋊C4—1461no—
164C2×C42—731no—
165C4⋊C8—1462no—
166#102—22no—
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×D4C22⋊D7312yes—
182C22×C4—21no—
183C22×C4—731no—
184C22×C4—731no—
185C22×C4—1461no—
186C22×C4C22×D7311yescharacteristic
187D8—1468no—
188C2×C8—21no—
189C2×C8—21no—
190C2×C8—21no—
191C2×C8—732no—
192C2×C8—1461no—
193C2×C8—1461no—
194C4⋊C4—21no—
195C4⋊C4—21no—
196C4⋊C4—1461no—
197C4⋊C4—1461no—
198C22⋊C4—2922no—
199C22⋊C4—2922no—
200C22⋊C4—2922no—
201C22⋊C4—2922no—
202C42—1461no—
203C42—1461no—
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—
218C23D4×D7311yescharacteristic
219D4—22no—
220D4—22no—
221D4—41no—
222D4—41no—
223D4—2921no—
224D4—2921no—
225D4—1462no—
226D4—1462no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—2921no—
231C2×C4—2921no—
232C2×C4—2921no—
233C2×C4—732no—
234C2×C4—1461no—
235C2×C4—1461no—
236C2×C4—1461no—
237C2×C4—1461no—
238C2×C4—1461no—
239C2×C4D4×D7311yescharacteristic
240C2×C4D4×D7311yescharacteristic
241C2×C4C2×C22⋊D7311yescharacteristic
242C2×C4#1192402711yescharacteristic
243C2×C4#1192402811yescharacteristic
244C2×C4#1192402811yescharacteristic
245C8—41no—
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#1455656311yescharacteristic
262C22#1455656411yescharacteristic
263C22#1455656411yescharacteristic
264C22D8×D7311yescharacteristic
265C22#1455661211yescharacteristic
266C22#1455661511yescharacteristic
267C22#1455661811yescharacteristic
268C4—81no—
269C4—2921no—
270C4—5841no—
271C4—1462no—
272C4#1455655911yescharacteristic
273C4#1455657311yescharacteristic
274C4#1455657411yescharacteristic
275C4#1455657711yescharacteristic
276C2—82no—
277C2—5842no—
278C2#1798850211yescharacteristic
279C2#1798878011yescharacteristic
280C2#1798878111yescharacteristic
281C2#1798880111yescharacteristic
282C2#1798880411yescharacteristic
283C2#1798882211yescharacteristic
284C2#1798883911yescharacteristic
subgroupG/H
centerC23D4×D73
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×#102×C73C2
socleC23×C73C2×D4
hypercenterC2×#102D73
hypocenterC73#2054
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#14556520C2semidirect
3. C2×#14556513C2semidirect
4. #17988490C2semidirect
5. #17988488C2semidirect
6. #17988349C2semidirect
7. C2×#102×C73C2semidirect
97. C2×Dic73D8semidirect
143. C73#2054semidirect
147. C2×#102D73semidirect