Finite Group Databasebeta

← #22619600

Subgroups — #22619600

Order 9344.

484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14556611C211yesmaximal, characteristic, complemented
2C2×#14556599C211yesmaximal, characteristic, complemented
3#17989168C211yesmaximal, characteristic, complemented
4#17989165C211yesmaximal, characteristic, complemented
5#17988836C212yesmaximal, complemented
6#17988832C212yesmaximal, complemented
7#17988827C212yesmaximal, complemented
8#17988822C212yesmaximal, complemented
9C2×#14556524C211yesmaximal, characteristic, complemented
10#17988589C211yesmaximal, characteristic, complemented
11#417×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2211yescharacteristic
13C2×#11924028C2211yescharacteristic
14#14556611—24no—
15C2×#11924018C2211yescharacteristic
16C2×#11924016C2211yescharacteristic
17C2×#11924015C2211yescharacteristic
18C2×#11924013C2211yescharacteristic
19#14556599—24no—
20C2×#11924011C2212yes—
21C22×#10596831C2211yescharacteristic
22C2×C8×D73C2212yes—
23#14556571—21no—
24#14556571C2212yes—
25#14556570—21no—
26#14556567C2212yes—
27#14556566—21no—
28#14556566C2212yes—
29#14556565—21no—
30#14556565—22no—
31#14556563—22no—
32#14556562C2212yes—
33C2×C4⋊Dic73C2211yescharacteristic
34#14556524C2212yes—
35#14556524C2212yes—
36#14556516C2212yes—
37#14556513C2212yes—
38C2×#41×C73C2211yescharacteristic
39C2×M16×C73C2211yescharacteristic
40C2×C4⋊C4×C73C2211yescharacteristic
41#103×C73C2212yes—
42#102×C73C2212yes—
43#11924028—22no—
44#11924028—22no—
45#11924028—22no—
46#11924028—22no—
47C2×Dic146D411yescharacteristic
48C2×Dic146C2311yescharacteristic
49C2×D292—22no—
50C2×D292D411yescharacteristic
51C2×D292C2311yescharacteristic
52C2×C22⋊D73—21no—
53C2×C22⋊D73—22no—
54C2×C22⋊D73D412yes—
55C22×Dic73—21no—
56C2×C4×D73—21no—
57C2×C4×D73C2312yes—
58#11924018—22no—
59#11924016—22no—
60#11924015—22no—
61#11924013—22no—
62#11924011—24no—
63C2×#10596831D414yescomplemented
64C2×#10596831C2311yescharacteristic
65C2×#10596831C2311yescharacteristic
66C8×D73—24no—
67C4⋊Dic73—21no—
68C4⋊Dic73—22no—
69C4⋊Dic73C2312yes—
70#11924007—22no—
71C22⋊Dic73—22no—
72#11924005—22no—
73#11924005—22no—
74#11924005—22no—
75#41×C73—22no—
76#41×C73—22no—
77C2×Q8×C73C2311yescharacteristic
78C2×D4×C73—21no—
79C2×D4×C73C2311yescharacteristic
80C22×C4×C73—21no—
81C22×C4×C73—21no—
82C22×C4×C73C2311yescharacteristic
83M16×C73—22no—
84C2×C8×C73C2312yes—
85C4⋊C4×C73—21no—
86C4⋊C4×C73C2312yes—
87C23×C73—21no—
88C23×C73C2×D411yescharacteristic
89C22×D73—21no—
90C22×D73C2×D412yes—
91Q8×C73—21no—
92Q8×C73—21no—
93D4×C73—21no—
94D4×C73—21no—
95D4×C73—42no—
96C2×C4×C73—22no—
97C2×C4×C73—21no—
98C2×C4×C73—42no—
99C2×C4×C73—81no—
100C2×C4×C73C2×D411yescharacteristic
101C2×C4×C73C2×D412yes—
102C2×C4×C73#4112yes—
103C2×C4×C73C2411yescharacteristic
104C22⋊D73—24no—
105C22⋊D73—42no—
106C22⋊D73—82no—
107C2×Dic73—21no—
108C2×Dic73—22no—
109C2×Dic73—81no—
110C2×Dic73C2×D412yes—
111D292—22no—
112D292—21no—
113D292—21no—
114D292—82no—
115C4×D73—22no—
116C4×D73—22no—
117C4×D73—42no—
118Dic146—22no—
119Dic146—21no—
120Dic146—21no—
121C8×C73—22no—
122#10596831C2×D412yes—
123#10596831C2×D412yes—
124C22×C73—21no—
125C22×C73—21no—
126C22×C73—41no—
127C22×C73—41no—
128C22×C73—41no—
129C22×C73#12112yes—
130C22×C73C22×D411yescharacteristic
131C2×D73—22no—
132C2×D73—22no—
133C2×D73—22no—
134C2×D73—41no—
135C2×D73—41no—
136C2×D73—41no—
137C4×C73—41no—
138C4×C73—42no—
139C4×C73#12112yes—
140C4×C73C22×D411yescharacteristic
141C4×C73C2×#4111yescharacteristic
142Dic73—22no—
143Dic73—41no—
144Dic73—42no—
145C2×C73—22no—
146C2×C73—81no—
147C2×C73C2×#12111yescharacteristic
148C2×C73#57611yescharacteristic
149C2×C73#57811yescharacteristic
150D73—42no—
151D73—81no—
152#3061—731nomaximal, Sylow
153C73#306111yescharacteristic, complemented, Sylow
154C2×#135—731no—
155C2×#131—731no—
156#537—731no—
157#537—731no—
158#468—732no—
159#468—732no—
160#467—732no—
161#466—732no—
162C2×#107—731no—
163#417—731no—
164#417D7311yescharacteristic, complemented
165C2×#41—731no—
166C2×#41—731no—
167C2×#41C2×D7311yescharacteristic
168#135—1464no—
169C2×Q16—731no—
170C2×SD16—731no—
171C2×SD16—731no—
172C2×D8—731no—
173#131—1464no—
174C2×M16—732no—
175C2×M16C2×D7311yescharacteristic
176C22×C8—731no—
177C22×C8—732no—
178C22⋊Q8—732no—
179C22⋊Q8—732no—
180C22⋊Q8—1461no—
181C22⋊Q8—1461no—
182#121—732no—
183#121—732no—
184#121—1461no—
185#121—1462no—
186#121—1461no—
187#121—1462no—
188C2×C4⋊C4—731no—
189C2×C4⋊C4C2×D7311yescharacteristic
190#107—732no—
191#107—732no—
192#103—732no—
193#103C2×D7312yes—
194#102—732no—
195#102C2×D7312yes—
196#41—22no—
197#41—22no—
198#41—1462no—
199#41—1462no—
200#41—1462no—
201#41—1462no—
202C2×Q8—731no—
203C2×Q8—731no—
204C2×Q8C22×D7311yescharacteristic
205C2×D4—21no—
206C2×D4—732no—
207C2×D4—731no—
208C2×D4—731no—
209C2×D4—1462no—
210C2×D4—1461no—
211C2×D4—1462no—
212C2×D4C22×D7311yescharacteristic
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—732no—
216C22×C4—1461no—
217C22×C4—1461no—
218C22×C4C22×D7311yescharacteristic
219Q16—1462no—
220SD16—1462no—
221SD16—1462no—
222D8—1462no—
223M16—22no—
224M16—1464no—
225C2×C8—734no—
226C2×C8—731no—
227C2×C8—731no—
228C2×C8—1464no—
229C2×C8C22×D7312yes—
230C4⋊C4—21no—
231C4⋊C4—732no—
232C4⋊C4—1462no—
233C4⋊C4—1462no—
234C4⋊C4—1461no—
235C4⋊C4C22×D7312yes—
236C22⋊C4—1462no—
237C22⋊C4—1462no—
238C22⋊C4—1462no—
239C22⋊C4—1462no—
240C23—21no—
241C23—732no—
242C23—1461no—
243C23D4×D7311yescharacteristic
244Q8—21no—
245Q8—21no—
246Q8—1461no—
247Q8—1461no—
248Q8—1462no—
249D4—21no—
250D4—21no—
251D4—42no—
252D4—2922no—
253D4—5842no—
254D4—5842no—
255D4—1464no—
256D4—1462no—
257D4—1461no—
258D4—1461no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—81no—
263C2×C4—2922no—
264C2×C4—5841no—
265C2×C4—732no—
266C2×C4—1462no—
267C2×C4—1461no—
268C2×C4—1462no—
269C2×C4—1462no—
270C2×C4D4×D7311yescharacteristic
271C2×C4D4×D7312yes—
272C2×C4#1192402812yes—
273C2×C4C23×D7311yescharacteristic
274C8—22no—
275C8—732no—
276C8—732no—
277C22—21no—
278C22—21no—
279C22—41no—
280C22—41no—
281C22—41no—
282C22—2921no—
283C22—2921no—
284C22—2921no—
285C22—1462no—
286C22—1462no—
287C22—1462no—
288C22#1455656412yes—
289C22C2×D4×D7311yescharacteristic
290C4—42no—
291C4—41no—
292C4—2922no—
293C4—2921no—
294C4—1462no—
295C4#1455656412yes—
296C4C2×D4×D7311yescharacteristic
297C4C2×#1192402811yescharacteristic
298C2—22no—
299C2—81no—
300C2—2922no—
301C2—5841no—
302C2C2×#1455656411yescharacteristic
303C2#1798939111yescharacteristic
304C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#417×C73C2
socleC22×C73C22×D4
hypercenter#417D73
hypocenterC73#3061
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#14556611C2semidirect
2. C2×#14556599C2semidirect
3. #17989168C2semidirect
4. #17989165C2semidirect
5. #17988836C2semidirect
6. #17988832C2semidirect
7. #17988827C2semidirect
8. #17988822C2semidirect
9. C2×#14556524C2semidirect
10. #17988589C2semidirect
11. #417×C73C2semidirect
63. C2×#10596831D4semidirect
153. C73#3061semidirect
164. #417D73semidirect