Finite Group Databasebeta

← #22619598

Subgroups — #22619598

Order 9344.

484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14556598C211yesmaximal, characteristic, complemented
3#17989165C211yesmaximal, characteristic, complemented
4#17988835C212yesmaximal, complemented
5#17988831C212yesmaximal, complemented
6#17988826C212yesmaximal, complemented
7#17988821C212yesmaximal, complemented
8C2×#14556524C211yesmaximal, characteristic, complemented
9#17988588C211yesmaximal, characteristic, complemented
10#17988586C211yesmaximal, characteristic, complemented
11#537×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2211yescharacteristic
13#14556611—24no—
14C2×#11924018C2211yescharacteristic
15C2×#11924016C2211yescharacteristic
16C2×#11924015C2211yescharacteristic
17C2×#11924013C2211yescharacteristic
18#14556598—24no—
19C2×#11924012C2212yes—
20C2×#11924012C2211yescharacteristic
21C22×#10596831C2212yes—
22C22×#10596831C2211yescharacteristic
23#14556570C2212yes—
24#14556567—21no—
25#14556565C2212yes—
26#14556563—22no—
27#14556562—21no—
28C2×C4⋊Dic73C2211yescharacteristic
29#14556524C2212yes—
30#14556524C2212yes—
31#14556515C2212yes—
32#14556514C2212yes—
33#14556512C2212yes—
34#14556511C2212yes—
35C2×#41×C73C2211yescharacteristic
36C2×#41×C73C2211yescharacteristic
37C22⋊Q8×C73—21no—
38C22⋊Q8×C73C2212yes—
39#121×C73—21no—
40#121×C73—22no—
41#121×C73C2212yes—
42C2×C4⋊C4×C73C2211yescharacteristic
43#11924028—22no—
44#11924028—22no—
45C2×Dic146C2311yescharacteristic
46C2×D292C2311yescharacteristic
47C2×C22⋊D73—21no—
48C2×C22⋊D73—22no—
49C22×Dic73—21no—
50C2×C4×D73—21no—
51#11924018—22no—
52#11924016—22no—
53#11924015—22no—
54#11924013—22no—
55#11924012—22no—
56#11924012—24no—
57C2×#10596831—24no—
58C2×#10596831D414yescomplemented
59C2×#10596831C2312yes—
60C2×#10596831C2311yescharacteristic
61C2×#10596831C2311yescharacteristic
62C4⋊Dic73—21no—
63C4⋊Dic73C2312yes—
64#11924007—22no—
65C22⋊Dic73—22no—
66#11924005—22no—
67#41×C73—22no—
68#41×C73—22no—
69#41×C73—22no—
70#41×C73—22no—
71C2×Q8×C73D411yescharacteristic
72C2×Q8×C73C2311yescharacteristic
73C2×D4×C73—21no—
74C2×D4×C73—22no—
75C2×D4×C73D411yescharacteristic
76C2×D4×C73D412yes—
77C2×D4×C73C2311yescharacteristic
78C22×C4×C73—21no—
79C22×C4×C73—21no—
80C22×C4×C73C2312yes—
81C22×C4×C73C2311yescharacteristic
82C4⋊C4×C73—21no—
83C4⋊C4×C73—22no—
84C4⋊C4×C73C2312yes—
85C22⋊C4×C73—22no—
86C22⋊C4×C73—22no—
87C23×C73—21no—
88C23×C73C2×D412yes—
89C23×C73C2×D411yescharacteristic
90C22×D73—21no—
91Q8×C73—22no—
92Q8×C73—21no—
93Q8×C73—21no—
94D4×C73—24no—
95D4×C73—22no—
96D4×C73—21no—
97D4×C73—21no—
98D4×C73—42no—
99D4×C73—82no—
100C2×C4×C73—22no—
101C2×C4×C73—22no—
102C2×C4×C73—22no—
103C2×C4×C73—21no—
104C2×C4×C73—42no—
105C2×C4×C73—81no—
106C2×C4×C73C2×D412yes—
107C2×C4×C73C2×D412yes—
108C2×C4×C73C2×D411yescharacteristic
109C2×C4×C73#4112yes—
110C2×C4×C73C2411yescharacteristic
111C22⋊D73—42no—
112C22⋊D73—82no—
113C2×Dic73—22no—
114C2×Dic73—21no—
115C2×Dic73—81no—
116D292—21no—
117D292—21no—
118C4×D73—42no—
119Dic146—21no—
120Dic146—21no—
121#10596831—22no—
122#10596831C2×D412yes—
123#10596831C2×D412yes—
124C22×C73—21no—
125C22×C73—21no—
126C22×C73—22no—
127C22×C73—22no—
128C22×C73—22no—
129C22×C73—41no—
130C22×C73—41no—
131C22×C73—41no—
132C22×C73#12112yes—
133C22×C73C22×D411yescharacteristic
134C2×D73—41no—
135C2×D73—41no—
136C2×D73—41no—
137C4×C73—22no—
138C4×C73—41no—
139C4×C73—42no—
140C4×C73#12112yes—
141C4×C73C22×D411yescharacteristic
142C4×C73C2×#4111yescharacteristic
143Dic73—41no—
144Dic73—42no—
145C2×C73—22no—
146C2×C73—42no—
147C2×C73—81no—
148C2×C73C2×#12111yescharacteristic
149C2×C73#57611yescharacteristic
150C2×C73#57811yescharacteristic
151D73—81no—
152#3061—731nomaximal, Sylow
153C73#306111yescharacteristic, complemented, Sylow
154C2×#135—731no—
155C2×#131—731no—
156#537—731no—
157#537D7311yescharacteristic, complemented
158#468—732no—
159#468—732no—
160#467—732no—
161#466—732no—
162C2×#107—731no—
163#417—731no—
164#417—731no—
165C2×#41—731no—
166C2×#41C2×D7311yescharacteristic
167C2×#41C2×D7311yescharacteristic
168#135—1464no—
169C2×Q16—731no—
170C2×SD16—731no—
171C2×SD16—731no—
172C2×D8—731no—
173#131—1464no—
174C2×M16—731no—
175C2×M16—732no—
176C22×C8—731no—
177C22×C8—732no—
178C22⋊Q8—21no—
179C22⋊Q8—732no—
180C22⋊Q8—1461no—
181C22⋊Q8C2×D7312yes—
182#121—21no—
183#121—22no—
184#121—732no—
185#121—1461no—
186#121—1462no—
187#121C2×D7312yes—
188C2×C4⋊C4—731no—
189C2×C4⋊C4C2×D7311yescharacteristic
190#107—732no—
191#107—732no—
192#103—732no—
193#103—732no—
194#102—732no—
195#102—732no—
196#41—22no—
197#41—22no—
198#41—22no—
199#41—22no—
200#41—1462no—
201#41—1462no—
202C2×Q8—731no—
203C2×Q8C22⋊D7311yescharacteristic
204C2×Q8C22×D7311yescharacteristic
205C2×D4—21no—
206C2×D4—22no—
207C2×D4—731no—
208C2×D4—1461no—
209C2×D4—1462no—
210C2×D4C22⋊D7312yes—
211C2×D4C22⋊D7311yescharacteristic
212C2×D4C22×D7311yescharacteristic
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—1461no—
216C22×C4—1461no—
217C22×C4C22×D7312yes—
218C22×C4C22×D7311yescharacteristic
219Q16—1462no—
220SD16—1462no—
221SD16—1462no—
222D8—1462no—
223M16—1464no—
224M16—1462no—
225C2×C8—734no—
226C2×C8—731no—
227C2×C8—731no—
228C2×C8—732no—
229C2×C8—1464no—
230C4⋊C4—21no—
231C4⋊C4—22no—
232C4⋊C4—732no—
233C4⋊C4—1462no—
234C4⋊C4—1461no—
235C4⋊C4C22×D7312yes—
236C22⋊C4—22no—
237C22⋊C4—22no—
238C22⋊C4—1462no—
239C22⋊C4—1462no—
240C23—21no—
241C23—1461no—
242C23C2×C22⋊D7312yes—
243C23C2×C22⋊D7311yescharacteristic
244Q8—22no—
245Q8—21no—
246Q8—21no—
247Q8—1461no—
248Q8—1461no—
249D4—24no—
250D4—22no—
251D4—21no—
252D4—21no—
253D4—42no—
254D4—82no—
255D4—2922no—
256D4—5842no—
257D4—1461no—
258D4—1461no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—42no—
264C2×C4—81no—
265C2×C4—2922no—
266C2×C4—5841no—
267C2×C4—1462no—
268C2×C4—1461no—
269C2×C4D4×D7312yes—
270C2×C4C2×C22⋊D7312yes—
271C2×C4C2×C22⋊D7311yescharacteristic
272C2×C4#1192402712yes—
273C2×C4C23×D7311yescharacteristic
274C8—732no—
275C8—732no—
276C8—1462no—
277C22—21no—
278C22—21no—
279C22—22no—
280C22—22no—
281C22—22no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—2921no—
286C22—2921no—
287C22—2921no—
288C22#1455656312yes—
289C22C22×C22⋊D7311yescharacteristic
290C4—22no—
291C4—42no—
292C4—41no—
293C4—2922no—
294C4—2921no—
295C4#1455656312yes—
296C4C2×D4×D7311yescharacteristic
297C4C2×#1192402711yescharacteristic
298C2—22no—
299C2—42no—
300C2—81no—
301C2—5841no—
302C2C2×#1455656311yescharacteristic
303C2#1798939011yescharacteristic
304C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#537×C73C2
socleC22×C73C22×D4
hypercenter#537D73
hypocenterC73#3061
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#14556611C2semidirect
2. C2×#14556598C2semidirect
3. #17989165C2semidirect
4. #17988835C2semidirect
5. #17988831C2semidirect
6. #17988826C2semidirect
7. #17988821C2semidirect
8. C2×#14556524C2semidirect
9. #17988588C2semidirect
10. #17988586C2semidirect
11. #537×C73C2semidirect
58. C2×#10596831D4semidirect
153. C73#3061semidirect
157. #537D73semidirect