Finite Group Databasebeta

← #22619486

Subgroups — #22619486

Order 9344.

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

normal subgroups only

This group has 472 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×#14556622C211yesmaximal, characteristic, complemented
2C2×#14556613C211yesmaximal, characteristic
3#17989161C211yesmaximal, characteristic, complemented
4#17989068C211yesmaximal, characteristic, complemented
5#17988812C212yesmaximal, complemented
6#17988805C212yesmaximal, complemented
7#17988796C212yesmaximal, complemented
8#17988791C212yesmaximal, complemented
9#17988613C211yesmaximal, characteristic, complemented
10#17988586C211yesmaximal, characteristic, complemented
11C2×#103×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2211yescharacteristic
13C2×#11924028C2211yescharacteristic
14#14556622—24no—
15#14556613—24no—
16C2×Dic292C2211yescharacteristic
17C2×#11924018C2212yes—
18C2×#11924017C2211yescharacteristic
19C2×#11924017C2211yescharacteristic
20C2×#11924015C2212yes—
21C2×D584C2211yescharacteristic
22C2×#11924012C2211yescharacteristic
23#14556589C2212yes—
24#14556580C2212yes—
25#14556574—22no—
26#14556567—21no—
27#14556567—21no—
28#14556556C2212yes—
29#14556553C2212yes—
30C4×C22⋊D73—22no—
31#14556550C2211yescharacteristic
32#14556549—21no—
33C4⋊C4×D73—21no—
34#14556520C2212yes—
35#14556520C2212yes—
36#14556514C2212yes—
37#14556511C2212yes—
38C22×Q8×C73C2211yescharacteristic
39C22×C8×C73C2211yescharacteristic
40C2×C4⋊C4×C73C2211yescharacteristic
41#103×C73C2212yes—
42#103×C73C2212yes—
43#11924028—22no—
44#11924028—22no—
45#11924028—22no—
46#11924028D414yes—
47C2×Dic146C2311yescharacteristic
48C2×Dic146C2311yescharacteristic
49C2×D292C2311yescharacteristic
50C2×D292C2311yescharacteristic
51C2×C22⋊D73—21no—
52C2×C22⋊D73—21no—
53C2×C4×D73—21no—
54C2×C4×D73—21no—
55C2×C4×D73—22no—
56Dic292—22no—
57#11924018—24no—
58#11924017—22no—
59#11924017—22no—
60#11924015—24no—
61D584—22no—
62#11924012—22no—
63C2×#10596831C2312yes—
64C4⋊Dic73D411yescharacteristic
65C4⋊Dic73D411yescharacteristic
66#11924007—22no—
67#11924007—22no—
68#11924007—22no—
69C22⋊Dic73D412yes—
70#11924005—22no—
71#11924005—22no—
72#11924005—22no—
73C4×Dic73—22no—
74C4×Dic73C2312yes—
75C2×Q8×C73—21no—
76C2×Q8×C73—22no—
77C2×Q8×C73—22no—
78C2×Q8×C73C2312yes—
79C22×C4×C73—21no—
80C22×C4×C73—21no—
81C22×C4×C73C2311yescharacteristic
82C2×C8×C73—22no—
83C2×C8×C73C2311yescharacteristic
84C2×C8×C73C2311yescharacteristic
85C4⋊C4×C73—21no—
86C4⋊C4×C73C2312yes—
87C23×C73C2×D411yescharacteristic
88C22×D73—21no—
89C22×D73—21no—
90Q8×C73—22no—
91Q8×C73—22no—
92Q8×C73—42no—
93C2×C4×C73—22no—
94C2×C4×C73—22no—
95C2×C4×C73—42no—
96C2×C4×C73—81no—
97C2×C4×C73C2×D411yescharacteristic
98C2×C4×C73C2×D412yes—
99C2×C4×C73#4112yes—
100C2×C4×C73C2411yescharacteristic
101C22⋊D73—24no—
102C22⋊D73—42no—
103C2×Dic73—21no—
104C2×Dic73—21no—
105C2×Dic73C2×D412yes—
106C2×Dic73C2×D412yes—
107D292—21no—
108D292—21no—
109D292—21no—
110D292C2×D412yes—
111C4×D73—24no—
112C4×D73—42no—
113C4×D73—82no—
114Dic146—21no—
115Dic146—21no—
116Dic146—21no—
117Dic146C2×D412yes—
118C8×C73—21no—
119C8×C73—21no—
120#10596831—22no—
121C22×C73—21no—
122C22×C73—21no—
123C22×C73#12112yes—
124C22×C73C22×D411yescharacteristic
125C2×D73—22no—
126C2×D73—41no—
127C2×D73—41no—
128C2×D73—41no—
129C2×D73—41no—
130C2×D73—41no—
131C4×C73—42no—
132C4×C73—42no—
133C4×C73#12112yes—
134C4×C73C22×D411yescharacteristic
135C4×C73C2×#4111yescharacteristic
136Dic73—22no—
137Dic73—22no—
138Dic73—22no—
139Dic73—41no—
140C2×C73—22no—
141C2×C73C2×#12111yescharacteristic
142C2×C73#57711yescharacteristic
143C2×C73#57811yescharacteristic
144D73—42no—
145D73—81no—
146#3046—731nomaximal, Sylow
147C73#304611yescharacteristic, complemented, Sylow
148C2×#137—731no—
149C2×#135—731no—
150#536—731no—
151#520—731no—
152#464—732no—
153#463—732no—
154#462—732no—
155#461—732no—
156#424—731no—
157#417—731no—
158C2×#103D7311yescharacteristic, complemented
159C2×#41—731no—
160C2×#41—731no—
161C22×Q8C2×D7311yescharacteristic
162#137—1464no—
163#135—1464no—
164C2×Q16—732no—
165C2×Q16—731no—
166C2×SD16—732no—
167C2×SD16—731no—
168C2×SD16—731no—
169C2×D8—731no—
170C2×M16—731no—
171C22×C8C2×D7311yescharacteristic
172C4⋊Q8—732no—
173#124—732no—
174#123—1462no—
175C22⋊Q8—1461no—
176C22⋊Q8—1461no—
177C4×Q8—732no—
178C4×D4—732no—
179C4×D4—1462no—
180#117—731no—
181#117—1461no—
182C2×C4⋊C4—1461no—
183C2×C4⋊C4C2×D7311yescharacteristic
184C4⋊C8—732no—
185C4⋊C8—732no—
186#103—732no—
187#103C2×D7312yes—
188#103C2×D7312yes—
189#102—732no—
190#41—734no—
191#41—1462no—
192#41—1462no—
193#41—1462no—
194C2×Q8—21no—
195C2×Q8—22no—
196C2×Q8—22no—
197C2×Q8—731no—
198C2×Q8—731no—
199C2×Q8C22×D7312yes—
200C2×D4—731no—
201C2×D4—731no—
202C2×D4—1461no—
203C2×D4—1461no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—1462no—
207C22×C4—1461no—
208C22×C4—1461no—
209C22×C4C22×D7311yescharacteristic
210Q16—1462no—
211Q16—1464no—
212SD16—1462no—
213SD16—1462no—
214SD16—1464no—
215D8—1462no—
216M16—1462no—
217C2×C8—22no—
218C2×C8—732no—
219C2×C8C22×D7311yescharacteristic
220C2×C8C22×D7311yescharacteristic
221C4⋊C4—21no—
222C4⋊C4—731no—
223C4⋊C4—731no—
224C4⋊C4—1462no—
225C4⋊C4—1462no—
226C4⋊C4—1462no—
227C4⋊C4C22×D7312yes—
228C22⋊C4—732no—
229C22⋊C4—1462no—
230C22⋊C4—1462no—
231C22⋊C4—1462no—
232C42—732no—
233C42—1462no—
234C23—1461no—
235C23—1461no—
236C23D4×D7311yescharacteristic
237Q8—22no—
238Q8—22no—
239Q8—42no—
240Q8—732no—
241Q8—1461no—
242Q8—1461no—
243Q8—1461no—
244D4—2922no—
245D4—732no—
246D4—1464no—
247D4—1461no—
248D4—1461no—
249D4—1461no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—81no—
254C2×C4—2922no—
255C2×C4—5842no—
256C2×C4—732no—
257C2×C4—732no—
258C2×C4—1461no—
259C2×C4—1461no—
260C2×C4—1464no—
261C2×C4D4×D7311yescharacteristic
262C2×C4D4×D7312yes—
263C2×C4#1192402812yes—
264C2×C4C23×D7311yescharacteristic
265C8—21no—
266C8—21no—
267C8—1462no—
268C22—21no—
269C22—21no—
270C22—2921no—
271C22—2921no—
272C22—2921no—
273C22—2921no—
274C22—2921no—
275C22—1462no—
276C22#1455656412yes—
277C22C2×D4×D7311yescharacteristic
278C4—42no—
279C4—42no—
280C4—2921no—
281C4—1462no—
282C4—1462no—
283C4—1462no—
284C4#1455656412yes—
285C4C2×D4×D7311yescharacteristic
286C4C2×#1192402811yescharacteristic
287C2—22no—
288C2—2922no—
289C2—5841no—
290C2C2×#1455656411yescharacteristic
291C2#1798939311yescharacteristic
292C2#1798940011yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#103×C73C2
socleC22×C73C22×D4
hypercenterC2×#103D73
hypocenterC73#3046
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C2×#14556622C2semidirect
3. #17989161C2semidirect
4. #17989068C2semidirect
5. #17988812C2semidirect
6. #17988805C2semidirect
7. #17988796C2semidirect
8. #17988791C2semidirect
9. #17988613C2semidirect
10. #17988586C2semidirect
11. C2×#103×C73C2semidirect
147. C73#3046semidirect
158. C2×#103D73semidirect