Finite Group Databasebeta

← #22618809

Subgroups — #22618809

Order 9344.

484 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556612C211yesmaximal, characteristic
2#17989069C211yesmaximal, characteristic, complemented
3#17989066C211yesmaximal, characteristic, complemented
4#17988697C211yesmaximal, characteristic, complemented
5#17988696C211yesmaximal, characteristic, complemented
6#17988692C211yesmaximal, characteristic, complemented
7#17988691C211yesmaximal, characteristic, complemented
8C4×#11924017C211yesmaximal, characteristic, complemented
9SD16×Dic73C211yesmaximal, characteristic, complemented
10#17988674C211yesmaximal, characteristic, complemented
11#106×D73C211yesmaximal, characteristic, complemented
12#17988587C211yesmaximal, characteristic, complemented
13#17988585C211yesmaximal, characteristic, complemented
14#17988541C211yesmaximal, characteristic, complemented
15C4×SD16×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×#11924027C2211yescharacteristic
18#14556612C418yescomplemented
19C2×#11924018C2211yescharacteristic
20C2×#11924017C2211yescharacteristic
21C2×#11924013C2211yescharacteristic
22C2×#11924011C2211yescharacteristic
23C2×C8×D73C2211yescharacteristic
24Q8×Dic73C2211yescharacteristic
25C4×Dic146C2211yescharacteristic
26#14556556C2211yescharacteristic
27C4×D292—21no—
28C4×D292C2211yescharacteristic
29D4×Dic73C2211yescharacteristic
30#14556553—21no—
31#14556553C2211yescharacteristic
32C4×C22⋊D73—21no—
33#14556551—21no—
34#14556548—21no—
35#14556548C2211yescharacteristic
36#14556547—21no—
37C2×#11924007—21no—
38C4⋊C4×D73—21no—
39C4⋊C4×D73C2211yescharacteristic
40C4⋊C4×D73C2211yescharacteristic
41#14556523C2211yescharacteristic
42#14556522C2211yescharacteristic
43#14556522C2211yescharacteristic
44#14556516C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556514C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556512C2211yescharacteristic
49#14556511C2211yescharacteristic
50#14556502C2211yescharacteristic
51#14556501C2211yescharacteristic
52C8×Dic73C2211yescharacteristic
53C2×SD16×C73C2211yescharacteristic
54C4×Q8×C73C2211yescharacteristic
55C4×D4×C73C2211yescharacteristic
56#106×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59C4×C8×C73C2211yescharacteristic
60#11924029—22no—
61#11924029C2×C414yescomplemented
62#11924027—22no—
63#11924027C2×C414yescomplemented
64C2×Dic146C2311yescharacteristic
65C2×D292—21no—
66C2×D292C2311yescharacteristic
67C2×C22⋊D73—21no—
68C22×Dic73—21no—
69C22×Dic73—21no—
70C2×C4×D73—21no—
71C2×C4×D73—21no—
72C2×C4×D73—21no—
73C2×C4×D73—21no—
74C2×C4×D73—21no—
75C2×C4×D73C2311yescharacteristic
76#11924018C2×C414yescomplemented
77#11924017C2×C414yescomplemented
78#11924013C2×C414yescomplemented
79#11924011—22no—
80C2×#10596831C2311yescharacteristic
81C2×#10596831C2311yescharacteristic
82C8×D73C2×C414yescomplemented
83C4⋊Dic73—21no—
84C4⋊Dic73C2311yescharacteristic
85C4⋊Dic73C2311yescharacteristic
86#11924007—21no—
87#11924007—21no—
88#11924007—21no—
89#11924007—21no—
90#11924007D411yescharacteristic
91#11924007D411yescharacteristic
92C22⋊Dic73—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005D411yescharacteristic
96#11924005D411yescharacteristic
97C4×Dic73—21no—
98C4×Dic73—21no—
99C4×Dic73—21no—
100C4×Dic73C2311yescharacteristic
101C2×Q8×C73C2311yescharacteristic
102C2×D4×C73C2311yescharacteristic
103C22×C4×C73—21no—
104SD16×C73C2×C414yescomplemented
105C2×C8×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C4⋊C4×C73—21no—
108C4⋊C4×C73C2311yescharacteristic
109C4⋊C4×C73C2311yescharacteristic
110C22⋊C4×C73—21no—
111C42×C73—21no—
112C42×C73C2311yescharacteristic
113C23×C73—21no—
114C22×D73—21no—
115C22×D73C2×D411yescharacteristic
116Q8×C73—21no—
117Q8×C73C22×C412yes—
118D4×C73—21no—
119D4×C73C22×C412yes—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—81no—
124C2×C4×C73C2×D411yescharacteristic
125C2×C4×C73C2×D411yescharacteristic
126C2×C4×C73C2411yescharacteristic
127C22⋊D73—24no—
128C2×Dic73—21no—
129C2×Dic73—24no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—81no—
133C2×Dic73C2×D411yescharacteristic
134C2×Dic73C2×D411yescharacteristic
135C2×Dic73C2×D411yescharacteristic
136D292—24no—
137D292—21no—
138D292C22×C412yes—
139C4×D73—24no—
140C4×D73—81no—
141C4×D73—81no—
142C4×D73—81no—
143C4×D73—81no—
144C4×D73C22×C412yes—
145C4×D73#4112yes—
146Dic146—21no—
147Dic146C22×C412yes—
148C8×C73—21no—
149C8×C73C22×C412yes—
150#10596831—21no—
151#10596831C22×C412yes—
152C22×C73—22no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73C22×D411yescharacteristic
156C2×D73—21no—
157C2×D73—21no—
158C2×D73—22no—
159C2×D73—41no—
160C2×D73—41no—
161C2×D73C4×D412yes—
162C4×C73—22no—
163C4×C73—21no—
164C4×C73—21no—
165C4×C73—41no—
166C4×C73—41no—
167C4×C73C23×C411yescharacteristic
168C4×C73C2×#4111yescharacteristic
169Dic73—22no—
170Dic73—21no—
171Dic73—21no—
172Dic73—41no—
173Dic73—41no—
174Dic73C4×D412yes—
175C2×C73—42no—
176C2×C73C2×C4×D411yescharacteristic
177C2×C73#57711yescharacteristic
178C2×C73#57711yescharacteristic
179D73—22no—
180D73—42no—
181#2952—731nomaximal, Sylow
182C73#295211yescharacteristic, complemented, Sylow
183C2×#135—731no—
184#520—731no—
185#520—731no—
186#442—731no—
187#442—731no—
188#441—731no—
189#441—731no—
190C4×SD16—731no—
191C4×SD16—731no—
192C4×SD16—731no—
193C4×SD16D7311yescharacteristic, complemented
194C2×#106—731no—
195#417—731no—
196#417—731no—
197#405—731no—
198C2×#41—731no—
199C2×#41—731no—
200#135—738no—
201C2×Q16—731no—
202C2×SD16—731no—
203C2×SD16C2×D7311yescharacteristic
204C2×D8—731no—
205C2×M16—731no—
206C22×C8—731no—
207C4×Q8—731no—
208C4×Q8—731no—
209C4×Q8—731no—
210C4×Q8C2×D7311yescharacteristic
211C4×D4—731no—
212C4×D4—731no—
213C4×D4—731no—
214C4×D4—1461no—
215C4×D4—1461no—
216C4×D4—1461no—
217C4×D4—1461no—
218C4×D4C2×D7311yescharacteristic
219#117—731no—
220#117—1461no—
221#117—1461no—
222C2×C4⋊C4—731no—
223C2×C4⋊C4—731no—
224C2×C4⋊C4—1461no—
225C2×C4⋊C4—1461no—
226#106—731no—
227#106—731no—
228#106—731no—
229#106C2×D7311yescharacteristic
230#103—731no—
231#103—731no—
232#103—731no—
233#103C2×D7311yescharacteristic
234#102—731no—
235#102—731no—
236#102—731no—
237#102C2×D7311yescharacteristic
238#97—731no—
239#97—731no—
240C4×C8—731no—
241C4×C8C2×D7311yescharacteristic
242#41—734no—
243#41—734no—
244#41—1462no—
245#41—1462no—
246C2×Q8—731no—
247C2×Q8C22×D7311yescharacteristic
248C2×D4—731no—
249C2×D4—1461no—
250C2×D4—1461no—
251C2×D4C22×D7311yescharacteristic
252C22×C4—21no—
253C22×C4—731no—
254C22×C4—1461no—
255C22×C4—1461no—
256C22×C4—1461no—
257C22×C4—1461no—
258C22×C4—1461no—
259C22×C4—1461no—
260C22×C4—1461no—
261Q16—734no—
262SD16—734no—
263SD16C4×D7314yescomplemented
264D8—734no—
265M16—1462no—
266C2×C8—731no—
267C2×C8—734no—
268C2×C8—731no—
269C2×C8C22×D7311yescharacteristic
270C2×C8C22×D7311yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—731no—
273C4⋊C4—731no—
274C4⋊C4—731no—
275C4⋊C4—731no—
276C4⋊C4—1461no—
277C4⋊C4—1461no—
278C4⋊C4—1461no—
279C4⋊C4—1461no—
280C4⋊C4—1461no—
281C4⋊C4C22×D7311yescharacteristic
282C4⋊C4C22×D7311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—731no—
285C22⋊C4—731no—
286C22⋊C4—1461no—
287C22⋊C4—1461no—
288C22⋊C4—1461no—
289C42—21no—
290C42—731no—
291C42—1461no—
292C42—1461no—
293C42—1461no—
294C42C22×D7311yescharacteristic
295C23—21no—
296C23—731no—
297C23—1461no—
298Q8—21no—
299Q8—732no—
300Q8—1461no—
301Q8C2×C4×D7312yes—
302D4—21no—
303D4—732no—
304D4—1464no—
305D4—1464no—
306D4—1461no—
307D4C2×C4×D7312yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—5841no—
313C2×C4—5841no—
314C2×C4—5841no—
315C2×C4—5841no—
316C2×C4—5841no—
317C2×C4—731no—
318C2×C4—732no—
319C2×C4—732no—
320C2×C4—731no—
321C2×C4—731no—
322C2×C4—1464no—
323C2×C4—1461no—
324C2×C4—1461no—
325C2×C4—1464no—
326C2×C4—1461no—
327C2×C4D4×D7311yescharacteristic
328C2×C4D4×D7311yescharacteristic
329C2×C4C23×D7311yescharacteristic
330C8—21no—
331C8—732no—
332C8—1461no—
333C8C2×C4×D7312yes—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—2921no—
338C22—2921no—
339C22—732no—
340C22—1462no—
341C22—1461no—
342C22—1461no—
343C22C2×D4×D7311yescharacteristic
344C4—21no—
345C4—21no—
346C4—22no—
347C4—41no—
348C4—41no—
349C4—2921no—
350C4—2921no—
351C4—732no—
352C4—1461no—
353C4—1461no—
354C4—1462no—
355C4C22×C4×D7311yescharacteristic
356C4#41×D7311yescharacteristic
357C2—42no—
358C2—2922no—
359C2—1462no—
360C2C4×D4×D7311yescharacteristic
361C2#1798939311yescharacteristic
362C2#1798939411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC4×C73C23×C4
FrattiniC2×C4C23×D73
FittingC4×SD16×C73C2
socleC22×C73C22×D4
hypercenterC4×SD16D73
hypocenterC73#2952
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #17989069C2semidirect
3. #17989066C2semidirect
4. #17988697C2semidirect
5. #17988696C2semidirect
6. #17988692C2semidirect
7. #17988691C2semidirect
8. C4×#11924017C2semidirect
9. SD16×Dic73C2semidirect
10. #17988674C2semidirect
11. #106×D73C2semidirect
12. #17988587C2semidirect
13. #17988585C2semidirect
14. #17988541C2semidirect
15. C4×SD16×C73C2semidirect
18. #14556612C4semidirect
61. #11924029C2×C4semidirect
63. #11924027C2×C4semidirect
76. #11924018C2×C4semidirect
77. #11924017C2×C4semidirect
78. #11924013C2×C4semidirect
82. C8×D73C2×C4semidirect
104. SD16×C73C2×C4semidirect
182. C73#2952semidirect
193. C4×SD16D73semidirect
263. SD16C4×D73semidirect