Finite Group Databasebeta

← #22621505

Subgroups — #22621505

Order 9344.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556623C211yesmaximal, characteristic, complemented
2C22×#11924018C211yesmaximal, characteristic, complemented
3#17989250C211yesmaximal, characteristic, complemented
4#17989248C211yesmaximal, characteristic
5#17988980C211yesmaximal, characteristic, complemented
6#17988844C211yesmaximal, characteristic, complemented
7#17988818C211yesmaximal, characteristic, complemented
8#17988812C211yesmaximal, characteristic, complemented
9#17988795C211yesmaximal, characteristic, complemented
10#17988752C211yesmaximal, characteristic, complemented
11#17988741C211yesmaximal, characteristic, complemented
12#17988728C211yesmaximal, characteristic, complemented
13#17988691C211yesmaximal, characteristic, complemented
14#17988655C211yesmaximal, characteristic, complemented
15#451×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C22×Dic146C2211yescharacteristic
18C2×Q8×D73C2211yescharacteristic
19#14556623—24no—
20C2×#11924018—24no—
21C2×#11924018C2211yescharacteristic
22C2×#11924018C2211yescharacteristic
23C2×#11924018C2211yescharacteristic
24C2×#11924018C2211yescharacteristic
25C2×#11924017C2211yescharacteristic
26C2×#11924017C2211yescharacteristic
27C2×#11924015C2211yescharacteristic
28C2×#11924011C2211yescharacteristic
29C22×#10596831C2211yescharacteristic
30#14556590—21no—
31#14556589C2211yescharacteristic
32#14556580—21no—
33#14556580C2211yescharacteristic
34#14556571C2211yescharacteristic
35#14556569—21no—
36#14556568—21no—
37#14556567—21no—
38#14556567C2211yescharacteristic
39#14556565—21no—
40#14556565C2211yescharacteristic
41Q8×Dic73C2211yescharacteristic
42#14556556C2211yescharacteristic
43C4×C22⋊D73—21no—
44C4×C22⋊D73C2211yescharacteristic
45#14556551—21no—
46#14556522C2211yescharacteristic
47#14556520C2211yescharacteristic
48#14556516C2211yescharacteristic
49#14556516C2211yescharacteristic
50#14556515C2211yescharacteristic
51#14556511C2211yescharacteristic
52#14556503C2211yescharacteristic
53#14556501C2211yescharacteristic
54C22×Q8×C73C2211yescharacteristic
55C2×Q16×C73C2211yescharacteristic
56C2×Q16×C73C2211yescharacteristic
57C22⋊Q8×C73C2211yescharacteristic
58#103×C73C2211yescharacteristic
59#103×C73C2211yescharacteristic
60C22⋊C8×C73C2211yescharacteristic
61#11924029—22no—
62#11924029—41no—
63C2×Dic146—22no—
64C2×Dic146—21no—
65C2×Dic146—21no—
66C2×Dic146—41no—
67C2×Dic146C2311yescharacteristic
68C2×Dic146C2311yescharacteristic
69Q8×D73—22no—
70Q8×D73—41no—
71C2×D292—21no—
72C2×D292C2311yescharacteristic
73C2×C22⋊D73—21no—
74C2×C22⋊D73D411yescharacteristic
75C22×Dic73—21no—
76C2×C4×D73—21no—
77C2×C4×D73—21no—
78C2×C4×D73C2311yescharacteristic
79#11924018—22no—
80#11924018—22no—
81#11924018—22no—
82#11924018D414yescomplemented
83#11924017—22no—
84#11924017—41no—
85#11924015—22no—
86#11924011—22no—
87C2×#10596831—22no—
88C2×#10596831C2311yescharacteristic
89C2×#10596831C2311yescharacteristic
90C4⋊Dic73—21no—
91C4⋊Dic73—21no—
92C4⋊Dic73C2311yescharacteristic
93#11924007—21no—
94#11924007—21no—
95#11924007—21no—
96#11924007—21no—
97#11924007D411yescharacteristic
98C22⋊Dic73D411yescharacteristic
99#11924005—21no—
100#11924005—21no—
101#11924005—21no—
102#11924005—21no—
103#11924005—21no—
104#11924005D411yescharacteristic
105C4×Dic73—21no—
106C4×Dic73—21no—
107C4×Dic73C2311yescharacteristic
108C2×Q8×C73—21no—
109C2×Q8×C73—22no—
110C2×Q8×C73—41no—
111C2×Q8×C73C2311yescharacteristic
112C2×Q8×C73C2311yescharacteristic
113C2×Q8×C73C2311yescharacteristic
114C22×C4×C73—21no—
115C22×C4×C73C2311yescharacteristic
116Q16×C73—22no—
117Q16×C73—41no—
118C2×C8×C73C2311yescharacteristic
119C2×C8×C73C2311yescharacteristic
120C4⋊C4×C73—21no—
121C4⋊C4×C73C2311yescharacteristic
122C22⋊C4×C73—21no—
123C23×C73C2×D411yescharacteristic
124C22×D73—21no—
125C22×D73C2×D411yescharacteristic
126Q8×C73—21no—
127Q8×C73—21no—
128Q8×C73—21no—
129Q8×C73—21no—
130Q8×C73—21no—
131Q8×C73—42no—
132Q8×C73C2×D412yes—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73—42no—
140C2×C4×C73C2×D411yescharacteristic
141C2×C4×C73C2411yescharacteristic
142C22⋊D73—22no—
143C22⋊D73—42no—
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73—21no—
147C2×Dic73—42no—
148C2×Dic73C2×D411yescharacteristic
149C2×Dic73C2×D411yescharacteristic
150C2×Dic73C2×D411yescharacteristic
151D292—21no—
152D292—21no—
153D292—42no—
154C4×D73—21no—
155C4×D73—21no—
156C4×D73—42no—
157C4×D73—42no—
158Dic146—21no—
159Dic146—21no—
160Dic146—21no—
161Dic146—42no—
162Dic146—42no—
163Dic146C2×D412yes—
164C8×C73—21no—
165C8×C73—21no—
166#10596831—21no—
167#10596831C2×D412yes—
168C22×C73—21no—
169C22×C73—21no—
170C22×C73#13712yescomplemented
171C22×C73C22×D411yescharacteristic
172C2×D73—21no—
173C2×D73—21no—
174C2×D73—21no—
175C2×D73—41no—
176C2×D73—41no—
177C2×D73—41no—
178C4×C73—21no—
179C4×C73—22no—
180C4×C73—41no—
181C4×C73—41no—
182C4×C73—41no—
183C4×C73C22×D411yescharacteristic
184C4×C73H(5,𝔽2)11yescharacteristic
185Dic73—22no—
186Dic73—21no—
187Dic73—21no—
188Dic73—21no—
189Dic73—41no—
190Dic73—41no—
191C2×C73—22no—
192C2×C73D4211yescharacteristic
193C2×C73C2×#13711yescharacteristic
194C2×C73#57811yescharacteristic
195D73—41no—
196D73—81no—
197#3270—731nomaximal, Sylow
198C73#327011yescharacteristic, complemented, Sylow
199C2×#137—731no—
200C22×Q16—731no—
201D4×Q8—731no—
202#548—731no—
203#497—731no—
204#470—731no—
205#465—731no—
206#464—731no—
207#462—731no—
208#452—731no—
209#451—731no—
210#451D7311yescharacteristic, complemented
211#448—731no—
212#441—731no—
213#435—731no—
214C2×#41—731no—
215C22×Q8—731no—
216C22×Q8—731no—
217C22×Q8C2×D7311yescharacteristic
218#137—1464no—
219C2×Q16—731no—
220C2×Q16—731no—
221C2×Q16—731no—
222C2×Q16—731no—
223C2×Q16—1464no—
224C2×Q16C2×D7311yescharacteristic
225C2×Q16C2×D7311yescharacteristic
226C2×SD16—731no—
227C2×SD16—731no—
228C2×SD16—731no—
229C2×M16—731no—
230C22×C8—731no—
231C4⋊Q8—731no—
232C4⋊Q8—1461no—
233#124—731no—
234#124—1461no—
235C22⋊Q8—731no—
236C22⋊Q8—731no—
237C22⋊Q8—1461no—
238C22⋊Q8—1461no—
239C22⋊Q8—1461no—
240C22⋊Q8C2×D7311yescharacteristic
241#121—731no—
242#121—1461no—
243C4×Q8—731no—
244C4×Q8—731no—
245C4×D4—731no—
246C4×D4—1461no—
247C4×D4—1461no—
248#106—731no—
249C4⋊C8—731no—
250#103—731no—
251#103—731no—
252#103—731no—
253#103C2×D7311yescharacteristic
254#103C2×D7311yescharacteristic
255#102—731no—
256C22⋊C8—731no—
257C22⋊C8C2×D7311yescharacteristic
258#97—731no—
259#41—2921no—
260#41—1462no—
261C2×Q8—21no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—2921no—
265C2×Q8—2921no—
266C2×Q8—731no—
267C2×Q8—731no—
268C2×Q8—1462no—
269C2×Q8—1461no—
270C2×Q8—1462no—
271C2×Q8—1461no—
272C2×Q8C22×D7311yescharacteristic
273C2×Q8C22×D7311yescharacteristic
274C2×Q8C22×D7311yescharacteristic
275C2×D4—731no—
276C2×D4—731no—
277C2×D4—1461no—
278C2×D4—1461no—
279C22×C4—21no—
280C22×C4—731no—
281C22×C4—1461no—
282C22×C4—1461no—
283C22×C4—1461no—
284C22×C4C22×D7311yescharacteristic
285Q16—22no—
286Q16—41no—
287Q16—734no—
288Q16—1462no—
289Q16—1462no—
290Q16—1462no—
291SD16—2921no—
292SD16—1462no—
293SD16—1462no—
294M16—1462no—
295C2×C8—731no—
296C2×C8—731no—
297C2×C8—1462no—
298C2×C8C22×D7311yescharacteristic
299C2×C8C22×D7311yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—731no—
302C4⋊C4—731no—
303C4⋊C4—1461no—
304C4⋊C4—1461no—
305C4⋊C4—1461no—
306C4⋊C4—1461no—
307C4⋊C4—1461no—
308C4⋊C4—1461no—
309C4⋊C4C22×D7311yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—731no—
312C22⋊C4—731no—
313C22⋊C4—1461no—
314C22⋊C4—1461no—
315C22⋊C4—1461no—
316C22⋊C4—1461no—
317C22⋊C4—1461no—
318C42—731no—
319C42—1461no—
320C42—1461no—
321C23—731no—
322C23—1461no—
323C23D4×D7311yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—42no—
330Q8—2922no—
331Q8—2922no—
332Q8—732no—
333Q8—1461no—
334Q8—1461no—
335Q8—1461no—
336Q8D4×D7312yes—
337D4—2922no—
338D4—2922no—
339D4—1462no—
340D4—1461no—
341D4—1461no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—2922no—
350C2×C4—2922no—
351C2×C4—2922no—
352C2×C4—731no—
353C2×C4—731no—
354C2×C4—731no—
355C2×C4—1461no—
356C2×C4—1461no—
357C2×C4—1461no—
358C2×C4—1461no—
359C2×C4—1461no—
360C2×C4D4×D7311yescharacteristic
361C2×C4C23×D7311yescharacteristic
362C8—21no—
363C8—21no—
364C8—732no—
365C8—1461no—
366C22—21no—
367C22—21no—
368C22—2921no—
369C22—2921no—
370C22—2921no—
371C22—1461no—
372C22—1461no—
373C22—1461no—
374C22#1455662312yescomplemented
375C22C2×D4×D7311yescharacteristic
376C4—21no—
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—2921no—
382C4—2921no—
383C4—1461no—
384C4—1461no—
385C4—1461no—
386C4—1462no—
387C4C2×D4×D7311yescharacteristic
388C4#1455663611yescharacteristic
389C2—22no—
390C2—2921no—
391C2—5841no—
392C2#1798921911yescharacteristic
393C2C2×#1455662311yescharacteristic
394C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#451×C73C2
socleC22×C73C22×D4
hypercenter#451D73
hypocenterC73#3270
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C2×#14556623C2semidirect
2. C22×#11924018C2semidirect
3. #17989250C2semidirect
5. #17988980C2semidirect
6. #17988844C2semidirect
7. #17988818C2semidirect
8. #17988812C2semidirect
9. #17988795C2semidirect
10. #17988752C2semidirect
11. #17988741C2semidirect
12. #17988728C2semidirect
13. #17988691C2semidirect
14. #17988655C2semidirect
15. #451×C73C2semidirect
82. #11924018D4semidirect
170. C22×C73#137semidirect
198. C73#3270semidirect
210. #451D73semidirect
374. C22#14556623semidirect