Finite Group Databasebeta

← #22621027

Subgroups — #22621027

Order 9344.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989208C211yesmaximal, characteristic, complemented
2#17989156C211yesmaximal, characteristic, complemented
3#17988976C211yesmaximal, characteristic, complemented
4#17988971C211yesmaximal, characteristic, complemented
5#17988947C211yesmaximal, characteristic, complemented
6#17988934C211yesmaximal, characteristic, complemented
7#17988810C211yesmaximal, characteristic, complemented
8#17988803C211yesmaximal, characteristic, complemented
9#17988788C211yesmaximal, characteristic, complemented
10#17988783C211yesmaximal, characteristic, complemented
11#17988751C211yesmaximal, characteristic, complemented
12#17988740C211yesmaximal, characteristic, complemented
13#17988734C211yesmaximal, characteristic, complemented
14#17988723C211yesmaximal, characteristic, complemented
15#433×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C22×D292C2211yescharacteristic
18C2×Dic292C2211yescharacteristic, complemented
19C2×#11924017C2211yescharacteristic
20C2×#11924017C2211yescharacteristic
21C2×#11924017C2211yescharacteristic, complemented
22C2×#11924017C2211yescharacteristic, complemented
23C2×D584C2211yescharacteristic
24C2×D584C2211yescharacteristic
25C2×D584C2211yescharacteristic, complemented
26#14556591C2211yescharacteristic, complemented
27#14556588C2211yescharacteristic
28#14556588C2211yescharacteristic
29#14556586—21no—
30#14556579C2211yescharacteristic
31#14556579C2211yescharacteristic
32#14556579C2211yescharacteristic, complemented
33#14556577—21no—
34#14556573—21no—
35#14556570C2211yescharacteristic
36#14556569—21no—
37#14556566—21no—
38#14556566—21no—
39#14556565C2211yescharacteristic
40#14556561—21no—
41#14556561—21no—
42C4×Dic146C2211yescharacteristic, complemented
43C4×D292C2211yescharacteristic, complemented
44#14556516C2211yescharacteristic, complemented
45#14556516C2211yescharacteristic, complemented
46#14556513C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556513C2211yescharacteristic
49#14556513C2211yescharacteristic
50#14556513C2211yescharacteristic, complemented
51#14556513C2211yescharacteristic, complemented
52#117×C73C2211yescharacteristic
53C4⋊C8×C73C2211yescharacteristic, complemented
54C4⋊C8×C73C2211yescharacteristic, complemented
55C22⋊C8×C73C2211yescharacteristic
56C22⋊C8×C73C2211yescharacteristic
57#97×C73C2211yescharacteristic, complemented
58C4×C8×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60#11924028—41no—
61#11924028—41no—
62C2×Dic146—21no—
63C2×Dic146C2311yescharacteristic
64C2×Dic146C2311yescharacteristic
65C2×D292—21no—
66C2×D292—21no—
67C2×D292—21no—
68C2×D292—21no—
69C2×D292—21no—
70C2×D292—41no—
71C2×D292—41no—
72C2×D292C2311yescharacteristic
73C2×D292C2311yescharacteristic
74C2×D292C2311yescharacteristic
75C2×D292C2311yescharacteristic
76C2×C22⋊D73—21no—
77C2×C22⋊D73—21no—
78C2×C4×D73—21no—
79C2×C4×D73—21no—
80Dic292—41no—
81#11924017—41no—
82#11924017—41no—
83#11924017—41no—
84#11924017—41no—
85D584—41no—
86D584—41no—
87D584—41no—
88C4⋊Dic73—21no—
89C4⋊Dic73C2311yescharacteristic
90C4⋊Dic73C2311yescharacteristic
91#11924007—21no—
92#11924007—21no—
93C22⋊Dic73—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005—21no—
97#11924005—21no—
98#11924005—21no—
99#11924005—21no—
100#11924005—21no—
101#11924005—21no—
102C4×Dic73—21no—
103C22×C4×C73C2311yescharacteristic
104C2×C8×C73C2311yescharacteristic
105C2×C8×C73C2311yescharacteristic
106C2×C8×C73C2311yescharacteristic
107C2×C8×C73C2311yescharacteristic
108C4⋊C4×C73D411yescharacteristic
109C4⋊C4×C73D411yescharacteristic
110C22⋊C4×C73D411yescharacteristic
111C22⋊C4×C73D411yescharacteristic
112C42×C73C2311yescharacteristic
113C42×C73C2311yescharacteristic
114C23×C73C2×D411yescharacteristic
115C22×D73—21no—
116C22×D73—21no—
117C22×D73—21no—
118C22×D73—21no—
119C22×D73—42no—
120C22×D73—81no—
121C22×D73—81no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73C2×D411yescharacteristic
125C2×C4×C73C2×D411yescharacteristic
126C2×C4×C73C2×D411yescharacteristic
127C2×C4×C73C2×D411yescharacteristic
128C2×C4×C73C2×D411yescharacteristic
129C2×C4×C73C2411yescharacteristic
130C22⋊D73—42no—
131C22⋊D73—81no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136D292—21no—
137D292—21no—
138D292—21no—
139D292—21no—
140D292—21no—
141D292—21no—
142D292—21no—
143D292—21no—
144D292—42no—
145D292—81no—
146D292—81no—
147D292—81no—
148D292—81no—
149C4×D73—42no—
150C4×D73—81no—
151Dic146—21no—
152Dic146—21no—
153Dic146—21no—
154Dic146—21no—
155Dic146—81no—
156C8×C73—21no—
157C8×C73—21no—
158C8×C73—21no—
159C8×C73—21no—
160C22×C73—21no—
161C22×C73—21no—
162C22×C73—21no—
163C22×C73C22×D411yescharacteristic
164C2×D73—41no—
165C2×D73—41no—
166C2×D73—41no—
167C2×D73—41no—
168C2×D73—41no—
169C2×D73—41no—
170C2×D73—41no—
171C2×D73—41no—
172C2×D73—41no—
173C2×D73—41no—
174C2×D73—41no—
175C2×D73—41no—
176C2×D73—84no—
177C4×C73—21no—
178C4×C73—21no—
179C4×C73—21no—
180C4×C73—21no—
181C4×C73—21no—
182C4×C73H(5,𝔽2)11yescharacteristic
183C4×C73H(5,𝔽2)11yescharacteristic
184Dic73—41no—
185Dic73—41no—
186Dic73—41no—
187Dic73—41no—
188C2×C73—41no—
189C2×C73#53511yescharacteristic
190C2×C73#57611yescharacteristic
191C2×C73#57711yescharacteristic
192D73—81no—
193D73—81no—
194D73—81no—
195D73—81no—
196#3224—731nomaximal, Sylow
197C73#322411yescharacteristic, complemented, Sylow
198#542—731no—
199#535—731no—
200#496—731no—
201#495—731no—
202#489—731no—
203#486—731no—
204#464—731no—
205#463—731no—
206#460—731no—
207#459—731no—
208#452—731no—
209#450—731no—
210#449—731no—
211#447—731no—
212#433D7311yescharacteristic, complemented
213C2×#41—731no—
214C22×D4—731no—
215C2×Q16—731no—
216C2×SD16—731no—
217C2×SD16—731no—
218C2×SD16—731no—
219C2×SD16—731no—
220C2×D8—731no—
221C2×D8—731no—
222C2×D8—731no—
223C4⋊Q8—731no—
224#127—731no—
225#127—731no—
226#126—1461no—
227#124—731no—
228#124—731no—
229#124—731no—
230#124—1461no—
231#123—1461no—
232C22⋊Q8—731no—
233C22⋊Q8—1461no—
234#121—731no—
235#121—1461no—
236#121—1461no—
237#120—1461no—
238#120—1461no—
239C4×Q8—731no—
240C4×D4—731no—
241#117C2×D7311yescharacteristic
242C4⋊C8C2×D7311yescharacteristic, complemented
243C4⋊C8C2×D7311yescharacteristic, complemented
244#103—731no—
245#103—731no—
246#102—731no—
247#102—731no—
248#102—731no—
249#102—731no—
250#102—731no—
251#102—731no—
252C22⋊C8C2×D7311yescharacteristic
253C22⋊C8C2×D7311yescharacteristic
254#97C2×D7311yescharacteristic, complemented
255C4×C8C2×D7311yescharacteristic, complemented
256C24—1461no—
257#41—2921no—
258#41—2921no—
259C2×Q8—731no—
260C2×Q8—731no—
261C2×Q8—1461no—
262C2×D4—2921no—
263C2×D4—2921no—
264C2×D4—731no—
265C2×D4—731no—
266C2×D4—731no—
267C2×D4—731no—
268C2×D4—1461no—
269C2×D4—1461no—
270C2×D4—1461no—
271C2×D4—1461no—
272C2×D4—1461no—
273C2×D4—1461no—
274C2×D4—1461no—
275C22×C4—1461no—
276C22×C4—1461no—
277C22×C4C22×D7311yescharacteristic
278Q16—2921no—
279SD16—2921no—
280SD16—2921no—
281SD16—2921no—
282SD16—2921no—
283D8—2921no—
284D8—2921no—
285D8—2921no—
286C2×C8C22×D7311yescharacteristic
287C2×C8C22×D7311yescharacteristic
288C2×C8C22×D7311yescharacteristic
289C2×C8C22×D7311yescharacteristic
290C4⋊C4—731no—
291C4⋊C4—731no—
292C4⋊C4—1461no—
293C4⋊C4—1461no—
294C4⋊C4—1461no—
295C4⋊C4D29211yescharacteristic
296C4⋊C4D29211yescharacteristic
297C22⋊C4—1461no—
298C22⋊C4—1461no—
299C22⋊C4—1461no—
300C22⋊C4—1461no—
301C22⋊C4—1461no—
302C22⋊C4—1461no—
303C22⋊C4—1461no—
304C22⋊C4—1461no—
305C22⋊C4—1461no—
306C22⋊C4D29211yescharacteristic
307C22⋊C4D29211yescharacteristic
308C42—1461no—
309C42C22×D7311yescharacteristic
310C42C22×D7311yescharacteristic
311C23—2922no—
312C23—5841no—
313C23—5841no—
314C23—1461no—
315C23—1461no—
316C23—1461no—
317C23—1461no—
318C23C2×D29211yescharacteristic
319Q8—5841no—
320Q8—1461no—
321Q8—1461no—
322Q8—1461no—
323Q8—1461no—
324D4—2922no—
325D4—2922no—
326D4—5841no—
327D4—5841no—
328D4—5841no—
329D4—5841no—
330D4—5841no—
331D4—1461no—
332D4—1461no—
333D4—1461no—
334D4—1461no—
335D4—1461no—
336D4—1461no—
337D4—1461no—
338D4—1461no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—2922no—
342C2×C4—5841no—
343C2×C4—1461no—
344C2×C4—1461no—
345C2×C4—1461no—
346C2×C4—1461no—
347C2×C4C2×D29211yescharacteristic
348C2×C4C2×D29211yescharacteristic
349C2×C4C2×D29211yescharacteristic
350C2×C4C2×D29211yescharacteristic
351C2×C4C2×D29211yescharacteristic
352C2×C4C23×D7311yescharacteristic
353C8—21no—
354C8—21no—
355C8—21no—
356C8—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—2921no—
361C22—2921no—
362C22—2921no—
363C22—2921no—
364C22—2921no—
365C22—2921no—
366C22—2921no—
367C22—2921no—
368C22—2921no—
369C22—2921no—
370C22—2921no—
371C22—2921no—
372C22—5844no—
373C22C22×D29211yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—2921no—
380C4—2921no—
381C4—2921no—
382C4—2921no—
383C4#1455663711yescharacteristic
384C4#1455663711yescharacteristic
385C2—41no—
386C2—5841no—
387C2—5841no—
388C2—5841no—
389C2—5841no—
390C2#1798915611yescharacteristic
391C2#1798939211yescharacteristic
392C2#1798939911yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#433×C73C2
socleC22×C73C22×D4
hypercenter#433D73
hypocenterC73#3224
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #17989208C2semidirect
2. #17989156C2semidirect
3. #17988976C2semidirect
4. #17988971C2semidirect
5. #17988947C2semidirect
6. #17988934C2semidirect
7. #17988810C2semidirect
8. #17988803C2semidirect
9. #17988788C2semidirect
10. #17988783C2semidirect
11. #17988751C2semidirect
12. #17988740C2semidirect
13. #17988734C2semidirect
14. #17988723C2semidirect
15. #433×C73C2semidirect
18. C2×Dic292C22semidirect
21. C2×#11924017C22semidirect
22. C2×#11924017C22semidirect
25. C2×D584C22semidirect
26. #14556591C22semidirect
32. #14556579C22semidirect
42. C4×Dic146C22semidirect
43. C4×D292C22semidirect
44. #14556516C22semidirect
45. #14556516C22semidirect
50. #14556513C22semidirect
51. #14556513C22semidirect
53. C4⋊C8×C73C22semidirect
54. C4⋊C8×C73C22semidirect
57. #97×C73C22semidirect
58. C4×C8×C73C22semidirect
197. C73#3224semidirect
212. #433D73semidirect
242. C4⋊C8C2×D73semidirect
243. C4⋊C8C2×D73semidirect
254. #97C2×D73semidirect
255. C4×C8C2×D73semidirect