Finite Group Databasebeta

← #21456915

Subgroups — #21456915

Order 7808.

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#16840383C211yesmaximal, characteristic, complemented
2#16840331C211yesmaximal, characteristic, complemented
3#16840151C211yesmaximal, characteristic, complemented
4#16840146C211yesmaximal, characteristic, complemented
5#16840122C211yesmaximal, characteristic, complemented
6#16840109C211yesmaximal, characteristic, complemented
7#16839985C211yesmaximal, characteristic, complemented
8#16839978C211yesmaximal, characteristic, complemented
9#16839963C211yesmaximal, characteristic, complemented
10#16839958C211yesmaximal, characteristic, complemented
11#16839926C211yesmaximal, characteristic, complemented
12#16839915C211yesmaximal, characteristic, complemented
13#16839909C211yesmaximal, characteristic, complemented
14#16839898C211yesmaximal, characteristic, complemented
15C61×#433C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C2×Dic244C2211yescharacteristic, complemented
19C2×#11758190C2211yescharacteristic
20C2×#11758190C2211yescharacteristic
21C2×#11758190C2211yescharacteristic, complemented
22C2×#11758190C2211yescharacteristic, complemented
23C2×D488C2211yescharacteristic
24C2×D488C2211yescharacteristic
25C2×D488C2211yescharacteristic, complemented
26#14519777C2211yescharacteristic, complemented
27#14519774C2211yescharacteristic
28#14519774C2211yescharacteristic
29#14519772—21no—
30#14519765C2211yescharacteristic
31#14519765C2211yescharacteristic
32#14519765C2211yescharacteristic, complemented
33#14519763—21no—
34#14519759—21no—
35#14519756C2211yescharacteristic
36#14519755—21no—
37#14519752—21no—
38#14519752—21no—
39#14519751C2211yescharacteristic
40#14519747—21no—
41#14519747—21no—
42C4×Dic122C2211yescharacteristic, complemented
43C4×D244C2211yescharacteristic, complemented
44#14519702C2211yescharacteristic, complemented
45#14519702C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519699C2211yescharacteristic
50#14519699C2211yescharacteristic, complemented
51#14519699C2211yescharacteristic, complemented
52#117×C61C2211yescharacteristic
53C4⋊C8×C61C2211yescharacteristic, complemented
54C4⋊C8×C61C2211yescharacteristic, complemented
55C22⋊C8×C61C2211yescharacteristic
56C22⋊C8×C61C2211yescharacteristic
57#97×C61C2211yescharacteristic, complemented
58C4×C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C22×C4×C61C2311yescharacteristic
61C2×C22⋊D61—21no—
62C2×C22⋊D61—21no—
63#11758222—41no—
64#11758222—41no—
65C2×D244—21no—
66C2×D244—21no—
67C2×D244—21no—
68C2×D244—21no—
69C2×D244—21no—
70C2×D244—41no—
71C2×D244—41no—
72C2×D244C2311yescharacteristic
73C2×D244C2311yescharacteristic
74C2×D244C2311yescharacteristic
75C2×D244C2311yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×Dic122—21no—
79C2×Dic122C2311yescharacteristic
80C2×Dic122C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C2×C8×C61C2311yescharacteristic
84C2×C8×C61C2311yescharacteristic
85C4⋊C4×C61D411yescharacteristic
86C4⋊C4×C61D411yescharacteristic
87C22⋊C4×C61D411yescharacteristic
88C22⋊C4×C61D411yescharacteristic
89C42×C61C2311yescharacteristic
90C42×C61C2311yescharacteristic
91C22⋊Dic61—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196—21no—
105C4×Dic61—21no—
106Dic244—41no—
107D488—41no—
108D488—41no—
109D488—41no—
110#11758190—41no—
111#11758190—41no—
112#11758190—41no—
113#11758190—41no—
114C23×C61C2×D411yescharacteristic
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—42no—
120C22×D61—81no—
121C22×D61—81no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C22⋊D61—42no—
131C22⋊D61—81no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136D244—21no—
137D244—21no—
138D244—21no—
139D244—21no—
140D244—21no—
141D244—21no—
142D244—21no—
143D244—21no—
144D244—42no—
145D244—81no—
146D244—81no—
147D244—81no—
148D244—81no—
149C4×D61—42no—
150C4×D61—81no—
151Dic122—21no—
152Dic122—21no—
153Dic122—21no—
154Dic122—21no—
155Dic122—81no—
156C8×C61—21no—
157C8×C61—21no—
158C8×C61—21no—
159C8×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61C22×D411yescharacteristic
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—84no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61H(5,𝔽2)11yescharacteristic
183C4×C61H(5,𝔽2)11yescharacteristic
184Dic61—41no—
185Dic61—41no—
186Dic61—41no—
187Dic61—41no—
188#3224—611nomaximal, Sylow
189C2×C61—41no—
190C2×C61#53511yescharacteristic
191C2×C61#57611yescharacteristic
192C2×C61#57711yescharacteristic
193D61—81no—
194D61—81no—
195D61—81no—
196D61—81no—
197#542—611no—
198#535—611no—
199#496—611no—
200#495—611no—
201#489—611no—
202#486—611no—
203#464—611no—
204#463—611no—
205#460—611no—
206#459—611no—
207#452—611no—
208#450—611no—
209#449—611no—
210#447—611no—
211#433D6111yescharacteristic, complemented
212C61#322411yescharacteristic, complemented, Sylow
213C2×#41—611no—
214C22×D4—611no—
215C2×Q16—611no—
216C2×SD16—611no—
217C2×SD16—611no—
218C2×SD16—611no—
219C2×SD16—611no—
220C2×D8—611no—
221C2×D8—611no—
222C2×D8—611no—
223C4⋊Q8—611no—
224#127—611no—
225#127—611no—
226#126—1221no—
227#124—611no—
228#124—611no—
229#124—611no—
230#124—1221no—
231#123—1221no—
232C22⋊Q8—611no—
233C22⋊Q8—1221no—
234#121—611no—
235#121—1221no—
236#121—1221no—
237#120—1221no—
238#120—1221no—
239C4×Q8—611no—
240C4×D4—611no—
241#117C2×D6111yescharacteristic
242C4⋊C8C2×D6111yescharacteristic, complemented
243C4⋊C8C2×D6111yescharacteristic, complemented
244#103—611no—
245#103—611no—
246#102—611no—
247#102—611no—
248#102—611no—
249#102—611no—
250#102—611no—
251#102—611no—
252C22⋊C8C2×D6111yescharacteristic
253C22⋊C8C2×D6111yescharacteristic
254#97C2×D6111yescharacteristic, complemented
255C4×C8C2×D6111yescharacteristic, complemented
256C24—1221no—
257#41—2441no—
258#41—2441no—
259C2×Q8—611no—
260C2×Q8—611no—
261C2×Q8—1221no—
262C2×D4—611no—
263C2×D4—611no—
264C2×D4—611no—
265C2×D4—611no—
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—2441no—
274C2×D4—2441no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4C22×D6111yescharacteristic
278Q16—2441no—
279SD16—2441no—
280SD16—2441no—
281SD16—2441no—
282SD16—2441no—
283D8—2441no—
284D8—2441no—
285D8—2441no—
286C2×C8C22×D6111yescharacteristic
287C2×C8C22×D6111yescharacteristic
288C2×C8C22×D6111yescharacteristic
289C2×C8C22×D6111yescharacteristic
290C4⋊C4—611no—
291C4⋊C4—611no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4D24411yescharacteristic
296C4⋊C4D24411yescharacteristic
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C22⋊C4D24411yescharacteristic
307C22⋊C4D24411yescharacteristic
308C42—1221no—
309C42C22×D6111yescharacteristic
310C42C22×D6111yescharacteristic
311C23—1221no—
312C23—1221no—
313C23—1221no—
314C23—1221no—
315C23—4881no—
316C23—4881no—
317C23—2442no—
318C23C2×D24411yescharacteristic
319Q8—1221no—
320Q8—1221no—
321Q8—1221no—
322Q8—1221no—
323Q8—4881no—
324D4—1221no—
325D4—1221no—
326D4—1221no—
327D4—1221no—
328D4—1221no—
329D4—1221no—
330D4—1221no—
331D4—1221no—
332D4—4881no—
333D4—4881no—
334D4—4881no—
335D4—4881no—
336D4—4881no—
337D4—2442no—
338D4—2442no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—4881no—
346C2×C4—2442no—
347C2×C4C2×D24411yescharacteristic
348C2×C4C2×D24411yescharacteristic
349C2×C4C2×D24411yescharacteristic
350C2×C4C2×D24411yescharacteristic
351C2×C4C2×D24411yescharacteristic
352C2×C4C23×D6111yescharacteristic
353C8—21no—
354C8—21no—
355C8—21no—
356C8—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—4884no—
361C22—2441no—
362C22—2441no—
363C22—2441no—
364C22—2441no—
365C22—2441no—
366C22—2441no—
367C22—2441no—
368C22—2441no—
369C22—2441no—
370C22—2441no—
371C22—2441no—
372C22—2441no—
373C22C22×D24411yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—2441no—
380C4—2441no—
381C4—2441no—
382C4—2441no—
383C4#1451982311yescharacteristic
384C4#1451982311yescharacteristic
385C2—41no—
386C2—4881no—
387C2—4881no—
388C2—4881no—
389C2—4881no—
390C2#1684033111yescharacteristic
391C2#1684056711yescharacteristic
392C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#433C2
socleC22×C61C22×D4
hypercenter#433D61
hypocenterC61#3224
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #16840383C2semidirect
2. #16840331C2semidirect
3. #16840151C2semidirect
4. #16840146C2semidirect
5. #16840122C2semidirect
6. #16840109C2semidirect
7. #16839985C2semidirect
8. #16839978C2semidirect
9. #16839963C2semidirect
10. #16839958C2semidirect
11. #16839926C2semidirect
12. #16839915C2semidirect
13. #16839909C2semidirect
14. #16839898C2semidirect
15. C61×#433C2semidirect
18. C2×Dic244C22semidirect
21. C2×#11758190C22semidirect
22. C2×#11758190C22semidirect
25. C2×D488C22semidirect
26. #14519777C22semidirect
32. #14519765C22semidirect
42. C4×Dic122C22semidirect
43. C4×D244C22semidirect
44. #14519702C22semidirect
45. #14519702C22semidirect
50. #14519699C22semidirect
51. #14519699C22semidirect
53. C4⋊C8×C61C22semidirect
54. C4⋊C8×C61C22semidirect
57. #97×C61C22semidirect
58. C4×C8×C61C22semidirect
211. #433D61semidirect
212. C61#3224semidirect
242. C4⋊C8C2×D61semidirect
243. C4⋊C8C2×D61semidirect
254. #97C2×D61semidirect
255. C4×C8C2×D61semidirect