Finite Group Databasebeta

← #21456914

Subgroups — #21456914

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#16840386C211yesmaximal, characteristic, complemented
2#16840330C211yesmaximal, characteristic, complemented
3#16840151C211yesmaximal, characteristic, complemented
4#16840144C211yesmaximal, characteristic, complemented
5#16840110C211yesmaximal, characteristic, complemented
6#16839987C211yesmaximal, characteristic, complemented
7#16839980C211yesmaximal, characteristic, complemented
8#16839961C211yesmaximal, characteristic, complemented
9#16839956C211yesmaximal, characteristic, complemented
10#16839927C211yesmaximal, characteristic, complemented
11#16839914C211yesmaximal, characteristic, complemented
12#16839910C211yesmaximal, characteristic, complemented
13#16839897C211yesmaximal, characteristic, complemented
14#16839824C211yesmaximal, characteristic, complemented
15C61×#489C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C2×#11758202C2211yescharacteristic, complemented
19C2×#11758190C2211yescharacteristic
20C2×#11758190C2211yescharacteristic, complemented
21C2×#11758200C2211yescharacteristic
22C2×#11758201C2211yescharacteristic, complemented
23C2×D488C2211yescharacteristic
24C2×D488C2211yescharacteristic, complemented
25C2×#11758199C2211yescharacteristic
26#14519774C2211yescharacteristic
27#14519773C2211yescharacteristic
28#14519772—21no—
29#14519766—21no—
30#14519766C2211yescharacteristic
31#14519765C2211yescharacteristic, complemented
32#14519762—21no—
33#14519757C2211yescharacteristic
34#14519753—21no—
35#14519752C2211yescharacteristic
36#14519750—21no—
37#14519750—21no—
38#14519747—21no—
39#14519747—21no—
40#14519742C2211yescharacteristic, complemented
41#14519739C2211yescharacteristic, complemented
42#14519734C2211yescharacteristic
43#14519706C2211yescharacteristic, complemented
44#14519706C2211yescharacteristic, complemented
45#14519697C2211yescharacteristic
46#14519697C2211yescharacteristic
47#14519697C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic, complemented
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51C4×#92418C2211yescharacteristic, complemented
52C4⋊Q8×C61C2211yescharacteristic, complemented
53#124×C61C2211yescharacteristic
54#103×C61C2211yescharacteristic, complemented
55#103×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×Q8×C61—21no—
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66#11758226—41no—
67#11758226—41no—
68D4×D61—41no—
69D4×D61—41no—
70C2×D244—21no—
71C2×D244—21no—
72C2×D244—21no—
73C2×D244—21no—
74C2×D244C2311yescharacteristic
75C2×D244C2311yescharacteristic
76C2×D244C2311yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61C2311yescharacteristic
80C2×Dic122C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C4⋊C4×C61—21no—
84C4⋊C4×C61C2311yescharacteristic
85C4⋊C4×C61C2311yescharacteristic
86C22⋊C4×C61—21no—
87C22⋊C4×C61—21no—
88C42×C61C2311yescharacteristic
89#11758202—41no—
90#11758201—41no—
91#11758200—41no—
92#11758199—41no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198D411yescharacteristic
101#11758198D411yescharacteristic
102C4⋊Dic61—21no—
103#11758196—21no—
104#11758196D411yescharacteristic
105#11758196D411yescharacteristic
106C4×Dic61—21no—
107C4×Dic61C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110D488—41no—
111D488—41no—
112#11758190—41no—
113#11758190—41no—
114C23×C61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—42no—
119C22×D61—81no—
120C22×D61—81no—
121C22×D61C2×D411yescharacteristic
122Q8×C61—21no—
123Q8×C61—21no—
124Q8×C61—81no—
125D4×C61—21no—
126D4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2411yescharacteristic
133C22⋊D61—42no—
134C22⋊D61—81no—
135C22⋊D61—81no—
136C2×Dic61—21no—
137C2×Dic61C2×D411yescharacteristic
138C2×Dic61C2×D411yescharacteristic
139C2×Dic61C2×D411yescharacteristic
140D244—21no—
141D244—21no—
142D244—21no—
143D244—21no—
144D244—21no—
145D244—21no—
146D244—42no—
147D244—81no—
148D244—81no—
149D244—81no—
150C4×D61—21no—
151C4×D61—21no—
152C4×D61—42no—
153C4×D61—81no—
154Dic122—21no—
155Dic122—21no—
156C8×C61—21no—
157C8×C61—21no—
158#92418—21no—
159#92418—21no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61C22×D411yescharacteristic
164C2×D61—21no—
165C2×D61—21no—
166C2×D61—21no—
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—41no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61H(5,𝔽2)11yescharacteristic
183C4×C61H(5,𝔽2)11yescharacteristic
184Dic61—21no—
185Dic61—21no—
186Dic61—21no—
187Dic61—41no—
188#3224—611nomaximal, Sylow
189C2×C61—81no—
190C2×C61#53511yescharacteristic
191C2×C61#57611yescharacteristic
192C2×C61#57711yescharacteristic
193D61—41no—
194D61—81no—
195D61—81no—
196D61—81no—
197#542—611no—
198#535—611no—
199#496—611no—
200#495—611no—
201#489D6111yescharacteristic, complemented
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#433—611no—
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⋊Q8C2×D6111yescharacteristic, complemented
224#127—611no—
225#127—611no—
226#126—1221no—
227#124—611no—
228#124—611no—
229#124—1221no—
230#124C2×D6111yescharacteristic
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#117—611no—
242C4⋊C8—611no—
243C4⋊C8—611no—
244#103C2×D6111yescharacteristic, complemented
245#103C2×D6111yescharacteristic, complemented
246#102—611no—
247#102—611no—
248#102—611no—
249#102—611no—
250#102C2×D6111yescharacteristic
251#102C2×D6111yescharacteristic
252C22⋊C8—611no—
253C22⋊C8—611no—
254#97C2×D6111yescharacteristic, complemented
255C4×C8—611no—
256C24—1221no—
257#41—2441no—
258#41—2441no—
259C2×Q8—21no—
260C2×Q8—611no—
261C2×Q8C22×D6111yescharacteristic
262C2×D4—611no—
263C2×D4—611no—
264C2×D4—611no—
265C2×D4—1221no—
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—2441no—
273C2×D4—2441no—
274C2×D4C22×D6111yescharacteristic
275C22×C4—611no—
276C22×C4—1221no—
277C22×C4—1221no—
278Q16—2441no—
279SD16—2441no—
280SD16—2441no—
281SD16—2441no—
282SD16—2441no—
283D8—2441no—
284D8—2441no—
285D8—2441no—
286C2×C8—611no—
287C2×C8—611no—
288C2×C8C22×D6111yescharacteristic
289C2×C8C22×D6111yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—611no—
292C4⋊C4—611no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4C22×D6111yescharacteristic
296C4⋊C4C22×D6111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—611no—
300C22⋊C4—611no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C42—611no—
309C42—1221no—
310C42C22×D6111yescharacteristic
311C23—21no—
312C23—611no—
313C23—1221no—
314C23—1221no—
315C23—1221no—
316C23—4881no—
317C23—4881no—
318C23—2442no—
319Q8—21no—
320Q8—21no—
321Q8—81no—
322Q8—1221no—
323Q8—1221no—
324D4—21no—
325D4—21no—
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—21no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—4881no—
349C2×C4—2442no—
350C2×C4D4×D6111yescharacteristic
351C2×C4D4×D6111yescharacteristic
352C2×C4C23×D6111yescharacteristic
353C8—21no—
354C8—21no—
355C8—1221no—
356C8—1221no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—1221no—
361C22—1221no—
362C22—1221no—
363C22—4884no—
364C22—2441no—
365C22—2441no—
366C22—2441no—
367C22—2441no—
368C22—2441no—
369C22—2441no—
370C22—2441no—
371C22—2441no—
372C22—2441no—
373C22C2×D4×D6111yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—1221no—
380C4—1221no—
381C4—1221no—
382C4—2441no—
383C4#1451982311yescharacteristic
384C4#1451982311yescharacteristic
385C2—81no—
386C2—4881no—
387C2—4881no—
388C2—4881no—
389C2—2441no—
390C2#1684033011yescharacteristic
391C2#1684056611yescharacteristic
392C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#489C2
socleC22×C61C22×D4
hypercenter#489D61
hypocenterC61#3224
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #16840386C2semidirect
2. #16840330C2semidirect
3. #16840151C2semidirect
4. #16840144C2semidirect
5. #16840110C2semidirect
6. #16839987C2semidirect
7. #16839980C2semidirect
8. #16839961C2semidirect
9. #16839956C2semidirect
10. #16839927C2semidirect
11. #16839914C2semidirect
12. #16839910C2semidirect
13. #16839897C2semidirect
14. #16839824C2semidirect
15. C61×#489C2semidirect
18. C2×#11758202C22semidirect
20. C2×#11758190C22semidirect
22. C2×#11758201C22semidirect
24. C2×D488C22semidirect
31. #14519765C22semidirect
40. #14519742C22semidirect
41. #14519739C22semidirect
43. #14519706C22semidirect
44. #14519706C22semidirect
47. #14519697C22semidirect
48. #14519697C22semidirect
51. C4×#92418C22semidirect
52. C4⋊Q8×C61C22semidirect
54. #103×C61C22semidirect
55. #103×C61C22semidirect
58. #97×C61C22semidirect
201. #489D61semidirect
212. C61#3224semidirect
223. C4⋊Q8C2×D61semidirect
244. #103C2×D61semidirect
245. #103C2×D61semidirect
254. #97C2×D61semidirect