Finite Group Databasebeta

← #21456750

Subgroups — #21456750

Order 7808.

438 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840308C211yesmaximal, characteristic, complemented
2#16840307C211yesmaximal, characteristic, complemented
3#16840137C211yesmaximal, characteristic, complemented
4#16840133C211yesmaximal, characteristic, complemented
5#16840111C211yesmaximal, characteristic, complemented
6#16840107C211yesmaximal, characteristic, complemented
7#16839980C211yesmaximal, characteristic, complemented
8#16839979C211yesmaximal, characteristic, complemented
9#16839976C211yesmaximal, characteristic, complemented
10#16839975C211yesmaximal, characteristic, complemented
11#16839909C211yesmaximal, characteristic, complemented
12#16839907C211yesmaximal, characteristic, complemented
13#16839905C211yesmaximal, characteristic, complemented
14#16839812C211yesmaximal, characteristic, complemented
15C61×#449C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758224—21no—
18C2×#11758190C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21C2×D488C2211yescharacteristic
22C2×#11758199C2211yescharacteristic
23C2×#11758199C2211yescharacteristic
24#14519776C2211yescharacteristic
25#14519775C2211yescharacteristic
26#14519773C2211yescharacteristic
27#14519773C2211yescharacteristic
28#14519766C2211yescharacteristic
29#14519764C2211yescharacteristic
30#14519763—21no—
31#14519751C2211yescharacteristic
32#14519749—21no—
33#14519749—21no—
34#14519749—21no—
35D4×Dic61C2211yescharacteristic
36#14519739C2211yescharacteristic
37C4×C22⋊D61—21no—
38C4×C22⋊D61—21no—
39#14519737—21no—
40C2×C4×Dic61C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519697C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50C8×Dic61C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×#41×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C2×D8×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59#41×C61—41no—
60#41×C61—41no—
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61—21no—
64C2×D4×C61C2311yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C22×Dic61—21no—
75C22×Dic61D411yescharacteristic
76C22×Dic61D411yescharacteristic
77#11758224—44no—
78#11758222—41no—
79#11758222—41no—
80C2×D244C2311yescharacteristic
81C2×D244C2311yescharacteristic
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×Dic122—21no—
85C2×Dic122C2311yescharacteristic
86SD16×C61—41no—
87D8×C61—41no—
88C2×C8×C61C2311yescharacteristic
89C2×C8×C61C2311yescharacteristic
90C4⋊C4×C61C2311yescharacteristic
91C22⋊C4×C61—21no—
92C22⋊Dic61—21no—
93C22⋊Dic61—21no—
94C22⋊Dic61—21no—
95#11758201—41no—
96#11758200—41no—
97#11758199—41no—
98#11758199—41no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103C4⋊Dic61C2311yescharacteristic
104#11758196—21no—
105#11758196—21no—
106#11758196—21no—
107C4×Dic61D411yescharacteristic
108C4×Dic61D411yescharacteristic
109C4×Dic61C2311yescharacteristic
110C4×Dic61C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112C2×#92418C2311yescharacteristic
113D488—41no—
114#11758190—41no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61C2×D411yescharacteristic
118C22×D61—21no—
119C22×D61—21no—
120Q8×C61—21no—
121Q8×C61—21no—
122D4×C61—21no—
123D4×C61—21no—
124D4×C61—21no—
125D4×C61—21no—
126D4×C61—42no—
127D4×C61—42no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—42no—
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2411yescharacteristic
135C22⋊D61—42no—
136C22⋊D61—42no—
137C22⋊D61—42no—
138C22⋊D61—42no—
139C22⋊D61—42no—
140C22⋊D61—42no—
141C2×Dic61—22no—
142C2×Dic61—22no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—42no—
146C2×Dic61C2×D411yescharacteristic
147C2×Dic61C2×D411yescharacteristic
148C2×Dic61C2×D411yescharacteristic
149C2×Dic61C2×D411yescharacteristic
150D244—21no—
151D244—21no—
152D244—21no—
153D244—21no—
154C4×D61—42no—
155C4×D61—42no—
156Dic122—21no—
157Dic122—21no—
158Dic122—42no—
159C8×C61—21no—
160C8×C61—21no—
161#92418—21no—
162#92418—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61C22×D411yescharacteristic
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—41no—
179C4×C61—21no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61H(5,𝔽2)11yescharacteristic
183C4×C61H(5,𝔽2)11yescharacteristic
184Dic61—21no—
185Dic61—21no—
186Dic61—41no—
187Dic61—41no—
188Dic61#13512yes—
189Dic61AGL(1,ℤ/8)12yes—
190#3207—611nomaximal, Sylow
191C2×C61—41no—
192C2×C61—81no—
193C2×C61—81no—
194C2×C61#53511yescharacteristic
195C2×C61C2×#13511yescharacteristic
196C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
197D61—81no—
198D61—81no—
199#532—611no—
200#532—611no—
201#493—611no—
202#492—611no—
203#487—611no—
204#486—611no—
205#463—611no—
206#463—611no—
207#463—611no—
208#463—611no—
209#449—611no—
210#449—611no—
211#449—611no—
212#449D6111yescharacteristic, complemented
213#431—611no—
214C61#320711yescharacteristic, complemented, Sylow
215C2×#41—611no—
216C2×#41—1221no—
217C2×#41C2×D6111yescharacteristic
218C2×SD16—611no—
219C2×SD16—611no—
220C2×SD16—611no—
221C2×SD16C2×D6111yescharacteristic
222C2×D8—611no—
223C2×D8—611no—
224C2×D8—611no—
225C2×D8C2×D6111yescharacteristic
226C4⋊Q8—611no—
227C4⋊Q8—611no—
228#127—611no—
229#127—611no—
230#124—611no—
231#124—611no—
232#124—1221no—
233#121—611no—
234#121—1221no—
235#121—1221no—
236#121—1221no—
237#121C2×D6111yescharacteristic
238C4×D4—611no—
239C4×D4—611no—
240C4×D4—1221no—
241C4×D4—1221no—
242C4×D4—1221no—
243C2×C42—611no—
244C4⋊C8—611no—
245C4⋊C8—611no—
246#103—611no—
247#103—611no—
248#103—611no—
249#103C2×D6111yescharacteristic
250#102—611no—
251#102—611no—
252#102—611no—
253#102C2×D6111yescharacteristic
254C22⋊C8—611no—
255C22⋊C8C2×D6111yescharacteristic
256C4×C8—611no—
257C4×C8—611no—
258#41—41no—
259#41—41no—
260#41—2441no—
261#41—2441no—
262#41—2444no—
263C2×Q8—611no—
264C2×Q8—1221no—
265C2×Q8C22×D6111yescharacteristic
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—611no—
269C2×D4—611no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4C22×D6111yescharacteristic
277C2×D4C22×D6111yescharacteristic
278C22×C4—21no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4C22×D6111yescharacteristic
285SD16—41no—
286SD16—2441no—
287SD16—2441no—
288SD16—2441no—
289D8—41no—
290D8—2441no—
291D8—2441no—
292D8—2441no—
293C2×C8—611no—
294C2×C8—611no—
295C2×C8C22×D6111yescharacteristic
296C2×C8C22×D6111yescharacteristic
297C4⋊C4—611no—
298C4⋊C4—1221no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4C22×D6111yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C42—611no—
311C42—611no—
312C42—611no—
313C42—611no—
314C23—21no—
315C23—21no—
316C23—1221no—
317C23—1221no—
318C23D4×D6111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—1221no—
322Q8—1221no—
323Q8—2442no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—42no—
330D4—1221no—
331D4—1221no—
332D4—1221no—
333D4—1221no—
334D4—2442no—
335D4—2442no—
336D4—2442no—
337D4—2442no—
338D4—2442no—
339D4—2442no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—1222no—
350C2×C4—1222no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4D4×D6111yescharacteristic
357C2×C4C23×D6111yescharacteristic
358C8—21no—
359C8—21no—
360C8—1221no—
361C8—1221no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—2441no—
372C22—2441no—
373C22—2441no—
374C22—2441no—
375C22—2441no—
376C22—2441no—
377C22C2×D4×D6111yescharacteristic
378C4—21no—
379C4—41no—
380C4—41no—
381C4—612no—
382C4—612no—
383C4—1221no—
384C4—1221no—
385C4—2441no—
386C4—2441no—
387C4#1451982211yescharacteristic
388C4#1451982211yescharacteristic
389C2—41no—
390C2—81no—
391C2—81no—
392C2—4881no—
393C2—4881no—
394C2#1684032711yescharacteristic
395C2#135×D6111yescharacteristic
396C2AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#449C2
socleC22×C61C22×D4
hypercenter#449D61
hypocenterC61#3207
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #16840308C2semidirect
2. #16840307C2semidirect
3. #16840137C2semidirect
4. #16840133C2semidirect
5. #16840111C2semidirect
6. #16840107C2semidirect
7. #16839980C2semidirect
8. #16839979C2semidirect
9. #16839976C2semidirect
10. #16839975C2semidirect
11. #16839909C2semidirect
12. #16839907C2semidirect
13. #16839905C2semidirect
14. #16839812C2semidirect
15. C61×#449C2semidirect
212. #449D61semidirect
214. C61#3207semidirect