Finite Group Databasebeta

← #21456751

Subgroups — #21456751

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#16840311C211yesmaximal, characteristic, complemented
2#16840309C211yesmaximal, characteristic, complemented
3#16840137C211yesmaximal, characteristic, complemented
4#16840133C211yesmaximal, characteristic, complemented
5#16840111C211yesmaximal, characteristic, complemented
6#16840107C211yesmaximal, characteristic, complemented
7#16839978C211yesmaximal, characteristic, complemented
8#16839977C211yesmaximal, characteristic, complemented
9#16839974C211yesmaximal, characteristic, complemented
10#16839910C211yesmaximal, characteristic, complemented
11#16839908C211yesmaximal, characteristic, complemented
12#16839906C211yesmaximal, characteristic, complemented
13#16839904C211yesmaximal, characteristic, complemented
14#16839814C211yesmaximal, characteristic, complemented
15C61×#463C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758222—21no—
18C2×#11758224C2211yescharacteristic
19C2×#11758190C2211yescharacteristic
20C2×#11758200C2211yescharacteristic
21C2×#11758201C2211yescharacteristic
22C2×D488C2211yescharacteristic
23C2×#11758199C2211yescharacteristic
24C2×#11758199C2211yescharacteristic
25#14519776C2211yescharacteristic
26#14519775C2211yescharacteristic
27#14519773C2211yescharacteristic
28#14519773C2211yescharacteristic
29#14519765C2211yescharacteristic
30#14519763—21no—
31#14519752C2211yescharacteristic
32#14519750—21no—
33#14519750—21no—
34#14519750—21no—
35#14519748C2211yescharacteristic
36C4×D244C2211yescharacteristic
37C4×C22⋊D61—21no—
38#14519737—21no—
39#14519737—21no—
40C42×D61C2211yescharacteristic
41C4⋊#92418C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519700C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50C8×Dic61C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C2×D8×C61C2211yescharacteristic
54#124×C61C2211yescharacteristic
55C4×D4×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61—21no—
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C22×Dic61—21no—
70#11758226—41no—
71#11758226—41no—
72#11758224—41no—
73#11758224—41no—
74#11758222—44no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244C2311yescharacteristic
78C2×D244C2311yescharacteristic
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61D411yescharacteristic
82C2×C4×D61D411yescharacteristic
83C2×C4×D61C2311yescharacteristic
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⋊C4×C61—21no—
93C22⋊C4×C61—21no—
94C42×C61C2311yescharacteristic
95C22⋊Dic61—21no—
96#11758201—41no—
97#11758200—41no—
98#11758199—41no—
99#11758199—41no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104C4⋊Dic61C2311yescharacteristic
105#11758196—21no—
106#11758196—21no—
107#11758196—21no—
108C4×Dic61D411yescharacteristic
109C4×Dic61D411yescharacteristic
110C4×Dic61C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112C2×#92418C2311yescharacteristic
113D488—41no—
114#11758190—41no—
115C23×C61—21no—
116C23×C61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61C2×D411yescharacteristic
120Q8×C61—21no—
121Q8×C61—21no—
122D4×C61—21no—
123D4×C61—21no—
124D4×C61—21no—
125D4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—42no—
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2411yescharacteristic
132C22⋊D61—42no—
133C22⋊D61—42no—
134C22⋊D61—42no—
135C22⋊D61—42no—
136C22⋊D61—42no—
137C22⋊D61—42no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—42no—
141C2×Dic61C2×D411yescharacteristic
142C2×Dic61C2×D411yescharacteristic
143C2×Dic61C2×D411yescharacteristic
144D244—21no—
145D244—21no—
146D244—21no—
147D244—21no—
148D244—42no—
149D244—42no—
150C4×D61—21no—
151C4×D61—21no—
152C4×D61—22no—
153C4×D61—22no—
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—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61C22×D411yescharacteristic
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—41no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61H(5,𝔽2)11yescharacteristic
184C4×C61H(5,𝔽2)11yescharacteristic
185Dic61—21no—
186Dic61—41no—
187Dic61—41no—
188Dic61#13512yes—
189Dic61AGL(1,ℤ/8)12yes—
190#3207—611nomaximal, Sylow
191C2×C61—81no—
192C2×C61—81no—
193C2×C61#53511yescharacteristic
194C2×C61C2×#13511yescharacteristic
195C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
196D61—41no—
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#463D6111yescharacteristic, complemented
209#449—611no—
210#449—611no—
211#449—611no—
212#449—611no—
213#431—611no—
214C61#320711yescharacteristic, complemented, Sylow
215C2×#41—611no—
216C2×#41—611no—
217C2×#41—1221no—
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—1221no—
232#124C2×D6111yescharacteristic
233#121—611no—
234#121—611no—
235#121—1221no—
236#121—1221no—
237#121—1221no—
238C4×D4—611no—
239C4×D4—1221no—
240C4×D4—1221no—
241C4×D4—1221no—
242C4×D4C2×D6111yescharacteristic
243C2×C42—611no—
244C4⋊C8—611no—
245C4⋊C8C2×D6111yescharacteristic
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⋊C8—611no—
256C4×C8—611no—
257C4×C8—611no—
258#41—2444no—
259#41—2441no—
260#41—2441no—
261#41—2441no—
262#41—2441no—
263C2×Q8—611no—
264C2×Q8—1221no—
265C2×Q8C22×D6111yescharacteristic
266C2×D4—611no—
267C2×D4—611no—
268C2×D4—1221no—
269C2×D4—1221no—
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—611no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4—1221no—
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—21no—
304C22⋊C4—21no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C42—611no—
311C42—611no—
312C42—611no—
313C42C22×D6111yescharacteristic
314C23—21no—
315C23—21no—
316C23—611no—
317C23—1221no—
318C23—1221no—
319Q8—21no—
320Q8—21no—
321Q8—1221no—
322Q8—1221no—
323Q8—2442no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—1221no—
329D4—1221no—
330D4—1221no—
331D4—1221no—
332D4—2442no—
333D4—2442no—
334D4—2442no—
335D4—2442no—
336D4—2442no—
337D4—2442no—
338D4—2442no—
339D4—2442no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—1222no—
347C2×C4—1222no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—2442no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4D4×D6111yescharacteristic
356C2×C4D4×D6111yescharacteristic
357C2×C4C23×D6111yescharacteristic
358C8—21no—
359C8—21no—
360C8—1221no—
361C8—1221no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—1221no—
369C22—1221no—
370C22—1221no—
371C22—2441no—
372C22—2441no—
373C22—2441no—
374C22—2441no—
375C22—2441no—
376C22—2441no—
377C22C2×D4×D6111yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—612no—
383C4—612no—
384C4—1221no—
385C4—2441no—
386C4—2441no—
387C4#1451982211yescharacteristic
388C4#1451982311yescharacteristic
389C2—81no—
390C2—81no—
391C2—4881no—
392C2—4881no—
393C2—2441no—
394C2#1684032811yescharacteristic
395C2#135×D6111yescharacteristic
396C2AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#463C2
socleC22×C61C22×D4
hypercenter#463D61
hypocenterC61#3207
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #16840311C2semidirect
2. #16840309C2semidirect
3. #16840137C2semidirect
4. #16840133C2semidirect
5. #16840111C2semidirect
6. #16840107C2semidirect
7. #16839978C2semidirect
8. #16839977C2semidirect
9. #16839974C2semidirect
10. #16839910C2semidirect
11. #16839908C2semidirect
12. #16839906C2semidirect
13. #16839904C2semidirect
14. #16839814C2semidirect
15. C61×#463C2semidirect
208. #463D61semidirect
214. C61#3207semidirect