Finite Group Databasebeta

← #21457832

Subgroups — #21457832

Order 7808.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840462C211yesmaximal, characteristic, complemented
2#16840432C211yesmaximal, characteristic, complemented
3#16840126C211yesmaximal, characteristic, complemented
4#16840085C211yesmaximal, characteristic, complemented
5#16840074C211yesmaximal, characteristic, complemented
6#16840070C211yesmaximal, characteristic, complemented
7#16840012C211yesmaximal, characteristic, complemented
8#16839995C211yesmaximal, characteristic, complemented
9#16839904C211yesmaximal, characteristic, complemented
10#16839904C211yesmaximal, characteristic, complemented
11#16839862C211yesmaximal, characteristic, complemented
12#16839832C211yesmaximal, characteristic, complemented
13#16839760C211yesmaximal, characteristic, complemented
14#16839755C211yesmaximal, characteristic, complemented
15C61×#459C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758189C2211yescharacteristic
20C2×C8×D61C2211yescharacteristic
21#14519773—21no—
22#14519770—21no—
23#14519769C2211yescharacteristic
24#14519760—21no—
25#14519750—21no—
26#14519749—21no—
27#14519749—21no—
28#14519748C2211yescharacteristic
29#14519748C2211yescharacteristic
30#14519748C2211yescharacteristic
31#14519748C2211yescharacteristic
32C4×Dic122C2211yescharacteristic
33C4×D244C2211yescharacteristic
34D4×Dic61—21no—
35C4×C22⋊D61—21no—
36#14519735C2211yescharacteristic
37C4⋊C4×D61C2211yescharacteristic
38#14519711C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519709C2211yescharacteristic
41#14519702C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519700C2211yescharacteristic
44#14519698C2211yescharacteristic
45#14519698C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519688C2211yescharacteristic
52C2×D8×C61C2211yescharacteristic
53C2×D8×C61C2211yescharacteristic
54#127×C61C2211yescharacteristic
55C4×D4×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×D4×C61—21no—
60C2×D4×C61—21no—
61C2×D4×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C22×C4×C61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73#11758224—22no—
74#11758224—22no—
75#11758224—41no—
76#11758224—41no—
77C2×D244D411yescharacteristic
78C2×C4×D61—21no—
79C2×C4×D61C2311yescharacteristic
80C2×C4×D61C2311yescharacteristic
81C2×Dic122C2311yescharacteristic
82D8×C61—41no—
83D8×C61—41no—
84C2×C8×C61C2311yescharacteristic
85C2×C8×C61C2311yescharacteristic
86C4⋊C4×C61C2311yescharacteristic
87C22⋊C4×C61—21no—
88C42×C61C2311yescharacteristic
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92C22⋊Dic61—21no—
93#11758200—22no—
94#11758198—21no—
95#11758198D411yescharacteristic
96#11758198D411yescharacteristic
97C4⋊Dic61D411yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109#11758189—41no—
110C8×D61—41no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C22×D61C2×D411yescharacteristic
115C22×D61C2×D411yescharacteristic
116D4×C61—21no—
117D4×C61—21no—
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—21no—
121D4×C61—21no—
122D4×C61—42no—
123D4×C61—81no—
124C2×C4×C61—21no—
125C2×C4×C61—81no—
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2411yescharacteristic
129C22⋊D61—42no—
130C22⋊D61—42no—
131C22⋊D61—42no—
132C22⋊D61—81no—
133C22⋊D61—81no—
134C22⋊D61—81no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61C2×D411yescharacteristic
142C2×Dic61C2×D411yescharacteristic
143D244—41no—
144C4×D61—21no—
145C4×D61—21no—
146C4×D61—21no—
147C4×D61—21no—
148C4×D61—81no—
149Dic122—21no—
150Dic122#4112yes—
151C8×C61—21no—
152C8×C61—21no—
153#92418—21no—
154#92418—21no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61C22×D411yescharacteristic
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—21no—
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—21no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—41no—
174C4×C61C2×#4111yescharacteristic
175C4×C61H(5,𝔽2)11yescharacteristic
176Dic61—22no—
177Dic61—21no—
178Dic61—21no—
179Dic61—41no—
180Dic61—41no—
181Dic61—41no—
182#3309—611nomaximal, Sylow
183C2×C61—81no—
184C2×C61—81no—
185C2×C61—81no—
186C2×C61#54611yescharacteristic
187C2×C61#57511yescharacteristic
188C2×C61#57611yescharacteristic
189D61—41no—
190D61—41no—
191#553—611no—
192#550—611no—
193#490—611no—
194#482—611no—
195#480—611no—
196#479—611no—
197#469—611no—
198#466—611no—
199#459D6111yescharacteristic, complemented
200#449—611no—
201#449—611no—
202#440—611no—
203#435—611no—
204#417—611no—
205#416—611no—
206C61#330911yescharacteristic, complemented, Sylow
207C2×#41—611no—
208C2×#41—611no—
209C2×SD16—611no—
210C2×D8C2×D6111yescharacteristic
211C2×D8C2×D6111yescharacteristic
212C2×M16—611no—
213C22×C8—611no—
214#127—1221no—
215#127C2×D6111yescharacteristic
216#126—1221no—
217#125—611no—
218#123—1221no—
219#121—611no—
220#121—611no—
221#121—611no—
222#121—611no—
223#121—1221no—
224#121—1221no—
225#121—1221no—
226C4×Q8—611no—
227C4×D4—611no—
228C4×D4—1221no—
229C4×D4—1221no—
230C4×D4C2×D6111yescharacteristic
231#117—611no—
232C2×C4⋊C4—611no—
233#107—611no—
234#107—611no—
235#106—611no—
236C4⋊C8C2×D6111yescharacteristic
237#103—611no—
238#103—611no—
239#103—611no—
240#102—611no—
241#102—611no—
242#102—611no—
243#102—611no—
244#102—611no—
245#102C2×D6111yescharacteristic
246#102C2×D6111yescharacteristic
247C22⋊C8—611no—
248C22⋊C8—611no—
249#97—611no—
250#41—1222no—
251#41—1222no—
252#41—2441no—
253#41—2441no—
254C2×Q8—611no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—611no—
258C2×D4—1221no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4C22×D6111yescharacteristic
265C2×D4C22×D6111yescharacteristic
266C2×D4C22×D6111yescharacteristic
267C22×C4—21no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273SD16—1222no—
274D8—41no—
275D8—41no—
276M16—2441no—
277C2×C8—611no—
278C2×C8—611no—
279C2×C8—2441no—
280C2×C8C22×D6111yescharacteristic
281C2×C8C22×D6111yescharacteristic
282C4⋊C4—611no—
283C4⋊C4—611no—
284C4⋊C4—611no—
285C4⋊C4—611no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C4⋊C4C22×D6111yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—611no—
293C22⋊C4—611no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C42—1221no—
300C42—1221no—
301C42C22×D6111yescharacteristic
302C23—21no—
303C23—21no—
304C23—21no—
305C23—611no—
306C23—611no—
307Q8—612no—
308Q8—1221no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—81no—
317D4—4881no—
318D4—4881no—
319D4—4881no—
320D4—2441no—
321D4—2442no—
322D4—2442no—
323D4—2442no—
324C2×C4—21no—
325C2×C4—81no—
326C2×C4—611no—
327C2×C4—611no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—4881no—
337C2×C4—2442no—
338C2×C4—2442no—
339C2×C4D4×D6111yescharacteristic
340C2×C4D4×D6111yescharacteristic
341C2×C4C23×D6111yescharacteristic
342C8—21no—
343C8—21no—
344C8—1221no—
345C8—1221no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—1221no—
356C22—1221no—
357C22—1221no—
358C22—1221no—
359C22—1221no—
360C22—1221no—
361C22C2×D4×D6111yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—1221no—
366C4—1221no—
367C4—1222no—
368C4—2441no—
369C4—2441no—
370C4—2441no—
371C4#41×D6111yescharacteristic
372C4#1451982211yescharacteristic
373C2—81no—
374C2—81no—
375C2—81no—
376C2—2441no—
377C2—2441no—
378C2#1684040911yescharacteristic
379C2#1684055811yescharacteristic
380C2#1684056311yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#459C2
socleC22×C61C22×D4
hypercenter#459D61
hypocenterC61#3309
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #16840462C2semidirect
2. #16840432C2semidirect
3. #16840126C2semidirect
4. #16840085C2semidirect
5. #16840074C2semidirect
6. #16840070C2semidirect
7. #16840012C2semidirect
8. #16839995C2semidirect
9. #16839904C2semidirect
10. #16839904C2semidirect
11. #16839862C2semidirect
12. #16839832C2semidirect
13. #16839760C2semidirect
14. #16839755C2semidirect
15. C61×#459C2semidirect
199. #459D61semidirect
206. C61#3309semidirect