Finite Group Databasebeta

← #21458016

Subgroups — #21458016

Order 7808.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840456C211yesmaximal, characteristic, complemented
2#16840406C211yesmaximal, characteristic, complemented
3#16840115C211yesmaximal, characteristic, complemented
4#16840103C211yesmaximal, characteristic, complemented
5#16840074C211yesmaximal, characteristic, complemented
6#16840060C211yesmaximal, characteristic, complemented
7#16840014C211yesmaximal, characteristic, complemented
8#16840008C211yesmaximal, characteristic, complemented
9#16839976C211yesmaximal, characteristic, complemented
10#16839908C211yesmaximal, characteristic, complemented
11#16839896C211yesmaximal, characteristic, complemented
12#16839842C211yesmaximal, characteristic, complemented
13#16839838C211yesmaximal, characteristic, complemented
14#16839760C211yesmaximal, characteristic, complemented
15C61×#418C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×#11758190C2211yescharacteristic, complemented
18C2×#11758199C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×#11758189C2211yescharacteristic, complemented
21#14519771—21no—
22#14519768C2211yescharacteristic, complemented
23#14519764C2211yescharacteristic
24#14519759—21no—
25#14519758—21no—
26#14519756C2211yescharacteristic
27#14519752C2211yescharacteristic, complemented
28#14519751C2211yescharacteristic
29#14519750—21no—
30#14519749—21no—
31#14519748C2211yescharacteristic
32#14519746—21no—
33C4×D244—21no—
34D4×Dic61C2211yescharacteristic
35#14519739C2211yescharacteristic, complemented
36C4×C22⋊D61C2211yescharacteristic
37C4⋊C4×D61C2211yescharacteristic, complemented
38C2×C22⋊Dic61—21no—
39#14519711C2211yescharacteristic, complemented
40#14519710C2211yescharacteristic, complemented
41#14519708C2211yescharacteristic, complemented
42#14519706C2211yescharacteristic, complemented
43#14519702C2211yescharacteristic, complemented
44#14519700C2211yescharacteristic, complemented
45#14519700C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic, complemented
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C22×D4×C61C2211yescharacteristic
53C2×M16×C61C2211yescharacteristic
54#117×C61C2211yescharacteristic
55#102×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C24×C61—21no—
60C2×D4×C61—22no—
61C2×D4×C61—21no—
62C2×D4×C61—41no—
63C2×D4×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72#11758224—22no—
73#11758224—41no—
74C2×D244—21no—
75C2×D244C2311yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61C2311yescharacteristic
79C2×Dic122C2311yescharacteristic
80M16×C61—41no—
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C42×C61—21no—
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92C22⋊Dic61D411yescharacteristic
93#11758199—22no—
94#11758199—41no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198D411yescharacteristic
99C4⋊Dic61—21no—
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105#11758196D411yescharacteristic
106C4×Dic61C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109#11758190—41no—
110#11758189—41no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—42no—
114C23×C61—42no—
115C23×C61—81no—
116C23×C61C2×D411yescharacteristic
117C22×D61—21no—
118C22×D61C2×D411yescharacteristic
119D4×C61—21no—
120D4×C61—21no—
121D4×C61—21no—
122D4×C61—42no—
123D4×C61#4112yes—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C22⋊D61—41no—
131C22⋊D61—42no—
132C22⋊D61—81no—
133C22⋊D61—81no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—42no—
138C2×Dic61—81no—
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141C2×Dic61C2×D411yescharacteristic
142D244—21no—
143D244—21no—
144D244—42no—
145C4×D61—21no—
146C4×D61—21no—
147C4×D61—81no—
148C4×D61—81no—
149Dic122—21no—
150Dic122—21no—
151C8×C61—21no—
152C8×C61—21no—
153#92418—21no—
154#92418—21no—
155C22×C61—22no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—84no—
165C22×C61C22×D411yescharacteristic
166C2×D61—21no—
167C2×D61—21no—
168C2×D61—21no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—41no—
172C4×C61—21no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61C2×#4111yescharacteristic
176C4×C61H(5,𝔽2)11yescharacteristic
177Dic61—21no—
178Dic61—21no—
179Dic61—21no—
180Dic61—41no—
181Dic61—41no—
182Dic61—41no—
183#3322—611nomaximal, Sylow
184C2×C61—41no—
185C2×C61—42no—
186C2×C61—81no—
187C2×C61#54611yescharacteristic
188C2×C61#57511yescharacteristic
189C2×C61#57611yescharacteristic
190D61—41no—
191D61—81no—
192#553—611no—
193#546—611no—
194#488—611no—
195#485—611no—
196#480—611no—
197#478—611no—
198#469—611no—
199#468—611no—
200#463—611no—
201#449—611no—
202#447—611no—
203C4×D8—611no—
204#436—611no—
205#418D6111yescharacteristic, complemented
206#417—611no—
207C61#332211yescharacteristic, complemented, Sylow
208C2×#41—611no—
209C22×D4C2×D6111yescharacteristic
210C2×SD16—611no—
211C2×D8—611no—
212C2×D8—611no—
213C2×M16—611no—
214C2×M16C2×D6111yescharacteristic
215#126—1221no—
216#125—611no—
217#124—611no—
218#123—1221no—
219#123—1221no—
220C22⋊Q8—611no—
221#121—611no—
222#121—611no—
223#121—611no—
224#121—1221no—
225#121—1221no—
226#120—1221no—
227C4×D4—611no—
228C4×D4—611no—
229C4×D4—611no—
230C4×D4—1221no—
231#117C2×D6111yescharacteristic
232C2×C4⋊C4—611no—
233C2×C22⋊C4—1221no—
234#107—611no—
235#107—611no—
236#106—611no—
237C4⋊C8—611no—
238#103—611no—
239#103—611no—
240#103—611no—
241#102—611no—
242#102—611no—
243#102—611no—
244#102C2×D6111yescharacteristic
245#102C2×D6111yescharacteristic
246#102C2×D6111yescharacteristic
247#102C2×D6111yescharacteristic
248C22⋊C8—611no—
249C22⋊C8—611no—
250C4×C8—611no—
251C24—21no—
252#41—1222no—
253#41—2441no—
254C2×Q8—611no—
255C2×D4—22no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4—611no—
259C2×D4—611no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4C22×D6111yescharacteristic
265C2×D4C22×D6111yescharacteristic
266C22×C4—611no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4C22×D6111yescharacteristic
272SD16—2441no—
273D8—1222no—
274D8—2441no—
275M16—41no—
276M16—2441no—
277C2×C8—611no—
278C2×C8—611no—
279C2×C8C22×D6111yescharacteristic
280C2×C8C22×D6111yescharacteristic
281C4⋊C4—611no—
282C4⋊C4—611no—
283C4⋊C4—611no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C4⋊C4C22×D6111yescharacteristic
289C4⋊C4C22×D6111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—611no—
292C22⋊C4—611no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C42—21no—
302C42—611no—
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—611no—
309C23—1221no—
310C23D4×D6111yescharacteristic
311Q8—1221no—
312Q8—1221no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—1221no—
318D4—1221no—
319D4—4881no—
320D4—4881no—
321D4—2442no—
322D4—2441no—
323D4—2442no—
324D4#1175822212yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—611no—
330C2×C4—611no—
331C2×C4—611no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—4881no—
338C2×C4—4881no—
339C2×C4—4881no—
340C2×C4—2442no—
341C2×C4D4×D6111yescharacteristic
342C2×C4C23×D6111yescharacteristic
343C8—21no—
344C8—21no—
345C8—1221no—
346C8—1221no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—84no—
357C22—1221no—
358C22—1221no—
359C22—1221no—
360C22—2441no—
361C22—2441no—
362C22—2441no—
363C22C2×D4×D6111yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—1221no—
368C4—1221no—
369C4—1221no—
370C4—2441no—
371C4—2441no—
372C4—2441no—
373C4C2×#1175822211yescharacteristic
374C4#1451982211yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—4881no—
379C2—2441no—
380C2#1684040211yescharacteristic
381C2#1684055811yescharacteristic
382C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#418C2
socleC22×C61C22×D4
hypercenter#418D61
hypocenterC61#3322
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #16840456C2semidirect
2. #16840406C2semidirect
3. #16840115C2semidirect
4. #16840103C2semidirect
5. #16840074C2semidirect
6. #16840060C2semidirect
7. #16840014C2semidirect
8. #16840008C2semidirect
9. #16839976C2semidirect
10. #16839908C2semidirect
11. #16839896C2semidirect
12. #16839842C2semidirect
13. #16839838C2semidirect
14. #16839760C2semidirect
15. C61×#418C2semidirect
17. C2×#11758190C22semidirect
20. C2×#11758189C22semidirect
22. #14519768C22semidirect
27. #14519752C22semidirect
35. #14519739C22semidirect
37. C4⋊C4×D61C22semidirect
39. #14519711C22semidirect
40. #14519710C22semidirect
41. #14519708C22semidirect
42. #14519706C22semidirect
43. #14519702C22semidirect
44. #14519700C22semidirect
45. #14519700C22semidirect
46. #14519699C22semidirect
50. #14519689C22semidirect
51. C8×Dic61C22semidirect
205. #418D61semidirect
207. C61#3322semidirect