Finite Group Databasebeta

← #21457826

Subgroups — #21457826

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#16840460C211yesmaximal, characteristic, complemented
2#16840431C211yesmaximal, characteristic, complemented
3#16840125C211yesmaximal, characteristic, complemented
4#16840085C211yesmaximal, characteristic, complemented
5#16840075C211yesmaximal, characteristic, complemented
6#16840067C211yesmaximal, characteristic, complemented
7#16840015C211yesmaximal, characteristic, complemented
8#16839997C211yesmaximal, characteristic, complemented
9#16839956C211yesmaximal, characteristic, complemented
10#16839910C211yesmaximal, characteristic, complemented
11#16839907C211yesmaximal, characteristic, complemented
12#16839865C211yesmaximal, characteristic, complemented
13#16839831C211yesmaximal, characteristic, complemented
14#16839757C211yesmaximal, characteristic, complemented
15C61×#417C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758201C2211yescharacteristic
18C2×D488C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×C8×D61C2211yescharacteristic
21#14519773—21no—
22#14519773C2211yescharacteristic
23#14519772—21no—
24#14519768C2211yescharacteristic
25#14519762—21no—
26#14519752C2211yescharacteristic
27#14519751—21no—
28#14519751—21no—
29#14519751C2211yescharacteristic
30#14519751C2211yescharacteristic
31#14519748—21no—
32#14519748C2211yescharacteristic
33Q8×Dic61C2211yescharacteristic
34#14519739C2211yescharacteristic
35C4×C22⋊D61—21no—
36C4×C22⋊D61—21no—
37C4×C22⋊D61C2211yescharacteristic
38#14519735C2211yescharacteristic
39#14519710C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519687C2211yescharacteristic
52C2×#41×C61C2211yescharacteristic
53C2×M16×C61C2211yescharacteristic
54C2×C4⋊C4×C61C2211yescharacteristic
55#103×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59#41×C61—22no—
60#41×C61—41no—
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61C2311yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C2×C22⋊D61D411yescharacteristic
73#11758226—22no—
74#11758226—41no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244C2311yescharacteristic
78C2×D244C2311yescharacteristic
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61C2311yescharacteristic
82M16×C61—41no—
83C2×C8×C61C2311yescharacteristic
84C2×C8×C61C2311yescharacteristic
85C4⋊C4×C61—21no—
86C4⋊C4×C61C2311yescharacteristic
87C4⋊C4×C61C2311yescharacteristic
88C22⋊Dic61—21no—
89C22⋊Dic61D411yescharacteristic
90#11758201—22no—
91#11758199—41no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198D411yescharacteristic
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102#11758196—21no—
103#11758196D411yescharacteristic
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109D488—41no—
110C8×D61—41no—
111C23×C61—21no—
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61C2×D411yescharacteristic
116Q8×C61—21no—
117Q8×C61#4112yes—
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—42no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—42no—
127C2×C4×C61—81no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C22⋊D61—41no—
131C22⋊D61—42no—
132C22⋊D61—42no—
133C22⋊D61—81no—
134C22⋊D61—81no—
135C22⋊D61—81no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61C2×D411yescharacteristic
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141D244—21no—
142D244—21no—
143D244—21no—
144D244—21no—
145D244—42no—
146D244—81no—
147C4×D61—21no—
148C4×D61—21no—
149C4×D61—42no—
150C4×D61—81no—
151C8×C61—21no—
152C8×C61—21no—
153#92418—21no—
154#92418—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61C22×D411yescharacteristic
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—21no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C4×C61—22no—
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—
182#3309—611nomaximal, Sylow
183C2×C61—41no—
184C2×C61—81no—
185C2×C61#54611yescharacteristic
186C2×C61#57511yescharacteristic
187C2×C61#57611yescharacteristic
188D61—41no—
189D61—81no—
190D61—81no—
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#459—611no—
200#449—611no—
201#449—611no—
202#440—611no—
203#435—611no—
204#417D6111yescharacteristic, complemented
205#416—611no—
206C61#330911yescharacteristic, complemented, Sylow
207C2×#41—611no—
208C2×#41C2×D6111yescharacteristic
209C2×SD16—611no—
210C2×D8—611no—
211C2×D8—611no—
212C2×M16C2×D6111yescharacteristic
213C22×C8—611no—
214#127—611no—
215#127—1221no—
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—611no—
229C4×D4—1221no—
230C4×D4—1221no—
231#117—611no—
232C2×C4⋊C4C2×D6111yescharacteristic
233#107—611no—
234#107—611no—
235#106—611no—
236C4⋊C8—611no—
237#103—611no—
238#103C2×D6111yescharacteristic
239#103C2×D6111yescharacteristic
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—22no—
251#41—41no—
252#41—1222no—
253#41—2441no—
254C2×Q8C22×D6111yescharacteristic
255C2×D4—21no—
256C2×D4—611no—
257C2×D4—611no—
258C2×D4—611no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4—1221no—
265C2×D4—1221no—
266C2×D4C22×D6111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—611no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4C22×D6111yescharacteristic
273SD16—1222no—
274D8—2441no—
275D8—2441no—
276M16—41no—
277C2×C8—611no—
278C2×C8—611no—
279C2×C8—2441no—
280C2×C8C22×D6111yescharacteristic
281C2×C8C22×D6111yescharacteristic
282C4⋊C4—21no—
283C4⋊C4—611no—
284C4⋊C4—611no—
285C4⋊C4—611no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4C22×D6111yescharacteristic
290C4⋊C4C22×D6111yescharacteristic
291C22⋊C4—611no—
292C22⋊C4—611no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C42—611no—
300C42—1221no—
301C42—1221no—
302C23—21no—
303C23—611no—
304C23—1221no—
305C23—1221no—
306C23D4×D6111yescharacteristic
307Q8—21no—
308Q8#1175822212yes—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—1221no—
313D4—1221no—
314D4—1221no—
315D4—1221no—
316D4—4881no—
317D4—4881no—
318D4—4881no—
319D4—4881no—
320D4—2442no—
321D4—2441no—
322D4—2442no—
323D4—2442no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—81no—
331C2×C4—611no—
332C2×C4—611no—
333C2×C4—611no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—4881no—
339C2×C4—2442no—
340C2×C4D4×D6111yescharacteristic
341C2×C4C23×D6111yescharacteristic
342C8—21no—
343C8—21no—
344C8—1221no—
345C8—1221no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—1221no—
353C22—1221no—
354C22—1221no—
355C22—2441no—
356C22—2441no—
357C22—2441no—
358C22—2441no—
359C22—2441no—
360C22—2441no—
361C22C2×D4×D6111yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—41no—
366C4—1221no—
367C4—1221no—
368C4—1221no—
369C4—2441no—
370C4—2441no—
371C4C2×#1175822211yescharacteristic
372C4#1451982211yescharacteristic
373C2—41no—
374C2—81no—
375C2—4881no—
376C2—4881no—
377C2—2441no—
378C2#1684040211yescharacteristic
379C2#1684056111yescharacteristic
380C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#417C2
socleC22×C61C22×D4
hypercenter#417D61
hypocenterC61#3309
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #16840460C2semidirect
2. #16840431C2semidirect
3. #16840125C2semidirect
4. #16840085C2semidirect
5. #16840075C2semidirect
6. #16840067C2semidirect
7. #16840015C2semidirect
8. #16839997C2semidirect
9. #16839956C2semidirect
10. #16839910C2semidirect
11. #16839907C2semidirect
12. #16839865C2semidirect
13. #16839831C2semidirect
14. #16839757C2semidirect
15. C61×#417C2semidirect
204. #417D61semidirect
206. C61#3309semidirect