Finite Group Databasebeta

← #21456018

Subgroups — #21456018

Order 7808.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840367C211yesmaximal, characteristic, complemented
2#16840080C211yesmaximal, characteristic, complemented
3#16840075C211yesmaximal, characteristic, complemented
4#16840069C211yesmaximal, characteristic, complemented
5#16840062C211yesmaximal, characteristic, complemented
6#16839962C211yesmaximal, characteristic, complemented
7#16839957C211yesmaximal, characteristic, complemented
8#16839907C211yesmaximal, characteristic, complemented
9#16839907C211yesmaximal, characteristic, complemented
10#16839872C211yesmaximal, characteristic, complemented
11#16839860C211yesmaximal, characteristic, complemented
12C4×#11758201C211yesmaximal, characteristic, complemented
13C4×#11758199C211yesmaximal, characteristic, complemented
14#16839823C211yesmaximal, characteristic, complemented
15C61×#520C211yesmaximal, characteristic, complemented
16C2×#11758201C2211yescharacteristic
17C2×#11758201C2211yescharacteristic
18C2×#11758199C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20#14519774C2211yescharacteristic
21#14519769C2211yescharacteristic
22#14519762—21no—
23#14519762—21no—
24#14519751C2211yescharacteristic
25#14519751C2211yescharacteristic
26#14519750—21no—
27#14519750—21no—
28C4×D244C2211yescharacteristic
29C4×D244C2211yescharacteristic
30#14519710C2211yescharacteristic
31#14519710C2211yescharacteristic
32#14519708C2211yescharacteristic
33#14519708C2211yescharacteristic
34C4⋊#92418C2211yescharacteristic
35C4⋊#92418C2211yescharacteristic
36#14519701C2211yescharacteristic
37#14519701C2211yescharacteristic
38#14519698C2211yescharacteristic
39#14519698C2211yescharacteristic
40#14519697C2211yescharacteristic
41#14519697C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44C22⋊#92418C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46#14519688C2211yescharacteristic
47C4×#92418C2211yescharacteristic
48C2×#41×C61C2211yescharacteristic
49C4×Q8×C61C2211yescharacteristic
50C4×Q8×C61C2211yescharacteristic
51C4×D4×C61—21no—
52C4×D4×C61—21no—
53C4×D4×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55#117×C61—21no—
56#117×C61C2211yescharacteristic
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61C2211yescharacteristic
59#41×C61—22no—
60#41×C61—22no—
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61C2311yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C2311yescharacteristic
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×D244—21no—
72C2×D244—21no—
73C2×D244C2311yescharacteristic
74C2×D244C2311yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61D411yescharacteristic
81C4⋊C4×C61D411yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C22⋊C4×C61—21no—
85C22⋊C4×C61—21no—
86C22⋊C4×C61D411yescharacteristic
87C22⋊C4×C61D411yescharacteristic
88C42×C61—21no—
89C42×C61—21no—
90C42×C61C2311yescharacteristic
91C42×C61C2311yescharacteristic
92#11758201—22no—
93#11758201—22no—
94#11758199—22no—
95#11758199—22no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102#11758196—21no—
103#11758196—21no—
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C23×C61—21no—
109C23×C61C2×D411yescharacteristic
110C22×D61—21no—
111C22×D61—21no—
112Q8×C61—21no—
113Q8×C61#4112yes—
114D4×C61—24no—
115D4×C61—21no—
116D4×C61#4112yes—
117C2×C4×C61—24no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—81no—
124C2×C4×C61—81no—
125C2×C4×C61—81no—
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2411yescharacteristic
132C22⋊D61—81no—
133C22⋊D61—81no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136D244—21no—
137D244—21no—
138D244—21no—
139D244—21no—
140D244—81no—
141D244—81no—
142C4×D61—81no—
143C4×D61—81no—
144#92418—21no—
145#92418—21no—
146#92418—21no—
147#92418—21no—
148C22×C61—21no—
149C22×C61—22no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61C22×D411yescharacteristic
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C4×C61—21no—
162C4×C61—22no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61C2×#4111yescharacteristic
170C4×C61C2×#4111yescharacteristic
171Dic61—41no—
172Dic61—41no—
173#3119—611nomaximal, Sylow
174C2×C61—41no—
175C2×C61—42no—
176C2×C61#52511yescharacteristic
177C2×C61#57611yescharacteristic
178C2×C61#57711yescharacteristic
179D61—81no—
180D61—81no—
181#540—611no—
182#520D6111yescharacteristic, complemented
183#481—611no—
184#480—611no—
185#479—611no—
186#478—611no—
187#460—611no—
188#459—611no—
189#449—611no—
190#449—611no—
191#442—611no—
192#440—611no—
193C4×SD16—611no—
194C4×D8—611no—
195#433—611no—
196C61#311911yescharacteristic, complemented, Sylow
197C2×#41C2×D6111yescharacteristic
198C2×SD16—611no—
199C2×SD16—611no—
200C2×D8—611no—
201C2×D8—611no—
202#127—611no—
203#125—611no—
204#123—1221no—
205#123—1221no—
206#121—611no—
207#121—611no—
208#121—1221no—
209#121—1221no—
210C4×Q8C2×D6111yescharacteristic
211C4×Q8C2×D6111yescharacteristic
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—611no—
215C4×D4—611no—
216C4×D4C2×D6111yescharacteristic
217C4×D4C2×D6111yescharacteristic
218#117—21no—
219#117C2×D6111yescharacteristic
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×D6111yescharacteristic
222#107—611no—
223#107—611no—
224#106—611no—
225#106—611no—
226C4⋊C8—611no—
227C4⋊C8—611no—
228#103—611no—
229#103—611no—
230#102—611no—
231#102—611no—
232#102—611no—
233#102—611no—
234#102—611no—
235#102—611no—
236C22⋊C8—611no—
237C22⋊C8—611no—
238#97—611no—
239C4×C8—611no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D6111yescharacteristic
243C2×D4—21no—
244C2×D4—611no—
245C2×D4—611no—
246C2×D4—1221no—
247C2×D4—1221no—
248C2×D4—1221no—
249C2×D4—1221no—
250C2×D4C22×D6111yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4C22×D6111yescharacteristic
258SD16—1222no—
259SD16—1222no—
260D8—1222no—
261D8—1222no—
262C2×C8—611no—
263C2×C8—611no—
264C2×C8—611no—
265C2×C8—611no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—611no—
270C4⋊C4—611no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4C22⋊D6111yescharacteristic
274C4⋊C4C22⋊D6111yescharacteristic
275C4⋊C4C22×D6111yescharacteristic
276C4⋊C4C22×D6111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4C22⋊D6111yescharacteristic
284C22⋊C4C22⋊D6111yescharacteristic
285C42—21no—
286C42—21no—
287C42C22×D6111yescharacteristic
288C42C22×D6111yescharacteristic
289C23—21no—
290C23—1221no—
291C23—1221no—
292C23C2×C22⋊D6111yescharacteristic
293Q8—21no—
294Q8#1175822212yes—
295D4—24no—
296D4—21no—
297D4—1221no—
298D4—1221no—
299D4—1221no—
300D4—1221no—
301D4—4881no—
302D4—4881no—
303D4—4881no—
304D4—4881no—
305D4#1175822212yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—4881no—
318C2×C4—4881no—
319C2×C4C2×C22⋊D6111yescharacteristic
320C2×C4C2×C22⋊D6111yescharacteristic
321C2×C4C2×C22⋊D6111yescharacteristic
322C2×C4C2×C22⋊D6111yescharacteristic
323C2×C4C2×C22⋊D6111yescharacteristic
324C2×C4C23×D6111yescharacteristic
325C8—1221no—
326C8—1221no—
327C8—1221no—
328C8—1221no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—2441no—
336C22—2441no—
337C22—2441no—
338C22—2441no—
339C22—2441no—
340C22—2441no—
341C22C22×C22⋊D6111yescharacteristic
342C4—21no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—2441no—
351C4—2441no—
352C4C2×#1175822211yescharacteristic
353C4C2×#1175822211yescharacteristic
354C2—41no—
355C2—42no—
356C2—4881no—
357C2—4881no—
358C2#1684027311yescharacteristic
359C2#1684056511yescharacteristic
360C2#1684057011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#520C2
socleC22×C61C22×D4
hypercenter#520D61
hypocenterC61#3119
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #16840367C2semidirect
2. #16840080C2semidirect
3. #16840075C2semidirect
4. #16840069C2semidirect
5. #16840062C2semidirect
6. #16839962C2semidirect
7. #16839957C2semidirect
8. #16839907C2semidirect
9. #16839907C2semidirect
10. #16839872C2semidirect
11. #16839860C2semidirect
12. C4×#11758201C2semidirect
13. C4×#11758199C2semidirect
14. #16839823C2semidirect
15. C61×#520C2semidirect
182. #520D61semidirect
196. C61#3119semidirect