Finite Group Databasebeta

← #21457257

Subgroups — #21457257

Order 7808.

370 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840368C211yesmaximal, characteristic, complemented
2#16840363C211yesmaximal, characteristic, complemented
3#16840065C211yesmaximal, characteristic, complemented
4#16840061C211yesmaximal, characteristic, complemented
5#16840059C211yesmaximal, characteristic, complemented
6#16840016C211yesmaximal, characteristic, complemented
7#16840014C211yesmaximal, characteristic, complemented
8#16839999C211yesmaximal, characteristic, complemented
9#16839997C211yesmaximal, characteristic, complemented
10#16839958C211yesmaximal, characteristic, complemented
11#16839957C211yesmaximal, characteristic, complemented
12#16839956C211yesmaximal, characteristic, complemented
13#16839956C211yesmaximal, characteristic, complemented
14#16839787C211yesmaximal, characteristic, complemented
15C61×#478C211yesmaximal, characteristic, complemented
16C2×D488C2211yescharacteristic
17C2×D488C2211yescharacteristic
18C2×#11758199C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22#14519774C2211yescharacteristic
23#14519773C2211yescharacteristic
24#14519768C2211yescharacteristic
25#14519762—21no—
26#14519762—21no—
27#14519760—21no—
28#14519759—21no—
29#14519752—21no—
30#14519752—21no—
31#14519752C2211yescharacteristic
32#14519752C2211yescharacteristic
33#14519752C2211yescharacteristic
34#14519751—21no—
35#14519750—21no—
36#14519748C2211yescharacteristic
37C4×D244C2211yescharacteristic
38#14519739C2211yescharacteristic
39#14519739C2211yescharacteristic
40#14519734C2211yescharacteristic
41#14519710C2211yescharacteristic
42#14519708C2211yescharacteristic
43C4⋊#92418C2211yescharacteristic
44#14519706C2211yescharacteristic
45#14519706C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519697C2211yescharacteristic
51#14519697C2211yescharacteristic
52#125×C61C2211yescharacteristic
53C4×D4×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×D4×C61C2311yescharacteristic
60C22×C4×C61—21no—
61C2×C22⋊D61—21no—
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64C2×D244—21no—
65C2×D244—21no—
66C2×D244—21no—
67C2×D244—21no—
68C2×D244—21no—
69C2×D244C2311yescharacteristic
70C2×D244C2311yescharacteristic
71C2×D244C2311yescharacteristic
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61C2311yescharacteristic
76C2×C8×C61C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61C2311yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C42×C61C2311yescharacteristic
85C22⋊Dic61—21no—
86#11758199—41no—
87#11758199—41no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198D411yescharacteristic
95#11758198D411yescharacteristic
96C4⋊Dic61—21no—
97C4⋊Dic61C2311yescharacteristic
98#11758196—21no—
99#11758196D411yescharacteristic
100#11758196D411yescharacteristic
101C4×Dic61C2311yescharacteristic
102C2×#92418C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104D488—41no—
105D488—41no—
106#11758189—41no—
107C8×D61—41no—
108C23×C61—21no—
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—21no—
112C22×D61C2×D411yescharacteristic
113D4×C61—21no—
114D4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—81no—
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2×D411yescharacteristic
121C2×C4×C61C2411yescharacteristic
122C22⋊D61—81no—
123C22⋊D61—81no—
124C22⋊D61—81no—
125C2×Dic61—21no—
126C2×Dic61C2×D411yescharacteristic
127C2×Dic61C2×D411yescharacteristic
128C2×Dic61C2×D411yescharacteristic
129D244—21no—
130D244—21no—
131D244—21no—
132D244—21no—
133D244—21no—
134D244—21no—
135D244—81no—
136D244—81no—
137D244—81no—
138D244—81no—
139D244—81no—
140C4×D61—21no—
141C4×D61—21no—
142C4×D61—81no—
143C4×D61—81no—
144C4×D61—81no—
145C8×C61—21no—
146C8×C61—21no—
147#92418—21no—
148#92418—21no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61C22×D411yescharacteristic
153C2×D61—21no—
154C2×D61—21no—
155C2×D61—21no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61H(5,𝔽2)11yescharacteristic
171C4×C612−1+411yescharacteristic
172Dic61—21no—
173Dic61—21no—
174Dic61—21no—
175Dic61—41no—
176#3259—611nomaximal, Sylow
177C2×C61—81no—
178C2×C61#53711yescharacteristic
179C2×C61#57611yescharacteristic
180C2×C61#57611yescharacteristic
181D61—41no—
182D61—81no—
183D61—81no—
184D61—81no—
185#540—611no—
186#540—611no—
187#478—611no—
188#478—611no—
189#478—611no—
190#478D6111yescharacteristic, complemented
191#469—611no—
192#469—611no—
193#466—611no—
194#466—611no—
195#459—611no—
196#459—611no—
197#459—611no—
198#459—611no—
199#424—611no—
200C61#325911yescharacteristic, complemented, Sylow
201C2×D8—611no—
202C2×D8—611no—
203C2×D8—611no—
204C2×D8—611no—
205C2×M16—611no—
206C22×C8—611no—
207#127—611no—
208#127—611no—
209#125—611no—
210#125C2×D6111yescharacteristic
211#123—1221no—
212#123—1221no—
213#123—1221no—
214#123—1221no—
215#121—611no—
216#121—611no—
217#121—611no—
218#121—611no—
219#121—1221no—
220#121—1221no—
221#121—1221no—
222#121—1221no—
223C4×D4—611no—
224C4×D4—611no—
225C4×D4—611no—
226C4×D4C2×D6111yescharacteristic
227#117—611no—
228#107—611no—
229#107C2×D6111yescharacteristic
230#106—611no—
231#106C2×D6111yescharacteristic
232C4⋊C8—611no—
233C4⋊C8—611no—
234C4⋊C8—611no—
235C4⋊C8C2×D6111yescharacteristic
236#102—611no—
237#102—611no—
238#102—611no—
239#102—611no—
240#102—611no—
241#102—611no—
242#102C2×D6111yescharacteristic
243#102C2×D6111yescharacteristic
244C2×D4—611no—
245C2×D4—611no—
246C2×D4—611no—
247C2×D4—1221no—
248C2×D4—1221no—
249C2×D4—1221no—
250C2×D4—1221no—
251C2×D4—1221no—
252C2×D4—1221no—
253C2×D4—1221no—
254C2×D4—1221no—
255C2×D4C22×D6111yescharacteristic
256C22×C4—21no—
257C22×C4—611no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261D8—2441no—
262D8—2441no—
263D8—2441no—
264D8—2441no—
265M16—2441no—
266C2×C8—611no—
267C2×C8—611no—
268C2×C8—2441no—
269C2×C8C22×D6111yescharacteristic
270C2×C8C22×D6111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—611no—
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4C22×D6111yescharacteristic
279C4⋊C4C22×D6111yescharacteristic
280C4⋊C4C22×D6111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—611no—
283C22⋊C4—611no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C42—611no—
292C42C22×D6111yescharacteristic
293C23—21no—
294C23—611no—
295C23—1221no—
296C23—1221no—
297C23—1221no—
298D4—21no—
299D4—21no—
300D4—1221no—
301D4—1221no—
302D4—1221no—
303D4—1221no—
304D4—1221no—
305D4—1221no—
306D4—4881no—
307D4—4881no—
308D4—4881no—
309D4—4881no—
310D4—4881no—
311D4—4881no—
312D4—4881no—
313D4—4881no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—81no—
318C2×C4—611no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—4881no—
325C2×C4—4881no—
326C2×C4—4881no—
327C2×C4D4×D6111yescharacteristic
328C2×C4D4×D6111yescharacteristic
329C2×C4C23×D6111yescharacteristic
330C8—21no—
331C8—21no—
332C8—1221no—
333C8—1221no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—1221no—
338C22—1221no—
339C22—1221no—
340C22—2441no—
341C22—2441no—
342C22—2441no—
343C22—2441no—
344C22—2441no—
345C22—2441no—
346C22—2441no—
347C22—2441no—
348C22—2441no—
349C22C2×D4×D6111yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—1221no—
356C4—1221no—
357C4—1221no—
358C4—2441no—
359C4#1451982311yescharacteristic
360C4#1451982511yescharacteristic
361C2—81no—
362C2—4881no—
363C2—4881no—
364C2—4881no—
365C2—2441no—
366C2#1684034211yescharacteristic
367C2#1684056411yescharacteristic
368C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#478C2
socleC22×C61C22×D4
hypercenter#478D61
hypocenterC61#3259
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #16840368C2semidirect
2. #16840363C2semidirect
3. #16840065C2semidirect
4. #16840061C2semidirect
5. #16840059C2semidirect
6. #16840016C2semidirect
7. #16840014C2semidirect
8. #16839999C2semidirect
9. #16839997C2semidirect
10. #16839958C2semidirect
11. #16839957C2semidirect
12. #16839956C2semidirect
13. #16839956C2semidirect
14. #16839787C2semidirect
15. C61×#478C2semidirect
190. #478D61semidirect
200. C61#3259semidirect