Finite Group Databasebeta

← #21456012

Subgroups — #21456012

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#16840242C211yesmaximal, characteristic, complemented
2#16840078C211yesmaximal, characteristic, complemented
3#16840073C211yesmaximal, characteristic, complemented
4#16840066C211yesmaximal, characteristic, complemented
5#16840059C211yesmaximal, characteristic, complemented
6#16839959C211yesmaximal, characteristic, complemented
7#16839954C211yesmaximal, characteristic, complemented
8#16839905C211yesmaximal, characteristic, complemented
9#16839905C211yesmaximal, characteristic, complemented
10#16839872C211yesmaximal, characteristic, complemented
11#16839862C211yesmaximal, characteristic, complemented
12C4×#11758200C211yesmaximal, characteristic, complemented
13C4×#11758199C211yesmaximal, characteristic, complemented
14#16839823C211yesmaximal, characteristic, complemented
15C61×#540C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758200C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21C4×Dic122C2211yescharacteristic
22C4×Dic122C2211yescharacteristic
23C4×D244C2211yescharacteristic
24C4×D244C2211yescharacteristic
25#14519737—21no—
26#14519737—21no—
27#14519735—21no—
28C2×C4⋊Dic61C2211yescharacteristic
29C4⋊C4×D61—21no—
30#14519710C2211yescharacteristic
31#14519710C2211yescharacteristic
32#14519708C2211yescharacteristic
33#14519708C2211yescharacteristic
34C4⋊#92418C2211yescharacteristic
35C4⋊#92418C2211yescharacteristic
36#14519700C2211yescharacteristic
37#14519700C2211yescharacteristic
38#14519698C2211yescharacteristic
39#14519698C2211yescharacteristic
40#14519698C2211yescharacteristic
41#14519698C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44C22⋊#92418C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46#14519688C2211yescharacteristic
47C4×#92418C2211yescharacteristic
48#127×C61C2211yescharacteristic
49#125×C61C2211yescharacteristic
50#123×C61—21no—
51#123×C61—21no—
52#121×C61—21no—
53#121×C61—21no—
54#121×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56C4×D4×C61C2211yescharacteristic
57C4×D4×C61C2211yescharacteristic
58#117×C61C2211yescharacteristic
59C2×D4×C61—21no—
60C2×D4×C61—21no—
61C2×D4×C61—21no—
62C2×D4×C61—21no—
63C2×D4×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—21no—
69C22×Dic61—21no—
70#11758222—22no—
71#11758222—22no—
72C2×D244C2311yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×Dic122C2311yescharacteristic
77C4⋊C4×C61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61D411yescharacteristic
80C4⋊C4×C61D411yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C22⋊C4×C61—21no—
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C22⋊C4×C61D411yescharacteristic
88C22⋊C4×C61D411yescharacteristic
89C42×C61C2311yescharacteristic
90C42×C61C2311yescharacteristic
91#11758200—22no—
92#11758200—22no—
93#11758199—22no—
94#11758199—22no—
95#11758198—21no—
96#11758198—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100#11758196—21no—
101#11758196—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C23×C61—21no—
109C23×C61—21no—
110C23×C61C2×D411yescharacteristic
111C22×D61—21no—
112D4×C61—21no—
113D4×C61—21no—
114D4×C61—21no—
115D4×C61—21no—
116D4×C61—81no—
117D4×C61—81no—
118D4×C61—81no—
119D4×C61—81no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
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—24no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—81no—
137D244—21no—
138D244#4112yes—
139C4×D61—24no—
140C4×D61—81no—
141C4×D61—81no—
142Dic122—21no—
143Dic122#4112yes—
144#92418—21no—
145#92418—21no—
146#92418—21no—
147#92418—21no—
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61C22×D411yescharacteristic
158C2×D61—22no—
159C2×D61—41no—
160C2×D61—41no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61C2×#4111yescharacteristic
169C4×C61C2×#4111yescharacteristic
170Dic61—22no—
171Dic61—41no—
172Dic61—41no—
173#3119—611nomaximal, Sylow
174C2×C61—41no—
175C2×C61—81no—
176C2×C61—81no—
177C2×C61#52511yescharacteristic
178C2×C61#57611yescharacteristic
179C2×C61#57711yescharacteristic
180D61—42no—
181#540D6111yescharacteristic, complemented
182#520—611no—
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×#41—611no—
198C2×SD16—611no—
199C2×SD16—611no—
200C2×D8—611no—
201C2×D8—611no—
202#127C2×D6111yescharacteristic
203#125C2×D6111yescharacteristic
204#123—21no—
205#123—21no—
206#121—21no—
207#121—21no—
208#121C2×D6111yescharacteristic
209#121C2×D6111yescharacteristic
210C4×Q8—611no—
211C4×Q8—611no—
212C4×D4—611no—
213C4×D4—611no—
214C4×D4—1221no—
215C4×D4—1221no—
216C4×D4C2×D6111yescharacteristic
217C4×D4C2×D6111yescharacteristic
218#117—1221no—
219#117C2×D6111yescharacteristic
220C2×C4⋊C4—611no—
221C2×C4⋊C4—1221no—
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—1222no—
241#41—1222no—
242C2×Q8—611no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—611no—
248C2×D4—1221no—
249C2×D4C22×D6111yescharacteristic
250C2×D4C22×D6111yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—1221no—
254C22×C4—1221no—
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—611no—
269C4⋊C4—611no—
270C4⋊C4—1221no—
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—21no—
280C22⋊C4—21no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4C22⋊D6111yescharacteristic
284C22⋊C4C22⋊D6111yescharacteristic
285C42—1221no—
286C42—1221no—
287C42C22×D6111yescharacteristic
288C42C22×D6111yescharacteristic
289C23—21no—
290C23—21no—
291C23—1221no—
292C23C2×C22⋊D6111yescharacteristic
293Q8—612no—
294Q8—1221no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—81no—
303D4—612no—
304D4—1224no—
305D4—1221no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—1224no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—4881no—
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—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—1222no—
339C22—2441no—
340C22—2441no—
341C22C22×C22⋊D6111yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—1222no—
350C4—2441no—
351C4—2441no—
352C4#41×D6111yescharacteristic
353C4#41×D6111yescharacteristic
354C2—41no—
355C2—81no—
356C2—81no—
357C2—2442no—
358C2#1684026911yescharacteristic
359C2#1684056511yescharacteristic
360C2#1684057311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#540C2
socleC22×C61C22×D4
hypercenter#540D61
hypocenterC61#3119
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #16840242C2semidirect
2. #16840078C2semidirect
3. #16840073C2semidirect
4. #16840066C2semidirect
5. #16840059C2semidirect
6. #16839959C2semidirect
7. #16839954C2semidirect
8. #16839905C2semidirect
9. #16839905C2semidirect
10. #16839872C2semidirect
11. #16839862C2semidirect
12. C4×#11758200C2semidirect
13. C4×#11758199C2semidirect
14. #16839823C2semidirect
15. C61×#540C2semidirect
181. #540D61semidirect
196. C61#3119semidirect