Finite Group Databasebeta

← #21456019

Subgroups — #21456019

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#16840365C211yesmaximal, characteristic, complemented
2#16840245C211yesmaximal, characteristic, complemented
3#16840081C211yesmaximal, characteristic, complemented
4#16840073C211yesmaximal, characteristic, complemented
5#16840067C211yesmaximal, characteristic, complemented
6#16840064C211yesmaximal, characteristic, complemented
7#16839960C211yesmaximal, characteristic, complemented
8#16839955C211yesmaximal, characteristic, complemented
9#16839907C211yesmaximal, characteristic, complemented
10#16839874C211yesmaximal, characteristic, complemented
11#16839865C211yesmaximal, characteristic, complemented
12SD16×Dic61C211yesmaximal, characteristic, complemented
13#16839842C211yesmaximal, characteristic, complemented
14#16839820C211yesmaximal, characteristic, complemented
15C61×#449C211yesmaximal, characteristic, complemented
16C2×#11758201C2211yescharacteristic
17C2×#11758199C2211yescharacteristic
18#14519773C2211yescharacteristic
19#14519768C2211yescharacteristic
20#14519761—21no—
21#14519759—21no—
22#14519751C2211yescharacteristic
23#14519749—21no—
24#14519748—21no—
25Q8×Dic61C2211yescharacteristic
26Q8×Dic61C2211yescharacteristic
27D4×Dic61—21no—
28D4×Dic61—21no—
29D4×Dic61C2211yescharacteristic
30D4×Dic61C2211yescharacteristic
31D4×Dic61C2211yescharacteristic
32#14519739C2211yescharacteristic
33#14519736—21no—
34#14519736C2211yescharacteristic
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61C2211yescharacteristic
37#14519710C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519709C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×#41×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C2×D8×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59#41×C61—22no—
60#41×C61—22no—
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61—21no—
64C2×D4×C61C2311yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C2×D244C2311yescharacteristic
76C2×C4×D61—21no—
77SD16×C61—22no—
78D8×C61—22no—
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C22⋊C4×C61—21no—
83C22⋊Dic61—21no—
84C22⋊Dic61—21no—
85C22⋊Dic61—21no—
86C22⋊Dic61D411yescharacteristic
87C22⋊Dic61D411yescharacteristic
88#11758201—22no—
89#11758199—22no—
90#11758198—21no—
91#11758198—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61D411yescharacteristic
97C4⋊Dic61D411yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101#11758196—21no—
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61C2311yescharacteristic
105C4×Dic61C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C23×C61—21no—
109C23×C61—21no—
110C23×C61C2×D411yescharacteristic
111C22×D61—21no—
112Q8×C61—21no—
113Q8×C61#4112yes—
114D4×C61—24no—
115D4×C61—21no—
116D4×C61—21no—
117D4×C61—21no—
118D4×C61—81no—
119D4×C61#4112yes—
120C2×C4×C61—24no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2411yescharacteristic
127C22⋊D61—81no—
128C22⋊D61—81no—
129C22⋊D61—81no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—81no—
134C2×Dic61—81no—
135C2×Dic61—81no—
136C2×Dic61—81no—
137C2×Dic61C2×D411yescharacteristic
138C2×Dic61C2×D411yescharacteristic
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141D244—21no—
142D244—21no—
143C4×D61—81no—
144C8×C61—21no—
145C8×C61—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×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61C22×D411yescharacteristic
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C4×C61—21no—
162C4×C61—22no—
163C4×C61—41no—
164C4×C61C2×#4111yescharacteristic
165C4×C61C2×#4111yescharacteristic
166Dic61—21no—
167Dic61—21no—
168Dic61—21no—
169Dic61—21no—
170Dic61—41no—
171Dic61—41no—
172Dic61—41no—
173#3119—611nomaximal, Sylow
174C2×C61—41no—
175C2×C61—42no—
176C2×C61—81no—
177C2×C61#52511yescharacteristic
178C2×C61#57611yescharacteristic
179C2×C61#57711yescharacteristic
180D61—81no—
181#540—611no—
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#449D6111yescharacteristic, complemented
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×SD16C2×D6111yescharacteristic
200C2×D8—611no—
201C2×D8C2×D6111yescharacteristic
202#127—611no—
203#125—611no—
204#123—1221no—
205#123—1221no—
206#121—611no—
207#121—1221no—
208#121—1221no—
209#121C2×D6111yescharacteristic
210C4×Q8—611no—
211C4×Q8—611no—
212C4×D4—611no—
213C4×D4—611no—
214C4×D4—611no—
215C4×D4—611no—
216C4×D4—1221no—
217C4×D4—1221no—
218#117—611no—
219#117—1221no—
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#103C2×D6111yescharacteristic
230#102—611no—
231#102—611no—
232#102—611no—
233#102—611no—
234#102—611no—
235#102C2×D6111yescharacteristic
236C22⋊C8—611no—
237C22⋊C8C2×D6111yescharacteristic
238#97—611no—
239C4×C8—611no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D6111yescharacteristic
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—611no—
246C2×D4—1221no—
247C2×D4—1221no—
248C2×D4—1221no—
249C2×D4C22×D6111yescharacteristic
250C2×D4C22×D6111yescharacteristic
251C22×C4—21no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4C22×D6111yescharacteristic
258SD16—22no—
259SD16—1222no—
260D8—22no—
261D8—1222no—
262C2×C8—611no—
263C2×C8—611no—
264C2×C8C22×D6111yescharacteristic
265C2×C8C22×D6111yescharacteristic
266C4⋊C4—611no—
267C4⋊C4—611no—
268C4⋊C4—611no—
269C4⋊C4—611no—
270C4⋊C4—611no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4C22×D6111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—611no—
279C22⋊C4—611no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C42—611no—
286C42—611no—
287C42—1221no—
288C42—1221no—
289C23—21no—
290C23—21no—
291C23—1221no—
292C23D4×D6111yescharacteristic
293Q8—21no—
294Q8#1175822412yes—
295D4—24no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—1221no—
301D4—1221no—
302D4—4881no—
303D4—4881no—
304D4—4881no—
305D4#1175822412yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—611no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—4881no—
319C2×C4—4881no—
320C2×C4—4881no—
321C2×C4—4881no—
322C2×C4—4881no—
323C2×C4D4×D6111yescharacteristic
324C2×C4C23×D6111yescharacteristic
325C8—21no—
326C8—21no—
327C8—1221no—
328C8—1221no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—2441no—
339C22—2441no—
340C22—2441no—
341C22C2×D4×D6111yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—1221no—
346C4—1221no—
347C4—1221no—
348C4—1221no—
349C4—2441no—
350C4—2441no—
351C4—2441no—
352C4C2×#1175822411yescharacteristic
353C4C2×#1175822411yescharacteristic
354C2—41no—
355C2—42no—
356C2—81no—
357C2—4881no—
358C2#1684026811yescharacteristic
359C2#1684056611yescharacteristic
360C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#449C2
socleC22×C61C22×D4
hypercenter#449D61
hypocenterC61#3119
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #16840365C2semidirect
2. #16840245C2semidirect
3. #16840081C2semidirect
4. #16840073C2semidirect
5. #16840067C2semidirect
6. #16840064C2semidirect
7. #16839960C2semidirect
8. #16839955C2semidirect
9. #16839907C2semidirect
10. #16839874C2semidirect
11. #16839865C2semidirect
12. SD16×Dic61C2semidirect
13. #16839842C2semidirect
14. #16839820C2semidirect
15. C61×#449C2semidirect
190. #449D61semidirect
196. C61#3119semidirect