Finite Group Databasebeta

← #21457725

Subgroups — #21457725

Order 7808.

398 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#16840464C211yesmaximal, characteristic, complemented
2#16840423C211yesmaximal, characteristic, complemented
3#16840118C211yesmaximal, characteristic, complemented
4#16840101C211yesmaximal, characteristic, complemented
5#16840081C211yesmaximal, characteristic, complemented
6#16840067C211yesmaximal, characteristic, complemented
7#16839996C211yesmaximal, characteristic, complemented
8#16839988C211yesmaximal, characteristic, complemented
9#16839979C211yesmaximal, characteristic, complemented
10#16839906C211yesmaximal, characteristic, complemented
11SD16×Dic61C211yesmaximal, characteristic, complemented
12#16839825C211yesmaximal, characteristic, complemented
13#16839757C211yesmaximal, characteristic, complemented
14C2×#14519701C211yesmaximal, characteristic, complemented
15C61×#448C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758199C2211yescharacteristic
18C22×#92418C2211yescharacteristic
19C2×C8×D61C2211yescharacteristic
20#14519770—21no—
21#14519768C2211yescharacteristic
22#14519766—21no—
23#14519766C2211yescharacteristic
24#14519761—21no—
25#14519753—21no—
26#14519753C2211yescharacteristic
27#14519751—21no—
28#14519751C2211yescharacteristic
29#14519749—21no—
30#14519748C2211yescharacteristic
31Q8×Dic61C2211yescharacteristic
32D4×Dic61—21no—
33D4×Dic61C2211yescharacteristic
34C4×C22⋊D61—21no—
35C4×C22⋊D61C2211yescharacteristic
36#14519735C2211yescharacteristic
37C2×C4⋊Dic61C2211yescharacteristic
38#14519710C2211yescharacteristic
39#14519709C2211yescharacteristic
40#14519709C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519701C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519701C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C22×Q8×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55#121×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×Q8×C61—22no—
61C2×Q8×C61—41no—
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61—21no—
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61D411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61—21no—
73#11758226—22no—
74#11758226—41no—
75C2×D244—21no—
76C2×D244C2311yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61C2311yescharacteristic
79SD16×C61—22no—
80SD16×C61—41no—
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C22⋊C4×C61—21no—
85C22⋊Dic61—21no—
86C22⋊Dic61—21no—
87C22⋊Dic61D411yescharacteristic
88#11758199—41no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198D411yescharacteristic
95C4⋊Dic61—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101#11758196—21no—
102#11758196—21no—
103#11758196D411yescharacteristic
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61C2311yescharacteristic
107C2×#92418—41no—
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C8×D61—41no—
111C23×C61—21no—
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114C22×D61C2×D411yescharacteristic
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61—21no—
118Q8×C61—42no—
119Q8×C61#4112yes—
120D4×C61—21no—
121D4×C61—21no—
122D4×C61—42no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—42no—
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2411yescharacteristic
131C22⋊D61—22no—
132C22⋊D61—42no—
133C22⋊D61—81no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—81no—
138C2×Dic61—81no—
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141C2×Dic61C2×D411yescharacteristic
142D244—21no—
143D244—21no—
144D244—42no—
145C4×D61—21no—
146C4×D61—21no—
147C4×D61—42no—
148C8×C61—21no—
149C8×C61—21no—
150#92418—21no—
151#92418—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61#13512yes—
158C22×C61C22×D411yescharacteristic
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C4×C61—22no—
166C4×C61—21no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61C2×#4111yescharacteristic
170C4×C61H(5,𝔽2)11yescharacteristic
171Dic61—21no—
172Dic61—21no—
173Dic61—21no—
174Dic61—41no—
175Dic61—41no—
176Dic61—41no—
177#3301—611nomaximal, Sylow
178C2×C61—22no—
179C2×C61—81no—
180C2×C61#54611yescharacteristic
181C2×C61C2×#13511yescharacteristic
182C2×C61#57711yescharacteristic
183D61—41no—
184D61—81no—
185#553—611no—
186#548—611no—
187#488—611no—
188#485—611no—
189#481—611no—
190#479—611no—
191#466—611no—
192#465—611no—
193#463—611no—
194#449—611no—
195#448D6111yescharacteristic, complemented
196C4×SD16—611no—
197C8×D4—611no—
198#416—611no—
199C2×#103—611no—
200C61#330111yescharacteristic, complemented, Sylow
201C2×#41—611no—
202C22×Q8C2×D6111yescharacteristic
203C2×SD16C2×D6111yescharacteristic
204C2×SD16C2×D6111yescharacteristic
205C2×D8—611no—
206C22×C8—611no—
207C22×C8—611no—
208#126—1221no—
209#125—611no—
210#124—611no—
211#124—1221no—
212#123—1221no—
213C22⋊Q8—611no—
214C22⋊Q8—1221no—
215#121—611no—
216#121—611no—
217#121—1221no—
218#121—1221no—
219#121C2×D6111yescharacteristic
220C4×Q8—611no—
221C4×D4—611no—
222C4×D4—611no—
223C4×D4—1221no—
224C4×D4—1221no—
225#117—611no—
226C2×C4⋊C4—611no—
227#107—611no—
228#106—611no—
229#106—611no—
230C4⋊C8—611no—
231#103—611no—
232#103—611no—
233#103—611no—
234#103—611no—
235#103C2×D6111yescharacteristic
236#103C2×D6111yescharacteristic
237#102—611no—
238#102—611no—
239#102—611no—
240#102—611no—
241C22⋊C8—611no—
242C22⋊C8C2×D6111yescharacteristic
243C4×C8—611no—
244#41—1222no—
245#41—2441no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D6111yescharacteristic
250C2×Q8C22×D6111yescharacteristic
251C2×D4—21no—
252C2×D4—611no—
253C2×D4—611no—
254C2×D4—1221no—
255C2×D4—1221no—
256C2×D4—1221no—
257C2×D4C22×D6111yescharacteristic
258C22×C4—21no—
259C22×C4—611no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4C22×D6111yescharacteristic
264SD16—22no—
265SD16—41no—
266D8—2441no—
267C2×C8—611no—
268C2×C8—611no—
269C2×C8—2441no—
270C2×C8—2441no—
271C2×C8C22×D6111yescharacteristic
272C2×C8C22×D6111yescharacteristic
273C4⋊C4—611no—
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—611no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4C22×D6111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—611no—
285C22⋊C4—611no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C42—611no—
294C42—1221no—
295C42—1221no—
296C23—21no—
297C23—611no—
298C23—1221no—
299C23D4×D6111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#1175822412yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—1222no—
309D4—1221no—
310D4—1221no—
311D4—4881no—
312D4—2442no—
313D4—2442no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—611no—
321C2×C4—611no—
322C2×C4—611no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—4881no—
329C2×C4—4881no—
330C2×C4—2442no—
331C2×C4D4×D6111yescharacteristic
332C2×C4C23×D6111yescharacteristic
333C8—21no—
334C8—21no—
335C8—1221no—
336C8—1221no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—1221no—
343C22—1221no—
344C22—1221no—
345C22—2441no—
346C22—2441no—
347C22—2441no—
348C22#1451979812yes—
349C22C2×D4×D6111yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—1221no—
355C4—1221no—
356C4—1221no—
357C4—2441no—
358C4—2441no—
359C4—2441no—
360C4C2×#1175822411yescharacteristic
361C4#1451982211yescharacteristic
362C2—22no—
363C2—81no—
364C2—4881no—
365C2—2441no—
366C2#1684039911yescharacteristic
367C2C2×#1451979811yescharacteristic
368C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#448C2
socleC22×C61C22×D4
hypercenter#448D61
hypocenterC61#3301
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. #16840464C2semidirect
2. #16840423C2semidirect
3. #16840118C2semidirect
4. #16840101C2semidirect
5. #16840081C2semidirect
6. #16840067C2semidirect
7. #16839996C2semidirect
8. #16839988C2semidirect
9. #16839979C2semidirect
10. #16839906C2semidirect
11. SD16×Dic61C2semidirect
12. #16839825C2semidirect
13. #16839757C2semidirect
14. C2×#14519701C2semidirect
15. C61×#448C2semidirect
195. #448D61semidirect
200. C61#3301semidirect