Finite Group Databasebeta

← #21457724

Subgroups — #21457724

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#16840456C211yesmaximal, characteristic, complemented
2#16840422C211yesmaximal, characteristic, complemented
3#16840118C211yesmaximal, characteristic, complemented
4#16840082C211yesmaximal, characteristic, complemented
5#16840068C211yesmaximal, characteristic, complemented
6#16839999C211yesmaximal, characteristic, complemented
7#16839993C211yesmaximal, characteristic, complemented
8#16839980C211yesmaximal, characteristic, complemented
9#16839909C211yesmaximal, characteristic, complemented
10#16839902C211yesmaximal, characteristic, complemented
11#16839849C211yesmaximal, characteristic, complemented
12#16839825C211yesmaximal, characteristic, complemented
13#16839756C211yesmaximal, characteristic, complemented
14#103×D61C211yesmaximal, characteristic, complemented
15C61×#485C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×D488C2211yescharacteristic
21C22×#92418C2211yescharacteristic
22C2×C8×D61C2211yescharacteristic
23#14519771—21no—
24#14519768C2211yescharacteristic
25#14519766C2211yescharacteristic
26#14519763—21no—
27#14519759—21no—
28#14519755—21no—
29#14519752C2211yescharacteristic
30#14519752C2211yescharacteristic
31#14519751C2211yescharacteristic
32#14519750—21no—
33#14519750—21no—
34#14519742C2211yescharacteristic
35C4×D244—21no—
36#14519739—21no—
37#14519739C2211yescharacteristic
38C4×C22⋊D61C2211yescharacteristic
39C4⋊C4×D61C2211yescharacteristic
40#14519708C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519700C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C22⋊Q8×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C2×C22⋊D61—21no—
62C2×C22⋊D61—21no—
63C2×C22⋊D61D411yescharacteristic
64Q8×D61—22no—
65Q8×D61—41no—
66#11758222—22no—
67#11758222—41no—
68C2×D244—21no—
69C2×D244—21no—
70C2×D244C2311yescharacteristic
71C2×D244C2311yescharacteristic
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61C2311yescharacteristic
77C2×Dic122—21no—
78C2×Dic122C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C4⋊C4×C61—21no—
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C42×C61—21no—
88C22⋊Dic61D411yescharacteristic
89#11758201—41no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198D411yescharacteristic
97C4⋊Dic61—21no—
98C4⋊Dic61C2311yescharacteristic
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196D411yescharacteristic
103C4×Dic61—21no—
104C4×Dic61C2311yescharacteristic
105C2×#92418—41no—
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108D488—41no—
109#11758190—22no—
110C8×D61—41no—
111C23×C61C2×D411yescharacteristic
112C22×D61—21no—
113C22×D61—21no—
114C22×D61C2×D411yescharacteristic
115Q8×C61—21no—
116Q8×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2411yescharacteristic
125C22⋊D61—22no—
126C22⋊D61—42no—
127C22⋊D61—81no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132C2×Dic61C2×D411yescharacteristic
133D244—21no—
134D244—21no—
135D244—21no—
136D244—21no—
137D244—42no—
138D244—42no—
139C4×D61—21no—
140C4×D61—21no—
141C4×D61—42no—
142C4×D61—42no—
143C4×D61—81no—
144C4×D61—81no—
145Dic122—21no—
146Dic122—42no—
147Dic122#4112yes—
148C8×C61—21no—
149C8×C61—21no—
150#92418—21no—
151#92418—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61C22×D411yescharacteristic
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61#13512yes—
165C4×C61—21no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61C2×#4111yescharacteristic
171C4×C61H(5,𝔽2)11yescharacteristic
172Dic61—22no—
173Dic61—21no—
174Dic61—21no—
175Dic61—21no—
176Dic61—41no—
177#3301—611nomaximal, Sylow
178C2×C61—41no—
179C2×C61#54611yescharacteristic
180C2×C61C2×#13511yescharacteristic
181C2×C61#57711yescharacteristic
182D61—22no—
183D61—81no—
184D61—81no—
185#553—611no—
186#548—611no—
187#488—611no—
188#485D6111yescharacteristic, complemented
189#481—611no—
190#479—611no—
191#466—611no—
192#465—611no—
193#463—611no—
194#449—611no—
195#448—611no—
196C4×SD16—611no—
197C8×D4—611no—
198#416—611no—
199C2×#103—611no—
200C61#330111yescharacteristic, complemented, Sylow
201C2×#41—611no—
202C22×Q8—611no—
203C2×SD16—611no—
204C2×SD16—611no—
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—1221no—
214C22⋊Q8C2×D6111yescharacteristic
215#121—611no—
216#121—611no—
217#121—611no—
218#121—1221no—
219#121—1221no—
220C4×Q8—611no—
221C4×D4—611no—
222C4×D4—611no—
223C4×D4—1221no—
224C4×D4—1221no—
225#117C2×D6111yescharacteristic
226C2×C4⋊C4—611no—
227#107C2×D6111yescharacteristic
228#106—611no—
229#106C2×D6111yescharacteristic
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—611no—
247C2×Q8—1221no—
248C2×Q8—1222no—
249C2×Q8—2441no—
250C2×Q8C22×D6111yescharacteristic
251C2×D4—611no—
252C2×D4—611no—
253C2×D4—611no—
254C2×D4—1221no—
255C2×D4—1221no—
256C2×D4—1221no—
257C2×D4—1221no—
258C22×C4—611no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4C22×D6111yescharacteristic
264SD16—1222no—
265SD16—2441no—
266D8—2441no—
267C2×C8—611no—
268C2×C8—611no—
269C2×C8—2441no—
270C2×C8—2441no—
271C2×C8C22×D6111yescharacteristic
272C2×C8C22×D6111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4C22×D6111yescharacteristic
281C4⋊C4C22×D6111yescharacteristic
282C4⋊C4C22×D6111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—611no—
286C22⋊C4—611no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C42—21no—
294C42—611no—
295C42—1221no—
296C23—611no—
297C23—1221no—
298C23—1221no—
299C23D4×D6111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—612no—
303Q8—1221no—
304Q8—2442no—
305D4—1222no—
306D4—1221no—
307D4—1221no—
308D4—1221no—
309D4—1221no—
310D4—4881no—
311D4—2442no—
312D4—2442no—
313D4—2442no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—611no—
321C2×C4—611no—
322C2×C4—611no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—4881no—
328C2×C4—4881no—
329C2×C4—2442no—
330C2×C4—2442no—
331C2×C4D4×D6111yescharacteristic
332C2×C4C23×D6111yescharacteristic
333C8—21no—
334C8—21no—
335C8—1221no—
336C8—1221no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—612no—
341C22—1221no—
342C22—1221no—
343C22—2441no—
344C22—2441no—
345C22—2441no—
346C22—2441no—
347C22—2441no—
348C22—2441no—
349C22C2×D4×D6111yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—1221no—
356C4—1221no—
357C4—1221no—
358C4—1222no—
359C4—2441no—
360C4#41×D6111yescharacteristic
361C4#1451982311yescharacteristic
362C2—41no—
363C2—1222no—
364C2—4881no—
365C2—4881no—
366C2#1684040411yescharacteristic
367C2#135×D6111yescharacteristic
368C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#485C2
socleC22×C61C22×D4
hypercenter#485D61
hypocenterC61#3301
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #16840456C2semidirect
2. #16840422C2semidirect
3. #16840118C2semidirect
4. #16840082C2semidirect
5. #16840068C2semidirect
6. #16839999C2semidirect
7. #16839993C2semidirect
8. #16839980C2semidirect
9. #16839909C2semidirect
10. #16839902C2semidirect
11. #16839849C2semidirect
12. #16839825C2semidirect
13. #16839756C2semidirect
14. #103×D61C2semidirect
15. C61×#485C2semidirect
188. #485D61semidirect
200. C61#3301semidirect