Finite Group Databasebeta

← #21456930

Subgroups — #21456930

Order 7808.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840383C211yesmaximal, characteristic, complemented
2#16840338C211yesmaximal, characteristic, complemented
3#16840156C211yesmaximal, characteristic, complemented
4#16840146C211yesmaximal, characteristic, complemented
5#16840122C211yesmaximal, characteristic, complemented
6#16840113C211yesmaximal, characteristic, complemented
7#16839985C211yesmaximal, characteristic, complemented
8#16839978C211yesmaximal, characteristic, complemented
9#16839973C211yesmaximal, characteristic, complemented
10#16839968C211yesmaximal, characteristic, complemented
11#16839926C211yesmaximal, characteristic, complemented
12#16839920C211yesmaximal, characteristic, complemented
13#16839909C211yesmaximal, characteristic
14#16839903C211yesmaximal, characteristic, complemented
15C61×#433C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18C2×Dic244C2211yescharacteristic
19C2×Dic244C2211yescharacteristic
20C2×Dic244C2211yescharacteristic
21C2×#11758190C2211yescharacteristic
22C2×#11758190C2211yescharacteristic
23C2×#11758190C2211yescharacteristic
24C2×#11758190C2211yescharacteristic
25C2×D488C2211yescharacteristic
26#14519777C2211yescharacteristic
27#14519777C2211yescharacteristic
28#14519777C2211yescharacteristic
29#14519772—21no—
30#14519765C2211yescharacteristic
31#14519765C2211yescharacteristic
32#14519765C2211yescharacteristic
33#14519763—21no—
34#14519761—21no—
35#14519761—21no—
36#14519759—21no—
37#14519757—21no—
38#14519757—21no—
39#14519756C2211yescharacteristic
40#14519755—21no—
41#14519751C2211yescharacteristic
42C4×Dic122C2211yescharacteristic
43C4×D244C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519702C2211yescharacteristic
46#14519702C2211yescharacteristic
47#14519702C2211yescharacteristic
48#14519702C2211yescharacteristic
49#14519702C2211yescharacteristic
50#14519699C2211yescharacteristic
51#14519699C2211yescharacteristic
52#117×C61C2211yescharacteristic
53C4⋊C8×C61C2211yescharacteristic
54C4⋊C8×C61C2211yescharacteristic
55C22⋊C8×C61C2211yescharacteristic
56C22⋊C8×C61C2211yescharacteristic
57#97×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C2×C22⋊D61—21no—
61C2×C22⋊D61—21no—
62C22×Dic61—21no—
63#11758222—41no—
64#11758222—41no—
65C2×D244C2311yescharacteristic
66C2×D244C2311yescharacteristic
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×Dic122—21no—
70C2×Dic122—21no—
71C2×Dic122—41no—
72C2×Dic122—41no—
73C2×Dic122C2311yescharacteristic
74C2×Dic122C2311yescharacteristic
75C2×Dic122C2311yescharacteristic
76C2×Dic122C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C4⋊C4×C61D411yescharacteristic
82C4⋊C4×C61D411yescharacteristic
83C22⋊C4×C61D411yescharacteristic
84C22⋊C4×C61D411yescharacteristic
85C42×C61C2311yescharacteristic
86C42×C61C2311yescharacteristic
87C22⋊Dic61—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196—21no—
105C4×Dic61—21no—
106Dic244—41no—
107Dic244—41no—
108Dic244—41no—
109D488—41no—
110#11758190—41no—
111#11758190—41no—
112#11758190—41no—
113#11758190—41no—
114C23×C61C2×D411yescharacteristic
115C22×D61—21no—
116C22×D61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61C2×D411yescharacteristic
120C2×C4×C61C2×D411yescharacteristic
121C2×C4×C61C2×D411yescharacteristic
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2411yescharacteristic
125C22⋊D61—42no—
126C22⋊D61—81no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—42no—
134D244—21no—
135D244—21no—
136D244—21no—
137D244—21no—
138C4×D61—42no—
139C4×D61—81no—
140Dic122—21no—
141Dic122—21no—
142Dic122—21no—
143Dic122—21no—
144Dic122—21no—
145Dic122—21no—
146Dic122—21no—
147Dic122—21no—
148Dic122—42no—
149Dic122—81no—
150C8×C61—21no—
151C8×C61—21no—
152C8×C61—21no—
153C8×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61C22×D411yescharacteristic
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61H(5,𝔽2)11yescharacteristic
170C4×C61H(5,𝔽2)11yescharacteristic
171Dic61—41no—
172Dic61—41no—
173Dic61—41no—
174Dic61—41no—
175Dic61—41no—
176Dic61—41no—
177#3225—611nomaximal, Sylow
178C2×C61—41no—
179C2×C61#53511yescharacteristic
180C2×C61#57711yescharacteristic
181C2×C61#57811yescharacteristic
182D61—81no—
183D61—81no—
184#542—611no—
185#536—611no—
186#497—611no—
187#495—611no—
188#489—611no—
189#487—611no—
190#464—611no—
191#463—611no—
192#462—611no—
193#461—611no—
194#452—611no—
195#451—611no—
196#449—611no—
197#448—611no—
198#433D6111yescharacteristic, complemented
199C61#322511yescharacteristic, complemented, Sylow
200C2×#41—611no—
201C22×Q8—611no—
202C2×Q16—611no—
203C2×Q16—611no—
204C2×Q16—611no—
205C2×SD16—611no—
206C2×SD16—611no—
207C2×SD16—611no—
208C2×SD16—611no—
209C2×D8—611no—
210C4⋊Q8—611no—
211C4⋊Q8—611no—
212C4⋊Q8—611no—
213#126—1221no—
214#124—611no—
215#124—611no—
216#124—611no—
217#124—1221no—
218#123—1221no—
219#123—1221no—
220#123—1221no—
221C22⋊Q8—611no—
222C22⋊Q8—1221no—
223C22⋊Q8—1221no—
224C22⋊Q8—1221no—
225#121—611no—
226C4×Q8—611no—
227C4×D4—611no—
228#117C2×D6111yescharacteristic
229C4⋊C8C2×D6111yescharacteristic
230C4⋊C8C2×D6111yescharacteristic
231#103—611no—
232#103—611no—
233#103—611no—
234#103—611no—
235#103—611no—
236#103—611no—
237#102—611no—
238#102—611no—
239C22⋊C8C2×D6111yescharacteristic
240C22⋊C8C2×D6111yescharacteristic
241#97C2×D6111yescharacteristic
242C4×C8C2×D6111yescharacteristic
243#41—2441no—
244#41—2441no—
245C2×Q8—611no—
246C2×Q8—611no—
247C2×Q8—611no—
248C2×Q8—611no—
249C2×Q8—1221no—
250C2×Q8—1221no—
251C2×Q8—2441no—
252C2×Q8—2441no—
253C2×D4—611no—
254C2×D4—611no—
255C2×D4—1221no—
256C2×D4—1221no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4C22×D6111yescharacteristic
261Q16—2441no—
262Q16—2441no—
263Q16—2441no—
264SD16—2441no—
265SD16—2441no—
266SD16—2441no—
267SD16—2441no—
268D8—2441no—
269C2×C8C22×D6111yescharacteristic
270C2×C8C22×D6111yescharacteristic
271C2×C8C22×D6111yescharacteristic
272C2×C8C22×D6111yescharacteristic
273C4⋊C4—611no—
274C4⋊C4—611no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4D24411yescharacteristic
283C4⋊C4D24411yescharacteristic
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4D24411yescharacteristic
294C22⋊C4D24411yescharacteristic
295C42—1221no—
296C42C22×D6111yescharacteristic
297C42C22×D6111yescharacteristic
298C23—1221no—
299C23—1221no—
300C23C2×D24411yescharacteristic
301Q8—1221no—
302Q8—1221no—
303Q8—1221no—
304Q8—1221no—
305Q8—1221no—
306Q8—1221no—
307Q8—1221no—
308Q8—1221no—
309Q8—4881no—
310Q8—2442no—
311D4—1221no—
312D4—1221no—
313D4—1221no—
314D4—1221no—
315D4—4881no—
316D4—2442no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—4881no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4C2×D24411yescharacteristic
329C2×C4C2×D24411yescharacteristic
330C2×C4C2×D24411yescharacteristic
331C2×C4C2×D24411yescharacteristic
332C2×C4C2×D24411yescharacteristic
333C2×C4C23×D6111yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—2441no—
342C22—2441no—
343C22—2441no—
344C22—2441no—
345C22—2441no—
346C22—2441no—
347C22C22×D24411yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—2441no—
354C4—2441no—
355C4—2441no—
356C4—2441no—
357C4—2441no—
358C4—2441no—
359C4#1451982311yescharacteristic
360C4#1451982311yescharacteristic
361C2—41no—
362C2—4881no—
363C2—4881no—
364C2#1684033111yescharacteristic
365C2#1684057411yescharacteristic
366C2#1684057911yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#433C2
socleC22×C61C22×D4
hypercenter#433D61
hypocenterC61#3225
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #16840383C2semidirect
2. #16840338C2semidirect
3. #16840156C2semidirect
4. #16840146C2semidirect
5. #16840122C2semidirect
6. #16840113C2semidirect
7. #16839985C2semidirect
8. #16839978C2semidirect
9. #16839973C2semidirect
10. #16839968C2semidirect
11. #16839926C2semidirect
12. #16839920C2semidirect
14. #16839903C2semidirect
15. C61×#433C2semidirect
198. #433D61semidirect
199. C61#3225semidirect