Finite Group Databasebeta

← #21456502

Subgroups — #21456502

Order 7808.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840383C211yesmaximal, characteristic, complemented
2#16840367C211yesmaximal, characteristic, complemented
3#16840171C211yesmaximal, characteristic, complemented
4#16840151C211yesmaximal, characteristic, complemented
5#16840117C211yesmaximal, characteristic, complemented
6#16840109C211yesmaximal, characteristic, complemented
7#16840015C211yesmaximal, characteristic, complemented
8#16840008C211yesmaximal, characteristic, complemented
9#16839998C211yesmaximal, characteristic, complemented
10#16839991C211yesmaximal, characteristic, complemented
11#16839875C211yesmaximal, characteristic, complemented
12#16839864C211yesmaximal, characteristic, complemented
13C4×#11758190C211yesmaximal, characteristic, complemented
14C4×D488C211yesmaximal, characteristic, complemented
15C61×#405C211yesmaximal, characteristic, complemented
16C2×#11758190C2211yescharacteristic
17C2×#11758190C2211yescharacteristic
18C2×D488C2211yescharacteristic
19C2×D488C2211yescharacteristic
20#14519777C2211yescharacteristic
21#14519774C2211yescharacteristic
22#14519772—21no—
23#14519769C2211yescharacteristic
24#14519765C2211yescharacteristic
25#14519763—21no—
26#14519762—21no—
27#14519762—21no—
28#14519759—21no—
29#14519756C2211yescharacteristic
30#14519755—21no—
31#14519751C2211yescharacteristic
32#14519751C2211yescharacteristic
33#14519751C2211yescharacteristic
34#14519750—21no—
35#14519750—21no—
36C4×Dic122C2211yescharacteristic
37C4×D244C2211yescharacteristic
38C4×D244C2211yescharacteristic
39C4×D244C2211yescharacteristic
40#14519711C2211yescharacteristic
41#14519711C2211yescharacteristic
42#14519709C2211yescharacteristic
43#14519709C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519702C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519699C2211yescharacteristic
50#14519699C2211yescharacteristic
51#14519699C2211yescharacteristic
52C2×M16×C61C2211yescharacteristic
53C22×C8×C61C2211yescharacteristic
54#117×C61C2211yescharacteristic
55#97×C61C2211yescharacteristic
56#97×C61C2211yescharacteristic
57C4×C8×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C2×C22⋊D61—21no—
61C2×C22⋊D61—21no—
62C2×C22⋊D61—21no—
63C2×D244—21no—
64C2×D244—21no—
65C2×D244C2311yescharacteristic
66C2×D244C2311yescharacteristic
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×Dic122—21no—
72C2×Dic122C2311yescharacteristic
73M16×C61—22no—
74C2×C8×C61—22no—
75C2×C8×C61C2311yescharacteristic
76C2×C8×C61C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C4⋊C4×C61D411yescharacteristic
80C4⋊C4×C61D411yescharacteristic
81C22⋊C4×C61D411yescharacteristic
82C22⋊C4×C61D411yescharacteristic
83C42×C61C2311yescharacteristic
84C42×C61C2311yescharacteristic
85C22⋊Dic61—21no—
86#11758198—21no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103C4×Dic61—21no—
104D488—22no—
105D488—22no—
106#11758190—22no—
107#11758190—22no—
108C23×C61C2×D411yescharacteristic
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61C2×D411yescharacteristic
115C2×C4×C61C2×D411yescharacteristic
116C2×C4×C61C2×D411yescharacteristic
117C2×C4×C61C2×D411yescharacteristic
118C2×C4×C61C2×D411yescharacteristic
119C2×C4×C61C2411yescharacteristic
120C22⋊D61—81no—
121C22⋊D61—81no—
122C22⋊D61—81no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128D244—21no—
129D244—21no—
130D244—21no—
131D244—21no—
132D244—21no—
133D244—21no—
134D244—81no—
135D244—81no—
136C4×D61—81no—
137C4×D61—81no—
138C4×D61—81no—
139Dic122—21no—
140Dic122—21no—
141Dic122—81no—
142C8×C61—21no—
143C8×C61—21no—
144C8×C61#4112yes—
145C8×C61#4112yes—
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61C22×D411yescharacteristic
150C2×D61—41no—
151C2×D61—41no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—41no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61C2×#4111yescharacteristic
165C4×C61C2×#4111yescharacteristic
166Dic61—41no—
167Dic61—41no—
168Dic61—41no—
169Dic61—41no—
170Dic61—41no—
171#3179—611nomaximal, Sylow
172C2×C61—41no—
173C2×C61#53211yescharacteristic
174C2×C61#57611yescharacteristic
175C2×C61#57711yescharacteristic
176D61—81no—
177D61—81no—
178D61—81no—
179#542—611no—
180#540—611no—
181#501—611no—
182#496—611no—
183#488—611no—
184#486—611no—
185#469—611no—
186#468—611no—
187#466—611no—
188#465—611no—
189#442—611no—
190#440—611no—
191C4×SD16—611no—
192C4×D8—611no—
193#405D6111yescharacteristic, complemented
194C61#317911yescharacteristic, complemented, Sylow
195C2×SD16—611no—
196C2×SD16—611no—
197C2×D8—611no—
198C2×D8—611no—
199C2×M16C2×D6111yescharacteristic
200C22×C8C2×D6111yescharacteristic
201C4⋊Q8—611no—
202#127—611no—
203#126—1221no—
204#125—611no—
205#124—611no—
206#124—1221no—
207#123—1221no—
208#123—1221no—
209#123—1221no—
210C22⋊Q8—611no—
211C22⋊Q8—1221no—
212#121—611no—
213#121—611no—
214#121—611no—
215#121—1221no—
216#121—1221no—
217C4×Q8—611no—
218C4×D4—611no—
219C4×D4—611no—
220C4×D4—611no—
221#117C2×D6111yescharacteristic
222#107—611no—
223#107—611no—
224#106—611no—
225#106—611no—
226#103—611no—
227#103—611no—
228#102—611no—
229#102—611no—
230#102—611no—
231#102—611no—
232#102—611no—
233#102—611no—
234#97C2×D6111yescharacteristic
235#97C2×D6111yescharacteristic
236C4×C8C2×D6111yescharacteristic
237C4×C8C2×D6111yescharacteristic
238C2×Q8—611no—
239C2×Q8—1221no—
240C2×D4—611no—
241C2×D4—611no—
242C2×D4—611no—
243C2×D4—1221no—
244C2×D4—1221no—
245C2×D4—1221no—
246C2×D4—1221no—
247C2×D4—1221no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4C22×D6111yescharacteristic
252SD16—1222no—
253SD16—1222no—
254D8—1222no—
255D8—1222no—
256M16—22no—
257C2×C8—22no—
258C2×C8C22×D6111yescharacteristic
259C2×C8C22×D6111yescharacteristic
260C2×C8C22×D6111yescharacteristic
261C2×C8C22×D6111yescharacteristic
262C4⋊C4—611no—
263C4⋊C4—611no—
264C4⋊C4—611no—
265C4⋊C4—611no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4D24411yescharacteristic
272C4⋊C4D24411yescharacteristic
273C22⋊C4—1221no—
274C22⋊C4—1221no—
275C22⋊C4—1221no—
276C22⋊C4—1221no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4D24411yescharacteristic
283C22⋊C4D24411yescharacteristic
284C42—1221no—
285C42C22×D6111yescharacteristic
286C42C22×D6111yescharacteristic
287C23—1221no—
288C23—1221no—
289C23—1221no—
290C23C2×D24411yescharacteristic
291Q8—1221no—
292Q8—1221no—
293Q8—4881no—
294D4—1221no—
295D4—1221no—
296D4—1221no—
297D4—1221no—
298D4—1221no—
299D4—1221no—
300D4—4881no—
301D4—4881no—
302D4—4881no—
303D4—4881no—
304D4—4881no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—4881no—
313C2×C4—4881no—
314C2×C4—4881no—
315C2×C4C2×D24411yescharacteristic
316C2×C4C2×D24411yescharacteristic
317C2×C4C2×D24411yescharacteristic
318C2×C4C2×D24411yescharacteristic
319C2×C4C2×D24411yescharacteristic
320C2×C4C23×D6111yescharacteristic
321C8—21no—
322C8—21no—
323C8#1175822212yes—
324C8#1175822212yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—2441no—
329C22—2441no—
330C22—2441no—
331C22—2441no—
332C22—2441no—
333C22—2441no—
334C22—2441no—
335C22—2441no—
336C22—2441no—
337C22C22×D24411yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—2441no—
344C4—2441no—
345C4—2441no—
346C4—2441no—
347C4—2441no—
348C4C2×#1175822211yescharacteristic
349C4C2×#1175822211yescharacteristic
350C2—41no—
351C2—4881no—
352C2—4881no—
353C2—4881no—
354C2#1684031211yescharacteristic
355C2#1684056711yescharacteristic
356C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#405C2
socleC22×C61C22×D4
hypercenter#405D61
hypocenterC61#3179
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #405

Complements

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

NH ≅ G/Ntype
1. #16840383C2semidirect
2. #16840367C2semidirect
3. #16840171C2semidirect
4. #16840151C2semidirect
5. #16840117C2semidirect
6. #16840109C2semidirect
7. #16840015C2semidirect
8. #16840008C2semidirect
9. #16839998C2semidirect
10. #16839991C2semidirect
11. #16839875C2semidirect
12. #16839864C2semidirect
13. C4×#11758190C2semidirect
14. C4×D488C2semidirect
15. C61×#405C2semidirect
193. #405D61semidirect
194. C61#3179semidirect