Finite Group Databasebeta

← #21458886

Subgroups — #21458886

Order 7808.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840497C211yesmaximal, characteristic, complemented
2#16840484C211yesmaximal, characteristic, complemented
3#16840155C211yesmaximal, characteristic, complemented
4#16840151C211yesmaximal, characteristic
5#16840147C211yesmaximal, characteristic, complemented
6#16839987C211yesmaximal, characteristic, complemented
7#16839984C211yesmaximal, characteristic, complemented
8#16839980C211yesmaximal, characteristic, complemented
9#16839980C211yesmaximal, characteristic, complemented
10#16839966C211yesmaximal, characteristic, complemented
11#16839962C211yesmaximal, characteristic, complemented
12#16839890C211yesmaximal, characteristic, complemented
13#16839873C211yesmaximal, characteristic, complemented
14#16839849C211yesmaximal, characteristic, complemented
15C61×#441C211yesmaximal, characteristic, complemented
16C2×#11758202C2211yescharacteristic
17C2×#11758190C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21C2×#11758201C2211yescharacteristic
22C2×D488C2211yescharacteristic
23C2×D488C2211yescharacteristic
24#14519775C2211yescharacteristic
25#14519774C2211yescharacteristic
26#14519772—21no—
27#14519771—21no—
28#14519766C2211yescharacteristic
29#14519766C2211yescharacteristic
30#14519766C2211yescharacteristic
31#14519765—21no—
32#14519765C2211yescharacteristic
33#14519762—21no—
34#14519762—21no—
35#14519755—21no—
36C4×Dic122C2211yescharacteristic
37#14519742C2211yescharacteristic
38C4×D244—21no—
39#14519739C2211yescharacteristic
40#14519739C2211yescharacteristic
41#14519739C2211yescharacteristic
42#14519734—21no—
43C4⋊#92418C2211yescharacteristic
44#14519706C2211yescharacteristic
45#14519706C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×Q16×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54C4×Q8×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61C2×D244—21no—
62C2×D244—21no—
63C2×D244C2311yescharacteristic
64C2×D244C2311yescharacteristic
65C2×D244C2311yescharacteristic
66C2×C4×D61—21no—
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×Dic122D411yescharacteristic
70C2×Dic122C2311yescharacteristic
71Q16×C61—22no—
72C2×C8×C61C2311yescharacteristic
73C2×C8×C61C2311yescharacteristic
74C4⋊C4×C61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61C2311yescharacteristic
77C4⋊C4×C61C2311yescharacteristic
78C42×C61—21no—
79C42×C61—21no—
80C42×C61C2311yescharacteristic
81#11758202—41no—
82#11758201—41no—
83#11758201—41no—
84#11758201—41no—
85#11758198—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—
94#11758198—21no—
95#11758198—21no—
96C4⋊Dic61D411yescharacteristic
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196D411yescharacteristic
101#11758196D411yescharacteristic
102C4×Dic61—21no—
103C4×Dic61C2311yescharacteristic
104C4×Dic61C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107D488—22no—
108D488—41no—
109#11758190—22no—
110#11758190—41no—
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—21no—
114Q8×C61—21no—
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2411yescharacteristic
125C2×Dic61—21no—
126C2×Dic61C2×D411yescharacteristic
127C2×Dic61C2×D411yescharacteristic
128C2×Dic61C2×D411yescharacteristic
129C2×Dic61C2×D411yescharacteristic
130D244—21no—
131D244—21no—
132D244—21no—
133D244—21no—
134D244—21no—
135D244—21no—
136D244—42no—
137D244—81no—
138C4×D61—42no—
139C4×D61—81no—
140C4×D61—81no—
141Dic122—21no—
142Dic122—21no—
143Dic122—41no—
144C8×C61—21no—
145C8×C61#4112yes—
146#92418—21no—
147#92418—21no—
148C22×C61C22×D411yescharacteristic
149C2×D61—41no—
150C2×D61—41no—
151C2×D61—41no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61C2×#4111yescharacteristic
165C4×C61H(5,𝔽2)11yescharacteristic
166Dic61—21no—
167Dic61—21no—
168Dic61—21no—
169Dic61—21no—
170Dic61—41no—
171#3401—611nomaximal, Sylow
172C2×C61#55011yescharacteristic
173C2×C61#57511yescharacteristic
174C2×C61#57711yescharacteristic
175D61—81no—
176D61—81no—
177D61—81no—
178#559—611no—
179#556—611no—
180#497—611no—
181#496—611no—
182#495—611no—
183#464—611no—
184#464—611no—
185#463—611no—
186#463—611no—
187#461—611no—
188#460—611no—
189#446—611no—
190#442—611no—
191#441D6111yescharacteristic, complemented
192C4×SD16—611no—
193C61#340111yescharacteristic, complemented, Sylow
194C2×Q16—611no—
195C2×Q16C2×D6111yescharacteristic
196C2×SD16—611no—
197C2×SD16—611no—
198C2×SD16—611no—
199C2×SD16—611no—
200C2×SD16—611no—
201C2×D8—611no—
202C2×D8—611no—
203C4⋊Q8—611no—
204#127—611no—
205#126—1221no—
206#126—1221no—
207#124—611no—
208#124—611no—
209#124—611no—
210#124—611no—
211#124—1221no—
212#123—1221no—
213#123—1221no—
214C22⋊Q8—1221no—
215C4×Q8—611no—
216C4×Q8—611no—
217C4×Q8C2×D6111yescharacteristic
218C4×Q8C2×D6111yescharacteristic
219C4×D4—611no—
220C4×D4—611no—
221C4×D4—611no—
222C4×D4—1221no—
223#117—1221no—
224#106C2×D6111yescharacteristic
225C4⋊C8—611no—
226C4⋊C8—611no—
227C4⋊C8—611no—
228#103—611no—
229#103C2×D6111yescharacteristic
230#103C2×D6111yescharacteristic
231#102—611no—
232#102—611no—
233#102—611no—
234#97—611no—
235#97C2×D6111yescharacteristic
236C4×C8—611no—
237C2×Q8—611no—
238C2×Q8—611no—
239C2×Q8C22×D6111yescharacteristic
240C2×Q8C22×D6111yescharacteristic
241C2×D4—611no—
242C2×D4—611no—
243C2×D4—611no—
244C2×D4—1221no—
245C2×D4—1221no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1221no—
249Q16—22no—
250Q16—2441no—
251SD16—1222no—
252SD16—2441no—
253SD16—2441no—
254SD16—2441no—
255SD16—2441no—
256D8—1222no—
257D8—2441no—
258C2×C8—611no—
259C2×C8—611no—
260C2×C8C22×D6111yescharacteristic
261C2×C8C22×D6111yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—611no—
265C4⋊C4—611no—
266C4⋊C4—611no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—1221no—
270C4⋊C4C22×D6111yescharacteristic
271C4⋊C4C22×D6111yescharacteristic
272C22⋊C4—1221no—
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⋊C4—1221no—
283C42—21no—
284C42—21no—
285C42—611no—
286C42—611no—
287C42—1221no—
288C42C22×D6111yescharacteristic
289C23—1221no—
290C23—1221no—
291C23—1221no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—1221no—
297Q8—1221no—
298Q8—2441no—
299D4—1221no—
300D4—1221no—
301D4—1221no—
302D4—1221no—
303D4—1221no—
304D4—1221no—
305D4—4881no—
306D4—2442no—
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—4881no—
317C2×C4—4881no—
318C2×C4—2442no—
319C2×C4D4×D6111yescharacteristic
320C2×C4D4×D6111yescharacteristic
321C2×C4C23×D6111yescharacteristic
322C8—21no—
323C8—1221no—
324C8—1221no—
325C8#1175822212yes—
326C22—2441no—
327C22—2441no—
328C22—2441no—
329C22—2441no—
330C22—2441no—
331C22—2441no—
332C22—2441no—
333C22—2441no—
334C22—2441no—
335C22C2×D4×D6111yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—1221no—
343C4—1221no—
344C4—1221no—
345C4—1221no—
346C4—2441no—
347C4C2×#1175822211yescharacteristic
348C4#1451982311yescharacteristic
349C2—4881no—
350C2—4881no—
351C2—4881no—
352C2#1684043311yescharacteristic
353C2#1684056111yescharacteristic
354C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#441C2
socleC22×C61C22×D4
hypercenter#441D61
hypocenterC61#3401
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #16840497C2semidirect
2. #16840484C2semidirect
3. #16840155C2semidirect
5. #16840147C2semidirect
6. #16839987C2semidirect
7. #16839984C2semidirect
8. #16839980C2semidirect
9. #16839980C2semidirect
10. #16839966C2semidirect
11. #16839962C2semidirect
12. #16839890C2semidirect
13. #16839873C2semidirect
14. #16839849C2semidirect
15. C61×#441C2semidirect
191. #441D61semidirect
193. C61#3401semidirect