Finite Group Databasebeta

← #21458879

Subgroups — #21458879

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#16840485C211yesmaximal, characteristic, complemented
2#16840157C211yesmaximal, characteristic, complemented
3#16840149C211yesmaximal, characteristic
4#16840144C211yesmaximal, characteristic, complemented
5#16839984C211yesmaximal, characteristic, complemented
6#16839981C211yesmaximal, characteristic, complemented
7#16839977C211yesmaximal, characteristic, complemented
8#16839974C211yesmaximal, characteristic, complemented
9#16839967C211yesmaximal, characteristic, complemented
10#16839959C211yesmaximal, characteristic, complemented
11#16839893C211yesmaximal, characteristic, complemented
12#16839872C211yesmaximal, characteristic, complemented
13#16839867C211yesmaximal, characteristic, complemented
14C4×#11758200C211yesmaximal, characteristic, complemented
15C61×#559C211yesmaximal, characteristic, complemented
16C2×#11758202C2211yescharacteristic
17C2×#11758202C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758200C2211yescharacteristic
21C2×#11758200C2211yescharacteristic
22C2×#11758201C2211yescharacteristic
23C2×#11758199C2211yescharacteristic
24C2×#11758199C2211yescharacteristic
25#14519777C2211yescharacteristic
26#14519772—21no—
27#14519772—21no—
28#14519765C2211yescharacteristic
29#14519765C2211yescharacteristic
30#14519753—21no—
31C4×Dic122C2211yescharacteristic
32C4×Dic122C2211yescharacteristic
33C4×D244C2211yescharacteristic
34#14519735—21no—
35#14519708C2211yescharacteristic
36C4⋊#92418C2211yescharacteristic
37C4⋊#92418C2211yescharacteristic
38C4⋊#92418C2211yescharacteristic
39#14519701C2211yescharacteristic
40#14519700C2211yescharacteristic
41#14519700C2211yescharacteristic
42#14519698C2211yescharacteristic
43#14519698C2211yescharacteristic
44#14519697C2211yescharacteristic
45#14519688C2211yescharacteristic
46#14519688C2211yescharacteristic
47C4×#92418C2211yescharacteristic
48#127×C61C2211yescharacteristic
49#124×C61—21no—
50#124×C61C2211yescharacteristic
51#124×C61C2211yescharacteristic
52#123×C61—21no—
53#123×C61—21no—
54C4×Q8×C61C2211yescharacteristic
55C4×Q8×C61C2211yescharacteristic
56C4×D4×C61—21no—
57C4×D4×C61C2211yescharacteristic
58C4×D4×C61C2211yescharacteristic
59C2×Q8×C61D411yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61—21no—
62C2×D4×C61—21no—
63C2×D4×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
69C2×Dic122C2311yescharacteristic
70C2×Dic122C2311yescharacteristic
71C4⋊C4×C61—21no—
72C4⋊C4×C61D411yescharacteristic
73C4⋊C4×C61D411yescharacteristic
74C4⋊C4×C61D411yescharacteristic
75C4⋊C4×C61C2311yescharacteristic
76C22⋊C4×C61—21no—
77C22⋊C4×C61—21no—
78C22⋊C4×C61—21no—
79C22⋊C4×C61—21no—
80C22⋊C4×C61—21no—
81C22⋊C4×C61—21no—
82C42×C61—21no—
83C42×C61C2311yescharacteristic
84C42×C61C2311yescharacteristic
85C42×C61C2311yescharacteristic
86#11758202—22no—
87#11758202—41no—
88#11758201—41no—
89#11758200—22no—
90#11758200—41no—
91#11758200—41no—
92#11758200—41no—
93#11758199—22no—
94#11758199—41no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C23×C61—21no—
112C23×C61—21no—
113C22×D61—21no—
114Q8×C61—21no—
115Q8×C61—21no—
116Q8×C61—41no—
117D4×C61—21no—
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—21no—
121D4×C61—42no—
122D4×C61—81no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—81no—
126C2×C4×C61—81no—
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2411yescharacteristic
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137D244—21no—
138D244—21no—
139C4×D61—42no—
140Dic122—21no—
141Dic122—21no—
142Dic122—21no—
143Dic122—21no—
144#92418—21no—
145#92418—21no—
146#92418—21no—
147#92418#4112yes—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61C22×D411yescharacteristic
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61C2×#4111yescharacteristic
167C4×C61H(5,𝔽2)11yescharacteristic
168Dic61—41no—
169Dic61—41no—
170Dic61—41no—
171#3401—611nomaximal, Sylow
172C2×C61—81no—
173C2×C61—81no—
174C2×C61#55011yescharacteristic
175C2×C61#57511yescharacteristic
176C2×C61#57711yescharacteristic
177D61—81no—
178#559D6111yescharacteristic, complemented
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#441—611no—
192C4×SD16—611no—
193C61#340111yescharacteristic, complemented, Sylow
194C2×Q16—611no—
195C2×Q16—611no—
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#127C2×D6111yescharacteristic
205#126—1221no—
206#126—1221no—
207#124—21no—
208#124—611no—
209#124—611no—
210#124C2×D6111yescharacteristic
211#124C2×D6111yescharacteristic
212#123—21no—
213#123—21no—
214C22⋊Q8—1221no—
215C4×Q8—611no—
216C4×Q8—611no—
217C4×Q8C2×D6111yescharacteristic
218C4×Q8C2×D6111yescharacteristic
219C4×D4—21no—
220C4×D4—611no—
221C4×D4C2×D6111yescharacteristic
222C4×D4C2×D6111yescharacteristic
223#117—1221no—
224#106—611no—
225C4⋊C8—611no—
226C4⋊C8—611no—
227C4⋊C8—611no—
228#103—611no—
229#103—611no—
230#103—611no—
231#102—611no—
232#102—611no—
233#102—611no—
234#97—611no—
235#97—611no—
236C4×C8—611no—
237C2×Q8—611no—
238C2×Q8—611no—
239C2×Q8C22⋊D6111yescharacteristic
240C2×Q8C22×D6111yescharacteristic
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—611no—
244C2×D4C22×D6111yescharacteristic
245C2×D4C22×D6111yescharacteristic
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—1221no—
249Q16—1222no—
250Q16—2441no—
251SD16—1222no—
252SD16—2441no—
253SD16—2441no—
254SD16—2441no—
255SD16—2441no—
256D8—1222no—
257D8—2441no—
258C2×C8—611no—
259C2×C8—611no—
260C2×C8—611no—
261C2×C8—611no—
262C4⋊C4—21no—
263C4⋊C4—611no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4C22⋊D6111yescharacteristic
269C4⋊C4C22⋊D6111yescharacteristic
270C4⋊C4C22⋊D6111yescharacteristic
271C4⋊C4C22×D6111yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C42—21no—
284C42—1221no—
285C42—1221no—
286C42C22×D6111yescharacteristic
287C42C22×D6111yescharacteristic
288C42C22×D6111yescharacteristic
289C23—21no—
290C23—21no—
291C23—1221no—
292Q8—21no—
293Q8—21no—
294Q8—41no—
295Q8—1221no—
296Q8—1221no—
297Q8—1221no—
298Q8—1221no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—42no—
304D4—81no—
305D4—1221no—
306D4—1221no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—2442no—
315C2×C4C2×C22⋊D6111yescharacteristic
316C2×C4C2×C22⋊D6111yescharacteristic
317C2×C4C2×C22⋊D6111yescharacteristic
318C2×C4C2×C22⋊D6111yescharacteristic
319C2×C4C2×C22⋊D6111yescharacteristic
320C2×C4C2×C22⋊D6111yescharacteristic
321C2×C4C23×D6111yescharacteristic
322C8—612no—
323C8—1221no—
324C8—1221no—
325C8—1221no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—2441no—
333C22—2441no—
334C22—2441no—
335C22C22×C22⋊D6111yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—2441no—
345C4—2441no—
346C4—2441no—
347C4#41×D6111yescharacteristic
348C4#1451982311yescharacteristic
349C2—81no—
350C2—81no—
351C2—4881no—
352C2#1684043111yescharacteristic
353C2#1684056011yescharacteristic
354C2#1684057311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#559C2
socleC22×C61C22×D4
hypercenter#559D61
hypocenterC61#3401
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #16840485C2semidirect
2. #16840157C2semidirect
4. #16840144C2semidirect
5. #16839984C2semidirect
6. #16839981C2semidirect
7. #16839977C2semidirect
8. #16839974C2semidirect
9. #16839967C2semidirect
10. #16839959C2semidirect
11. #16839893C2semidirect
12. #16839872C2semidirect
13. #16839867C2semidirect
14. C4×#11758200C2semidirect
15. C61×#559C2semidirect
178. #559D61semidirect
193. C61#3401semidirect