Finite Group Databasebeta

← #21458903

Subgroups — #21458903

Order 7808.

380 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#16840497C211yesmaximal, characteristic, complemented
2#16840152C211yesmaximal, characteristic, complemented
3#16840149C211yesmaximal, characteristic, complemented
4#16840144C211yesmaximal, characteristic, complemented
5#16839984C211yesmaximal, characteristic, complemented
6#16839981C211yesmaximal, characteristic, complemented
7#16839977C211yesmaximal, characteristic, complemented
8#16839974C211yesmaximal, characteristic, complemented
9#16839957C211yesmaximal, characteristic, complemented
10#16839954C211yesmaximal, characteristic, complemented
11#16839893C211yesmaximal, characteristic, complemented
12#16839862C211yesmaximal, characteristic, complemented
13#16839860C211yesmaximal, characteristic, complemented
14C4×#11758199C211yesmaximal, characteristic, complemented
15C61×#559C211yesmaximal, characteristic, complemented
16C2×#11758202C2211yescharacteristic
17C2×#11758200C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21C2×#11758199C2211yescharacteristic
22C2×#11758199C2211yescharacteristic
23C2×#11758199C2211yescharacteristic
24C2×#11758199C2211yescharacteristic
25#14519774C2211yescharacteristic
26#14519766—21no—
27#14519765C2211yescharacteristic
28#14519765C2211yescharacteristic
29#14519762—21no—
30#14519762—21no—
31C4×Dic122C2211yescharacteristic
32C4×D244C2211yescharacteristic
33C4×D244C2211yescharacteristic
34#14519739—21no—
35#14519710C2211yescharacteristic
36C4⋊#92418C2211yescharacteristic
37C4⋊#92418C2211yescharacteristic
38C4⋊#92418C2211yescharacteristic
39#14519701C2211yescharacteristic
40#14519700C2211yescharacteristic
41#14519698C2211yescharacteristic
42#14519698C2211yescharacteristic
43#14519697C2211yescharacteristic
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×D244—21no—
68C2×D244—21no—
69C2×D244C2311yescharacteristic
70C2×D244C2311yescharacteristic
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×Dic122C2311yescharacteristic
74C4⋊C4×C61—21no—
75C4⋊C4×C61D411yescharacteristic
76C4⋊C4×C61D411yescharacteristic
77C4⋊C4×C61D411yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C22⋊C4×C61—21no—
80C22⋊C4×C61—21no—
81C22⋊C4×C61—21no—
82C22⋊C4×C61—21no—
83C22⋊C4×C61—21no—
84C22⋊C4×C61—21no—
85C42×C61—21no—
86C42×C61C2311yescharacteristic
87C42×C61C2311yescharacteristic
88C42×C61C2311yescharacteristic
89#11758202—41no—
90#11758201—22no—
91#11758201—41no—
92#11758200—22no—
93#11758200—41no—
94#11758199—22no—
95#11758199—41no—
96#11758199—41no—
97#11758199—41no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104C4⋊Dic61C2311yescharacteristic
105#11758196—21no—
106C4×Dic61—21no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C23×C61—21no—
112C23×C61—21no—
113C22×D61—21no—
114C22×D61—21no—
115Q8×C61—21no—
116Q8×C61—21no—
117Q8×C61—41no—
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—21no—
121D4×C61—21no—
122D4×C61—42no—
123D4×C61—81no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—81no—
127C2×C4×C61—81no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2411yescharacteristic
135C2×Dic61—21no—
136C2×Dic61—21no—
137D244—21no—
138D244—21no—
139D244—21no—
140D244—21no—
141D244—42no—
142D244—81no—
143C4×D61—81no—
144C4×D61—81no—
145Dic122—21no—
146Dic122—21no—
147#92418—21no—
148#92418—21no—
149#92418—21no—
150#92418#4112yes—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
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×C61—21no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61C2×#4111yescharacteristic
173C4×C61H(5,𝔽2)11yescharacteristic
174Dic61—41no—
175Dic61—41no—
176#3403—611nomaximal, Sylow
177C2×C61—81no—
178C2×C61—81no—
179C2×C61#55011yescharacteristic
180C2×C61#57511yescharacteristic
181C2×C61#57611yescharacteristic
182D61—81no—
183D61—81no—
184#559—611no—
185#559D6111yescharacteristic, complemented
186#496—611no—
187#496—611no—
188#495—611no—
189#464—611no—
190#464—611no—
191#463—611no—
192#463—611no—
193#459—611no—
194#459—611no—
195#446—611no—
196#440—611no—
197#440—611no—
198C4×D8—611no—
199C61#340311yescharacteristic, complemented, Sylow
200C2×Q16—611no—
201C2×SD16—611no—
202C2×SD16—611no—
203C2×SD16—611no—
204C2×SD16—611no—
205C2×D8—611no—
206C2×D8—611no—
207C2×D8—611no—
208C2×D8—611no—
209#127—611no—
210#127C2×D6111yescharacteristic
211#124—21no—
212#124—611no—
213#124—611no—
214#124—1221no—
215#124C2×D6111yescharacteristic
216#124C2×D6111yescharacteristic
217#123—21no—
218#123—21no—
219#123—1221no—
220#123—1221no—
221C4×Q8—611no—
222C4×Q8C2×D6111yescharacteristic
223C4×Q8C2×D6111yescharacteristic
224C4×D4—21no—
225C4×D4—611no—
226C4×D4—611no—
227C4×D4—1221no—
228C4×D4C2×D6111yescharacteristic
229C4×D4C2×D6111yescharacteristic
230#107—611no—
231C4⋊C8—611no—
232C4⋊C8—611no—
233C4⋊C8—611no—
234#103—611no—
235#103—611no—
236#102—611no—
237#102—611no—
238#102—611no—
239#102—611no—
240#97—611no—
241#97—611no—
242C4×C8—611no—
243C2×Q8—611no—
244C2×Q8C22⋊D6111yescharacteristic
245C2×Q8C22×D6111yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—611no—
249C2×D4—611no—
250C2×D4—1221no—
251C2×D4—1221no—
252C2×D4C22×D6111yescharacteristic
253C2×D4C22×D6111yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—1221no—
257C22×C4—1221no—
258Q16—2441no—
259SD16—1222no—
260SD16—1222no—
261SD16—2441no—
262SD16—2441no—
263D8—1222no—
264D8—2441no—
265D8—2441no—
266D8—2441no—
267C2×C8—611no—
268C2×C8—611no—
269C2×C8—611no—
270C2×C8—611no—
271C4⋊C4—21no—
272C4⋊C4—611no—
273C4⋊C4—1221no—
274C4⋊C4C22⋊D6111yescharacteristic
275C4⋊C4C22⋊D6111yescharacteristic
276C4⋊C4C22⋊D6111yescharacteristic
277C4⋊C4C22×D6111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C42—21no—
291C42—1221no—
292C42C22×D6111yescharacteristic
293C42C22×D6111yescharacteristic
294C42C22×D6111yescharacteristic
295C23—21no—
296C23—21no—
297C23—1221no—
298C23—1221no—
299Q8—21no—
300Q8—21no—
301Q8—41no—
302Q8—1221no—
303Q8—1221no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—1221no—
311D4—1221no—
312D4—1221no—
313D4—1221no—
314D4—4881no—
315D4—2442no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—4881no—
323C2×C4—4881no—
324C2×C4C2×C22⋊D6111yescharacteristic
325C2×C4C2×C22⋊D6111yescharacteristic
326C2×C4C2×C22⋊D6111yescharacteristic
327C2×C4C2×C22⋊D6111yescharacteristic
328C2×C4C2×C22⋊D6111yescharacteristic
329C2×C4C2×C22⋊D6111yescharacteristic
330C2×C4C23×D6111yescharacteristic
331C8—612no—
332C8—1221no—
333C8—1221no—
334C8—1221no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—2441no—
342C22—2441no—
343C22—2441no—
344C22—2441no—
345C22—2441no—
346C22—2441no—
347C22C22×C22⋊D6111yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—2441no—
357C4—2441no—
358C4#41×D6111yescharacteristic
359C4#1451982311yescharacteristic
360C2—81no—
361C2—81no—
362C2—4881no—
363C2—4881no—
364C2#1684043111yescharacteristic
365C2#1684056011yescharacteristic
366C2#1684056511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#559C2
socleC22×C61C22×D4
hypercenter#559D61
hypocenterC61#3403
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. #16840497C2semidirect
2. #16840152C2semidirect
3. #16840149C2semidirect
4. #16840144C2semidirect
5. #16839984C2semidirect
6. #16839981C2semidirect
7. #16839977C2semidirect
8. #16839974C2semidirect
9. #16839957C2semidirect
10. #16839954C2semidirect
11. #16839893C2semidirect
12. #16839862C2semidirect
13. #16839860C2semidirect
14. C4×#11758199C2semidirect
15. C61×#559C2semidirect
185. #559D61semidirect
199. C61#3403semidirect