Finite Group Databasebeta

← #21457999

Subgroups — #21457999

Order 7808.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840421C211yesmaximal, characteristic, complemented
2#16840124C211yesmaximal, characteristic, complemented
3#16840103C211yesmaximal, characteristic, complemented
4#16840086C211yesmaximal, characteristic, complemented
5#16840044C211yesmaximal, characteristic, complemented
6#16840013C211yesmaximal, characteristic, complemented
7#16839989C211yesmaximal, characteristic, complemented
8#16839977C211yesmaximal, characteristic, complemented
9#16839905C211yesmaximal, characteristic, complemented
10#16839900C211yesmaximal, characteristic, complemented
11#16839862C211yesmaximal, characteristic, complemented
12#16839834C211yesmaximal, characteristic, complemented
13#16839770C211yesmaximal, characteristic, complemented
14#16839756C211yesmaximal, characteristic, complemented
15C61×#555C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21C2×#11758194C2211yescharacteristic
22C22×#92418C2211yescharacteristic
23#14519765C2211yescharacteristic
24#14519763—21no—
25#14519756C2211yescharacteristic
26#14519755—21no—
27#14519751C2211yescharacteristic
28#14519749—21no—
29C4×Dic122C2211yescharacteristic
30#14519737—21no—
31#14519710C2211yescharacteristic
32#14519708C2211yescharacteristic
33#14519708C2211yescharacteristic
34C4⋊#92418C2211yescharacteristic
35#14519700C2211yescharacteristic
36#14519700C2211yescharacteristic
37#14519700C2211yescharacteristic
38#14519700C2211yescharacteristic
39#14519700C2211yescharacteristic
40#14519700C2211yescharacteristic
41#14519698C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44#14519697C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic
47#14519688C2211yescharacteristic
48C4⋊Q8×C61C2211yescharacteristic
49#124×C61—21no—
50#124×C61—21no—
51#121×C61—21no—
52#121×C61C2211yescharacteristic
53#121×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55C4×D4×C61C2211yescharacteristic
56#117×C61—21no—
57#117×C61C2211yescharacteristic
58#117×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×D4×C61—21no—
61C2×D4×C61—21no—
62C2×D4×C61D411yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C22×Dic61—21no—
70#11758222—22no—
71#11758222—41no—
72C2×D244C2311yescharacteristic
73C2×C4×D61—21no—
74C2×Dic122—22no—
75C2×Dic122—21no—
76C2×Dic122—41no—
77C2×Dic122C2311yescharacteristic
78C2×Dic122C2311yescharacteristic
79C4⋊C4×C61—21no—
80C4⋊C4×C61D411yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C22⋊C4×C61—21no—
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C22⋊C4×C61—21no—
88C22⋊C4×C61—21no—
89C22⋊C4×C61D411yescharacteristic
90C22⋊C4×C61D411yescharacteristic
91C42×C61—21no—
92C42×C61—21no—
93C42×C61C2311yescharacteristic
94C22⋊Dic61—21no—
95#11758200—22no—
96#11758200—41no—
97#11758199—41no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101C4⋊Dic61C2311yescharacteristic
102#11758196—21no—
103#11758196—21no—
104C4×Dic61—21no—
105#11758194—41no—
106C2×#92418—41no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C23×C61—21no—
112C23×C61C2×D411yescharacteristic
113C23×C61C2×D411yescharacteristic
114C22×D61—21no—
115Q8×C61—81no—
116D4×C61—21no—
117D4×C61—21no—
118D4×C61—41no—
119D4×C61—81no—
120D4×C61—81no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—42no—
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2411yescharacteristic
134C22⋊D61—42no—
135C22⋊D61—42no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—42no—
140D244—21no—
141D244—21no—
142C4×D61—42no—
143Dic122—21no—
144Dic122—21no—
145Dic122—21no—
146Dic122—42no—
147Dic122#4112yes—
148#92418—21no—
149#92418—21no—
150#92418—21no—
151#92418—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61C22×D411yescharacteristic
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61C2×#4111yescharacteristic
173C4×C61H(5,𝔽2)11yescharacteristic
174Dic61—22no—
175Dic61—41no—
176Dic61—41no—
177#3321—611nomaximal, Sylow
178C2×C61—41no—
179C2×C61—41no—
180C2×C61—81no—
181C2×C61#54611yescharacteristic
182C2×C61#57511yescharacteristic
183C2×C61#57711yescharacteristic
184D61—81no—
185#555D6111yescharacteristic, complemented
186#548—611no—
187#489—611no—
188#485—611no—
189#482—611no—
190#475—611no—
191#469—611no—
192#465—611no—
193#463—611no—
194#449—611no—
195#448—611no—
196#440—611no—
197#435—611no—
198#419—611no—
199#416—611no—
200C61#332111yescharacteristic, complemented, Sylow
201C2×#41—611no—
202C22×Q8—611no—
203C2×SD16—611no—
204C2×SD16—611no—
205C2×D8—611no—
206C2×M16—611no—
207C22×C8—611no—
208C4⋊Q8C2×D6111yescharacteristic
209#124—21no—
210#124—21no—
211#124—611no—
212#124—1221no—
213C22⋊Q8—611no—
214C22⋊Q8—1221no—
215#121—21no—
216#121—611no—
217#121—1221no—
218#121C2×D6111yescharacteristic
219#121C2×D6111yescharacteristic
220C4×Q8—611no—
221C4×D4—1221no—
222C4×D4C2×D6111yescharacteristic
223C4×D4C2×D6111yescharacteristic
224#117—21no—
225#117C2×D6111yescharacteristic
226#117C2×D6111yescharacteristic
227#107—611no—
228#106—611no—
229#106—611no—
230C4⋊C8—611no—
231#103—611no—
232#103—611no—
233#103—611no—
234#103—611no—
235#103—611no—
236#103—611no—
237#102—611no—
238#102—611no—
239#102—611no—
240#102—611no—
241C22⋊C8—611no—
242C22⋊C8—611no—
243#97—611no—
244#41—1222no—
245#41—2441no—
246C2×Q8—21no—
247C2×Q8—611no—
248C2×Q8—611no—
249C2×Q8—1222no—
250C2×Q8—1221no—
251C2×Q8—2441no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—611no—
255C2×D4—1221no—
256C2×D4—1221no—
257C2×D4C22⋊D6111yescharacteristic
258C2×D4C22×D6111yescharacteristic
259C22×C4—21no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4C22×D6111yescharacteristic
263C22×C4C22×D6111yescharacteristic
264SD16—1222no—
265SD16—2441no—
266D8—2441no—
267M16—2441no—
268C2×C8—611no—
269C2×C8—611no—
270C2×C8—611no—
271C2×C8—611no—
272C2×C8—2441no—
273C4⋊C4—21no—
274C4⋊C4—611no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4C22⋊D6111yescharacteristic
278C4⋊C4C22×D6111yescharacteristic
279C4⋊C4C22×D6111yescharacteristic
280C4⋊C4C22×D6111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4C22⋊D6111yescharacteristic
291C22⋊C4C22⋊D6111yescharacteristic
292C42—21no—
293C42—21no—
294C42—1221no—
295C42C22×D6111yescharacteristic
296C23—21no—
297C23—1221no—
298C23C2×C22⋊D6111yescharacteristic
299C23C2×C22⋊D6111yescharacteristic
300Q8—81no—
301Q8—612no—
302Q8—1221no—
303Q8—1221no—
304Q8—1221no—
305Q8—2442no—
306D4—21no—
307D4—21no—
308D4—41no—
309D4—81no—
310D4—81no—
311D4—1221no—
312D4—1221no—
313D4—2442no—
314D4—2442no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4C2×C22⋊D6111yescharacteristic
329C2×C4C2×C22⋊D6111yescharacteristic
330C2×C4C2×C22⋊D6111yescharacteristic
331C2×C4C2×C22⋊D6111yescharacteristic
332C2×C4C23×D6111yescharacteristic
333C8—1221no—
334C8—1221no—
335C8—1221no—
336C8—1221no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—2441no—
347C22—2441no—
348C22—2441no—
349C22C22×C22⋊D6111yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—1222no—
358C4—2441no—
359C4—2441no—
360C4#41×D6111yescharacteristic
361C4#1451982311yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—4881no—
366C2#1684040011yescharacteristic
367C2#1684056011yescharacteristic
368C2#1684057311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#555C2
socleC22×C61C22×D4
hypercenter#555D61
hypocenterC61#3321
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #16840421C2semidirect
2. #16840124C2semidirect
3. #16840103C2semidirect
4. #16840086C2semidirect
5. #16840044C2semidirect
6. #16840013C2semidirect
7. #16839989C2semidirect
8. #16839977C2semidirect
9. #16839905C2semidirect
10. #16839900C2semidirect
11. #16839862C2semidirect
12. #16839834C2semidirect
13. #16839770C2semidirect
14. #16839756C2semidirect
15. C61×#555C2semidirect
185. #555D61semidirect
200. C61#3321semidirect