Finite Group Databasebeta

← #21458289

Subgroups — #21458289

Order 7808.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840458C211yesmaximal, characteristic, complemented
2#16840168C211yesmaximal, characteristic, complemented
3#16840083C211yesmaximal, characteristic, complemented
4#16840080C211yesmaximal, characteristic, complemented
5#16840078C211yesmaximal, characteristic, complemented
6#16840075C211yesmaximal, characteristic, complemented
7#16840062C211yesmaximal, characteristic, complemented
8#16840049C211yesmaximal, characteristic, complemented
9#16840013C211yesmaximal, characteristic, complemented
10#16839996C211yesmaximal, characteristic, complemented
11#16839872C211yesmaximal, characteristic, complemented
12#16839834C211yesmaximal, characteristic, complemented
13#16839802C211yesmaximal, characteristic, complemented
14C2×#14519708C211yesmaximal, characteristic, complemented
15C61×#547C211yesmaximal, characteristic, complemented
16C2×#11758199C2211yescharacteristic
17C2×#11758194C2211yescharacteristic
18C22×#92418C2211yescharacteristic
19#14519772—21no—
20#14519769C2211yescharacteristic
21#14519759—21no—
22#14519751C2211yescharacteristic
23#14519751C2211yescharacteristic
24#14519749—21no—
25C4×D244C2211yescharacteristic
26#14519737—21no—
27#14519736C2211yescharacteristic
28C2×C4⋊Dic61C2211yescharacteristic
29#14519710C2211yescharacteristic
30#14519710C2211yescharacteristic
31#14519710C2211yescharacteristic
32#14519708C2211yescharacteristic
33#14519708C2211yescharacteristic
34#14519708C2211yescharacteristic
35#14519708C2211yescharacteristic
36#14519708C2211yescharacteristic
37#14519708C2211yescharacteristic
38C4⋊#92418C2211yescharacteristic
39#14519698C2211yescharacteristic
40#14519698C2211yescharacteristic
41#14519698C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44#14519697C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic
47#14519688C2211yescharacteristic
48C2×#41×C61—21no—
49C4⋊Q8×C61C2211yescharacteristic
50#123×C61—21no—
51#123×C61—21no—
52C22⋊Q8×C61—21no—
53#121×C61C2211yescharacteristic
54#121×C61C2211yescharacteristic
55C4×D4×C61C2211yescharacteristic
56C4×D4×C61C2211yescharacteristic
57C2×C4⋊C4×C61C2211yescharacteristic
58C2×C4⋊C4×C61C2211yescharacteristic
59#41×C61—44no—
60C2×Q8×C61—21no—
61C2×D4×C61—21no—
62C2×D4×C61—21no—
63C2×D4×C61D411yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C2×C22⋊D61—21no—
71C2×C22⋊D61—21no—
72C22×Dic61—21no—
73C2×D244C2311yescharacteristic
74C2×C4×D61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61—21no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61D411yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C4⋊C4×C61C2311yescharacteristic
81C4⋊C4×C61C2311yescharacteristic
82C22⋊C4×C61—21no—
83C22⋊C4×C61—21no—
84C22⋊C4×C61—21no—
85C22⋊C4×C61D411yescharacteristic
86C22⋊C4×C61D411yescharacteristic
87C42×C61C2311yescharacteristic
88C22⋊Dic61—21no—
89#11758199—22no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61C2311yescharacteristic
95C4⋊Dic61C2311yescharacteristic
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99C4×Dic61—21no—
100#11758194—22no—
101C2×#92418—22no—
102C2×#92418C2311yescharacteristic
103C2×#92418C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C23×C61—21no—
107C23×C61C2×D411yescharacteristic
108C23×C61C2×D411yescharacteristic
109C22×D61—21no—
110Q8×C61—42no—
111D4×C61—22no—
112D4×C61—21no—
113D4×C61—21no—
114D4×C61—42no—
115D4×C61—42no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—42no—
124C2×C4×C61—42no—
125C2×C4×C61—42no—
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2411yescharacteristic
131C22⋊D61—42no—
132C22⋊D61—81no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—81no—
137D244—21no—
138D244—21no—
139C4×D61—81no—
140#92418—21no—
141#92418—21no—
142#92418—21no—
143#92418#4112yescomplemented
144C22×C61—21no—
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61AGL(1,ℤ/8)12yes—
153C22×C61C22×D411yescharacteristic
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—41no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61C2×#4111yescharacteristic
165C4×C612−1+411yescharacteristic
166Dic61—41no—
167Dic61—41no—
168Dic61—41no—
169#3345—611nomaximal, Sylow
170C2×C61—22no—
171C2×C61—41no—
172C2×C61—81no—
173C2×C61#54711yescharacteristic
174C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
175C2×C61#57711yescharacteristic
176D61—81no—
177#553—611no—
178#547D6111yescharacteristic, complemented
179#501—611no—
180#482—611no—
181#481—611no—
182#481—611no—
183#480—611no—
184#478—611no—
185#476—611no—
186#469—611no—
187#466—611no—
188#442—611no—
189#435—611no—
190#428—611no—
191C2×#106—611no—
192C61#334511yescharacteristic, complemented, Sylow
193C2×#41—21no—
194C2×D8—611no—
195C2×M16—611no—
196C22×C8—611no—
197C4⋊Q8C2×D6111yescharacteristic
198#126—1221no—
199#125—611no—
200#123—21no—
201#123—21no—
202#123—1221no—
203C22⋊Q8—21no—
204#121—611no—
205#121—611no—
206#121—1221no—
207#121C2×D6111yescharacteristic
208#121C2×D6111yescharacteristic
209C4×D4—611no—
210C4×D4—1221no—
211C4×D4C2×D6111yescharacteristic
212C4×D4C2×D6111yescharacteristic
213#117—611no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4C2×D6111yescharacteristic
216C2×C4⋊C4C2×D6111yescharacteristic
217#107—611no—
218#107—611no—
219#107—611no—
220#106—611no—
221#106—611no—
222#106—611no—
223#106—611no—
224#106—611no—
225#106—611no—
226C4⋊C8—611no—
227#102—611no—
228#102—611no—
229#102—611no—
230#102—611no—
231#102—611no—
232#102—611no—
233C22⋊C8—611no—
234C22⋊C8—611no—
235#97—611no—
236#41—44no—
237C2×Q8—21no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—611no—
241C2×D4—1221no—
242C2×D4—1221no—
243C2×D4C22⋊D6111yescharacteristic
244C2×D4C22×D6111yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4C22×D6111yescharacteristic
251C22×C4C22×D6111yescharacteristic
252D8—1222no—
253M16—1222no—
254C2×C8—611no—
255C2×C8—611no—
256C2×C8—611no—
257C2×C8—611no—
258C2×C8—1222no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—611no—
263C4⋊C4—611no—
264C4⋊C4—611no—
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—1221no—
276C22⋊C4—1221no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4C22⋊D6111yescharacteristic
280C22⋊C4C22⋊D6111yescharacteristic
281C42—1221no—
282C42C22×D6111yescharacteristic
283C23—21no—
284C23—1221no—
285C23C2×C22⋊D6111yescharacteristic
286C23C2×C22⋊D6111yescharacteristic
287Q8—42no—
288D4—22no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—42no—
293D4—1221no—
294D4—1221no—
295D4—4881no—
296D4—2442no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—4881no—
311C2×C4—4881no—
312C2×C4C2×C22⋊D6111yescharacteristic
313C2×C4C2×C22⋊D6111yescharacteristic
314C2×C4C2×C22⋊D6111yescharacteristic
315C2×C4C2×C22⋊D6111yescharacteristic
316C2×C4C23×D6111yescharacteristic
317C8—612no—
318C8—1221no—
319C8—1221no—
320C8—1221no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—2441no—
330C22—2441no—
331C22—2441no—
332C22#1451980312yes—
333C22C22×C22⋊D6111yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—2441no—
342C4—2441no—
343C4—2441no—
344C4#41×D6111yescharacteristic
345C4#1451982411yescharacteristic
346C2—22no—
347C2—41no—
348C2—81no—
349C2—4881no—
350C2#1684041111yescharacteristic
351C2C2×#1451980311yescharacteristic
352C2#1684057011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#547C2
socleC22×C61C22×D4
hypercenter#547D61
hypocenterC61#3345
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #16840458C2semidirect
2. #16840168C2semidirect
3. #16840083C2semidirect
4. #16840080C2semidirect
5. #16840078C2semidirect
6. #16840075C2semidirect
7. #16840062C2semidirect
8. #16840049C2semidirect
9. #16840013C2semidirect
10. #16839996C2semidirect
11. #16839872C2semidirect
12. #16839834C2semidirect
13. #16839802C2semidirect
14. C2×#14519708C2semidirect
15. C61×#547C2semidirect
143. #92418#41semidirect
178. #547D61semidirect
192. C61#3345semidirect