Finite Group Databasebeta

← #21458120

Subgroups — #21458120

Order 7808.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840413C211yesmaximal, characteristic, complemented
2#16840411C211yesmaximal, characteristic, complemented
3#16840111C211yesmaximal, characteristic, complemented
4#16840097C211yesmaximal, characteristic, complemented
5#16840096C211yesmaximal, characteristic, complemented
6#16840040C211yesmaximal, characteristic, complemented
7#16840011C211yesmaximal, characteristic, complemented
8#16840008C211yesmaximal, characteristic, complemented
9#16839966C211yesmaximal, characteristic, complemented
10#16839908C211yesmaximal, characteristic, complemented
11#16839907C211yesmaximal, characteristic, complemented
12#16839842C211yesmaximal, characteristic, complemented
13#16839838C211yesmaximal, characteristic, complemented
14#16839760C211yesmaximal, characteristic, complemented
15C61×#417C211yesmaximal, characteristic, complemented
16C2×#11758222—21no—
17C2×#11758224C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21C2×#11758189C2211yescharacteristic
22#14519776C2211yescharacteristic
23#14519775C2211yescharacteristic
24#14519762—21no—
25#14519760—21no—
26#14519760—21no—
27#14519758—21no—
28#14519756C2211yescharacteristic
29#14519755—21no—
30#14519753C2211yescharacteristic
31#14519752C2211yescharacteristic
32#14519751C2211yescharacteristic
33#14519749—21no—
34D4×Dic61C2211yescharacteristic
35#14519739C2211yescharacteristic
36C4×C22⋊D61C2211yescharacteristic
37C2×#11758196—21no—
38C4⋊C4×D61C2211yescharacteristic
39#14519711C2211yescharacteristic
40#14519710C2211yescharacteristic
41#14519710C2211yescharacteristic
42#14519706C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519698C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×#41×C61C2211yescharacteristic
53C2×M16×C61C2211yescharacteristic
54C2×C4⋊C4×C61C2211yescharacteristic
55#103×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59#41×C61—22no—
60#41×C61—41no—
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61C2311yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72#11758224—22no—
73#11758224—41no—
74#11758222—44no—
75C2×D244—21no—
76C2×D244C2311yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61C2311yescharacteristic
80C2×Dic122—21no—
81C2×Dic122C2311yescharacteristic
82M16×C61—41no—
83C2×C8×C61C2311yescharacteristic
84C2×C8×C61C2311yescharacteristic
85C4⋊C4×C61—21no—
86C4⋊C4×C61C2311yescharacteristic
87C4⋊C4×C61C2311yescharacteristic
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61D411yescharacteristic
91#11758201—41no—
92#11758199—22no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198D411yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106#11758196D411yescharacteristic
107C4×Dic61C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110#11758190—41no—
111#11758189—41no—
112C23×C61—21no—
113C23×C61C2×D411yescharacteristic
114C22×D61—21no—
115C22×D61C2×D411yescharacteristic
116Q8×C61—21no—
117Q8×C61—21no—
118D4×C61—21no—
119D4×C61—42no—
120D4×C61#4112yescomplemented
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—42no—
127C2×C4×C61—42no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C22⋊D61—22no—
131C22⋊D61—42no—
132C22⋊D61—42no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—42no—
137C2×Dic61—42no—
138C2×Dic61C2×D411yescharacteristic
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141D244—21no—
142D244—21no—
143D244—42no—
144C4×D61—21no—
145C4×D61—21no—
146C4×D61—42no—
147C4×D61—42no—
148Dic122—21no—
149Dic122—21no—
150Dic122—42no—
151C8×C61—21no—
152C8×C61—21no—
153#92418—21no—
154#92418—21no—
155C22×C61—22no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61C22×D411yescharacteristic
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—21no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—41no—
168C4×C61—21no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61C2×#4111yescharacteristic
173C4×C61H(5,𝔽2)11yescharacteristic
174Dic61—21no—
175Dic61—21no—
176Dic61—41no—
177Dic61—41no—
178Dic61—41no—
179Dic61AGL(1,ℤ/8)12yes—
180#3330—611nomaximal, Sylow
181C2×C61—41no—
182C2×C61—42no—
183C2×C61#54611yescharacteristic
184C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
185C2×C61#57811yescharacteristic
186D61—41no—
187D61—81no—
188#547—611no—
189#547—611no—
190#487—611no—
191#484—611no—
192#484—611no—
193#474—611no—
194#468—611no—
195#468—611no—
196#461—611no—
197#449—611no—
198#449—611no—
199C4×D8—611no—
200#436—611no—
201#417—611no—
202#417D6111yescharacteristic, complemented
203C61#333011yescharacteristic, complemented, Sylow
204C2×#41—611no—
205C2×#41—1221no—
206C2×#41C2×D6111yescharacteristic
207C2×SD16—611no—
208C2×SD16—611no—
209C2×D8—611no—
210C2×M16—611no—
211C2×M16C2×D6111yescharacteristic
212C4⋊Q8—611no—
213C4⋊Q8—611no—
214#123—1221no—
215#123—1221no—
216#123—1221no—
217#123—1221no—
218C22⋊Q8—611no—
219C22⋊Q8—611no—
220C22⋊Q8—1221no—
221#121—611no—
222#121—611no—
223#121—1221no—
224C4×D4—611no—
225C4×D4—611no—
226C4×D4—611no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4C2×D6111yescharacteristic
230#107—611no—
231#107—611no—
232#107—611no—
233C4⋊C8—611no—
234#103—611no—
235#103—611no—
236#103—611no—
237#103—611no—
238#103C2×D6111yescharacteristic
239#103C2×D6111yescharacteristic
240#102—611no—
241#102—611no—
242#102C2×D6111yescharacteristic
243#102C2×D6111yescharacteristic
244C22⋊C8—611no—
245C22⋊C8—611no—
246C4×C8—611no—
247#41—22no—
248#41—41no—
249#41—1222no—
250#41—2444no—
251#41—2441no—
252C2×Q8—611no—
253C2×Q8—1221no—
254C2×Q8C22×D6111yescharacteristic
255C2×D4—21no—
256C2×D4—611no—
257C2×D4—611no—
258C2×D4—1221no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4C22×D6111yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—611no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4C22×D6111yescharacteristic
270SD16—2441no—
271SD16—2441no—
272D8—1222no—
273M16—41no—
274M16—2441no—
275C2×C8—611no—
276C2×C8—611no—
277C2×C8C22×D6111yescharacteristic
278C2×C8C22×D6111yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—611no—
281C4⋊C4—611no—
282C4⋊C4—611no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4C22×D6111yescharacteristic
290C4⋊C4C22×D6111yescharacteristic
291C22⋊C4—611no—
292C22⋊C4—611no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C42—611no—
300C23—21no—
301C23—611no—
302C23—1221no—
303C23D4×D6111yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1221no—
307Q8—1221no—
308Q8—2442no—
309D4—21no—
310D4—42no—
311D4—1222no—
312D4—1221no—
313D4—1221no—
314D4—2442no—
315D4—2442no—
316D4—2442no—
317D4#1175822212yescomplemented
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—611no—
326C2×C4—611no—
327C2×C4—611no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—2442no—
334C2×C4—2442no—
335C2×C4—2442no—
336C2×C4—2442no—
337C2×C4D4×D6111yescharacteristic
338C2×C4C23×D6111yescharacteristic
339C8—21no—
340C8—21no—
341C8—1221no—
342C8—1221no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—22no—
347C22—41no—
348C22—41no—
349C22—1221no—
350C22—1221no—
351C22—1221no—
352C22—2441no—
353C22—2441no—
354C22—2441no—
355C22C2×D4×D6111yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—612no—
361C4—1221no—
362C4—1221no—
363C4—2441no—
364C4—2441no—
365C4—2441no—
366C4C2×#1175822211yescharacteristic
367C4#1451982211yescharacteristic
368C2—41no—
369C2—42no—
370C2—4881no—
371C2—2441no—
372C2#1684040211yescharacteristic
373C2AGL(1,ℤ/8)×D6111yescharacteristic
374C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#417C2
socleC22×C61C22×D4
hypercenter#417D61
hypocenterC61#3330
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #16840413C2semidirect
2. #16840411C2semidirect
3. #16840111C2semidirect
4. #16840097C2semidirect
5. #16840096C2semidirect
6. #16840040C2semidirect
7. #16840011C2semidirect
8. #16840008C2semidirect
9. #16839966C2semidirect
10. #16839908C2semidirect
11. #16839907C2semidirect
12. #16839842C2semidirect
13. #16839838C2semidirect
14. #16839760C2semidirect
15. C61×#417C2semidirect
120. D4×C61#41semidirect
202. #417D61semidirect
203. C61#3330semidirect
317. D4#11758222semidirect