Finite Group Databasebeta

← #21458007

Subgroups — #21458007

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#16840477C211yesmaximal, characteristic, complemented
2#16840421C211yesmaximal, characteristic, complemented
3#16840122C211yesmaximal, characteristic, complemented
4#16840104C211yesmaximal, characteristic, complemented
5#16840087C211yesmaximal, characteristic, complemented
6#16840048C211yesmaximal, characteristic, complemented
7#16840015C211yesmaximal, characteristic, complemented
8#16839991C211yesmaximal, characteristic, complemented
9#16839978C211yesmaximal, characteristic, complemented
10#16839909C211yesmaximal, characteristic, complemented
11#16839903C211yesmaximal, characteristic, complemented
12#16839864C211yesmaximal, characteristic, complemented
13#16839772C211yesmaximal, characteristic, complemented
14#16839759C211yesmaximal, characteristic, complemented
15C61×#435C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758190C2211yescharacteristic
20C2×D488C2211yescharacteristic
21#14519777C2211yescharacteristic
22#14519765C2211yescharacteristic
23#14519763—21no—
24#14519763—21no—
25#14519763—21no—
26#14519756C2211yescharacteristic
27#14519755—21no—
28#14519751C2211yescharacteristic
29#14519751C2211yescharacteristic
30#14519751C2211yescharacteristic
31#14519749—21no—
32#14519748—21no—
33C4×Dic122C2211yescharacteristic
34C4×D244C2211yescharacteristic
35#14519737—21no—
36#14519736C2211yescharacteristic
37#14519736C2211yescharacteristic
38#14519735—21no—
39#14519711C2211yescharacteristic
40#14519709C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519702C2211yescharacteristic
46#14519702C2211yescharacteristic
47#14519702C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519699C2211yescharacteristic
50#14519699C2211yescharacteristic
51#14519699C2211yescharacteristic
52C2×M16×C61C2211yescharacteristic
53C22×C8×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55C4⋊C8×C61C2211yescharacteristic
56C22⋊C8×C61C2211yescharacteristic
57C22⋊C8×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×D4×C61D411yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C22×Dic61—21no—
67#11758222—22no—
68#11758222—41no—
69C2×D244C2311yescharacteristic
70C2×D244C2311yescharacteristic
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×Dic122—22no—
74C2×Dic122—21no—
75C2×Dic122—21no—
76C2×Dic122—41no—
77C2×Dic122C2311yescharacteristic
78C2×Dic122C2311yescharacteristic
79M16×C61—41no—
80C2×C8×C61—41no—
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C2×C8×C61C2311yescharacteristic
84C2×C8×C61C2311yescharacteristic
85C4⋊C4×C61D411yescharacteristic
86C22⋊C4×C61D411yescharacteristic
87C22⋊C4×C61D411yescharacteristic
88C42×C61C2311yescharacteristic
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98C4⋊Dic61—21no—
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108D488—41no—
109#11758190—22no—
110#11758190—41no—
111C23×C61C2×D411yescharacteristic
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115D4×C61—41no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61C2×D411yescharacteristic
121C2×C4×C61C2×D411yescharacteristic
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2411yescharacteristic
125C22⋊D61—42no—
126C22⋊D61—42no—
127C22⋊D61—81no—
128C22⋊D61—81no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—42no—
136D244—21no—
137D244—21no—
138D244—21no—
139D244—21no—
140C4×D61—42no—
141C4×D61—42no—
142Dic122—21no—
143Dic122—21no—
144Dic122—21no—
145Dic122—42no—
146Dic122—81no—
147Dic122#4112yes—
148C8×C61—21no—
149C8×C61—21no—
150C8×C61—21no—
151C8×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61C22×D411yescharacteristic
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61C2×#4111yescharacteristic
170C4×C61H(5,𝔽2)11yescharacteristic
171Dic61—22no—
172Dic61—41no—
173Dic61—41no—
174Dic61—41no—
175Dic61—41no—
176Dic61—41no—
177#3321—611nomaximal, Sylow
178C2×C61—41no—
179C2×C61—41no—
180C2×C61#54611yescharacteristic
181C2×C61#57511yescharacteristic
182C2×C61#57711yescharacteristic
183D61—81no—
184D61—81no—
185#555—611no—
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#435D6111yescharacteristic, complemented
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×M16C2×D6111yescharacteristic
207C22×C8C2×D6111yescharacteristic
208C4⋊Q8—611no—
209#124—611no—
210#124—1221no—
211#124—1221no—
212#124—1221no—
213C22⋊Q8—611no—
214C22⋊Q8—1221no—
215#121—611no—
216#121—611no—
217#121—611no—
218#121—1221no—
219#121—1221no—
220C4×Q8—611no—
221C4×D4—611no—
222C4×D4—1221no—
223C4×D4C2×D6111yescharacteristic
224#117—611no—
225#117—611no—
226#117—1221no—
227#107—611no—
228#106—611no—
229#106—611no—
230C4⋊C8C2×D6111yescharacteristic
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⋊C8C2×D6111yescharacteristic
242C22⋊C8C2×D6111yescharacteristic
243#97C2×D6111yescharacteristic
244#41—1222no—
245#41—2441no—
246C2×Q8—611no—
247C2×Q8—611no—
248C2×Q8—1222no—
249C2×Q8—1221no—
250C2×Q8—1221no—
251C2×Q8—2441no—
252C2×D4—611no—
253C2×D4—611no—
254C2×D4—1221no—
255C2×D4—1221no—
256C2×D4—1221no—
257C2×D4—1221no—
258C2×D4D24411yescharacteristic
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4C22×D6111yescharacteristic
263C22×C4C22×D6111yescharacteristic
264SD16—1222no—
265SD16—2441no—
266D8—2441no—
267M16—41no—
268C2×C8—41no—
269C2×C8C22×D6111yescharacteristic
270C2×C8C22×D6111yescharacteristic
271C2×C8C22×D6111yescharacteristic
272C2×C8C22×D6111yescharacteristic
273C4⋊C4—611no—
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—611no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—1221no—
280C4⋊C4D24411yescharacteristic
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4D24411yescharacteristic
291C22⋊C4D24411yescharacteristic
292C42—1221no—
293C42—1221no—
294C42—1221no—
295C42C22×D6111yescharacteristic
296C23—1221no—
297C23—1221no—
298C23C2×D24411yescharacteristic
299C23C2×D24411yescharacteristic
300Q8—612no—
301Q8—1221no—
302Q8—1221no—
303Q8—1221no—
304Q8—4881no—
305Q8—2442no—
306D4—41no—
307D4—1221no—
308D4—1221no—
309D4—1221no—
310D4—1221no—
311D4—4881no—
312D4—4881no—
313D4—2442no—
314D4—2442no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4C2×D24411yescharacteristic
329C2×C4C2×D24411yescharacteristic
330C2×C4C2×D24411yescharacteristic
331C2×C4C2×D24411yescharacteristic
332C2×C4C23×D6111yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—2441no—
344C22—2441no—
345C22—2441no—
346C22—2441no—
347C22—2441no—
348C22—2441no—
349C22C22×D24411yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—1222no—
355C4—2441no—
356C4—2441no—
357C4—2441no—
358C4—2441no—
359C4—2441no—
360C4#41×D6111yescharacteristic
361C4#1451982211yescharacteristic
362C2—41no—
363C2—41no—
364C2—4881no—
365C2—4881no—
366C2#1684040711yescharacteristic
367C2#1684056211yescharacteristic
368C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#435C2
socleC22×C61C22×D4
hypercenter#435D61
hypocenterC61#3321
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #16840477C2semidirect
2. #16840421C2semidirect
3. #16840122C2semidirect
4. #16840104C2semidirect
5. #16840087C2semidirect
6. #16840048C2semidirect
7. #16840015C2semidirect
8. #16839991C2semidirect
9. #16839978C2semidirect
10. #16839909C2semidirect
11. #16839903C2semidirect
12. #16839864C2semidirect
13. #16839772C2semidirect
14. #16839759C2semidirect
15. C61×#435C2semidirect
197. #435D61semidirect
200. C61#3321semidirect