Finite Group Databasebeta

← #21457812

Subgroups — #21457812

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#16840421C211yesmaximal, characteristic, complemented
2#16840416C211yesmaximal, characteristic, complemented
3#16840122C211yesmaximal, characteristic, complemented
4#16840098C211yesmaximal, characteristic, complemented
5#16840076C211yesmaximal, characteristic, complemented
6#16840058C211yesmaximal, characteristic, complemented
7#16840008C211yesmaximal, characteristic, complemented
8#16839998C211yesmaximal, characteristic, complemented
9#16839978C211yesmaximal, characteristic, complemented
10#16839909C211yesmaximal, characteristic, complemented
11#16839903C211yesmaximal, characteristic, complemented
12#16839864C211yesmaximal, characteristic, complemented
13#16839764C211yesmaximal, characteristic, complemented
14C2×#14519702C211yesmaximal, characteristic, complemented
15C61×#435C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758224—21no—
18C22×Dic122C2211yescharacteristic
19C2×#11758190C2211yescharacteristic
20C2×#11758190C2211yescharacteristic
21C2×D488C2211yescharacteristic
22#14519777C2211yescharacteristic
23#14519765C2211yescharacteristic
24#14519763—21no—
25#14519761—21no—
26#14519761—21no—
27#14519757—21no—
28#14519756C2211yescharacteristic
29#14519755—21no—
30#14519751C2211yescharacteristic
31#14519751C2211yescharacteristic
32#14519751C2211yescharacteristic
33#14519749—21no—
34C4×Dic122C2211yescharacteristic
35C4×D244C2211yescharacteristic
36#14519737—21no—
37C2×C4⋊Dic61C2211yescharacteristic
38C2×C4⋊Dic61C2211yescharacteristic
39#14519711C2211yescharacteristic
40#14519711C2211yescharacteristic
41#14519711C2211yescharacteristic
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—
67C22×Dic61—21no—
68C22×Dic61—21no—
69#11758224—44no—
70#11758222—22no—
71#11758222—41no—
72C2×D244C2311yescharacteristic
73C2×D244C2311yescharacteristic
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×Dic122—22no—
77C2×Dic122—21no—
78C2×Dic122—21no—
79C2×Dic122—41no—
80C2×Dic122C2311yescharacteristic
81C2×Dic122C2311yescharacteristic
82M16×C61—41no—
83C2×C8×C61—41no—
84C2×C8×C61C2311yescharacteristic
85C2×C8×C61C2311yescharacteristic
86C2×C8×C61C2311yescharacteristic
87C2×C8×C61C2311yescharacteristic
88C4⋊C4×C61D411yescharacteristic
89C22⋊C4×C61D411yescharacteristic
90C22⋊C4×C61D411yescharacteristic
91C42×C61C2311yescharacteristic
92C22⋊Dic61—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61C2311yescharacteristic
103C4⋊Dic61C2311yescharacteristic
104C4⋊Dic61C2311yescharacteristic
105C4⋊Dic61C2311yescharacteristic
106#11758196—21no—
107#11758196—21no—
108C4×Dic61—21no—
109D488—41no—
110#11758190—22no—
111#11758190—41no—
112C23×C61C2×D411yescharacteristic
113C23×C61C2×D411yescharacteristic
114C22×D61—21no—
115C22×D61—21no—
116D4×C61—22no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61C2×D411yescharacteristic
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2411yescharacteristic
126C22⋊D61—42no—
127C22⋊D61—42no—
128C22⋊D61—42no—
129C22⋊D61—42no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—42no—
137C2×Dic61—42no—
138C2×Dic61—42no—
139D244—21no—
140D244—21no—
141D244—21no—
142D244—21no—
143C4×D61—42no—
144C4×D61—42no—
145Dic122—21no—
146Dic122—21no—
147Dic122—21no—
148Dic122—42no—
149Dic122—42no—
150Dic122#4112yescomplemented
151C8×C61—21no—
152C8×C61—21no—
153C8×C61—21no—
154C8×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61AGL(1,ℤ/8)12yes—
161C22×C61C22×D411yescharacteristic
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—41no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61C2×#4111yescharacteristic
173C4×C61H(5,𝔽2)11yescharacteristic
174Dic61—22no—
175Dic61—41no—
176Dic61—41no—
177Dic61—41no—
178Dic61—41no—
179Dic61—41no—
180#3308—611nomaximal, Sylow
181C2×C61—22no—
182C2×C61—41no—
183C2×C61#54611yescharacteristic
184C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
185C2×C61#57811yescharacteristic
186D61—81no—
187D61—81no—
188#548—611no—
189#547—611no—
190#489—611no—
191#484—611no—
192#480—611no—
193#477—611no—
194#468—611no—
195#466—611no—
196#463—611no—
197#449—611no—
198#448—611no—
199#440—611no—
200#435D6111yescharacteristic, complemented
201#417—611no—
202C2×#103—611no—
203C61#330811yescharacteristic, complemented, Sylow
204C2×#41—611no—
205C2×#41—1221no—
206C22×Q8—611no—
207C2×SD16—611no—
208C2×SD16—611no—
209C2×D8—611no—
210C2×M16C2×D6111yescharacteristic
211C22×C8C2×D6111yescharacteristic
212C4⋊Q8—611no—
213#124—611no—
214#124—1221no—
215#123—1221no—
216#123—1221no—
217C22⋊Q8—611no—
218C22⋊Q8—1221no—
219C22⋊Q8—1221no—
220#121—611no—
221#121—611no—
222#121—611no—
223#121—1221no—
224C4×Q8—611no—
225C4×D4—611no—
226C4×D4—1221no—
227C4×D4C2×D6111yescharacteristic
228C2×C4⋊C4—611no—
229C2×C4⋊C4—611no—
230#107—611no—
231#107—611no—
232#107—611no—
233C4⋊C8C2×D6111yescharacteristic
234#103—611no—
235#103—611no—
236#103—611no—
237#103—611no—
238#103—611no—
239#103—611no—
240#102—611no—
241#102—611no—
242#102—611no—
243#102—611no—
244C22⋊C8C2×D6111yescharacteristic
245C22⋊C8C2×D6111yescharacteristic
246#97C2×D6111yescharacteristic
247#41—1222no—
248#41—2441no—
249#41—2444no—
250C2×Q8—611no—
251C2×Q8—611no—
252C2×Q8—1222no—
253C2×Q8—1221no—
254C2×Q8—1221no—
255C2×Q8—2441no—
256C2×D4—611no—
257C2×D4—611no—
258C2×D4—1221no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4D24411yescharacteristic
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4C22×D6111yescharacteristic
269C22×C4C22×D6111yescharacteristic
270SD16—1222no—
271SD16—2441no—
272D8—2441no—
273M16—41no—
274C2×C8—41no—
275C2×C8C22×D6111yescharacteristic
276C2×C8C22×D6111yescharacteristic
277C2×C8C22×D6111yescharacteristic
278C2×C8C22×D6111yescharacteristic
279C4⋊C4—611no—
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⋊C4D24411yescharacteristic
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4D24411yescharacteristic
297C22⋊C4D24411yescharacteristic
298C42—1221no—
299C42C22×D6111yescharacteristic
300C23—1221no—
301C23—1221no—
302C23C2×D24411yescharacteristic
303C23C2×D24411yescharacteristic
304Q8—612no—
305Q8—1221no—
306Q8—1221no—
307Q8—1221no—
308Q8—2442no—
309Q8—2442no—
310D4—22no—
311D4—1221no—
312D4—1221no—
313D4—1221no—
314D4—1221no—
315D4—2442no—
316D4—2442no—
317D4—2442no—
318D4—2442no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—2442no—
330C2×C4—2442no—
331C2×C4—2442no—
332C2×C4—2442no—
333C2×C4—2442no—
334C2×C4C2×D24411yescharacteristic
335C2×C4C2×D24411yescharacteristic
336C2×C4C2×D24411yescharacteristic
337C2×C4C2×D24411yescharacteristic
338C2×C4C23×D6111yescharacteristic
339C8—21no—
340C8—21no—
341C8—21no—
342C8—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—2441no—
349C22—2441no—
350C22—2441no—
351C22—2441no—
352C22—2441no—
353C22—2441no—
354C22#1451980512yes—
355C22C22×D24411yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—1222no—
361C4—2441no—
362C4—2441no—
363C4—2441no—
364C4—2441no—
365C4—2441no—
366C4#41×D6111yescharacteristic
367C4#1451982211yescharacteristic
368C2—22no—
369C2—41no—
370C2—4881no—
371C2—4881no—
372C2#1684040711yescharacteristic
373C2C2×#1451980511yescharacteristic
374C2#1684057911yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#435C2
socleC22×C61C22×D4
hypercenter#435D61
hypocenterC61#3308
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. #16840421C2semidirect
2. #16840416C2semidirect
3. #16840122C2semidirect
4. #16840098C2semidirect
5. #16840076C2semidirect
6. #16840058C2semidirect
7. #16840008C2semidirect
8. #16839998C2semidirect
9. #16839978C2semidirect
10. #16839909C2semidirect
11. #16839903C2semidirect
12. #16839864C2semidirect
13. #16839764C2semidirect
14. C2×#14519702C2semidirect
15. C61×#435C2semidirect
150. Dic122#41semidirect
200. #435D61semidirect
203. C61#3308semidirect