Finite Group Databasebeta

← #21457827

Subgroups — #21457827

Order 7808.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840458C211yesmaximal, characteristic, complemented
2#16840433C211yesmaximal, characteristic, complemented
3#16840127C211yesmaximal, characteristic, complemented
4#16840087C211yesmaximal, characteristic, complemented
5#16840076C211yesmaximal, characteristic, complemented
6#16840070C211yesmaximal, characteristic, complemented
7#16840015C211yesmaximal, characteristic, complemented
8#16839998C211yesmaximal, characteristic, complemented
9#16839958C211yesmaximal, characteristic, complemented
10#16839909C211yesmaximal, characteristic, complemented
11#16839909C211yesmaximal, characteristic, complemented
12#16839864C211yesmaximal, characteristic, complemented
13#16839764C211yesmaximal, characteristic, complemented
14#16839759C211yesmaximal, characteristic, complemented
15C61×#435C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×D488C2211yescharacteristic
20C2×D488C2211yescharacteristic
21#14519774C2211yescharacteristic
22#14519773—21no—
23#14519772—21no—
24#14519769C2211yescharacteristic
25#14519759—21no—
26#14519751C2211yescharacteristic
27#14519751C2211yescharacteristic
28#14519751C2211yescharacteristic
29#14519751C2211yescharacteristic
30#14519750—21no—
31#14519750—21no—
32#14519749—21no—
33C4×Dic122C2211yescharacteristic
34C4×D244C2211yescharacteristic
35#14519739—21no—
36#14519737—21no—
37#14519736C2211yescharacteristic
38C2×C4⋊Dic61C2211yescharacteristic
39#14519711C2211yescharacteristic
40#14519711C2211yescharacteristic
41#14519709C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519702C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
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—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C22×Dic61—21no—
69#11758222—22no—
70#11758222—22no—
71#11758222—41no—
72#11758222—41no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244C2311yescharacteristic
76C2×D244C2311yescharacteristic
77C2×D244C2311yescharacteristic
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
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—
98C4⋊Dic61—21no—
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108D488—41no—
109D488—41no—
110#11758190—22no—
111C23×C61C2×D411yescharacteristic
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116D4×C61—41no—
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—81no—
130C22⋊D61—81no—
131C22⋊D61—81no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—81no—
138D244—21no—
139D244—21no—
140D244—21no—
141D244—21no—
142D244—21no—
143D244—21no—
144D244—42no—
145D244—81no—
146C4×D61—42no—
147C4×D61—42no—
148C4×D61—81no—
149Dic122—21no—
150Dic122#4112yes—
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×C61—21no—
161C22×C61C22×D411yescharacteristic
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61C2×#4111yescharacteristic
176C4×C61H(5,𝔽2)11yescharacteristic
177Dic61—22no—
178Dic61—41no—
179Dic61—41no—
180Dic61—41no—
181Dic61—41no—
182#3309—611nomaximal, Sylow
183C2×C61—41no—
184C2×C61—41no—
185C2×C61#54611yescharacteristic
186C2×C61#57511yescharacteristic
187C2×C61#57611yescharacteristic
188D61—81no—
189D61—81no—
190D61—81no—
191#553—611no—
192#550—611no—
193#490—611no—
194#482—611no—
195#480—611no—
196#479—611no—
197#469—611no—
198#466—611no—
199#459—611no—
200#449—611no—
201#449—611no—
202#440—611no—
203#435D6111yescharacteristic, complemented
204#417—611no—
205#416—611no—
206C61#330911yescharacteristic, complemented, Sylow
207C2×#41—611no—
208C2×#41—611no—
209C2×SD16—611no—
210C2×D8—611no—
211C2×D8—611no—
212C2×M16C2×D6111yescharacteristic
213C22×C8C2×D6111yescharacteristic
214#127—611no—
215#127—1221no—
216#126—1221no—
217#125—611no—
218#123—1221no—
219#121—611no—
220#121—611no—
221#121—611no—
222#121—611no—
223#121—1221no—
224#121—1221no—
225#121—1221no—
226C4×Q8—611no—
227C4×D4—611no—
228C4×D4—1221no—
229C4×D4—1221no—
230C4×D4C2×D6111yescharacteristic
231#117—611no—
232C2×C4⋊C4—611no—
233#107—611no—
234#107—611no—
235#106—611no—
236C4⋊C8C2×D6111yescharacteristic
237#103—611no—
238#103—611no—
239#103—611no—
240#102—611no—
241#102—611no—
242#102—611no—
243#102—611no—
244#102—611no—
245#102—611no—
246#102—611no—
247C22⋊C8C2×D6111yescharacteristic
248C22⋊C8C2×D6111yescharacteristic
249#97C2×D6111yescharacteristic
250#41—1222no—
251#41—1222no—
252#41—2441no—
253#41—2441no—
254C2×Q8—611no—
255C2×D4—611no—
256C2×D4—611no—
257C2×D4—611no—
258C2×D4—1221no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4—1221no—
265C2×D4—1221no—
266C2×D4D24411yescharacteristic
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4C22×D6111yescharacteristic
272C22×C4C22×D6111yescharacteristic
273SD16—1222no—
274D8—2441no—
275D8—2441no—
276M16—41no—
277C2×C8—41no—
278C2×C8C22×D6111yescharacteristic
279C2×C8C22×D6111yescharacteristic
280C2×C8C22×D6111yescharacteristic
281C2×C8C22×D6111yescharacteristic
282C4⋊C4—611no—
283C4⋊C4—611no—
284C4⋊C4—611no—
285C4⋊C4—611no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C4⋊C4D24411yescharacteristic
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4D24411yescharacteristic
298C22⋊C4D24411yescharacteristic
299C42—1221no—
300C42—1221no—
301C42C22×D6111yescharacteristic
302C23—1221no—
303C23—1221no—
304C23—1221no—
305C23C2×D24411yescharacteristic
306C23C2×D24411yescharacteristic
307Q8—612no—
308Q8—1221no—
309D4—41no—
310D4—1221no—
311D4—1221no—
312D4—1221no—
313D4—1221no—
314D4—1221no—
315D4—1221no—
316D4—4881no—
317D4—4881no—
318D4—4881no—
319D4—4881no—
320D4—2442no—
321D4—2442no—
322D4—2442no—
323D4—2442no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—4881no—
334C2×C4—4881no—
335C2×C4—2442no—
336C2×C4—2442no—
337C2×C4C2×D24411yescharacteristic
338C2×C4C2×D24411yescharacteristic
339C2×C4C2×D24411yescharacteristic
340C2×C4C2×D24411yescharacteristic
341C2×C4C23×D6111yescharacteristic
342C8—21no—
343C8—21no—
344C8—21no—
345C8—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—2441no—
353C22—2441no—
354C22—2441no—
355C22—2441no—
356C22—2441no—
357C22—2441no—
358C22—2441no—
359C22—2441no—
360C22—2441no—
361C22C22×D24411yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—1222no—
367C4—2441no—
368C4—2441no—
369C4—2441no—
370C4—2441no—
371C4#41×D6111yescharacteristic
372C4#1451982211yescharacteristic
373C2—41no—
374C2—41no—
375C2—4881no—
376C2—4881no—
377C2—4881no—
378C2#1684040711yescharacteristic
379C2#1684056211yescharacteristic
380C2#1684056711yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#435C2
socleC22×C61C22×D4
hypercenter#435D61
hypocenterC61#3309
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. #16840458C2semidirect
2. #16840433C2semidirect
3. #16840127C2semidirect
4. #16840087C2semidirect
5. #16840076C2semidirect
6. #16840070C2semidirect
7. #16840015C2semidirect
8. #16839998C2semidirect
9. #16839958C2semidirect
10. #16839909C2semidirect
11. #16839909C2semidirect
12. #16839864C2semidirect
13. #16839764C2semidirect
14. #16839759C2semidirect
15. C61×#435C2semidirect
203. #435D61semidirect
206. C61#3309semidirect