Finite Group Databasebeta

← #21457819

Subgroups — #21457819

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#16840433C211yesmaximal, characteristic, complemented
2#16840128C211yesmaximal, characteristic, complemented
3#16840086C211yesmaximal, characteristic, complemented
4#16840075C211yesmaximal, characteristic, complemented
5#16840066C211yesmaximal, characteristic, complemented
6#16840013C211yesmaximal, characteristic, complemented
7#16839996C211yesmaximal, characteristic, complemented
8#16839957C211yesmaximal, characteristic, complemented
9#16839905C211yesmaximal, characteristic, complemented
10#16839905C211yesmaximal, characteristic, complemented
11#16839862C211yesmaximal, characteristic, complemented
12#16839834C211yesmaximal, characteristic, complemented
13#16839761C211yesmaximal, characteristic, complemented
14#16839756C211yesmaximal, characteristic, complemented
15C61×#553C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758222C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21C2×#11758194C2211yescharacteristic
22C22×#92418C2211yescharacteristic
23#14519774C2211yescharacteristic
24#14519773—21no—
25#14519751C2211yescharacteristic
26#14519751C2211yescharacteristic
27#14519750—21no—
28#14519750—21no—
29C4×Dic122C2211yescharacteristic
30#14519739—21no—
31#14519710C2211yescharacteristic
32#14519710C2211yescharacteristic
33#14519708C2211yescharacteristic
34C4⋊#92418C2211yescharacteristic
35#14519700C2211yescharacteristic
36#14519700C2211yescharacteristic
37#14519700C2211yescharacteristic
38#14519698C2211yescharacteristic
39#14519697C2211yescharacteristic
40#14519697C2211yescharacteristic
41#14519697C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44#14519697C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic
47#14519688C2211yescharacteristic
48#126×C61—21no—
49#125×C61C2211yescharacteristic
50#123×C61—21no—
51#121×C61—21no—
52#121×C61C2211yescharacteristic
53#121×C61C2211yescharacteristic
54C4×D4×C61—21no—
55C4×D4×C61C2211yescharacteristic
56C4×D4×C61C2211yescharacteristic
57#117×C61C2211yescharacteristic
58C2×C4⋊C4×C61C2211yescharacteristic
59C2×D4×C61—21no—
60C2×D4×C61—21no—
61C2×D4×C61D411yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71#11758222—22no—
72#11758222—22no—
73#11758222—41no—
74#11758222—41no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244C2311yescharacteristic
78C2×D244C2311yescharacteristic
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×Dic122C2311yescharacteristic
82C4⋊C4×C61—21no—
83C4⋊C4×C61—21no—
84C4⋊C4×C61—21no—
85C4⋊C4×C61D411yescharacteristic
86C4⋊C4×C61C2311yescharacteristic
87C4⋊C4×C61C2311yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C22⋊C4×C61—21no—
90C22⋊C4×C61—21no—
91C22⋊C4×C61—21no—
92C22⋊C4×C61—21no—
93C22⋊C4×C61D411yescharacteristic
94C22⋊C4×C61D411yescharacteristic
95C42×C61—21no—
96C42×C61C2311yescharacteristic
97#11758200—22no—
98#11758199—41no—
99#11758199—41no—
100#11758198—21no—
101#11758198—21no—
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104C4×Dic61—21no—
105#11758194—41no—
106C2×#92418—41no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C23×C61—21no—
112C23×C61C2×D411yescharacteristic
113C23×C61C2×D411yescharacteristic
114C22×D61—21no—
115C22×D61—21no—
116D4×C61—21no—
117D4×C61—21no—
118D4×C61—41no—
119D4×C61—42no—
120D4×C61—81no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2411yescharacteristic
135C22⋊D61—42no—
136C22⋊D61—42no—
137C22⋊D61—81no—
138C22⋊D61—81no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141D244—21no—
142D244—21no—
143D244—21no—
144D244—21no—
145D244—42no—
146D244—81no—
147C4×D61—42no—
148C4×D61—42no—
149Dic122—21no—
150Dic122#4112yes—
151#92418—21no—
152#92418—21no—
153#92418—21no—
154#92418—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61C22×D411yescharacteristic
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×C61—41no—
176C4×C61—41no—
177C4×C61—41no—
178C4×C61C2×#4111yescharacteristic
179C4×C61H(5,𝔽2)11yescharacteristic
180Dic61—22no—
181Dic61—41no—
182#3309—611nomaximal, Sylow
183C2×C61—41no—
184C2×C61—41no—
185C2×C61—81no—
186C2×C61#54611yescharacteristic
187C2×C61#57511yescharacteristic
188C2×C61#57611yescharacteristic
189D61—81no—
190D61—81no—
191#553D6111yescharacteristic, complemented
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#435—611no—
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×M16—611no—
213C22×C8—611no—
214#127—611no—
215#127—1221no—
216#126—21no—
217#125C2×D6111yescharacteristic
218#123—21no—
219#121—21no—
220#121—611no—
221#121—611no—
222#121—1221no—
223#121—1221no—
224#121C2×D6111yescharacteristic
225#121C2×D6111yescharacteristic
226C4×Q8—611no—
227C4×D4—21no—
228C4×D4—1221no—
229C4×D4C2×D6111yescharacteristic
230C4×D4C2×D6111yescharacteristic
231#117C2×D6111yescharacteristic
232C2×C4⋊C4C2×D6111yescharacteristic
233#107—611no—
234#107—611no—
235#106—611no—
236C4⋊C8—611no—
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⋊C8—611no—
248C22⋊C8—611no—
249#97—611no—
250#41—1222no—
251#41—1222no—
252#41—2441no—
253#41—2441no—
254C2×Q8—611no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—611no—
258C2×D4—611no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4—1221no—
265C2×D4C22⋊D6111yescharacteristic
266C2×D4C22×D6111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4C22×D6111yescharacteristic
272C22×C4C22×D6111yescharacteristic
273SD16—1222no—
274D8—2441no—
275D8—2441no—
276M16—2441no—
277C2×C8—611no—
278C2×C8—611no—
279C2×C8—611no—
280C2×C8—611no—
281C2×C8—2441no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—611no—
286C4⋊C4—1221no—
287C4⋊C4C22⋊D6111yescharacteristic
288C4⋊C4C22×D6111yescharacteristic
289C4⋊C4C22×D6111yescharacteristic
290C4⋊C4C22×D6111yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4C22⋊D6111yescharacteristic
298C22⋊C4C22⋊D6111yescharacteristic
299C42—21no—
300C42—1221no—
301C42C22×D6111yescharacteristic
302C23—21no—
303C23—1221no—
304C23—1221no—
305C23C2×C22⋊D6111yescharacteristic
306C23C2×C22⋊D6111yescharacteristic
307Q8—612no—
308Q8—1221no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—42no—
313D4—81no—
314D4—1221no—
315D4—1221no—
316D4—1221no—
317D4—1221no—
318D4—4881no—
319D4—4881no—
320D4—4881no—
321D4—2442no—
322D4—2442no—
323D4—2442no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—2442no—
336C2×C4—2442no—
337C2×C4C2×C22⋊D6111yescharacteristic
338C2×C4C2×C22⋊D6111yescharacteristic
339C2×C4C2×C22⋊D6111yescharacteristic
340C2×C4C2×C22⋊D6111yescharacteristic
341C2×C4C23×D6111yescharacteristic
342C8—1221no—
343C8—1221no—
344C8—1221no—
345C8—1221no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—2441no—
356C22—2441no—
357C22—2441no—
358C22—2441no—
359C22—2441no—
360C22—2441no—
361C22C22×C22⋊D6111yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—1222no—
370C4—2441no—
371C4#41×D6111yescharacteristic
372C4#1451982311yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—4881no—
377C2—4881no—
378C2#1684040011yescharacteristic
379C2#1684056011yescharacteristic
380C2#1684056511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#553C2
socleC22×C61C22×D4
hypercenter#553D61
hypocenterC61#3309
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #16840433C2semidirect
2. #16840128C2semidirect
3. #16840086C2semidirect
4. #16840075C2semidirect
5. #16840066C2semidirect
6. #16840013C2semidirect
7. #16839996C2semidirect
8. #16839957C2semidirect
9. #16839905C2semidirect
10. #16839905C2semidirect
11. #16839862C2semidirect
12. #16839834C2semidirect
13. #16839761C2semidirect
14. #16839756C2semidirect
15. C61×#553C2semidirect
191. #553D61semidirect
206. C61#3309semidirect