Finite Group Databasebeta

← #21456790

Subgroups — #21456790

Order 7808.

400 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840311C211yesmaximal, characteristic, complemented
2#16840291C211yesmaximal, characteristic, complemented
3#16840144C211yesmaximal, characteristic, complemented
4#16840117C211yesmaximal, characteristic, complemented
5#16840116C211yesmaximal, characteristic, complemented
6#16839970C211yesmaximal, characteristic, complemented
7#16839965C211yesmaximal, characteristic, complemented
8#16839960C211yesmaximal, characteristic, complemented
9#16839955C211yesmaximal, characteristic, complemented
10#16839923C211yesmaximal, characteristic, complemented
11#16839921C211yesmaximal, characteristic, complemented
12#16839906C211yesmaximal, characteristic, complemented
13#16839904C211yesmaximal, characteristic, complemented
14#16839813C211yesmaximal, characteristic, complemented
15C61×#495C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758224C2211yescharacteristic
18C2×#11758202C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21C2×#11758199C2211yescharacteristic
22#14519775C2211yescharacteristic
23#14519773C2211yescharacteristic
24#14519770—21no—
25#14519769C2211yescharacteristic
26#14519765C2211yescharacteristic
27#14519759—21no—
28#14519753C2211yescharacteristic
29#14519750—21no—
30#14519750—21no—
31#14519748C2211yescharacteristic
32Q8×Dic61C2211yescharacteristic
33D4×Dic61C2211yescharacteristic
34#14519737—21no—
35#14519737—21no—
36#14519737—21no—
37#14519733—21no—
38C42×D61C2211yescharacteristic
39#14519706C2211yescharacteristic
40#14519706C2211yescharacteristic
41#14519702C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519701C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51C4×#92418C2211yescharacteristic
52C2×Q16×C61C2211yescharacteristic
53C2×SD16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic
55C2×D8×C61C2211yescharacteristic
56#124×C61C2211yescharacteristic
57#124×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69#11758226—41no—
70#11758226—41no—
71#11758224—41no—
72#11758224—41no—
73C2×D244—21no—
74C2×D244C2311yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61D411yescharacteristic
77C2×C4×D61D411yescharacteristic
78C2×C4×D61C2311yescharacteristic
79C2×Dic122C2311yescharacteristic
80Q16×C61—41no—
81SD16×C61—41no—
82SD16×C61—41no—
83D8×C61—41no—
84C2×C8×C61C2311yescharacteristic
85C2×C8×C61C2311yescharacteristic
86C22⋊C4×C61—21no—
87C22⋊C4×C61—21no—
88C22⋊C4×C61—21no—
89C22⋊C4×C61—21no—
90C42×C61C2311yescharacteristic
91C22⋊Dic61—21no—
92C22⋊Dic61—21no—
93#11758202—41no—
94#11758201—41no—
95#11758200—41no—
96#11758199—41no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106#11758196—21no—
107#11758196—21no—
108C4×Dic61—21no—
109C4×Dic61D411yescharacteristic
110C4×Dic61D411yescharacteristic
111C4×Dic61C2311yescharacteristic
112C2×#92418C2311yescharacteristic
113C2×#92418C2311yescharacteristic
114C23×C61—21no—
115C23×C61—21no—
116C22×D61—21no—
117C22×D61C2×D411yescharacteristic
118Q8×C61—21no—
119Q8×C61—21no—
120Q8×C61—21no—
121Q8×C61—21no—
122D4×C61—21no—
123D4×C61—21no—
124D4×C61—21no—
125D4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2411yescharacteristic
131C22⋊D61—42no—
132C22⋊D61—42no—
133C22⋊D61—42no—
134C22⋊D61—42no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61C2×D411yescharacteristic
141C2×Dic61C2×D411yescharacteristic
142C2×Dic61C2×D411yescharacteristic
143D244—21no—
144D244—21no—
145D244—42no—
146C4×D61—21no—
147C4×D61—21no—
148C4×D61—22no—
149C4×D61—41no—
150C4×D61—42no—
151Dic122—21no—
152Dic122—21no—
153C8×C61—21no—
154C8×C61—21no—
155#92418—21no—
156#92418—21no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61C22×D411yescharacteristic
164C2×D61—21no—
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61—41no—
173C4×C61—41no—
174C4×C61H(5,𝔽2)11yescharacteristic
175C4×C61H(5,𝔽2)11yescharacteristic
176Dic61—21no—
177Dic61—21no—
178Dic61—41no—
179Dic61—41no—
180Dic61—41no—
181Dic61#13512yes—
182#3212—611nomaximal, Sylow
183C2×C61—81no—
184C2×C61—81no—
185C2×C61#53511yescharacteristic
186C2×C61C2×#13511yescharacteristic
187C2×C61#57511yescharacteristic
188D61—41no—
189D61—81no—
190#532—611no—
191#529—611no—
192#495—611no—
193#495D6111yescharacteristic, complemented
194#488—611no—
195#488—611no—
196#462—611no—
197#461—611no—
198#460—611no—
199#459—611no—
200#452—611no—
201#452—611no—
202#449—611no—
203#449—611no—
204#431—611no—
205C61#321211yescharacteristic, complemented, Sylow
206C2×#41—611no—
207C2×#41—611no—
208C2×Q16—611no—
209C2×Q16C2×D6111yescharacteristic
210C2×SD16—611no—
211C2×SD16—611no—
212C2×SD16C2×D6111yescharacteristic
213C2×SD16C2×D6111yescharacteristic
214C2×D8—611no—
215C2×D8C2×D6111yescharacteristic
216C4⋊Q8—611no—
217#127—611no—
218#126—1221no—
219#125—611no—
220#124—611no—
221#124C2×D6111yescharacteristic
222#124C2×D6111yescharacteristic
223#123—1221no—
224C22⋊Q8—611no—
225#121—611no—
226#121—1221no—
227#121—1221no—
228C4×Q8—611no—
229C4×D4—611no—
230C4×D4—1221no—
231C4×D4—1221no—
232C4×D4—1221no—
233#117—1221no—
234C2×C42—611no—
235C4⋊C8—611no—
236C4⋊C8—611no—
237#103—611no—
238#103—611no—
239#103—611no—
240#103—611no—
241#102—611no—
242#102—611no—
243#102—611no—
244#102—611no—
245C22⋊C8—611no—
246C22⋊C8—611no—
247C4×C8—611no—
248C4×C8C2×D6111yescharacteristic
249#41—2441no—
250#41—2441no—
251#41—2441no—
252#41—2441no—
253C2×Q8—611no—
254C2×Q8C22×D6111yescharacteristic
255C2×Q8C22×D6111yescharacteristic
256C2×D4—611no—
257C2×D4—1221no—
258C2×D4—1221no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4C22×D6111yescharacteristic
263C2×D4C22×D6111yescharacteristic
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1221no—
270Q16—41no—
271Q16—2441no—
272SD16—41no—
273SD16—41no—
274SD16—2441no—
275SD16—2441no—
276D8—41no—
277D8—2441no—
278C2×C8—611no—
279C2×C8—611no—
280C2×C8C22×D6111yescharacteristic
281C2×C8C22×D6111yescharacteristic
282C4⋊C4—611no—
283C4⋊C4—611no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C42—611no—
300C42—611no—
301C42—611no—
302C42—1221no—
303C42C22×D6111yescharacteristic
304C23—21no—
305C23—21no—
306C23—611no—
307C23—1221no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—1221no—
313Q8—1221no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—1221no—
319D4—1221no—
320D4—2442no—
321D4—2442no—
322D4—2442no—
323D4—2442no—
324D4—2442no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—611no—
328C2×C4—611no—
329C2×C4—611no—
330C2×C4—1222no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—2441no—
337C2×C4—2442no—
338C2×C4—2442no—
339C2×C4—2442no—
340C2×C4D4×D6111yescharacteristic
341C2×C4D4×D6111yescharacteristic
342C2×C4C23×D6111yescharacteristic
343C8—21no—
344C8—21no—
345C8—1221no—
346C8—1221no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—1221no—
354C22—1221no—
355C22—1221no—
356C22—2441no—
357C22—2441no—
358C22—2441no—
359C22C2×D4×D6111yescharacteristic
360C4—21no—
361C4—21no—
362C4—41no—
363C4—41no—
364C4—612no—
365C4—1221no—
366C4—1221no—
367C4—2441no—
368C4—2441no—
369C4—2441no—
370C4#1451982211yescharacteristic
371C4#1451982211yescharacteristic
372C2—81no—
373C2—81no—
374C2—4881no—
375C2—2441no—
376C2#1684032511yescharacteristic
377C2#135×D6111yescharacteristic
378C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#495C2
socleC22×C61C22×D4
hypercenter#495D61
hypocenterC61#3212
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #16840311C2semidirect
2. #16840291C2semidirect
3. #16840144C2semidirect
4. #16840117C2semidirect
5. #16840116C2semidirect
6. #16839970C2semidirect
7. #16839965C2semidirect
8. #16839960C2semidirect
9. #16839955C2semidirect
10. #16839923C2semidirect
11. #16839921C2semidirect
12. #16839906C2semidirect
13. #16839904C2semidirect
14. #16839813C2semidirect
15. C61×#495C2semidirect
193. #495D61semidirect
205. C61#3212semidirect