Finite Group Databasebeta

← #21456910

Subgroups — #21456910

Order 7808.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840377C211yesmaximal, characteristic, complemented
2#16840325C211yesmaximal, characteristic, complemented
3#16840150C211yesmaximal, characteristic, complemented
4#16840145C211yesmaximal, characteristic, complemented
5#16840120C211yesmaximal, characteristic, complemented
6#16840107C211yesmaximal, characteristic, complemented
7#16839985C211yesmaximal, characteristic, complemented
8#16839977C211yesmaximal, characteristic, complemented
9#16839959C211yesmaximal, characteristic, complemented
10#16839925C211yesmaximal, characteristic, complemented
11#16839914C211yesmaximal, characteristic, complemented
12#16839904C211yesmaximal, characteristic, complemented
13#16839894C211yesmaximal, characteristic, complemented
14#16839822C211yesmaximal, characteristic, complemented
15C61×#459C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C2×Dic244C2211yescharacteristic, complemented
19C2×#11758190C2211yescharacteristic
20C2×#11758200C2211yescharacteristic
21C2×#11758200C2211yescharacteristic, complemented
22C2×#11758200C2211yescharacteristic, complemented
23C2×#11758199C2211yescharacteristic
24#14519776C2211yescharacteristic, complemented
25#14519773C2211yescharacteristic
26#14519770—21no—
27#14519765C2211yescharacteristic
28#14519764C2211yescharacteristic
29#14519764C2211yescharacteristic, complemented
30#14519763—21no—
31#14519760—21no—
32#14519757C2211yescharacteristic
33#14519756—21no—
34#14519749—21no—
35#14519749—21no—
36#14519748C2211yescharacteristic
37#14519745—21no—
38#14519745—21no—
39C4×Dic122C2211yescharacteristic, complemented
40#14519734C2211yescharacteristic
41C4⋊#92418C2211yescharacteristic, complemented
42#14519702C2211yescharacteristic, complemented
43#14519700C2211yescharacteristic, complemented
44#14519699C2211yescharacteristic
45#14519698C2211yescharacteristic
46#14519698C2211yescharacteristic, complemented
47#14519697C2211yescharacteristic
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519687C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C2×D8×C61C2211yescharacteristic
53C2×D8×C61C2211yescharacteristic, complemented
54#127×C61C2211yescharacteristic
55C4×D4×C61C2211yescharacteristic, complemented
56C4⋊C8×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×D4×C61—21no—
61C2×D4×C61—21no—
62C2×D4×C61C2311yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C22×Dic61—21no—
72#11758224—41no—
73#11758224—41no—
74D4×D61—41no—
75D4×D61—41no—
76C2×D244C2311yescharacteristic
77C2×C4×D61C2311yescharacteristic
78C2×Dic122—21no—
79C2×Dic122C2311yescharacteristic
80C2×Dic122C2311yescharacteristic
81D8×C61—41no—
82D8×C61—41no—
83C2×C8×C61C2311yescharacteristic
84C2×C8×C61C2311yescharacteristic
85C4⋊C4×C61C2311yescharacteristic
86C22⋊C4×C61—21no—
87C42×C61C2311yescharacteristic
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92C22⋊Dic61—21no—
93#11758200—41no—
94#11758200—41no—
95#11758200—41no—
96#11758199—41no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198D411yescharacteristic
101#11758198D411yescharacteristic
102C4⋊Dic61—21no—
103C4⋊Dic61C2311yescharacteristic
104#11758196—21no—
105#11758196—21no—
106#11758196D411yescharacteristic
107#11758196D411yescharacteristic
108C4×Dic61—21no—
109C4×Dic61C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112Dic244—41no—
113#11758190—41no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C22×D61—21no—
118C22×D61—42no—
119C22×D61—81no—
120C22×D61—81no—
121C22×D61C2×D411yescharacteristic
122D4×C61—21no—
123D4×C61—21no—
124D4×C61—21no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—81no—
129D4×C61—81no—
130C2×C4×C61—21no—
131C2×C4×C61—81no—
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2411yescharacteristic
135C22⋊D61—42no—
136C22⋊D61—42no—
137C22⋊D61—81no—
138C22⋊D61—81no—
139C22⋊D61—81no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—42no—
144C2×Dic61C2×D411yescharacteristic
145C2×Dic61C2×D411yescharacteristic
146C2×Dic61C2×D411yescharacteristic
147D244—21no—
148D244—21no—
149C4×D61—21no—
150C4×D61—21no—
151Dic122—21no—
152Dic122—21no—
153Dic122—21no—
154Dic122—21no—
155Dic122—81no—
156C8×C61—21no—
157C8×C61—21no—
158#92418—21no—
159#92418—21no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61C22×D411yescharacteristic
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—84no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—41no—
180C4×C61H(5,𝔽2)11yescharacteristic
181C4×C61H(5,𝔽2)11yescharacteristic
182Dic61—21no—
183Dic61—21no—
184Dic61—21no—
185Dic61—41no—
186Dic61—41no—
187Dic61—41no—
188#3224—611nomaximal, Sylow
189C2×C61—81no—
190C2×C61—81no—
191C2×C61—81no—
192C2×C61#53511yescharacteristic
193C2×C61#57611yescharacteristic
194C2×C61#57711yescharacteristic
195D61—41no—
196D61—81no—
197#542—611no—
198#535—611no—
199#496—611no—
200#495—611no—
201#489—611no—
202#486—611no—
203#464—611no—
204#463—611no—
205#460—611no—
206#459D6111yescharacteristic, complemented
207#452—611no—
208#450—611no—
209#449—611no—
210#447—611no—
211#433—611no—
212C61#322411yescharacteristic, complemented, Sylow
213C2×#41—611no—
214C22×D4—611no—
215C2×Q16—611no—
216C2×SD16—611no—
217C2×SD16—611no—
218C2×SD16—611no—
219C2×SD16—611no—
220C2×D8—611no—
221C2×D8C2×D6111yescharacteristic
222C2×D8C2×D6111yescharacteristic, complemented
223C4⋊Q8—611no—
224#127—611no—
225#127C2×D6111yescharacteristic
226#126—1221no—
227#124—611no—
228#124—611no—
229#124—611no—
230#124—1221no—
231#123—1221no—
232C22⋊Q8—611no—
233C22⋊Q8—1221no—
234#121—611no—
235#121—1221no—
236#121—1221no—
237#120—1221no—
238#120—1221no—
239C4×Q8—611no—
240C4×D4C2×D6111yescharacteristic, complemented
241#117—611no—
242C4⋊C8—611no—
243C4⋊C8C2×D6111yescharacteristic, complemented
244#103—611no—
245#103—611no—
246#102—611no—
247#102—611no—
248#102—611no—
249#102—611no—
250#102C2×D6111yescharacteristic
251#102C2×D6111yescharacteristic, complemented
252C22⋊C8—611no—
253C22⋊C8—611no—
254#97—611no—
255C4×C8—611no—
256C24—1221no—
257#41—2441no—
258#41—2441no—
259C2×Q8—611no—
260C2×Q8—611no—
261C2×Q8—1221no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—611no—
265C2×D4—1221no—
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4—2441no—
271C2×D4—2441no—
272C2×D4C22×D6111yescharacteristic
273C2×D4C22×D6111yescharacteristic
274C2×D4C22×D6111yescharacteristic
275C22×C4—21no—
276C22×C4—611no—
277C22×C4—1221no—
278Q16—2441no—
279SD16—2441no—
280SD16—2441no—
281SD16—2441no—
282SD16—2441no—
283D8—41no—
284D8—41no—
285D8—2441no—
286C2×C8—611no—
287C2×C8—611no—
288C2×C8C22×D6111yescharacteristic
289C2×C8C22×D6111yescharacteristic
290C4⋊C4—611no—
291C4⋊C4—611no—
292C4⋊C4—611no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4—1221no—
296C4⋊C4C22×D6111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—611no—
299C22⋊C4—611no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C42—611no—
309C42—1221no—
310C42C22×D6111yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—611no—
315C23—1221no—
316C23—4881no—
317C23—4881no—
318C23—2442no—
319Q8—1221no—
320Q8—1221no—
321Q8—1221no—
322Q8—1221no—
323Q8—4881no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—81no—
331D4—81no—
332D4—1221no—
333D4—1221no—
334D4—4881no—
335D4—4881no—
336D4—4881no—
337D4—2442no—
338D4—2442no—
339C2×C4—21no—
340C2×C4—81no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—2442no—
350C2×C4D4×D6111yescharacteristic
351C2×C4D4×D6111yescharacteristic
352C2×C4C23×D6111yescharacteristic
353C8—21no—
354C8—21no—
355C8—1221no—
356C8—1221no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—1221no—
367C22—1221no—
368C22—1221no—
369C22—4884no—
370C22—2441no—
371C22—2441no—
372C22—2441no—
373C22C2×D4×D6111yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—1221no—
378C4—1221no—
379C4—1221no—
380C4—2441no—
381C4—2441no—
382C4—2441no—
383C4#1451982211yescharacteristic
384C4#1451982311yescharacteristic
385C2—81no—
386C2—81no—
387C2—81no—
388C2—4881no—
389C2—2441no—
390C2#1684032811yescharacteristic
391C2#1684056311yescharacteristic
392C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#459C2
socleC22×C61C22×D4
hypercenter#459D61
hypocenterC61#3224
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #16840377C2semidirect
2. #16840325C2semidirect
3. #16840150C2semidirect
4. #16840145C2semidirect
5. #16840120C2semidirect
6. #16840107C2semidirect
7. #16839985C2semidirect
8. #16839977C2semidirect
9. #16839959C2semidirect
10. #16839925C2semidirect
11. #16839914C2semidirect
12. #16839904C2semidirect
13. #16839894C2semidirect
14. #16839822C2semidirect
15. C61×#459C2semidirect
18. C2×Dic244C22semidirect
21. C2×#11758200C22semidirect
22. C2×#11758200C22semidirect
24. #14519776C22semidirect
29. #14519764C22semidirect
39. C4×Dic122C22semidirect
41. C4⋊#92418C22semidirect
42. #14519702C22semidirect
43. #14519700C22semidirect
46. #14519698C22semidirect
50. #14519687C22semidirect
51. C8×Dic61C22semidirect
53. C2×D8×C61C22semidirect
55. C4×D4×C61C22semidirect
56. C4⋊C8×C61C22semidirect
58. #102×C61C22semidirect
206. #459D61semidirect
212. C61#3224semidirect
222. C2×D8C2×D61semidirect
240. C4×D4C2×D61semidirect
243. C4⋊C8C2×D61semidirect
251. #102C2×D61semidirect