Finite Group Databasebeta

← #21456913

Subgroups — #21456913

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#16840383C211yesmaximal, characteristic, complemented
2#16840149C211yesmaximal, characteristic, complemented
3#16840144C211yesmaximal, characteristic, complemented
4#16840121C211yesmaximal, characteristic, complemented
5#16840108C211yesmaximal, characteristic, complemented
6#16839981C211yesmaximal, characteristic, complemented
7#16839974C211yesmaximal, characteristic, complemented
8#16839959C211yesmaximal, characteristic, complemented
9#16839954C211yesmaximal, characteristic, complemented
10#16839924C211yesmaximal, characteristic, complemented
11#16839913C211yesmaximal, characteristic, complemented
12#16839907C211yesmaximal, characteristic, complemented
13#16839896C211yesmaximal, characteristic, complemented
14#16839823C211yesmaximal, characteristic, complemented
15C61×#535C211yesmaximal, characteristic, complemented
16C2×#11758202C2211yescharacteristic, complemented
17C2×#11758200C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758200C2211yescharacteristic, complemented
20C2×#11758201C2211yescharacteristic, complemented
21C2×#11758199C2211yescharacteristic
22C2×#11758199C2211yescharacteristic
23C2×#11758199C2211yescharacteristic, complemented
24#14519777C2211yescharacteristic, complemented
25#14519772—21no—
26#14519765C2211yescharacteristic, complemented
27#14519763—21no—
28#14519759—21no—
29#14519756C2211yescharacteristic
30#14519755—21no—
31#14519751C2211yescharacteristic
32C4×Dic122C2211yescharacteristic, complemented
33C4×D244C2211yescharacteristic, complemented
34C4⋊#92418C2211yescharacteristic, complemented
35C4⋊#92418C2211yescharacteristic, complemented
36#14519701C2211yescharacteristic, complemented
37#14519701C2211yescharacteristic, complemented
38#14519698C2211yescharacteristic
39#14519698C2211yescharacteristic
40#14519698C2211yescharacteristic
41#14519698C2211yescharacteristic
42#14519698C2211yescharacteristic, complemented
43#14519698C2211yescharacteristic, complemented
44C22⋊#92418C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46#14519688C2211yescharacteristic, complemented
47C4×#92418C2211yescharacteristic, complemented
48C2×#41×C61C2211yescharacteristic
49C22×D4×C61C2211yescharacteristic
50#127×C61C2211yescharacteristic
51#127×C61C2211yescharacteristic
52#124×C61C2211yescharacteristic
53#124×C61C2211yescharacteristic
54#121×C61—21no—
55#121×C61—21no—
56#120×C61—21no—
57#120×C61—21no—
58#117×C61C2211yescharacteristic
59C24×C61—21no—
60#41×C61—41no—
61#41×C61—41no—
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61—21no—
64C2×D4×C61—21no—
65C2×D4×C61—21no—
66C2×D4×C61—21no—
67C2×D4×C61—21no—
68C2×D4×C61—21no—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C2×D4×C61C2311yescharacteristic
72C2×D4×C61C2311yescharacteristic
73C2×D4×C61C2311yescharacteristic
74C22×C4×C61—21no—
75C22×C4×C61C2311yescharacteristic
76C2×C22⋊D61—21no—
77C2×D244C2311yescharacteristic
78C2×C4×D61—21no—
79C2×Dic122—21no—
80C2×Dic122C2311yescharacteristic
81C4⋊C4×C61D411yescharacteristic
82C4⋊C4×C61D411yescharacteristic
83C22⋊C4×C61—21no—
84C22⋊C4×C61—21no—
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C22⋊C4×C61D411yescharacteristic
88C22⋊C4×C61D411yescharacteristic
89C42×C61C2311yescharacteristic
90C42×C61C2311yescharacteristic
91C22⋊Dic61—21no—
92#11758202—41no—
93#11758201—41no—
94#11758200—41no—
95#11758200—41no—
96#11758200—41no—
97#11758199—41no—
98#11758199—41no—
99#11758199—41no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103#11758198—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61C2311yescharacteristic
106C4⋊Dic61C2311yescharacteristic
107#11758196—21no—
108#11758196—21no—
109C4×Dic61—21no—
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112C2×#92418C2311yescharacteristic
113C2×#92418C2311yescharacteristic
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—42no—
118C23×C61—81no—
119C23×C61—81no—
120C23×C61C2×D411yescharacteristic
121C22×D61—21no—
122Q8×C61—21no—
123Q8×C61—21no—
124D4×C61—21no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—21no—
129D4×C61—21no—
130D4×C61—42no—
131D4×C61—42no—
132D4×C61—81no—
133D4×C61—81no—
134D4×C61—81no—
135D4×C61—81no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—42no—
140C2×C4×C61C2×D411yescharacteristic
141C2×C4×C61C2×D411yescharacteristic
142C2×C4×C61C2×D411yescharacteristic
143C2×C4×C61C2×D411yescharacteristic
144C2×C4×C61C2×D411yescharacteristic
145C2×C4×C61C2411yescharacteristic
146C22⋊D61—81no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150D244—21no—
151D244—21no—
152C4×D61—81no—
153Dic122—21no—
154Dic122—21no—
155Dic122—81no—
156#92418—21no—
157#92418—21no—
158#92418—21no—
159#92418—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—84no—
173C22×C61C22×D411yescharacteristic
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—41no—
183C4×C61H(5,𝔽2)11yescharacteristic
184C4×C61H(5,𝔽2)11yescharacteristic
185Dic61—41no—
186Dic61—41no—
187Dic61—41no—
188#3224—611nomaximal, Sylow
189C2×C61—41no—
190C2×C61—81no—
191C2×C61—81no—
192C2×C61—81no—
193C2×C61#53511yescharacteristic
194C2×C61#57611yescharacteristic
195C2×C61#57711yescharacteristic
196D61—81no—
197#542—611no—
198#535D6111yescharacteristic, complemented
199#496—611no—
200#495—611no—
201#489—611no—
202#486—611no—
203#464—611no—
204#463—611no—
205#460—611no—
206#459—611no—
207#452—611no—
208#450—611no—
209#449—611no—
210#447—611no—
211#433—611no—
212C61#322411yescharacteristic, complemented, Sylow
213C2×#41C2×D6111yescharacteristic
214C22×D4C2×D6111yescharacteristic
215C2×Q16—611no—
216C2×SD16—611no—
217C2×SD16—611no—
218C2×SD16—611no—
219C2×SD16—611no—
220C2×D8—611no—
221C2×D8—611no—
222C2×D8—611no—
223C4⋊Q8—611no—
224#127C2×D6111yescharacteristic
225#127C2×D6111yescharacteristic
226#126—1221no—
227#124—611no—
228#124—1221no—
229#124C2×D6111yescharacteristic
230#124C2×D6111yescharacteristic
231#123—1221no—
232C22⋊Q8—611no—
233C22⋊Q8—1221no—
234#121—21no—
235#121—21no—
236#121—611no—
237#120—21no—
238#120—21no—
239C4×Q8—611no—
240C4×D4—611no—
241#117C2×D6111yescharacteristic
242C4⋊C8—611no—
243C4⋊C8—611no—
244#103—611no—
245#103—611no—
246#102—611no—
247#102—611no—
248#102—611no—
249#102—611no—
250#102—611no—
251#102—611no—
252C22⋊C8—611no—
253C22⋊C8—611no—
254#97—611no—
255C4×C8—611no—
256C24—21no—
257#41—41no—
258#41—41no—
259C2×Q8—611no—
260C2×Q8—1221no—
261C2×Q8C22×D6111yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—611no—
271C2×D4—1221no—
272C2×D4C22×D6111yescharacteristic
273C2×D4C22×D6111yescharacteristic
274C2×D4C22×D6111yescharacteristic
275C22×C4—21no—
276C22×C4—1221no—
277C22×C4C22×D6111yescharacteristic
278Q16—2441no—
279SD16—2441no—
280SD16—2441no—
281SD16—2441no—
282SD16—2441no—
283D8—2441no—
284D8—2441no—
285D8—2441no—
286C2×C8—611no—
287C2×C8—611no—
288C2×C8—611no—
289C2×C8—611no—
290C4⋊C4—611no—
291C4⋊C4—611no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4C22⋊D6111yescharacteristic
296C4⋊C4C22⋊D6111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C22⋊C4C22⋊D6111yescharacteristic
307C22⋊C4C22⋊D6111yescharacteristic
308C42—1221no—
309C42C22×D6111yescharacteristic
310C42C22×D6111yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—1221no—
318C23C2×C22⋊D6111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—1221no—
322Q8—1221no—
323Q8—4881no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4—81no—
334D4—81no—
335D4—81no—
336D4—1221no—
337D4—1221no—
338D4—4881no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—4881no—
347C2×C4C2×C22⋊D6111yescharacteristic
348C2×C4C2×C22⋊D6111yescharacteristic
349C2×C4C2×C22⋊D6111yescharacteristic
350C2×C4C2×C22⋊D6111yescharacteristic
351C2×C4C2×C22⋊D6111yescharacteristic
352C2×C4C23×D6111yescharacteristic
353C8—1221no—
354C8—1221no—
355C8—1221no—
356C8—1221no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—84no—
370C22—2441no—
371C22—2441no—
372C22—2441no—
373C22C22×C22⋊D6111yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—2441no—
381C4—2441no—
382C4—2441no—
383C4#1451982211yescharacteristic
384C4#1451982211yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—81no—
389C2—4881no—
390C2#1684032911yescharacteristic
391C2#1684056511yescharacteristic
392C2#1684057311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#535C2
socleC22×C61C22×D4
hypercenter#535D61
hypocenterC61#3224
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #16840383C2semidirect
2. #16840149C2semidirect
3. #16840144C2semidirect
4. #16840121C2semidirect
5. #16840108C2semidirect
6. #16839981C2semidirect
7. #16839974C2semidirect
8. #16839959C2semidirect
9. #16839954C2semidirect
10. #16839924C2semidirect
11. #16839913C2semidirect
12. #16839907C2semidirect
13. #16839896C2semidirect
14. #16839823C2semidirect
15. C61×#535C2semidirect
16. C2×#11758202C22semidirect
19. C2×#11758200C22semidirect
20. C2×#11758201C22semidirect
23. C2×#11758199C22semidirect
24. #14519777C22semidirect
26. #14519765C22semidirect
32. C4×Dic122C22semidirect
33. C4×D244C22semidirect
34. C4⋊#92418C22semidirect
35. C4⋊#92418C22semidirect
36. #14519701C22semidirect
37. #14519701C22semidirect
42. #14519698C22semidirect
43. #14519698C22semidirect
46. #14519688C22semidirect
47. C4×#92418C22semidirect
198. #535D61semidirect
212. C61#3224semidirect