Finite Group Databasebeta

← #21456571

Subgroups — #21456571

Order 7808.

468 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D61C211yesmaximal, characteristic, complemented
2#121×D61C211yesmaximal, characteristic
3#16840094C211yesmaximal, characteristic, complemented
4#16840091C211yesmaximal, characteristic, complemented
5#16840082C211yesmaximal, characteristic, complemented
6#16840079C211yesmaximal, characteristic, complemented
7#16839993C211yesmaximal, characteristic, complemented
8#16839991C211yesmaximal, characteristic, complemented
9#16839989C211yesmaximal, characteristic, complemented
10#16839914C211yesmaximal, characteristic, complemented
11#16839911C211yesmaximal, characteristic, complemented
12#16839902C211yesmaximal, characteristic, complemented
13#16839899C211yesmaximal, characteristic, complemented
14C2×#14519689C211yesmaximal, characteristic, complemented
15C61×#465C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic, complemented
17C2×D4×D61—21no—
18C2×D4×D61C2211yescharacteristic
19C22×C4×D61C2211yescharacteristic
20C2×#11758190C2211yescharacteristic, complemented
21C2×#11758200C2211yescharacteristic, complemented
22C2×#11758201C2211yescharacteristic, complemented
23C22×#92418C2211yescharacteristic, complemented
24#14519757C2211yescharacteristic
25#14519756C2211yescharacteristic, complemented
26#14519755—21no—
27#14519754—21no—
28#14519753C2211yescharacteristic
29#14519752C2211yescharacteristic
30#14519751C2211yescharacteristic
31#14519750—21no—
32#14519749—21no—
33#14519748C2211yescharacteristic
34C4⋊C4×D61—21no—
35C4⋊C4×D61C2211yescharacteristic
36C4⋊C4×D61C2211yescharacteristic, complemented
37C22⋊C4×D61—21no—
38C22⋊C4×D61—21no—
39#14519709C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519708C2211yescharacteristic, complemented
42#14519702C2211yescharacteristic, complemented
43#14519701C2211yescharacteristic, complemented
44#14519700C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic, complemented
46#14519698C2211yescharacteristic, complemented
47#14519697C2211yescharacteristic, complemented
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic, complemented
51#14519689C2211yescharacteristic, complemented
52C2×SD16×C61C2211yescharacteristic, complemented
53C22×C8×C61C2211yescharacteristic, complemented
54C22⋊Q8×C61C2211yescharacteristic, complemented
55#121×C61C2211yescharacteristic
56#106×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58#102×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C23×D61D411yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C22×Dic61D411yescharacteristic
69Q8×D61—41no—
70Q8×D61—41no—
71D4×D61—41no—
72D4×D61—41no—
73D4×D61—44no—
74C2×D244—21no—
75C2×D244C2311yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C4×D61D411yescharacteristic
82C2×C4×D61D411yescharacteristic
83C2×C4×D61C2311yescharacteristic
84C2×C4×D61C2311yescharacteristic
85C2×Dic122—21no—
86C2×Dic122C2311yescharacteristic
87SD16×C61—41no—
88C2×C8×C61—41no—
89C2×C8×C61C2311yescharacteristic
90C2×C8×C61C2311yescharacteristic
91C4⋊C4×C61—21no—
92C4⋊C4×C61C2311yescharacteristic
93C4⋊C4×C61C2311yescharacteristic
94C22⋊C4×C61—21no—
95C22⋊C4×C61—21no—
96C22⋊Dic61—21no—
97C22⋊Dic61—21no—
98#11758201—41no—
99#11758200—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—
109#11758196—21no—
110#11758196—21no—
111C2×#92418—41no—
112C2×#92418C2311yescharacteristic
113C2×#92418C2311yescharacteristic
114#11758190—41no—
115C23×C61—21no—
116C23×C61C2×D411yescharacteristic
117C22×D61—21no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—42no—
121C22×D61—42no—
122C22×D61—42no—
123C22×D61SD1614yescomplemented
124C22×D61C2×D411yescharacteristic
125C22×D61C2×D411yescharacteristic
126Q8×C61—21no—
127Q8×C61—21no—
128D4×C61—21no—
129D4×C61—21no—
130D4×C61—42no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61C2×D411yescharacteristic
137C2×C4×C61C2411yescharacteristic
138C22⋊D61—42no—
139C22⋊D61—42no—
140C22⋊D61—42no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—41no—
145C2×Dic61C2×D411yescharacteristic
146C2×Dic61C2×D411yescharacteristic
147D244—21no—
148D244—21no—
149D244—42no—
150C4×D61—21no—
151C4×D61—21no—
152C4×D61—21no—
153C4×D61—21no—
154C4×D61—41no—
155C4×D61—41no—
156C4×D61—42no—
157C4×D61—42no—
158C4×D61—42no—
159Dic122—21no—
160Dic122—21no—
161Dic122—42no—
162C8×C61—21no—
163C8×C61—21no—
164#92418—21no—
165#92418—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61C2×SD1612yes—
172C22×C61C22×D411yescharacteristic
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—44no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—84no—
182C2×D61C2×SD1612yes—
183C2×D61C2×SD1612yes—
184C4×C61—21no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61—41no—
188C4×C61H(5,𝔽2)11yescharacteristic
189C4×C61H(5,𝔽2)11yescharacteristic
190Dic61—21no—
191Dic61—21no—
192Dic61—41no—
193Dic61—41no—
194Dic61—41no—
195#3187—611nomaximal, Sylow
196C2×C61—22no—
197C2×C61—81no—
198C2×C61#53411yescharacteristic
199C2×C61C22×SD1611yescharacteristic
200C2×C61#57511yescharacteristic
201D61—22no—
202D61—22no—
203D61—81no—
204C2×C22⋊Q8—611no—
205C2×#121—611no—
206#483—611no—
207#483—611no—
208#481—611no—
209#481—611no—
210#465—611no—
211#465—611no—
212#465—611no—
213#465D6111yescharacteristic, complemented
214#450—611no—
215#450—611no—
216#448—611no—
217#448—611no—
218C2×C22⋊C8—611no—
219C61#318711yescharacteristic, complemented, Sylow
220C22×Q8—611no—
221C22×D4—611no—
222C22×D4—1221no—
223C23×C4—611no—
224C2×SD16—611no—
225C2×SD16—611no—
226C2×SD16—611no—
227C2×SD16C2×D6111yescharacteristic, complemented
228C22×C8—611no—
229C22×C8C2×D6111yescharacteristic, complemented
230C22⋊Q8—611no—
231C22⋊Q8—611no—
232C22⋊Q8—611no—
233C22⋊Q8—1221no—
234C22⋊Q8—1221no—
235C22⋊Q8C2×D6111yescharacteristic, complemented
236#121—611no—
237#121—611no—
238#121—611no—
239#121—1221no—
240#121—1221no—
241#121C2×D6111yescharacteristic
242C2×C4⋊C4—611no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—1221no—
245C2×C22⋊C4—1221no—
246C2×C22⋊C4—1221no—
247#106—611no—
248#106—611no—
249#106—611no—
250#106C2×D6111yescharacteristic, complemented
251#103—611no—
252#103—611no—
253#103—611no—
254#103C2×D6111yescharacteristic, complemented
255#102—611no—
256#102—611no—
257#102—611no—
258#102C2×D6111yescharacteristic, complemented
259C22⋊C8—611no—
260C22⋊C8—611no—
261C22⋊C8—611no—
262C22⋊C8—611no—
263C24—611no—
264C24—1221no—
265C2×Q8—611no—
266C2×Q8—1221no—
267C2×Q8—2441no—
268C2×Q8—2441no—
269C2×Q8C22×D6111yescharacteristic
270C2×D4—21no—
271C2×D4—611no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4—2441no—
277C2×D4—2441no—
278C2×D4—2444no—
279C2×D4C22×D6111yescharacteristic
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—1221no—
286C22×C4—1221no—
287C22×C4—1221no—
288C22×C4—2441no—
289C22×C4—2441no—
290C22×C4C22×D6111yescharacteristic
291SD16—41no—
292SD16—2441no—
293SD16—2441no—
294SD16—2441no—
295C2×C8—41no—
296C2×C8—611no—
297C2×C8—611no—
298C2×C8—2441no—
299C2×C8C22×D6111yescharacteristic
300C2×C8C22×D6111yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—611no—
303C4⋊C4—611no—
304C4⋊C4—1221no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4C22×D6111yescharacteristic
310C4⋊C4C22×D6111yescharacteristic
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—1221no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C22⋊C4—1221no—
318C22⋊C4—1221no—
319C23—21no—
320C23—611no—
321C23—611no—
322C23—614no—
323C23—1221no—
324C23—2441no—
325C23—2441no—
326C23—2442no—
327C23—2442no—
328C23—2442no—
329C23D4×D6111yescharacteristic
330Q8—21no—
331Q8—21no—
332Q8—1221no—
333Q8—1221no—
334Q8—2442no—
335D4—21no—
336D4—21no—
337D4—42no—
338D4—1221no—
339D4—1221no—
340D4—2442no—
341D4—2442no—
342D4—2442no—
343D4—2442no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—611no—
350C2×C4—611no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2442no—
361C2×C4—2442no—
362C2×C4—2442no—
363C2×C4—2441no—
364C2×C4D4×D6111yescharacteristic
365C2×C4C23×D6111yescharacteristic
366C8—21no—
367C8—21no—
368C8—1221no—
369C8—1221no—
370C22—21no—
371C22—21no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—612no—
376C22—612no—
377C22—1221no—
378C22—1221no—
379C22—1221no—
380C22—1221no—
381C22—4884no—
382C22—2444no—
383C22—2441no—
384C22—2441no—
385C22—2441no—
386C22SD16×D6112yes—
387C22C2×D4×D6111yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—1221no—
393C4—1221no—
394C4—2441no—
395C4—2441no—
396C4—2441no—
397C4#1451982211yescharacteristic
398C4#1451982311yescharacteristic
399C2—22no—
400C2—81no—
401C2—1222no—
402C2—1222no—
403C2—4881no—
404C2#1684032011yescharacteristic
405C2C2×SD16×D6111yescharacteristic
406C2#1684055911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#465C2
socleC22×C61C22×D4
hypercenter#465D61
hypocenterC61#3187
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C22⋊Q8×D61C2semidirect
3. #16840094C2semidirect
4. #16840091C2semidirect
5. #16840082C2semidirect
6. #16840079C2semidirect
7. #16839993C2semidirect
8. #16839991C2semidirect
9. #16839989C2semidirect
10. #16839914C2semidirect
11. #16839911C2semidirect
12. #16839902C2semidirect
13. #16839899C2semidirect
14. C2×#14519689C2semidirect
15. C61×#465C2semidirect
16. C2×Q8×D61C22semidirect
20. C2×#11758190C22semidirect
21. C2×#11758200C22semidirect
22. C2×#11758201C22semidirect
23. C22×#92418C22semidirect
25. #14519756C22semidirect
36. C4⋊C4×D61C22semidirect
39. #14519709C22semidirect
40. #14519708C22semidirect
41. #14519708C22semidirect
42. #14519702C22semidirect
43. #14519701C22semidirect
44. #14519700C22semidirect
45. #14519699C22semidirect
46. #14519698C22semidirect
47. #14519697C22semidirect
50. #14519689C22semidirect
51. #14519689C22semidirect
52. C2×SD16×C61C22semidirect
53. C22×C8×C61C22semidirect
54. C22⋊Q8×C61C22semidirect
56. #106×C61C22semidirect
57. #103×C61C22semidirect
58. #102×C61C22semidirect
123. C22×D61SD16semidirect
213. #465D61semidirect
219. C61#3187semidirect
227. C2×SD16C2×D61semidirect
229. C22×C8C2×D61semidirect
235. C22⋊Q8C2×D61semidirect
250. #106C2×D61semidirect
254. #103C2×D61semidirect
258. #102C2×D61semidirect