Finite Group Databasebeta

← #21457333

Subgroups — #21457333

Order 7808.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519806C211yesmaximal, characteristic, complemented
2C22×#11758200C211yesmaximal, characteristic, complemented
3#16840425C211yesmaximal, characteristic, complemented
4#16840406C211yesmaximal, characteristic
5#16840153C211yesmaximal, characteristic, complemented
6#16840007C211yesmaximal, characteristic, complemented
7#16840001C211yesmaximal, characteristic, complemented
8#16839983C211yesmaximal, characteristic, complemented
9#16839965C211yesmaximal, characteristic, complemented
10#16839925C211yesmaximal, characteristic, complemented
11#16839920C211yesmaximal, characteristic, complemented
12#16839899C211yesmaximal, characteristic, complemented
13#16839859C211yesmaximal, characteristic, complemented
14#16839830C211yesmaximal, characteristic, complemented
15C61×#450C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C22×Dic122C2211yescharacteristic
18C2×Q8×D61C2211yescharacteristic, complemented
19#14519806—24no—
20C2×Dic244C2211yescharacteristic, complemented
21C2×Dic244C2211yescharacteristic, complemented
22C2×#11758202C2211yescharacteristic, complemented
23C2×#11758200—24no—
24C2×#11758200C2211yescharacteristic
25C2×#11758200C2211yescharacteristic
26C2×#11758200C2211yescharacteristic
27C2×#11758200C2211yescharacteristic
28C2×#11758189C2211yescharacteristic, complemented
29C22×#92418C2211yescharacteristic
30#14519776—21no—
31#14519775C2211yescharacteristic, complemented
32#14519764C2211yescharacteristic
33#14519758—21no—
34#14519757C2211yescharacteristic, complemented
35#14519756C2211yescharacteristic
36#14519755—21no—
37#14519754—21no—
38#14519749—21no—
39#14519748C2211yescharacteristic
40#14519746—21no—
41#14519742C2211yescharacteristic, complemented
42D4×Dic61C2211yescharacteristic
43C4×C22⋊D61C2211yescharacteristic
44#14519737—21no—
45C2×C22⋊Dic61—21no—
46#14519710C2211yescharacteristic, complemented
47#14519706C2211yescharacteristic, complemented
48#14519702C2211yescharacteristic, complemented
49#14519702C2211yescharacteristic, complemented
50#14519701C2211yescharacteristic, complemented
51#14519700C2211yescharacteristic, complemented
52#14519689C2211yescharacteristic, complemented
53#14519687C2211yescharacteristic, complemented
54C22×D4×C61C2211yescharacteristic
55C2×SD16×C61C2211yescharacteristic
56C2×SD16×C61C2211yescharacteristic
57C22⋊Q8×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59#102×C61C2211yescharacteristic
60C22⋊C8×C61C2211yescharacteristic
61C24×C61—21no—
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61—22no—
64C2×D4×C61—21no—
65C2×D4×C61—41no—
66C2×D4×C61C2311yescharacteristic
67C2×D4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C2×C22⋊D61D411yescharacteristic
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75Q8×D61—22no—
76Q8×D61—41no—
77#11758224—22no—
78#11758224—41no—
79C2×C4×D61—21no—
80C2×C4×D61C2311yescharacteristic
81C2×Dic122—22no—
82C2×Dic122—21no—
83C2×Dic122—21no—
84C2×Dic122—41no—
85C2×Dic122C2311yescharacteristic
86C2×Dic122C2311yescharacteristic
87C2×Dic122C2311yescharacteristic
88SD16×C61—22no—
89SD16×C61—41no—
90C2×C8×C61C2311yescharacteristic
91C2×C8×C61C2311yescharacteristic
92C4⋊C4×C61—21no—
93C4⋊C4×C61C2311yescharacteristic
94C22⋊C4×C61—21no—
95C22⋊Dic61—21no—
96C22⋊Dic61—21no—
97C22⋊Dic61—21no—
98C22⋊Dic61—21no—
99C22⋊Dic61—21no—
100C22⋊Dic61D411yescharacteristic
101#11758202—22no—
102#11758200—22no—
103#11758200—22no—
104#11758200—22no—
105#11758200D414yescomplemented
106#11758198—21no—
107#11758198D411yescharacteristic
108C4⋊Dic61—21no—
109C4⋊Dic61C2311yescharacteristic
110#11758196—21no—
111#11758196—21no—
112#11758196—21no—
113#11758196—21no—
114#11758196D411yescharacteristic
115C4×Dic61—21no—
116C4×Dic61C2311yescharacteristic
117C2×#92418—22no—
118C2×#92418C2311yescharacteristic
119C2×#92418C2311yescharacteristic
120Dic244—22no—
121Dic244—41no—
122#11758189—22no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—42no—
126C23×C61—42no—
127C23×C61—81no—
128C23×C61C2×D411yescharacteristic
129C22×D61C2×D411yescharacteristic
130Q8×C61—21no—
131Q8×C61—21no—
132D4×C61—21no—
133D4×C61—21no—
134D4×C61—21no—
135D4×C61—42no—
136D4×C61C2×D412yes—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61C2×D411yescharacteristic
142C2×C4×C61C2411yescharacteristic
143C22⋊D61—22no—
144C22⋊D61—42no—
145C22⋊D61—81no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—42no—
151C2×Dic61—42no—
152C2×Dic61—81no—
153C2×Dic61C2×D411yescharacteristic
154C2×Dic61C2×D411yescharacteristic
155C2×Dic61C2×D411yescharacteristic
156C4×D61—21no—
157C4×D61—21no—
158C4×D61—42no—
159Dic122—21no—
160Dic122—21no—
161Dic122—21no—
162Dic122—21no—
163Dic122—21no—
164Dic122—42no—
165Dic122—42no—
166Dic122C2×D412yes—
167C8×C61—21no—
168C8×C61—21no—
169#92418—21no—
170#92418C2×D412yes—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—22no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—84no—
180C22×C61#13712yescomplemented
181C22×C61C22×D411yescharacteristic
182C2×D61—21no—
183C2×D61—21no—
184C2×D61—21no—
185C4×C61—21no—
186C4×C61—41no—
187C4×C61—41no—
188C4×C61C22×D411yescharacteristic
189C4×C61H(5,𝔽2)11yescharacteristic
190Dic61—22no—
191Dic61—21no—
192Dic61—21no—
193Dic61—21no—
194Dic61—41no—
195Dic61—41no—
196Dic61—41no—
197#3266—611nomaximal, Sylow
198C2×C61—22no—
199C2×C61—42no—
200C2×C61—81no—
201C2×C61D4211yescharacteristic
202C2×C61C2×#13711yescharacteristic
203C2×C61#57711yescharacteristic
204D61—41no—
205C2×#137—611no—
206C22×SD16—611no—
207D4×Q8—611no—
208#546—611no—
209#497—611no—
210#468—611no—
211#467—611no—
212#464—611no—
213#461—611no—
214#452—611no—
215#451—611no—
216#450D6111yescharacteristic, complemented
217#448—611no—
218#440—611no—
219#435—611no—
220C61#326611yescharacteristic, complemented, Sylow
221C2×#41—611no—
222C22×Q8—611no—
223C22×Q8—611no—
224C22×D4C2×D6111yescharacteristic
225#137—1224no—
226C2×Q16—611no—
227C2×Q16—611no—
228C2×Q16—611no—
229C2×SD16—611no—
230C2×SD16—611no—
231C2×SD16—611no—
232C2×SD16—611no—
233C2×SD16—1224no—
234C2×SD16C2×D6111yescharacteristic
235C2×SD16C2×D6111yescharacteristic
236C2×M16—611no—
237C22×C8—611no—
238C4⋊Q8—611no—
239C4⋊Q8—1221no—
240#124—611no—
241#123—1221no—
242C22⋊Q8—611no—
243C22⋊Q8—611no—
244C22⋊Q8—1221no—
245C22⋊Q8—1221no—
246C22⋊Q8C2×D6111yescharacteristic
247#121—611no—
248#121—1221no—
249#120—1221no—
250C4×Q8—611no—
251C4×D4—611no—
252C4×D4—611no—
253C4×D4—1221no—
254C2×C22⋊C4—1221no—
255#107—611no—
256C4⋊C8—611no—
257#103—611no—
258#103—611no—
259#103—611no—
260#103—611no—
261#102C2×D6111yescharacteristic
262#102C2×D6111yescharacteristic
263C22⋊C8—611no—
264C22⋊C8C2×D6111yescharacteristic
265#97—611no—
266C24—21no—
267#41—1222no—
268#41—2441no—
269C2×Q8—611no—
270C2×Q8—611no—
271C2×Q8—611no—
272C2×Q8—1221no—
273C2×Q8—1222no—
274C2×Q8—1221no—
275C2×Q8—1222no—
276C2×Q8—2441no—
277C2×Q8—2441no—
278C2×Q8C22×D6111yescharacteristic
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—41no—
282C2×D4—611no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4C22×D6111yescharacteristic
286C2×D4C22×D6111yescharacteristic
287C22×C4—611no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4—1221no—
292C22×C4C22×D6111yescharacteristic
293Q16—1222no—
294Q16—1222no—
295Q16—2441no—
296SD16—22no—
297SD16—41no—
298SD16—614no—
299SD16—1222no—
300SD16—1222no—
301SD16—1222no—
302M16—1222no—
303C2×C8—611no—
304C2×C8—611no—
305C2×C8—1222no—
306C2×C8C22×D6111yescharacteristic
307C2×C8C22×D6111yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—611no—
310C4⋊C4—611no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C4⋊C4—1221no—
314C4⋊C4—1221no—
315C4⋊C4—1221no—
316C4⋊C4C22×D6111yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—611no—
319C22⋊C4—611no—
320C22⋊C4—1221no—
321C22⋊C4—1221no—
322C22⋊C4—1221no—
323C22⋊C4—1221no—
324C22⋊C4—1221no—
325C22⋊C4—1221no—
326C42—611no—
327C42—1221no—
328C23—21no—
329C23—21no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23—611no—
334C23D4×D6111yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—612no—
338Q8—1221no—
339Q8—1221no—
340Q8—1221no—
341Q8—1221no—
342Q8—1221no—
343Q8—2442no—
344Q8—2442no—
345D4—21no—
346D4—21no—
347D4—21no—
348D4—42no—
349D4—1222no—
350D4—4881no—
351D4—2442no—
352D4D4×D6112yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—611no—
358C2×C4—611no—
359C2×C4—611no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—4881no—
367C2×C4—2442no—
368C2×C4—2442no—
369C2×C4—2442no—
370C2×C4D4×D6111yescharacteristic
371C2×C4C23×D6111yescharacteristic
372C8—21no—
373C8—21no—
374C8—612no—
375C8—1221no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—84no—
385C22—1221no—
386C22—1221no—
387C22—1221no—
388C22#1451980612yescomplemented
389C22C2×D4×D6111yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—1221no—
394C4—1221no—
395C4—1221no—
396C4—1222no—
397C4—2441no—
398C4—2441no—
399C4—2441no—
400C4C2×D4×D6111yescharacteristic
401C4#1451982211yescharacteristic
402C2—22no—
403C2—42no—
404C2—81no—
405C2—2441no—
406C2#1684039411yescharacteristic
407C2C2×#1451980611yescharacteristic
408C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#450C2
socleC22×C61C22×D4
hypercenter#450D61
hypocenterC61#3266
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#14519806C2semidirect
2. C22×#11758200C2semidirect
3. #16840425C2semidirect
5. #16840153C2semidirect
6. #16840007C2semidirect
7. #16840001C2semidirect
8. #16839983C2semidirect
9. #16839965C2semidirect
10. #16839925C2semidirect
11. #16839920C2semidirect
12. #16839899C2semidirect
13. #16839859C2semidirect
14. #16839830C2semidirect
15. C61×#450C2semidirect
18. C2×Q8×D61C22semidirect
20. C2×Dic244C22semidirect
21. C2×Dic244C22semidirect
22. C2×#11758202C22semidirect
28. C2×#11758189C22semidirect
31. #14519775C22semidirect
34. #14519757C22semidirect
41. #14519742C22semidirect
46. #14519710C22semidirect
47. #14519706C22semidirect
48. #14519702C22semidirect
49. #14519702C22semidirect
50. #14519701C22semidirect
51. #14519700C22semidirect
52. #14519689C22semidirect
53. #14519687C22semidirect
105. #11758200D4semidirect
180. C22×C61#137semidirect
216. #450D61semidirect
220. C61#3266semidirect
388. C22#14519806semidirect