Finite Group Databasebeta

← #21452382

Subgroups — #21452382

Order 7808.

680 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519759C211yesmaximal, characteristic, complemented
2C2×#14519746C211yesmaximal, characteristic
3#16839690C211yesmaximal, characteristic, complemented
4#16839687C211yesmaximal, characteristic, complemented
5#16839685C211yesmaximal, characteristic, complemented
6#16839685C211yesmaximal, characteristic, complemented
7#16839678C211yesmaximal, characteristic, complemented
8#16839677C211yesmaximal, characteristic, complemented
9#16839662C211yesmaximal, characteristic, complemented
10#16839655C211yesmaximal, characteristic, complemented
11#16839650C211yesmaximal, characteristic, complemented
12#16839638C211yesmaximal, characteristic, complemented
13#16839638C211yesmaximal, characteristic, complemented
14#16839618C211yesmaximal, characteristic, complemented
15C61×#379C211yesmaximal, characteristic, complemented
16C22×C22⋊D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C4×D61C2211yescharacteristic, complemented
20#14519759—24no—
21#14519746—24no—
22C2×C4⋊Dic61C2211yescharacteristic, complemented
23C2×C4⋊Dic61C2211yescharacteristic, complemented
24C2×#11758196C2211yescharacteristic, complemented
25C2×#11758196C2211yescharacteristic, complemented
26C2×#11758196C2211yescharacteristic, complemented
27C2×C22⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
32C2×C22⋊Dic61C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic
35C2×C22⋊Dic61C2211yescharacteristic
36C2×#11758198C2211yescharacteristic, complemented
37C2×#11758198C2211yescharacteristic, complemented
38C2×#11758198C2211yescharacteristic, complemented
39C2×C4×Dic61C2211yescharacteristic, complemented
40#14519684C2211yescharacteristic, complemented
41#14519684C2211yescharacteristic, complemented
42#14519684C2211yescharacteristic, complemented
43#14519684C2211yescharacteristic, complemented
44#14519684C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46C25×C61C2211yescharacteristic
47C2×C22⋊C4×C61C2211yescharacteristic
48C2×C22⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61C2211yescharacteristic
53C24×C61—22no—
54C24×C61—22no—
55C24×C61—22no—
56C24×C61—41no—
57C24×C61—41no—
58C24×C61—41no—
59C24×C61—41no—
60C24×C61C2311yescharacteristic
61C24×C61C2311yescharacteristic
62C24×C61C2311yescharacteristic
63C23×D61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—22no—
69C2×C22⋊D61—22no—
70C2×C22⋊D61—22no—
71C2×C22⋊D61—22no—
72C2×C22⋊D61—41no—
73C2×C22⋊D61—41no—
74C2×C22⋊D61—41no—
75C2×C22⋊D61—41no—
76C2×C22⋊D61D414yes—
77C22×Dic61C2311yescharacteristic
78C22×Dic61C2311yescharacteristic
79C22×Dic61C2311yescharacteristic
80C22×Dic61C2311yescharacteristic
81C22×Dic61C2311yescharacteristic
82C22×Dic61C2311yescharacteristic
83C22×Dic61C2311yescharacteristic
84C2×C4×D61—22no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C22⋊C4×C61—22no—
88C22⋊C4×C61—22no—
89C22⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C22⋊Dic61—22no—
94C22⋊Dic61—22no—
95C22⋊Dic61—22no—
96C22⋊Dic61—22no—
97C22⋊Dic61—22no—
98C22⋊Dic61—41no—
99C22⋊Dic61—41no—
100C22⋊Dic61—41no—
101C22⋊Dic61—41no—
102#11758198—22no—
103#11758198—41no—
104#11758198—41no—
105C4⋊Dic61—22no—
106C4⋊Dic61—41no—
107#11758196—22no—
108#11758196—41no—
109#11758196—41no—
110C4×Dic61—41no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—44no—
130C23×C61—44no—
131C23×C61—44no—
132C23×C61—44no—
133C23×C61—44no—
134C23×C61—44no—
135C23×C61—44no—
136C23×C61C2×D412yes—
137C23×C61#4112yes—
138C23×C61#4112yes—
139C23×C61C2411yescharacteristic
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—21no—
144C22×D61—21no—
145C22×D61—21no—
146C22×D61C2×D412yes—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C22⋊D61—44no—
160C22⋊D61—44no—
161C22⋊D61—44no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61C2×D412yes—
183C4×D61—44no—
184C22×C61—22no—
185C22×C61—22no—
186C22×C61—22no—
187C22×C61—22no—
188C22×C61—22no—
189C22×C61—22no—
190C22×C61—22no—
191C22×C61—22no—
192C22×C61—22no—
193C22×C61—416no—
194C22×C61—41no—
195C22×C61—41no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61—41no—
199C22×C61—41no—
200C22×C61—41no—
201C22×C61—41no—
202C22×C61—41no—
203C22×C61—41no—
204C22×C61—41no—
205C22×C61—41no—
206C22×C61C22×D411yescharacteristic
207C22×C61C2×#4111yescharacteristic
208C22×C61C2×#4111yescharacteristic
209C22×C61H(5,𝔽2)11yescharacteristic
210C22×C61H(5,𝔽2)11yescharacteristic
211C22×C61H(5,𝔽2)11yescharacteristic
212C22×C61H(5,𝔽2)11yescharacteristic
213C2×D61—22no—
214C2×D61—22no—
215C2×D61—22no—
216C2×D61—41no—
217C2×D61—41no—
218C2×D61—41no—
219C2×D61—41no—
220C4×C61—41no—
221C4×C61—41no—
222C4×C61—41no—
223C4×C61—41no—
224Dic61—22no—
225Dic61—41no—
226Dic61—41no—
227Dic61—41no—
228Dic61—41no—
229Dic61—41no—
230Dic61—41no—
231#2697—611nomaximal, Sylow
232C2×C61—42no—
233C2×C61—42no—
234C2×C61—42no—
235C2×C61#53411yescharacteristic
236C2×C61#53811yescharacteristic
237C2×C61#53811yescharacteristic
238C2×C61#54611yescharacteristic
239C2×C61#54611yescharacteristic
240C2×C61#55111yescharacteristic
241C2×C61#56011yescharacteristic
242D61—42no—
243C2×#123—611no—
244C2×#120—611no—
245#397—611no—
246#397—611no—
247#396—611no—
248#396—611no—
249#394—611no—
250#394—611no—
251#390—611no—
252#388—611no—
253#388—611no—
254#386—611no—
255#386—611no—
256#379—611no—
257#379D6111yescharacteristic, complemented
258C61#269711yescharacteristic, complemented, Sylow
259C25C2×D6111yescharacteristic
260C22×D4—611no—
261C22×D4—611no—
262C22×D4—611no—
263C23×C4—611no—
264#123—1224no—
265#120—1224no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—611no—
268C2×C4⋊C4—611no—
269C2×C4⋊C4—611no—
270C2×C4⋊C4—611no—
271C2×C22⋊C4—611no—
272C2×C22⋊C4—611no—
273C2×C22⋊C4—611no—
274C2×C22⋊C4—611no—
275C2×C22⋊C4—611no—
276C2×C22⋊C4—611no—
277C2×C22⋊C4—611no—
278C2×C22⋊C4—611no—
279C2×C22⋊C4—611no—
280C2×C22⋊C4—611no—
281C2×C22⋊C4—611no—
282C2×C22⋊C4—611no—
283C2×C22⋊C4C2×D6111yescharacteristic
284C2×C22⋊C4C2×D6111yescharacteristic
285C2×C22⋊C4C2×D6111yescharacteristic
286C2×C22⋊C4C2×D6111yescharacteristic
287C2×C22⋊C4C2×D6111yescharacteristic
288C2×C22⋊C4C2×D6111yescharacteristic
289C2×C42—611no—
290#95—611no—
291#95—611no—
292#95—611no—
293#95—611no—
294#95—611no—
295#95—611no—
296C24—22no—
297C24—22no—
298C24—22no—
299C24—41no—
300C24—41no—
301C24—41no—
302C24—41no—
303C24—611no—
304C24C22×D6111yescharacteristic
305C24C22×D6111yescharacteristic
306C24C22×D6111yescharacteristic
307C2×D4—614no—
308C2×D4—1222no—
309C2×D4—1222no—
310C2×D4—1222no—
311C2×D4—1222no—
312C2×D4—2441no—
313C2×D4—2441no—
314C2×D4—2441no—
315C2×D4—2441no—
316C22×C4—611no—
317C22×C4—611no—
318C22×C4—611no—
319C22×C4—611no—
320C22×C4—611no—
321C22×C4—611no—
322C22×C4—611no—
323C22×C4—1222no—
324C22×C4—2441no—
325C22×C4—2441no—
326C22×C4C22×D6111yescharacteristic
327C22×C4C22×D6111yescharacteristic
328C22×C4C22×D6111yescharacteristic
329C22×C4C22×D6111yescharacteristic
330C4⋊C4—1222no—
331C4⋊C4—1222no—
332C4⋊C4—2441no—
333C4⋊C4—2441no—
334C4⋊C4—2441no—
335C22⋊C4—22no—
336C22⋊C4—22no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—1222no—
342C22⋊C4—1222no—
343C22⋊C4—1222no—
344C22⋊C4—1222no—
345C22⋊C4—1222no—
346C22⋊C4—1222no—
347C22⋊C4—2441no—
348C22⋊C4—2441no—
349C22⋊C4—2441no—
350C22⋊C4—2441no—
351C22⋊C4—2441no—
352C22⋊C4—2441no—
353C42—2441no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—44no—
373C23—44no—
374C23—44no—
375C23—44no—
376C23—44no—
377C23—44no—
378C23—44no—
379C23—612no—
380C23—1221no—
381C23—1221no—
382C23—1221no—
383C23—1221no—
384C23—1221no—
385C23—1221no—
386C23#1175822212yes—
387C23D4×D6112yes—
388C23#1175822412yes—
389C23C23×D6111yescharacteristic
390D4—2444no—
391D4—2444no—
392D4—2444no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—612no—
406C2×C4—1221no—
407C2×C4—1221no—
408C2×C4—1221no—
409C2×C4—1221no—
410C2×C4—1221no—
411C2×C4—1221no—
412C2×C4—1221no—
413C2×C4—1221no—
414C2×C4—1221no—
415C2×C4—1221no—
416C2×C4—1221no—
417C2×C4—1221no—
418C2×C4—1221no—
419C2×C4—1221no—
420C2×C4—1221no—
421C2×C4—1221no—
422C2×C4—1221no—
423C2×C4—1221no—
424C2×C4—1221no—
425C2×C4—1221no—
426C2×C4—2444no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—416no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—1222no—
450C22—1222no—
451C22—1222no—
452C22—2441no—
453C22—2441no—
454C22—2441no—
455C22—2441no—
456C22C2×D4×D6111yescharacteristic
457C22C2×#1175822411yescharacteristic
458C22C2×#1175822211yescharacteristic
459C22#1451982211yescharacteristic
460C22#1451982211yescharacteristic
461C22#1451982211yescharacteristic
462C22#1451982211yescharacteristic
463C4—41no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—1222no—
468C4—2441no—
469C4—2441no—
470C4—2441no—
471C4—2441no—
472C4—2441no—
473C4—2441no—
474C2—42no—
475C2—42no—
476C2—42no—
477C2—2442no—
478C2#1684032211yescharacteristic
479C2#1684034711yescharacteristic
480C2#1684035011yescharacteristic
481C2#1684039911yescharacteristic
482C2#1684040211yescharacteristic
483C2#1684043811yescharacteristic
484C2#1684050111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#379C2
hypercenter#379D61
hypocenterC61#2697
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#14519759C2semidirect
3. #16839690C2semidirect
4. #16839687C2semidirect
5. #16839685C2semidirect
6. #16839685C2semidirect
7. #16839678C2semidirect
8. #16839677C2semidirect
9. #16839662C2semidirect
10. #16839655C2semidirect
11. #16839650C2semidirect
12. #16839638C2semidirect
13. #16839638C2semidirect
14. #16839618C2semidirect
15. C61×#379C2semidirect
19. C22×C4×D61C22semidirect
22. C2×C4⋊Dic61C22semidirect
23. C2×C4⋊Dic61C22semidirect
24. C2×#11758196C22semidirect
25. C2×#11758196C22semidirect
26. C2×#11758196C22semidirect
36. C2×#11758198C22semidirect
37. C2×#11758198C22semidirect
38. C2×#11758198C22semidirect
39. C2×C4×Dic61C22semidirect
40. #14519684C22semidirect
41. #14519684C22semidirect
42. #14519684C22semidirect
43. #14519684C22semidirect
44. #14519684C22semidirect
45. #14519684C22semidirect
257. #379D61semidirect
258. C61#2697semidirect