Finite Group Databasebeta

← #21449487

Subgroups — #21449487

Order 7808.

780 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519755C211yesmaximal, characteristic, complemented
2C2×#14519754C211yesmaximal, characteristic, complemented
3C22×#11758198C211yesmaximal, characteristic
4C2×C22⋊C4×D61C211yesmaximal, characteristic
5#16839697C211yesmaximal, characteristic, complemented
6#16839686C211yesmaximal, characteristic, complemented
7#16839684C211yesmaximal, characteristic, complemented
8#16839675C211yesmaximal, characteristic, complemented
9#16839636C211yesmaximal, characteristic, complemented
10#16839635C211yesmaximal, characteristic, complemented
11#16839634C211yesmaximal, characteristic, complemented
12#16839633C211yesmaximal, characteristic, complemented
13#16839621C211yesmaximal, characteristic, complemented
14#16839617C211yesmaximal, characteristic
15C61×#380C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×Dic122C2211yescharacteristic, complemented
18C23×Dic61C2211yescharacteristic
19C22×C4×D61C2211yescharacteristic
20C22×C4×D61C2211yescharacteristic
21#14519755—24no—
22#14519754—24no—
23C2×C4⋊Dic61C2211yescharacteristic, complemented
24C2×#11758196C2211yescharacteristic, complemented
25C2×#11758196C2211yescharacteristic, complemented
26C2×#11758196C2211yescharacteristic, complemented
27C2×#11758196C2211yescharacteristic, complemented
28C2×#11758196C2211yescharacteristic, complemented
29C2×#11758196C2211yescharacteristic, complemented
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
32C2×#11758198—24no—
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic
43C22⋊C4×D61—24no—
44#14519684C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47#14519684C2211yescharacteristic, complemented
48C23×C4×C61C2211yescharacteristic
49C2×C4⋊C4×C61C2211yescharacteristic, complemented
50C2×C4⋊C4×C61C2211yescharacteristic, complemented
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61C2211yescharacteristic
53#95×C61C2211yescharacteristic, complemented
54#95×C61C2211yescharacteristic, complemented
55C24×C61C2311yescharacteristic
56C23×D61—22no—
57C23×D61—22no—
58C23×D61—22no—
59C23×D61—22no—
60C23×D61—41no—
61C23×D61—41no—
62C23×D61Q814yescomplemented
63C23×D61C2311yescharacteristic
64C23×D61C2311yescharacteristic
65C22×C4×C61—22no—
66C22×C4×C61—22no—
67C22×C4×C61—41no—
68C22×C4×C61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C22×C4×C61C2311yescharacteristic
71C22×C4×C61C2311yescharacteristic
72C22×C4×C61C2311yescharacteristic
73C22×C4×C61C2311yescharacteristic
74C22×Dic61—22no—
75C22×Dic61—22no—
76C22×Dic61—41no—
77C22×Dic61C2311yescharacteristic
78C22×Dic61C2311yescharacteristic
79C22×Dic61C2311yescharacteristic
80C22×Dic61C2311yescharacteristic
81C22×Dic61C2311yescharacteristic
82C22×Dic61C2311yescharacteristic
83C2×C4×D61—22no—
84C2×C4×D61—22no—
85C2×C4×D61—22no—
86C2×C4×D61—22no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C2×Dic122—22no—
90C2×Dic122—22no—
91C2×Dic122—41no—
92C4⋊C4×C61—22no—
93C4⋊C4×C61—41no—
94C22⋊C4×C61—22no—
95C22⋊C4×C61—22no—
96C22⋊Dic61—22no—
97C22⋊Dic61D414yes—
98#11758198—22no—
99#11758198—22no—
100#11758198—22no—
101#11758198—22no—
102#11758198—22no—
103#11758198—22no—
104#11758198—22no—
105#11758198—41no—
106#11758198—41no—
107#11758198D414yes—
108C4⋊Dic61—22no—
109#11758196—22no—
110#11758196—22no—
111#11758196—22no—
112#11758196—22no—
113#11758196—41no—
114#11758196—41no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61C2×D412yes—
120C23×C61C2×Q812yes—
121C23×C61#4112yes—
122C23×C61C2411yescharacteristic
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—28no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—28no—
135C22×D61—44no—
136C22×D61—44no—
137C22×D61—44no—
138C22×D61—44no—
139C22×D61—44no—
140C22×D61C2×D412yes—
141C22×D61C2×Q812yes—
142C22×D61C2×Q812yes—
143C22×D61#4112yes—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
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—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—44no—
162C2×C4×C61C2×D412yes—
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—44no—
179C2×Dic61C2×D412yes—
180C2×Dic61C2×D412yes—
181C2×Dic61C2×D412yes—
182C4×D61—44no—
183C4×D61—44no—
184Dic122—44no—
185C22×C61—22no—
186C22×C61—22no—
187C22×C61—22no—
188C22×C61—22no—
189C22×C61—22no—
190C22×C61—22no—
191C22×C61C22⋊Q814yescomplemented
192C22×C61C22×D411yescharacteristic
193C22×C61C22×D411yescharacteristic
194C22×C61C22×Q811yescharacteristic
195C22×C61C2×#4111yescharacteristic
196C22×C61C2×#4111yescharacteristic
197C22×C61H(5,𝔽2)11yescharacteristic
198C22×C61H(5,𝔽2)11yescharacteristic
199C2×D61—22no—
200C2×D61—22no—
201C2×D61—22no—
202C2×D61—22no—
203C2×D61—22no—
204C2×D61—22no—
205C2×D61—22no—
206C2×D61—22no—
207C2×D61—22no—
208C2×D61—416no—
209C2×D61—41no—
210C2×D61—41no—
211C2×D61—41no—
212C2×D61—41no—
213C2×D61C22⋊Q814yescomplemented
214C4×C61—22no—
215C4×C61—41no—
216C4×C61—41no—
217C4×C61—41no—
218C4×C61—41no—
219C4×C61—41no—
220Dic61—22no—
221Dic61—22no—
222Dic61—22no—
223Dic61—41no—
224Dic61—41no—
225Dic61—41no—
226#2437—611nomaximal, Sylow
227C2×C61—24no—
228C2×C61C2×C22⋊Q811yescharacteristic
229C2×C61C2×C22⋊Q811yescharacteristic
230C2×C61#54311yescharacteristic
231C2×C61D4211yescharacteristic
232C2×C61#54611yescharacteristic
233C2×C61#54611yescharacteristic
234C2×C61#55111yescharacteristic
235D61—24no—
236D61—42no—
237C2×C22⋊Q8—611no—
238C2×C22⋊Q8—611no—
239C22×C22⋊C4—611no—
240C22×C22⋊C4—611no—
241#399—611no—
242#396—611no—
243#396—611no—
244#393—611no—
245#385—611no—
246#385—611no—
247#385—611no—
248#385—611no—
249#380—611no—
250#380D6111yescharacteristic, complemented
251#379—611no—
252C61#243711yescharacteristic, complemented, Sylow
253C25—611no—
254C22×Q8—611no—
255C23×C4—611no—
256C23×C4—611no—
257C23×C4—611no—
258C23×C4C2×D6111yescharacteristic
259C22⋊Q8—1224no—
260C22⋊Q8—1224no—
261C2×C4⋊C4—611no—
262C2×C4⋊C4—611no—
263C2×C4⋊C4—611no—
264C2×C4⋊C4—611no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4—611no—
267C2×C4⋊C4—611no—
268C2×C4⋊C4C2×D6111yescharacteristic, complemented
269C2×C4⋊C4C2×D6111yescharacteristic, complemented
270C2×C22⋊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—1224no—
283C2×C22⋊C4—1224no—
284C2×C22⋊C4C2×D6111yescharacteristic
285C2×C22⋊C4C2×D6111yescharacteristic
286#95—611no—
287#95—611no—
288#95—611no—
289#95—611no—
290#95C2×D6111yescharacteristic, complemented
291#95C2×D6111yescharacteristic, complemented
292C24—611no—
293C24—611no—
294C24—614no—
295C24—1222no—
296C24—1222no—
297C24—1222no—
298C24—1222no—
299C24—2441no—
300C24—2441no—
301C24C22×D6111yescharacteristic
302C2×Q8—1222no—
303C2×Q8—1222no—
304C2×Q8—2441no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—41no—
308C22×C4—611no—
309C22×C4—611no—
310C22×C4—611no—
311C22×C4—611no—
312C22×C4—611no—
313C22×C4—611no—
314C22×C4—1222no—
315C22×C4—1222no—
316C22×C4—1222no—
317C22×C4—1222no—
318C22×C4—1222no—
319C22×C4—1222no—
320C22×C4—2441no—
321C22×C4—2441no—
322C22×C4—2441no—
323C22×C4C22×D6111yescharacteristic
324C22×C4C22×D6111yescharacteristic
325C22×C4C22×D6111yescharacteristic
326C22×C4C22×D6111yescharacteristic
327C22×C4C22×D6111yescharacteristic
328C22×C4C22×D6111yescharacteristic
329C4⋊C4—22no—
330C4⋊C4—41no—
331C4⋊C4—1222no—
332C4⋊C4—1222no—
333C4⋊C4—1222no—
334C4⋊C4—1222no—
335C4⋊C4—1222no—
336C4⋊C4—2441no—
337C4⋊C4—2441no—
338C22⋊C4—22no—
339C22⋊C4—22no—
340C22⋊C4—614no—
341C22⋊C4—614no—
342C22⋊C4—1222no—
343C22⋊C4—1222no—
344C22⋊C4—1222no—
345C22⋊C4—1222no—
346C22⋊C4—1222no—
347C22⋊C4—1222no—
348C22⋊C4—1222no—
349C22⋊C4—1222no—
350C22⋊C4—2441no—
351C22⋊C4—2441no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—612no—
357C23—612no—
358C23—612no—
359C23—612no—
360C23—1228no—
361C23—1221no—
362C23—1221no—
363C23—1221no—
364C23—1221no—
365C23—1221no—
366C23—1221no—
367C23—1221no—
368C23—1221no—
369C23—1221no—
370C23—1221no—
371C23—1228no—
372C23—2444no—
373C23—2444no—
374C23—2444no—
375C23—2444no—
376C23—2444no—
377C23#1175822212yes—
378C23D4×D6112yes—
379C23Q8×D6112yes—
380C23C23×D6111yescharacteristic
381Q8—2444no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—44no—
400C2×C4—612no—
401C2×C4—612no—
402C2×C4—612no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—1221no—
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—2444no—
419C2×C4—2444no—
420C2×C4—2444no—
421C2×C4D4×D6112yes—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—614no—
429C22—1222no—
430C22—1222no—
431C22—1222no—
432C22—1222no—
433C22—1222no—
434C22—1222no—
435C22—1222no—
436C22—1222no—
437C22—1222no—
438C22—24416no—
439C22—2441no—
440C22—2441no—
441C22—2441no—
442C22—2441no—
443C22#1451975514yescomplemented
444C22C2×D4×D6111yescharacteristic
445C22C2×D4×D6111yescharacteristic
446C22C2×Q8×D6111yescharacteristic
447C22#41×D6111yescharacteristic
448C22C2×#1175822211yescharacteristic
449C22#1451982211yescharacteristic
450C22#1451982311yescharacteristic
451C4—22no—
452C4—41no—
453C4—41no—
454C4—41no—
455C4—41no—
456C4—41no—
457C4—1222no—
458C4—1222no—
459C4—1222no—
460C4—2441no—
461C4—2441no—
462C4—2441no—
463C2—24no—
464C2—1224no—
465C2—2442no—
466C2C22⋊Q8×D6111yescharacteristic
467C2C2×#1451975511yescharacteristic
468C2#1684038711yescharacteristic
469C2#1684039611yescharacteristic
470C2#1684040111yescharacteristic
471C2#1684040211yescharacteristic
472C2#1684043611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#380C2
hypercenter#380D61
hypocenterC61#2437
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×#14519755C2semidirect
2. C2×#14519754C2semidirect
5. #16839697C2semidirect
6. #16839686C2semidirect
7. #16839684C2semidirect
8. #16839675C2semidirect
9. #16839636C2semidirect
10. #16839635C2semidirect
11. #16839634C2semidirect
12. #16839633C2semidirect
13. #16839621C2semidirect
15. C61×#380C2semidirect
17. C22×Dic122C22semidirect
23. C2×C4⋊Dic61C22semidirect
24. C2×#11758196C22semidirect
25. C2×#11758196C22semidirect
26. C2×#11758196C22semidirect
27. C2×#11758196C22semidirect
28. C2×#11758196C22semidirect
29. C2×#11758196C22semidirect
44. #14519684C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
47. #14519684C22semidirect
49. C2×C4⋊C4×C61C22semidirect
50. C2×C4⋊C4×C61C22semidirect
53. #95×C61C22semidirect
54. #95×C61C22semidirect
62. C23×D61Q8semidirect
191. C22×C61C22⋊Q8semidirect
213. C2×D61C22⋊Q8semidirect
250. #380D61semidirect
252. C61#2437semidirect
268. C2×C4⋊C4C2×D61semidirect
269. C2×C4⋊C4C2×D61semidirect
290. #95C2×D61semidirect
291. #95C2×D61semidirect
443. C22#14519755semidirect