Finite Group Databasebeta

← #21448799

Subgroups — #21448799

Order 7808.

928 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519745C211yesmaximal, characteristic
2C2×D4×Dic61C211yesmaximal, characteristic, complemented
3C2×#14519737C211yesmaximal, characteristic, complemented
4C22×#11758198C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D61C211yesmaximal, characteristic, complemented
6#16839662C211yesmaximal, characteristic, complemented
7#16839654C211yesmaximal, characteristic, complemented
8#16839651C211yesmaximal, characteristic, complemented
9#16839639C211yesmaximal, characteristic, complemented
10#16839638C211yesmaximal, characteristic, complemented
11#16839636C211yesmaximal, characteristic, complemented
12#16839634C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
14#16839609C211yesmaximal, characteristic, complemented
15C61×#386C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C23×Dic61C2211yescharacteristic
20C23×Dic61C2211yescharacteristic, complemented
21C22×C4×D61C2211yescharacteristic
22C22×C4×D61C2211yescharacteristic
23#14519745C418yescomplemented
24D4×Dic61—24no—
25#14519737—24no—
26C2×C4⋊Dic61C2211yescharacteristic, complemented
27C2×#11758196C2211yescharacteristic, complemented
28C2×#11758196C2211yescharacteristic, complemented
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic, complemented
32C2×#11758198—24no—
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C22⋊C4×D61—24no—
42C2×C4×Dic61C2211yescharacteristic, complemented
43C2×C4×Dic61C2211yescharacteristic, complemented
44C2×C4×Dic61C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47#14519684C2211yescharacteristic, complemented
48#14519684C2211yescharacteristic, complemented
49C22×D4×C61C2211yescharacteristic
50C23×C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61C2211yescharacteristic, complemented
53C2×C22⋊C4×C61C2211yescharacteristic, complemented
54#95×C61C2211yescharacteristic, complemented
55#95×C61C2211yescharacteristic, complemented
56C24×C61C2311yescharacteristic
57C24×C61C2311yescharacteristic
58C23×D61—22no—
59C23×D61—22no—
60C23×D61—22no—
61C23×D61—22no—
62C23×D61—41no—
63C23×D61—41no—
64C23×D61C2×C414yescomplemented
65C23×D61C2311yescharacteristic
66C23×D61C2311yescharacteristic
67C2×D4×C61—22no—
68C2×D4×C61—22no—
69C2×D4×C61C2×C414yescomplemented
70C22×C4×C61—22no—
71C22×C4×C61—22no—
72C22×C4×C61—41no—
73C22×C4×C61C2311yescharacteristic
74C22×C4×C61C2311yescharacteristic
75C22×C4×C61C2311yescharacteristic
76C22×C4×C61C2311yescharacteristic
77C22×C4×C61C2311yescharacteristic
78C2×C22⋊D61—22no—
79C2×C22⋊D61—22no—
80C2×C22⋊D61—41no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61C2×C414yescomplemented
83C2×C22⋊D61C2×C414yescomplemented
84C22×Dic61—22no—
85C22×Dic61—22no—
86C22×Dic61—22no—
87C22×Dic61—22no—
88C22×Dic61—41no—
89C22×Dic61—41no—
90C22×Dic61C2311yescharacteristic
91C22×Dic61C2311yescharacteristic
92C22×Dic61C2311yescharacteristic
93C22×Dic61C2311yescharacteristic
94C22×Dic61C2311yescharacteristic
95C22×Dic61C2311yescharacteristic
96C2×C4×D61—22no—
97C2×C4×D61—22no—
98C2×C4×D61—22no—
99C2×C4×D61—22no—
100C2×C4×D61—41no—
101C2×C4×D61—41no—
102C22⋊C4×C61—22no—
103C22⋊C4×C61—22no—
104C22⋊C4×C61—41no—
105C22⋊Dic61—22no—
106C22⋊Dic61C2×C414yescomplemented
107C22⋊Dic61D414yescomplemented
108#11758198—22no—
109#11758198—22no—
110#11758198—22no—
111#11758198—22no—
112#11758198—22no—
113#11758198C2×C414yescomplemented
114#11758198C2×C414yescomplemented
115#11758198D414yescomplemented
116C4⋊Dic61—22no—
117#11758196—22no—
118#11758196—41no—
119C4×Dic61—22no—
120C4×Dic61—22no—
121C4×Dic61—41no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—21no—
130C23×C61—21no—
131C23×C61—21no—
132C23×C61C22×C412yes—
133C23×C61C22×C412yes—
134C23×C61C2×D412yes—
135C23×C61#4112yes—
136C23×C61C2411yescharacteristic
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—28no—
142C22×D61—21no—
143C22×D61—21no—
144C22×D61—21no—
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—28no—
149C22×D61—44no—
150C22×D61—44no—
151C22×D61—44no—
152C22×D61—44no—
153C22×D61—44no—
154C22×D61C22×C412yes—
155C22×D61C22×C412yes—
156C22×D61C2×D412yes—
157C22×D61#4112yes—
158D4×C61—28no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—44no—
173C2×C4×C61C22×C412yes—
174C2×C4×C61C2×D412yes—
175C22⋊D61—28no—
176C22⋊D61—44no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—44no—
191C2×Dic61—44no—
192C2×Dic61C22×C412yes—
193C2×Dic61C22×C412yes—
194C2×Dic61C2×D412yes—
195C2×Dic61C2×D412yes—
196C2×Dic61C2×D412yes—
197C4×D61—44no—
198C4×D61—44no—
199C22×C61—22no—
200C22×C61—22no—
201C22×C61—22no—
202C22×C61—22no—
203C22×C61—22no—
204C22×C61—22no—
205C22×C61—22no—
206C22×C61—22no—
207C22×C61—22no—
208C22×C61—41no—
209C22×C61—41no—
210C22×C61—41no—
211C22×C61—41no—
212C22×C61C4×D414yescomplemented
213C22×C61C23×C411yescharacteristic
214C22×C61C22×D411yescharacteristic
215C22×C61C22×D411yescharacteristic
216C22×C61C2×#4111yescharacteristic
217C22×C61C2×#4111yescharacteristic
218C22×C61H(5,𝔽2)11yescharacteristic
219C22×C61H(5,𝔽2)11yescharacteristic
220C2×D61—22no—
221C2×D61—22no—
222C2×D61—22no—
223C2×D61—22no—
224C2×D61—22no—
225C2×D61—22no—
226C2×D61—22no—
227C2×D61—22no—
228C2×D61—22no—
229C2×D61—416no—
230C2×D61—41no—
231C2×D61—41no—
232C2×D61—41no—
233C2×D61—41no—
234C2×D61C4×D414yescomplemented
235C4×C61—22no—
236C4×C61—22no—
237C4×C61—41no—
238C4×C61—41no—
239C4×C61—41no—
240Dic61—22no—
241Dic61—22no—
242Dic61—22no—
243Dic61—22no—
244Dic61—22no—
245Dic61—41no—
246#2358—611nomaximal, Sylow
247C2×C61—24no—
248C2×C61—42no—
249C2×C61C2×C4×D411yescharacteristic
250C2×C61C2×C4×D411yescharacteristic
251C2×C61#51811yescharacteristic
252C2×C61D4211yescharacteristic
253C2×C61#54611yescharacteristic
254C2×C61#54611yescharacteristic
255C2×C61#55111yescharacteristic
256D61—24no—
257D61—42no—
258C2×#120—611no—
259C2×C4×D4—611no—
260C2×C4×D4—611no—
261C22×C22⋊C4—611no—
262C22×C22⋊C4—611no—
263#390—611no—
264#388—611no—
265#388—611no—
266#386—611no—
267#386—611no—
268#386D6111yescharacteristic, complemented
269#385—611no—
270#385—611no—
271C4×C22⋊C4—611no—
272C4×C22⋊C4—611no—
273C61#235811yescharacteristic, complemented, Sylow
274C25—611no—
275C22×D4—611no—
276C22×D4—611no—
277C22×D4C2×D6111yescharacteristic
278C23×C4—611no—
279C23×C4—611no—
280C23×C4—611no—
281C23×C4—611no—
282C23×C4C2×D6111yescharacteristic
283#120—618no—
284C4×D4—1224no—
285C4×D4—1224no—
286C2×C4⋊C4—611no—
287C2×C4⋊C4—611no—
288C2×C4⋊C4—611no—
289C2×C22⋊C4—611no—
290C2×C22⋊C4—611no—
291C2×C22⋊C4—611no—
292C2×C22⋊C4—611no—
293C2×C22⋊C4—611no—
294C2×C22⋊C4—611no—
295C2×C22⋊C4—611no—
296C2×C22⋊C4—611no—
297C2×C22⋊C4—611no—
298C2×C22⋊C4—611no—
299C2×C22⋊C4—611no—
300C2×C22⋊C4—1224no—
301C2×C22⋊C4—1224no—
302C2×C22⋊C4C2×D6111yescharacteristic
303C2×C22⋊C4C2×D6111yescharacteristic, complemented
304C2×C22⋊C4C2×D6111yescharacteristic, complemented
305C2×C42—611no—
306C2×C42—611no—
307C2×C42—611no—
308#95—611no—
309#95—611no—
310#95—611no—
311#95—611no—
312#95C2×D6111yescharacteristic, complemented
313#95C2×D6111yescharacteristic, complemented
314C24—611no—
315C24—611no—
316C24—614no—
317C24—1222no—
318C24—1222no—
319C24—1222no—
320C24—1222no—
321C24—2441no—
322C24—2441no—
323C24C22×D6111yescharacteristic
324C24C22×D6111yescharacteristic
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—614no—
328C2×D4—614no—
329C2×D4—1222no—
330C2×D4—1222no—
331C2×D4—2441no—
332C2×D4—2441no—
333C2×D4C4×D6114yescomplemented
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—41no—
337C22×C4—611no—
338C22×C4—611no—
339C22×C4—611no—
340C22×C4—611no—
341C22×C4—611no—
342C22×C4—611no—
343C22×C4—1222no—
344C22×C4—1222no—
345C22×C4—1222no—
346C22×C4—1222no—
347C22×C4—1222no—
348C22×C4—1222no—
349C22×C4—1222no—
350C22×C4—1222no—
351C22×C4—2441no—
352C22×C4—2441no—
353C22×C4—2441no—
354C22×C4—2441no—
355C22×C4C22×D6111yescharacteristic
356C22×C4C22×D6111yescharacteristic
357C22×C4C22×D6111yescharacteristic
358C22×C4C22×D6111yescharacteristic
359C22×C4C22×D6111yescharacteristic
360C4⋊C4—1222no—
361C4⋊C4—1222no—
362C4⋊C4—2441no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—41no—
366C22⋊C4—614no—
367C22⋊C4—614no—
368C22⋊C4—614no—
369C22⋊C4—614no—
370C22⋊C4—614no—
371C22⋊C4—1222no—
372C22⋊C4—1222no—
373C22⋊C4—1222no—
374C22⋊C4—1222no—
375C22⋊C4—1222no—
376C22⋊C4—1222no—
377C42—1222no—
378C42—1222no—
379C42—2441no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—612no—
391C23—612no—
392C23—612no—
393C23—612no—
394C23—1228no—
395C23—1221no—
396C23—1221no—
397C23—1221no—
398C23—1221no—
399C23—1221no—
400C23—1221no—
401C23—1221no—
402C23—1221no—
403C23—1221no—
404C23—1221no—
405C23—1228no—
406C23—2444no—
407C23—2444no—
408C23—2444no—
409C23—2444no—
410C23—2444no—
411C23C2×C4×D6112yes—
412C23C2×C4×D6112yes—
413C23D4×D6112yes—
414C23#1175822412yes—
415C23C23×D6111yescharacteristic
416D4—28no—
417D4—1228no—
418D4—2444no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—44no—
433C2×C4—612no—
434C2×C4—612no—
435C2×C4—612no—
436C2×C4—612no—
437C2×C4—612no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—1221no—
441C2×C4—1221no—
442C2×C4—1221no—
443C2×C4—1221no—
444C2×C4—1221no—
445C2×C4—1221no—
446C2×C4—1221no—
447C2×C4—1221no—
448C2×C4—1221no—
449C2×C4—1221no—
450C2×C4—1221no—
451C2×C4—2444no—
452C2×C4—2444no—
453C2×C4—2444no—
454C2×C4—2444no—
455C2×C4C2×C4×D6112yes—
456C2×C4D4×D6112yes—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—614no—
471C22—1222no—
472C22—1222no—
473C22—1222no—
474C22—1222no—
475C22—1222no—
476C22—1222no—
477C22—1222no—
478C22—1222no—
479C22—1222no—
480C22—24416no—
481C22—2441no—
482C22—2441no—
483C22—2441no—
484C22—2441no—
485C22#1451973714yescomplemented
486C22C22×C4×D6111yescharacteristic
487C22C2×D4×D6111yescharacteristic
488C22C2×D4×D6111yescharacteristic
489C22#41×D6111yescharacteristic
490C22C2×#1175822411yescharacteristic
491C22#1451982211yescharacteristic
492C22#1451982311yescharacteristic
493C4—22no—
494C4—22no—
495C4—41no—
496C4—41no—
497C4—41no—
498C4—1222no—
499C4—1222no—
500C4—1222no—
501C4—1222no—
502C4—1222no—
503C4—2441no—
504C2—24no—
505C2—42no—
506C2—1224no—
507C2—2442no—
508C2C4×D4×D6111yescharacteristic
509C2C2×#1451973711yescharacteristic
510C2#1684023411yescharacteristic
511C2#1684039611yescharacteristic
512C2#1684039911yescharacteristic
513C2#1684040111yescharacteristic
514C2#1684043511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#386C2
socleC23×C61C24
hypercenter#386D61
hypocenterC61#2358
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic61C2semidirect
3. C2×#14519737C2semidirect
4. C22×#11758198C2semidirect
5. C2×C22⋊C4×D61C2semidirect
6. #16839662C2semidirect
7. #16839654C2semidirect
8. #16839651C2semidirect
9. #16839639C2semidirect
10. #16839638C2semidirect
11. #16839636C2semidirect
12. #16839634C2semidirect
13. C4×C22⋊Dic61C2semidirect
14. #16839609C2semidirect
15. C61×#386C2semidirect
20. C23×Dic61C22semidirect
23. #14519745C4semidirect
26. C2×C4⋊Dic61C22semidirect
27. C2×#11758196C22semidirect
28. C2×#11758196C22semidirect
31. C2×C22⋊Dic61C22semidirect
42. C2×C4×Dic61C22semidirect
43. C2×C4×Dic61C22semidirect
44. C2×C4×Dic61C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
47. #14519684C22semidirect
48. #14519684C22semidirect
52. C2×C22⋊C4×C61C22semidirect
53. C2×C22⋊C4×C61C22semidirect
54. #95×C61C22semidirect
55. #95×C61C22semidirect
64. C23×D61C2×C4semidirect
69. C2×D4×C61C2×C4semidirect
82. C2×C22⋊D61C2×C4semidirect
83. C2×C22⋊D61C2×C4semidirect
106. C22⋊Dic61C2×C4semidirect
107. C22⋊Dic61D4semidirect
113. #11758198C2×C4semidirect
114. #11758198C2×C4semidirect
115. #11758198D4semidirect
212. C22×C61C4×D4semidirect
234. C2×D61C4×D4semidirect
268. #386D61semidirect
273. C61#2358semidirect
303. C2×C22⋊C4C2×D61semidirect
304. C2×C22⋊C4C2×D61semidirect
312. #95C2×D61semidirect
313. #95C2×D61semidirect
333. C2×D4C4×D61semidirect
485. C22#14519737semidirect