Finite Group Databasebeta

← #21449208

Subgroups — #21449208

Order 7808.

814 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519762C211yesmaximal, characteristic, complemented
2C2×#14519747C211yesmaximal, characteristic
3C2×C22⋊C4×D61C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D61C211yesmaximal, characteristic, complemented
5#16839690C211yesmaximal, characteristic, complemented
6#16839678C211yesmaximal, characteristic, complemented
7#16839677C211yesmaximal, characteristic, complemented
8#16839640C211yesmaximal, characteristic, complemented
9#16839640C211yesmaximal, characteristic, complemented
10#16839640C211yesmaximal, characteristic, complemented
11#16839636C211yesmaximal, characteristic, complemented
12#16839624C211yesmaximal, characteristic, complemented
13#16839621C211yesmaximal, characteristic, complemented
14#16839619C211yesmaximal, characteristic, complemented
15C61×#397C211yesmaximal, characteristic, complemented
16C24×D61C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×D244C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C4×D61C2211yescharacteristic
21C22×C4×D61C2211yescharacteristic
22C22×C4×D61C2211yescharacteristic
23C22×C4×D61C2211yescharacteristic
24#14519762—24no—
25#14519747—24no—
26C2×C4⋊Dic61C2211yescharacteristic, complemented
27C2×#11758196C2211yescharacteristic, complemented
28C2×#11758196C2211yescharacteristic, complemented
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic, complemented
38C2×#11758198C2211yescharacteristic, complemented
39C2×#11758198C2211yescharacteristic, complemented
40C2×#11758198C2211yescharacteristic, complemented
41C22⋊C4×D61—24no—
42C22⋊C4×D61—24no—
43#14519684C2211yescharacteristic, complemented
44#14519684C2211yescharacteristic, complemented
45#14519684C2211yescharacteristic, complemented
46#14519684C2211yescharacteristic, complemented
47#14519684C2211yescharacteristic, complemented
48C2×C4⋊C4×C61C2211yescharacteristic, complemented
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic, complemented
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×D61D414yes—
63C23×D61C2311yescharacteristic
64C23×D61C2311yescharacteristic
65C23×D61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C22×C4×C61C2311yescharacteristic
71C22×C4×C61C2311yescharacteristic
72C2×C22⋊D61—22no—
73C2×C22⋊D61—41no—
74C2×C22⋊D61—41no—
75C22×Dic61C2311yescharacteristic
76C22×Dic61C2311yescharacteristic
77C22×Dic61C2311yescharacteristic
78C22×Dic61C2311yescharacteristic
79C22×Dic61C2311yescharacteristic
80C2×D244—22no—
81C2×D244—22no—
82C2×D244—22no—
83C2×D244—22no—
84C2×D244—22no—
85C2×D244—22no—
86C2×C4×D61—22no—
87C2×C4×D61—22no—
88C2×C4×D61—22no—
89C2×C4×D61—22no—
90C2×C4×D61—22no—
91C2×C4×D61—22no—
92C2×C4×D61—22no—
93C2×C4×D61—22no—
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C2×C4×D61—41no—
98C4⋊C4×C61—22no—
99C22⋊C4×C61—22no—
100C22⋊C4×C61—22no—
101C22⋊C4×C61—22no—
102C22⋊Dic61—22no—
103C22⋊Dic61—22no—
104#11758198—22no—
105#11758198—22no—
106#11758198—22no—
107#11758198—22no—
108#11758198—22no—
109#11758198—22no—
110#11758198—22no—
111#11758198—41no—
112#11758198—41no—
113#11758198D414yescomplemented
114C4⋊Dic61—41no—
115#11758196—22no—
116#11758196—41no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61C2×D412yes—
124C23×C61C2411yescharacteristic
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—28no—
134C22×D61—28no—
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—44no—
143C22×D61—44no—
144C22×D61—44no—
145C22×D61—44no—
146C22×D61—44no—
147C22×D61C2×D412yes—
148C22×D61C2×D412yes—
149C22×D61C2×D412yes—
150C22×D61#4112yes—
151C22×D61#4112yes—
152C22×D61#4112yes—
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—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×C61C2×D412yes—
171C22⋊D61—44no—
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×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61C2×D412yes—
187D244—44no—
188D244—44no—
189C4×D61—44no—
190C4×D61—44no—
191C4×D61—44no—
192C4×D61—44no—
193C22×C61—22no—
194C22×C61—22no—
195C22×C61—22no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61—41no—
199C22×C61—41no—
200C22×C61C22×D411yescharacteristic
201C22×C61C22×D411yescharacteristic
202C22×C61C2×#4111yescharacteristic
203C22×C61C2×#4111yescharacteristic
204C22×C61C2×#4111yescharacteristic
205C22×C61H(5,𝔽2)11yescharacteristic
206C22×C61H(5,𝔽2)11yescharacteristic
207C2×D61—22no—
208C2×D61—22no—
209C2×D61—22no—
210C2×D61—22no—
211C2×D61—22no—
212C2×D61—22no—
213C2×D61—22no—
214C2×D61—22no—
215C2×D61—22no—
216C2×D61—22no—
217C2×D61—22no—
218C2×D61—22no—
219C2×D61—416no—
220C2×D61—41no—
221C2×D61—41no—
222C2×D61—41no—
223C2×D61—41no—
224C2×D61—41no—
225C2×D61—41no—
226C2×D61—41no—
227C2×D61#12114yes—
228C2×D61#12314yescomplemented
229C4×C61—22no—
230C4×C61—41no—
231C4×C61—41no—
232C4×C61—41no—
233C4×C61—41no—
234C4×C61—41no—
235Dic61—22no—
236Dic61—41no—
237Dic61—41no—
238Dic61—41no—
239Dic61—41no—
240#2412—611nomaximal, Sylow
241C2×C61—42no—
242C2×C61C2×#12111yescharacteristic
243C2×C61C2×#12311yescharacteristic
244C2×C61#53411yescharacteristic
245C2×C61#54611yescharacteristic
246C2×C61#54611yescharacteristic
247C2×C61#55111yescharacteristic
248C2×C61#55111yescharacteristic
249D61—24no—
250D61—24no—
251D61—81no—
252C2×#123—611no—
253C2×#120—611no—
254C22×C22⋊C4—611no—
255C22×C22⋊C4—611no—
256#397—611no—
257#397D6111yescharacteristic, complemented
258#394—611no—
259#394—611no—
260#386—611no—
261#386—611no—
262#386—611no—
263#385—611no—
264#381—611no—
265#380—611no—
266#380—611no—
267C61#241211yescharacteristic, complemented, Sylow
268C25—611no—
269C22×D4—611no—
270C22×D4—611no—
271C22×D4—611no—
272C23×C4—611no—
273C23×C4—611no—
274C23×C4—611no—
275C23×C4—611no—
276#123—1224no—
277#120—1224no—
278C2×C4⋊C4—611no—
279C2×C4⋊C4—611no—
280C2×C4⋊C4—611no—
281C2×C4⋊C4C2×D6111yescharacteristic, complemented
282C2×C22⋊C4—611no—
283C2×C22⋊C4—611no—
284C2×C22⋊C4—611no—
285C2×C22⋊C4—611no—
286C2×C22⋊C4—611no—
287C2×C22⋊C4—611no—
288C2×C22⋊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—1224no—
295C2×C22⋊C4—1224no—
296C2×C22⋊C4C2×D6111yescharacteristic
297C2×C22⋊C4C2×D6111yescharacteristic
298C2×C22⋊C4C2×D6111yescharacteristic
299#95—611no—
300#95—611no—
301#95—611no—
302#95—611no—
303#95—611no—
304#95C2×D6111yescharacteristic, complemented
305#95C2×D6111yescharacteristic, complemented
306#95C2×D6111yescharacteristic, complemented
307C24—611no—
308C24—611no—
309C24—614no—
310C24—611no—
311C24—1222no—
312C24—1222no—
313C24—1222no—
314C24—1222no—
315C24—2441no—
316C24—2441no—
317C24C22×D6111yescharacteristic
318C2×D4—1222no—
319C2×D4—1222no—
320C2×D4—1222no—
321C2×D4—1222no—
322C2×D4—1222no—
323C2×D4—1222no—
324C2×D4—1222no—
325C2×D4—2441no—
326C2×D4—2441no—
327C22×C4—611no—
328C22×C4—611no—
329C22×C4—611no—
330C22×C4—611no—
331C22×C4—611no—
332C22×C4—1222no—
333C22×C4—1222no—
334C22×C4—1222no—
335C22×C4—1222no—
336C22×C4—1222no—
337C22×C4—1222no—
338C22×C4—1222no—
339C22×C4—1222no—
340C22×C4—2441no—
341C22×C4—2441no—
342C22×C4—2441no—
343C22×C4—2441no—
344C22×C4C22×D6111yescharacteristic
345C22×C4C22×D6111yescharacteristic
346C22×C4C22×D6111yescharacteristic
347C22×C4C22×D6111yescharacteristic
348C22×C4C22×D6111yescharacteristic
349C22×C4C22×D6111yescharacteristic
350C4⋊C4—22no—
351C4⋊C4—1222no—
352C4⋊C4—2441no—
353C4⋊C4—2441no—
354C22⋊C4—22no—
355C22⋊C4—22no—
356C22⋊C4—22no—
357C22⋊C4—614no—
358C22⋊C4—1222no—
359C22⋊C4—1222no—
360C22⋊C4—1222no—
361C22⋊C4—1222no—
362C22⋊C4—1222no—
363C22⋊C4—1222no—
364C22⋊C4—1222no—
365C22⋊C4—1222no—
366C22⋊C4—1222no—
367C22⋊C4—2441no—
368C22⋊C4—2441no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—612no—
376C23—612no—
377C23—612no—
378C23—612no—
379C23—612no—
380C23—612no—
381C23—1228no—
382C23—1228no—
383C23—1221no—
384C23—1221no—
385C23—1221no—
386C23—1221no—
387C23—1221no—
388C23—1221no—
389C23—1221no—
390C23—1221no—
391C23—1221no—
392C23—1221no—
393C23—1221no—
394C23—1221no—
395C23—1221no—
396C23—1221no—
397C23—1221no—
398C23—2444no—
399C23—2444no—
400C23—2444no—
401C23—2444no—
402C23—2444no—
403C23D4×D6112yes—
404C23C23×D6111yescharacteristic
405D4—2444no—
406D4—2444no—
407D4—2444no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—612no—
426C2×C4—1221no—
427C2×C4—1221no—
428C2×C4—1221no—
429C2×C4—1221no—
430C2×C4—1221no—
431C2×C4—1221no—
432C2×C4—1221no—
433C2×C4—1221no—
434C2×C4—1221no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—2444no—
441C2×C4—2444no—
442C2×C4—2444no—
443C2×C4—2444no—
444C2×C4D4×D6112yes—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—614no—
453C22—614no—
454C22—1222no—
455C22—1222no—
456C22—1222no—
457C22—1222no—
458C22—1222no—
459C22—1222no—
460C22—1222no—
461C22—1222no—
462C22—1222no—
463C22—1222no—
464C22—1222no—
465C22—1222no—
466C22—24416no—
467C22—2441no—
468C22—2441no—
469C22—2441no—
470C22—2441no—
471C22—2441no—
472C22—2441no—
473C22—2441no—
474C22C2×D4×D6111yescharacteristic
475C22C2×D4×D6111yescharacteristic
476C22#41×D6111yescharacteristic
477C22#41×D6111yescharacteristic
478C22#41×D6111yescharacteristic
479C22#1451982311yescharacteristic
480C22#1451982311yescharacteristic
481C4—22no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—1222no—
488C4—2441no—
489C4—2441no—
490C4—2441no—
491C4—2441no—
492C2—42no—
493C2—1224no—
494C2—1224no—
495C2—4881no—
496C2#121×D6111yescharacteristic
497C2#123×D6111yescharacteristic
498C2#1684032311yescharacteristic
499C2#1684040411yescharacteristic
500C2#1684040511yescharacteristic
501C2#1684043711yescharacteristic
502C2#1684043711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#397C2
hypercenter#397D61
hypocenterC61#2412
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#14519762C2semidirect
3. C2×C22⋊C4×D61C2semidirect
4. C2×C22⋊C4×D61C2semidirect
5. #16839690C2semidirect
6. #16839678C2semidirect
7. #16839677C2semidirect
8. #16839640C2semidirect
9. #16839640C2semidirect
10. #16839640C2semidirect
11. #16839636C2semidirect
12. #16839624C2semidirect
13. #16839621C2semidirect
14. #16839619C2semidirect
15. C61×#397C2semidirect
26. C2×C4⋊Dic61C22semidirect
27. C2×#11758196C22semidirect
28. C2×#11758196C22semidirect
37. C2×#11758198C22semidirect
38. C2×#11758198C22semidirect
39. C2×#11758198C22semidirect
40. C2×#11758198C22semidirect
43. #14519684C22semidirect
44. #14519684C22semidirect
45. #14519684C22semidirect
46. #14519684C22semidirect
47. #14519684C22semidirect
48. C2×C4⋊C4×C61C22semidirect
52. #95×C61C22semidirect
53. #95×C61C22semidirect
54. #95×C61C22semidirect
113. #11758198D4semidirect
228. C2×D61#123semidirect
257. #397D61semidirect
267. C61#2412semidirect
281. C2×C4⋊C4C2×D61semidirect
304. #95C2×D61semidirect
305. #95C2×D61semidirect
306. #95C2×D61semidirect