Finite Group Databasebeta

← #21449425

Subgroups — #21449425

Order 7808.

914 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#11758224C211yesmaximal, characteristic, complemented
2C2×#14519758C211yesmaximal, characteristic, complemented
3C2×#14519749C211yesmaximal, characteristic, complemented
4#16839682C211yesmaximal, characteristic, complemented
5#16839677C211yesmaximal, characteristic, complemented
6#16839674C211yesmaximal, characteristic, complemented
7#16839670C211yesmaximal, characteristic, complemented
8#16839642C211yesmaximal, characteristic, complemented
9#16839642C211yesmaximal, characteristic, complemented
10#16839641C211yesmaximal, characteristic, complemented
11#16839638C211yesmaximal, characteristic, complemented
12#16839634C211yesmaximal, characteristic, complemented
13#16839633C211yesmaximal, characteristic, complemented
14C2×#14519684C211yesmaximal, characteristic, complemented
15C2×#121×C61C211yesmaximal, characteristic, complemented
16C2×#11758224—24no—
17C2×#11758224—24no—
18C2×#11758224—24no—
19C22×Dic122C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic
21C22×C22⋊D61C2211yescharacteristic
22C22×C22⋊D61C2211yescharacteristic
23C23×Dic61C2211yescharacteristic
24C23×Dic61C2211yescharacteristic
25C23×Dic61C2211yescharacteristic
26C22×C4×D61C2211yescharacteristic
27#14519758—24no—
28#14519749—24no—
29C2×#11758196C2211yescharacteristic
30C2×#11758196C2211yescharacteristic
31C2×#11758196C2211yescharacteristic
32C2×C22⋊Dic61C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic
35C2×C22⋊Dic61C2211yescharacteristic
36C2×C22⋊Dic61C2211yescharacteristic
37C2×C22⋊Dic61C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47#14519684C2211yescharacteristic
48#14519684C2211yescharacteristic
49C22×D4×C61C2211yescharacteristic
50C22×D4×C61C2211yescharacteristic
51C22×D4×C61C2211yescharacteristic
52C23×C4×C61C2211yescharacteristic
53#121×C61—24no—
54C2×C4⋊C4×C61C2211yescharacteristic
55C2×C22⋊C4×C61C2211yescharacteristic
56C2×C22⋊C4×C61C2211yescharacteristic
57C24×C61C2311yescharacteristic
58C24×C61C2311yescharacteristic
59C24×C61C2311yescharacteristic
60C23×D61C2311yescharacteristic
61C2×D4×C61—22no—
62C2×D4×C61—22no—
63C2×D4×C61—22no—
64C2×D4×C61—22no—
65C2×D4×C61—22no—
66C2×D4×C61—22no—
67C2×D4×C61—22no—
68C2×D4×C61—41no—
69C2×D4×C61D414yescomplemented
70C22×C4×C61—22no—
71C22×C4×C61—22no—
72C22×C4×C61—41no—
73C22×C4×C61C2311yescharacteristic
74C22×C4×C61C2311yescharacteristic
75C22×C4×C61C2311yescharacteristic
76C22×C4×C61C2311yescharacteristic
77C2×C22⋊D61—22no—
78C2×C22⋊D61—22no—
79C2×C22⋊D61—22no—
80C2×C22⋊D61—22no—
81C2×C22⋊D61—22no—
82C2×C22⋊D61—22no—
83C2×C22⋊D61—22no—
84C2×C22⋊D61—41no—
85C2×C22⋊D61D414yescomplemented
86C22×Dic61—22no—
87C22×Dic61—22no—
88C22×Dic61—22no—
89C22×Dic61—22no—
90C22×Dic61—22no—
91C22×Dic61—22no—
92C22×Dic61—22no—
93C22×Dic61—41no—
94C22×Dic61D414yescomplemented
95C22×Dic61C2311yescharacteristic
96C22×Dic61C2311yescharacteristic
97C22×Dic61C2311yescharacteristic
98C22×Dic61C2311yescharacteristic
99C22×Dic61C2311yescharacteristic
100C22×Dic61C2311yescharacteristic
101C22×Dic61C2311yescharacteristic
102#11758224—232no—
103C2×C4×D61—22no—
104C2×C4×D61—22no—
105C2×C4×D61—22no—
106C2×Dic122—22no—
107C2×Dic122—22no—
108C2×Dic122—22no—
109C4⋊C4×C61—22no—
110C22⋊C4×C61—22no—
111C22⋊C4×C61—22no—
112C22⋊Dic61—22no—
113C22⋊Dic61—22no—
114C22⋊Dic61—22no—
115C22⋊Dic61—22no—
116C22⋊Dic61—22no—
117C22⋊Dic61—41no—
118#11758198—22no—
119#11758198—22no—
120#11758198—41no—
121#11758196—22no—
122#11758196—22no—
123#11758196—22no—
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×C61—21no—
133C23×C61—21no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61—21no—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61—21no—
140C23×C61—21no—
141C23×C61C2×D412yes—
142C23×C61C2×D412yes—
143C23×C61C2×D412yes—
144C23×C61C2×D412yes—
145C23×C61C2411yescharacteristic
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—21no—
151C22×D61—21no—
152C22×D61C2×D412yes—
153D4×C61—28no—
154D4×C61—44no—
155D4×C61—44no—
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—44no—
167C2×C4×C61C2×D412yes—
168C2×C4×C61#4112yescomplemented
169C22⋊D61—28no—
170C22⋊D61—28no—
171C22⋊D61—44no—
172C2×Dic61—28no—
173C2×Dic61—28no—
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×Dic61—21no—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—44no—
192C2×Dic61C2×D412yes—
193C2×Dic61C2×D412yes—
194C2×Dic61C2×D412yes—
195C2×Dic61#4112yescomplemented
196C4×D61—28no—
197Dic122—28no—
198C22×C61—22no—
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—41no—
208C22×C61—41no—
209C22×C61—41no—
210C22×C61—41no—
211C22×C61—41no—
212C22×C61—41no—
213C22×C61—41no—
214C22×C61—41no—
215C22×C61—41no—
216C22×C61—41no—
217C22×C61—41no—
218C22×C61#12014yes—
219C22×C61C22×D411yescharacteristic
220C22×C61C22×D411yescharacteristic
221C22×C61C22×D411yescharacteristic
222C22×C61C2×#4111yescharacteristic
223C22×C61C2×#4111yescharacteristic
224C22×C61H(5,𝔽2)11yescharacteristic
225C22×C612−1+411yescharacteristic
226C2×D61—22no—
227C2×D61—22no—
228C2×D61—22no—
229C2×D61—41no—
230C2×D61—41no—
231C2×D61—41no—
232C2×D61—41no—
233C4×C61—22no—
234C4×C61—22no—
235C4×C61—41no—
236C4×C61—41no—
237Dic61—22no—
238Dic61—22no—
239Dic61—22no—
240Dic61—22no—
241Dic61—41no—
242Dic61—41no—
243Dic61—41no—
244#2430—611nomaximal, Sylow
245C2×C61—24no—
246C2×C61—42no—
247C2×C61—81no—
248C2×C61C2×#12011yescharacteristic
249C2×C61#53211yescharacteristic
250C2×C61#53711yescharacteristic
251C2×C61#54611yescharacteristic
252C2×C61#54611yescharacteristic
253C2×C61#54711yescharacteristic
254C2×C61#54711yescharacteristic
255D61—42no—
256C22×#41—611no—
257C2×#123—611no—
258C2×#121—611no—
259C2×#121D6111yescharacteristic, complemented
260#395—611no—
261#394—611no—
262#393—611no—
263#392—611no—
264#386—611no—
265#386—611no—
266#386—611no—
267#386—611no—
268#385—611no—
269#385—611no—
270C2×#95—611no—
271C61#243011yescharacteristic, complemented, Sylow
272C2×#41—1224no—
273C2×#41—1224no—
274C2×#41—1224no—
275C22×Q8—611no—
276C22×D4—611no—
277C22×D4—611no—
278C22×D4—611no—
279C22×D4C2×D6111yescharacteristic
280C22×D4C2×D6111yescharacteristic
281C22×D4C2×D6111yescharacteristic
282C23×C4—611no—
283C23×C4—611no—
284C23×C4—611no—
285C23×C4—611no—
286C23×C4C2×D6111yescharacteristic
287#123—1224no—
288#121—24no—
289#121—1224no—
290C2×C4⋊C4—611no—
291C2×C4⋊C4—611no—
292C2×C4⋊C4—611no—
293C2×C4⋊C4C2×D6111yescharacteristic
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—611no—
301C2×C22⋊C4—611no—
302C2×C22⋊C4—611no—
303C2×C22⋊C4C2×D6111yescharacteristic
304C2×C22⋊C4C2×D6111yescharacteristic
305#95—611no—
306#95—611no—
307#95—611no—
308#95—611no—
309#95—611no—
310#95—611no—
311#95—611no—
312#95—611no—
313C24—611no—
314C24C22×D6111yescharacteristic
315C24C22×D6111yescharacteristic
316C24C22×D6111yescharacteristic
317#41—12232no—
318C2×Q8—1222no—
319C2×Q8—1222no—
320C2×Q8—1222no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—41no—
329C2×D4—614no—
330C2×D4—1222no—
331C2×D4—1222no—
332C2×D4—1222no—
333C2×D4—1222no—
334C2×D4—1222no—
335C2×D4—1222no—
336C2×D4—1222no—
337C2×D4—2441no—
338C2×D4C22⋊D6114yescomplemented
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—41no—
342C22×C4—614no—
343C22×C4—611no—
344C22×C4—611no—
345C22×C4—611no—
346C22×C4—611no—
347C22×C4—611no—
348C22×C4—611no—
349C22×C4—611no—
350C22×C4—1222no—
351C22×C4—1222no—
352C22×C4—1222no—
353C22×C4—1222no—
354C22×C4—1222no—
355C22×C4—1222no—
356C22×C4—1222no—
357C22×C4—1222no—
358C22×C4—1222no—
359C22×C4—1222no—
360C22×C4—2441no—
361C22×C4C22×D6111yescharacteristic
362C22×C4C22×D6111yescharacteristic
363C22×C4C22×D6111yescharacteristic
364C22×C4C22×D6111yescharacteristic
365C4⋊C4—22no—
366C4⋊C4—1222no—
367C4⋊C4—1222no—
368C4⋊C4—1222no—
369C22⋊C4—22no—
370C22⋊C4—22no—
371C22⋊C4—1222no—
372C22⋊C4—1222no—
373C22⋊C4—1222no—
374C22⋊C4—1222no—
375C22⋊C4—1222no—
376C22⋊C4—1222no—
377C22⋊C4—1222no—
378C22⋊C4—2441no—
379C22⋊C4—2441no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—612no—
398C23—1221no—
399C23—1221no—
400C23—1221no—
401C23—1221no—
402C23—1221no—
403C23—1221no—
404C23D4×D6112yes—
405C23D4×D6112yes—
406C23C2×C22⋊D6112yes—
407C23C2×C22⋊D6112yes—
408C23C23×D6111yescharacteristic
409Q8—1228no—
410D4—28no—
411D4—44no—
412D4—44no—
413D4—1228no—
414D4—1228no—
415D4—2444no—
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—21no—
426C2×C4—44no—
427C2×C4—612no—
428C2×C4—612no—
429C2×C4—612no—
430C2×C4—612no—
431C2×C4—1228no—
432C2×C4—1228no—
433C2×C4—1221no—
434C2×C4—1221no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—1221no—
441C2×C4—1228no—
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#1175822412yescomplemented
453C2×C4C2×C22⋊D6112yes—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—1222no—
475C22—1222no—
476C22—1222no—
477C22—2441no—
478C22—2441no—
479C22—2441no—
480C22—2441no—
481C22#1451974514yes—
482C22C2×D4×D6111yescharacteristic
483C22C2×D4×D6111yescharacteristic
484C22C22×C22⋊D6111yescharacteristic
485C22#41×D6111yescharacteristic
486C22C2×#1175822411yescharacteristic
487C22#1451982211yescharacteristic
488C22#1451982411yescharacteristic
489C4—22no—
490C4—22no—
491C4—41no—
492C4—41no—
493C4—1222no—
494C4—1222no—
495C4—1222no—
496C4—1222no—
497C4—2441no—
498C4—2441no—
499C4—2441no—
500C2—24no—
501C2—42no—
502C2—81no—
503C2—2442no—
504C2C2×#1451974511yescharacteristic
505C2#1684030711yescharacteristic
506C2#1684033911yescharacteristic
507C2#1684040111yescharacteristic
508C2#1684040611yescharacteristic
509C2#1684041111yescharacteristic
510C2#1684041211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#121×C61C2
hypercenterC2×#121D61
hypocenterC61#2430
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#11758224C2semidirect
2. C2×#14519758C2semidirect
3. C2×#14519749C2semidirect
4. #16839682C2semidirect
5. #16839677C2semidirect
6. #16839674C2semidirect
7. #16839670C2semidirect
8. #16839642C2semidirect
9. #16839642C2semidirect
10. #16839641C2semidirect
11. #16839638C2semidirect
12. #16839634C2semidirect
13. #16839633C2semidirect
14. C2×#14519684C2semidirect
15. C2×#121×C61C2semidirect
69. C2×D4×C61D4semidirect
85. C2×C22⋊D61D4semidirect
94. C22×Dic61D4semidirect
168. C2×C4×C61#41semidirect
195. C2×Dic61#41semidirect
259. C2×#121D61semidirect
271. C61#2430semidirect
338. C2×D4C22⋊D61semidirect
452. C2×C4#11758224semidirect