Finite Group Databasebeta

← #21449433

Subgroups — #21449433

Order 7808.

952 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#11758224C211yesmaximal, characteristic, complemented
2C2×#14519773C211yesmaximal, characteristic, complemented
3C2×#14519763C211yesmaximal, characteristic, complemented
4C2×#14519749C211yesmaximal, characteristic, complemented
5#16839671C211yesmaximal, characteristic, complemented
6#16839670C211yesmaximal, characteristic, complemented
7#16839670C211yesmaximal, characteristic, complemented
8#16839666C211yesmaximal, characteristic, complemented
9#16839662C211yesmaximal, characteristic, complemented
10#16839642C211yesmaximal, characteristic, complemented
11#16839640C211yesmaximal, characteristic, complemented
12#16839639C211yesmaximal, characteristic, complemented
13#16839638C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
15C61×#392C211yesmaximal, characteristic, complemented
16C2×#11758224—24no—
17C2×#11758224—24no—
18C2×#11758224—24no—
19C22×Dic122C2211yescharacteristic
20C22×D244C2211yescharacteristic
21C22×C22⋊D61C2211yescharacteristic
22C22×C22⋊D61C2211yescharacteristic
23C22×C22⋊D61C2211yescharacteristic
24C22×C22⋊D61C2211yescharacteristic
25C22×C22⋊D61C2211yescharacteristic
26C22×C22⋊D61C2211yescharacteristic
27C23×Dic61C2211yescharacteristic
28C23×Dic61C2211yescharacteristic
29C22×C4×D61C2211yescharacteristic
30#14519773—24no—
31#14519763—24no—
32#14519749—24no—
33C2×#11758196C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic
35C2×C22⋊Dic61C2211yescharacteristic
36C2×C22⋊Dic61C2211yescharacteristic
37C2×C22⋊Dic61C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic
43C2×C4×Dic61C2211yescharacteristic
44C2×C4×Dic61C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47#14519684C2211yescharacteristic
48#14519684C2211yescharacteristic
49#14519684C2211yescharacteristic
50C22×D4×C61C2211yescharacteristic
51C22×D4×C61C2211yescharacteristic
52C22×D4×C61C2211yescharacteristic
53C2×C22⋊C4×C61C2211yescharacteristic
54C2×C22⋊C4×C61C2211yescharacteristic
55C2×C22⋊C4×C61C2211yescharacteristic
56#95×C61C2211yescharacteristic
57C24×C61C2311yescharacteristic
58C24×C61C2311yescharacteristic
59C24×C61C2311yescharacteristic
60C23×D61C2311yescharacteristic
61C23×D61C2311yescharacteristic
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×C61—41no—
70C2×D4×C61—41no—
71C22×C4×C61C2311yescharacteristic
72C22×C4×C61C2311yescharacteristic
73C22×C4×C61C2311yescharacteristic
74C22×C4×C61C2311yescharacteristic
75C2×C22⋊D61—22no—
76C2×C22⋊D61—22no—
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—22no—
85C2×C22⋊D61—22no—
86C2×C22⋊D61—22no—
87C2×C22⋊D61—22no—
88C2×C22⋊D61—41no—
89C2×C22⋊D61—41no—
90C2×C22⋊D61—41no—
91C2×C22⋊D61—41no—
92C2×C22⋊D61D414yescomplemented
93C22×Dic61—22no—
94C22×Dic61—22no—
95C22×Dic61—22no—
96C22×Dic61—22no—
97C22×Dic61—22no—
98C22×Dic61D414yescomplemented
99C22×Dic61C2311yescharacteristic
100C22×Dic61C2311yescharacteristic
101C22×Dic61C2311yescharacteristic
102C22×Dic61C2311yescharacteristic
103C22×Dic61C2311yescharacteristic
104C22×Dic61C2311yescharacteristic
105#11758224—232no—
106C2×D244—22no—
107C2×D244—22no—
108C2×D244—41no—
109C2×C4×D61—22no—
110C2×C4×D61—22no—
111C2×C4×D61—22no—
112C2×Dic122—22no—
113C2×Dic122—22no—
114C2×Dic122D414yescomplemented
115C22⋊C4×C61—22no—
116C22⋊C4×C61—22no—
117C22⋊C4×C61—41no—
118C22⋊Dic61—22no—
119C22⋊Dic61—22no—
120C22⋊Dic61—22no—
121C22⋊Dic61—41no—
122#11758198—22no—
123#11758198—22no—
124#11758198—22no—
125#11758198—41no—
126#11758198—41no—
127#11758196—22no—
128C4×Dic61—22no—
129C4×Dic61—22no—
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×C61—21no—
142C23×C61—21no—
143C23×C61—21no—
144C23×C61—21no—
145C23×C61—21no—
146C23×C61—21no—
147C23×C61—21no—
148C23×C61—21no—
149C23×C61C2×D412yes—
150C23×C61C2×D412yes—
151C23×C61C2411yescharacteristic
152C22×D61—21no—
153C22×D61—21no—
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—21no—
157C22×D61—21no—
158C22×D61—21no—
159C22×D61—21no—
160C22×D61—21no—
161C22×D61—21no—
162C22×D61—21no—
163C22×D61—21no—
164C22×D61—21no—
165C22×D61C2×D412yes—
166D4×C61—28no—
167D4×C61—44no—
168D4×C61—44no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—21no—
177C2×C4×C61—21no—
178C2×C4×C61—21no—
179C2×C4×C61C2×D412yes—
180C2×C4×C61#4112yescomplemented
181C22⋊D61—28no—
182C22⋊D61—28no—
183C22⋊D61—44no—
184C22⋊D61—44no—
185C22⋊D61—44no—
186C22⋊D61—44no—
187C2×Dic61—28no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—21no—
192C2×Dic61—21no—
193C2×Dic61—21no—
194C2×Dic61—28no—
195C2×Dic61—21no—
196C2×Dic61—21no—
197C2×Dic61—21no—
198C2×Dic61—21no—
199C2×Dic61—21no—
200C2×Dic61—21no—
201C2×Dic61C2×D412yes—
202C2×Dic61C2×D412yes—
203C2×Dic61C2×D412yes—
204C2×Dic61C2×D412yes—
205C2×Dic61C2×D412yes—
206C2×Dic61#4112yescomplemented
207D244—44no—
208C4×D61—28no—
209Dic122—28no—
210C22×C61—22no—
211C22×C61—22no—
212C22×C61—22no—
213C22×C61—22no—
214C22×C61—22no—
215C22×C61—22no—
216C22×C61—41no—
217C22×C61—41no—
218C22×C61—41no—
219C22×C61—41no—
220C22×C61—41no—
221C22×C61—41no—
222C22×C61—41no—
223C22×C61—41no—
224C22×C61—41no—
225C22×C61—41no—
226C22×C61—41no—
227C22×C61—41no—
228C22×C61—41no—
229C22×C61—41no—
230C22×C61—41no—
231C22×C61C22×D411yescharacteristic
232C22×C61C22×D411yescharacteristic
233C22×C61C22×D411yescharacteristic
234C22×C61C2×#4111yescharacteristic
235C22×C61C2×#4111yescharacteristic
236C22×C61H(5,𝔽2)11yescharacteristic
237C22×C61H(5,𝔽2)11yescharacteristic
238C2×D61—22no—
239C2×D61—22no—
240C2×D61—22no—
241C2×D61—41no—
242C2×D61—41no—
243C2×D61—41no—
244C2×D61—41no—
245C2×D61—41no—
246C2×D61—41no—
247C2×D61—41no—
248C2×D61—41no—
249C2×D61—41no—
250C2×D61—41no—
251C2×D61—41no—
252C4×C61—22no—
253C4×C61—22no—
254C4×C61—41no—
255C4×C61—41no—
256Dic61—22no—
257Dic61—22no—
258Dic61—22no—
259Dic61—41no—
260Dic61—41no—
261Dic61#12014yes—
262#2431—611nomaximal, Sylow
263C2×C61—42no—
264C2×C61—42no—
265C2×C61—81no—
266C2×C61C2×#12011yescharacteristic
267C2×C61#53211yescharacteristic
268C2×C61#53511yescharacteristic
269C2×C61#54611yescharacteristic
270C2×C61#54611yescharacteristic
271C2×C61#55011yescharacteristic
272C2×C61#55011yescharacteristic
273D61—42no—
274D61—81no—
275C22×#41—611no—
276C2×#127—611no—
277C2×#124—611no—
278C2×#121—611no—
279#392—611no—
280#392—611no—
281#392—611no—
282#392D6111yescharacteristic, complemented
283#391—611no—
284#390—611no—
285#386—611no—
286#386—611no—
287#386—611no—
288#386—611no—
289C4×C22⋊C4—611no—
290C61#243111yescharacteristic, complemented, Sylow
291C2×#41—1224no—
292C2×#41—1224no—
293C2×#41—1224no—
294C22×Q8—611no—
295C22×D4—611no—
296C22×D4—611no—
297C22×D4—611no—
298C22×D4—611no—
299C22×D4—611no—
300C22×D4—611no—
301C22×D4—611no—
302C22×D4C2×D6111yescharacteristic
303C22×D4C2×D6111yescharacteristic
304C22×D4C2×D6111yescharacteristic
305C23×C4—611no—
306C23×C4—611no—
307C23×C4—611no—
308#127—1224no—
309#124—1224no—
310#121—1224no—
311C2×C4⋊C4—611no—
312C2×C22⋊C4—611no—
313C2×C22⋊C4—611no—
314C2×C22⋊C4—611no—
315C2×C22⋊C4—611no—
316C2×C22⋊C4—611no—
317C2×C22⋊C4—611no—
318C2×C22⋊C4—611no—
319C2×C22⋊C4—611no—
320C2×C22⋊C4—611no—
321C2×C22⋊C4C2×D6111yescharacteristic
322C2×C22⋊C4C2×D6111yescharacteristic
323C2×C22⋊C4C2×D6111yescharacteristic
324C2×C42—611no—
325C2×C42—611no—
326#95—611no—
327#95—611no—
328#95—611no—
329#95—611no—
330#95—611no—
331#95C2×D6111yescharacteristic
332C24—611no—
333C24—611no—
334C24C22×D6111yescharacteristic
335C24C22×D6111yescharacteristic
336C24C22×D6111yescharacteristic
337#41—12232no—
338C2×Q8—614no—
339C2×Q8—1222no—
340C2×Q8—1222no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—22no—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—614no—
351C2×D4—1222no—
352C2×D4—1222no—
353C2×D4—1222no—
354C2×D4—1222no—
355C2×D4—1222no—
356C2×D4—1222no—
357C2×D4—1222no—
358C2×D4—1222no—
359C2×D4—1222no—
360C2×D4—1222no—
361C2×D4—1222no—
362C2×D4—1222no—
363C2×D4—1222no—
364C2×D4—1222no—
365C2×D4—1222no—
366C2×D4—2441no—
367C2×D4—2441no—
368C2×D4—2441no—
369C2×D4—2441no—
370C2×D4—2441no—
371C22×C4—611no—
372C22×C4—614no—
373C22×C4—611no—
374C22×C4—611no—
375C22×C4—611no—
376C22×C4—611no—
377C22×C4—611no—
378C22×C4—1222no—
379C22×C4—1222no—
380C22×C4—1222no—
381C22×C4—1222no—
382C22×C4—1222no—
383C22×C4—1222no—
384C22×C4—1222no—
385C22×C4—1222no—
386C22×C4C22×D6111yescharacteristic
387C22×C4C22×D6111yescharacteristic
388C22×C4C22×D6111yescharacteristic
389C22×C4C22×D6111yescharacteristic
390C4⋊C4—1222no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—41no—
394C22⋊C4—1222no—
395C22⋊C4—1222no—
396C22⋊C4—1222no—
397C22⋊C4—1222no—
398C22⋊C4—1222no—
399C22⋊C4—1222no—
400C22⋊C4—2441no—
401C22⋊C4—2441no—
402C22⋊C4—2441no—
403C42—1222no—
404C42—1222no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—612no—
425C23—1221no—
426C23—1221no—
427C23—1221no—
428C23—1221no—
429C23—1221no—
430C23—1221no—
431C23—1221no—
432C23—1221no—
433C23—1221no—
434C23—1221no—
435C23—1221no—
436C23—1221no—
437C23—1221no—
438C23D4×D6112yes—
439C23D4×D6112yes—
440C23C23×D6111yescharacteristic
441Q8—1228no—
442D4—28no—
443D4—44no—
444D4—44no—
445D4—1228no—
446D4—1228no—
447D4—2444no—
448D4—2444no—
449D4—2444no—
450D4—2444no—
451D4—2444no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—612no—
463C2×C4—612no—
464C2×C4—612no—
465C2×C4—612no—
466C2×C4—612no—
467C2×C4—612no—
468C2×C4—1228no—
469C2×C4—1228no—
470C2×C4—1228no—
471C2×C4—1221no—
472C2×C4—1221no—
473C2×C4—1221no—
474C2×C4—1221no—
475C2×C4—1221no—
476C2×C4—1221no—
477C2×C4—1221no—
478C2×C4—1221no—
479C2×C4—1221no—
480C2×C4—1221no—
481C2×C4—1221no—
482C2×C4—1221no—
483C2×C4D4×D6112yes—
484C2×C4#1175822412yescomplemented
485C22—22no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—1222no—
507C22—1222no—
508C22—1222no—
509C22—2441no—
510C22—2441no—
511C22—2441no—
512C22—2441no—
513C22—2441no—
514C22—2441no—
515C22—2441no—
516C22—2441no—
517C22—2441no—
518C22—2441no—
519C22—2441no—
520C22C2×D4×D6111yescharacteristic
521C22C2×D4×D6111yescharacteristic
522C22C2×D4×D6111yescharacteristic
523C22#41×D6111yescharacteristic
524C22C2×#1175822411yescharacteristic
525C22#1451982211yescharacteristic
526C22#1451982211yescharacteristic
527C4—22no—
528C4—22no—
529C4—41no—
530C4—41no—
531C4—614no—
532C4—1222no—
533C4—1222no—
534C4—1222no—
535C4—2441no—
536C4—2441no—
537C2—42no—
538C2—42no—
539C2—81no—
540C2—4881no—
541C2—2442no—
542C2#120×D6111yescharacteristic
543C2#1684030711yescharacteristic
544C2#1684032711yescharacteristic
545C2#1684039911yescharacteristic
546C2#1684040111yescharacteristic
547C2#1684043011yescharacteristic
548C2#1684043211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#392C2
hypercenter#392D61
hypocenterC61#2431
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×#11758224C2semidirect
2. C2×#14519773C2semidirect
3. C2×#14519763C2semidirect
4. C2×#14519749C2semidirect
5. #16839671C2semidirect
6. #16839670C2semidirect
7. #16839670C2semidirect
8. #16839666C2semidirect
9. #16839662C2semidirect
10. #16839642C2semidirect
11. #16839640C2semidirect
12. #16839639C2semidirect
13. #16839638C2semidirect
14. C22⋊C4×Dic61C2semidirect
15. C61×#392C2semidirect
92. C2×C22⋊D61D4semidirect
98. C22×Dic61D4semidirect
114. C2×Dic122D4semidirect
180. C2×C4×C61#41semidirect
206. C2×Dic61#41semidirect
282. #392D61semidirect
290. C61#2431semidirect
484. C2×C4#11758224semidirect