Finite Group Databasebeta

← #21449436

Subgroups — #21449436

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×#11758222C211yesmaximal, characteristic, complemented
2C2×#14519773C211yesmaximal, characteristic, complemented
3C2×#14519763C211yesmaximal, characteristic, complemented
4C2×#14519750C211yesmaximal, characteristic, complemented
5#16839672C211yesmaximal, characteristic, complemented
6#16839671C211yesmaximal, characteristic, complemented
7#16839671C211yesmaximal, characteristic, complemented
8#16839670C211yesmaximal, characteristic, complemented
9#16839666C211yesmaximal, characteristic, complemented
10#16839662C211yesmaximal, characteristic, complemented
11#16839641C211yesmaximal, characteristic, complemented
12#16839640C211yesmaximal, characteristic, complemented
13#16839638C211yesmaximal, characteristic, complemented
14#16839609C211yesmaximal, characteristic, complemented
15C61×#386C211yesmaximal, characteristic, complemented
16C2×#11758222—24no—
17C2×#11758222—24no—
18C2×#11758222—24no—
19C22×Dic122C2211yescharacteristic
20C22×D244C2211yescharacteristic
21C22×D244C2211yescharacteristic
22C22×D244C2211yescharacteristic
23C22×C22⋊D61C2211yescharacteristic
24C22×C22⋊D61C2211yescharacteristic
25C22×C22⋊D61C2211yescharacteristic
26C22×C22⋊D61C2211yescharacteristic
27C22×C22⋊D61C2211yescharacteristic
28C22×C22⋊D61C2211yescharacteristic
29C22×C4×D61C2211yescharacteristic
30C22×C4×D61C2211yescharacteristic
31#14519773—24no—
32#14519763—24no—
33#14519750—24no—
34C2×#11758196C2211yescharacteristic
35C2×C22⋊Dic61C2211yescharacteristic
36C2×C22⋊Dic61C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic
43C2×#11758198C2211yescharacteristic
44C2×C4×Dic61C2211yescharacteristic
45C2×C4×Dic61C2211yescharacteristic
46#14519684C2211yescharacteristic
47#14519684C2211yescharacteristic
48#14519684C2211yescharacteristic
49#14519684C2211yescharacteristic
50C22×D4×C61C2211yescharacteristic
51C23×C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61C2211yescharacteristic
53C2×C22⋊C4×C61C2211yescharacteristic
54C2×C22⋊C4×C61C2211yescharacteristic
55#95×C61C2211yescharacteristic
56#95×C61C2211yescharacteristic
57C24×C61C2311yescharacteristic
58C24×C61C2311yescharacteristic
59C23×D61C2311yescharacteristic
60C23×D61C2311yescharacteristic
61C23×D61C2311yescharacteristic
62C2×D4×C61—22no—
63C2×D4×C61—22no—
64C2×D4×C61—41no—
65C22×C4×C61—22no—
66C22×C4×C61—22no—
67C22×C4×C61—22no—
68C22×C4×C61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C22×C4×C61C2311yescharacteristic
71C22×C4×C61C2311yescharacteristic
72C22×C4×C61C2311yescharacteristic
73C2×C22⋊D61—22no—
74C2×C22⋊D61—22no—
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—41no—
87C2×C22⋊D61—41no—
88C2×C22⋊D61—41no—
89C2×C22⋊D61—41no—
90C2×C22⋊D61D414yescomplemented
91C22×Dic61C2311yescharacteristic
92C22×Dic61C2311yescharacteristic
93C22×Dic61C2311yescharacteristic
94C22×Dic61C2311yescharacteristic
95C22×Dic61C2311yescharacteristic
96#11758222—232no—
97C2×D244—22no—
98C2×D244—22no—
99C2×D244—22no—
100C2×D244—22no—
101C2×D244—22no—
102C2×D244—22no—
103C2×D244—41no—
104C2×D244—41no—
105C2×D244—41no—
106C2×C4×D61—22no—
107C2×C4×D61—22no—
108C2×C4×D61—22no—
109C2×C4×D61—22no—
110C2×C4×D61—22no—
111C2×C4×D61D414yescomplemented
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—41no—
120#11758198—22no—
121#11758198—22no—
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×C61C2×D412yes—
144C23×C61C2411yescharacteristic
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—21no—
151C22×D61—21no—
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×D61C2×D412yes—
165C22×D61C2×D412yes—
166D4×C61—44no—
167C2×C4×C61—28no—
168C2×C4×C61—21no—
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×C61—21no—
180C2×C4×C61C2×D412yes—
181C2×C4×C61C2×D412yes—
182C2×C4×C61#4112yescomplemented
183C22⋊D61—28no—
184C22⋊D61—28no—
185C22⋊D61—44no—
186C22⋊D61—44no—
187C22⋊D61—44no—
188C22⋊D61—44no—
189C2×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—21no—
192C2×Dic61—21no—
193C2×Dic61—21no—
194C2×Dic61—21no—
195C2×Dic61—21no—
196C2×Dic61—21no—
197C2×Dic61—21no—
198C2×Dic61—21no—
199C2×Dic61C2×D412yes—
200C2×Dic61C2×D412yes—
201C2×Dic61C2×D412yes—
202C2×Dic61C2×D412yes—
203C2×Dic61#4112yescomplemented
204D244—28no—
205D244—44no—
206D244—44no—
207C4×D61—28no—
208C4×D61—28no—
209Dic122—28no—
210C22×C61—22no—
211C22×C61—22no—
212C22×C61—22no—
213C22×C61—41no—
214C22×C61—41no—
215C22×C61—41no—
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×C61C22×D411yescharacteristic
225C22×C61C22×D411yescharacteristic
226C22×C61C22×D411yescharacteristic
227C22×C61C2×#4111yescharacteristic
228C22×C61C2×#4111yescharacteristic
229C22×C61H(5,𝔽2)11yescharacteristic
230C22×C61H(5,𝔽2)11yescharacteristic
231C2×D61—22no—
232C2×D61—22no—
233C2×D61—22no—
234C2×D61—22no—
235C2×D61—22no—
236C2×D61—22no—
237C2×D61—41no—
238C2×D61—41no—
239C2×D61—41no—
240C2×D61—41no—
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—22no—
255C4×C61—41no—
256C4×C61—41no—
257Dic61—22no—
258Dic61—22no—
259Dic61—41no—
260Dic61—41no—
261Dic61#12014yes—
262#2431—611nomaximal, Sylow
263C2×C61—42no—
264C2×C61—81no—
265C2×C61C2×#12011yescharacteristic
266C2×C61#53211yescharacteristic
267C2×C61#53511yescharacteristic
268C2×C61#54611yescharacteristic
269C2×C61#54611yescharacteristic
270C2×C61#55011yescharacteristic
271C2×C61#55011yescharacteristic
272D61—42no—
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#392—611no—
283#391—611no—
284#390—611no—
285#386—611no—
286#386—611no—
287#386—611no—
288#386D6111yescharacteristic, complemented
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×D4—611no—
303C22×D4—611no—
304C22×D4C2×D6111yescharacteristic
305C23×C4—611no—
306C23×C4—611no—
307C23×C4C2×D6111yescharacteristic
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#95C2×D6111yescharacteristic
331#95C2×D6111yescharacteristic
332C24—611no—
333C24—611no—
334C24—611no—
335C24C22×D6111yescharacteristic
336C24C22×D6111yescharacteristic
337#41—12232no—
338C2×Q8—614no—
339C2×Q8—1222no—
340C2×Q8—1222no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—41no—
344C2×D4—614no—
345C2×D4—1222no—
346C2×D4—1222no—
347C2×D4—1222no—
348C2×D4—1222no—
349C2×D4—1222no—
350C2×D4—1222no—
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—2441no—
365C2×D4—2441no—
366C2×D4—2441no—
367C2×D4—2441no—
368C2×D4—2441no—
369C2×D4—2441no—
370C2×D4—2441no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—611no—
375C22×C4—611no—
376C22×C4—611no—
377C22×C4—614no—
378C22×C4—611no—
379C22×C4—611no—
380C22×C4—1222no—
381C22×C4—1222no—
382C22×C4—1222no—
383C22×C4—1222no—
384C22×C4—1222no—
385C22×C4C22×D6111yescharacteristic
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—612no—
419C23—612no—
420C23—1221no—
421C23—1221no—
422C23—1221no—
423C23—1221no—
424C23—1221no—
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—
438C23—1221no—
439C23D4×D6112yes—
440C23C23×D6111yescharacteristic
441Q8—1228no—
442D4—44no—
443D4—1228no—
444D4—1228no—
445D4—1228no—
446D4—2444no—
447D4—2444no—
448D4—2444no—
449D4—2444no—
450D4—2444no—
451D4—2444no—
452C2×C4—28no—
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—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—612no—
466C2×C4—612no—
467C2×C4—612no—
468C2×C4—612no—
469C2×C4—612no—
470C2×C4—1228no—
471C2×C4—1228no—
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#1175822212yescomplemented
483C2×C4D4×D6112yes—
484C2×C4D4×D6112yes—
485C22—22no—
486C22—22no—
487C22—22no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—1222no—
500C22—1222no—
501C22—1222no—
502C22—1222no—
503C22—1222no—
504C22—1222no—
505C22—2441no—
506C22—2441no—
507C22—2441no—
508C22—2441no—
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×#1175822211yescharacteristic
525C22#1451982211yescharacteristic
526C22#1451982311yescharacteristic
527C4—22no—
528C4—22no—
529C4—22no—
530C4—41no—
531C4—41no—
532C4—614no—
533C4—1222no—
534C4—1222no—
535C4—2441no—
536C4—2441no—
537C2—42no—
538C2—81no—
539C2—4881no—
540C2—2442no—
541C2—2442no—
542C2#120×D6111yescharacteristic
543C2#1684030911yescharacteristic
544C2#1684032811yescharacteristic
545C2#1684040211yescharacteristic
546C2#1684040411yescharacteristic
547C2#1684043011yescharacteristic
548C2#1684043311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#386C2
hypercenter#386D61
hypocenterC61#2431
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C22×#11758222C2semidirect
2. C2×#14519773C2semidirect
3. C2×#14519763C2semidirect
4. C2×#14519750C2semidirect
5. #16839672C2semidirect
6. #16839671C2semidirect
7. #16839671C2semidirect
8. #16839670C2semidirect
9. #16839666C2semidirect
10. #16839662C2semidirect
11. #16839641C2semidirect
12. #16839640C2semidirect
13. #16839638C2semidirect
14. #16839609C2semidirect
15. C61×#386C2semidirect
90. C2×C22⋊D61D4semidirect
111. C2×C4×D61D4semidirect
114. C2×Dic122D4semidirect
182. C2×C4×C61#41semidirect
203. C2×Dic61#41semidirect
288. #386D61semidirect
290. C61#2431semidirect
482. C2×C4#11758222semidirect