Finite Group Databasebeta

← #21452079

Subgroups — #21452079

Order 7808.

734 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519758C211yesmaximal, characteristic, complemented
2C2×#14519749C211yesmaximal, characteristic, complemented
3C2×#14519749C211yesmaximal, characteristic, complemented
4#16839676C211yesmaximal, characteristic, complemented
5#16839676C211yesmaximal, characteristic, complemented
6#16839670C211yesmaximal, characteristic, complemented
7#16839670C211yesmaximal, characteristic, complemented
8#16839670C211yesmaximal, characteristic, complemented
9#16839670C211yesmaximal, characteristic, complemented
10#16839653C211yesmaximal, characteristic, complemented
11#16839646C211yesmaximal, characteristic, complemented
12#16839642C211yesmaximal, characteristic, complemented
13#16839642C211yesmaximal, characteristic, complemented
14#16839642C211yesmaximal, characteristic, complemented
15C2×#127×C61C211yesmaximal, characteristic, complemented
16C22×C22⋊D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C23×Dic61C2211yescharacteristic
21C23×Dic61C2211yescharacteristic
22#14519758—24no—
23#14519749—24no—
24#14519749—24no—
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
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
47C22×D4×C61C2211yescharacteristic
48C22×D4×C61C2211yescharacteristic
49C22×D4×C61C2211yescharacteristic
50C22×D4×C61C2211yescharacteristic
51C22×D4×C61C2211yescharacteristic
52C22×D4×C61C2211yescharacteristic
53#127×C61—24no—
54C2×C42×C61C2211yescharacteristic
55C24×C61C2311yescharacteristic
56C24×C61C2311yescharacteristic
57C24×C61C2311yescharacteristic
58C24×C61C2311yescharacteristic
59C23×D61C2311yescharacteristic
60C2×D4×C61—22no—
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—22no—
69C2×D4×C61—41no—
70C2×D4×C61—41no—
71C2×D4×C61—41no—
72C2×D4×C61—41no—
73C2×D4×C61—41no—
74C2×D4×C61—41no—
75C2×D4×C61—41no—
76C2×D4×C61—41no—
77C2×D4×C61D414yescomplemented
78C22×C4×C61C2311yescharacteristic
79C22×C4×C61C2311yescharacteristic
80C22×C4×C61C2311yescharacteristic
81C2×C22⋊D61—22no—
82C2×C22⋊D61—22no—
83C2×C22⋊D61—22no—
84C2×C22⋊D61—22no—
85C2×C22⋊D61—41no—
86C2×C22⋊D61—41no—
87C2×C22⋊D61—41no—
88C2×C22⋊D61—41no—
89C2×C22⋊D61—41no—
90C2×C22⋊D61—41no—
91C2×C22⋊D61—41no—
92C2×C22⋊D61—41no—
93C22×Dic61—22no—
94C22×Dic61—22no—
95C22×Dic61—22no—
96C22×Dic61—41no—
97C22×Dic61—41no—
98C22×Dic61—41no—
99C22×Dic61C2311yescharacteristic
100C22×Dic61C2311yescharacteristic
101C22×Dic61C2311yescharacteristic
102C22×Dic61C2311yescharacteristic
103C22×Dic61C2311yescharacteristic
104C22×Dic61C2311yescharacteristic
105C22×Dic61C2311yescharacteristic
106C42×C61—22no—
107C22⋊Dic61—22no—
108C22⋊Dic61—22no—
109C22⋊Dic61—22no—
110C22⋊Dic61—22no—
111C22⋊Dic61—22no—
112C22⋊Dic61—41no—
113C22⋊Dic61—41no—
114C22⋊Dic61—41no—
115C22⋊Dic61—41no—
116C22⋊Dic61—41no—
117#11758198—22no—
118#11758198—22no—
119#11758198—22no—
120#11758196—22no—
121#11758196—22no—
122#11758196D414yescomplemented
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×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—
159D4×C61—44no—
160D4×C61—44no—
161D4×C61—44no—
162D4×C61—44no—
163D4×C61—44no—
164D4×C61—44no—
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×C61C2×D412yes—
172C2×C4×C61C2×D412yes—
173C2×C4×C61#4112yes—
174C22⋊D61—44no—
175C22⋊D61—44no—
176C22⋊D61—44no—
177C22⋊D61—44no—
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—21no—
192C2×Dic61—21no—
193C2×Dic61—21no—
194C2×Dic61—21no—
195C2×Dic61—21no—
196C2×Dic61—21no—
197C2×Dic61—44no—
198C2×Dic61—44no—
199C2×Dic61C2×D412yes—
200C2×Dic61C2×D412yes—
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—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×C61C22×D411yescharacteristic
230C22×C61C22×D411yescharacteristic
231C22×C61C2×#4111yescharacteristic
232C22×C61H(5,𝔽2)11yescharacteristic
233C22×C61H(5,𝔽2)11yescharacteristic
234C22×C61H(5,𝔽2)11yescharacteristic
235C22×C61H(5,𝔽2)11yescharacteristic
236C2×D61—41no—
237C2×D61—41no—
238C2×D61—41no—
239C2×D61—41no—
240C2×D61—41no—
241C2×D61—41no—
242C2×D61—41no—
243C4×C61—22no—
244C4×C61—22no—
245C4×C61—22no—
246Dic61—22no—
247Dic61—22no—
248Dic61—41no—
249Dic61—41no—
250Dic61—41no—
251Dic61—41no—
252Dic61—41no—
253#2673—611nomaximal, Sylow
254C2×C61—42no—
255C2×C61—42no—
256C2×C61—81no—
257C2×C61—81no—
258C2×C61#53411yescharacteristic
259C2×C61#53511yescharacteristic
260C2×C61#54011yescharacteristic
261C2×C61D4211yescharacteristic
262C2×C61#54611yescharacteristic
263C2×C61#55011yescharacteristic
264C2×C61#56011yescharacteristic
265D61—81no—
266C2×#127D6111yescharacteristic, complemented
267C2×#123—611no—
268C2×#121—611no—
269C2×#121—611no—
270#394—611no—
271#394—611no—
272#392—611no—
273#392—611no—
274#392—611no—
275#392—611no—
276#388—611no—
277#387—611no—
278#386—611no—
279#386—611no—
280#386—611no—
281C61#267311yescharacteristic, complemented, Sylow
282C22×D4—611no—
283C22×D4—611no—
284C22×D4—611no—
285C22×D4—611no—
286C22×D4C2×D6111yescharacteristic
287C22×D4C2×D6111yescharacteristic
288C22×D4C2×D6111yescharacteristic
289C22×D4C2×D6111yescharacteristic
290C22×D4C2×D6111yescharacteristic
291C22×D4C2×D6111yescharacteristic
292C23×C4—611no—
293C23×C4—611no—
294#127—24no—
295#123—1224no—
296#121—1224no—
297#121—1224no—
298C2×C4⋊C4—611no—
299C2×C4⋊C4—611no—
300C2×C4⋊C4—611no—
301C2×C22⋊C4—611no—
302C2×C22⋊C4—611no—
303C2×C22⋊C4—611no—
304C2×C22⋊C4—611no—
305C2×C22⋊C4—611no—
306C2×C22⋊C4—611no—
307C2×C22⋊C4—611no—
308C2×C22⋊C4—611no—
309C2×C22⋊C4—611no—
310C2×C22⋊C4—611no—
311C2×C22⋊C4—611no—
312C2×C22⋊C4—611no—
313C2×C22⋊C4—611no—
314C2×C42C2×D6111yescharacteristic
315#95—611no—
316#95—611no—
317#95—611no—
318#95—611no—
319#95—611no—
320#95—611no—
321C24—611no—
322C24C22×D6111yescharacteristic
323C24C22×D6111yescharacteristic
324C24C22×D6111yescharacteristic
325C24C22×D6111yescharacteristic
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—1222no—
344C2×D4—1222no—
345C2×D4—1222no—
346C2×D4—1222no—
347C2×D4—2441no—
348C2×D4—2441no—
349C2×D4—2441no—
350C2×D4—2441no—
351C2×D4—2441no—
352C2×D4—2441no—
353C2×D4—2441no—
354C2×D4—2441no—
355C2×D4C22⋊D6114yescomplemented
356C22×C4—611no—
357C22×C4—611no—
358C22×C4—611no—
359C22×C4—611no—
360C22×C4—611no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—1222no—
364C22×C4—1222no—
365C22×C4—1222no—
366C22×C4—2441no—
367C22×C4—2441no—
368C22×C4—2441no—
369C22×C4C22×D6111yescharacteristic
370C22×C4C22×D6111yescharacteristic
371C22×C4C22×D6111yescharacteristic
372C4⋊C4—614no—
373C4⋊C4—1222no—
374C4⋊C4—1222no—
375C22⋊C4—1222no—
376C22⋊C4—1222no—
377C22⋊C4—1222no—
378C22⋊C4—1222no—
379C22⋊C4—1222no—
380C22⋊C4—1222no—
381C22⋊C4—1222no—
382C22⋊C4—1222no—
383C22⋊C4—2441no—
384C22⋊C4—2441no—
385C22⋊C4—2441no—
386C22⋊C4—2441no—
387C22⋊C4—2441no—
388C42—22no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—1221no—
416C23—1221no—
417C23—1221no—
418C23—1221no—
419C23—1221no—
420C23—1221no—
421C23—1221no—
422C23C2×C22⋊D6112yes—
423C23C2×C22⋊D6112yes—
424C23C23×D6111yescharacteristic
425D4—44no—
426D4—44no—
427D4—44no—
428D4—44no—
429D4—44no—
430D4—44no—
431D4—2444no—
432D4—2444no—
433D4—2444no—
434D4—2444no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—612no—
442C2×C4—612no—
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—1221no—
452C2×C4—1221no—
453C2×C4—1221no—
454C2×C4—1221no—
455C2×C4—1221no—
456C2×C4—1221no—
457C2×C4—1221no—
458C2×C4—1221no—
459C2×C4—1221no—
460C2×C4—1221no—
461C2×C4—1221no—
462C2×C4—2444no—
463C2×C4—2444no—
464C2×C4D4×D6112yes—
465C2×C4#1175822412yes—
466C2×C4C2×C22⋊D6112yes—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—22no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—2441no—
496C22—2441no—
497C22—2441no—
498C22—2441no—
499C22—2441no—
500C22—2441no—
501C22—2441no—
502C22C2×D4×D6111yescharacteristic
503C22C22×C22⋊D6111yescharacteristic
504C22C2×#1175822411yescharacteristic
505C22#1451982211yescharacteristic
506C22#1451982211yescharacteristic
507C22#1451982211yescharacteristic
508C22#1451982211yescharacteristic
509C4—22no—
510C4—22no—
511C4—22no—
512C4—1222no—
513C4—1222no—
514C4—2441no—
515C4—2441no—
516C4—2441no—
517C4—2441no—
518C4—2441no—
519C2—42no—
520C2—42no—
521C2—81no—
522C2—81no—
523C2—4881no—
524C2#1684032111yescharacteristic
525C2#1684032511yescharacteristic
526C2#1684036611yescharacteristic
527C2D4×C22⋊D6111yescharacteristic
528C2#1684040611yescharacteristic
529C2#1684043211yescharacteristic
530C2#1684049911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#127×C61C2
hypercenterC2×#127D61
hypocenterC61#2673
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#14519758C2semidirect
2. C2×#14519749C2semidirect
3. C2×#14519749C2semidirect
4. #16839676C2semidirect
5. #16839676C2semidirect
6. #16839670C2semidirect
7. #16839670C2semidirect
8. #16839670C2semidirect
9. #16839670C2semidirect
10. #16839653C2semidirect
11. #16839646C2semidirect
12. #16839642C2semidirect
13. #16839642C2semidirect
14. #16839642C2semidirect
15. C2×#127×C61C2semidirect
77. C2×D4×C61D4semidirect
122. #11758196D4semidirect
266. C2×#127D61semidirect
281. C61#2673semidirect
355. C2×D4C22⋊D61semidirect