Finite Group Databasebeta

← #29690212

Subgroups — #29690212

Order 15616.

670 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448217C211yesmaximal, characteristic
2#21446435C211yesmaximal, characteristic
3#21446429C211yesmaximal, characteristic
4#21446428C211yesmaximal, characteristic
5#21446422C211yesmaximal, characteristic
6#21446384C211yesmaximal, characteristic, complemented
7#21446382C211yesmaximal, characteristic, complemented
8#21446377C211yesmaximal, characteristic, complemented
9#21446375C211yesmaximal, characteristic, complemented
10#21445972C211yesmaximal, characteristic, complemented
11#21445938C211yesmaximal, characteristic, complemented
12#21445799C211yesmaximal, characteristic
13#21445678C211yesmaximal, characteristic, complemented
14#21445678C211yesmaximal, characteristic, complemented
15C61×#1797C211yesmaximal, characteristic
16C2×C4⋊#92418C2211yescharacteristic
17C2×C4⋊#92418C2211yescharacteristic
18C2×#14519706C2211yescharacteristic
19C2×#14519706C2211yescharacteristic
20C2×#14519706C2211yescharacteristic
21C2×#14519706C2211yescharacteristic
22C2×C22⋊#92418C2211yescharacteristic
23C2×C22⋊#92418C2211yescharacteristic
24C2×#14519687C2211yescharacteristic
25C2×#14519687C2211yescharacteristic
26C2×C8×Dic61C2211yescharacteristic
27C2×C8×Dic61C2211yescharacteristic
28#16839630C411yescharacteristic
29#16839630C411yescharacteristic
30#16839628C411yescharacteristic
31#16839628C411yescharacteristic
32#16839625C411yescharacteristic
33#16839625C411yescharacteristic
34#16839622C411yescharacteristic
35#16839622C411yescharacteristic
36C4×C4⋊Dic61C2211yescharacteristic
37C4×C4⋊Dic61C2211yescharacteristic
38C4×C22⋊Dic61C2211yescharacteristic
39C4×C22⋊Dic61C2211yescharacteristic
40#16839608C2211yescharacteristic
41#16839608C2211yescharacteristic
42#16839517C2211yescharacteristic
43#16839517C2211yescharacteristic
44#16839516C2211yescharacteristic
45#16839516C2211yescharacteristic
46#16839516C2211yescharacteristic
47#16839516C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C22×C42×C61C2211yescharacteristic
53C2×C4⋊C8×C61C2211yescharacteristic
54C2×C4⋊C8×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×#92418C2311yescharacteristic
60C22×#92418C2311yescharacteristic
61C22×#92418C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63C2×C4⋊Dic61C2×C411yescharacteristic
64C2×C4⋊Dic61C2×C411yescharacteristic
65C2×C4⋊Dic61C2×C411yescharacteristic
66C2×C4⋊Dic61C2×C411yescharacteristic
67C2×C22⋊Dic61C2×C411yescharacteristic
68C2×C22⋊Dic61C2×C411yescharacteristic
69C2×C22⋊Dic61C2×C411yescharacteristic
70C2×C22⋊Dic61C2×C411yescharacteristic
71C2×C4×Dic61C2311yescharacteristic
72C2×C4×Dic61C2311yescharacteristic
73C2×C4×Dic61C2311yescharacteristic
74C2×C4×Dic61C2311yescharacteristic
75C4⋊#92418—22no—
76C4⋊#92418—22no—
77#14519706—41no—
78#14519706—41no—
79#14519706—41no—
80#14519706—41no—
81C22⋊#92418—41no—
82C22⋊#92418—41no—
83#14519687—41no—
84#14519687—41no—
85C8×Dic61—41no—
86C8×Dic61—41no—
87#14519684C2×C411yescharacteristic
88#14519684C2×C411yescharacteristic
89#14519684C2×C411yescharacteristic
90#14519684C2×C411yescharacteristic
91#14519684C2×C411yescharacteristic
92#14519684C2×C411yescharacteristic
93#14519684C2×C411yescharacteristic
94#14519684C2×C411yescharacteristic
95#14519684C2×C411yescharacteristic
96#14519684C2×C411yescharacteristic
97#14519684C2×C411yescharacteristic
98#14519684C2×C411yescharacteristic
99#14519684C2×C411yescharacteristic
100#14519684C2×C411yescharacteristic
101#14519684C2×C411yescharacteristic
102#14519684C2×C411yescharacteristic
103C23×C4×C61C2×C411yescharacteristic
104C23×C4×C61C2×C411yescharacteristic
105C23×C4×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C2×C42×C61—22no—
111C2×C42×C61—22no—
112C2×C42×C61C2×C411yescharacteristic
113C2×C42×C61C2×C411yescharacteristic
114C2×C42×C61C2311yescharacteristic
115C2×C42×C61C2311yescharacteristic
116C4⋊C8×C61—22no—
117C4⋊C8×C61—22no—
118C22⋊C8×C61—41no—
119C22⋊C8×C61—41no—
120C24×C61C22×C411yescharacteristic
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—41no—
132C22×C4×C61—41no—
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C2411yescharacteristic
139C22×Dic61C22×C411yescharacteristic
140C22×Dic61C22×C411yescharacteristic
141C22×Dic61C22×C411yescharacteristic
142C22×Dic61C22×C411yescharacteristic
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C411yescharacteristic
146C22×Dic61C22×C411yescharacteristic
147C2×C8×C61—21no—
148C2×C8×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C42×C61—22no—
160C42×C61—22no—
161C42×C61—21no—
162C42×C61—21no—
163C42×C61#4112yes—
164C42×C61#4112yes—
165C22⋊Dic61—22no—
166C22⋊Dic61—22no—
167C22⋊Dic61—41no—
168C22⋊Dic61—41no—
169C4⋊Dic61—22no—
170C4⋊Dic61—22no—
171C4⋊Dic61—41no—
172C4⋊Dic61—41no—
173C4×Dic61—21no—
174C4×Dic61—21no—
175C4×Dic61—21no—
176C4×Dic61—21no—
177C4×Dic61—21no—
178C4×Dic61—21no—
179C4×Dic61—21no—
180C4×Dic61—21no—
181C2×#92418—21no—
182C2×#92418—21no—
183C2×#92418—21no—
184C2×#92418—21no—
185C2×#92418—21no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C23×C61—21no—
194C23×C61—21no—
195C23×C61—21no—
196C23×C61—21no—
197C23×C61—21no—
198C23×C61—21no—
199C23×C61#13112yes—
200C23×C61C23×C411yescharacteristic
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—44no—
214C2×C4×C61—44no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61#11712yes—
220C2×C4×C61#11712yes—
221C2×C4×C61#13112yes—
222C2×C4×C61C2×#4111yescharacteristic
223C2×C4×C61C2×#4111yescharacteristic
224C2×C4×C61H(5,𝔽2)11yescharacteristic
225C2×C4×C61H(5,𝔽2)11yescharacteristic
226C2×C4×C612−1+411yescharacteristic
227C2×C4×C612−1+411yescharacteristic
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C8×C61—41no—
253C8×C61—41no—
254C8×C61—41no—
255C8×C61—41no—
256#92418—41no—
257#92418—41no—
258#92418—41no—
259#92418—41no—
260#21928—611nomaximal, Sylow
261C22×C61—22no—
262C22×C61—22no—
263C22×C61—22no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61C2×#11711yescharacteristic
269C22×C61#52011yescharacteristic
270C22×C61#52011yescharacteristic
271C22×C61C2×#13111yescharacteristic
272C22×C61C2×#13111yescharacteristic
273C22×C61#56811yescharacteristic
274C22×C61#56811yescharacteristic
275C4×C61—22no—
276C4×C61—22no—
277C4×C61—22no—
278C4×C61—41no—
279C4×C61—41no—
280C4×C61#54011yescharacteristic
281C4×C61#54111yescharacteristic
282C4×C61#54211yescharacteristic
283C4×C61#54211yescharacteristic
284Dic61—41no—
285Dic61—41no—
286Dic61—41no—
287Dic61—41no—
288Dic61—41no—
289Dic61—41no—
290Dic61—41no—
291Dic61—41no—
292#2283—611no—
293#1924—611no—
294#1924—611no—
295#1923—611no—
296#1923—611no—
297#1917—611no—
298#1917—611no—
299#1916—611no—
300#1916—611no—
301#1843—611no—
302#1832—611no—
303#1797—611no—
304#1797D6111yescharacteristic
305#1768—611no—
306#1768—611no—
307C2×C61—42no—
308C2×C61#231411yescharacteristic
309C2×C61#292411yescharacteristic
310C2×C61#292411yescharacteristic
311C2×C61#299211yescharacteristic
312C2×C61#299311yescharacteristic
313C2×C61#299411yescharacteristic
314C2×C61#299511yescharacteristic
315C22×C42C2×D6111yescharacteristic
316C2×C4⋊C8—611no—
317C2×C4⋊C8—611no—
318C2×C4⋊C8—611no—
319C2×C4⋊C8—611no—
320C2×C4⋊C8—611no—
321C2×C4⋊C8—611no—
322C2×C4⋊C8C2×D6111yescharacteristic
323C2×C4⋊C8C2×D6111yescharacteristic
324C2×C22⋊C8—611no—
325C2×C22⋊C8—611no—
326C2×C22⋊C8C2×D6111yescharacteristic
327C2×C22⋊C8C2×D6111yescharacteristic
328C2×#97—611no—
329C2×#97—611no—
330C2×C4×C8—611no—
331C2×C4×C8—611no—
332#383—611no—
333#383—611no—
334#382—611no—
335#382—611no—
336#381—611no—
337#381—611no—
338#380—611no—
339#380—611no—
340C4×C4⋊C4—611no—
341C4×C4⋊C4—611no—
342C4×C22⋊C4—611no—
343C4×C22⋊C4—611no—
344#376—611no—
345#376—611no—
346#336—611no—
347#336—611no—
348#336—611no—
349#336—611no—
350#336—611no—
351#336—611no—
352#336—611no—
353#336—611no—
354#336—611no—
355#336—611no—
356#336C2×D6111yescharacteristic
357#336C2×D6111yescharacteristic
358C61#2192811yescharacteristic, complemented, Sylow
359C23×C4C4×D6111yescharacteristic
360C23×C4C4×D6111yescharacteristic
361C23×C4C22×D6111yescharacteristic
362C22×C8—611no—
363C22×C8—611no—
364C22×C8—611no—
365C22×C8—611no—
366C22×C8C22×D6111yescharacteristic
367C22×C8C22×D6111yescharacteristic
368C22×C8C22×D6111yescharacteristic
369C22×C8C22×D6111yescharacteristic
370C2×C4⋊C4—611no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—611no—
374C2×C22⋊C4—611no—
375C2×C22⋊C4—611no—
376C2×C22⋊C4—611no—
377C2×C22⋊C4—611no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—611no—
381C2×C42—611no—
382C2×C42—611no—
383C2×C42—611no—
384C2×C42C4×D6111yescharacteristic
385C2×C42C4×D6111yescharacteristic
386C2×C42C22×D6111yescharacteristic
387C2×C42C22×D6111yescharacteristic
388C4⋊C8—22no—
389C4⋊C8—22no—
390C4⋊C8—1222no—
391C4⋊C8—1222no—
392C4⋊C8—2441no—
393C4⋊C8—2441no—
394C4⋊C8—2441no—
395C4⋊C8—2441no—
396C22⋊C8—41no—
397C22⋊C8—41no—
398C22⋊C8—2441no—
399C22⋊C8—2441no—
400#97—2441no—
401#97—2441no—
402C4×C8—2441no—
403C4×C8—2441no—
404#95—611no—
405#95—611no—
406#95—611no—
407#95—611no—
408#95—611no—
409#95—611no—
410#95—611no—
411#95—611no—
412#95—611no—
413#95—611no—
414#95—611no—
415#95—611no—
416#95—611no—
417#95—611no—
418#95—611no—
419#95—611no—
420C24C2×C4×D6111yescharacteristic
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—611no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4—611no—
441C22×C4C2×C4×D6111yescharacteristic
442C22×C4C2×C4×D6111yescharacteristic
443C22×C4C2×C4×D6111yescharacteristic
444C22×C4C2×C4×D6111yescharacteristic
445C22×C4C2×C4×D6111yescharacteristic
446C22×C4C23×D6111yescharacteristic
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C4⋊C4—1222no—
472C4⋊C4—1222no—
473C4⋊C4—2441no—
474C4⋊C4—2441no—
475C22⋊C4—1222no—
476C22⋊C4—1222no—
477C22⋊C4—2441no—
478C22⋊C4—2441no—
479C42—21no—
480C42—21no—
481C42—22no—
482C42—22no—
483C42—1221no—
484C42—1221no—
485C42—1221no—
486C42—1221no—
487C42—1221no—
488C42—1221no—
489C42—1221no—
490C42—1221no—
491C42#1175822412yes—
492C42#1175822412yes—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23#1451978512yes—
500C23C22×C4×D6111yescharacteristic
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—44no—
514C2×C4—44no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—1221no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—1221no—
523C2×C4—1221no—
524C2×C4—1221no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4#1451973312yes—
544C2×C4#1451973312yes—
545C2×C4#1451978312yes—
546C2×C4C2×#1175822411yescharacteristic
547C2×C4C2×#1175822411yescharacteristic
548C2×C4#1451982211yescharacteristic
549C2×C4#1451982311yescharacteristic
550C2×C4#1451982411yescharacteristic
551C2×C4#1451982511yescharacteristic
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—2441no—
557C8—2441no—
558C8—2441no—
559C8—2441no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22C2×#1451973311yescharacteristic
568C22#1684024211yescharacteristic
569C22#1684024311yescharacteristic
570C22C2×#1451978311yescharacteristic
571C22C2×#1451978511yescharacteristic
572C22#1684052811yescharacteristic
573C22#1684052811yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—41no—
578C4—41no—
579C4—2441no—
580C4—2441no—
581C4—2441no—
582C4—2441no—
583C4—2441no—
584C4—2441no—
585C4—2441no—
586C4—2441no—
587C4#1684036511yescharacteristic
588C4#1684037211yescharacteristic
589C4#1684037911yescharacteristic
590C4#1684038511yescharacteristic
591C2—42no—
592C2#2144842611yescharacteristic
593C2#2145447311yescharacteristic
594C2#2145447911yescharacteristic
595C2#2145496011yescharacteristic
596C2#2145497011yescharacteristic
597C2#2145497511yescharacteristic
598C2#2145498611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1797C2
prime radicalC24×C61C22×C4
cosocleC22×C4×C61C24
hypercenter#1797D61
hypocenterC61#21928
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
6. #21446384C2semidirect
7. #21446382C2semidirect
8. #21446377C2semidirect
9. #21446375C2semidirect
10. #21445972C2semidirect
11. #21445938C2semidirect
13. #21445678C2semidirect
14. #21445678C2semidirect
358. C61#21928semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214482172
#214464352
#214464292
#214464282
#214464222
#214463842
#214463822
#214463772
#214463752
#214459722
#214459382
#214457992
#214456782
C61×#17972
#2192861