Finite Group Databasebeta

← #29690227

Subgroups — #29690227

Order 15616.

648 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448317C211yesmaximal, 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#21445970C211yesmaximal, characteristic, complemented
11#21445935C211yesmaximal, characteristic, complemented
12#21445803C211yesmaximal, characteristic
13#21445678C211yesmaximal, characteristic, complemented
14#21445678C211yesmaximal, characteristic, complemented
15C61×#1798C211yesmaximal, 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#16839655C411yescharacteristic
29#16839655C411yescharacteristic
30#16839655C411yescharacteristic
31#16839655C411yescharacteristic
32#16839648C411yescharacteristic
33#16839648C411yescharacteristic
34#16839648C411yescharacteristic
35#16839648C411yescharacteristic
36C4×C4⋊Dic61C2211yescharacteristic
37C4×C4⋊Dic61C2211yescharacteristic
38C4×C22⋊Dic61C2211yescharacteristic
39C4×C22⋊Dic61C2211yescharacteristic
40#16839608C2211yescharacteristic
41C42×Dic61C2211yescharacteristic
42#16839517C2211yescharacteristic
43#16839517C2211yescharacteristic
44#16839516C2211yescharacteristic
45#16839516C2211yescharacteristic
46#16839516C2211yescharacteristic
47#16839516C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#117×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×Dic61C2×C411yescharacteristic
72C2×C4×Dic61C2×C411yescharacteristic
73C2×C4×Dic61C2×C411yescharacteristic
74C2×C4×Dic61C2×C411yescharacteristic
75C2×C4×Dic61C2311yescharacteristic
76C2×C4×Dic61C2311yescharacteristic
77C2×C4×Dic61C2311yescharacteristic
78C2×C4×Dic61C2311yescharacteristic
79C4⋊#92418—22no—
80C4⋊#92418—22no—
81#14519706—41no—
82#14519706—41no—
83#14519706—41no—
84#14519706—41no—
85C22⋊#92418—41no—
86C22⋊#92418—41no—
87#14519687—41no—
88#14519687—41no—
89C8×Dic61—41no—
90C8×Dic61—41no—
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×C61C2311yescharacteristic
104C22×C8×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108#117×C61—22no—
109#117×C61—22no—
110C2×C4⋊C4×C61C2×C411yescharacteristic
111C2×C4⋊C4×C61C2×C411yescharacteristic
112C2×C22⋊C4×C61C2×C411yescharacteristic
113C2×C22⋊C4×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—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61C22×C411yescharacteristic
128C22×C4×C61C22×C411yescharacteristic
129C22×C4×C61C22×C411yescharacteristic
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C2411yescharacteristic
133C22×Dic61C22×C411yescharacteristic
134C22×Dic61C22×C411yescharacteristic
135C22×Dic61C22×C411yescharacteristic
136C22×Dic61C22×C411yescharacteristic
137C22×Dic61C22×C411yescharacteristic
138C22×Dic61C22×C411yescharacteristic
139C22×Dic61C22×C411yescharacteristic
140C22×Dic61C22×C411yescharacteristic
141C2×C8×C61—21no—
142C2×C8×C61—21no—
143C2×C8×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61—21no—
147C2×C8×C61—21no—
148C2×C8×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C4⋊C4×C61—22no—
154C4⋊C4×C61—22no—
155C22⋊C4×C61—22no—
156C22⋊C4×C61—22no—
157C42×C61—21no—
158C42×C61—21no—
159C42×C61#4112yes—
160C42×C61#4112yes—
161C22⋊Dic61—22no—
162C22⋊Dic61—22no—
163C22⋊Dic61—41no—
164C22⋊Dic61—41no—
165C4⋊Dic61—22no—
166C4⋊Dic61—22no—
167C4⋊Dic61—41no—
168C4⋊Dic61—41no—
169C4×Dic61—21no—
170C4×Dic61—21no—
171C4×Dic61—21no—
172C4×Dic61—21no—
173C4×Dic61—21no—
174C4×Dic61—21no—
175C4×Dic61—21no—
176C4×Dic61—21no—
177C4×Dic61—22no—
178C4×Dic61—22no—
179C4×Dic61—41no—
180C4×Dic61—41no—
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—21no—
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—21no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61#11712yes—
219C2×C4×C61#11712yes—
220C2×C4×C61C2×#4111yescharacteristic
221C2×C4×C61C2×#4111yescharacteristic
222C2×C4×C61H(5,𝔽2)11yescharacteristic
223C2×C4×C61H(5,𝔽2)11yescharacteristic
224C2×C4×C612−1+411yescharacteristic
225C2×C4×C612−1+411yescharacteristic
226C2×Dic61—21no—
227C2×Dic61—21no—
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#13112yes—
249C2×Dic61#13112yes—
250C8×C61—41no—
251C8×C61—41no—
252C8×C61—41no—
253C8×C61—41no—
254#92418—41no—
255#92418—41no—
256#92418—41no—
257#92418—41no—
258#21929—611nomaximal, Sylow
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61C2×#11711yescharacteristic
267C22×C61#52011yescharacteristic
268C22×C61#52011yescharacteristic
269C22×C61C2×#13111yescharacteristic
270C22×C61C2×#13111yescharacteristic
271C22×C61#56811yescharacteristic
272C22×C61#56811yescharacteristic
273C4×C61—22no—
274C4×C61—22no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61#54011yescharacteristic
279C4×C61#54111yescharacteristic
280C4×C61#54211yescharacteristic
281C4×C61#54211yescharacteristic
282Dic61—22no—
283Dic61—22no—
284Dic61—41no—
285Dic61—41no—
286Dic61—41no—
287Dic61—41no—
288Dic61—41no—
289Dic61—41no—
290#2298—611no—
291#1924—611no—
292#1924—611no—
293#1923—611no—
294#1923—611no—
295#1917—611no—
296#1917—611no—
297#1916—611no—
298#1916—611no—
299#1842—611no—
300#1831—611no—
301#1798—611no—
302#1798D6111yescharacteristic
303#1768—611no—
304#1768—611no—
305C2×C61—81no—
306C2×C61#231411yescharacteristic
307C2×C61#292511yescharacteristic
308C2×C61#292511yescharacteristic
309C2×C61#299211yescharacteristic
310C2×C61#299311yescharacteristic
311C2×C61#299411yescharacteristic
312C2×C61#299511yescharacteristic
313C2×#117C2×D6111yescharacteristic
314C2×C4⋊C8—611no—
315C2×C4⋊C8—611no—
316C2×C4⋊C8—611no—
317C2×C4⋊C8—611no—
318C2×C4⋊C8—611no—
319C2×C4⋊C8—611no—
320C2×C4⋊C8C2×D6111yescharacteristic
321C2×C4⋊C8C2×D6111yescharacteristic
322C2×C22⋊C8—611no—
323C2×C22⋊C8—611no—
324C2×C22⋊C8C2×D6111yescharacteristic
325C2×C22⋊C8C2×D6111yescharacteristic
326C2×#97—611no—
327C2×#97—611no—
328C2×C4×C8—611no—
329C2×C4×C8—611no—
330#388—611no—
331#388—611no—
332#388—611no—
333#388—611no—
334#387—611no—
335#387—611no—
336#387—611no—
337#387—611no—
338C4×C4⋊C4—611no—
339C4×C4⋊C4—611no—
340C4×C22⋊C4—611no—
341C4×C22⋊C4—611no—
342#376—611no—
343C43—611no—
344#336—611no—
345#336—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#336C2×D6111yescharacteristic
355#336C2×D6111yescharacteristic
356C61#2192911yescharacteristic, complemented, Sylow
357C23×C4C22×D6111yescharacteristic
358C22×C8—611no—
359C22×C8—611no—
360C22×C8—611no—
361C22×C8—611no—
362C22×C8C22×D6111yescharacteristic
363C22×C8C22×D6111yescharacteristic
364C22×C8C22×D6111yescharacteristic
365C22×C8C22×D6111yescharacteristic
366#117—22no—
367#117—22no—
368C2×C4⋊C4—611no—
369C2×C4⋊C4—611no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4C4×D6111yescharacteristic
373C2×C4⋊C4C4×D6111yescharacteristic
374C2×C22⋊C4—611no—
375C2×C22⋊C4—611no—
376C2×C22⋊C4—611no—
377C2×C22⋊C4—611no—
378C2×C22⋊C4C4×D6111yescharacteristic
379C2×C22⋊C4C4×D6111yescharacteristic
380C2×C42—611no—
381C2×C42—611no—
382C2×C42—611no—
383C2×C42—611no—
384C2×C42—611no—
385C2×C42—611no—
386C2×C42—611no—
387C2×C42—611no—
388C2×C42C22×D6111yescharacteristic
389C2×C42C22×D6111yescharacteristic
390C4⋊C8—22no—
391C4⋊C8—22no—
392C4⋊C8—1222no—
393C4⋊C8—1222no—
394C4⋊C8—2441no—
395C4⋊C8—2441no—
396C4⋊C8—2441no—
397C4⋊C8—2441no—
398C22⋊C8—41no—
399C22⋊C8—41no—
400C22⋊C8—2441no—
401C22⋊C8—2441no—
402#97—2441no—
403#97—2441no—
404C4×C8—2441no—
405C4×C8—2441no—
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—
418C24C2×C4×D6111yescharacteristic
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—611no—
426C22×C4—611no—
427C22×C4—611no—
428C22×C4—611no—
429C22×C4—611no—
430C22×C4—611no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4C2×C4×D6111yescharacteristic
434C22×C4C2×C4×D6111yescharacteristic
435C22×C4C2×C4×D6111yescharacteristic
436C22×C4C2×C4×D6111yescharacteristic
437C22×C4C2×C4×D6111yescharacteristic
438C22×C4C23×D6111yescharacteristic
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—1222no—
466C4⋊C4—1222no—
467C4⋊C4—2441no—
468C4⋊C4—2441no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—1222no—
472C22⋊C4—1222no—
473C22⋊C4—2441no—
474C22⋊C4—2441no—
475C42—21no—
476C42—21no—
477C42—1222no—
478C42—1222no—
479C42—1221no—
480C42—1221no—
481C42—1221no—
482C42—1221no—
483C42—1221no—
484C42—1221no—
485C42—1221no—
486C42—1221no—
487C42—2441no—
488C42—2441no—
489C42#1175822412yes—
490C42#1175822412yes—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23C22×C4×D6111yescharacteristic
499C2×C4—21no—
500C2×C4—21no—
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—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—612no—
517C2×C4—612no—
518C2×C4—1221no—
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#1451973312yes—
541C2×C4#1451973312yes—
542C2×C4C2×#1175822411yescharacteristic
543C2×C4C2×#1175822411yescharacteristic
544C2×C4#1451982211yescharacteristic
545C2×C4#1451982311yescharacteristic
546C2×C4#1451982411yescharacteristic
547C2×C4#1451982511yescharacteristic
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—2441no—
553C8—2441no—
554C8—2441no—
555C8—2441no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22C2×#1451973311yescharacteristic
564C22#1684024211yescharacteristic
565C22#1684024311yescharacteristic
566C22#131×D6111yescharacteristic
567C22#131×D6111yescharacteristic
568C22#1684052711yescharacteristic
569C22#1684052711yescharacteristic
570C4—22no—
571C4—22no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—1222no—
576C4—1222no—
577C4—2441no—
578C4—2441no—
579C4—2441no—
580C4—2441no—
581C4—2441no—
582C4—2441no—
583C4#1684036511yescharacteristic
584C4#1684037211yescharacteristic
585C4#1684037911yescharacteristic
586C4#1684038511yescharacteristic
587C2—81no—
588C2#2144842611yescharacteristic
589C2#2145448111yescharacteristic
590C2#2145448111yescharacteristic
591C2#2145495611yescharacteristic
592C2#2145496611yescharacteristic
593C2#2145497311yescharacteristic
594C2#2145498411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1798C2
prime radicalC24×C61C22×C4
cosocleC22×C4×C61C24
hypercenter#1798D61
hypocenterC61#21929
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1798

Complements

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

NH ≅ G/Ntype
6. #21446384C2semidirect
7. #21446382C2semidirect
8. #21446377C2semidirect
9. #21446375C2semidirect
10. #21445970C2semidirect
11. #21445935C2semidirect
13. #21445678C2semidirect
14. #21445678C2semidirect
356. C61#21929semidirect

Maximal subgroups

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

subgroupindex
#214483172
#214464352
#214464292
#214464282
#214464222
#214463842
#214463822
#214463772
#214463752
#214459702
#214459352
#214458032
#214456782
C61×#17982
#2192961