Finite Group Databasebeta

← #29649348

Subgroups — #29649348

Order 15616.

594 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454944C211yesmaximal, characteristic
2#21454786C211yesmaximal, characteristic
3#21444605C211yesmaximal, characteristic, complemented
4#21444602C211yesmaximal, characteristic, complemented
5#21444600C211yesmaximal, characteristic, complemented
6#21444597C211yesmaximal, characteristic, complemented
7#21444595C211yesmaximal, characteristic, complemented
8#21444593C211yesmaximal, characteristic, complemented
9#21444587C211yesmaximal, characteristic, complemented
10#21444584C211yesmaximal, characteristic, complemented
11#21444580C211yesmaximal, characteristic, complemented
12#21444572C211yesmaximal, characteristic, complemented
13#21444569C211yesmaximal, characteristic, complemented
14C2×#16839514C211yesmaximal, characteristic, complemented
15C61×#2990C211yesmaximal, characteristic
16#16839893—21no—
17#16839893C411yescharacteristic
18#16839893C411yescharacteristic
19#16839840C411yescharacteristic
20#16839840C411yescharacteristic
21#16839834—21no—
22#16839834—21no—
23#16839834C411yescharacteristic
24#16839834C411yescharacteristic
25#16839834C411yescharacteristic
26#16839834C411yescharacteristic
27D4×#92418—21no—
28#16839819C2211yescharacteristic
29#16839819C2211yescharacteristic
30#16839815C2211yescharacteristic
31#16839815C2211yescharacteristic
32#16839815C2211yescharacteristic
33#16839815C2211yescharacteristic
34#16839786C2211yescharacteristic
35C2×C4⋊#92418C2211yescharacteristic
36C2×C4⋊#92418C2211yescharacteristic
37C4×#11758194C2211yescharacteristic
38C4×#11758194C2211yescharacteristic
39C2×C4×#92418C2211yescharacteristic
40#16839514C2211yescharacteristic
41#16839514C2211yescharacteristic
42#16839514C2211yescharacteristic
43#16839514C2211yescharacteristic
44#16839514C2211yescharacteristic
45#16839514C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839514C2211yescharacteristic
48#16839514C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839512C2211yescharacteristic
52#16839512C2211yescharacteristic
53#16839512C2211yescharacteristic
54#16839512C2211yescharacteristic
55#16839512C2211yescharacteristic
56C4×#41×C61C2211yescharacteristic
57C61×#446—21no—
58C61×#435—21no—
59C61×#435—21no—
60C8×D4×C61—21no—
61C61×#432C2211yescharacteristic
62C61×#432C2211yescharacteristic
63C61×#431C2211yescharacteristic
64C61×#423C2211yescharacteristic
65C2×C4⋊C8×C61C2211yescharacteristic
66C2×C4⋊C8×C61C2211yescharacteristic
67C2×#11758194—21no—
68C2×#11758194C2×C411yescharacteristic
69C2×#11758194C2×C411yescharacteristic
70C2×#11758194C2×C411yescharacteristic
71C2×#11758194C2×C411yescharacteristic
72C22×#92418—21no—
73C22×#92418—21no—
74C22×#92418C2×C411yescharacteristic
75C22×#92418C2×C411yescharacteristic
76C4⋊#92418—21no—
77C4⋊#92418—21no—
78C4⋊#92418—21no—
79C4⋊#92418C2×C411yescharacteristic
80C4⋊#92418C2×C411yescharacteristic
81C4⋊#92418C2×C411yescharacteristic
82C4⋊#92418C2×C411yescharacteristic
83C4⋊#92418C2×C411yescharacteristic
84C4⋊#92418C2×C411yescharacteristic
85C4⋊#92418C2311yescharacteristic
86C4⋊#92418C2311yescharacteristic
87C4⋊#92418C2311yescharacteristic
88C4⋊#92418C2311yescharacteristic
89C22⋊#92418—21no—
90C22⋊#92418—21no—
91C22⋊#92418—21no—
92C22⋊#92418C2×C411yescharacteristic
93C22⋊#92418C2×C411yescharacteristic
94C22⋊#92418C2×C411yescharacteristic
95C22⋊#92418C2×C411yescharacteristic
96C22⋊#92418C2×C411yescharacteristic
97C22⋊#92418C2×C411yescharacteristic
98#14519688—21no—
99#14519688—21no—
100#14519688C2×C411yescharacteristic
101#14519688C2×C411yescharacteristic
102#14519688C2×C411yescharacteristic
103#14519688C2×C411yescharacteristic
104C4×#92418—21no—
105C4×#92418C2×C411yescharacteristic
106C4×#92418C2×C411yescharacteristic
107C4×#92418C2311yescharacteristic
108C4×#92418C2311yescharacteristic
109C4×#92418C2311yescharacteristic
110C4×#92418C2311yescharacteristic
111C2×#41×C61Q811yescharacteristic
112C2×M16×C61—21no—
113C22×C8×C61—21no—
114C22×C8×C61—21no—
115C4×Q8×C61C2×C411yescharacteristic
116C4×Q8×C61D411yescharacteristic
117C4×D4×C61C2×C411yescharacteristic
118C4×D4×C61C2×C411yescharacteristic
119C4×D4×C61C2×C411yescharacteristic
120C4×D4×C61D411yescharacteristic
121C4×D4×C61D411yescharacteristic
122C4×D4×C61D411yescharacteristic
123#117×C61Q811yescharacteristic
124#117×C61Q811yescharacteristic
125#117×C61Q811yescharacteristic
126C2×C42×C61C2311yescharacteristic
127C2×C42×C61C2311yescharacteristic
128C2×C42×C61C2311yescharacteristic
129C4⋊C8×C61—21no—
130C4⋊C8×C61—21no—
131C4⋊C8×C61—21no—
132C4⋊C8×C61C2311yescharacteristic
133C4⋊C8×C61C2311yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C22⋊C8×C61—21no—
139#97×C61—21no—
140#97×C61—21no—
141C4×C8×C61—21no—
142#41×C61—42no—
143C2×Q8×C61C4⋊C411yescharacteristic
144C2×D4×C61C4⋊C411yescharacteristic
145C2×D4×C61C4⋊C411yescharacteristic
146C2×D4×C61C4⋊C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×Q811yescharacteristic
154C22×C4×C61C2×Q811yescharacteristic
155C22×C4×C61C2×Q811yescharacteristic
156M16×C61—81no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—81no—
162C2×C8×C61—81no—
163C4⋊C4×C61C4⋊C411yescharacteristic
164C4⋊C4×C61C4⋊C411yescharacteristic
165C4⋊C4×C61C4⋊C411yescharacteristic
166C4⋊C4×C61C4⋊C411yescharacteristic
167C4⋊C4×C61C4⋊C411yescharacteristic
168C4⋊C4×C61C4⋊C411yescharacteristic
169C22⋊C4×C61C4⋊C411yescharacteristic
170C22⋊C4×C61C4⋊C411yescharacteristic
171C22⋊C4×C61C4⋊C411yescharacteristic
172C22⋊C4×C61C4⋊C411yescharacteristic
173C22⋊C4×C61C4⋊C411yescharacteristic
174C22⋊C4×C61C4⋊C411yescharacteristic
175C42×C61C22×C411yescharacteristic
176C42×C61C22×C411yescharacteristic
177C42×C61C22×C411yescharacteristic
178C42×C61C2×D411yescharacteristic
179C42×C61C2×D411yescharacteristic
180C42×C61C2×D411yescharacteristic
181C42×C61C2×Q811yescharacteristic
182C42×C61C2×Q811yescharacteristic
183C42×C61C2×Q811yescharacteristic
184C42×C61C2411yescharacteristic
185#11758194—22no—
186#11758194—22no—
187#11758194—41no—
188#11758194—41no—
189#11758194—81no—
190C2×#92418—22no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—41no—
196C2×#92418—81no—
197C2×#92418—81no—
198C2×#92418C22×C411yescharacteristic
199C2×#92418C22×C411yescharacteristic
200C2×#92418C22×C411yescharacteristic
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C22×C411yescharacteristic
204C2×#92418C22×C411yescharacteristic
205C2×#92418C22×C411yescharacteristic
206C23×C61C2×C4⋊C411yescharacteristic
207C23×C61C2×C4⋊C411yescharacteristic
208C23×C61C2×C4⋊C411yescharacteristic
209Q8×C61—41no—
210D4×C61—22no—
211D4×C61—22no—
212D4×C61—41no—
213C2×C4×C61—22no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61C2×C4⋊C411yescharacteristic
229C2×C4×C61C2×C4⋊C411yescharacteristic
230C2×C4×C61C2×C4⋊C411yescharacteristic
231C2×C4×C61C2×C4⋊C411yescharacteristic
232C2×C4×C61C2×C4⋊C411yescharacteristic
233C2×C4×C61C2×C4⋊C411yescharacteristic
234C2×C4×C61C2×C4⋊C411yescharacteristic
235C2×C4×C61C2×C4⋊C411yescharacteristic
236C2×C4×C61C2×C4⋊C411yescharacteristic
237C2×C4×C61C23×C411yescharacteristic
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C22×Q811yescharacteristic
240C8×C61—41no—
241C8×C61—41no—
242C8×C61—41no—
243C8×C61—41no—
244#92418—21no—
245#92418—21no—
246#92418—21no—
247#92418—21no—
248#92418—21no—
249#92418—21no—
250#92418—21no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#92418—41no—
255#92418#13112yes—
256#17840—611nomaximal, Sylow
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—21no—
265C22×C61#43012yes—
266C22×C61C22×C4⋊C411yescharacteristic
267C4×C61—21no—
268C4×C61—21no—
269C4×C61—21no—
270C4×C61—21no—
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—21no—
276C4×C61—21no—
277C4×C61C2×#13111yescharacteristic
278C4×C61#56811yescharacteristic
279C4×C61#57611yescharacteristic
280C4×C61#57811yescharacteristic
281#2990—611no—
282#2990D6111yescharacteristic
283#2965—611no—
284#1573—611no—
285#1573—611no—
286#1572—611no—
287#1572—611no—
288#1571—611no—
289#1571—611no—
290#1569—611no—
291#1569—611no—
292#1568—611no—
293#1565—611no—
294#1565—611no—
295C2×#335—611no—
296C2×C61—22no—
297C2×C61—41no—
298C2×C61—41no—
299C2×C61#290611yescharacteristic
300C2×C61#291311yescharacteristic
301C2×C61C2×#43011yescharacteristic
302C4×#41C2×D6111yescharacteristic
303#446—21no—
304#446—611no—
305#446—611no—
306#446—1221no—
307#436—611no—
308#436—611no—
309#435—21no—
310#435—21no—
311#435—611no—
312#435—611no—
313#435—611no—
314#435—611no—
315#435—1221no—
316#435—1221no—
317C8×D4—21no—
318C8×D4—1221no—
319#432—611no—
320#432—611no—
321#432C2×D6111yescharacteristic
322#432C2×D6111yescharacteristic
323#431—611no—
324#431—611no—
325#431—611no—
326#431—611no—
327#431C2×D6111yescharacteristic
328#423—611no—
329#423C2×D6111yescharacteristic
330C2×C4⋊C8—611no—
331C2×C4⋊C8—611no—
332C2×C4⋊C8C2×D6111yescharacteristic
333C2×C4⋊C8C2×D6111yescharacteristic
334C4×M16—611no—
335C4×M16—611no—
336C2×C4×C8—611no—
337#335—611no—
338#335—611no—
339#335—611no—
340#335—611no—
341#335—611no—
342#335—611no—
343#335—611no—
344#335—611no—
345#335—611no—
346#335—611no—
347#334—611no—
348#334—611no—
349#334—611no—
350#334—611no—
351#334—611no—
352#334—611no—
353C61#1784011yescharacteristic, complemented, Sylow
354C2×#41Dic12211yescharacteristic
355C2×M16—21no—
356C2×M16—611no—
357C2×M16—611no—
358C2×M16—611no—
359C2×M16—611no—
360C2×M16—1221no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—611no—
364C22×C8—611no—
365C22×C8—1221no—
366C22×C8—1221no—
367C4×Q8C4×D6111yescharacteristic
368C4×Q8C22⋊D6111yescharacteristic
369C4×D4C4×D6111yescharacteristic
370C4×D4C4×D6111yescharacteristic
371C4×D4C4×D6111yescharacteristic
372C4×D4C22⋊D6111yescharacteristic
373C4×D4C22⋊D6111yescharacteristic
374C4×D4C22⋊D6111yescharacteristic
375#117Dic12211yescharacteristic
376#117Dic12211yescharacteristic
377#117Dic12211yescharacteristic
378C2×C42C22×D6111yescharacteristic
379C2×C42C22×D6111yescharacteristic
380C2×C42C22×D6111yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—611no—
385C4⋊C8—611no—
386C4⋊C8—611no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—611no—
391C4⋊C8—611no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396C4⋊C8—1221no—
397C4⋊C8C22×D6111yescharacteristic
398C4⋊C8C22×D6111yescharacteristic
399C4⋊C8C22×D6111yescharacteristic
400C4⋊C8C22×D6111yescharacteristic
401C22⋊C8—21no—
402C22⋊C8—21no—
403C22⋊C8—21no—
404C22⋊C8—611no—
405C22⋊C8—611no—
406C22⋊C8—611no—
407C22⋊C8—611no—
408C22⋊C8—611no—
409C22⋊C8—611no—
410C22⋊C8—1221no—
411C22⋊C8—1221no—
412C22⋊C8—1221no—
413#97—21no—
414#97—21no—
415#97—611no—
416#97—611no—
417#97—611no—
418#97—611no—
419#97—1221no—
420#97—1221no—
421C4×C8—21no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—611no—
428C4×C8—1221no—
429#41—42no—
430C2×Q8#1175819611yescharacteristic
431C2×D4#1175819611yescharacteristic
432C2×D4#1175819611yescharacteristic
433C2×D4#1175819611yescharacteristic
434C22×C4C2×Dic12211yescharacteristic
435C22×C4C2×Dic12211yescharacteristic
436C22×C4C2×Dic12211yescharacteristic
437C22×C4C2×C4×D6111yescharacteristic
438C22×C4C2×C4×D6111yescharacteristic
439C22×C4C2×C4×D6111yescharacteristic
440C22×C4C2×C22⋊D6111yescharacteristic
441C22×C4C2×C22⋊D6111yescharacteristic
442C22×C4C2×C22⋊D6111yescharacteristic
443M16—81no—
444M16—1222no—
445M16—1222no—
446M16—4881no—
447M16—2441no—
448M16—2441no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—81no—
454C2×C8—81no—
455C2×C8—611no—
456C2×C8—611no—
457C2×C8—611no—
458C2×C8—611no—
459C2×C8—611no—
460C2×C8—611no—
461C2×C8—611no—
462C2×C8—611no—
463C2×C8—1222no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—4881no—
469C2×C8—4881no—
470C2×C8—2441no—
471C4⋊C4#1175819611yescharacteristic
472C4⋊C4#1175819611yescharacteristic
473C4⋊C4#1175819611yescharacteristic
474C4⋊C4#1175819611yescharacteristic
475C4⋊C4#1175819611yescharacteristic
476C4⋊C4#1175819611yescharacteristic
477C22⋊C4#1175819611yescharacteristic
478C22⋊C4#1175819611yescharacteristic
479C22⋊C4#1175819611yescharacteristic
480C22⋊C4#1175819611yescharacteristic
481C22⋊C4#1175819611yescharacteristic
482C22⋊C4#1175819611yescharacteristic
483C42C2×Dic12211yescharacteristic
484C42C2×Dic12211yescharacteristic
485C42C2×Dic12211yescharacteristic
486C42C2×C4×D6111yescharacteristic
487C42C2×C4×D6111yescharacteristic
488C42C2×C4×D6111yescharacteristic
489C42C2×C22⋊D6111yescharacteristic
490C42C2×C22⋊D6111yescharacteristic
491C42C2×C22⋊D6111yescharacteristic
492C42C23×D6111yescharacteristic
493C23C2×#1175819611yescharacteristic
494C23C2×#1175819611yescharacteristic
495C23C2×#1175819611yescharacteristic
496Q8—41no—
497D4—22no—
498D4—22no—
499D4—41no—
500C2×C4—22no—
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—41no—
514C2×C4—41no—
515C2×C4C2×#1175819611yescharacteristic
516C2×C4C2×#1175819611yescharacteristic
517C2×C4C2×#1175819611yescharacteristic
518C2×C4C2×#1175819611yescharacteristic
519C2×C4C2×#1175819611yescharacteristic
520C2×C4C2×#1175819611yescharacteristic
521C2×C4C2×#1175819611yescharacteristic
522C2×C4C2×#1175819611yescharacteristic
523C2×C4C2×#1175819611yescharacteristic
524C2×C4C22×C4×D6111yescharacteristic
525C2×C4C22×C22⋊D6111yescharacteristic
526C2×C4C22×Dic12211yescharacteristic
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—612no—
532C8—1221no—
533C8—1221no—
534C8—1221no—
535C8—1221no—
536C8—1221no—
537C8—1221no—
538C8—1221no—
539C8—2441no—
540C8—2441no—
541C8—2441no—
542C8—2441no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22#1683981012yes—
552C22C22×#1175819611yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4#131×D6111yescharacteristic
564C4#1684052711yescharacteristic
565C4#1684056511yescharacteristic
566C4#1684057711yescharacteristic
567C2—22no—
568C2—41no—
569C2—41no—
570C2#2145438511yescharacteristic
571C2#2145441711yescharacteristic
572C2C2×#1683981011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2990C2
socleC22×C61C22×C4⋊C4
prime radicalC2×#41×C61Q8
cosocleC42×C61C24
hypercenter#2990D61
hypocenterC61#17840
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
3. #21444605C2semidirect
4. #21444602C2semidirect
5. #21444600C2semidirect
6. #21444597C2semidirect
7. #21444595C2semidirect
8. #21444593C2semidirect
9. #21444587C2semidirect
10. #21444584C2semidirect
11. #21444580C2semidirect
12. #21444572C2semidirect
13. #21444569C2semidirect
14. C2×#16839514C2semidirect
353. C61#17840semidirect

Maximal subgroups

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

subgroupindex
#214549442
#214547862
#214446052
#214446022
#214446002
#214445972
#214445952
#214445932
#214445872
#214445842
#214445802
#214445722
#214445692
C2×#168395142
C61×#29902
#1784061