Finite Group Databasebeta

← #29649293

Subgroups — #29649293

Order 15616.

588 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454786C211yesmaximal, characteristic
2#21454485C211yesmaximal, characteristic
3#21444610C211yesmaximal, characteristic, complemented
4#21444607C211yesmaximal, characteristic, complemented
5#21444605C211yesmaximal, characteristic, complemented
6#21444602C211yesmaximal, characteristic, complemented
7#21444600C211yesmaximal, characteristic, complemented
8#21444597C211yesmaximal, characteristic, complemented
9#21444587C211yesmaximal, characteristic, complemented
10#21444584C211yesmaximal, characteristic, complemented
11#21444580C211yesmaximal, characteristic, complemented
12#21444572C211yesmaximal, characteristic, complemented
13#21444569C211yesmaximal, characteristic, complemented
14#21444565C211yesmaximal, characteristic, complemented
15C61×#2925C211yesmaximal, characteristic
16#16839893C411yescharacteristic
17#16839893C411yescharacteristic
18#16839840C411yescharacteristic
19#16839840C411yescharacteristic
20#16839834C411yescharacteristic
21#16839834C411yescharacteristic
22#16839834C411yescharacteristic
23#16839834C411yescharacteristic
24#16839823—21no—
25#16839823—21no—
26#16839819C2211yescharacteristic
27#16839819C2211yescharacteristic
28#16839815C2211yescharacteristic
29#16839815C2211yescharacteristic
30#16839815C2211yescharacteristic
31#16839815C2211yescharacteristic
32#16839815C2211yescharacteristic
33#16839786C2211yescharacteristic
34C2×C4⋊#92418C2211yescharacteristic
35#16839729—21no—
36#16839718—21no—
37C4×#11758194C2211yescharacteristic
38C4×#11758194C2211yescharacteristic
39C2×C4×#92418C2211yescharacteristic
40#16839514C2211yescharacteristic
41#16839514C2211yescharacteristic
42#16839514C2211yescharacteristic
43#16839514C2211yescharacteristic
44#16839514C2211yescharacteristic
45#16839514C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839514C2211yescharacteristic
48#16839512C2211yescharacteristic
49#16839512C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839512C2211yescharacteristic
52#16839512C2211yescharacteristic
53#16839512C2211yescharacteristic
54#16839512C2211yescharacteristic
55#16839512C2211yescharacteristic
56C4×#41×C61C2211yescharacteristic
57C61×#433—21no—
58C61×#433—21no—
59C61×#432C2211yescharacteristic
60C61×#432C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C61×#431C2211yescharacteristic
63C61×#423C2211yescharacteristic
64C2×C4⋊C8×C61C2211yescharacteristic
65C61×#408—21no—
66C61×#405—21no—
67C2×#11758194—21no—
68C2×#11758194C2×C411yescharacteristic
69C2×#11758194C2×C411yescharacteristic
70C2×#11758194C2×C411yescharacteristic
71C2×#11758194C2×C411yescharacteristic
72C22×#92418—21no—
73C22×#92418C2×C411yescharacteristic
74C22×#92418C2×C411yescharacteristic
75C4⋊#92418—21no—
76C4⋊#92418—21no—
77C4⋊#92418C2×C411yescharacteristic
78C4⋊#92418C2×C411yescharacteristic
79C4⋊#92418C2×C411yescharacteristic
80C4⋊#92418C2×C411yescharacteristic
81C4⋊#92418C2×C411yescharacteristic
82C4⋊#92418C2×C411yescharacteristic
83C4⋊#92418C2311yescharacteristic
84C4⋊#92418C2311yescharacteristic
85C4⋊#92418C2311yescharacteristic
86C4⋊#92418C2311yescharacteristic
87C22⋊#92418—21no—
88C22⋊#92418—21no—
89C22⋊#92418—21no—
90C22⋊#92418—21no—
91C22⋊#92418C2×C411yescharacteristic
92C22⋊#92418C2×C411yescharacteristic
93C22⋊#92418C2×C411yescharacteristic
94C22⋊#92418C2×C411yescharacteristic
95C22⋊#92418C2×C411yescharacteristic
96C22⋊#92418C2×C411yescharacteristic
97#14519688—21no—
98#14519688—21no—
99#14519688C2×C411yescharacteristic
100#14519688C2×C411yescharacteristic
101#14519688C2×C411yescharacteristic
102#14519688C2×C411yescharacteristic
103C4×#92418—21no—
104C4×#92418—21no—
105C4×#92418C2×C411yescharacteristic
106C4×#92418C2×C411yescharacteristic
107C4×#92418C2311yescharacteristic
108C4×#92418C2311yescharacteristic
109C4×#92418C2311yescharacteristic
110C4×#92418C2311yescharacteristic
111C2×#41×C61D411yescharacteristic
112C2×M16×C61—21no—
113C22×C8×C61—21no—
114C4×Q8×C61C2×C411yescharacteristic
115C4×Q8×C61Q811yescharacteristic
116C4×D4×C61C2×C411yescharacteristic
117C4×D4×C61C2×C411yescharacteristic
118C4×D4×C61C2×C411yescharacteristic
119C4×D4×C61Q811yescharacteristic
120C4×D4×C61Q811yescharacteristic
121C4×D4×C61Q811yescharacteristic
122#117×C61D411yescharacteristic
123#117×C61D411yescharacteristic
124#117×C61D411yescharacteristic
125C2×C42×C61C2311yescharacteristic
126C2×C42×C61C2311yescharacteristic
127C2×C42×C61C2311yescharacteristic
128C4⋊C8×C61—21no—
129C4⋊C8×C61—21no—
130C4⋊C8×C61C2311yescharacteristic
131C4⋊C8×C61C2311yescharacteristic
132C4⋊C8×C61C2311yescharacteristic
133C4⋊C8×C61C2311yescharacteristic
134C22⋊C8×C61—21no—
135C22⋊C8×C61—21no—
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138#97×C61—21no—
139#97×C61—21no—
140C4×C8×C61—21no—
141C4×C8×C61—21no—
142#41×C61—41no—
143#41×C61—41no—
144C2×Q8×C61C4⋊C411yescharacteristic
145C2×D4×C61C4⋊C411yescharacteristic
146C2×D4×C61C4⋊C411yescharacteristic
147C2×D4×C61C4⋊C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×Q811yescharacteristic
155C22×C4×C61C2×Q811yescharacteristic
156C22×C4×C61C2×Q811yescharacteristic
157M16×C61—42no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—42no—
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—42no—
190C2×#92418—22no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—41no—
196C2×#92418—42no—
197C2×#92418C22×C411yescharacteristic
198C2×#92418C22×C411yescharacteristic
199C2×#92418C22×C411yescharacteristic
200C2×#92418C22×C411yescharacteristic
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C22×C411yescharacteristic
204C2×#92418C22×C411yescharacteristic
205C23×C61C2×C4⋊C411yescharacteristic
206C23×C61C2×C4⋊C411yescharacteristic
207C23×C61C2×C4⋊C411yescharacteristic
208Q8×C61—41no—
209D4×C61—41no—
210D4×C61—41no—
211D4×C61—41no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
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—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61C2×C4⋊C411yescharacteristic
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×C61C23×C411yescharacteristic
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61C22×Q811yescharacteristic
239C8×C61—41no—
240C8×C61—41no—
241C8×C61—41no—
242C8×C61—41no—
243#92418—21no—
244#92418—21no—
245#92418—21no—
246#92418—21no—
247#92418—21no—
248#92418—21no—
249#92418—21no—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#92418#13112yes—
255#17833—611nomaximal, Sylow
256C22×C61—21no—
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×C61C22×C4⋊C411yescharacteristic
266C4×C61—21no—
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×C61C2×#13111yescharacteristic
277C4×C61#56811yescharacteristic
278C4×C61#57511yescharacteristic
279C4×C61#57511yescharacteristic
280#2965—611no—
281#2925—611no—
282#2925D6111yescharacteristic
283#1574—611no—
284#1574—611no—
285#1573—611no—
286#1573—611no—
287#1572—611no—
288#1572—611no—
289#1569—611no—
290#1569—611no—
291#1568—611no—
292#1565—611no—
293#1565—611no—
294#1564—611no—
295C2×C61—41no—
296C2×C61—41no—
297C2×C61—41no—
298C2×C61#290611yescharacteristic
299C2×C61#291111yescharacteristic
300C2×C61#291611yescharacteristic
301C4×#41C2×D6111yescharacteristic
302#446—611no—
303#446—611no—
304#436—611no—
305#436—611no—
306#435—611no—
307#435—611no—
308#435—611no—
309#435—611no—
310#433—21no—
311#433—21no—
312#433—1221no—
313#433—1221no—
314#432—611no—
315#432—611no—
316#432C2×D6111yescharacteristic
317#432C2×D6111yescharacteristic
318#431—611no—
319#431—611no—
320#431—611no—
321#431—611no—
322#431—611no—
323#431C2×D6111yescharacteristic
324#431C2×D6111yescharacteristic
325#423—611no—
326#423C2×D6111yescharacteristic
327C2×C4⋊C8—611no—
328C2×C4⋊C8C2×D6111yescharacteristic
329#408—21no—
330#408—1221no—
331#405—21no—
332#405—1221no—
333C4×M16—611no—
334C4×M16—611no—
335C2×C4×C8—611no—
336#335—611no—
337#335—611no—
338#335—611no—
339#335—611no—
340#335—611no—
341#335—611no—
342#335—611no—
343#335—611no—
344#334—611no—
345#334—611no—
346#334—611no—
347#334—611no—
348#334—611no—
349#334—611no—
350#334—611no—
351#334—611no—
352C61#1783311yescharacteristic, complemented, Sylow
353C2×#41C22⋊D6111yescharacteristic
354C2×M16—21no—
355C2×M16—611no—
356C2×M16—611no—
357C2×M16—611no—
358C2×M16—611no—
359C2×M16—1221no—
360C22×C8—21no—
361C22×C8—611no—
362C22×C8—611no—
363C22×C8—1221no—
364C4×Q8Dic12211yescharacteristic
365C4×Q8C4×D6111yescharacteristic
366C4×D4Dic12211yescharacteristic
367C4×D4Dic12211yescharacteristic
368C4×D4Dic12211yescharacteristic
369C4×D4C4×D6111yescharacteristic
370C4×D4C4×D6111yescharacteristic
371C4×D4C4×D6111yescharacteristic
372#117C22⋊D6111yescharacteristic
373#117C22⋊D6111yescharacteristic
374#117C22⋊D6111yescharacteristic
375C2×C42C22×D6111yescharacteristic
376C2×C42C22×D6111yescharacteristic
377C2×C42C22×D6111yescharacteristic
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—611no—
381C4⋊C8—611no—
382C4⋊C8—611no—
383C4⋊C8—611no—
384C4⋊C8—611no—
385C4⋊C8—611no—
386C4⋊C8—611no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8C22×D6111yescharacteristic
393C4⋊C8C22×D6111yescharacteristic
394C4⋊C8C22×D6111yescharacteristic
395C4⋊C8C22×D6111yescharacteristic
396C22⋊C8—21no—
397C22⋊C8—21no—
398C22⋊C8—21no—
399C22⋊C8—21no—
400C22⋊C8—611no—
401C22⋊C8—611no—
402C22⋊C8—611no—
403C22⋊C8—611no—
404C22⋊C8—611no—
405C22⋊C8—611no—
406C22⋊C8—1221no—
407C22⋊C8—1221no—
408C22⋊C8—1221no—
409C22⋊C8—1221no—
410#97—21no—
411#97—21no—
412#97—611no—
413#97—611no—
414#97—611no—
415#97—611no—
416#97—1221no—
417#97—1221no—
418C4×C8—21no—
419C4×C8—21no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—1221no—
427C4×C8—1221no—
428#41—41no—
429#41—41no—
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—42no—
444M16—1222no—
445M16—1222no—
446M16—2441no—
447M16—2441no—
448M16—2442no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—42no—
454C2×C8—611no—
455C2×C8—611no—
456C2×C8—611no—
457C2×C8—611no—
458C2×C8—611no—
459C2×C8—611no—
460C2×C8—611no—
461C2×C8—611no—
462C2×C8—1222no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—2441no—
468C2×C8—2442no—
469C4⋊C4#1175819611yescharacteristic
470C4⋊C4#1175819611yescharacteristic
471C4⋊C4#1175819611yescharacteristic
472C4⋊C4#1175819611yescharacteristic
473C4⋊C4#1175819611yescharacteristic
474C4⋊C4#1175819611yescharacteristic
475C22⋊C4#1175819611yescharacteristic
476C22⋊C4#1175819611yescharacteristic
477C22⋊C4#1175819611yescharacteristic
478C22⋊C4#1175819611yescharacteristic
479C22⋊C4#1175819611yescharacteristic
480C22⋊C4#1175819611yescharacteristic
481C42C2×Dic12211yescharacteristic
482C42C2×Dic12211yescharacteristic
483C42C2×Dic12211yescharacteristic
484C42C2×C4×D6111yescharacteristic
485C42C2×C4×D6111yescharacteristic
486C42C2×C4×D6111yescharacteristic
487C42C2×C22⋊D6111yescharacteristic
488C42C2×C22⋊D6111yescharacteristic
489C42C2×C22⋊D6111yescharacteristic
490C42C23×D6111yescharacteristic
491C23C2×#1175819611yescharacteristic
492C23C2×#1175819611yescharacteristic
493C23C2×#1175819611yescharacteristic
494Q8—41no—
495D4—41no—
496D4—41no—
497D4—41no—
498C2×C4—21no—
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—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4C2×#1175819611yescharacteristic
514C2×C4C2×#1175819611yescharacteristic
515C2×C4C2×#1175819611yescharacteristic
516C2×C4C2×#1175819611yescharacteristic
517C2×C4C2×#1175819611yescharacteristic
518C2×C4C2×#1175819611yescharacteristic
519C2×C4C2×#1175819611yescharacteristic
520C2×C4C2×#1175819611yescharacteristic
521C2×C4C2×#1175819611yescharacteristic
522C2×C4C22×C4×D6111yescharacteristic
523C2×C4C22×C22⋊D6111yescharacteristic
524C2×C4C22×Dic12211yescharacteristic
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—612no—
530C8—1221no—
531C8—1221no—
532C8—1221no—
533C8—1221no—
534C8—1221no—
535C8—1221no—
536C8—1221no—
537C8—2441no—
538C8—2441no—
539C8—2441no—
540C8—2441no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22C22×#1175819611yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4#131×D6111yescharacteristic
562C4#1684052711yescharacteristic
563C4#1684056011yescharacteristic
564C4#1684056011yescharacteristic
565C2—41no—
566C2—41no—
567C2—41no—
568C2#2145438511yescharacteristic
569C2#2145440811yescharacteristic
570C2#2145442811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2925C2
socleC22×C61C22×C4⋊C4
prime radicalC2×#41×C61D4
cosocleC42×C61C24
hypercenter#2925D61
hypocenterC61#17833
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2925

Complements

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

NH ≅ G/Ntype
3. #21444610C2semidirect
4. #21444607C2semidirect
5. #21444605C2semidirect
6. #21444602C2semidirect
7. #21444600C2semidirect
8. #21444597C2semidirect
9. #21444587C2semidirect
10. #21444584C2semidirect
11. #21444580C2semidirect
12. #21444572C2semidirect
13. #21444569C2semidirect
14. #21444565C2semidirect
352. C61#17833semidirect

Maximal subgroups

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

subgroupindex
#214547862
#214544852
#214446102
#214446072
#214446052
#214446022
#214446002
#214445972
#214445872
#214445842
#214445802
#214445722
#214445692
#214445652
C61×#29252
#1783361