Finite Group Databasebeta

← #29690649

Subgroups — #29690649

Order 15616.

658 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454455C211yesmaximal, characteristic
2C2×#16839822C211yesmaximal, characteristic
3#21454381C211yesmaximal, characteristic
4#21446595C211yesmaximal, characteristic, complemented
5#21446594C211yesmaximal, characteristic, complemented
6#21446592C211yesmaximal, characteristic, complemented
7#21446025C211yesmaximal, characteristic
8#21446025C211yesmaximal, characteristic
9#21446022C211yesmaximal, characteristic
10#21446022C211yesmaximal, characteristic
11#21445992C211yesmaximal, characteristic, complemented
12#21445989C211yesmaximal, characteristic, complemented
13#21445958C211yesmaximal, characteristic, complemented
14#21445955C211yesmaximal, characteristic, complemented
15C61×#1950C211yesmaximal, characteristic, complemented
16C2×M16×D61C2211yescharacteristic
17C2×M16×D61C2211yescharacteristic
18C2×#14519734C2211yescharacteristic
19#16839824—21no—
20#16839824—21no—
21#16839822C412yes—
22#16839822C412yes—
23#16839822C412yes—
24#16839822C412yes—
25#16839821—21no—
26#16839821—21no—
27C2×#14519713C2211yescharacteristic
28C2×#14519713C2211yescharacteristic
29C2×#14519712C2211yescharacteristic
30C2×#14519712C2211yescharacteristic
31C2×#14519712C2211yescharacteristic
32C2×#14519712C2211yescharacteristic
33#16839787—21no—
34#16839787—21no—
35#16839787—21no—
36#16839787—21no—
37#16839786C2211yescharacteristic
38#16839785C2211yescharacteristic
39#16839785C2211yescharacteristic
40#16839785C2211yescharacteristic
41#16839785C2211yescharacteristic
42C2×C4⋊#92418C2211yescharacteristic
43#16839725C2211yescharacteristic
44#16839725C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C4×#11758194C2211yescharacteristic
48C2×#14519687C2211yescharacteristic
49C2×C8×Dic61C2211yescharacteristic
50#16839527C2211yescharacteristic
51#16839527C2211yescharacteristic
52#16839526C2211yescharacteristic
53#16839526C2211yescharacteristic
54#16839526C2211yescharacteristic
55#16839526C2211yescharacteristic
56C2×#108×C61C2211yescharacteristic
57C2×#108×C61C2211yescharacteristic
58C61×#423C2211yescharacteristic
59C2×C4⋊C8×C61C2211yescharacteristic
60C4×M16×C61C2211yescharacteristic
61C61×#341C2211yescharacteristic
62C61×#341C2211yescharacteristic
63C22×C4×D61C2311yescharacteristic
64C2×#11758194C2311yescharacteristic
65C2×#11758194C2311yescharacteristic
66C2×#11758194C2311yescharacteristic
67C2×#11758194C2311yescharacteristic
68C2×#11758189—21no—
69C2×#11758189—21no—
70M16×D61—41no—
71M16×D61—41no—
72M16×D61—41no—
73M16×D61—41no—
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78#14519734C2×C411yescharacteristic
79#14519734C2×C411yescharacteristic
80#14519734C2×C411yescharacteristic
81#14519734C2×C411yescharacteristic
82#14519734D411yescharacteristic
83#14519734D411yescharacteristic
84#14519734D411yescharacteristic
85#14519734D411yescharacteristic
86C2×#11758196Q811yescharacteristic
87C2×#11758196Q811yescharacteristic
88C2×#11758198Q811yescharacteristic
89C2×#11758198Q811yescharacteristic
90C2×C4×Dic61C2311yescharacteristic
91#14519713—41no—
92#14519713—41no—
93#14519712—41no—
94#14519712—41no—
95#14519712—41no—
96#14519712—41no—
97C4⋊#92418—21no—
98C4⋊#92418—21no—
99C4⋊#92418C2×C412yes—
100C4⋊#92418C2×C412yes—
101#14519706—21no—
102#14519706—21no—
103#14519706—21no—
104#14519706—21no—
105#14519706—21no—
106#14519706—21no—
107#14519706—21no—
108#14519706—21no—
109#14519689—21no—
110#14519689—21no—
111#14519689—21no—
112#14519689—21no—
113#14519689C2×C412yes—
114#14519689C2×C412yes—
115#14519689C2×C412yes—
116#14519689C2×C412yes—
117#14519688—21no—
118#14519687C2×C412yes—
119#14519687C2×C412yes—
120C4×#92418—21no—
121C8×Dic61C2×C412yes—
122C8×Dic61C2×C412yes—
123C2×M16×C61C2311yescharacteristic
124C2×M16×C61C2311yescharacteristic
125C2×M16×C61C2311yescharacteristic
126C2×M16×C61C2311yescharacteristic
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C2×C42×C61C2311yescharacteristic
130#108×C61—41no—
131#108×C61—41no—
132C4⋊C8×C61—21no—
133C4⋊C8×C61—21no—
134C4⋊C8×C61C2×C412yes—
135C4⋊C8×C61C2×C412yes—
136#97×C61—21no—
137C4×C8×C61—21no—
138C23×D61C2×Q811yescharacteristic
139C22×C4×C61C2×Q811yescharacteristic
140C22×C4×C61C2×Q811yescharacteristic
141C22×C4×C61C2411yescharacteristic
142C22×Dic61C2×Q811yescharacteristic
143C22×Dic61C2×Q811yescharacteristic
144C22×Dic61C2×Q811yescharacteristic
145C2×C4×D61—21no—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61—21no—
149C2×C4×D61C22×C411yescharacteristic
150C2×C4×D61C22×C411yescharacteristic
151C2×C4×D61C2×D411yescharacteristic
152C2×C4×D61C2×D411yescharacteristic
153M16×C61—21no—
154M16×C61—21no—
155M16×C61—21no—
156M16×C61—21no—
157M16×C61—21no—
158M16×C61—21no—
159M16×C61—21no—
160M16×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61C22×C412yes—
170C2×C8×C61C22×C412yes—
171C42×C61C22×C411yescharacteristic
172C42×C61C22×C411yescharacteristic
173C42×C61C2×D411yescharacteristic
174C42×C61C2×D411yescharacteristic
175#11758198C4⋊C411yescharacteristic
176#11758198C4⋊C411yescharacteristic
177#11758198C4⋊C411yescharacteristic
178#11758198C4⋊C411yescharacteristic
179#11758198C4⋊C411yescharacteristic
180#11758198C4⋊C411yescharacteristic
181#11758198C4⋊C411yescharacteristic
182#11758198C4⋊C411yescharacteristic
183#11758196C4⋊C411yescharacteristic
184#11758196C4⋊C411yescharacteristic
185#11758196C4⋊C411yescharacteristic
186#11758196C4⋊C411yescharacteristic
187#11758196C4⋊C411yescharacteristic
188#11758196C4⋊C411yescharacteristic
189#11758196C4⋊C411yescharacteristic
190#11758196C4⋊C411yescharacteristic
191C4×Dic61C22×C411yescharacteristic
192C4×Dic61C22×C411yescharacteristic
193C4×Dic61C2×D411yescharacteristic
194C4×Dic61C2×D411yescharacteristic
195#11758194—21no—
196#11758194—21no—
197#11758194—21no—
198#11758194—21no—
199#11758194—21no—
200#11758194—21no—
201#11758194—21no—
202#11758194—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418C22×C412yes—
212C2×#92418C22×C412yes—
213#11758189—42no—
214#11758189—42no—
215C8×D61—42no—
216C8×D61—42no—
217C23×C61C22×Q811yescharacteristic
218C22×D61—21no—
219C22×D61—21no—
220C22×D61—41no—
221C22×D61—41no—
222C22×D61C2×C4⋊C411yescharacteristic
223C22×D61C2×C4⋊C411yescharacteristic
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61C2×C4⋊C411yescharacteristic
227C2×C4×C61C2×C4⋊C411yescharacteristic
228C2×C4×C61C2×C4⋊C411yescharacteristic
229C2×C4×C61C2×C4⋊C411yescharacteristic
230C2×C4×C61C23×C411yescharacteristic
231C2×C4×C61C22×D411yescharacteristic
232C2×C4×C61H(5,𝔽2)11yescharacteristic
233C2×C4×C61H(5,𝔽2)11yescharacteristic
234C2×C4×C612−1+411yescharacteristic
235C2×C4×C612−1+411yescharacteristic
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61C2×C4⋊C411yescharacteristic
241C2×Dic61C2×C4⋊C411yescharacteristic
242C2×Dic61C2×C4⋊C411yescharacteristic
243C2×Dic61C2×C4⋊C411yescharacteristic
244C2×Dic61C2×C4⋊C411yescharacteristic
245C2×Dic61C2×C4⋊C411yescharacteristic
246C4×D61—21no—
247C4×D61—21no—
248C4×D61—21no—
249C4×D61—21no—
250C4×D61—21no—
251C4×D61—21no—
252C4×D61—21no—
253C4×D61—21no—
254C8×C61—22no—
255C8×C61—22no—
256C8×C61—41no—
257C8×C61—41no—
258C8×C61—41no—
259C8×C61—41no—
260#92418—22no—
261#92418—22no—
262#92418—41no—
263#92418—41no—
264#92418—41no—
265#92418—41no—
266#21995—611nomaximal, Sylow
267C22×C61—21no—
268C22×C61—21no—
269C22×C61C22×C4⋊C411yescharacteristic
270C22×C61#54411yescharacteristic
271C22×C61#54411yescharacteristic
272C2×D61—21no—
273C2×D61—21no—
274C2×D61—21no—
275C2×D61—21no—
276C2×D61—21no—
277C2×D61—21no—
278C2×D61—81no—
279C2×D61—81no—
280C4×C61—21no—
281C4×C61—21no—
282C4×C61—21no—
283C4×C61—21no—
284C4×C61#52011yescharacteristic
285C4×C61#52011yescharacteristic
286C4×C61#53511yescharacteristic
287C4×C61#53611yescharacteristic
288Dic61—21no—
289Dic61—21no—
290Dic61—21no—
291Dic61—21no—
292Dic61—21no—
293Dic61—21no—
294#2921—611no—
295C2×#433—611no—
296#2905—611no—
297#1950—611no—
298#1950—611no—
299#1950—611no—
300#1950D6111yescharacteristic, complemented
301#1855—611no—
302#1855—611no—
303#1855—611no—
304#1855—611no—
305#1849—611no—
306#1848—611no—
307#1838—611no—
308#1837—611no—
309C2×C61—21no—
310C2×C61—21no—
311C2×C61#231711yescharacteristic
312C2×C61#291611yescharacteristic
313C2×C61#291611yescharacteristic
314D61—41no—
315D61—41no—
316C22×M16—611no—
317C22×M16—611no—
318C2×#117—611no—
319#433—612no—
320#433—612no—
321#433—612no—
322#433—612no—
323#433—1221no—
324#433—1221no—
325#433—1221no—
326#433—1221no—
327C2×#108—611no—
328C2×#108—611no—
329C2×#108—611no—
330C2×#108—611no—
331C2×#108—611no—
332C2×#108—611no—
333C2×#108C2×D6111yescharacteristic
334C2×#108C2×D6111yescharacteristic
335#424—1221no—
336#424—1221no—
337#424—1221no—
338#424—1221no—
339#423—611no—
340#423—611no—
341#423—611no—
342#423—611no—
343#423—611no—
344#423C2×D6111yescharacteristic
345C2×C4⋊C8—611no—
346C2×C4⋊C8C2×D6111yescharacteristic
347#407—611no—
348#407—611no—
349C2×C22⋊C8—611no—
350C2×C22⋊C8—611no—
351C4×M16—611no—
352C4×M16C2×D6111yescharacteristic
353C2×#97—611no—
354C2×C4×C8—611no—
355#341—611no—
356#341—611no—
357#341—611no—
358#341—611no—
359#341—611no—
360#341—611no—
361#341C2×D6111yescharacteristic
362#341C2×D6111yescharacteristic
363C61#2199511yescharacteristic, complemented, Sylow
364C23×C4—611no—
365C2×M16—611no—
366C2×M16—611no—
367C2×M16—611no—
368C2×M16—611no—
369C2×M16—1221no—
370C2×M16—1221no—
371C2×M16—2441no—
372C2×M16—2441no—
373C2×M16—2441no—
374C2×M16—2441no—
375C2×M16C22×D6111yescharacteristic
376C2×M16C22×D6111yescharacteristic
377C2×M16C22×D6111yescharacteristic
378C2×M16C22×D6111yescharacteristic
379C22×C8—611no—
380C22×C8—611no—
381C22×C8—1221no—
382C22×C8—1221no—
383C22×C8C22×D6111yescharacteristic
384C22×C8C22×D6111yescharacteristic
385#117—611no—
386#117—611no—
387#117—611no—
388#117—611no—
389#117—611no—
390#117—611no—
391#117—611no—
392#117—611no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—611no—
395C2×C22⋊C4—611no—
396C2×C22⋊C4—611no—
397C2×C42—611no—
398C2×C42C22×D6111yescharacteristic
399#108—41no—
400#108—41no—
401#108—2441no—
402#108—2441no—
403#108—2441no—
404#108—2441no—
405#108—2441no—
406#108—2441no—
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8—612no—
410C4⋊C8—612no—
411C4⋊C8—1221no—
412C4⋊C8—1221no—
413C4⋊C8—1221no—
414C4⋊C8—1221no—
415C4⋊C8—1221no—
416C4⋊C8—1221no—
417C4⋊C8—1221no—
418C4⋊C8—1221no—
419C4⋊C8—1221no—
420C4⋊C8—1221no—
421C4⋊C8C4×D6112yes—
422C4⋊C8C4×D6112yes—
423C22⋊C8—612no—
424C22⋊C8—612no—
425C22⋊C8—612no—
426C22⋊C8—612no—
427C22⋊C8—1221no—
428C22⋊C8—1221no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431#97—21no—
432#97—612no—
433#97—612no—
434#97—1221no—
435C4×C8—21no—
436C4×C8—612no—
437C4×C8—612no—
438C4×C8—1221no—
439C24—611no—
440C22×C4—611no—
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—1221no—
450C22×C4—1221no—
451C22×C4Q8×D6111yescharacteristic
452C22×C4Q8×D6111yescharacteristic
453C22×C4C23×D6111yescharacteristic
454M16—21no—
455M16—21no—
456M16—21no—
457M16—21no—
458M16—21no—
459M16—21no—
460M16—21no—
461M16—21no—
462M16—1221no—
463M16—1221no—
464M16—1221no—
465M16—1221no—
466M16—1221no—
467M16—1221no—
468M16—1221no—
469M16—1221no—
470M16—2442no—
471M16—2442no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—612no—
481C2×C8—612no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—2442no—
491C2×C8—2442no—
492C2×C8C2×C4×D6112yes—
493C2×C8C2×C4×D6112yes—
494C4⋊C4—611no—
495C4⋊C4—611no—
496C4⋊C4—611no—
497C4⋊C4—611no—
498C4⋊C4—611no—
499C4⋊C4—611no—
500C4⋊C4—611no—
501C4⋊C4—611no—
502C22⋊C4—611no—
503C22⋊C4—611no—
504C22⋊C4—611no—
505C22⋊C4—611no—
506C22⋊C4—611no—
507C22⋊C4—611no—
508C22⋊C4—611no—
509C22⋊C4—611no—
510C42—611no—
511C42—611no—
512C42—611no—
513C42—611no—
514C42C2×C4×D6111yescharacteristic
515C42C2×C4×D6111yescharacteristic
516C42D4×D6111yescharacteristic
517C42D4×D6111yescharacteristic
518C23—611no—
519C23—611no—
520C23—1221no—
521C23—1221no—
522C23—2441no—
523C23—2441no—
524C23C2×Q8×D6111yescharacteristic
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—611no—
528C2×C4—611no—
529C2×C4—611no—
530C2×C4—611no—
531C2×C4—611no—
532C2×C4—611no—
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—2441no—
544C2×C4—2441no—
545C2×C4C4⋊C4×D6111yescharacteristic
546C2×C4C4⋊C4×D6111yescharacteristic
547C2×C4C4⋊C4×D6111yescharacteristic
548C2×C4C4⋊C4×D6111yescharacteristic
549C2×C4C22×C4×D6111yescharacteristic
550C2×C4C2×D4×D6111yescharacteristic
551C2×C4#1451982211yescharacteristic
552C2×C4#1451982311yescharacteristic
553C2×C4#1451982411yescharacteristic
554C2×C4#1451982511yescharacteristic
555C8—22no—
556C8—22no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—1222no—
562C8—1222no—
563C8—2441no—
564C8—2441no—
565C8—2441no—
566C8—2441no—
567C22—21no—
568C22—21no—
569C22—1221no—
570C22—1221no—
571C22—1221no—
572C22—1221no—
573C22—1221no—
574C22—1221no—
575C22—4881no—
576C22—4881no—
577C22C2×C4⋊C4×D6111yescharacteristic
578C22#1684038911yescharacteristic
579C22#1684039211yescharacteristic
580C4—21no—
581C4—21no—
582C4—21no—
583C4—21no—
584C4—1221no—
585C4—1221no—
586C4—1221no—
587C4—1221no—
588C4—1221no—
589C4—1221no—
590C4#1684024111yescharacteristic
591C4#1684024411yescharacteristic
592C4#1684032811yescharacteristic
593C4#1684033511yescharacteristic
594C2—21no—
595C2—21no—
596C2—2441no—
597C2—2441no—
598C2#2144844111yescharacteristic
599C2#2145442711yescharacteristic
600C2#2145442911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1950C2
socleC22×C61C22×C4⋊C4
prime radicalC23×D61C2×Q8
cosocleC22×C4×C61C24
hypercenter#1950D61
hypocenterC61#21995
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
4. #21446595C2semidirect
5. #21446594C2semidirect
6. #21446592C2semidirect
11. #21445992C2semidirect
12. #21445989C2semidirect
13. #21445958C2semidirect
14. #21445955C2semidirect
15. C61×#1950C2semidirect
300. #1950D61semidirect
363. C61#21995semidirect

Maximal subgroups

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

subgroupindex
#214544552
C2×#168398222
#214543812
#214465952
#214465942
#214465922
#214460252
#214460222
#214459922
#214459892
#214459582
#214459552
C61×#19502
#2199561