Finite Group Databasebeta

← #29709519

Subgroups — #29709519

Order 15616.

820 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758202C211yesmaximal, characteristic, complemented
2C2×#16839823C211yesmaximal, characteristic
3#21448501C211yesmaximal, characteristic
4#21447315C211yesmaximal, characteristic, complemented
5#21447250C211yesmaximal, characteristic
6#21447200C211yesmaximal, characteristic, complemented
7#21447197C211yesmaximal, characteristic, complemented
8#21447141C211yesmaximal, characteristic, complemented
9#21447015C211yesmaximal, characteristic
10#21447012C211yesmaximal, characteristic
11#21446827C211yesmaximal, characteristic
12C4×#14519708C211yesmaximal, characteristic, complemented
13#21445652C211yesmaximal, characteristic, complemented
14#21445649C211yesmaximal, characteristic, complemented
15C61×#2323C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C2×#14519756C2211yescharacteristic
18C2×C4×Dic122C2211yescharacteristic
19C4×#11758202—24no—
20#16839823—24no—
21C2×#14519710C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34C2×#14519688C2211yescharacteristic
35C2×C4×#92418C2211yescharacteristic
36#16839668C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839657—21no—
39#16839656—21no—
40#16839650—21no—
41#16839643—21no—
42#16839622C2211yescharacteristic
43C4×C4⋊Dic61C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50C2×C22⋊Q8×C61C2211yescharacteristic
51C2×C4×Q8×C61C2211yescharacteristic
52C2×#117×C61C2211yescharacteristic
53C61×#391C2211yescharacteristic
54C61×#389—21no—
55C61×#389C2211yescharacteristic
56C61×#388—21no—
57C61×#388—21no—
58C61×#387—21no—
59C61×#380C2211yescharacteristic
60C4×C4⋊C4×C61C2211yescharacteristic
61C22×Dic122C2311yescharacteristic
62C2×#11758202—22no—
63C2×#11758202—22no—
64C2×#11758202—22no—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69#14519756—22no—
70#14519756—22no—
71C4×Dic122—22no—
72C4×Dic122—22no—
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61—21no—
83#14519710—22no—
84#14519708—22no—
85#14519708—22no—
86C4⋊#92418—22no—
87C4⋊#92418—22no—
88#14519701—22no—
89#14519701—22no—
90#14519701—22no—
91#14519700—22no—
92#14519700—22no—
93#14519700—22no—
94C22⋊#92418—22no—
95C22⋊#92418—22no—
96#14519688—22no—
97C4×#92418D414yes—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103C22×Q8×C61C2311yescharacteristic
104C23×C4×C61C2311yescharacteristic
105C22⋊Q8×C61—22no—
106C22⋊Q8×C61—22no—
107C4×Q8×C61—22no—
108C4×Q8×C61—22no—
109#117×C61—22no—
110#117×C61—22no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61—21no—
114C2×C4⋊C4×C61D411yescharacteristic
115C2×C4⋊C4×C61D411yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61D411yescharacteristic
122C2×C22⋊C4×C61D411yescharacteristic
123C2×C42×C61—21no—
124C2×C42×C61—21no—
125C2×C42×C61C2311yescharacteristic
126C2×C42×C61C2311yescharacteristic
127#95×C61—21no—
128#95×C61—21no—
129#95×C61—21no—
130#95×C61—21no—
131#95×C61—21no—
132C24×C61C2×D411yescharacteristic
133C2×Q8×C61—21no—
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61#4112yes—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2411yescharacteristic
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122#4112yes—
165C4⋊C4×C61—24no—
166C4⋊C4×C61—22no—
167C4⋊C4×C61—22no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—42no—
174C4⋊C4×C61—81no—
175C4⋊C4×C61#4112yes—
176C22⋊C4×C61—24no—
177C22⋊C4×C61—22no—
178C22⋊C4×C61—22no—
179C22⋊C4×C61—81no—
180C42×C61—21no—
181C42×C61—21no—
182C42×C61—42no—
183C42×C61—81no—
184C42×C61C2×D412yes—
185C42×C61#4112yes—
186C22⋊Dic61—24no—
187C22⋊Dic61—81no—
188#11758202—28no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61#4112yes—
195#11758196—24no—
196#11758196—42no—
197#11758196—81no—
198C4×Dic61—42no—
199C4×Dic61—81no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418C2×D412yes—
211C2×#92418C2×D412yes—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61C22×D411yescharacteristic
220Q8×C61—22no—
221Q8×C61—22no—
222Q8×C61—41no—
223Q8×C61—41no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61#12112yes—
254C2×C4×C61#12112yes—
255C2×C4×C61C22×D411yescharacteristic
256C2×C4×C61C2×#4111yescharacteristic
257C2×C4×C61C2×#4111yescharacteristic
258C2×C4×C61C2×#4111yescharacteristic
259C2×C4×C61C2×#4111yescharacteristic
260C2×C4×C61C2×#4111yescharacteristic
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273Dic122—22no—
274Dic122—22no—
275Dic122—41no—
276Dic122—41no—
277#92418—22no—
278#92418—22no—
279#92418—41no—
280#92418—41no—
281#23704—611nomaximal, Sylow
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61C2×#12111yescharacteristic
290C22×C61#52511yescharacteristic
291C22×C61#52511yescharacteristic
292C22×C61#57711yescharacteristic
293C22×C61#57711yescharacteristic
294C22×C61#57811yescharacteristic
295C22×C61#57811yescharacteristic
296C4×C61—22no—
297C4×C61—22no—
298C4×C61—42no—
299C4×C61—41no—
300C4×C61—42no—
301C4×C61—41no—
302C4×C61—41no—
303C4×C61—81no—
304C4×C61—81no—
305C4×C61#52511yescharacteristic
306C4×C61#52911yescharacteristic
307C4×C61#52911yescharacteristic
308C4×C61#53211yescharacteristic
309Dic61—42no—
310Dic61—42no—
311Dic61—81no—
312Dic61—81no—
313C2×C4×Q16—611no—
314C2×#433—611no—
315#2323—611no—
316#2323D6111yescharacteristic
317#2087—611no—
318#2076—611no—
319#2066—611no—
320#2066—611no—
321#2056—611no—
322#2035—611no—
323#2035—611no—
324#2001—611no—
325C4×#106—611no—
326#1763—611no—
327#1763—611no—
328C2×C61—81no—
329C2×C61#239211yescharacteristic
330C2×C61#305911yescharacteristic
331C2×C61#306011yescharacteristic
332C2×C61#312011yescharacteristic
333C2×C61#312011yescharacteristic
334C2×C61#312111yescharacteristic
335C2×C61#312111yescharacteristic
336C22×Q16—611no—
337C2×C22⋊Q8—611no—
338C2×C22⋊Q8C2×D6111yescharacteristic
339C2×C4×Q8—611no—
340C2×C4×Q8C2×D6111yescharacteristic
341C2×#117C2×D6111yescharacteristic
342C4×Q16—1224no—
343#433—1224no—
344C2×#107—611no—
345C2×#106—611no—
346C2×#106—611no—
347C2×C4⋊C8—611no—
348C2×C4⋊C8—611no—
349C2×#103—611no—
350C2×#103—611no—
351C2×#103—611no—
352C2×#103—611no—
353C2×#103—611no—
354C2×#103—611no—
355C2×C22⋊C8—611no—
356C2×C22⋊C8—611no—
357C2×#97—611no—
358C2×C4×C8—611no—
359#391—611no—
360#391C2×D6111yescharacteristic
361#389—21no—
362#389—611no—
363#389—1221no—
364#389C2×D6111yescharacteristic
365#388—21no—
366#388—21no—
367#388—1221no—
368#388—1221no—
369#387—21no—
370#387—1221no—
371#380—611no—
372#380C2×D6111yescharacteristic
373C4×C4⋊C4—611no—
374C4×C4⋊C4C2×D6111yescharacteristic
375#340—611no—
376#340—611no—
377#340—611no—
378#340—611no—
379#340—611no—
380#340—611no—
381C61#2370411yescharacteristic, complemented, Sylow
382C22×Q8—611no—
383C22×Q8C22×D6111yescharacteristic
384C23×C4C22×D6111yescharacteristic
385C2×Q16—1222no—
386C2×Q16—1222no—
387C2×Q16—1222no—
388C22×C8—611no—
389C22×C8—611no—
390C22×C8—611no—
391C22×C8—611no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—1222no—
395C22⋊Q8—1222no—
396C4×Q8—22no—
397C4×Q8—22no—
398C4×Q8—1222no—
399C4×Q8—1222no—
400#117—22no—
401#117—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—611no—
407C2×C4⋊C4—611no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4C22⋊D6111yescharacteristic
412C2×C4⋊C4C22⋊D6111yescharacteristic
413C2×C4⋊C4C22×D6111yescharacteristic
414C2×C4⋊C4C22×D6111yescharacteristic
415C2×C4⋊C4C22×D6111yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—1221no—
419C2×C22⋊C4—1221no—
420C2×C22⋊C4C22⋊D6111yescharacteristic
421C2×C22⋊C4C22⋊D6111yescharacteristic
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—1221no—
425C2×C42—1221no—
426C2×C42C22×D6111yescharacteristic
427C2×C42C22×D6111yescharacteristic
428#107—1222no—
429#106—1222no—
430#106—1222no—
431C4⋊C8—1222no—
432C4⋊C8—1222no—
433#103—1222no—
434#103—1222no—
435#103—1222no—
436#103—1222no—
437#103—1222no—
438#103—1222no—
439C22⋊C8—1222no—
440C22⋊C8—1222no—
441#97—1222no—
442C4×C8—614no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—1221no—
449#95—1221no—
450#95—1221no—
451#95—1221no—
452#95—1221no—
453C24C2×C22⋊D6111yescharacteristic
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—612no—
460C2×Q8—1221no—
461C2×Q8—1221no—
462C2×Q8—1221no—
463C2×Q8—1221no—
464C2×Q8—1221no—
465C2×Q8#1175822212yes—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4C2×C22⋊D6111yescharacteristic
481C22×C4C2×C22⋊D6111yescharacteristic
482C22×C4C2×C22⋊D6111yescharacteristic
483C22×C4C2×C22⋊D6111yescharacteristic
484C22×C4C2×C22⋊D6111yescharacteristic
485C22×C4C23×D6111yescharacteristic
486Q16—1228no—
487C2×C8—612no—
488C2×C8—612no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1221no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C4⋊C4—24no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—42no—
508C4⋊C4—81no—
509C4⋊C4—612no—
510C4⋊C4—1224no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—4881no—
517C4⋊C4—2442no—
518C4⋊C4#1175822212yes—
519C22⋊C4—24no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—81no—
523C22⋊C4—1224no—
524C22⋊C4—4881no—
525C42—21no—
526C42—21no—
527C42—42no—
528C42—81no—
529C42—4881no—
530C42—2442no—
531C42D4×D6112yes—
532C42#1175822412yes—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23C22×C22⋊D6111yescharacteristic
541Q8—22no—
542Q8—22no—
543Q8—41no—
544Q8—41no—
545Q8—1222no—
546Q8—1222no—
547Q8—2441no—
548Q8—2441no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4#1451974912yes—
591C2×C4#1451974912yes—
592C2×C4C2×D4×D6111yescharacteristic
593C2×C4#41×D6111yescharacteristic
594C2×C4#41×D6111yescharacteristic
595C2×C4C2×#1175822411yescharacteristic
596C2×C4C2×#1175822211yescharacteristic
597C2×C4C2×#1175822211yescharacteristic
598C8—1222no—
599C8—1222no—
600C8—2441no—
601C8—2441no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22C2×#1451974911yescharacteristic
610C22#1684026911yescharacteristic
611C22#1684027311yescharacteristic
612C22#1684057011yescharacteristic
613C22#1684057311yescharacteristic
614C22#1684057711yescharacteristic
615C22#1684057711yescharacteristic
616C4—22no—
617C4—22no—
618C4—41no—
619C4—42no—
620C4—41no—
621C4—41no—
622C4—42no—
623C4—81no—
624C4—81no—
625C4—4881no—
626C4—4881no—
627C4—2442no—
628C4—2442no—
629C4#1684027111yescharacteristic
630C4#1684029211yescharacteristic
631C4#1684029411yescharacteristic
632C4#1684030911yescharacteristic
633C2—81no—
634C2#2144906111yescharacteristic
635C2#2145547111yescharacteristic
636C2#2145547811yescharacteristic
637C2#2145602711yescharacteristic
638C2#2145603311yescharacteristic
639C2#2145604211yescharacteristic
640C2#2145604811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2323C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
hypercenter#2323D61
hypocenterC61#23704
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
1. C2×C4×#11758202C2semidirect
4. #21447315C2semidirect
6. #21447200C2semidirect
7. #21447197C2semidirect
8. #21447141C2semidirect
12. C4×#14519708C2semidirect
13. #21445652C2semidirect
14. #21445649C2semidirect
381. C61#23704semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582022
C2×#168398232
#214485012
#214473152
#214472502
#214472002
#214471972
#214471412
#214470152
#214470122
#214468272
C4×#145197082
#214456522
#214456492
C61×#23232
#2370461