Finite Group Databasebeta

← #29709807

Subgroups — #29709807

Order 15616.

1126 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839798C211yesmaximal, characteristic, complemented
2C2×#16839759C211yesmaximal, characteristic
3C2×#16839756C211yesmaximal, characteristic
4#21448307C211yesmaximal, characteristic
5#21448222C211yesmaximal, characteristic, complemented
6#21447368C211yesmaximal, characteristic, complemented
7#21447364C211yesmaximal, characteristic, complemented
8#21447359C211yesmaximal, characteristic, complemented
9#21447354C211yesmaximal, characteristic, complemented
10#21447349C211yesmaximal, characteristic, complemented
11#21447344C211yesmaximal, characteristic, complemented
12#21447341C211yesmaximal, characteristic, complemented
13#21447337C211yesmaximal, characteristic, complemented
14C2×#16839516C211yesmaximal, characteristic, complemented
15C2×C61×#427C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C22×C4×Dic61C2211yescharacteristic
20#16839798—24no—
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25#16839759—24no—
26#16839756—24no—
27C2×#14519702C2211yescharacteristic
28C2×#14519702C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35#16839667C2211yescharacteristic
36#16839667C2211yescharacteristic
37#16839663C2211yescharacteristic
38#16839663C2211yescharacteristic
39#16839639—22no—
40#16839631C2211yescharacteristic
41#16839631C2211yescharacteristic
42#16839627C2211yescharacteristic
43#16839627C2211yescharacteristic
44#16839620—22no—
45C4×#11758196—22no—
46C4×#11758198—22no—
47#16839516C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51C23×C8×C61C2211yescharacteristic
52C2×#117×C61C2211yescharacteristic
53C2×#117×C61C2211yescharacteristic
54C61×#427—24no—
55C2×#107×C61C2211yescharacteristic
56C2×#107×C61C2211yescharacteristic
57C2×#106×C61C2211yescharacteristic
58C2×#106×C61C2211yescharacteristic
59C2×#11758222—22no—
60C2×#11758222—22no—
61C2×#11758222—22no—
62C2×#11758222—22no—
63C2×#11758222—22no—
64C2×#11758222Q814yes—
65C22×Dic122C2311yescharacteristic
66C22×D244C2311yescharacteristic
67C22×C22⋊D61—21no—
68C23×Dic61D412yes—
69C22×C4×D61—21no—
70C22×#92418—22no—
71C22×#92418—22no—
72C22×#92418D414yes—
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519736—22no—
76#14519736—22no—
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×#11758196—22no—
80C2×#11758196—22no—
81C2×C22⋊Dic61—21no—
82C2×#11758198—22no—
83C2×#11758198—22no—
84C2×C4×Dic61—22no—
85C2×C4×Dic61—22no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61D412yes—
88C2×C4×Dic61C2311yescharacteristic
89C2×C4×Dic61C2311yescharacteristic
90#14519710—22no—
91#14519710—22no—
92#14519708—22no—
93#14519708—22no—
94#14519702—22no—
95#14519702—22no—
96#14519700—22no—
97#14519700—22no—
98#14519699—22no—
99#14519699—22no—
100#14519697—22no—
101#14519697—22no—
102#14519684—22no—
103#14519684—22no—
104#14519684—22no—
105#14519684—22no—
106C23×C4×C61C2311yescharacteristic
107C22×C8×C61—22no—
108C22×C8×C61—22no—
109C22×C8×C61D414yes—
110C22×C8×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112#117×C61—22no—
113#117×C61—22no—
114#117×C61—22no—
115#117×C61—22no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—21no—
122C2×C42×C61—21no—
123C2×C42×C61—21no—
124#107×C61—22no—
125#107×C61—22no—
126#106×C61—22no—
127#106×C61—22no—
128C24×C61C2×D411yescharacteristic
129C23×D61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D412yes—
136C22×C4×C61C2×D412yes—
137C22×C4×C61C2×Q812yes—
138C22×C4×C61#4112yes—
139C22×C4×C61#4112yes—
140C22×C4×C61#4112yes—
141C22×C4×C61C2411yescharacteristic
142C2×C22⋊D61—24no—
143C2×C22⋊D61—42no—
144C2×C22⋊D61—42no—
145C22×Dic61—24no—
146C22×Dic61—21no—
147C22×Dic61—24no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—42no—
151C22×Dic61C2×D412yes—
152C22×Dic61C2×D412yes—
153#11758222—28no—
154#11758222—28no—
155#11758222—44no—
156#11758222—44no—
157C2×D244—21no—
158C2×D244—21no—
159C2×D244—21no—
160C2×D244—21no—
161C2×D244—21no—
162C2×D244C2×Q812yes—
163C2×C4×D61—24no—
164C2×C4×D61—42no—
165C2×C4×D61—42no—
166C2×Dic122—21no—
167C2×Dic122—21no—
168C2×Dic122—21no—
169C2×Dic122—21no—
170C2×Dic122—21no—
171C2×Dic122C2×Q812yes—
172C2×C8×C61—28no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61C2×D412yes—
178C2×C8×C61C2×D412yes—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C22⋊C4×C61—42no—
188C22⋊C4×C61—42no—
189C42×C61—42no—
190C42×C61—42no—
191C22⋊Dic61—42no—
192#11758198—44no—
193#11758198—44no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198#11758196—44no—
199#11758196—44no—
200C4×Dic61—24no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61—42no—
206C2×#92418—28no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418C2×D412yes—
212C2×#92418C2×D412yes—
213C23×C61—22no—
214C23×C61—22no—
215C23×C61C22⋊Q812yes—
216C23×C61#12312yes—
217C23×C61#12712yes—
218C23×C61C22×D411yescharacteristic
219C22×D61—22no—
220C22×D61—41no—
221C22×D61—41no—
222C22×D61—42no—
223C22×D61—42no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61—42no—
232C2×C4×C61C22⋊Q814yes—
233C2×C4×C61C22⋊Q814yes—
234C2×C4×C61C22⋊Q812yes—
235C2×C4×C61#12314yes—
236C2×C4×C61#12314yes—
237C2×C4×C61#12312yes—
238C2×C4×C61#12712yes—
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61C22×D411yescharacteristic
241C2×C4×C61C22×Q811yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C22⋊D61—48no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—48no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61#13514yes—
260D244—22no—
261D244—22no—
262D244—41no—
263D244—41no—
264C4×D61—48no—
265Dic122—22no—
266Dic122—22no—
267Dic122—41no—
268Dic122—41no—
269C8×C61—22no—
270C8×C61—22no—
271#92418—22no—
272#92418—22no—
273#23730—611nomaximal, Sylow
274C22×C61—24no—
275C22×C61—24no—
276C22×C61—22no—
277C22×C61—22no—
278C22×C61#39914yes—
279C22×C61C2×C22⋊Q811yescharacteristic
280C22×C61C2×#12311yescharacteristic
281C22×C61C2×#12711yescharacteristic
282C22×C61C2×#13512yes—
283C22×C61#57512yes—
284C2×D61—44no—
285C2×D61—42no—
286C2×D61—82no—
287C2×D61—81no—
288C2×D61—81no—
289C4×C61—81no—
290C4×C61—81no—
291C4×C61—81no—
292C4×C61—81no—
293C4×C61#39914yes—
294C4×C61C2×C22⋊Q811yescharacteristic
295C4×C61C2×C22⋊Q811yescharacteristic
296C4×C61C2×#12311yescharacteristic
297C4×C61C2×#12311yescharacteristic
298Dic61—24no—
299Dic61—42no—
300Dic61—42no—
301Dic61—81no—
302Dic61—81no—
303C2×#427—611no—
304C2×#427D6111yescharacteristic, complemented
305C2×#416—611no—
306C2×#416—611no—
307#2297—611no—
308#2285—611no—
309#2097—611no—
310#2097—611no—
311#2096—611no—
312#2095—611no—
313#2094—611no—
314#2093—611no—
315#2092—611no—
316#2092—611no—
317C2×#336—611no—
318C2×C61—24no—
319C2×C61C2×#39911yescharacteristic
320C2×C61#307612yes—
321C2×C61#309112yes—
322C2×C61#314711yescharacteristic
323C2×C61#315011yescharacteristic
324D61—82no—
325C22×#41—611no—
326C23×C8—611no—
327C23×C8C2×D6111yescharacteristic
328C2×#117—611no—
329C2×#117C2×D6111yescharacteristic
330C2×#117C2×D6111yescharacteristic
331C22×C42—611no—
332#427—24no—
333#427—1224no—
334C2×#107—611no—
335C2×#107—611no—
336C2×#107C2×D6111yescharacteristic
337C2×#107C2×D6111yescharacteristic
338C2×#106—611no—
339C2×#106—611no—
340C2×#106C2×D6111yescharacteristic
341C2×#106C2×D6111yescharacteristic
342#416—1224no—
343#416—1224no—
344C2×#103—611no—
345C2×#103—611no—
346C2×#103—611no—
347C2×#103—611no—
348C2×#102—611no—
349C2×#102—611no—
350C2×#102—611no—
351C2×#102—611no—
352#391—611no—
353#391—611no—
354#390—611no—
355#390—611no—
356#386—1222no—
357#384—611no—
358#384—611no—
359#382—611no—
360#382—611no—
361#380—1222no—
362C4×C4⋊C4—1222no—
363C4×C22⋊C4—1222no—
364#336—611no—
365#336—611no—
366#336—611no—
367#336—611no—
368C61#2373011yescharacteristic, complemented, Sylow
369C2×#41—614no—
370C2×#41—1222no—
371C2×#41—1222no—
372C2×#41—1222no—
373C2×#41—1222no—
374C2×#41—1222no—
375C22×Q8—611no—
376C22×D4—611no—
377C22×D4—1221no—
378C23×C4—612no—
379C23×C4—1221no—
380C23×C4C22×D6111yescharacteristic
381C22×C8—22no—
382C22×C8—22no—
383C22×C8—614no—
384C22×C8—611no—
385C22×C8—611no—
386C22×C8—1222no—
387C22×C8—1222no—
388C22×C8C22⋊D6114yes—
389C22×C8C22×D6111yescharacteristic
390C22×C8C22×D6111yescharacteristic
391#117—22no—
392#117—22no—
393#117—22no—
394#117—22no—
395#117—1222no—
396#117—1222no—
397C2×C4⋊C4—611no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—1222no—
400C2×C4⋊C4—1222no—
401C2×C4⋊C4C22×D6111yescharacteristic
402C2×C4⋊C4C22×D6111yescharacteristic
403C2×C4⋊C4C22×D6111yescharacteristic
404C2×C4⋊C4C22×D6111yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—1222no—
408C2×C22⋊C4—1222no—
409C2×C22⋊C4—1221no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—612no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—1222no—
416C2×C42—1222no—
417C2×C42—1221no—
418#107—22no—
419#107—22no—
420#107—1222no—
421#107—1222no—
422#106—22no—
423#106—22no—
424#106—1222no—
425#106—1222no—
426#103—1222no—
427#103—1222no—
428#103—1222no—
429#103—1222no—
430#102—1222no—
431#102—1222no—
432#102—1222no—
433#102—1222no—
434#95—1222no—
435#95—1222no—
436#95—1222no—
437#95—1222no—
438C24—1221no—
439C24D4×D6111yescharacteristic
440#41—1228no—
441#41—1228no—
442#41—2444no—
443#41—2444no—
444C2×Q8—612no—
445C2×Q8—1221no—
446C2×Q8—1221no—
447C2×Q8—1221no—
448C2×Q8—1221no—
449C2×Q8—1221no—
450C2×D4—612no—
451C2×D4—1224no—
452C2×D4—1221no—
453C2×D4—1221no—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4—1221no—
457C2×D4—2442no—
458C2×D4—2442no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—612no—
464C22×C4—612no—
465C22×C4—1224no—
466C22×C4—1221no—
467C22×C4—1224no—
468C22×C4—1224no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—2442no—
472C22×C4—2442no—
473C22×C4—2442no—
474C22×C4#1175822212yes—
475C22×C4#1175822212yes—
476C22×C4D4×D6112yes—
477C22×C4D4×D6111yescharacteristic
478C22×C4Q8×D6112yes—
479C22×C4#1175822612yes—
480C22×C4C2×C22⋊D6112yes—
481C22×C4C23×D6111yescharacteristic
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—28no—
487C2×C8—612no—
488C2×C8—612no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1228no—
494C2×C8C2×C22⋊D6112yes—
495C2×C8C2×C22⋊D6112yes—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—1221no—
508C4⋊C4—2444no—
509C4⋊C4—2444no—
510C22⋊C4—42no—
511C22⋊C4—42no—
512C22⋊C4—2444no—
513C22⋊C4—2444no—
514C22⋊C4—2442no—
515C42—42no—
516C42—42no—
517C42—1221no—
518C42—1221no—
519C42—1221no—
520C42—1221no—
521C42—1224no—
522C42—2442no—
523C23—22no—
524C23—22no—
525C23—1222no—
526C23—2441no—
527C23—2442no—
528C23—2441no—
529C23—2442no—
530C23#1451975512yes—
531C23#1451976212yes—
532C23#1451977312yes—
533C23C2×D4×D6111yescharacteristic
534Q8—1222no—
535Q8—1222no—
536Q8—2441no—
537Q8—2441no—
538D4—1222no—
539D4—1222no—
540D4—2448no—
541D4—2441no—
542D4—2441no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—614no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—1222no—
555C2×C4—1222no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—2448no—
559C2×C4—2442no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4—2442no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2448no—
566C2×C4#1451975314yes—
567C2×C4#1451975512yes—
568C2×C4#1451975514yes—
569C2×C4#1451976014yes—
570C2×C4#1451976212yes—
571C2×C4#1451976214yes—
572C2×C4#1451977312yes—
573C2×C4C2×D4×D6111yescharacteristic
574C2×C4C22×C22⋊D6111yescharacteristic
575C2×C4C2×Q8×D6111yescharacteristic
576C2×C4C2×#1175822211yescharacteristic
577C2×C4C2×#1175822211yescharacteristic
578C2×C4C2×#1175822611yescharacteristic
579C8—22no—
580C8—22no—
581C8—1222no—
582C8—1222no—
583C22—22no—
584C22—24no—
585C22—22no—
586C22—24no—
587C22—4881no—
588C22—4882no—
589C22—4881no—
590C22—2442no—
591C22—2444no—
592C22#1683969714yes—
593C22C2×#1451975511yescharacteristic
594C22C2×#1451976211yescharacteristic
595C22C2×#1451977311yescharacteristic
596C22#135×D6112yes—
597C22#1684055912yes—
598C4—81no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—1224no—
603C4—4881no—
604C4—4881no—
605C4—2442no—
606C4—2442no—
607C4#1683969714yes—
608C4C2×#1451975311yescharacteristic
609C4C2×#1451975511yescharacteristic
610C4C2×#1451976011yescharacteristic
611C4C2×#1451976211yescharacteristic
612C2—24no—
613C2—4882no—
614C2C2×#1683969711yescharacteristic
615C2#2145560512yes—
616C2#2145573612yes—
617C2#2145624311yescharacteristic
618C2#2145626211yescharacteristic
subgroupG/H
centerC22×C4D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#427C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
hypercenterC2×#427D61
hypocenterC61#23730
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
1. C2×#16839798C2semidirect
5. #21448222C2semidirect
6. #21447368C2semidirect
7. #21447364C2semidirect
8. #21447359C2semidirect
9. #21447354C2semidirect
10. #21447349C2semidirect
11. #21447344C2semidirect
12. #21447341C2semidirect
13. #21447337C2semidirect
14. C2×#16839516C2semidirect
15. C2×C61×#427C2semidirect
304. C2×#427D61semidirect
368. C61#23730semidirect

Maximal subgroups

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

subgroupindex
C2×#168397982
C2×#168397592
C2×#168397562
#214483072
#214482222
#214473682
#214473642
#214473592
#214473542
#214473492
#214473442
#214473412
#214473372
C2×#168395162
C2×C61×#4272
#2373061