Finite Group Databasebeta

← #30610058

Subgroups — #30610058

Order 15616.

1020 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462495C211yesmaximal, characteristic, complemented
2C2×#16840779C211yesmaximal, characteristic, complemented
3#21461092C212yesmaximal, complemented
4#21461090C212yesmaximal, complemented
5#21461086C214yesmaximal, complemented
6#21461053C214yesmaximal, complemented
7C2×#16840298C211yesmaximal, characteristic
8#16840783C2212yes—
9#16840782—21no—
10#16840779—21no—
11#16840779—21no—
12#16840779C2212yes—
13#16840779C2212yes—
14#16840779C2212yes—
15#16840778—21no—
16#16840765—21no—
17C2×#14519844—21no—
18#16840732C2212yes—
19C2×C22⋊#92420C2212yes—
20C4×#11758217—21no—
21C2×C4×#92420—21no—
22#16840607C2218yes—
23#16840606C2218yes—
24#16840298—21no—
25#16840298—21no—
26#16840298—21no—
27#16840298—21no—
28#16840298—21no—
29#16840298—21no—
30#16840298—21no—
31#16840298—21no—
32C2×#14519772C412yes—
33C2×#14519768C2211yescharacteristic
34C2×#14519766C2211yescharacteristic
35C2×#14519761C2212yes—
36C2×#14519751C411yescharacteristic
37C2×Q8×Dic61C411yescharacteristic
38C2×#14519739C411yescharacteristic
39C2×#14519737C412yes—
40C2×#14519735C2212yes—
41C22×C4×Dic61C2211yescharacteristic
42C2×C22⋊Q8×C61C411yescharacteristic
43C2×#11758217—22no—
44C22×#92420—22no—
45#14519844—22no—
46#14519844—22no—
47#14519844—22no—
48C4⋊#92420—22no—
49C22⋊#92420—22no—
50C22⋊#92420—22no—
51C22⋊#92420C2314yes—
52C22⋊#92420C2314yes—
53#14519832—22no—
54C4×#92420—22no—
55C4×#92420—22no—
56C4×#92420—22no—
57C22×D244C2×C411yescharacteristic
58C22×C22⋊D61C2×C412yes—
59C23×Dic61C2×C411yescharacteristic
60C23×Dic61C2311yescharacteristic
61C22×C4×D61C2×C412yes—
62#14519772—22no—
63#14519772—22no—
64#14519772—22no—
65#14519772—22no—
66#14519768—21no—
67#14519768—21no—
68#14519768—21no—
69#14519768—21no—
70#14519766—21no—
71#14519766—21no—
72#14519766—21no—
73#14519766—21no—
74#14519761—22no—
75#14519761—22no—
76#14519761—22no—
77#14519761—22no—
78#14519751—21no—
79#14519751—21no—
80#14519751—21no—
81#14519751—21no—
82Q8×Dic61—21no—
83Q8×Dic61—21no—
84Q8×Dic61—21no—
85Q8×Dic61—21no—
86#14519739—21no—
87#14519739—21no—
88#14519739—21no—
89#14519739—21no—
90#14519737—22no—
91#14519737—22no—
92#14519737—22no—
93#14519737—22no—
94#14519735—22no—
95#14519735—22no—
96#14519735—22no—
97#14519735—22no—
98C2×C4⋊Dic61C2×C411yescharacteristic
99C2×C4⋊Dic61C2×C412yes—
100C2×C4⋊Dic61C2312yes—
101C2×#11758196C2×C412yes—
102C2×#11758198C2×C412yes—
103C2×#11758198C2×C412yes—
104C2×#11758198C2×C412yes—
105C2×#11758198C2312yes—
106C2×C4×Dic61C2×C412yes—
107C2×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61C2×C411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61D411yescharacteristic
114C2×C4×Dic61D411yescharacteristic
115C2×C4×Dic61D411yescharacteristic
116C2×C4×Dic61D411yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118C2×C4×Dic61C2311yescharacteristic
119C22×Q8×C61C2×C411yescharacteristic
120C23×C4×C61C2×C411yescharacteristic
121C22⋊Q8×C61—21no—
122C22⋊Q8×C61—21no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—21no—
125C2×C4⋊C4×C61C2×C412yes—
126C2×C4⋊C4×C61C2×C411yescharacteristic
127C2×C22⋊C4×C61C2×C412yes—
128C24×C61C22×C411yescharacteristic
129C23×D61C22×C412yes—
130C2×Q8×C61—21no—
131C2×Q8×C61—21no—
132C2×Q8×C61—42no—
133C22×C4×C61—42no—
134C22×C4×C61C22⋊C411yescharacteristic
135C22×C4×C61C22⋊C411yescharacteristic
136C22×C4×C61C22⋊C411yescharacteristic
137C22×C4×C61C22⋊C411yescharacteristic
138C22×C4×C61C22×C412yes—
139C22×C4×C61C22×C411yescharacteristic
140C22×C4×C61C22×C412yes—
141C22×C4×C61C22×C411yescharacteristic
142C2×C22⋊D61—22no—
143C2×C22⋊D61—22no—
144C2×C22⋊D61—44no—
145C22×Dic61—24no—
146C22×Dic61—42no—
147C22×Dic61C22⋊C411yescharacteristic
148C22×Dic61C22⋊C411yescharacteristic
149C22×Dic61C22⋊C411yescharacteristic
150C22×Dic61C22⋊C411yescharacteristic
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C412yes—
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61C2×D411yescharacteristic
159C22×Dic61C2411yescharacteristic
160C2×D244—21no—
161C2×D244—21no—
162C2×D244—42no—
163C2×C4×D61—22no—
164C2×C4×D61—22no—
165C2×C4×D61—28no—
166#11758217—44no—
167C2×#92420—24no—
168C2×#92420—24no—
169C2×#92420—44no—
170C4⋊C4×C61—22no—
171C4⋊C4×C61—22no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C22⋊C4×C61—22no—
175C22⋊C4×C61—22no—
176#11758198—22no—
177#11758198—22no—
178#11758198—22no—
179#11758198—22no—
180#11758198—22no—
181#11758198—22no—
182#11758198—22no—
183#11758198—22no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—22no—
187C4⋊Dic61—22no—
188C4⋊Dic61—22no—
189C4⋊Dic61—22no—
190#11758196—22no—
191#11758196—22no—
192C4×Dic61—22no—
193C4×Dic61—22no—
194C4×Dic61C22⋊C411yescharacteristic
195C4×Dic61C22⋊C411yescharacteristic
196C4×Dic61C22⋊C411yescharacteristic
197C4×Dic61C22⋊C411yescharacteristic
198C4×Dic61C22⋊C411yescharacteristic
199C4×Dic61C22⋊C411yescharacteristic
200C4×Dic61C22⋊C411yescharacteristic
201C4×Dic61C22⋊C411yescharacteristic
202C4×Dic61C2×D411yescharacteristic
203C4×Dic61C2×D411yescharacteristic
204C4×Dic61C2×D411yescharacteristic
205C4×Dic61C2×D411yescharacteristic
206C4×Dic61C2×D411yescharacteristic
207C4×Dic61C2×D411yescharacteristic
208C4×Dic61C2×D411yescharacteristic
209C4×Dic61C2×D411yescharacteristic
210C23×C61—22no—
211C23×C61—22no—
212C23×C61—41no—
213C23×C61C2×C22⋊C411yescharacteristic
214C23×C61C2×C22⋊C411yescharacteristic
215C23×C61C23×C411yescharacteristic
216C22×D61—22no—
217C22×D61—24no—
218C22×D61—42no—
219C22×D61—42no—
220Q8×C61—42no—
221Q8×C61—42no—
222C2×C4×C61—22no—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—24no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—42no—
232C2×C4×C61C2×C22⋊C411yescharacteristic
233C2×C4×C61C2×C22⋊C411yescharacteristic
234C2×C4×C61C2×C22⋊C411yescharacteristic
235C2×C4×C61C2×C22⋊C411yescharacteristic
236C22⋊D61—44no—
237C22⋊D61—44no—
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61—22no—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—42no—
251C2×Dic61C2×C22⋊C411yescharacteristic
252C2×Dic61C2×C22⋊C411yescharacteristic
253C2×Dic61C2×C22⋊C411yescharacteristic
254C2×Dic61C2×C22⋊C411yescharacteristic
255C2×Dic61C2×C22⋊C411yescharacteristic
256C2×Dic61C2×C22⋊C411yescharacteristic
257C2×Dic61#13114yes—
258C2×Dic61C22×D411yescharacteristic
259C2×Dic61C22×D411yescharacteristic
260D244—42no—
261D244—42no—
262C4×D61—44no—
263C4×D61—44no—
264#92420—44no—
265#92420—44no—
266#17376—611nomaximal, Sylow
267C22×C61—21no—
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—21no—
273C22×C61—21no—
274C22×C61—44no—
275C22×C61#41012yes—
276C22×C61C22×C22⋊C411yescharacteristic
277C22×C61C2×#13112yes—
278C2×D61—42no—
279C2×D61—42no—
280C2×D61—42no—
281C2×D61—84no—
282C4×C61—21no—
283C4×C61—21no—
284C4×C61—21no—
285C4×C61—42no—
286C4×C61—42no—
287C4×C61#41312yes—
288Dic61—21no—
289Dic61—21no—
290Dic61—21no—
291Dic61—21no—
292Dic61—21no—
293Dic61—21no—
294Dic61—42no—
295Dic61#40812yes—
296Dic61#40812yes—
297C2×#529—611no—
298#2920—611no—
299C2×#431—611no—
300#1470—612no—
301#1469—612no—
302#1468—614no—
303#1458—614no—
304C2×C61—22no—
305C2×C61—22no—
306C2×C61—41no—
307C2×C61C2×#40811yescharacteristic
308C2×C61C2×#41011yescharacteristic
309C2×C61C2×#41311yescharacteristic
310D61—82no—
311#529—1221no—
312#529—1221no—
313#529—1221no—
314#529—1221no—
315#529—1221no—
316#529—1221no—
317#529—1221no—
318#529—1221no—
319C2×#126—612no—
320C2×#125—611no—
321C2×#124—611no—
322C2×#123—612no—
323C2×C22⋊Q8#692311yescharacteristic
324C2×#121—611no—
325C2×C4×Q8—611no—
326C2×C4×D4—611no—
327C2×C4×D4—612no—
328C2×#117—612no—
329C22×C42—611no—
330#432—612no—
331#432—1221no—
332#431—612no—
333#431—612no—
334#431—612no—
335#431—1221no—
336#431—1221no—
337#431—1221no—
338#423—1221no—
339C2×C4⋊C8—1221no—
340#407—612no—
341C2×C22⋊C8—612no—
342C4×M16—1221no—
343C2×C4×C8—1221no—
344#324—618no—
345#323—618no—
346C61#1737611yescharacteristic, complemented, Sylow
347C22×Q8C2×#692311yescharacteristic
348C22×D4—612no—
349C22×D4—611no—
350C23×C4—611no—
351C23×C4—611no—
352C23×C4—612no—
353C23×C4C2×#692311yescharacteristic
354C2×M16—1222no—
355C22×C8—1222no—
356#126—1222no—
357#126—1222no—
358#126—1222no—
359#126—1222no—
360#125—1221no—
361#125—1221no—
362#125—1221no—
363#125—1221no—
364#124—1221no—
365#124—1221no—
366#124—1221no—
367#124—1221no—
368#123—1222no—
369#123—1222no—
370#123—1222no—
371#123—1222no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376#121—1221no—
377#121—1221no—
378#121—1221no—
379#121—1221no—
380C4×Q8—1221no—
381C4×Q8—1221no—
382C4×Q8—1221no—
383C4×Q8—1221no—
384C4×D4—1221no—
385C4×D4—1221no—
386C4×D4—1221no—
387C4×D4—1221no—
388C4×D4—1222no—
389C4×D4—1222no—
390C4×D4—1222no—
391C4×D4—1222no—
392#117—1222no—
393#117—1222no—
394#117—1222no—
395#117—1222no—
396C2×C4⋊C4—612no—
397C2×C4⋊C4—612no—
398C2×C4⋊C4—611no—
399C2×C4⋊C4—612no—
400C2×C4⋊C4C2×#692312yes—
401C2×C4⋊C4C2×#692311yescharacteristic
402C2×C22⋊C4—612no—
403C2×C22⋊C4—612no—
404C2×C22⋊C4—612no—
405C2×C22⋊C4—612no—
406C2×C22⋊C4C2×#692312yes—
407C2×C42—611no—
408C2×C42—611no—
409C2×C42—611no—
410C2×C42—611no—
411C2×C42—611no—
412C2×C42—611no—
413C2×C42—611no—
414C2×C42—611no—
415C2×C42—611no—
416C2×C42—611no—
417C2×C42—611no—
418C2×C42—611no—
419C2×C42—612no—
420C4⋊C8—1222no—
421C4⋊C8—1222no—
422C4⋊C8—1222no—
423C4⋊C8—1222no—
424C22⋊C8—614no—
425C22⋊C8—614no—
426C22⋊C8—1222no—
427C22⋊C8—1222no—
428#97—1222no—
429C4×C8—1222no—
430C4×C8—1222no—
431C4×C8—1222no—
432C24—612no—
433C24C22×#692311yescharacteristic
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—42no—
437C2×D4—1222no—
438C2×D4—1222no—
439C2×D4—1221no—
440C2×D4—1221no—
441C2×D4—2442no—
442C2×D4—2444no—
443C22×C4—42no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—611no—
449C22×C4—611no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—612no—
457C22×C4—1222no—
458C22×C4—1222no—
459C22×C4—1228no—
460C22×C4—1224no—
461C22×C4—2442no—
462C22×C4C22⋊#692311yescharacteristic
463C22×C4C22⋊#692311yescharacteristic
464C22×C4C22⋊#692311yescharacteristic
465C22×C4C22⋊#692311yescharacteristic
466C22×C4C22×#692312yes—
467C22×C4C22×#692311yescharacteristic
468C22×C4C22×#692312yes—
469C22×C4C22×#692311yescharacteristic
470M16—2444no—
471C2×C8—1224no—
472C2×C8—1224no—
473C2×C8—2444no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—1222no—
479C4⋊C4—1222no—
480C4⋊C4—1222no—
481C4⋊C4—1222no—
482C4⋊C4—1222no—
483C4⋊C4—1222no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—1222no—
489C22⋊C4—1222no—
490C22⋊C4—1222no—
491C22⋊C4—1222no—
492C22⋊C4—1222no—
493C22⋊C4—1222no—
494C22⋊C4—1222no—
495C22⋊C4—1222no—
496C42—611no—
497C42—611no—
498C42—611no—
499C42—611no—
500C42—611no—
501C42—611no—
502C42—611no—
503C42—611no—
504C42—611no—
505C42—611no—
506C42—611no—
507C42—611no—
508C42—611no—
509C42—611no—
510C42—611no—
511C42—611no—
512C42—1222no—
513C42—1222no—
514C23—22no—
515C23—22no—
516C23—41no—
517C23—1224no—
518C23—1222no—
519C23—2442no—
520C23—2442no—
521C23C2×C22⋊#692311yescharacteristic
522C23C2×C22⋊#692311yescharacteristic
523C23C23×#692311yescharacteristic
524Q8—42no—
525Q8—42no—
526D4—2442no—
527D4—2444no—
528D4—2444no—
529D4—2442no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—24no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—611no—
541C2×C4—611no—
542C2×C4—614no—
543C2×C4—611no—
544C2×C4—611no—
545C2×C4—611no—
546C2×C4—611no—
547C2×C4—611no—
548C2×C4—611no—
549C2×C4—1222no—
550C2×C4—1222no—
551C2×C4—1222no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—1222no—
555C2×C4—1222no—
556C2×C4—1222no—
557C2×C4—2444no—
558C2×C4—2444no—
559C2×C4—2441no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2442no—
564C2×C4C2×C22⋊#692311yescharacteristic
565C2×C4C2×C22⋊#692311yescharacteristic
566C2×C4C2×C22⋊#692311yescharacteristic
567C2×C4C2×C22⋊#692311yescharacteristic
568C8—2444no—
569C8—2444no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—44no—
578C22—4884no—
579C22—2442no—
580C22—2442no—
581C22—2442no—
582C22#1684074312yes—
583C22C22×C22⋊#692311yescharacteristic
584C22D61⋊#13112yes—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—42no—
589C4—42no—
590C4—612no—
591C4—612no—
592C4—1221no—
593C4—1221no—
594C4—1221no—
595C4—1221no—
596C4—1221no—
597C4—1221no—
598C4—2442no—
599C4#1684074912yes—
600C2—22no—
601C2—22no—
602C2—41no—
603C2—4882no—
604C2D61⋊#40811yescharacteristic
605C2C2×#1684074311yescharacteristic
606C2C2×#1684074911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519751C4
cosocleC22×Dic61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61#17376
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #21462495C2semidirect
2. C2×#16840779C2semidirect
3. #21461092C2semidirect
4. #21461090C2semidirect
5. #21461086C2semidirect
6. #21461053C2semidirect
346. C61#17376semidirect

Maximal subgroups

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

subgroupindex
#214624952
C2×#168407792
#214610922
#214610902
#214610862
#214610532
C2×#168402982
#1737661