Finite Group Databasebeta

← #29689459

Subgroups — #29689459

Order 15616.

1050 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840314C211yesmaximal, characteristic
2#21448214C211yesmaximal, characteristic
3#21448213C211yesmaximal, characteristic
4#21446805C211yesmaximal, characteristic
5#21446804C211yesmaximal, characteristic
6#21446803C211yesmaximal, characteristic
7#21446802C214yesmaximal
8#21445895C214yesmaximal
9C61×#1996C211yesmaximal, characteristic
10#16840314—21no—
11#16840314—21no—
12#16840314—21no—
13#16840314—21no—
14#16840314—21no—
15#16840314—21no—
16#16840314—21no—
17#16840314—21no—
18C2×#14519776C411yescharacteristic, complemented
19C2×#14519775C411yescharacteristic, complemented
20C2×#14519767C412yescomplemented
21C2×#14519756C2211yescharacteristic
22C2×#14519754C2212yes—
23C2×Q8×Dic61C411yescharacteristic, complemented
24C2×#14519742C412yescomplemented
25C2×#14519742C411yescharacteristic, complemented
26C2×#14519733C2212yes—
27C22×C4×Dic61C2211yescharacteristic
28#16839629—21no—
29#16839629—21no—
30#16839627—21no—
31#16839626—21no—
32#16839623C2212yes—
33#16839623C2212yes—
34#16839622C2211yescharacteristic
35#16839620C2212yes—
36C4⋊C4×Dic61—21no—
37C4×#11758196—21no—
38C22⋊C4×Dic61C2212yes—
39C4×C22⋊Dic61C2211yescharacteristic
40#16839608—21no—
41#16839607—21no—
42#16839529C2214yes—
43#16839528C2214yes—
44#16839528C2214yes—
45C2×C22⋊Q8×C61C2211yescharacteristic
46C61×#380C2211yescharacteristic
47C4×C22⋊C4×C61C2211yescharacteristic
48C61×#342C2214yes—
49C22×Dic122C2×C412yes—
50C22×Dic122C2×C411yescharacteristic
51C23×Dic61C2311yescharacteristic
52C23×Dic61C2311yescharacteristic
53#14519776—21no—
54#14519776—21no—
55#14519776—21no—
56#14519776—21no—
57#14519775—21no—
58#14519775—21no—
59#14519775—21no—
60#14519775—21no—
61#14519767—22no—
62#14519767—22no—
63#14519767—22no—
64#14519767—22no—
65#14519756—21no—
66#14519756—21no—
67#14519756—21no—
68#14519756—21no—
69#14519754—22no—
70#14519754—22no—
71#14519754—22no—
72#14519754—22no—
73Q8×Dic61—21no—
74Q8×Dic61—21no—
75Q8×Dic61—21no—
76Q8×Dic61—21no—
77#14519742—21no—
78#14519742—21no—
79#14519742—21no—
80#14519742—21no—
81#14519742—22no—
82#14519742—22no—
83#14519742—22no—
84#14519742—22no—
85#14519733—22no—
86#14519733—22no—
87#14519733—22no—
88#14519733—22no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61C2×C412yes—
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×#11758196—22no—
93C2×#11758196C2×C412yes—
94C2×#11758196C2×C412yes—
95C2×#11758196C2×C412yes—
96C2×#11758196C2×C412yes—
97C2×#11758196C2×C412yes—
98C2×C22⋊Dic61C2312yes—
99C2×C22⋊Dic61C2312yes—
100C2×C22⋊Dic61C2312yes—
101C2×C4×Dic61—21no—
102C2×C4×Dic61—22no—
103C2×C4×Dic61C2×C412yes—
104C2×C4×Dic61C2×C412yes—
105C2×C4×Dic61C2×C411yescharacteristic
106C2×C4×Dic61C2×C411yescharacteristic
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
117#14519684—21no—
118#14519684—21no—
119#14519684—22no—
120#14519684—22no—
121#14519684—22no—
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125C22×Q8×C61C2×C411yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C22⋊Q8×C61—21no—
128C22⋊Q8×C61—21no—
129C22⋊Q8×C61—21no—
130C22⋊Q8×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61C2×C412yes—
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61C2312yes—
135C2×C22⋊C4×C61C2312yes—
136C2×C22⋊C4×C61C2312yes—
137C2×C42×C61—21no—
138#95×C61—21no—
139#95×C61—21no—
140C24×C61C2411yescharacteristic
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—42no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—42no—
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C412yes—
149C22×C4×C61C22×C412yes—
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—42no—
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C412yes—
164C22×Dic61C22×C412yes—
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C2×D411yescharacteristic
167C22×Dic61C2×D411yescharacteristic
168C22×Dic61C2×D411yescharacteristic
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171C22×Dic61C2×D411yescharacteristic
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C2×Dic122—21no—
175C2×Dic122—21no—
176C2×Dic122—22no—
177C2×Dic122—22no—
178C2×Dic122—44no—
179C2×Dic122—42no—
180C4⋊C4×C61—22no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—42no—
185C22⋊C4×C61—22no—
186C22⋊C4×C61—22no—
187C22⋊C4×C61—22no—
188C22⋊C4×C61—24no—
189C22⋊C4×C61—22no—
190C42×C61—42no—
191C22⋊Dic61—22no—
192C22⋊Dic61—22no—
193C22⋊Dic61—22no—
194C22⋊Dic61—22no—
195C22⋊Dic61—24no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—22no—
199C4⋊Dic61—22no—
200C4⋊Dic61—42no—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206#11758196—22no—
207#11758196—22no—
208#11758196—22no—
209#11758196—22no—
210#11758196—22no—
211#11758196—44no—
212C4×Dic61—22no—
213C4×Dic61—22no—
214C4×Dic61—22no—
215C4×Dic61—22no—
216C4×Dic61—44no—
217C4×Dic61—42no—
218C4×Dic61C22⋊C411yescharacteristic
219C4×Dic61C22⋊C411yescharacteristic
220C4×Dic61C22⋊C411yescharacteristic
221C4×Dic61C22⋊C411yescharacteristic
222C4×Dic61C22⋊C411yescharacteristic
223C4×Dic61C22⋊C411yescharacteristic
224C4×Dic61C22⋊C411yescharacteristic
225C4×Dic61C22⋊C411yescharacteristic
226C4×Dic61C22⋊C411yescharacteristic
227C4×Dic61C22⋊C411yescharacteristic
228C4×Dic61C22⋊C411yescharacteristic
229C4×Dic61C22⋊C411yescharacteristic
230C4×Dic61C22⋊C411yescharacteristic
231C4×Dic61C22⋊C411yescharacteristic
232C4×Dic61C22⋊C411yescharacteristic
233C4×Dic61C22⋊C411yescharacteristic
234C23×C61—41no—
235C23×C61—41no—
236C23×C61C23×C411yescharacteristic
237C23×C61C22×D411yescharacteristic
238C23×C61C22×D411yescharacteristic
239C23×C612−1+412yes—
240C23×C612−1+412yes—
241Q8×C61—42no—
242Q8×C61—42no—
243C2×C4×C61—22no—
244C2×C4×C61—22no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—22no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—42no—
252C2×C4×C61—42no—
253C2×C4×C61—42no—
254C2×C4×C61—42no—
255C2×C4×C61—42no—
256C2×C4×C61—42no—
257C2×C4×C61—42no—
258C2×C4×C61—42no—
259C2×C4×C61C2×C22⋊C411yescharacteristic
260C2×C4×C61C2×C22⋊C411yescharacteristic
261C2×C4×C61C2×C22⋊C411yescharacteristic
262C2×C4×C61C2×C22⋊C411yescharacteristic
263C2×Dic61—22no—
264C2×Dic61—22no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—22no—
268C2×Dic61—22no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—22no—
272C2×Dic61—22no—
273C2×Dic61—22no—
274C2×Dic61—22no—
275C2×Dic61—22no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—42no—
280C2×Dic61—42no—
281C2×Dic61—42no—
282C2×Dic61—42no—
283C2×Dic61—42no—
284C2×Dic61—42no—
285C2×Dic61—42no—
286C2×Dic61—42no—
287C2×Dic61C2×C22⋊C411yescharacteristic
288C2×Dic61C2×C22⋊C411yescharacteristic
289C2×Dic61C2×C22⋊C411yescharacteristic
290C2×Dic61C2×C22⋊C411yescharacteristic
291C2×Dic61C2×C22⋊C411yescharacteristic
292C2×Dic61C2×C22⋊C411yescharacteristic
293C2×Dic61C2×C22⋊C411yescharacteristic
294C2×Dic61C2×C22⋊C411yescharacteristic
295Dic122—44no—
296Dic122—42no—
297Dic122—42no—
298Dic122—44no—
299#21826—611nomaximal, Sylow
300C22×C61—21no—
301C22×C61—21no—
302C22×C61—21no—
303C22×C61—21no—
304C22×C61—21no—
305C22×C61—21no—
306C22×C61—42no—
307C22×C61—42no—
308C22×C61C22×C22⋊C411yescharacteristic
309C22×C61#51912yes—
310C22×C61#53611yescharacteristic
311C22×C61#53612yes—
312C22×C61#53611yescharacteristic
313C4×C61—21no—
314C4×C61—21no—
315C4×C61—21no—
316C4×C61—42no—
317C4×C61—42no—
318C4×C61—82no—
319C4×C61—82no—
320C4×C61#41012yes—
321Dic61—21no—
322Dic61—21no—
323Dic61—21no—
324Dic61—21no—
325Dic61—21no—
326Dic61—21no—
327Dic61—21no—
328Dic61—42no—
329Dic61—42no—
330Dic61—82no—
331Dic61—82no—
332Dic61#41012yes—
333C2×#533—611no—
334#2283—611no—
335#2283—611no—
336#1996—611no—
337#1996—611no—
338#1996—614no—
339#1996—611no—
340#1996D6111yescharacteristic
341#1820—614no—
342C2×C61—21no—
343C2×C61—22no—
344C2×C61—21no—
345C2×C61—22no—
346C2×C61#231011yescharacteristic
347C2×C61C2×#41011yescharacteristic
348C2×C61C2×#41011yescharacteristic
349#533—1221no—
350#533—1221no—
351#533—1221no—
352#533—1221no—
353#533—1221no—
354#533—1221no—
355#533—1221no—
356#533—1221no—
357C2×C4⋊Q8—611no—
358C2×C4⋊Q8—611no—
359C2×#125—612no—
360C2×C22⋊Q8—611no—
361C2×C22⋊Q8—612no—
362C2×C22⋊Q8C2×D6111yescharacteristic
363C2×C4×Q8—611no—
364C2×C4×Q8—611no—
365C2×C4×Q8—612no—
366C2×#117—612no—
367C22×C42—611no—
368#383—1221no—
369#383—1221no—
370#382—1221no—
371#382—1221no—
372#381—612no—
373#381—612no—
374#380—611no—
375#380—612no—
376#380C2×D6111yescharacteristic
377C4×C4⋊C4—1221no—
378C4×C4⋊C4—1221no—
379C4×C22⋊C4—611no—
380C4×C22⋊C4—612no—
381C4×C22⋊C4C2×D6111yescharacteristic
382#376—1221no—
383#376—1221no—
384#342—614no—
385#342—614no—
386#342—614no—
387#342C2×D6114yes—
388C61#2182611yescharacteristic, complemented, Sylow
389C22×Q8—612no—
390C22×Q8—611no—
391C22×Q8C4×D6111yescharacteristic
392C23×C4—611no—
393C23×C4—611no—
394C23×C4C22×D6111yescharacteristic
395C4⋊Q8—1221no—
396C4⋊Q8—1221no—
397C4⋊Q8—1221no—
398C4⋊Q8—1221no—
399C4⋊Q8—1221no—
400C4⋊Q8—1221no—
401C4⋊Q8—1221no—
402C4⋊Q8—1221no—
403#125—1222no—
404#125—1222no—
405#125—1222no—
406#125—1222no—
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C22⋊Q8—21no—
410C22⋊Q8—21no—
411C22⋊Q8—1222no—
412C22⋊Q8—1222no—
413C22⋊Q8—1222no—
414C22⋊Q8—1222no—
415C22⋊Q8—1221no—
416C22⋊Q8—1221no—
417C22⋊Q8—1221no—
418C22⋊Q8—1221no—
419C4×Q8—1222no—
420C4×Q8—1222no—
421C4×Q8—1222no—
422C4×Q8—1222no—
423C4×Q8—1221no—
424C4×Q8—1221no—
425C4×Q8—1221no—
426C4×Q8—1221no—
427C4×Q8—1221no—
428C4×Q8—1221no—
429C4×Q8—1221no—
430C4×Q8—1221no—
431#117—1222no—
432#117—1222no—
433#117—1222no—
434#117—1222no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—612no—
437C2×C4⋊C4—612no—
438C2×C4⋊C4—612no—
439C2×C4⋊C4—612no—
440C2×C4⋊C4—612no—
441C2×C4⋊C4—612no—
442C2×C4⋊C4—611no—
443C2×C4⋊C4—1222no—
444C2×C4⋊C4—1221no—
445C2×C4⋊C4C4×D6112yes—
446C2×C4⋊C4C4×D6111yescharacteristic
447C2×C22⋊C4—612no—
448C2×C22⋊C4—612no—
449C2×C22⋊C4—612no—
450C2×C22⋊C4C22×D6112yes—
451C2×C22⋊C4C22×D6112yes—
452C2×C22⋊C4C22×D6112yes—
453C2×C42—21no—
454C2×C42—611no—
455C2×C42—611no—
456C2×C42—611no—
457C2×C42—611no—
458C2×C42—611no—
459C2×C42—611no—
460C2×C42—611no—
461C2×C42—611no—
462C2×C42—611no—
463C2×C42—611no—
464C2×C42—611no—
465C2×C42—611no—
466C2×C42—612no—
467C2×C42—612no—
468C2×C42—1222no—
469C2×C42—1221no—
470#95—21no—
471#95—21no—
472#95—1222no—
473#95—1222no—
474#95—1222no—
475#95—1222no—
476#95—1222no—
477#95—1222no—
478#95—1221no—
479#95—1221no—
480C24C23×D6111yescharacteristic
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—42no—
484C2×Q8—1222no—
485C2×Q8—1222no—
486C2×Q8—1221no—
487C2×Q8—1221no—
488C2×Q8—2442no—
489C2×Q8—2444no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—42no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—611no—
496C22×C4—611no—
497C22×C4—611no—
498C22×C4—611no—
499C22×C4—611no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—611no—
504C22×C4—611no—
505C22×C4—612no—
506C22×C4—612no—
507C22×C4—1222no—
508C22×C4—1222no—
509C22×C4—1222no—
510C22×C4—1222no—
511C22×C4—2442no—
512C22×C4C2×C4×D6111yescharacteristic
513C22×C4C2×C4×D6112yes—
514C22×C4C2×C4×D6112yes—
515C22×C4C2×C4×D6111yescharacteristic
516C22×C4D4×D6111yescharacteristic
517C22×C4D4×D6111yescharacteristic
518C22×C4D4×D6111yescharacteristic
519C22×C4D4×D6111yescharacteristic
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—42no—
525C4⋊C4—1222no—
526C4⋊C4—1222no—
527C4⋊C4—1222no—
528C4⋊C4—1222no—
529C4⋊C4—1222no—
530C4⋊C4—1222no—
531C4⋊C4—1222no—
532C4⋊C4—1222no—
533C4⋊C4—1222no—
534C4⋊C4—1222no—
535C4⋊C4—1222no—
536C4⋊C4—1222no—
537C4⋊C4—1221no—
538C4⋊C4—1221no—
539C4⋊C4—2442no—
540C4⋊C4—2444no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—24no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—1222no—
547C22⋊C4—1222no—
548C22⋊C4—1222no—
549C22⋊C4—1222no—
550C22⋊C4—1224no—
551C42—42no—
552C42—611no—
553C42—611no—
554C42—611no—
555C42—611no—
556C42—611no—
557C42—611no—
558C42—611no—
559C42—611no—
560C42—611no—
561C42—611no—
562C42—611no—
563C42—611no—
564C42—611no—
565C42—611no—
566C42—611no—
567C42—611no—
568C42—1222no—
569C42—1222no—
570C42—1222no—
571C42—1222no—
572C42—2442no—
573C42—2444no—
574C23—41no—
575C23—41no—
576C23C22×C4×D6111yescharacteristic
577C23C2×D4×D6111yescharacteristic
578C23C2×D4×D6111yescharacteristic
579C23#1451982412yes—
580C23#1451982512yes—
581Q8—42no—
582Q8—42no—
583Q8—2442no—
584Q8—2444no—
585Q8—2444no—
586Q8—2442no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—611no—
604C2×C4—611no—
605C2×C4—611no—
606C2×C4—611no—
607C2×C4—611no—
608C2×C4—611no—
609C2×C4—611no—
610C2×C4—611no—
611C2×C4—1222no—
612C2×C4—1222no—
613C2×C4—1222no—
614C2×C4—1222no—
615C2×C4—1222no—
616C2×C4—1221no—
617C2×C4—1221no—
618C2×C4—1222no—
619C2×C4—1222no—
620C2×C4—1221no—
621C2×C4—1221no—
622C2×C4—1222no—
623C2×C4—1222no—
624C2×C4—2441no—
625C2×C4—2441no—
626C2×C4—2441no—
627C2×C4—2442no—
628C2×C4—2442no—
629C2×C4—2442no—
630C2×C4—2442no—
631C2×C4—2442no—
632C2×C4—2442no—
633C2×C4—2442no—
634C2×C4—2442no—
635C2×C4C22⋊C4×D6111yescharacteristic
636C2×C4C22⋊C4×D6111yescharacteristic
637C2×C4C22⋊C4×D6111yescharacteristic
638C2×C4C22⋊C4×D6111yescharacteristic
639C22—21no—
640C22—21no—
641C22—21no—
642C22—21no—
643C22—21no—
644C22—21no—
645C22—42no—
646C22—42no—
647C22C2×C22⋊C4×D6111yescharacteristic
648C22#1684023812yes—
649C22#1684033211yescharacteristic
650C22#1684033512yes—
651C22#1684033711yescharacteristic
652C4—21no—
653C4—21no—
654C4—21no—
655C4—42no—
656C4—42no—
657C4—82no—
658C4—82no—
659C4—612no—
660C4—1221no—
661C4—1221no—
662C4—1221no—
663C4—1221no—
664C4—1221no—
665C4—1221no—
666C4—1221no—
667C4—4882no—
668C4—4882no—
669C4—2442no—
670C4—2442no—
671C4#1683973412yes—
672C2—21no—
673C2—22no—
674C2—21no—
675C2—22no—
676C2#2144840211yescharacteristic
677C2#410×D6111yescharacteristic
678C2C2×#1683973411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1996C2
socleC22×C61C22×C22⋊C4
prime radical, cosocleC24×C61C24
hypercenter#1996D61
hypocenterC61#21826
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
18. C2×#14519776C4semidirect
19. C2×#14519775C4semidirect
20. C2×#14519767C4semidirect
23. C2×Q8×Dic61C4semidirect
24. C2×#14519742C4semidirect
25. C2×#14519742C4semidirect
388. C61#21826semidirect

Maximal subgroups

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

subgroupindex
C2×#168403142
#214482142
#214482132
#214468052
#214468042
#214468032
#214468022
#214458952
C61×#19962
#2182661