Finite Group Databasebeta

← #14484694

Subgroups — #14484694

Order 1920.

2136 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
1C4×#6821C211yesmaximal, characteristic
2C5×#5569C211yesmaximal, characteristic, complemented
3C3×#65903C211yesmaximal, characteristic, complemented
4Q8×#1204C211yesmaximal, characteristic, complemented
5#11755200C211yesmaximal, characteristic
6#11755200C211yesmaximal, characteristic
7#11755147C211yesmaximal, characteristic, complemented
8#11753625C213yesmaximal, complemented
9#11753583C213yesmaximal, complemented
10#11753522C213yesmaximal, complemented
11#11753434C213yesmaximal, complemented
12#11752616C213yesmaximal, complemented
13#11752591C213yesmaximal, complemented
14C4×D15⋊Q8C213yesmaximal, complemented
15#11752471C213yesmaximal, complemented
16#10618916—31nomaximal, Hall
17C2×#6821C2211yescharacteristic
18C2×D15⋊Q8C2213yes—
19C3×C4×C5×Q8C2211yescharacteristic
20Q8×Dic15C2211yescharacteristic
21#91782C2213yes—
22#91781C2213yes—
23C4×D60C2213yes—
24C42×D15C2213yes—
25C5×Q8×Dic3C2211yescharacteristic
26C5×Q8×Dic3C2211yescharacteristic
27C5×#890C2213yes—
28C5×#888C2213yes—
29C5×#870C2213yes—
30C4×C5×Dic6C2213yes—
31C3×Q8×Dic5C2211yescharacteristic
32C3×Q8×Dic5C2211yescharacteristic
33C3×#4036C2213yes—
34C3×#4034C2213yes—
35C3×#4016C2213yes—
36C3×C4×Dic10C2213yes—
37#91470C2213yes—
38#91470C2213yes—
39#91469C2213yes—
40#91468C2213yes—
41C4×#1204C2213yes—
42C4×#1204C2213yes—
43#91437C2213yes—
44#91429C2216yes—
45#91428C2213yes—
46#91428C2213yes—
47#91424C2216yes—
48#91419C2216yes—
49#91418C2213yes—
50#91418C2213yes—
51#91411C2216yes—
52#91404C2213yes—
53#91404C2213yes—
54C4×#1200C2213yes—
55C4×#1200C2213yes—
56#91388C2213yes—
57#91381C2213yes—
58#91377C2216yes—
59#91377C2216yes—
60#91347C2213yes—
61#91347C2213yes—
62#91344C2213yes—
63#91331C2213yes—
64#91325C2213yes—
65#91325C2216yes—
66#91325C2211yescharacteristic
67#87015—51nomaximal, Hall
68C5×#557—31no—
69#66062—33no—
70#66061—33no—
71#66024—33no—
72#66024—33no—
73#66022—33no—
74#66022—33no—
75#65913—33no—
76C4×#713—31no—
77C4×#713—31no—
78C4×#713—31no—
79C4×Q8×D5—33no—
80#65903—31no—
81#65903D311yescharacteristic, complemented
82Q8×Dic10—31no—
83C2×C3×C5×Q8C2311yescharacteristic
84#6821Q818yescomplemented
85C2×D60C2313yes—
86C2×C4×D15C2313yes—
87C2×C4×D15C2313yes—
88C2×C4×D15C2313yes—
89C2×C5×Dic6C2313yes—
90C2×C3×Dic10C2313yes—
91C2×#1204C2313yes—
92C2×#1204C2316yes—
93C2×#1204C2311yescharacteristic
94C2×#1200C2313yes—
95C2×#1200C2313yes—
96C2×#1200C2313yes—
97C2×#1200C2313yes—
98D15⋊Q8—212no—
99C3×C5×C4⋊C4C2313yes—
100C3×C42×C5C2313yes—
101#6714C2316yes—
102C4⋊Dic15C2313yes—
103C4×Dic15C2313yes—
104C4×Dic15C2311yescharacteristic
105C4×Dic15C2313yes—
106C5×C4⋊Dic3C2313yes—
107C5×C4⋊Dic3C2313yes—
108C5×C4⋊Dic3C2313yes—
109C5×Dic3⋊C4C2311yescharacteristic
110C5×Dic3⋊C4C2313yes—
111C5×Dic3⋊C4C2316yes—
112C4×C5×Dic3C2313yes—
113C4×C5×Dic3C2313yes—
114C3×C4⋊Dic5C2313yes—
115C3×C4⋊Dic5C2313yes—
116C3×C4⋊Dic5C2313yes—
117C3×#683C2311yescharacteristic
118C3×#683C2313yes—
119C3×#683C2316yes—
120C3×C4×Dic5C2313yes—
121C3×C4×Dic5C2313yes—
122Dic3⋊Dic5C2313yes—
123Dic3⋊Dic5C2313yes—
124#6669C2316yes—
125#6669C2311yescharacteristic
126#6669C2313yes—
127#6668C2313yes—
128#6668C2313yes—
129#6667C2316yes—
130#6667C2316yes—
131Dic3×Dic5C2311yescharacteristic
132Dic3×Dic5C2311yescharacteristic
133Dic3×Dic5C2313yes—
134Dic3×Dic5C2313yes—
135C3×#557—51no—
136#5728—53no—
137#5727—53no—
138#5690—53no—
139#5690—53no—
140#5688—53no—
141#5688—53no—
142#5579—53no—
143C4×#239—51no—
144C4×#239—51no—
145C4×#239—51no—
146C4×D3×Q8—53no—
147#5569—51no—
148#5569D511yescharacteristic, complemented
149Q8×Dic6—51no—
150C2×#713—31no—
151C2×Q8×D5—33no—
152C5×C4⋊Q8—33no—
153C5×#125—33no—
154C5×#125—33no—
155C4×C5×Q8—31no—
156C4×C5×Q8—31no—
157C4×C5×Q8—33no—
158C4×C5×Q8C2×D311yescharacteristic
159#4092—36no—
160Q8×Dic5—31no—
161Q8×Dic5—33no—
162Q8×Dic5C2×D311yescharacteristic
163Q8×Dic5C2×D311yescharacteristic
164#4043—36no—
165#4042—36no—
166#4042—36no—
167#4042—36no—
168#4042—36no—
169#4039—33no—
170#4039—33no—
171#4039—33no—
172#4038—33no—
173#4038—33no—
174#4038—33no—
175D5×C4⋊C4—33no—
176D5×C4⋊C4—33no—
177D5×C4⋊C4—33no—
178#4036—33no—
179#4036C2×D313yes—
180#4034—33no—
181#4034—33no—
182#4034—33no—
183#4034C2×D313yes—
184#4033—33no—
185#4033—36no—
186#4033—31no—
187#4033—33no—
188C4×D20—33no—
189C4×D20—33no—
190C4×D20—33no—
191C42×D5—33no—
192C42×D5—33no—
193C42×D5—33no—
194#4016—33no—
195#4016C2×D313yes—
196#4015—33no—
197C4×Dic10—33no—
198C4×Dic10—33no—
199C4×Dic10C2×D313yes—
200Q8×#41—151noSylow
201C22×D15C2413yes—
202C3×C5×Q8C2×Q814yescomplemented
203C2×C3×C4×C5C2411yescharacteristic
204C2×C3×C4×C5C2413yes—
205C2×C3×C4×C5C2413yes—
206C2×Dic15C2413yes—
207C2×Dic15C2411yescharacteristic
208C2×Dic15C2411yescharacteristic
209D60C2×Q8112yescomplemented
210C4×D15—26no—
211C4×D15—43no—
212C4×D15C2×Q8112yescomplemented
213C2×C5×Dic3C2413yes—
214C2×C5×Dic3C2413yes—
215C2×C5×Dic3C2411yescharacteristic
216C2×C5×Dic3C2411yescharacteristic
217C5×Dic6—26no—
218C2×C3×Dic5C2413yes—
219C2×C3×Dic5C2413yes—
220C2×C3×Dic5C2411yescharacteristic
221C2×C3×Dic5C2411yescharacteristic
222C3×Dic10—26no—
223#1204—26no—
224#1204—46no—
225#1204#4114yescomplemented
226#1200—26no—
227#1200—26no—
228#1200—43no—
229#1200—43no—
230C2×#239—51no—
231C2×D3×Q8—53no—
232C3×C4⋊Q8—53no—
233C3×#125—53no—
234C3×#125—53no—
235C3×C4×Q8—51no—
236C3×C4×Q8—51no—
237C3×C4×Q8—53no—
238C3×C4×Q8C2×D511yescharacteristic
239#946—56no—
240Q8×Dic3—51no—
241Q8×Dic3—53no—
242Q8×Dic3C2×D511yescharacteristic
243Q8×Dic3C2×D511yescharacteristic
244#897—56no—
245#896—56no—
246#896—56no—
247#896—56no—
248#896—56no—
249#893—53no—
250#893—53no—
251#893—53no—
252#892—53no—
253#892—53no—
254#892—53no—
255D3×C4⋊C4—53no—
256D3×C4⋊C4—53no—
257D3×C4⋊C4—53no—
258#890—53no—
259#890C2×D513yes—
260#888—53no—
261#888—53no—
262#888—53no—
263#888C2×D513yes—
264#887—53no—
265#887—56no—
266#887—53no—
267#887—51no—
268C4×D12—53no—
269C4×D12—53no—
270C4×D12—53no—
271C42×D3—53no—
272C42×D3—53no—
273C42×D3—53no—
274#870—53no—
275#870C2×D513yes—
276#869—53no—
277C4×Dic6—53no—
278C4×Dic6—53no—
279C4×Dic6C2×D513yes—
280C2×C5×Q8—33no—
281C2×C5×Q8C22×D311yescharacteristic
282#713—38no—
283Q8×D5—612no—
284C2×D20—33no—
285C2×C4×D5—33no—
286C2×C4×D5—33no—
287C2×C4×D5—33no—
288C2×C4×D5—33no—
289C2×C4×D5—33no—
290C2×C4×D5—33no—
291C2×C4×D5—33no—
292C2×Dic10—31no—
293C2×Dic10—33no—
294C2×Dic10—36no—
295C2×Dic10C22×D313yes—
296C5×C4⋊C4—31no—
297C5×C4⋊C4—33no—
298C5×C4⋊C4—33no—
299C5×C4⋊C4—33no—
300C5×C4⋊C4—33no—
301C5×C4⋊C4—36no—
302C5×C4⋊C4C22×D313yes—
303C42×C5—33no—
304C42×C5—33no—
305C42×C5C22×D313yes—
306#685—36no—
307#685—36no—
308#685—36no—
309C4⋊Dic5—33no—
310C4⋊Dic5—33no—
311C4⋊Dic5—33no—
312C4⋊Dic5C22×D313yes—
313C4⋊Dic5C22×D313yes—
314C4⋊Dic5C22×D313yes—
315#683—33no—
316#683—33no—
317#683—31no—
318#683—33no—
319#683—36no—
320#683C22×D311yescharacteristic
321#683C22×D313yes—
322#683C22×D316yes—
323C4×Dic5—33no—
324C4×Dic5—31no—
325C4×Dic5—33no—
326C4×Dic5—31no—
327C4×Dic5—31no—
328C4×Dic5—33no—
329C4×Dic5—33no—
330C4×Dic5C22×D313yes—
331C4×Dic5C22×D313yes—
332Q82—151no—
333#557—31no—
334#557—51no—
335#557—151no—
336#554—153no—
337#554—153no—
338#554—153no—
339D4×Q8—153no—
340#533—153no—
341#533—153no—
342#533—153no—
343C4×#41—151no—
344C4×#41—151no—
345C4×#41—151no—
346C2×C4×Q8—153no—
347C22×C3×C5C2511yescharacteristic
348C2×D15—23no—
349C2×D15—23no—
350C2×D15C22×Q816yes—
351C3×C4×C5—23no—
352C3×C4×C5—21no—
353C3×C4×C5C22×Q816yes—
354Dic15—23no—
355Dic15C22×Q812yes—
356Dic15C2×#4112yes—
357C3×Dic5—23no—
358C3×Dic5—21no—
359C3×Dic5—23no—
360C3×Dic5C2×#4112yes—
361C5×Dic3—23no—
362C5×Dic3—21no—
363C5×Dic3—23no—
364C5×Dic3C2×#4112yes—
365C2×C3×Q8—53no—
366C2×C3×Q8C22×D511yescharacteristic
367#239—58no—
368D3×Q8—1012no—
369C2×D12—53no—
370C2×C4×D3—53no—
371C2×C4×D3—53no—
372C2×C4×D3—53no—
373C2×C4×D3—53no—
374C2×C4×D3—53no—
375C2×C4×D3—53no—
376C2×C4×D3—53no—
377C2×Dic6—51no—
378C2×Dic6—53no—
379C2×Dic6—56no—
380C2×Dic6C22×D513yes—
381C3×C4⋊C4—51no—
382C3×C4⋊C4—53no—
383C3×C4⋊C4—56no—
384C3×C4⋊C4—53no—
385C3×C4⋊C4—53no—
386C3×C4⋊C4—53no—
387C3×C4⋊C4C22×D513yes—
388C3×C42—53no—
389C3×C42—53no—
390C3×C42C22×D513yes—
391(C2×D3)⋊C4—56no—
392(C2×D3)⋊C4—56no—
393(C2×D3)⋊C4—56no—
394C4⋊Dic3—53no—
395C4⋊Dic3—53no—
396C4⋊Dic3—53no—
397C4⋊Dic3C22×D513yes—
398C4⋊Dic3C22×D513yes—
399C4⋊Dic3C22×D513yes—
400Dic3⋊C4—51no—
401Dic3⋊C4—53no—
402Dic3⋊C4—56no—
403Dic3⋊C4—53no—
404Dic3⋊C4—53no—
405Dic3⋊C4C22×D511yescharacteristic
406Dic3⋊C4C22×D513yes—
407Dic3⋊C4C22×D516yes—
408C4×Dic3—53no—
409C4×Dic3—51no—
410C4×Dic3—53no—
411C4×Dic3—51no—
412C4×Dic3—51no—
413C4×Dic3—53no—
414C4×Dic3—53no—
415C4×Dic3C22×D513yes—
416C4×Dic3C22×D513yes—
417C22×D5—33no—
418C5×Q8—66no—
419C5×Q8D3×Q814yescomplemented
420C2×C4×C5—31no—
421C2×C4×C5—31no—
422C2×C4×C5—33no—
423C2×C4×C5—33no—
424C2×C4×C5C23×D311yescharacteristic
425C2×C4×C5C23×D313yes—
426C2×C4×C5C23×D313yes—
427C2×Dic5—31no—
428C2×Dic5—31no—
429C2×Dic5—33no—
430C2×Dic5C23×D311yescharacteristic
431C2×Dic5C23×D313yes—
432C2×Dic5C23×D313yes—
433C2×Dic5C23×D311yescharacteristic
434D20—312no—
435C4×D5—312no—
436C4×D5—66no—
437C4×D5—66no—
438C4×D5—66no—
439C4×D5—123no—
440C4×D5—123no—
441C4×D5—123no—
442Dic10—26no—
443Dic10—34no—
444Dic10—66no—
445Dic10—126no—
446C2×#41—151no—
447C22×Q8—153no—
448C4⋊Q8—33no—
449C4⋊Q8—53no—
450C4⋊Q8—153no—
451C4⋊Q8—153no—
452C4⋊Q8—153no—
453C4⋊Q8—153no—
454#125—33no—
455#125—33no—
456#125—53no—
457#125—53no—
458#125—153no—
459#125—153no—
460C22⋊Q8—156no—
461C22⋊Q8—156no—
462C22⋊Q8—156no—
463C22⋊Q8—156no—
464C22⋊Q8—156no—
465C22⋊Q8—156no—
466C4×Q8—31no—
467C4×Q8—31no—
468C4×Q8—33no—
469C4×Q8—51no—
470C4×Q8—51no—
471C4×Q8—53no—
472C4×Q8—153no—
473C4×Q8—153no—
474C4×Q8—151no—
475C4×Q8—153no—
476C4×Q8—156no—
477C4×Q8—153no—
478C4×Q8—153no—
479C4×Q8—151no—
480C4×Q8D3×D511yescharacteristic
481C4×D4—153no—
482C4×D4—153no—
483C4×D4—153no—
484C4×D4—153no—
485C4×D4—153no—
486C4×D4—153no—
487#117—153no—
488#117—153no—
489#117—153no—
490C2×C4⋊C4—153no—
491C2×C4⋊C4—153no—
492C2×C4⋊C4—153no—
493C2×C42—153no—
494C2×C42—153no—
495C2×C42—153no—
496C2×C3×C5C23×Q811yescharacteristic
497C2×C3×C5C22×#4111yescharacteristic
498C2×C3×C5#58511yescharacteristic
499D15—26no—
500C22×D3—53no—
501C3×Q8—106no—
502C3×Q8Q8×D514yescomplemented
503C2×C3×C4—51no—
504C2×C3×C4—51no—
505C2×C3×C4—53no—
506C2×C3×C4—53no—
507C2×C3×C4C23×D511yescharacteristic
508C2×C3×C4C23×D513yes—
509C2×C3×C4C23×D513yes—
510C2×Dic3—51no—
511C2×Dic3—51no—
512C2×Dic3—53no—
513C2×Dic3C23×D511yescharacteristic
514C2×Dic3C23×D513yes—
515C2×Dic3C23×D513yes—
516C2×Dic3C23×D511yescharacteristic
517D12—512no—
518C4×D3—512no—
519C4×D3—106no—
520C4×D3—106no—
521C4×D3—106no—
522C4×D3—203no—
523C4×D3—203no—
524C4×D3—203no—
525Dic6—26no—
526Dic6—54no—
527Dic6—106no—
528Dic6—206no—
529C22×C5C24×D311yescharacteristic
530C2×D5—36no—
531C2×D5—63no—
532C2×D5—63no—
533C4×C5—23no—
534C4×C5—21no—
535C4×C5—32no—
536C4×C5—63no—
537C4×C5—63no—
538C4×C5—61no—
539C4×C5C2×D3×Q816yes—
540Dic5—23no—
541Dic5—23no—
542Dic5—21no—
543Dic5—32no—
544Dic5—32no—
545Dic5—63no—
546Dic5D3×#4112yes—
547#41—158no—
548C2×Q8—33no—
549C2×Q8—53no—
550C2×Q8—151no—
551C2×Q8—153no—
552C2×Q8—156no—
553C2×Q8—3012no—
554C2×Q8C2×D3×D511yescharacteristic
555C2×D4—153no—
556C22×C4—153no—
557C22×C4—153no—
558C22×C4—153no—
559C22×C4—153no—
560C22×C4—153no—
561C22×C4—153no—
562C22×C4—153no—
563C4⋊C4—31no—
564C4⋊C4—33no—
565C4⋊C4—33no—
566C4⋊C4—33no—
567C4⋊C4—33no—
568C4⋊C4—36no—
569C4⋊C4—51no—
570C4⋊C4—53no—
571C4⋊C4—53no—
572C4⋊C4—53no—
573C4⋊C4—53no—
574C4⋊C4—56no—
575C4⋊C4—151no—
576C4⋊C4—153no—
577C4⋊C4—153no—
578C4⋊C4—153no—
579C4⋊C4—153no—
580C4⋊C4—153no—
581C4⋊C4—156no—
582C4⋊C4—153no—
583C4⋊C4C2×D3×D513yes—
584C22⋊C4—156no—
585C22⋊C4—156no—
586C22⋊C4—156no—
587C42—33no—
588C42—33no—
589C42—53no—
590C42—53no—
591C42—151no—
592C42—151no—
593C42—153no—
594C42—153no—
595C42—151no—
596C42—153no—
597C42—153no—
598C42C2×D3×D513yes—
599C3×C5Q8×#4111yescharacteristic, complemented, Hall
600C22×C3C24×D511yescharacteristic
601C2×D3—56no—
602C2×D3—103no—
603C2×D3—103no—
604C3×C4—23no—
605C3×C4—21no—
606C3×C4—52no—
607C3×C4—103no—
608C3×C4—103no—
609C3×C4—101no—
610C3×C4C2×Q8×D516yes—
611Dic3—23no—
612Dic3—23no—
613Dic3—21no—
614Dic3—52no—
615Dic3—52no—
616Dic3—103no—
617Dic3D5×#4112yes—
618C2×C5C22×D3×Q811yescharacteristic
619C2×C5C2×D3×#4111yescharacteristic
620C2×C5#596811yescharacteristic
621D5—66no—
622C23—153no—
623Q8—66no—
624Q8—106no—
625Q8—154no—
626Q8—306no—
627Q8—606no—
628Q8D15⋊Q814yescomplemented
629D4—1512no—
630C2×C4—31no—
631C2×C4—31no—
632C2×C4—33no—
633C2×C4—33no—
634C2×C4—51no—
635C2×C4—51no—
636C2×C4—53no—
637C2×C4—53no—
638C2×C4—151no—
639C2×C4—151no—
640C2×C4—1512no—
641C2×C4—153no—
642C2×C4—306no—
643C2×C4—306no—
644C2×C4—306no—
645C2×C4—603no—
646C2×C4—603no—
647C2×C4—603no—
648C2×C4C22×D3×D511yescharacteristic
649C2×C4C22×D3×D513yes—
650C2×C4C22×D3×D513yes—
651C2×C3C22×Q8×D511yescharacteristic
652C2×C3C2×D5×#4111yescharacteristic
653C2×C3#6628711yescharacteristic
654D3—106no—
655C5#8701511yescharacteristic, complemented, Sylow
656C22—156no—
657C22—303no—
658C22—303no—
659C22C23×D3×D511yescharacteristic
660C4—21no—
661C4—23no—
662C4—32no—
663C4—52no—
664C4—61no—
665C4—63no—
666C4—63no—
667C4—101no—
668C4—103no—
669C4—103no—
670C4—152no—
671C4—152no—
672C4—303no—
673C4C2×D15⋊Q816yes—
674C3#1061891611yescharacteristic, complemented, Sylow
675C2—306no—
676C2C22×D15⋊Q811yescharacteristic
677C2#1175705011yescharacteristic
678C2D3×D5×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C4×C5×Q8C22
prime radicalC2×#6821C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5Q8×#41
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C5×#5569C2semidirect
3. C3×#65903C2semidirect
4. Q8×#1204C2semidirect
7. #11755147C2semidirect
8. #11753625C2semidirect
9. #11753583C2semidirect
10. #11753522C2semidirect
11. #11753434C2semidirect
12. #11752616C2semidirect
13. #11752591C2semidirect
14. C4×D15⋊Q8C2semidirect
15. #11752471C2semidirect
81. #65903D3semidirect
84. #6821Q8semidirect
148. #5569D5semidirect
202. C3×C5×Q8C2×Q8semidirect
209. D60C2×Q8semidirect
212. C4×D15C2×Q8semidirect
225. #1204#41semidirect
419. C5×Q8D3×Q8semidirect
502. C3×Q8Q8×D5semidirect
599. C3×C5Q8×#41semidirect
628. Q8D15⋊Q8semidirect
655. C5#87015semidirect
674. C3#10618916semidirect

Maximal subgroups

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

subgroupindex
C4×#68212
C5×#55692
C3×#659032
Q8×#12042
#117552002
#117551472
#117536252
#117535832
#117535222
#117534342
#117526162
#117525912
C4×D15⋊Q82
#117524712
#106189163
#870155