Finite Group Databasebeta

← #11870827

Subgroups — #11870827

Order 1152.

823 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594387C211yesmaximal, characteristic
2D3×#887C211yesmaximal, characteristic
3#10592572C211yesmaximal, characteristic, complemented
4C3×#4884C211yesmaximal, characteristic
5C3×#4875C211yesmaximal, characteristic, complemented
6#10590952C211yesmaximal, characteristic
7#10590808C211yesmaximal, characteristic, complemented
8#10590790C211yesmaximal, characteristic, complemented
9#10590656C211yesmaximal, characteristic
10#10590604C211yesmaximal, characteristic
11#10590561C211yesmaximal, characteristic, complemented
12#10590488C211yesmaximal, characteristic, complemented
13#10590482C211yesmaximal, characteristic, complemented
14#10590482C211yesmaximal, characteristic, complemented
15#10590427C211yesmaximal, characteristic
16#81452—31nomaximal
17#81092—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19C2×#3746C2211yescharacteristic
20#64096C2211yescharacteristic
21#64096C2211yescharacteristic
22C3×#897C2211yescharacteristic
23C3×D3×C4⋊C4C2211yescharacteristic
24C3×#888C2211yescharacteristic
25C3×#887C2211yescharacteristic
26#63887—21no—
27#63878—21no—
28D3×Dic3⋊C4—21no—
29C4×D3×Dic3—21no—
30C4×D3×Dic3C2211yescharacteristic
31#63866C2211yescharacteristic
32#63857C2211yescharacteristic
33#63846—21no—
34#63844C2211yescharacteristic
35#63843—21no—
36#63843C2211yescharacteristic
37#63843C2211yescharacteristic
38#63838—21no—
39#63837—21no—
40C2×#3719C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43C32×#107C2211yescharacteristic
44C8×C3⋊Dic3C2211yescharacteristic
45#63637C2211yescharacteristic
46#63637C2211yescharacteristic
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#807C2211yescharacteristic
54C3×#807C2211yescharacteristic
55#63576C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic
61#5728—31no—
62#5622—31no—
63C4×D3×Q8—31no—
64C2×#887—31no—
65C3×#484—31no—
66C3×#477—31no—
67#5091—31no—
68#5050—31no—
69#5031—31no—
70#4970—31no—
71#4884—31no—
72#4884D311yescharacteristic
73#4875—31no—
74#4875D311yescharacteristic, complemented
75#4873—31no—
76#4873—31no—
77#4873—31no—
78#4873—31no—
79#4873—61no—
80#4849—31no—
81#4833—31no—
82#4809—31no—
83#4809—31no—
84#4795—31no—
85#4795—31no—
86#4790—31no—
87#4790—31no—
88#4790—31no—
89#4790—31no—
90#4739—31no—
91#4718—31no—
92C2×#634C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×C3×C4×D3—21no—
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×Dic6—21no—
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×D3×Dic3—21no—
101C2×D3×Dic3D411yescharacteristic
102C2×D3×Dic3D411yescharacteristic
103D3×Dic6—22no—
104D3×Dic6—22no—
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108#3750—21no—
109#3750—21no—
110C4×C3⋊Dic3—21no—
111C4×C3⋊Dic3—21no—
112C4×C3⋊Dic3C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114#3746—22no—
115C3×(C2×D3)⋊C4—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×C4×Dic3—21no—
123C3×C4×Dic3C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126#3724—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133Dic32—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32D411yescharacteristic
137Dic32D411yescharacteristic
138#3719—22no—
139#3719—22no—
140#3718—22no—
141#3104—91noSylow
142C2×D3×Q8—31no—
143C22×Dic6—31no—
144C3×C4⋊Q8—31no—
145C3×C22⋊Q8—31no—
146C3×C4×Q8—31no—
147C2×C3×C4⋊C4—31no—
148#946—61no—
149Q8×Dic3—31no—
150Q8×Dic3—31no—
151Q8×Dic3—61no—
152#944—31no—
153C2×#216—31no—
154C2×#216—31no—
155C2×#216—31no—
156C2×#216—31no—
157#924—31no—
158C2×Dic3⋊C4—61no—
159C2×C4×Dic3—31no—
160C2×C4×Dic3—61no—
161C2×Dic12—31no—
162C2×Dic12—31no—
163C2×Dic12—31no—
164C2×Dic12—31no—
165C2×Dic12—61no—
166#897—31no—
167#897C2×D311yescharacteristic
168#892—61no—
169D3×C4⋊C4—61no—
170D3×C4⋊C4C2×D311yescharacteristic
171#890—61no—
172#889—61no—
173#888C2×D311yescharacteristic
174#887—31no—
175#887—31no—
176#887—31no—
177#887—31no—
178#887—31no—
179#887—31no—
180#887—31no—
181#887—61no—
182#887—61no—
183#887—61no—
184#887—61no—
185#887—61no—
186#887—61no—
187#887C2×D311yescharacteristic
188#878—61no—
189#877—61no—
190C42×D3—31no—
191C42×D3—61no—
192#869—31no—
193C4×Dic6—31no—
194C4×Dic6—61no—
195C3×#107—21no—
196C3×#107—31no—
197C3×#107—31no—
198C3×#107C2×D311yescharacteristic
199C3×#107C2×D311yescharacteristic
200C3×C4⋊C8—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×C22⋊C8—31no—
206#830—31no—
207(C2×D3)⋊C8—31no—
208(C2×D3)⋊C8C2×D311yescharacteristic
209#816—31no—
210#816—31no—
211#816C2×D311yescharacteristic
212#816C2×D311yescharacteristic
213Dic3⋊C8—31no—
214Dic3⋊C8C2×D311yescharacteristic
215C8×Dic3—31no—
216C8×Dic3—31no—
217C8×Dic3—31no—
218C8×Dic3—31no—
219C8×Dic3—61no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—61no—
227#810—61no—
228#810C2×D311yescharacteristic
229#810C2×D311yescharacteristic
230#807—31no—
231#807—31no—
232#807C2×D311yescharacteristic
233#807C2×D311yescharacteristic
234C4⋊(C3⋊C8)—31no—
235C22×C3×D3C2×D411yescharacteristic
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4C2411yescharacteristic
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3C2×D411yescharacteristic
242C2×C3⋊Dic3C2×D411yescharacteristic
243#634—21no—
244#634—21no—
245#634—21no—
246#634#4112yes—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×C4×D3—21no—
255C3×C4×D3—21no—
256C3×C4×D3—42no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6—42no—
261C3×Dic6#4112yes—
262#627—24no—
263D3×Dic3—24no—
264D3×Dic3—41no—
265D3×Dic3Q1614yescomplemented
266C32×C8—21no—
267C3⋊(C3⋊C8)—21no—
268C3×C3⋊C8—21no—
269C3×C3⋊C8—21no—
270#533—91no—
271C2×C4×Q8—91no—
272#484—31no—
273#484—91no—
274#477—31no—
275#477—91no—
276#462—91no—
277#462—91no—
278#451—91no—
279#451—91no—
280C4×Q16—91no—
281C4×Q16—91no—
282C4×Q16—91no—
283C4×Q16—91no—
284#431—91no—
285C2×C3×Q8—31no—
286C2×C3×Q8—31no—
287C2×C3×Q8—61no—
288C22×C3×C4—31no—
289C22×C3×C4—61no—
290C22×Dic3—31no—
291C22×Dic3—31no—
292C22×Dic3—61no—
293D3×Q8—62no—
294D3×Q8—62no—
295C2×C4×D3—21no—
296C2×C4×D3—31no—
297C2×C4×D3—31no—
298C2×C4×D3—61no—
299C2×C4×D3C22×D311yescharacteristic
300C2×Dic6—21no—
301C2×Dic6—31no—
302C2×Dic6—31no—
303C2×Dic6—31no—
304C2×Dic6—31no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—62no—
308C2×Dic6—61no—
309C2×Dic6—61no—
310C2×Dic6—62no—
311C2×Dic6C22×D311yescharacteristic
312C2×Dic6C22×D311yescharacteristic
313C2×C3×C8—21no—
314C2×C3×C8—31no—
315C2×C3×C8—31no—
316C2×C3×C8C22×D311yescharacteristic
317C2×C3×C8C22×D311yescharacteristic
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4—61no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4—61no—
326C3×C4⋊C4C22×D311yescharacteristic
327C3×C4⋊C4C22×D311yescharacteristic
328C3×C4⋊C4C22×D311yescharacteristic
329C3×C4⋊C4C22×D311yescharacteristic
330C3×C22⋊C4—61no—
331C3×C42—31no—
332C3×C42—61no—
333#217—61no—
334#216—62no—
335#216—62no—
336#216—62no—
337#216—62no—
338(C2×D3)⋊C4—21no—
339(C2×D3)⋊C4—61no—
340C4⋊Dic3—21no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3C22×D311yescharacteristic
347C4⋊Dic3C22×D311yescharacteristic
348Dic3⋊C4—21no—
349Dic3⋊C4—21no—
350Dic3⋊C4—21no—
351Dic3⋊C4—61no—
352Dic3⋊C4—61no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—121no—
363Dic3⋊C4—121no—
364C4×Dic3—21no—
365C4×Dic3—31no—
366C4×Dic3—31no—
367C4×Dic3—31no—
368C4×Dic3—31no—
369C4×Dic3—31no—
370C4×Dic3—31no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—121no—
383C4×Dic3—121no—
384C4×Dic3C22×D311yescharacteristic
385C2×C3⋊C8—31no—
386C2×C3⋊C8—31no—
387C2×C3⋊C8—61no—
388C2×C3⋊C8C22×D311yescharacteristic
389C2×C3⋊C8C22×D311yescharacteristic
390Dic12—62no—
391Dic12—62no—
392Dic12—64no—
393Dic12—62no—
394Dic12—62no—
395C22×C32C22×D411yescharacteristic
396C2×C3×D3—21no—
397C2×C3×D3—21no—
398C2×C3×D3C2×Q1612yes—
399C32×C4—41no—
400C32×C4—41no—
401C32×C4C2×#4111yescharacteristic
402C32×C4C2×#4111yescharacteristic
403C3⋊Dic3—22no—
404C3⋊Dic3—21no—
405C3⋊Dic3—41no—
406C3⋊Dic3C2×Q1612yes—
407C3×Dic3—22no—
408C3×Dic3—21no—
409C3×Dic3—21no—
410C3×Dic3—41no—
411C3×Dic3—41no—
412C3×Dic3—41no—
413C3×Dic3C2×Q1612yes—
414C22×Q8—91no—
415C2×Q16—91no—
416C2×Q16—91no—
417C2×Q16—91no—
418C2×Q16—91no—
419C4⋊Q8—31no—
420C4⋊Q8—91no—
421#125—181no—
422C22⋊Q8—31no—
423C22⋊Q8—91no—
424C22⋊Q8—181no—
425C4×Q8—31no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×Q8—91no—
429C4×Q8—91no—
430C4×Q8—91no—
431C4×Q8—181no—
432C4×Q8—181no—
433C4×Q8—181no—
434#117—181no—
435C2×C4⋊C4—31no—
436C2×C4⋊C4—181no—
437C2×C42—91no—
438C2×C42—181no—
439#107—31no—
440#107—31no—
441#107—91no—
442#107D3211yescharacteristic
443C4⋊C8—31no—
444C4⋊C8—91no—
445#103—31no—
446#103—31no—
447#103—31no—
448#103—31no—
449#103—91no—
450#103—91no—
451#103—91no—
452#103—91no—
453C22⋊C8—31no—
454C22⋊C8—91no—
455C4×C8—91no—
456C4×C8—91no—
457C23×C3—31no—
458C22×D3D3×D411yescharacteristic
459C3×Q8—32no—
460C3×Q8—61no—
461C3×Q8—61no—
462C3×Q8—61no—
463C3×Q8—122no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—31no—
470C2×C3×C4—31no—
471C2×C3×C4—31no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—122no—
481C2×C3×C4C23×D311yescharacteristic
482C2×C3×C4C23×D311yescharacteristic
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—31no—
488C2×Dic3—31no—
489C2×Dic3—34no—
490C2×Dic3—31no—
491C2×Dic3—31no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—64no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—121no—
500C2×Dic3—121no—
501C2×Dic3—121no—
502C2×Dic3D3×D411yescharacteristic
503C2×Dic3D3×D411yescharacteristic
504C2×Dic3D3×D411yescharacteristic
505C4×D3—21no—
506C4×D3—21no—
507C4×D3—34no—
508C4×D3—42no—
509C4×D3—64no—
510C4×D3—121no—
511Dic6—21no—
512Dic6—21no—
513Dic6—21no—
514Dic6—32no—
515Dic6—32no—
516Dic6—42no—
517Dic6—62no—
518Dic6—64no—
519Dic6—64no—
520Dic6—61no—
521Dic6—61no—
522Dic6—62no—
523Dic6—61no—
524Dic6—61no—
525Dic6—61no—
526Dic6—61no—
527Dic6—121no—
528Dic6—121no—
529Dic6#23912yes—
530C3×C8—22no—
531C3×C8—21no—
532C3×C8—21no—
533C3×C8—61no—
534C3×C8—61no—
535C3⋊C8—21no—
536C3⋊C8—21no—
537C3⋊C8—61no—
538C3⋊C8—61no—
539C3⋊C8—121no—
540C2×C32#52511yescharacteristic
541C2×C32C22×Q1611yescharacteristic
542C2×C32#57511yescharacteristic
543C3×D3—22no—
544C2×Q8—31no—
545C2×Q8—31no—
546C2×Q8—61no—
547C2×Q8—91no—
548C2×Q8—91no—
549C2×Q8—181no—
550C2×Q8—182no—
551C2×Q8—182no—
552C22×C4—31no—
553C22×C4—61no—
554C22×C4—91no—
555C22×C4—91no—
556C22×C4—181no—
557Q16—182no—
558Q16—182no—
559Q16—182no—
560Q16—182no—
561C2×C8—31no—
562C2×C8—31no—
563C2×C8—91no—
564C2×C8C2×D3211yescharacteristic
565C4⋊C4—31no—
566C4⋊C4—31no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—181no—
572C4⋊C4—181no—
573C4⋊C4—181no—
574C4⋊C4—181no—
575C4⋊C4—181no—
576C4⋊C4—181no—
577C4⋊C4—181no—
578C4⋊C4—181no—
579C4⋊C4C2×D3211yescharacteristic
580C4⋊C4C2×D3211yescharacteristic
581C22⋊C4—61no—
582C22⋊C4—181no—
583C42—31no—
584C42—61no—
585C42—91no—
586C42—91no—
587C42—91no—
588C42—181no—
589C42—181no—
590C42—181no—
591C42—181no—
592C42—181no—
593C22×C3—21no—
594C22×C3—32no—
595C22×C3—61no—
596C22×C3—61no—
597C22×C3C2×D3×D411yescharacteristic
598C22×C3C2×D3×D411yescharacteristic
599C2×D3—21no—
600C2×D3—21no—
601C2×D3D3×Q1612yes—
602C3×C4—21no—
603C3×C4—21no—
604C3×C4—32no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—41no—
609C3×C4—62no—
610C3×C4—61no—
611C3×C4—61no—
612C3×C4—81no—
613C3×C4—81no—
614C3×C4—121no—
615C3×C4—121no—
616C3×C4—121no—
617C3×C4C2×#23911yescharacteristic
618C3×C4D3×#4111yescharacteristic
619C3×C4D3×#4111yescharacteristic
620C3×C4D3×#4111yescharacteristic
621Dic3—21no—
622Dic3—21no—
623Dic3—22no—
624Dic3—32no—
625Dic3—32no—
626Dic3—41no—
627Dic3—41no—
628Dic3—41no—
629Dic3—62no—
630Dic3—62no—
631Dic3—61no—
632Dic3—61no—
633Dic3—62no—
634Dic3—122no—
635Dic3—121no—
636Dic3—122no—
637Dic3—121no—
638Dic3—121no—
639Dic3D3×Q1612yes—
640C32#310411yescharacteristic, complemented, Sylow
641C23—31no—
642Q8—32no—
643Q8—61no—
644Q8—61no—
645Q8—61no—
646Q8—92no—
647Q8—122no—
648Q8—184no—
649Q8—181no—
650Q8—181no—
651Q8—181no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—31no—
655C2×C4—31no—
656C2×C4—31no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—94no—
664C2×C4—91no—
665C2×C4—91no—
666C2×C4—122no—
667C2×C4—184no—
668C2×C4—181no—
669C2×C4—181no—
670C2×C4—361no—
671C2×C4C22×D3211yescharacteristic
672C8—21no—
673C8—61no—
674C8—61no—
675C8—181no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—62no—
680C2×C3#562711yescharacteristic
681C2×C3#565611yescharacteristic
682C2×C3C2×D3×Q1611yescharacteristic
683C2×C3C2×D3×Q1611yescharacteristic
684C2×C3#577311yescharacteristic
685C2×C3#577311yescharacteristic
686D3—22no—
687C22—32no—
688C22—61no—
689C22—61no—
690C22D32×D411yescharacteristic
691C4—32no—
692C4—41no—
693C4—41no—
694C4—61no—
695C4—62no—
696C4—61no—
697C4—92no—
698C4—121no—
699C4—121no—
700C4—121no—
701C4—182no—
702C4—181no—
703C4—361no—
704C4#6430611yescharacteristic
705C4D3×#23911yescharacteristic
706C3—21no—
707C3#8109211yescharacteristic, complemented
708C3#8145211yescharacteristic, complemented
709C2—62no—
710C2#1059461511yescharacteristic
711C2#1059472811yescharacteristic
712C2D32×Q1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#107D32
hypocenterC32#3104
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
3. #10592572C2semidirect
5. C3×#4875C2semidirect
7. #10590808C2semidirect
8. #10590790C2semidirect
11. #10590561C2semidirect
12. #10590488C2semidirect
13. #10590482C2semidirect
14. #10590482C2semidirect
74. #4875D3semidirect
265. D3×Dic3Q16semidirect
640. C32#3104semidirect
707. C3#81092semidirect
708. C3#81452semidirect

Maximal subgroups

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

subgroupindex
#105943872
D3×#8872
#105925722
C3×#48842
C3×#48752
#105909522
#105908082
#105907902
#105906562
#105906042
#105905612
#105904882
#105904822
#105904272
#814523
#810923