Finite Group Databasebeta

← #11860955

Subgroups — #11860955

Order 1152.

1049 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5504C211yesmaximal, characteristic, complemented
2#10594990C211yesmaximal, characteristic, complemented
3C2×#63829C211yesmaximal, characteristic
4#10592665C211yesmaximal, characteristic, complemented
5C2×C3×#808C211yesmaximal, characteristic, complemented
6#10591087C211yesmaximal, characteristic, complemented
7#10591055C211yesmaximal, characteristic, complemented
8#10590589C212yesmaximal, complemented
9#10590480C212yesmaximal, complemented
10#10590479C212yesmaximal, complemented
11#10590458C212yesmaximal, complemented
12#82558—31nomaximal
13#79106—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C3×C4×#67—22no—
19C3×#926C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#893C2212yes—
23C3×#892—21no—
24C3×D3×C4⋊C4—21no—
25C3×#887C2212yes—
26#63952—22no—
27#63900—21no—
28#63894C2212yes—
29#63849—21no—
30#63844C2212yes—
31C2×#3719C2211yescharacteristic
32C2×#3717C2211yescharacteristic
33#63829C418yescomplemented
34C2×#3716C2211yescharacteristic
35C2×#3714C2211yescharacteristic
36#63637C2212yes—
37#63636C2212yes—
38C3×#808C2212yes—
39C3×#808C2212yes—
40#63565C2212yes—
41#63562C2212yes—
42#63554C2212yes—
43Dic3×C3⋊C8C2212yes—
44C3×#520—31no—
45C2×#950—31no—
46C2×#904—31no—
47#5523—31no—
48#5504—31no—
49#5504D311yescharacteristic, complemented
50C2×C3×#106—31no—
51#5232—31no—
52#5101—31no—
53#5030—32no—
54C4×#215—32no—
55C4×#214—32no—
56#5014—32no—
57#4997—31no—
58#4966—31no—
59#4966—31no—
60#4966—31no—
61#4966—61no—
62C2×#808D311yescharacteristic, complemented
63#4869—32no—
64#4853—32no—
65#4852—32no—
66#4852—32no—
67C22×C32×C4—21no—
68C22×C32×C4C2311yescharacteristic
69C2×#638—21no—
70#3828—22no—
71#3828C2×C414yescomplemented
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×#634C2311yescharacteristic
75C2×C3×#67—21no—
76C22×C3×Dic3—21no—
77C3×#235—22no—
78C3×#235C2×C414yescomplemented
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×C4×D3—22no—
82C2×C3×Dic6C2311yescharacteristic
83C2×#624—22no—
84C32×C4⋊C4—21no—
85C32×C4⋊C4C2312yes—
86#3748—22no—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×#217D412yes—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4⋊Dic3D411yescharacteristic
93C3×C4⋊Dic3C2312yes—
94C3×Dic3⋊C4—22no—
95C3×C4×Dic3—22no—
96C3×C4×Dic3C2312yes—
97C2×C3×C3⋊C8C2×C414yescomplemented
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2311yescharacteristic
100#3724—22no—
101#3722—22no—
102Dic32—22no—
103#3719C2×C414yescomplemented
104#3717C2×C414yescomplemented
105#3716C2×C414yescomplemented
106#3714C2×C414yescomplemented
107#2952—91noSylow
108C2×C3×#41—31no—
109C2×#235—31no—
110C2×#235—31no—
111C2×#235—61no—
112C2×#235C2×D311yescharacteristic
113C22×C3×C8—31no—
114C3×C4×Q8—32no—
115C3×C4×D4—32no—
116C3×C4×D4—62no—
117C3×#117—31no—
118C3×#117—61no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—31no—
121C2×C3×C4⋊C4—61no—
122C2×C3×C4⋊C4C2×D311yescharacteristic
123C2×C3×C4⋊C4C2×D311yescharacteristic
124#950—38no—
125C2×#216—31no—
126C2×#215—31no—
127C2×#214—31no—
128C2×#213—31no—
129C4×#67—22no—
130C4×#67—62no—
131#926C2×D311yescharacteristic
132C2×C4⋊Dic3C2×D311yescharacteristic
133C2×#208—31no—
134C2×#208—31no—
135C2×#208—61no—
136C22×C3⋊C8C2×D311yescharacteristic
137C2×Dic12—31no—
138#904—38no—
139C2×D24—31no—
140C2×#204—31no—
141C2×#204—31no—
142#893—32no—
143#893C2×D312yes—
144#892—21no—
145#892—61no—
146#892—61no—
147D3×C4⋊C4—21no—
148D3×C4⋊C4—61no—
149D3×C4⋊C4—61no—
150#887—32no—
151#887C2×D312yes—
152#67⋊C4—62no—
153C4×D12—32no—
154C4×Dic6—32no—
155C3×#106—32no—
156C3×#106—32no—
157#835—32no—
158#832—32no—
159#815—32no—
160C8×Dic3—32no—
161#810—32no—
162#810—32no—
163#810—32no—
164#810—62no—
165#809—32no—
166#809—32no—
167#809—32no—
168#809—62no—
169#808C2×D312yes—
170#808C2×D312yes—
171#803—32no—
172C4×C3⋊C8—32no—
173C23×C32C2×D411yescharacteristic
174C22×C3⋊D3—21no—
175C22×C3×D3—21no—
176C2×C32×C4—22no—
177C2×C32×C4—81no—
178C2×C32×C4C22×C412yes—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4#4112yes—
181C2×C32×C4C2411yescharacteristic
182#638—24no—
183C2×C3⋊Dic3—21no—
184C4⋊(C3⋊D3)—21no—
185C4⋊(C3⋊D3)C22×C412yes—
186C4×C3⋊D3—24no—
187#634—21no—
188#634C22×C412yes—
189C3×#67—24no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—81no—
193C2×C3×Dic3C2×D412yes—
194C2×C3×Dic3C2×D412yes—
195C3×D12—21no—
196C3×D12C22×C412yes—
197C3×C4×D3—24no—
198C3×C4×D3—82no—
199C3×Dic6—21no—
200C3×Dic6C22×C412yes—
201#624—82no—
202C3⋊(C3⋊C8)—22no—
203C3×C3⋊C8C22×C412yes—
204C3×C3⋊C8C22×C412yes—
205C2×#135—91no—
206#520—31no—
207#520—91no—
208#442—92no—
209#441—92no—
210C4×SD16—92no—
211C4×SD16—92no—
212C2×#106—31no—
213#417—91no—
214#417—91no—
215#405—91no—
216C3×#41—34no—
217C3×#41—62no—
218C2×C3×Q8—31no—
219C2×C3×D4—31no—
220C2×C3×D4—61no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—41no—
225C22×C3×C4—62no—
226C22×C3×C4—61no—
227C22×C3×C4—61no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C2×#67—21no—
231C2×#67—61no—
232C2×#67—61no—
233C2×#67—121no—
234C22×Dic3—21no—
235#235—22no—
236#235—34no—
237#235—34no—
238#235—64no—
239#235—62no—
240#235—62no—
241#235—122no—
242#235C4×D314yescomplemented
243C2×D12—31no—
244C2×D12—31no—
245C2×D12—61no—
246C2×D12C22×D311yescharacteristic
247C2×C4×D3—21no—
248C2×C4×D3—22no—
249C2×C4×D3—61no—
250C2×C4×D3—61no—
251C2×C4×D3—62no—
252C2×C4×D3—62no—
253C2×C4×D3—121no—
254C2×Dic6—31no—
255C2×Dic6—31no—
256C2×Dic6—61no—
257C2×Dic6C22×D311yescharacteristic
258C2×C3×C8—34no—
259C2×C3×C8—31no—
260C2×C3×C8—31no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—22no—
264C3×C4⋊C4—31no—
265C3×C4⋊C4—31no—
266C3×C4⋊C4—32no—
267C3×C4⋊C4—41no—
268C3×C4⋊C4—62no—
269C3×C4⋊C4—61no—
270C3×C4⋊C4C22×D312yes—
271C3×C4⋊C4C22×D312yes—
272C3×C22⋊C4—32no—
273C3×C22⋊C4—62no—
274C3×C42—32no—
275C3×C42—62no—
276#217#6712yes—
277#216—34no—
278#215—34no—
279#214—34no—
280#213—34no—
281(C2×D3)⋊C4—22no—
282(C2×D3)⋊C4—62no—
283(C2×D3)⋊C4—62no—
284C4⋊Dic3—21no—
285C4⋊Dic3#6711yescharacteristic
286C4⋊Dic3#6711yescharacteristic
287C4⋊Dic3C22×D312yes—
288Dic3⋊C4—22no—
289Dic3⋊C4—62no—
290Dic3⋊C4—62no—
291C4×Dic3—22no—
292C4×Dic3—62no—
293C4×Dic3—62no—
294C4×Dic3C22×D312yes—
295#208—62no—
296#208—62no—
297#208—122no—
298C2×C3⋊C8—32no—
299C2×C3⋊C8—32no—
300C2×C3⋊C8—62no—
301C2×C3⋊C8C4×D314yescomplemented
302C2×C3⋊C8C22×D311yescharacteristic
303C2×C3⋊C8C22×D311yescharacteristic
304Dic12—34no—
305D24—34no—
306#204—34no—
307#204—34no—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32C4×D412yes—
311C22×C32C22×D411yescharacteristic
312C2×C3⋊D3—22no—
313C2×C3⋊D3—41no—
314C2×C3⋊D3—41no—
315C2×C3×D3—22no—
316C2×C3×D3—41no—
317C2×C3×D3—41no—
318C32×C4—42no—
319C32×C4C4×D412yes—
320C32×C4C23×C411yescharacteristic
321C32×C4C2×#4111yescharacteristic
322C3⋊Dic3—22no—
323C3×Dic3—22no—
324C3×Dic3—22no—
325C3×Dic3—22no—
326C3×Dic3—42no—
327C2×#41—31no—
328C2×#41—91no—
329#135—98no—
330C2×Q16—91no—
331C2×SD16—91no—
332C2×SD16—91no—
333C2×D8—91no—
334C2×M16—91no—
335C22×C8—31no—
336C4×Q8—32no—
337C4×Q8—92no—
338C4×D4—32no—
339C4×D4—62no—
340C4×D4—92no—
341C4×D4—182no—
342#117—31no—
343#117—61no—
344#117—181no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—61no—
347C2×C4⋊C4—181no—
348C2×C4⋊C4D3211yescharacteristic
349#106—32no—
350#106—32no—
351#103—92no—
352#103—92no—
353#102—92no—
354#102—92no—
355#97—92no—
356C4×C8—92no—
357C23×C3—21no—
358C23×C3—61no—
359C23×C3D3×D411yescharacteristic
360C23×C3C2×#6711yescharacteristic
361C22×D3—21no—
362C22×D3—61no—
363C22×D3—61no—
364C22×D3—121no—
365C3×Q8—32no—
366C3×Q8—61no—
367C3×D4—32no—
368C3×D4—64no—
369C3×D4—61no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—21no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—21no—
376C2×C3×C4—32no—
377C2×C3×C4—32no—
378C2×C3×C4—42no—
379C2×C3×C4—61no—
380C2×C3×C4—64no—
381C2×C3×C4—62no—
382C2×C3×C4—81no—
383C2×C3×C4—81no—
384C2×C3×C4—82no—
385C2×C3×C4—242no—
386C2×C3×C4—241no—
387C2×C3×C4C2×C4×D312yes—
388C2×C3×C4C2×C4×D312yes—
389C2×C3×C4#23512yes—
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4#23912yes—
392C2×C3×C4C2×#6711yescharacteristic
393C2×C3×C4C23×D311yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395#67—24no—
396#67—64no—
397#67—64no—
398#67—124no—
399C2×Dic3—21no—
400C2×Dic3—22no—
401C2×Dic3—61no—
402C2×Dic3—61no—
403C2×Dic3—81no—
404C2×Dic3—121no—
405C2×Dic3C2×#6712yes—
406C2×Dic3C2×#6712yes—
407D12—21no—
408D12—32no—
409D12—32no—
410D12—62no—
411D12—61no—
412D12—61no—
413D12—121no—
414D12C2×C4×D312yes—
415C4×D3—24no—
416C4×D3—64no—
417C4×D3—64no—
418C4×D3—82no—
419C4×D3—124no—
420C4×D3—242no—
421C4×D3—242no—
422Dic6—21no—
423Dic6—32no—
424Dic6—32no—
425Dic6—62no—
426Dic6—61no—
427Dic6—61no—
428Dic6—121no—
429Dic6C2×C4×D312yes—
430C3×C8—32no—
431C3×C8—32no—
432C3⋊C8—62no—
433C3⋊C8—62no—
434C3⋊C8—122no—
435C3⋊C8C2×C4×D312yes—
436C3⋊C8C2×C4×D312yes—
437C2×C32—22no—
438C2×C32C2×C4×D411yescharacteristic
439C2×C32#57711yescharacteristic
440C2×C32#57711yescharacteristic
441C3⋊D3—42no—
442C3×D3—42no—
443#41—34no—
444#41—62no—
445#41—94no—
446#41—182no—
447C2×Q8—31no—
448C2×Q8—91no—
449C2×D4—31no—
450C2×D4—61no—
451C2×D4—91no—
452C2×D4—181no—
453C22×C4—21no—
454C22×C4—62no—
455C22×C4—61no—
456C22×C4—61no—
457C22×C4—182no—
458C22×C4—181no—
459C22×C4C2×D3211yescharacteristic
460Q16—94no—
461SD16—94no—
462SD16—94no—
463D8—94no—
464M16—182no—
465C2×C8—31no—
466C2×C8—31no—
467C2×C8—34no—
468C2×C8—92no—
469C4⋊C4—21no—
470C4⋊C4—31no—
471C4⋊C4—31no—
472C4⋊C4—32no—
473C4⋊C4—62no—
474C4⋊C4—61no—
475C4⋊C4—182no—
476C4⋊C4C2×D3212yes—
477C22⋊C4—32no—
478C22⋊C4—62no—
479C22⋊C4—182no—
480C42—32no—
481C42—62no—
482C42—182no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—22no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3—62no—
492C22×C3—121no—
493C22×C3—121no—
494C22×C3#89312yes—
495C22×C3C4×#6712yes—
496C22×C3C2×D3×D411yescharacteristic
497C22×C3C22×#6711yescharacteristic
498C2×D3—22no—
499C2×D3—41no—
500C2×D3—41no—
501C2×D3—62no—
502C2×D3—62no—
503C2×D3—122no—
504C2×D3—121no—
505C2×D3—121no—
506C2×D3—121no—
507C2×D3—121no—
508C2×D3—241no—
509C2×D3—241no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—22no—
513C3×C4—42no—
514C3×C4—42no—
515C3×C4—62no—
516C3×C4—62no—
517C3×C4—62no—
518C3×C4—82no—
519C3×C4—122no—
520C3×C4#89312yes—
521C3×C4C4×#6712yes—
522C3×C4C22×C4×D311yescharacteristic
523C3×C4C22×C4×D311yescharacteristic
524C3×C4C2×#23511yescharacteristic
525C3×C4C2×#23911yescharacteristic
526Dic3—22no—
527Dic3—22no—
528Dic3—22no—
529Dic3—42no—
530Dic3—62no—
531Dic3—62no—
532Dic3—122no—
533C32#295211yescharacteristic, complemented, Sylow
534C23—61no—
535C23—181no—
536C23D3×#6711yescharacteristic
537Q8—32no—
538Q8—61no—
539Q8—92no—
540Q8—181no—
541D4—32no—
542D4—64no—
543D4—61no—
544D4—92no—
545D4—184no—
546D4—181no—
547C2×C4—22no—
548C2×C4—32no—
549C2×C4—32no—
550C2×C4—61no—
551C2×C4—64no—
552C2×C4—62no—
553C2×C4—81no—
554C2×C4—181no—
555C2×C4—184no—
556C2×C4—242no—
557C2×C4—241no—
558C2×C4—722no—
559C2×C4#379912yes—
560C2×C4C4×D3212yes—
561C2×C4D3×#6711yescharacteristic
562C2×C4C22×D3211yescharacteristic
563C8—32no—
564C8—32no—
565C8—182no—
566C2×C3—22no—
567C2×C3—22no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—42no—
572C2×C3—122no—
573C2×C3C2×#89311yescharacteristic
574C2×C3#576211yescharacteristic
575C2×C3#576211yescharacteristic
576C2×C3C2×C4×#6711yescharacteristic
577C2×C3#583611yescharacteristic
578C2×C3#583711yescharacteristic
579D3—42no—
580D3—122no—
581D3—122no—
582D3—242no—
583C22—21no—
584C22—21no—
585C22—62no—
586C22—121no—
587C22—121no—
588C22—182no—
589C22—361no—
590C22—361no—
591C22#6390412yes—
592C22C2×D3×#6711yescharacteristic
593C4—42no—
594C4—62no—
595C4—62no—
596C4—62no—
597C4—122no—
598C4—182no—
599C4#6390412yes—
600C4C2×#379911yescharacteristic
601C4C2×C4×D3211yescharacteristic
602C3—21no—
603C3#7910611yescharacteristic, complemented
604C3#8255811yescharacteristic, complemented
605C2—22no—
606C2—122no—
607C2—362no—
608C2C2×#6390411yescharacteristic
609C2#1059510511yescharacteristic
610C2#1059531811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC2×#63829C2
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5504C2semidirect
2. #10594990C2semidirect
4. #10592665C2semidirect
5. C2×C3×#808C2semidirect
6. #10591087C2semidirect
7. #10591055C2semidirect
8. #10590589C2semidirect
9. #10590480C2semidirect
10. #10590479C2semidirect
11. #10590458C2semidirect
33. #63829C4semidirect
49. #5504D3semidirect
62. C2×#808D3semidirect
71. #3828C2×C4semidirect
78. C3×#235C2×C4semidirect
97. C2×C3×C3⋊C8C2×C4semidirect
103. #3719C2×C4semidirect
104. #3717C2×C4semidirect
105. #3716C2×C4semidirect
106. #3714C2×C4semidirect
242. #235C4×D3semidirect
301. C2×C3⋊C8C4×D3semidirect
533. C32#2952semidirect
603. C3#79106semidirect
604. C3#82558semidirect

Maximal subgroups

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

subgroupindex
C3×#55042
#105949902
C2×#638292
#105926652
C2×C3×#8082
#105910872
#105910552
#105905892
#105904802
#105904792
#105904582
#825583
#791063