Finite Group Databasebeta

← #11860894

Subgroups — #11860894

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
1#10594992C211yesmaximal, characteristic, complemented
2#10594990C211yesmaximal, characteristic, complemented
3C2×#63829C211yesmaximal, characteristic
4#10592832C211yesmaximal, characteristic, complemented
5C3×#5133C211yesmaximal, characteristic, complemented
6C3×#5122C211yesmaximal, characteristic, complemented
7C2×#63575C211yesmaximal, characteristic, complemented
8#10590795C212yesmaximal, complemented
9#10590793C212yesmaximal, complemented
10#10590747C212yesmaximal, complemented
11#10590745C212yesmaximal, complemented
12#78868—31nomaximal
13#78562—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C32×M16C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21#67⋊Dic3—22no—
22#63952—22no—
23#63900—21no—
24#63894C2212yes—
25Dic3×D12C2212yes—
26D3×C4⋊Dic3—21no—
27#63849—21no—
28#63844C2212yes—
29Dic3×Dic6C2212yes—
30#63841—21no—
31C2×#3719C2211yescharacteristic
32C2×#3717C2211yescharacteristic
33#63829C418yescomplemented
34C2×#3716C2211yescharacteristic
35C2×#3714C2211yescharacteristic
36#63648C2212yes—
37#63643C2212yes—
38C3×#821C2212yes—
39C3×#816C2212yes—
40C3×#815C2212yes—
41C3×C8×Dic3C2212yes—
42#63575C2212yes—
43#63575C2212yes—
44#5827—31no—
45C2×#950—31no—
46C2×#904—31no—
47#5523—31no—
48#5523—31no—
49#5504—31no—
50C3×#417—31no—
51C3×#405—31no—
52#5133—31no—
53#5133—31no—
54#5133—61no—
55#5133D311yescharacteristic, complemented
56#5122D311yescharacteristic, complemented
57C2×#818—31no—
58C2×#807—31no—
59#4817—32no—
60#4790—32no—
61#4757—32no—
62#4756—32no—
63#4710—32no—
64#4710—32no—
65C4×Dic12—32no—
66C4×D24—32no—
67C22×C32×C4C2311yescharacteristic
68C2×#638—21no—
69C22×C3⋊Dic3—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×Dic6C2311yescharacteristic
82C2×#624—22no—
83C2×D3×Dic3—22no—
84C32×M16—22no—
85C2×C32×C8C2312yes—
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)C2312yes—
88C3×#217D412yes—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3D411yescharacteristic
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4⋊Dic3C2312yes—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2×C414yescomplemented
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97#3724—22no—
98Dic3⋊Dic3—22no—
99#3722—22no—
100(C2×D3)⋊Dic3—22no—
101Dic32—22no—
102Dic32—22no—
103#3719C2×C414yescomplemented
104#3717C2×C414yescomplemented
105#3716C2×C414yescomplemented
106#3714C2×C414yescomplemented
107#2951—91noSylow
108C2×C3×#41—31no—
109C2×#235—31no—
110C2×#235—31no—
111C2×#235—61no—
112C2×#235C2×D311yescharacteristic
113C2×C3×M16—21no—
114C2×C3×M16C2×D311yescharacteristic
115C2×C3×M16C2×D311yescharacteristic
116C22×C3×C8—31no—
117C3×#117—31no—
118C2×C3×C4⋊C4—31no—
119#950—38no—
120Q8×Dic3—32no—
121C2×#216—31no—
122C2×#215—31no—
123D4×Dic3—32no—
124D4×Dic3—62no—
125C2×#214—31no—
126C2×#213—31no—
127C4×#67—62no—
128#926—61no—
129#926C2×D311yescharacteristic
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—61no—
133C2×C4⋊Dic3—61no—
134C2×C4⋊Dic3C2×D311yescharacteristic
135C22×C3⋊C8C2×D311yescharacteristic
136C2×Dic12—31no—
137#904—38no—
138C2×D24—31no—
139C2×#204—31no—
140C2×#204—31no—
141#893—32no—
142#892—61no—
143#892—61no—
144#892—61no—
145D3×C4⋊C4—61no—
146D3×C4⋊C4—61no—
147D3×C4⋊C4—61no—
148#887—32no—
149#67⋊C4—62no—
150#67⋊C4—62no—
151C4×D12—32no—
152C4×D12—32no—
153C4×Dic6—32no—
154C4×Dic6—32no—
155C3×#103—32no—
156C3×#102—32no—
157C3×#97—32no—
158C3×C4×C8—32no—
159#821—32no—
160#821—32no—
161#821—62no—
162#821C2×D312yes—
163#818—32no—
164#818—32no—
165#816—32no—
166#816—32no—
167#816—62no—
168#816C2×D312yes—
169#815C2×D312yes—
170C8×Dic3C2×D312yes—
171#807—32no—
172#807—32no—
173C23×C32C2×D411yescharacteristic
174C22×C3⋊D3—21no—
175C22×C3×D3—21no—
176C2×C32×C4C22×C412yes—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4#4112yes—
179C2×C32×C4C2411yescharacteristic
180#638—24no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3—81no—
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×Dic6—21no—
199C3×Dic6C22×C412yes—
200#624—82no—
201D3×Dic3—82no—
202C32×C8—22no—
203C3×C3⋊C8C22×C412yes—
204C3×C3⋊C8C22×C412yes—
205C2×#135—91no—
206#520—91no—
207#520—91no—
208#440—92no—
209#440—92no—
210C4×Q16—92no—
211C4×D8—92no—
212C2×#107—91no—
213#417—31no—
214#417—91no—
215#405—31no—
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—61no—
223C22×C3×C4—61no—
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C2×#67—21no—
227C2×#67—61no—
228C2×#67—61no—
229C2×#67—121no—
230C22×Dic3—21no—
231C22×Dic3—61no—
232C22×Dic3—61no—
233C22×Dic3—62no—
234C22×Dic3—121no—
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—61no—
249C2×C4×D3—61no—
250C2×C4×D3—62no—
251C2×C4×D3—62no—
252C2×C4×D3—62no—
253C2×C4×D3—121no—
254C2×Dic6—31no—
255C2×Dic6—31no—
256C2×Dic6—61no—
257C2×Dic6C22×D311yescharacteristic
258C3×M16—22no—
259C3×M16—22no—
260C3×M16—42no—
261C2×C3×C8—22no—
262C2×C3×C8—34no—
263C2×C3×C8—31no—
264C2×C3×C8—31no—
265C2×C3×C8C22×D312yes—
266C2×C3×C8C22×D312yes—
267C3×C4⋊C4—31no—
268C3×C4⋊C4—31no—
269C3×C4⋊C4—32no—
270C3×C4⋊C4—61no—
271C3×C22⋊C4—32no—
272C3×C42—32no—
273#217—62no—
274#217D1212yes—
275#216—34no—
276#215—34no—
277#214—34no—
278#213—34no—
279(C2×D3)⋊C4—62no—
280(C2×D3)⋊C4—62no—
281(C2×D3)⋊C4—62no—
282C4⋊Dic3—21no—
283C4⋊Dic3—32no—
284C4⋊Dic3—32no—
285C4⋊Dic3—62no—
286C4⋊Dic3—61no—
287C4⋊Dic3—61no—
288C4⋊Dic3—62no—
289C4⋊Dic3—121no—
290C4⋊Dic3D1211yescharacteristic
291C4⋊Dic3D1211yescharacteristic
292C4⋊Dic3C22×D312yes—
293Dic3⋊C4—62no—
294Dic3⋊C4—62no—
295Dic3⋊C4—62no—
296C4×Dic3—62no—
297C4×Dic3—62no—
298C4×Dic3—62no—
299C4×Dic3—62no—
300C4×Dic3C22×D312yes—
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×C4C4×D412yes—
319C32×C4C23×C411yescharacteristic
320C32×C4C2×#4111yescharacteristic
321C3⋊Dic3—22no—
322C3⋊Dic3—42no—
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×M16D3211yescharacteristic
335C22×C8—31no—
336C4×Q8—92no—
337C4×Q8—92no—
338C4×D4—92no—
339C4×D4—92no—
340C4×D4—182no—
341C4×D4—182no—
342#117—31no—
343#117—181no—
344#117—181no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—91no—
347C2×C4⋊C4—181no—
348C2×C4⋊C4—181no—
349#107—92no—
350#107—92no—
351#103—32no—
352#103—92no—
353#102—32no—
354#102—92no—
355#97—32no—
356C4×C8—32no—
357C23×C3—21no—
358C23×C3—61no—
359C23×C3C2×D1211yescharacteristic
360C23×C3D3×D411yescharacteristic
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—21no—
371C2×C3×C4—22no—
372C2×C3×C4—21no—
373C2×C3×C4—22no—
374C2×C3×C4—32no—
375C2×C3×C4—32no—
376C2×C3×C4—61no—
377C2×C3×C4—64no—
378C2×C3×C4—62no—
379C2×C3×C4—241no—
380C2×C3×C4C2×C4×D312yes—
381C2×C3×C4C2×C4×D312yes—
382C2×C3×C4C2×D1211yescharacteristic
383C2×C3×C4#23512yes—
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4#23712yes—
386C2×C3×C4C23×D311yescharacteristic
387C2×C3×C4C23×D311yescharacteristic
388#67—24no—
389#67—64no—
390#67—64no—
391#67—124no—
392C2×Dic3—21no—
393C2×Dic3—22no—
394C2×Dic3—61no—
395C2×Dic3—61no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—81no—
399C2×Dic3—121no—
400C2×Dic3—122no—
401C2×Dic3—242no—
402C2×Dic3—241no—
403C2×Dic3—241no—
404C2×Dic3—242no—
405C2×Dic3C2×D1212yes—
406C2×Dic3C2×D1212yes—
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—124no—
419C4×D3—242no—
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—22no—
431C3×C8—22no—
432C3×C8—32no—
433C3×C8—32no—
434C3×C8—42no—
435C3⋊C8C2×C4×D312yes—
436C3⋊C8C2×C4×D312yes—
437C2×C32—22no—
438C2×C32C2×C4×D411yescharacteristic
439C2×C32#57611yescharacteristic
440C2×C32#57811yescharacteristic
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—61no—
454C22×C4—61no—
455C22×C4—182no—
456C22×C4—182no—
457C22×C4—181no—
458C22×C4—181no—
459C22×C4C2×D3211yescharacteristic
460Q16—94no—
461SD16—94no—
462SD16—94no—
463D8—94no—
464M16—22no—
465C2×C8—31no—
466C2×C8—31no—
467C2×C8—34no—
468C2×C8C2×D3212yes—
469C4⋊C4—31no—
470C4⋊C4—31no—
471C4⋊C4—32no—
472C4⋊C4—61no—
473C4⋊C4—92no—
474C4⋊C4—182no—
475C4⋊C4—182no—
476C4⋊C4—181no—
477C22⋊C4—32no—
478C22⋊C4—182no—
479C22⋊C4—182no—
480C42—32no—
481C42—182no—
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×C3C4×D1212yes—
495C22×C3#67⋊C412yes—
496C22×C3C22×D1211yescharacteristic
497C22×C3C2×D3×D411yescharacteristic
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—62no—
514C3×C4—62no—
515C3×C4—62no—
516C3×C4—122no—
517C3×C4C4×D1212yes—
518C3×C4#67⋊C412yes—
519C3×C4C22×C4×D311yescharacteristic
520C3×C4C22×C4×D311yescharacteristic
521C3×C4C2×#23511yescharacteristic
522C3×C4C2×#23711yescharacteristic
523Dic3—22no—
524Dic3—22no—
525Dic3—22no—
526Dic3—42no—
527Dic3—62no—
528Dic3—62no—
529Dic3—122no—
530Dic3—122no—
531Dic3—122no—
532Dic3—242no—
533C32#295111yescharacteristic, complemented, Sylow
534C23—61no—
535C23—181no—
536C23D3×D1211yescharacteristic
537Q8—32no—
538Q8—61no—
539Q8—92no—
540Q8—181no—
541D4—32no—
542D4—64no—
543D4—61no—
544D4—92no—
545D4—184no—
546D4—181no—
547C2×C4—32no—
548C2×C4—32no—
549C2×C4—61no—
550C2×C4—64no—
551C2×C4—62no—
552C2×C4—181no—
553C2×C4—184no—
554C2×C4—182no—
555C2×C4—241no—
556C2×C4—722no—
557C2×C4—722no—
558C2×C4—721no—
559C2×C4C4×D3212yes—
560C2×C4D3×D1211yescharacteristic
561C2×C4#380412yes—
562C2×C4C22×D3211yescharacteristic
563C8—22no—
564C8—32no—
565C8—32no—
566C2×C3—22no—
567C2×C3—22no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—42no—
572C2×C3—122no—
573C2×C3C2×C4×D1211yescharacteristic
574C2×C3C2×#67⋊C411yescharacteristic
575C2×C3#575211yescharacteristic
576C2×C3#575311yescharacteristic
577C2×C3#577411yescharacteristic
578C2×C3#577911yescharacteristic
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#6388012yes—
592C22C2×D3×D1211yescharacteristic
593C4—62no—
594C4—62no—
595C4—62no—
596C4—122no—
597C4—182no—
598C4—362no—
599C4#6388012yes—
600C4C2×C4×D3211yescharacteristic
601C4C2×#380411yescharacteristic
602C3—21no—
603C3#7856211yescharacteristic, complemented
604C3#7886811yescharacteristic, complemented
605C2—22no—
606C2—122no—
607C2—362no—
608C2#1059471411yescharacteristic
609C2#1059472111yescharacteristic
610C2C2×#6388011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×#63829C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2951
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10594992C2semidirect
2. #10594990C2semidirect
4. #10592832C2semidirect
5. C3×#5133C2semidirect
6. C3×#5122C2semidirect
7. C2×#63575C2semidirect
8. #10590795C2semidirect
9. #10590793C2semidirect
10. #10590747C2semidirect
11. #10590745C2semidirect
33. #63829C4semidirect
55. #5133D3semidirect
56. #5122D3semidirect
71. #3828C2×C4semidirect
78. C3×#235C2×C4semidirect
94. 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#2951semidirect
603. C3#78562semidirect
604. C3#78868semidirect

Maximal subgroups

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

subgroupindex
#105949922
#105949902
C2×#638292
#105928322
C3×#51332
C3×#51222
C2×#635752
#105907952
#105907932
#105907472
#105907452
#788683
#785623