Finite Group Databasebeta

← #11905905

Subgroups — #11905905

Order 1152.

3124 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64315C212yesmaximal, complemented
2Q8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C3×#5577C211yesmaximal, characteristic, complemented
4C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
5#10595414C212yesmaximal, complemented
6#10594522C216yesmaximal, complemented
7#10594382C216yesmaximal, complemented
8#10593968C213yesmaximal, complemented
9#10593900C213yesmaximal, complemented
10Dic6×D12C213yesmaximal, complemented
11#10593897C213yesmaximal, complemented
12#86784—31nomaximal
13#85818—31nomaximal
14C2×Q8×C3⋊D3C2212yes—
15C2×C3×#239C2212yes—
16C2×C3×D3×Q8C2211yescharacteristic
17#64315—216no—
18C2×#3798C2216yes—
19C2×#3796C2216yes—
20C2×#3795C2216yes—
21C2×D3×Dic6C2216yes—
22C32×C4×Q8C2211yescharacteristic
23#64106C2216yes—
24C4×C4⋊(C3⋊D3)C2213yes—
25#64078C2213yes—
26C3×Q8×Dic3C2211yescharacteristic
27C3×#895C2216yes—
28C3×D3×C4⋊C4C2213yes—
29C3×#887C2213yes—
30C3×#874C2213yes—
31C3×C4×D12C2213yes—
32C3×C42×D3C2213yes—
33C3×C4×Dic6C2213yes—
34#63918C2213yes—
35#63916C2216yes—
36#63911C2213yes—
37#63909C2211yescharacteristic
38#63908C2213yes—
39#63908C2216yes—
40#63906C2216yes—
41C4×#626C2216yes—
42#63893C22112yes—
43Dic3×D12C2216yes—
44Dic3×D12C2216yes—
45#63886C22112yes—
46#63860C2216yes—
47#63857C2216yes—
48#63852C2216yes—
49C2×#1010—32no—
50C2×#1007—32no—
51C3×#550—31no—
52C2×C3×C4×Q8—31no—
53#5831—32no—
54#5718—33no—
55#5716—33no—
56#5608—36no—
57#5598—36no—
58#5577—33no—
59#5577D311yescharacteristic, complemented
60#5576—32no—
61#5576—36no—
62Q8×D12—31no—
63Q8×D12—31no—
64Q8×D12—33no—
65Q8×D12—61no—
66C4×D3×Q8D311yescharacteristic, complemented
67#5548—33no—
68D4×Dic6—33no—
69#5510—36no—
70#5477—33no—
71#5477—33no—
72C2×C32×Q8C2311yescharacteristic
73Q8×C3⋊D3—28no—
74C2×C4⋊(C3⋊D3)C2311yescharacteristic
75C2×C4×C3⋊D3C2316yes—
76C2×#634C2316yes—
77C3×#239—28no—
78C3×D3×Q8D418yescomplemented
79C2×C3×D12C2316yes—
80C2×C3×D12C2313yes—
81C2×C3×D12C2316yes—
82C2×C3×C4×D3C2316yes—
83C2×C3×C4×D3C2311yescharacteristic
84C2×C3×C4×D3C2313yes—
85C2×C3×C4×D3C2313yes—
86C2×C3×Dic6C2313yes—
87C2×#627C2316yes—
88C2×#626C2316yes—
89C2×#626C2312yes—
90C2×#626C2316yes—
91C2×#625C2316yes—
92C2×D3×Dic3C23112yes—
93#3798—224no—
94#3796—224no—
95#3795—224no—
96D3×Dic6—224no—
97C32×C4⋊C4C2313yes—
98C32×C42C2313yes—
99#3752C2316yes—
100C4⋊(C3⋊Dic3)C2313yes—
101C4⋊(C3⋊Dic3)C2316yes—
102C3×(C2×D3)⋊C4C2316yes—
103C3×C4⋊Dic3C2313yes—
104C3×C4⋊Dic3C2311yescharacteristic
105C3×Dic3⋊C4C2316yes—
106C3×C4×Dic3C2313yes—
107C3×C4×Dic3C2313yes—
108C3×C4×Dic3C2313yes—
109Dic3⋊Dic3C2316yes—
110#3722C2312yes—
111(C2×D3)⋊Dic3C2316yes—
112(C2×D3)⋊Dic3C23112yes—
113#3497—91noSylow
114C2×C3×#41—32no—
115C22×C3×Q8—31no—
116#1010—616no—
117#1007—616no—
118C2×#239—36no—
119C2×#239C2×D312yes—
120C2×D3×Q8—32no—
121C2×D3×Q8—32no—
122C2×D3×Q8—36no—
123C2×D3×Q8—62no—
124C2×D3×Q8C2×D311yescharacteristic
125C2×#237—36no—
126C2×#237—36no—
127C2×#235—36no—
128C2×#235—36no—
129C2×#235—36no—
130C22×Dic6—36no—
131C3×#127—33no—
132C3×#121—36no—
133C3×C4×Q8—21no—
134C3×C4×Q8—31no—
135C3×C4×Q8—33no—
136C3×C4×Q8—33no—
137C3×C4×Q8C2×D311yescharacteristic
138C3×C4×Q8C2×D311yescharacteristic
139C3×C4×D4—33no—
140C2×C3×C4⋊C4—33no—
141C2×C3×C42—33no—
142Q8×Dic3C2×D311yescharacteristic
143#940—33no—
144#939—312no—
145#938—33no—
146#938—36no—
147#938—36no—
148#936—36no—
149D4×Dic3—36no—
150D4×Dic3—36no—
151#930—33no—
152#930—36no—
153#930—36no—
154#930—31no—
155C4×#67—36no—
156#924—36no—
157#897—36no—
158#897—36no—
159#897—36no—
160#897—312no—
161#897—66no—
162#895—312no—
163#895—36no—
164#895—31no—
165#895C2×D316yes—
166D3×C4⋊C4C2×D313yes—
167#888—33no—
168#887C2×D313yes—
169#885—36no—
170#884—36no—
171#878—312no—
172#875—36no—
173#875—36no—
174#874—33no—
175#874C2×D313yes—
176C4×D12—36no—
177C4×D12—36no—
178C4×D12—36no—
179C4×D12—33no—
180C4×D12—33no—
181C4×D12—63no—
182C4×D12C2×D313yes—
183C42×D3C2×D313yes—
184#869—33no—
185#869—33no—
186#869—33no—
187#869—63no—
188C4×Dic6C2×D313yes—
189C22×C3⋊D3C2412yes—
190C22×C3×D3C2416yes—
191C22×C3×D3C2411yescharacteristic
192C32×Q8C2×D414yes—
193C2×C32×C4C2413yes—
194C2×C32×C4C2413yes—
195C2×C32×C4C2411yescharacteristic
196C2×C3⋊Dic3C2416yes—
197C4⋊(C3⋊D3)—22no—
198C4×C3⋊D3—212no—
199#634—212no—
200C2×C3×Dic3C2411yescharacteristic
201C2×C3×Dic3C2413yes—
202C2×C3×Dic3C2412yes—
203C2×C3×Dic3C2413yes—
204C3×D12—212no—
205C3×D12—26no—
206C3×D12—46no—
207C3×C4×D3—212no—
208C3×C4×D3—22no—
209C3×C4×D3—43no—
210C3×C4×D3C2×D4112yes—
211C3×Dic6C2×D4112yes—
212#627—212no—
213#626—24no—
214#626—212no—
215#626—46no—
216#625—212no—
217D3×Dic3—224no—
218C2×2−1+4—92no—
219#550—31no—
220#550—93no—
221D4×Q8—93no—
222D4×Q8—91no—
223#548—96no—
224#548—92no—
225#537—96no—
226#532—93no—
227#532—93no—
228C2×C4×Q8—31no—
229C3×#41—68no—
230C2×C3×Q8—21no—
231C2×C3×Q8—38no—
232C2×C3×Q8—33no—
233C2×C3×Q8C22×D311yescharacteristic
234C2×C3×Q8C22×D311yescharacteristic
235C2×C3×D4—33no—
236C2×C3×D4—36no—
237C2×C3×D4—36no—
238C22×C3×C4—33no—
239C22×C3×C4—36no—
240C22×C3×C4—31no—
241C22×C3×C4—33no—
242C2×#67—36no—
243C2×#67—36no—
244C2×#67—36no—
245C2×#67—32no—
246C2×#67—36no—
247C22×Dic3—312no—
248#239—28no—
249#239—624no—
250D3×Q8—624no—
251D3×Q8—68no—
252D3×Q8—68no—
253D3×Q8—128no—
254D3×Q8D1218yescomplemented
255#237—624no—
256#237—624no—
257#235—624no—
258#235—624no—
259#235—624no—
260C2×D12—36no—
261C2×D12—32no—
262C2×D12—31no—
263C2×D12—31no—
264C2×D12—36no—
265C2×D12—61no—
266C2×D12C22×D313yes—
267C2×D12C22×D316yes—
268C2×D12C22×D316yes—
269C2×C4×D3—312no—
270C2×C4×D3—36no—
271C2×C4×D3—36no—
272C2×C4×D3—66no—
273C2×C4×D3C22×D311yescharacteristic
274C2×C4×D3C22×D316yes—
275C2×C4×D3C22×D313yes—
276C2×C4×D3C22×D313yes—
277C2×Dic6—36no—
278C2×Dic6—36no—
279C2×Dic6—36no—
280C2×Dic6—36no—
281C2×Dic6—66no—
282C2×Dic6—624no—
283C2×Dic6C22×D313yes—
284C3×C4⋊C4—23no—
285C3×C4⋊C4—31no—
286C3×C4⋊C4—36no—
287C3×C4⋊C4—33no—
288C3×C4⋊C4C22×D313yes—
289C3×C4⋊C4C22×D313yes—
290C3×C22⋊C4—36no—
291C3×C42—23no—
292C3×C42—33no—
293C3×C42—33no—
294C3×C42—33no—
295C3×C42C22×D313yes—
296C3×C42C22×D313yes—
297#217—312no—
298#217—36no—
299(C2×D3)⋊C4—36no—
300(C2×D3)⋊C4—312no—
301(C2×D3)⋊C4—36no—
302(C2×D3)⋊C4—36no—
303(C2×D3)⋊C4—32no—
304(C2×D3)⋊C4—32no—
305(C2×D3)⋊C4—66no—
306(C2×D3)⋊C4C22×D316yes—
307C4⋊Dic3—33no—
308C4⋊Dic3—33no—
309C4⋊Dic3—36no—
310C4⋊Dic3—36no—
311C4⋊Dic3—36no—
312C4⋊Dic3—63no—
313C4⋊Dic3—66no—
314C4⋊Dic3C22×D313yes—
315C4⋊Dic3C22×D311yescharacteristic
316Dic3⋊C4—36no—
317Dic3⋊C4C22×D316yes—
318C4×Dic3C22×D313yes—
319C4×Dic3C22×D313yes—
320C4×Dic3C22×D313yes—
321C22×C32C2511yescharacteristic
322C2×C3⋊D3—22no—
323C2×C3⋊D3—22no—
324C2×C3⋊D3—22no—
325C2×C3×D3—21no—
326C2×C3×D3—21no—
327C2×C3×D3—26no—
328C2×C3×D3—26no—
329C2×C3×D3—26no—
330C2×C3×D3C22×D412yes—
331C32×C4—23no—
332C32×C4C22×D416yes—
333C32×C42−1+412yescomplemented
334C3⋊Dic3—26no—
335C3×Dic3—22no—
336C3×Dic3—21no—
337C3×Dic3—23no—
338C3×Dic3C22×D416yes—
3392−1+4—1816no—
340C2×#41—32no—
341C2×#41—96no—
342C2×#41—96no—
343C2×#41—96no—
344C22×Q8—31no—
345C22×Q8—96no—
346C22×Q8—92no—
347C4⋊Q8—93no—
348C4⋊Q8—93no—
349#127—33no—
350#127—93no—
351#124—96no—
352#124—96no—
353C22⋊Q8—912no—
354C22⋊Q8—96no—
355C22⋊Q8—96no—
356#121—36no—
357#121—96no—
358#121—91no—
359#121—96no—
360#121—912no—
361#121—93no—
362#121—96no—
363C4×Q8—31no—
364C4×Q8—33no—
365C4×Q8—33no—
366C4×Q8D3211yescharacteristic
367C4×D4—33no—
368C4×D4—96no—
369C4×D4—96no—
370C4×D4—96no—
371C4×D4—93no—
372C2×C4⋊C4—33no—
373C2×C42—33no—
374C23×C3—31no—
375C23×C3—36no—
376C22×D3—32no—
377C22×D3—32no—
378C22×D3—62no—
379C22×D3C23×D316yes—
380C22×D3C23×D311yescharacteristic
381C3×Q8—24no—
382C3×Q8—312no—
383C3×Q8C2×D1214yes—
384C3×Q8D3×D414yes—
385C3×D4—612no—
386C3×D4—66no—
387C3×D4—126no—
388C2×C3×C4—21no—
389C2×C3×C4—23no—
390C2×C3×C4—23no—
391C2×C3×C4—33no—
392C2×C3×C4—312no—
393C2×C3×C4—32no—
394C2×C3×C4—33no—
395C2×C3×C4—31no—
396C2×C3×C4—612no—
397C2×C3×C4—62no—
398C2×C3×C4—123no—
399C2×C3×C4C23×D313yes—
400C2×C3×C4C23×D313yes—
401C2×C3×C4C23×D313yes—
402C2×C3×C4C23×D313yes—
403C2×C3×C4C23×D311yescharacteristic
404C2×C3×C4C23×D311yescharacteristic
405#67—64no—
406#67—612no—
407#67—612no—
408#67—612no—
409#67—126no—
410C2×Dic3—36no—
411C2×Dic3—36no—
412C2×Dic3—66no—
413C2×Dic3—624no—
414C2×Dic3C23×D311yescharacteristic
415C2×Dic3C23×D313yes—
416C2×Dic3C23×D312yes—
417C2×Dic3C23×D313yes—
418D12—212no—
419D12—26no—
420D12—46no—
421D12—64no—
422D12—612no—
423D12—64no—
424D12—62no—
425D12—62no—
426D12—126no—
427C4×D3—212no—
428C4×D3—22no—
429C4×D3—43no—
430C4×D3—624no—
431C4×D3—612no—
432C4×D3—612no—
433C4×D3—1212no—
434C4×D3C2×D12112yes—
435Dic6—612no—
436Dic6—612no—
437Dic6—612no—
438Dic6—612no—
439Dic6—1212no—
440Dic6C2×D12112yes—
441C2×C32C23×D411yescharacteristic
442C2×C32C2×2−1+411yescharacteristic
443C2×C32#58511yescharacteristic
444C3⋊D3—42no—
445C3×D3—22no—
446C3×D3—46no—
447#41—68no—
448#41—1824no—
449#41—1824no—
450#41—1824no—
451C2×Q8—38no—
452C2×Q8—33no—
453C2×Q8—96no—
454C2×Q8—96no—
455C2×Q8—1824no—
456C2×Q8—188no—
457C2×Q8C2×D3211yescharacteristic
458C2×D4—33no—
459C2×D4—36no—
460C2×D4—36no—
461C2×D4—92no—
462C2×D4—96no—
463C2×D4—96no—
464C2×D4—96no—
465C2×D4—91no—
466C22×C4—33no—
467C22×C4—31no—
468C22×C4—36no—
469C22×C4—33no—
470C22×C4—912no—
471C22×C4—96no—
472C4⋊C4—36no—
473C4⋊C4—33no—
474C4⋊C4—31no—
475C4⋊C4—96no—
476C4⋊C4—93no—
477C4⋊C4—96no—
478C4⋊C4C2×D3213yes—
479C22⋊C4—36no—
480C22⋊C4—92no—
481C22⋊C4—96no—
482C22⋊C4—912no—
483C22⋊C4—96no—
484C42—33no—
485C42—33no—
486C42—33no—
487C42C2×D3213yes—
488C22×C3—21no—
489C22×C3—32no—
490C22×C3—61no—
491C22×C3—61no—
492C22×C3—66no—
493C22×C3—66no—
494C22×C3—66no—
495C22×C3C24×D311yescharacteristic
496C22×C3C24×D311yescharacteristic
497C2×D3—21no—
498C2×D3—21no—
499C2×D3—26no—
500C2×D3—26no—
501C2×D3—26no—
502C2×D3—64no—
503C2×D3—62no—
504C2×D3—62no—
505C2×D3—62no—
506C2×D3—62no—
507C2×D3—62no—
508C2×D3—62no—
509C2×D3—122no—
510C2×D3—122no—
511C2×D3C22×D1212yes—
512C3×C4—23no—
513C3×C4—23no—
514C3×C4—26no—
515C3×C4—22no—
516C3×C4—36no—
517C3×C4—43no—
518C3×C4—62no—
519C3×C4—61no—
520C3×C4—63no—
521C3×C4C22×D1216yes—
522C3×C4C2×D3×D416yes—
523C3×C4#100712yescomplemented
524C3×C4#101012yescomplemented
525Dic3—22no—
526Dic3—21no—
527Dic3—23no—
528Dic3—66no—
529Dic3—66no—
530Dic3—126no—
531Dic3C22×D1216yes—
532C32#349711yescharacteristic, complemented, Sylow
533C23—31no—
534C23—36no—
535C23—92no—
536Q8—312no—
537Q8—1812no—
538Q8—1812no—
539Q8D3×D1214yes—
540D4—612no—
541D4—66no—
542D4—126no—
543D4—1812no—
544D4—184no—
545D4—1812no—
546D4—182no—
547D4—366no—
548C2×C4—33no—
549C2×C4—312no—
550C2×C4—31no—
551C2×C4—33no—
552C2×C4—32no—
553C2×C4—612no—
554C2×C4—62no—
555C2×C4—96no—
556C2×C4—123no—
557C2×C4—1824no—
558C2×C4—1812no—
559C2×C4C22×D3213yes—
560C2×C4C22×D3213yes—
561C2×C4C22×D3211yescharacteristic
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—62no—
566C2×C3—126no—
567C2×C3C23×D1211yescharacteristic
568C2×C3C22×D3×D411yescharacteristic
569C2×C3C2×#100711yescharacteristic
570C2×C3C2×#101011yescharacteristic
571C2×C3#596411yescharacteristic
572C2×C3#596611yescharacteristic
573D3—22no—
574D3—46no—
575D3—124no—
576D3—122no—
577D3—122no—
578C22—32no—
579C22—61no—
580C22—61no—
581C22—66no—
582C22—66no—
583C22—66no—
584C22—182no—
585C22—182no—
586C22—182no—
587C22C23×D3211yescharacteristic
588C4—23no—
589C4—36no—
590C4—62no—
591C4—61no—
592C4—63no—
593C4—186no—
594C4C2×D3×D1216yes—
595C4#6431512yescomplemented
596C3—21no—
597C3#8581811yescharacteristic, complemented
598C3#8678411yescharacteristic, complemented
599C2—62no—
600C2—126no—
601C2—362no—
602C2C22×D3×D1211yescharacteristic
603C2C2×#6431511yescharacteristic
604C2#1059669611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3497
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64315C2semidirect
2. Q8×C4⋊(C3⋊D3)C2semidirect
3. C3×#5577C2semidirect
4. C3×C4×D3×Q8C2semidirect
5. #10595414C2semidirect
6. #10594522C2semidirect
7. #10594382C2semidirect
8. #10593968C2semidirect
9. #10593900C2semidirect
10. Dic6×D12C2semidirect
11. #10593897C2semidirect
59. #5577D3semidirect
66. C4×D3×Q8D3semidirect
78. C3×D3×Q8D4semidirect
254. D3×Q8D12semidirect
333. C32×C42−1+4semidirect
523. C3×C4#1007semidirect
524. C3×C4#1010semidirect
532. C32#3497semidirect
595. C4#64315semidirect
597. C3#85818semidirect
598. C3#86784semidirect

Maximal subgroups

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

subgroupindex
C2×#643152
Q8×C4⋊(C3⋊D3)2
C3×#55772
C3×C4×D3×Q82
#105954142
#105945222
#105943822
#105939682
#105939002
Dic6×D122
#105938972
#867843
#858183