Finite Group Databasebeta

← #11905903

Subgroups — #11905903

Order 1152.

3140 conjugacy classes of subgroups.

The subgroup lattice has 607 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64316C212yesmaximal, complemented
2#10596048C211yesmaximal, characteristic, complemented
3C3×Q8×D12C211yesmaximal, characteristic, complemented
4C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
5#10595342C212yesmaximal, complemented
6#10594523C216yesmaximal, complemented
7#10594329C216yesmaximal, complemented
8#10593970C213yesmaximal, complemented
9#10593968C213yesmaximal, complemented
10#10593903C213yesmaximal, complemented
11#10593902C213yesmaximal, complemented
12#86760—31nomaximal
13#85818—31nomaximal
14C2×#3832C2212yes—
15C2×C3×D3×Q8C2212yes—
16C2×C3×D3×Q8C2211yescharacteristic
17#64316—216no—
18C2×#3799C2216yes—
19C2×#3799C2216yes—
20C2×#3798C2216yes—
21C2×#3797C2216yes—
22C32×C4×Q8C2211yescharacteristic
23#64104C2216yes—
24#64083C2213yes—
25C4×C4⋊(C3⋊D3)C2213yes—
26C3×Q8×Dic3C2211yescharacteristic
27C3×#897C2216yes—
28C3×D3×C4⋊C4C2213yes—
29C3×#887C2213yes—
30C3×C4×D12C2213yes—
31C3×C42×D3C2213yes—
32C3×#869C2213yes—
33C3×C4×Dic6C2213yes—
34#63918C2213yes—
35#63911C2213yes—
36#63910C22112yes—
37#63909C2216yes—
38#63909C2213yes—
39#63909C2216yes—
40#63908C2211yescharacteristic
41#63906C2216yes—
42C4×#626C2216yes—
43#63895C22112yes—
44#63894C2216yes—
45#63894C2216yes—
46#63871C2216yes—
47#63864C2216yes—
48#63852C2216yes—
49C2×#1007—32no—
50C2×#1007—32no—
51C3×D4×Q8—31no—
52C2×C3×C4×Q8—31no—
53#5817—32no—
54#5727—33no—
55#5725—33no—
56#5633—36no—
57#5629—36no—
58#5577—31no—
59#5577—31no—
60#5577—33no—
61#5577—61no—
62#5576—32no—
63#5576—36no—
64Q8×D12—33no—
65Q8×D12D311yescharacteristic, complemented
66C4×D3×Q8D311yescharacteristic, complemented
67#5553—33no—
68#5548—33no—
69#5510—36no—
70#5477—33no—
71#5477—33no—
72C2×C32×Q8C2311yescharacteristic
73#3832—28no—
74C2×C4⋊(C3⋊D3)C2316yes—
75C2×C4⋊(C3⋊D3)C2313yes—
76C2×C4⋊(C3⋊D3)C2316yes—
77C2×C4×C3⋊D3C2316yes—
78C3×D3×Q8—28no—
79C3×D3×Q8D418yescomplemented
80C2×C3×D12C2311yescharacteristic
81C2×C3×C4×D3C2316yes—
82C2×C3×C4×D3C2311yescharacteristic
83C2×C3×C4×D3C2313yes—
84C2×C3×C4×D3C2313yes—
85C2×C3×Dic6C2316yes—
86C2×C3×Dic6C2313yes—
87C2×#627C2316yes—
88C2×#626C2316yes—
89C2×#626C2316yes—
90C2×#626C2316yes—
91C2×#625C2312yes—
92C2×#624C23112yes—
93#3799—224no—
94#3799—224no—
95#3798—224no—
96#3797—224no—
97C32×C4⋊C4C2313yes—
98C32×C42C2313yes—
99#3752C2316yes—
100C4⋊(C3⋊Dic3)C2311yescharacteristic
101C3×(C2×D3)⋊C4C2316yes—
102C3×C4⋊Dic3C2313yes—
103C3×C4⋊Dic3C2316yes—
104C3×C4⋊Dic3C2313yes—
105C3×Dic3⋊C4C2316yes—
106C3×C4×Dic3C2313yes—
107C3×C4×Dic3C2313yes—
108C3×C4×Dic3C2313yes—
109Dic3⋊Dic3C2316yes—
110#3722C2316yes—
111#3722C23112yes—
112(C2×D3)⋊Dic3C2312yes—
113#3497—91noSylow
114C22×C3×Q8—31no—
115C22×C3×Q8—32no—
116#1007—616no—
117#1007—616no—
118C2×#239—32no—
119C2×#239—32no—
120C2×#239—36no—
121C2×#239—36no—
122C2×#239—62no—
123C2×D3×Q8—36no—
124C2×D3×Q8—36no—
125C2×D3×Q8C2×D312yes—
126C2×D3×Q8C2×D311yescharacteristic
127C2×#235—36no—
128C2×#235—36no—
129C2×#235—36no—
130C2×#235—36no—
131C3×C4⋊Q8—33no—
132C3×C22⋊Q8—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—
142#947—36no—
143#946—36no—
144Q8×Dic3C2×D311yescharacteristic
145#940—33no—
146#938—31no—
147#930—31no—
148#930—36no—
149#930—33no—
150#930—36no—
151#930—36no—
152C4×#67—36no—
153#897—36no—
154#897—312no—
155#897C2×D316yes—
156#896—312no—
157#895—33no—
158#895—36no—
159#895—36no—
160#895—36no—
161#895—36no—
162#895—312no—
163#895—66no—
164#893—36no—
165#893—36no—
166D3×C4⋊C4C2×D313yes—
167#888—33no—
168#887C2×D313yes—
169#885—36no—
170#884—36no—
171#884—312no—
172#875—36no—
173#875—36no—
174#874—33no—
175#874—33no—
176#874—33no—
177#874—63no—
178C4×D12—36no—
179C4×D12—33no—
180C4×D12—33no—
181C4×D12—36no—
182C4×D12—36no—
183C4×D12—63no—
184C4×D12C2×D313yes—
185C42×D3C2×D313yes—
186#869—33no—
187#869C2×D313yes—
188C4×Dic6C2×D313yes—
189C22×C3⋊D3C2416yes—
190C22×C3×D3C2412yes—
191C22×C3×D3C2411yescharacteristic
192C32×Q8C2×D414yes—
193C2×C32×C4C2413yes—
194C2×C32×C4C2413yes—
195C2×C32×C4C2411yescharacteristic
196C2×C3⋊Dic3C2412yes—
197C4⋊(C3⋊D3)—212no—
198C4⋊(C3⋊D3)—26no—
199C4⋊(C3⋊D3)—46no—
200C4×C3⋊D3—212no—
201C2×C3×Dic3C2411yescharacteristic
202C2×C3×Dic3C2413yes—
203C2×C3×Dic3C2416yes—
204C2×C3×Dic3C2413yes—
205C3×D12—22no—
206C3×C4×D3—212no—
207C3×C4×D3—22no—
208C3×C4×D3—43no—
209C3×C4×D3C2×D4112yes—
210C3×Dic6—212no—
211C3×Dic6C2×D4112yes—
212#627—212no—
213#626—212no—
214#626—212no—
215#626—46no—
216#625—24no—
217#624—224no—
218C2×2−1+4—92no—
219#550—93no—
220#550—91no—
221D4×Q8—31no—
222D4×Q8—93no—
223#548—96no—
224#548—92no—
225#537—96no—
226#532—93no—
227#532—93no—
228C2×C4×Q8—31no—
229C2×C3×Q8—21no—
230C2×C3×Q8—38no—
231C2×C3×Q8—33no—
232C2×C3×Q8—36no—
233C2×C3×Q8—68no—
234C2×C3×Q8C22×D311yescharacteristic
235C2×C3×Q8C22×D311yescharacteristic
236C2×C3×D4—31no—
237C22×C3×C4—33no—
238C22×C3×C4—36no—
239C22×C3×C4—31no—
240C22×C3×C4—33no—
241C2×#67—32no—
242C2×#67—32no—
243C2×#67—36no—
244C2×#67—36no—
245C2×#67—36no—
246#239—624no—
247#239—68no—
248#239—68no—
249#239—624no—
250#239—128no—
251D3×Q8—28no—
252D3×Q8—624no—
253D3×Q8—624no—
254D3×Q8D1218yescomplemented
255#235—624no—
256#235—624no—
257#235—624no—
258#235—624no—
259C2×D12—36no—
260C2×D12—36no—
261C2×D12—33no—
262C2×D12—33no—
263C2×D12—36no—
264C2×D12—36no—
265C2×D12—36no—
266C2×D12—36no—
267C2×D12—36no—
268C2×D12—63no—
269C2×D12—66no—
270C2×D12—66no—
271C2×D12C22×D311yescharacteristic
272C2×C4×D3—36no—
273C2×C4×D3—36no—
274C2×C4×D3—312no—
275C2×C4×D3—312no—
276C2×C4×D3—66no—
277C2×C4×D3C22×D311yescharacteristic
278C2×C4×D3C22×D316yes—
279C2×C4×D3C22×D313yes—
280C2×C4×D3C22×D313yes—
281C2×Dic6—36no—
282C2×Dic6—36no—
283C2×Dic6C22×D316yes—
284C2×Dic6C22×D313yes—
285C3×C4⋊C4—23no—
286C3×C4⋊C4—33no—
287C3×C4⋊C4—36no—
288C3×C4⋊C4—36no—
289C3×C4⋊C4—33no—
290C3×C4⋊C4C22×D313yes—
291C3×C4⋊C4C22×D313yes—
292C3×C22⋊C4—36no—
293C3×C42—23no—
294C3×C42—33no—
295C3×C42—33no—
296C3×C42—33no—
297C3×C42C22×D313yes—
298C3×C42C22×D313yes—
299#217—32no—
300(C2×D3)⋊C4—32no—
301(C2×D3)⋊C4—36no—
302(C2×D3)⋊C4—36no—
303(C2×D3)⋊C4—36no—
304(C2×D3)⋊C4—312no—
305(C2×D3)⋊C4—312no—
306(C2×D3)⋊C4—36no—
307(C2×D3)⋊C4—66no—
308(C2×D3)⋊C4C22×D316yes—
309C4⋊Dic3—31no—
310C4⋊Dic3—31no—
311C4⋊Dic3—36no—
312C4⋊Dic3—61no—
313C4⋊Dic3C22×D313yes—
314C4⋊Dic3C22×D313yes—
315C4⋊Dic3C22×D316yes—
316Dic3⋊C4—36no—
317Dic3⋊C4C22×D316yes—
318C4×Dic3C22×D313yes—
319C4×Dic3C22×D313yes—
320C4×Dic3C22×D313yes—
321C22×C32C2511yescharacteristic
322C2×C3⋊D3—26no—
323C2×C3⋊D3—26no—
324C2×C3⋊D3—26no—
325C2×C3×D3—21no—
326C2×C3×D3—21no—
327C2×C3×D3—22no—
328C2×C3×D3—22no—
329C2×C3×D3—22no—
330C2×C3×D3C22×D412yes—
331C32×C4—23no—
332C32×C4C22×D416yes—
333C32×C42−1+412yescomplemented
334C3⋊Dic3—22no—
335C3×Dic3—26no—
336C3×Dic3—21no—
337C3×Dic3—23no—
338C3×Dic3C22×D416yes—
3392−1+4—1816no—
340C2×#41—96no—
341C2×#41—96no—
342C2×#41—96no—
343C2×#41—92no—
344C22×Q8—31no—
345C22×Q8—32no—
346C22×Q8—96no—
347C4⋊Q8—33no—
348C4⋊Q8—93no—
349#127—93no—
350#127—93no—
351#124—96no—
352#124—96no—
353C22⋊Q8—36no—
354C22⋊Q8—912no—
355C22⋊Q8—96no—
356#121—912no—
357#121—96no—
358#121—93no—
359#121—96no—
360#121—96no—
361#121—91no—
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—32no—
376C22×D3—36no—
377C22×D3—36no—
378C22×D3—66no—
379C22×D3C23×D312yes—
380C22×D3C23×D311yescharacteristic
381C3×Q8—24no—
382C3×Q8—312no—
383C3×Q8—612no—
384C3×Q8C2×D1214yes—
385C3×Q8D3×D414yes—
386C3×D4—62no—
387C2×C3×C4—21no—
388C2×C3×C4—23no—
389C2×C3×C4—23no—
390C2×C3×C4—33no—
391C2×C3×C4—312no—
392C2×C3×C4—36no—
393C2×C3×C4—33no—
394C2×C3×C4—31no—
395C2×C3×C4—612no—
396C2×C3×C4—62no—
397C2×C3×C4—123no—
398C2×C3×C4C23×D313yes—
399C2×C3×C4C23×D313yes—
400C2×C3×C4C23×D313yes—
401C2×C3×C4C23×D313yes—
402C2×C3×C4C23×D311yescharacteristic
403C2×C3×C4C23×D311yescharacteristic
404#67—612no—
405#67—64no—
406#67—64no—
407#67—612no—
408#67—126no—
409C2×Dic3—32no—
410C2×Dic3—32no—
411C2×Dic3—62no—
412C2×Dic3C23×D311yescharacteristic
413C2×Dic3C23×D313yes—
414C2×Dic3C23×D316yes—
415C2×Dic3C23×D313yes—
416D12—22no—
417D12—612no—
418D12—612no—
419D12—612no—
420D12—612no—
421D12—66no—
422D12—66no—
423D12—126no—
424D12—1212no—
425D12—126no—
426D12—126no—
427D12—126no—
428D12—246no—
429C4×D3—212no—
430C4×D3—22no—
431C4×D3—43no—
432C4×D3—624no—
433C4×D3—612no—
434C4×D3—612no—
435C4×D3—624no—
436C4×D3—1212no—
437C4×D3C2×D12112yes—
438Dic6—212no—
439Dic6—612no—
440Dic6—612no—
441Dic6C2×D12112yes—
442C2×C32C23×D411yescharacteristic
443C2×C32C2×2−1+411yescharacteristic
444C2×C32#58511yescharacteristic
445C3⋊D3—46no—
446C3×D3—22no—
447C3×D3—42no—
448#41—1824no—
449#41—1824no—
450#41—1824no—
451#41—188no—
452C2×Q8—38no—
453C2×Q8—33no—
454C2×Q8—36no—
455C2×Q8—68no—
456C2×Q8—96no—
457C2×Q8—1824no—
458C2×Q8C2×D3211yescharacteristic
459C2×D4—31no—
460C2×D4—96no—
461C2×D4—96no—
462C2×D4—96no—
463C2×D4—92no—
464C2×D4—93no—
465C2×D4—96no—
466C2×D4—96no—
467C22×C4—33no—
468C22×C4—31no—
469C22×C4—36no—
470C22×C4—33no—
471C22×C4—912no—
472C22×C4—96no—
473C4⋊C4—36no—
474C4⋊C4—33no—
475C4⋊C4—33no—
476C4⋊C4—36no—
477C4⋊C4—96no—
478C4⋊C4—91no—
479C4⋊C4C2×D3213yes—
480C22⋊C4—36no—
481C22⋊C4—96no—
482C22⋊C4—912no—
483C22⋊C4—92no—
484C22⋊C4—96no—
485C42—33no—
486C42—33no—
487C42—33no—
488C42C2×D3213yes—
489C22×C3—21no—
490C22×C3—32no—
491C22×C3—61no—
492C22×C3—61no—
493C22×C3—62no—
494C22×C3—62no—
495C22×C3—62no—
496C22×C3C24×D311yescharacteristic
497C22×C3C24×D311yescharacteristic
498C2×D3—21no—
499C2×D3—21no—
500C2×D3—22no—
501C2×D3—22no—
502C2×D3—22no—
503C2×D3—66no—
504C2×D3—66no—
505C2×D3—66no—
506C2×D3—66no—
507C2×D3—66no—
508C2×D3—66no—
509C2×D3—126no—
510C2×D3—126no—
511C2×D3—126no—
512C2×D3C22×D1212yes—
513C3×C4—23no—
514C3×C4—23no—
515C3×C4—26no—
516C3×C4—22no—
517C3×C4—36no—
518C3×C4—43no—
519C3×C4—66no—
520C3×C4—61no—
521C3×C4—63no—
522C3×C4C22×D1216yes—
523C3×C4C2×D3×D416yes—
524C3×C4#100712yescomplemented
525C3×C4#100712yescomplemented
526Dic3—26no—
527Dic3—21no—
528Dic3—23no—
529Dic3—62no—
530Dic3—62no—
531Dic3—122no—
532Dic3C22×D1216yes—
533C32#349711yescharacteristic, complemented, Sylow
534C23—31no—
535C23—32no—
536C23—96no—
537Q8—312no—
538Q8—612no—
539Q8—1812no—
540Q8D3×D1214yes—
541D4—62no—
542D4—1812no—
543D4—1812no—
544D4—184no—
545D4—1812no—
546D4—186no—
547D4—366no—
548D4—366no—
549C2×C4—33no—
550C2×C4—312no—
551C2×C4—31no—
552C2×C4—33no—
553C2×C4—36no—
554C2×C4—612no—
555C2×C4—62no—
556C2×C4—92no—
557C2×C4—123no—
558C2×C4—1824no—
559C2×C4—1812no—
560C2×C4C22×D3213yes—
561C2×C4C22×D3213yes—
562C2×C4C22×D3211yescharacteristic
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—62no—
567C2×C3—122no—
568C2×C3C23×D1211yescharacteristic
569C2×C3C22×D3×D411yescharacteristic
570C2×C3C2×#100711yescharacteristic
571C2×C3C2×#100711yescharacteristic
572C2×C3#596411yescharacteristic
573C2×C3#596811yescharacteristic
574D3—22no—
575D3—42no—
576D3—126no—
577D3—126no—
578D3—246no—
579C22—32no—
580C22—61no—
581C22—61no—
582C22—62no—
583C22—62no—
584C22—62no—
585C22—186no—
586C22—186no—
587C22—186no—
588C22C23×D3211yescharacteristic
589C4—23no—
590C4—36no—
591C4—66no—
592C4—61no—
593C4—63no—
594C4—182no—
595C4C2×D3×D1216yes—
596C4#6431612yescomplemented
597C3—21no—
598C3#8581811yescharacteristic, complemented
599C3#8676011yescharacteristic, complemented
600C2—62no—
601C2—122no—
602C2—366no—
603C2C22×D3×D1211yescharacteristic
604C2C2×#6431611yescharacteristic
605C2#1059669711yescharacteristic
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×#64316C2semidirect
2. #10596048C2semidirect
3. C3×Q8×D12C2semidirect
4. C3×C4×D3×Q8C2semidirect
5. #10595342C2semidirect
6. #10594523C2semidirect
7. #10594329C2semidirect
8. #10593970C2semidirect
9. #10593968C2semidirect
10. #10593903C2semidirect
11. #10593902C2semidirect
65. Q8×D12D3semidirect
66. C4×D3×Q8D3semidirect
79. C3×D3×Q8D4semidirect
254. D3×Q8D12semidirect
333. C32×C42−1+4semidirect
524. C3×C4#1007semidirect
525. C3×C4#1007semidirect
533. C32#3497semidirect
596. C4#64316semidirect
598. C3#85818semidirect
599. C3#86760semidirect

Maximal subgroups

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

subgroupindex
C2×#643162
#105960482
C3×Q8×D122
C3×C4×D3×Q82
#105953422
#105945232
#105943292
#105939702
#105939682
#105939032
#105939022
#867603
#858183