Finite Group Databasebeta

← #11906056

Subgroups — #11906056

Order 1152.

3092 conjugacy classes of subgroups.

The subgroup lattice has 602 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×Q8×D12C211yesmaximal, characteristic, complemented
4C3×C4×#239C211yesmaximal, characteristic, complemented
5Q8×#626C212yesmaximal, complemented
6#10594381C216yesmaximal, complemented
7#10594380C216yesmaximal, complemented
8#10593968C213yesmaximal, complemented
9#10593896C213yesmaximal, complemented
10#10593895C213yesmaximal, complemented
11D3×#869C213yesmaximal, complemented
12#86746—31nomaximal
13#85827—31nomaximal
14C2×Q8×C3⋊D3C2212yes—
15C2×C3×#239C2211yescharacteristic
16C2×C3×D3×Q8C2212yes—
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×#897C2216yes—
28C3×#893C2213yes—
29C3×#892C2213yes—
30C3×C4×D12C2213yes—
31C3×C4×D12C2213yes—
32C3×C42×D3C2213yes—
33C3×#869C2213yes—
34#63918C2216yes—
35#63918C2213yes—
36#63911C2211yescharacteristic
37#63909C2213yes—
38#63908C2213yes—
39#63906C2216yes—
40C4×#626C2216yes—
41#63891C22112yes—
42#63890C22112yes—
43D3×C4⋊Dic3C2216yes—
44D3×C4⋊Dic3C2216yes—
45#63871C2216yes—
46#63866C2216yes—
47#63857C2216yes—
48#63852C2216yes—
49C2×#1010—32no—
50C2×#1007—32no—
51C3×D4×Q8—31no—
52C3×C4×#41—31no—
53Q8×#67—32no—
54#5726—33no—
55D3×C4⋊Q8—33no—
56#5631—36no—
57#5628—36no—
58Q8×D12—32no—
59Q8×D12—31no—
60Q8×D12—31no—
61Q8×D12—61no—
62Q8×D12D311yescharacteristic, complemented
63C4×#239D311yescharacteristic, complemented
64#5555—36no—
65#5555—33no—
66#5555—33no—
67#5551—33no—
68#5548—33no—
69#5526—36no—
70#5477—33no—
71C2×#869—33no—
72C2×C32×Q8C2311yescharacteristic
73Q8×C3⋊D3—28no—
74C2×C4⋊(C3⋊D3)C2311yescharacteristic
75C2×C4×C3⋊D3C2316yes—
76C2×#634C2316yes—
77C3×#239D418yescomplemented
78C3×D3×Q8—28no—
79C2×C3×D12C2311yescharacteristic
80C2×C3×D12C2313yes—
81C2×C3×C4×D3C2313yes—
82C2×C3×C4×D3C2316yes—
83C2×C3×C4×D3C2313yes—
84C2×C3×C4×D3C2313yes—
85C2×C3×Dic6C2316yes—
86C2×#627C2316yes—
87C2×#626C2316yes—
88C2×#626C2312yes—
89C2×#626C2312yes—
90C2×#625C2316yes—
91C2×D3×Dic3C23112yes—
92#3798—224no—
93#3796—224no—
94#3795—224no—
95D3×Dic6—224no—
96C32×C4⋊C4C2313yes—
97C32×C42C2313yes—
98#3752C2316yes—
99C4⋊(C3⋊Dic3)C2313yes—
100C4⋊(C3⋊Dic3)C2316yes—
101C3×(C2×D3)⋊C4C2316yes—
102C3×(C2×D3)⋊C4C2316yes—
103C3×C4⋊Dic3C2313yes—
104C3×C4⋊Dic3C2316yes—
105C3×C4⋊Dic3C2313yes—
106C3×C4×Dic3C2313yes—
107C3×C4×Dic3C2313yes—
108C3×C4×Dic3C2311yescharacteristic
109Dic3⋊Dic3C23112yes—
110Dic3⋊Dic3C2316yes—
111#3722C2316yes—
112(C2×D3)⋊Dic3C2316yes—
113#3499—91noSylow
114C2×C3×#41—31no—
115C22×C3×Q8—32no—
116#1010—616no—
117#1007—616no—
118C2×#239—36no—
119C2×#239C2×D311yescharacteristic
120C2×D3×Q8—32no—
121C2×D3×Q8—32no—
122C2×D3×Q8—36no—
123C2×D3×Q8—62no—
124C2×D3×Q8C2×D312yes—
125C2×#237—36no—
126C2×#237—36no—
127C2×#235—36no—
128C2×#235—36no—
129C2×#235—36no—
130C22×Dic6—36no—
131C3×C4⋊Q8—33no—
132C3×C22⋊Q8—36no—
133C3×C4×Q8—21no—
134C3×C4×Q8—31no—
135C3×C4×Q8C2×D311yescharacteristic
136C3×C4×Q8C2×D311yescharacteristic
137C3×C4×D4—33no—
138C3×C4×D4—33no—
139C3×C4×D4—33no—
140C3×#117—33no—
141C2×C3×C42—33no—
142#946—36no—
143Q8×Dic3C2×D311yescharacteristic
144#944—36no—
145#940—31no—
146#938—33no—
147#930—33no—
148#930—36no—
149#930—33no—
150C4×#67—36no—
151C2×C4⋊Dic3—36no—
152C2×C4⋊Dic3—36no—
153#924—36no—
154#897—36no—
155#897—36no—
156#897—36no—
157#897—36no—
158#897—66no—
159#897C2×D316yes—
160#895—33no—
161#894—312no—
162#893C2×D313yes—
163#892C2×D313yes—
164D3×C4⋊C4—36no—
165D3×C4⋊C4—36no—
166#888—33no—
167#888—36no—
168#886—312no—
169#886—312no—
170#885—36no—
171#884—36no—
172#883—312no—
173#875—36no—
174#874—31no—
175C4×D12—36no—
176C4×D12—33no—
177C4×D12—33no—
178C4×D12—63no—
179C4×D12C2×D313yes—
180C4×D12C2×D313yes—
181C42×D3C2×D313yes—
182#869—36no—
183#869—33no—
184#869—33no—
185#869—33no—
186#869—36no—
187#869—63no—
188#869C2×D313yes—
189C22×C3⋊D3C2412yes—
190C22×C3×D3C2412yes—
191C22×C3×D3C2413yes—
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×Dic3C2413yes—
201C2×C3×Dic3C2416yes—
202C2×C3×Dic3C2411yescharacteristic
203C2×C3×Dic3C2411yescharacteristic
204C3×D12—22no—
205C3×D12C2×D4112yes—
206C3×C4×D3—212no—
207C3×C4×D3—26no—
208C3×C4×D3—26no—
209C3×C4×D3C2×D4112yes—
210C3×Dic6—212no—
211#627—212no—
212#626—212no—
213#626—24no—
214#626—24no—
215#625—212no—
216D3×Dic3—224no—
217C2×2−1+4—92no—
218D4×Q8—31no—
219D4×Q8—92no—
220D4×Q8—91no—
221#547—93no—
222#547—96no—
223#547—93no—
224#536—96no—
225#532—93no—
226C2×C4⋊Q8—93no—
227C4×#41—31no—
228C3×#41—38no—
229C2×C3×Q8—21no—
230C2×C3×Q8—36no—
231C2×C3×Q8—68no—
232C2×C3×Q8C22×D311yescharacteristic
233C2×C3×Q8C22×D311yescharacteristic
234C2×C3×D4—33no—
235C2×C3×D4—31no—
236C22×C3×C4—33no—
237C22×C3×C4—36no—
238C22×C3×C4—33no—
239C22×C3×C4—33no—
240C2×#67—36no—
241C2×#67—36no—
242C2×#67—32no—
243C2×#67—32no—
244C2×#67—36no—
245C22×Dic3—312no—
246#239—624no—
247#239D1218yescomplemented
248D3×Q8—28no—
249D3×Q8—68no—
250D3×Q8—68no—
251D3×Q8—624no—
252D3×Q8—128no—
253#237—624no—
254#237—624no—
255#235—624no—
256#235—624no—
257#235—624no—
258C2×D12—32no—
259C2×D12—32no—
260C2×D12—36no—
261C2×D12—31no—
262C2×D12—31no—
263C2×D12—61no—
264C2×D12C22×D311yescharacteristic
265C2×D12C22×D313yes—
266C2×C4×D3—312no—
267C2×C4×D3—36no—
268C2×C4×D3—36no—
269C2×C4×D3—66no—
270C2×C4×D3C22×D313yes—
271C2×C4×D3C22×D313yes—
272C2×C4×D3C22×D316yes—
273C2×C4×D3C22×D313yes—
274C2×Dic6—36no—
275C2×Dic6—36no—
276C2×Dic6—36no—
277C2×Dic6—36no—
278C2×Dic6—66no—
279C2×Dic6—624no—
280C2×Dic6C22×D316yes—
281C3×C4⋊C4—23no—
282C3×C4⋊C4—33no—
283C3×C4⋊C4—36no—
284C3×C4⋊C4—33no—
285C3×C4⋊C4C22×D313yes—
286C3×C4⋊C4C22×D313yes—
287C3×C22⋊C4—36no—
288C3×C22⋊C4—36no—
289C3×C42—23no—
290C3×C42—31no—
291C3×C42—33no—
292C3×C42—33no—
293C3×C42C22×D313yes—
294C3×C42C22×D313yes—
295#217—36no—
296(C2×D3)⋊C4—36no—
297(C2×D3)⋊C4—36no—
298(C2×D3)⋊C4—36no—
299(C2×D3)⋊C4—36no—
300(C2×D3)⋊C4—36no—
301(C2×D3)⋊C4—66no—
302(C2×D3)⋊C4C22×D316yes—
303(C2×D3)⋊C4C22×D316yes—
304C4⋊Dic3—33no—
305C4⋊Dic3—33no—
306C4⋊Dic3—36no—
307C4⋊Dic3—36no—
308C4⋊Dic3—36no—
309C4⋊Dic3—312no—
310C4⋊Dic3—63no—
311C4⋊Dic3—66no—
312C4⋊Dic3C22×D313yes—
313C4⋊Dic3C22×D316yes—
314C4⋊Dic3C22×D313yes—
315Dic3⋊C4—312no—
316Dic3⋊C4—36no—
317C4×Dic3C22×D311yescharacteristic
318C4×Dic3C22×D313yes—
319C4×Dic3C22×D313yes—
320C22×C32C2511yescharacteristic
321C2×C3⋊D3—22no—
322C2×C3⋊D3—22no—
323C2×C3⋊D3—22no—
324C2×C3×D3—23no—
325C2×C3×D3—23no—
326C2×C3×D3—22no—
327C2×C3×D3—22no—
328C2×C3×D3—22no—
329C2×C3×D3C22×D416yes—
330C32×C4—23no—
331C32×C4C22×D416yes—
332C32×C42−1+412yescomplemented
333C3⋊Dic3—26no—
334C3×Dic3—26no—
335C3×Dic3—23no—
336C3×Dic3C22×D412yes—
337C3×Dic32−1+412yescomplemented
3382−1+4—1816no—
339C2×#41—31no—
340C2×#41—96no—
341C2×#41—96no—
342C2×#41—96no—
343C22×Q8—32no—
344C22×Q8—96no—
345C22×Q8—92no—
346C4⋊Q8—33no—
347C4⋊Q8—93no—
348C4⋊Q8—96no—
349C4⋊Q8—96no—
350C4⋊Q8—93no—
351#127—91no—
352#124—96no—
353#123—912no—
354#123—912no—
355C22⋊Q8—36no—
356C22⋊Q8—96no—
357C22⋊Q8—96no—
358C22⋊Q8—96no—
359#121—96no—
360#121—93no—
361#121—93no—
362C4×Q8—31no—
363C4×Q8D3211yescharacteristic
364C4×D4—33no—
365C4×D4—33no—
366C4×D4—33no—
367C4×D4—96no—
368C4×D4—93no—
369#117—33no—
370C2×C4⋊C4—96no—
371C2×C4⋊C4—96no—
372C2×C42—33no—
373C23×C3—33no—
374C23×C3—32no—
375C22×D3—32no—
376C22×D3—32no—
377C22×D3—62no—
378C22×D3C23×D312yes—
379C22×D3C23×D313yes—
380C3×Q8—24no—
381C3×Q8—612no—
382C3×Q8C2×D1214yes—
383C3×Q8D3×D414yes—
384C3×D4—312no—
385C3×D4—62no—
386C2×C3×C4—21no—
387C2×C3×C4—23no—
388C2×C3×C4—23no—
389C2×C3×C4—31no—
390C2×C3×C4—31no—
391C2×C3×C4—312no—
392C2×C3×C4—36no—
393C2×C3×C4—33no—
394C2×C3×C4—66no—
395C2×C3×C4—612no—
396C2×C3×C4—66no—
397C2×C3×C4C23×D313yes—
398C2×C3×C4C23×D313yes—
399C2×C3×C4C23×D313yes—
400C2×C3×C4C23×D313yes—
401C2×C3×C4C23×D311yescharacteristic
402C2×C3×C4C23×D311yescharacteristic
403#67—612no—
404#67—612no—
405#67—612no—
406#67—64no—
407#67—64no—
408C2×Dic3—36no—
409C2×Dic3—36no—
410C2×Dic3—66no—
411C2×Dic3—624no—
412C2×Dic3C23×D313yes—
413C2×Dic3C23×D316yes—
414C2×Dic3C23×D311yescharacteristic
415C2×Dic3C23×D311yescharacteristic
416D12—22no—
417D12—64no—
418D12—64no—
419D12—64no—
420D12—612no—
421D12—62no—
422D12—62no—
423D12C2×D12112yes—
424C4×D3—212no—
425C4×D3—26no—
426C4×D3—26no—
427C4×D3—624no—
428C4×D3—612no—
429C4×D3—612no—
430C4×D3—1212no—
431C4×D3C2×D12112yes—
432Dic6—212no—
433Dic6—612no—
434Dic6—612no—
435Dic6—612no—
436Dic6—612no—
437Dic6—1212no—
438C2×C32C23×D411yescharacteristic
439C2×C32C2×2−1+411yescharacteristic
440C2×C32C2×2−1+411yescharacteristic
441C3⋊D3—42no—
442C3×D3—26no—
443C3×D3—42no—
444#41—38no—
445#41—1824no—
446#41—1824no—
447#41—1824no—
448C2×Q8—36no—
449C2×Q8—68no—
450C2×Q8—96no—
451C2×Q8—96no—
452C2×Q8—1824no—
453C2×Q8—188no—
454C2×Q8C2×D3211yescharacteristic
455C2×D4—33no—
456C2×D4—31no—
457C2×D4—92no—
458C2×D4—96no—
459C2×D4—92no—
460C2×D4—96no—
461C2×D4—91no—
462C22×C4—33no—
463C22×C4—33no—
464C22×C4—33no—
465C22×C4—36no—
466C22×C4—912no—
467C22×C4—96no—
468C4⋊C4—33no—
469C4⋊C4—36no—
470C4⋊C4—33no—
471C4⋊C4—96no—
472C4⋊C4—912no—
473C4⋊C4—93no—
474C4⋊C4—96no—
475C4⋊C4C2×D3213yes—
476C22⋊C4—36no—
477C22⋊C4—36no—
478C22⋊C4—96no—
479C22⋊C4—96no—
480C22⋊C4—96no—
481C42—31no—
482C42—33no—
483C42—33no—
484C42C2×D3213yes—
485C22×C3—21no—
486C22×C3—36no—
487C22×C3—63no—
488C22×C3—63no—
489C22×C3—62no—
490C22×C3—62no—
491C22×C3—62no—
492C22×C3C24×D311yescharacteristic
493C22×C3C24×D311yescharacteristic
494C2×D3—23no—
495C2×D3—23no—
496C2×D3—22no—
497C2×D3—22no—
498C2×D3—22no—
499C2×D3—64no—
500C2×D3—62no—
501C2×D3—62no—
502C2×D3—62no—
503C2×D3—62no—
504C2×D3—62no—
505C2×D3—62no—
506C2×D3—122no—
507C2×D3—122no—
508C2×D3C22×D1216yes—
509C3×C4—23no—
510C3×C4—23no—
511C3×C4—26no—
512C3×C4—22no—
513C3×C4—32no—
514C3×C4—32no—
515C3×C4—43no—
516C3×C4—66no—
517C3×C4—63no—
518C3×C4C22×D1216yes—
519C3×C4C2×D3×D416yes—
520C3×C4#100712yescomplemented
521C3×C4#101012yescomplemented
522Dic3—26no—
523Dic3—23no—
524Dic3—66no—
525Dic3—66no—
526Dic3—126no—
527Dic3C22×D1212yes—
528Dic3#101012yescomplemented
529C32#349911yescharacteristic, complemented, Sylow
530C23—33no—
531C23—32no—
532C23—92no—
533Q8—612no—
534Q8—1812no—
535Q8—1812no—
536Q8D3×D1214yes—
537D4—312no—
538D4—62no—
539D4—184no—
540D4—184no—
541D4—1812no—
542D4—1812no—
543D4—182no—
544C2×C4—31no—
545C2×C4—31no—
546C2×C4—312no—
547C2×C4—33no—
548C2×C4—36no—
549C2×C4—66no—
550C2×C4—612no—
551C2×C4—66no—
552C2×C4—96no—
553C2×C4—1824no—
554C2×C4—1812no—
555C2×C4C22×D3213yes—
556C2×C4C22×D3213yes—
557C2×C4C22×D3211yescharacteristic
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—66no—
562C2×C3—122no—
563C2×C3C23×D1211yescharacteristic
564C2×C3C22×D3×D411yescharacteristic
565C2×C3C2×#100711yescharacteristic
566C2×C3C2×#101011yescharacteristic
567C2×C3C2×#101011yescharacteristic
568C2×C3D3×2−1+411yescharacteristic
569D3—26no—
570D3—42no—
571D3—124no—
572D3—122no—
573D3—122no—
574C22—36no—
575C22—63no—
576C22—63no—
577C22—62no—
578C22—62no—
579C22—62no—
580C22—182no—
581C22—182no—
582C22—182no—
583C22C23×D3211yescharacteristic
584C4—23no—
585C4—32no—
586C4—32no—
587C4—66no—
588C4—63no—
589C4—186no—
590C4C2×D3×D1216yes—
591C4#6431512yescomplemented
592C3—21no—
593C3#8582711yescharacteristic, complemented
594C3#8674611yescharacteristic, complemented
595C2—66no—
596C2—122no—
597C2—362no—
598C2C22×D3×D1211yescharacteristic
599C2C2×#6431511yescharacteristic
600C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3499
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×Q8×D12C2semidirect
4. C3×C4×#239C2semidirect
5. Q8×#626C2semidirect
6. #10594381C2semidirect
7. #10594380C2semidirect
8. #10593968C2semidirect
9. #10593896C2semidirect
10. #10593895C2semidirect
11. D3×#869C2semidirect
62. Q8×D12D3semidirect
63. C4×#239D3semidirect
77. C3×#239D4semidirect
247. #239D12semidirect
332. C32×C42−1+4semidirect
337. C3×Dic32−1+4semidirect
520. C3×C4#1007semidirect
521. C3×C4#1010semidirect
528. Dic3#1010semidirect
529. C32#3499semidirect
591. C4#64315semidirect
593. C3#85827semidirect
594. C3#86746semidirect

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×Q8×D122
C3×C4×#2392
Q8×#6262
#105943812
#105943802
#105939682
#105938962
#105938952
D3×#8692
#867463
#858273