Finite Group Databasebeta

← #11707342

Subgroups — #11707342

Order 768.

7694 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3503C211yesmaximal, characteristic, complemented
2#87043C214yesmaximal, complemented
3#87023C212yesmaximal, complemented
4#87017C212yesmaximal, complemented
5#86929C2112yesmaximal, complemented
6#86751C216yesmaximal, complemented
7D4×#239C216yesmaximal, complemented
8#86597C216yesmaximal, complemented
9#86596C216yesmaximal, complemented
10#86276C213yesmaximal, complemented
11#86259C213yesmaximal, complemented
12C2×#5726C213yesmaximal, complemented
13#86205C213yesmaximal, complemented
14#85900C212yesmaximal, complemented
15D3×#520C212yesmaximal, complemented
16#41×D12C211yesmaximal, characteristic, complemented
17C4×#1009C211yesmaximal, characteristic, complemented
18#62985—31nomaximal, Sylow
19C2×#1009C2211yescharacteristic
20C2×D3×#41C2212yes—
21C22×#239C2216yescomplemented
22C3×Q82C2212yescomplemented
23C3×#557C2212yescomplemented
24C3×#554C2216yescomplemented
25C3×D4×Q8C2216yescomplemented
26C3×#544C2216yescomplemented
27C3×#533C2213yescomplemented
28C2×C3×C4⋊Q8C2213yescomplemented
29C3×#520C2212yes—
30C3×C4×#41C2211yescharacteristic
31#5827C2211yescharacteristic
32#5817C22112yescomplemented
33C2×#946C2216yescomplemented
34#5734C2213yescomplemented
35#5734C2216yescomplemented
36#5733C22112yescomplemented
37#5733C22112yescomplemented
38#5732C2213yescomplemented
39#5730C22112yescomplemented
40#5730C2211yescharacteristic, complemented
41#5730C2216yescomplemented
42#5728C2216yescomplemented
43#5726C22112yescomplemented
44#5726C22112yescomplemented
45#5726C2213yescomplemented
46#5726C22112yescomplemented
47#5726C2216yescomplemented
48#5726C2216yescomplemented
49#5726C2216yescomplemented
50#5725C22112yescomplemented
51#5725C2216yescomplemented
52#5697C22112yescomplemented
53#5695C2216yescomplemented
54#5695C22112yescomplemented
55#5695C22112yescomplemented
56#5694C2216yescomplemented
57#5694C22112yescomplemented
58#5691C22112yescomplemented
59#5645C22124yescomplemented
60#5644C22112yescomplemented
61#5642C2216yescomplemented
62#5637C22112yescomplemented
63#5637C22124yescomplemented
64#5630C2216yescomplemented
65#5630C22124yescomplemented
66#5627C22124yescomplemented
67#5627C22112yescomplemented
68#5585C22112yescomplemented
69#5584C2216yescomplemented
70#5580C22112yescomplemented
71#5580C2216yescomplemented
72#5577C2214yescomplemented
73#5577C2211yescharacteristic, complemented
74#5577C2216yescomplemented
75#5576C2212yescomplemented
76#5576C2214yescomplemented
77Q8×D12C2211yescharacteristic, complemented
78#5574C2212yescomplemented
79#5574C2214yescomplemented
80C4×#239C2216yescomplemented
81C4×#239C2212yescomplemented
82C4×D3×Q8C2214yescomplemented
83#5555C2213yescomplemented
84#5554C2216yescomplemented
85#5554C22112yescomplemented
86D4×D12C2213yescomplemented
87D4×D12C22112yescomplemented
88#5546C22112yescomplemented
89#5545C2216yescomplemented
90C4×D3×D4C2216yescomplemented
91C4×D3×D4C22112yescomplemented
92#5525C2216yescomplemented
93#5524C2216yescomplemented
94#5524C2216yescomplemented
95#5523C2213yescomplemented
96#5523C2216yescomplemented
97#5521C2213yescomplemented
98D3×#117C2216yescomplemented
99#5514C22112yescomplemented
100#5510C2216yescomplemented
101C2×#895C2216yescomplemented
102C2×#894C22112yescomplemented
103#5504C2216yescomplemented
104C2×D3×C4⋊C4C2216yescomplemented
105#5477C2213yescomplemented
106C4×#235C2213yescomplemented
107C2×C4×D12C2213yescomplemented
108C2×C4×D12C2213yescomplemented
109#3522—34no—
110#3520—36no—
111#3517—32no—
112#3513—312no—
113#3511—33no—
114#3506—33no—
115#3503D311yescharacteristic, complemented
116#3494—36no—
117#3492—36no—
118#3488—32no—
119#3482—32no—
120#3475—33no—
121D4×#41—36no—
122D4×#41—31no—
123C2×#547—33no—
124C4×H(5,𝔽2)—31no—
125C2×#520—32no—
126C2×C3×#41C2311yescharacteristic
127C22×C3×Q8C2316yes—
128#1009—28no—
129D3×#41—216no—
130C2×#239—424no—
131C2×#239C2316yes—
132C2×#239C2312yes—
133C2×#239C2312yes—
134C2×#239C23124yes—
135C2×#239C23112yes—
136C2×D3×Q8C2312yes—
137C2×#237C2316yes—
138C2×D3×D4C2316yes—
139C2×D3×D4C2316yes—
140C2×#235C2316yes—
141C2×#235C2313yes—
142C22×D12C2313yes—
143C22×D12C2313yes—
144C22×D12C23112yes—
145C22×C4×D3C2316yes—
146C22×C4×D3C2316yes—
147C22×C4×D3C23112yes—
148C3×C4⋊Q8C23112yes—
149C3×C4⋊Q8C2316yes—
150C3×C4⋊Q8C2316yes—
151C3×C4⋊Q8C2313yes—
152C3×C4⋊Q8C2316yes—
153C3×C4⋊Q8C2311yescharacteristic
154C3×#125C23112yes—
155C3×#125C2316yes—
156C3×C22⋊Q8C2316yes—
157C3×C22⋊Q8C23124yes—
158C3×C22⋊Q8C2316yes—
159C3×C4×Q8C2311yescharacteristic
160C3×C4×Q8C2314yes—
161C3×C4×Q8C2316yes—
162C3×C4×Q8C2311yescharacteristic
163C3×C4×Q8C2316yes—
164C3×C4×D4C2313yes—
165C3×C4×D4C23112yes—
166C3×C4×D4C2313yes—
167C3×#117C2316yes—
168C3×#117C2313yes—
169C2×C3×C4⋊C4C2316yes—
170C2×C3×C4⋊C4C2316yes—
171C2×C3×C42C2313yes—
172#947C23112yes—
173#947C23124yes—
174#947C2316yes—
175#946C2314yes—
176#946C23124yes—
177#946C2316yes—
178#946C23124yes—
179#946C23112yes—
180Q8×Dic3C2316yes—
181Q8×Dic3C2312yes—
182D4×Dic3C2316yes—
183#930C2316yes—
184#930C23124yes—
185#930C2316yes—
186C4×#67C2316yes—
187C4×#67C23124yes—
188C4×#67C2316yes—
189C2×(C2×D3)⋊C4C2316yes—
190C2×(C2×D3)⋊C4C23112yes—
191C2×(C2×D3)⋊C4C2316yes—
192#926C2313yes—
193C2×C4⋊Dic3C2313yes—
194C2×C4⋊Dic3C2313yes—
195C2×Dic3⋊C4C23112yes—
196#898C23112yes—
197#898C23124yes—
198#898C23112yes—
199#898C23112yes—
200#897C2316yes—
201#897C2312yes—
202#897C23112yes—
203#897C2316yes—
204#897C2316yes—
205#895C23124yes—
206#895C23112yes—
207#895C2316yes—
208#895C2316yes—
209#895C23112yes—
210#895C23112yes—
211#895C2316yes—
212#895C23112yes—
213#895C23112yes—
214#895C23112yes—
215#895C2316yes—
216#895C2316yes—
217#894C23112yes—
218#894C23124yes—
219#894C23112yes—
220#894C23124yes—
221#894C23124yes—
222#894C23124yes—
223#894C23112yes—
224#893C23112yes—
225#893C23124yes—
226#893C2316yes—
227#893C23112yes—
228#893C23112yes—
229#893C2316yes—
230#893C2312yes—
231#892C23112yes—
232#892C23112yes—
233#892C2316yes—
234#892C2316yes—
235#892C2316yes—
236#892C2316yes—
237D3×C4⋊C4C2316yes—
238D3×C4⋊C4C23112yes—
239D3×C4⋊C4C2312yes—
240D3×C4⋊C4C23112yes—
241D3×C4⋊C4C23112yes—
242D3×C4⋊C4C2316yes—
243#890C2312yes—
244#890C23112yes—
245#890C23112yes—
246#887C23112yes—
247#886C23112yes—
248#886C23112yes—
249#882C23124yes—
250#882C23112yes—
251#882C23112yes—
252#67⋊C4C23124yes—
253#67⋊C4C23112yes—
254D3×C22⋊C4C23112yes—
255D3×C22⋊C4C23112yes—
256#877C23112yes—
257#875C23112yes—
258#875C2316yes—
259#874C23112yes—
260#874C2313yes—
261C4×D12C2316yes—
262C4×D12C23112yes—
263C4×D12C2316yes—
264C4×D12C2313yes—
265C4×D12C2316yes—
266C4×D12C23112yes—
267C4×D12C23112yes—
268C4×D12C2311yescharacteristic
269C4×D12C2313yes—
270C4×D12C2313yes—
271C4×D12C2316yes—
272C4×D12C2316yes—
273C4×D12C2313yes—
274C4×D12C2316yes—
275C4×D12C2313yes—
276#872C23112yes—
277#872C2316yes—
278C42×D3C23112yes—
279C42×D3C2316yes—
280#869C2313yes—
281C4×Dic6C2313yes—
282C4×Dic6C23112yes—
283C4×Dic6C2311yescharacteristic
284C2×H(5,𝔽2)—31no—
285C22×#41—32no—
286C22×#41—36no—
287#559—312no—
288Q82C2×D312yescomplemented
289#557C2×D312yescomplemented
290#556—33no—
291#556—36no—
292#555—33no—
293#555—36no—
294#554—31no—
295#554—36no—
296#554—312no—
297#554C2×D316yescomplemented
298#553—36no—
299#553—312no—
300#553—312no—
301#553—312no—
302#552—36no—
303#552—312no—
304#552—36no—
305#551—312no—
306#551—324no—
307#550—36no—
308#550—31no—
309#550—34no—
310D4×Q8—31no—
311D4×Q8C2×D316yescomplemented
312#548—312no—
313#548—32no—
314#548—34no—
315#547—33no—
316#547—36no—
317#547—312no—
318#547—36no—
319#547—312no—
320#547—36no—
321#547—312no—
322#547—33no—
323#546—36no—
324#546—324no—
325#546—36no—
326#546—312no—
327D42—33no—
328D42—312no—
329#544C2×D316yescomplemented
330#542—312no—
331#542—312no—
332#540—312no—
333#539—324no—
334#538—312no—
335#537—36no—
336#535—36no—
337#533—36no—
338#533C2×D313yescomplemented
339#532—312no—
340#532—36no—
341#532—33no—
342C2×C4⋊Q8C2×D313yescomplemented
343#529—312no—
344#529—312no—
345#529—36no—
346#525—324no—
347#525—312no—
348#525—36no—
349#525—36no—
350C2×#123—312no—
351C2×C22⋊Q8—36no—
352C2×#121—36no—
353#520—31no—
354#520—34no—
355#520—32no—
356#520—312no—
357#520—36no—
358#520—33no—
359#520—36no—
360#520C2×D312yes—
361#518—36no—
362#518—33no—
363C4×#41—32no—
364C4×#41—36no—
365C4×#41—33no—
366C4×#41C2×D311yescharacteristic
367C2×C4×Q8—34no—
368C2×C4×D4—312no—
369C2×C4×D4—36no—
370C2×C4×D4—33no—
371C2×C4×D4—33no—
372C2×#117—36no—
373C22×C4⋊C4—36no—
374C23×D3C2416yes—
375C23×D3C2416yes—
376C3×#41#4118yescomplemented
377C2×C3×Q8—412no—
378C2×C3×Q8C2416yes—
379C2×C3×Q8C24112yes—
380C2×C3×Q8C2412yes—
381C2×C3×Q8C2411yescharacteristic
382C2×C3×D4C2413yes—
383C22×C3×C4C2413yes—
384C22×C3×C4C24112yes—
385C22×C3×C4C2413yes—
386C22×C3×C4C2413yes—
387C2×#67C24112yes—
388C2×#67C2416yes—
389C22×Dic3C2416yes—
390C22×Dic3C2416yes—
391#239—28no—
392#239—28no—
393#239—224no—
394#239—448no—
395#239—424no—
396D3×Q8—28no—
397#237—224no—
398D3×D4—224no—
399D3×D4—224no—
400#235—224no—
401#235—212no—
402C2×D12—212no—
403C2×D12—212no—
404C2×D12—424no—
405C2×D12C2413yes—
406C2×D12C2416yes—
407C2×D12C2416yes—
408C2×D12C2413yes—
409C2×D12C2416yes—
410C2×D12C24112yes—
411C2×D12C24112yes—
412C2×D12C2416yes—
413C2×D12C24124yes—
414C2×D12C2411yescharacteristic
415C2×C4×D3—224no—
416C2×C4×D3—412no—
417C2×C4×D3—424no—
418C2×C4×D3C2416yes—
419C2×C4×D3C2416yes—
420C2×C4×D3C2416yes—
421C2×C4×D3C24112yes—
422C2×C4×D3C2416yes—
423C2×C4×D3C2412yes—
424C2×C4×D3C2416yes—
425C2×C4×D3C2414yes—
426C2×C4×D3C2416yes—
427C2×C4×D3C24112yes—
428C2×C4×D3C24124yes—
429C2×Dic6C2411yescharacteristic
430C2×Dic6C2416yes—
431C3×C4⋊C4C24112yes—
432C3×C4⋊C4C2412yes—
433C3×C4⋊C4C24112yes—
434C3×C4⋊C4C24112yes—
435C3×C4⋊C4C2416yes—
436C3×C4⋊C4C2413yes—
437C3×C4⋊C4C2412yes—
438C3×C4⋊C4C2413yes—
439C3×C4⋊C4C24112yes—
440C3×C4⋊C4C2416yes—
441C3×C22⋊C4C24112yes—
442C3×C22⋊C4C2416yes—
443C3×C42C24112yes—
444C3×C42C2411yescharacteristic
445C3×C42C2413yes—
446C3×C42C2413yes—
447C3×C42C2413yes—
448#217C2416yes—
449(C2×D3)⋊C4C2416yes—
450(C2×D3)⋊C4C24112yes—
451(C2×D3)⋊C4C2416yes—
452(C2×D3)⋊C4C24112yes—
453(C2×D3)⋊C4C2412yes—
454(C2×D3)⋊C4C2414yes—
455(C2×D3)⋊C4C2416yes—
456(C2×D3)⋊C4C24112yes—
457(C2×D3)⋊C4C2416yes—
458(C2×D3)⋊C4C2416yes—
459(C2×D3)⋊C4C24112yes—
460(C2×D3)⋊C4C24112yes—
461(C2×D3)⋊C4C24112yes—
462(C2×D3)⋊C4C24112yes—
463(C2×D3)⋊C4C24124yes—
464C4⋊Dic3C2416yes—
465C4⋊Dic3C2413yes—
466C4⋊Dic3C2411yescharacteristic
467C4⋊Dic3C2413yes—
468C4⋊Dic3C2416yes—
469C4⋊Dic3C2411yescharacteristic
470C4⋊Dic3C2414yes—
471C4⋊Dic3C2416yes—
472C4⋊Dic3C24112yes—
473Dic3⋊C4C2412yes—
474Dic3⋊C4C2416yes—
475Dic3⋊C4C24124yes—
476Dic3⋊C4C2414yes—
477Dic3⋊C4C24112yes—
478C4×Dic3C24112yes—
479C4×Dic3C2412yes—
480C4×Dic3C2416yes—
481C4×Dic3C2416yes—
482C4×Dic3C24112yes—
483H(5,𝔽2)—68no—
484C2×#41—32no—
485C2×#41—36no—
486C2×#41—32no—
487C2×#41—324no—
488C2×#41—312no—
489C2×#41—36no—
490C2×#41—33no—
491C2×#41—36no—
492C2×#41—616no—
493C2×#41—1224no—
494C2×#41C22×D311yescharacteristic
495C22×Q8—32no—
496C22×Q8C22×D316yes—
497C22×D4—36no—
498C22×D4—36no—
499C22×D4—33no—
500C22×D4—33no—
501C22×D4—312no—
502C23×C4—36no—
503C23×C4—312no—
504C23×C4—36no—
505C4⋊Q8—33no—
506C4⋊Q8C22×D313yes—
507C4⋊Q8C22×D316yes—
508C4⋊Q8C22×D316yes—
509C4⋊Q8C22×D316yes—
510C4⋊Q8C22×D3112yes—
511C4⋊Q8C22×D311yescharacteristic
512#127—33no—
513#127—312no—
514#126—324no—
515#126—312no—
516#126—312no—
517#126—312no—
518#125—32no—
519#125—312no—
520#125—312no—
521#125C22×D3112yes—
522#125C22×D316yes—
523#124—36no—
524#124—312no—
525#124—324no—
526#124—312no—
527#124—36no—
528#123—312no—
529#123—324no—
530#123—324no—
531#123—324no—
532#123—312no—
533#123—324no—
534#123—312no—
535#123—312no—
536#123—312no—
537C22⋊Q8—36no—
538C22⋊Q8—312no—
539C22⋊Q8—324no—
540C22⋊Q8—324no—
541C22⋊Q8—34no—
542C22⋊Q8—32no—
543C22⋊Q8—36no—
544C22⋊Q8—36no—
545C22⋊Q8—36no—
546C22⋊Q8—312no—
547C22⋊Q8C22×D316yes—
548C22⋊Q8C22×D3124yes—
549C22⋊Q8C22×D316yes—
550#121—36no—
551#121—324no—
552#121—36no—
553#121—36no—
554#121—312no—
555#121—312no—
556#121—312no—
557#121—36no—
558#121—36no—
559#121—36no—
560#121—324no—
561#121—36no—
562#121—312no—
563#121—312no—
564#121—312no—
565#120—312no—
566#120—312no—
567#120—324no—
568C4×Q8—32no—
569C4×Q8—36no—
570C4×Q8—312no—
571C4×Q8—312no—
572C4×Q8—31no—
573C4×Q8—33no—
574C4×Q8C22×D314yes—
575C4×Q8C22×D311yescharacteristic
576C4×Q8C22×D316yes—
577C4×Q8C22×D311yescharacteristic
578C4×Q8C22×D316yes—
579C4×D4—36no—
580C4×D4—36no—
581C4×D4—324no—
582C4×D4—36no—
583C4×D4—36no—
584C4×D4—312no—
585C4×D4—32no—
586C4×D4—36no—
587C4×D4—312no—
588C4×D4—324no—
589C4×D4—312no—
590C4×D4—312no—
591C4×D4—324no—
592C4×D4—31no—
593C4×D4—33no—
594C4×D4—36no—
595C4×D4—33no—
596C4×D4—36no—
597C4×D4—36no—
598C4×D4—312no—
599C4×D4—36no—
600C4×D4—36no—
601C4×D4—33no—
602C4×D4—33no—
603C4×D4—33no—
604C4×D4—312no—
605C4×D4—36no—
606C4×D4—312no—
607C4×D4C22×D313yes—
608C4×D4C22×D3112yes—
609C4×D4C22×D313yes—
610#117—33no—
611#117—36no—
612#117—36no—
613#117—36no—
614#117—312no—
615#117—36no—
616#117—312no—
617#117—312no—
618#117—312no—
619#117—36no—
620#117C22×D316yes—
621#117C22×D313yes—
622C2×C4⋊C4—33no—
623C2×C4⋊C4—312no—
624C2×C4⋊C4—33no—
625C2×C4⋊C4—36no—
626C2×C4⋊C4—312no—
627C2×C4⋊C4—312no—
628C2×C4⋊C4—312no—
629C2×C4⋊C4—32no—
630C2×C4⋊C4—36no—
631C2×C4⋊C4C22×D316yes—
632C2×C4⋊C4C22×D316yes—
633C2×C22⋊C4—36no—
634C2×C22⋊C4—36no—
635C2×C22⋊C4—312no—
636C2×C22⋊C4—312no—
637C2×C22⋊C4—312no—
638C2×C42—312no—
639C2×C42—36no—
640C2×C42C22×D313yes—
641C23×C3C2513yes—
642C22×D3—212no—
643C22×D3—212no—
644C22×D3—212no—
645C22×D3—46no—
646C22×D3—46no—
647C22×D3—46no—
648C22×D3C2516yes—
649C22×D3C2516yes—
650C22×D3C2512yes—
651C3×Q8—212no—
652C3×Q8—412no—
653C3×Q8—42no—
654C3×Q8C2×#4114yescomplemented
655C3×D4C2×#41112yescomplemented
656C2×C3×C4—26no—
657C2×C3×C4—412no—
658C2×C3×C4—43no—
659C2×C3×C4C2×#41112yescomplemented
660C2×C3×C4C2514yes—
661C2×C3×C4C2513yes—
662C2×C3×C4C25112yes—
663C2×C3×C4C2513yes—
664C2×C3×C4C2511yescharacteristic
665C2×C3×C4C2513yes—
666C2×C3×C4C2511yescharacteristic
667C2×C3×C4C2511yescharacteristic
668#67—212no—
669#67—224no—
670C2×Dic3—212no—
671C2×Dic3—46no—
672C2×Dic3C2512yes—
673C2×Dic3C2516yes—
674C2×Dic3C2512yes—
675C2×Dic3C2516yes—
676C2×Dic3C2512yes—
677D12—212no—
678D12—224no—
679D12—26no—
680D12—212no—
681D12—212no—
682D12—26no—
683D12—424no—
684D12—46no—
685D12—412no—
686D12H(5,𝔽2)14yescomplemented
687C4×D3—224no—
688C4×D3—24no—
689C4×D3—212no—
690C4×D3—212no—
691C4×D3—212no—
692C4×D3—212no—
693C4×D3—212no—
694C4×D3—424no—
695C4×D3—412no—
696C4×D3—46no—
697C4×D3—44no—
698Dic6—22no—
699Dic6—212no—
700C24—36no—
701C24—36no—
702#41—624no—
703#41—68no—
704#41—68no—
705#41—624no—
706#41—624no—
707#41—612no—
708#41—1248no—
709#41—1224no—
710#41#23918yescomplemented
711C2×Q8—31no—
712C2×Q8—36no—
713C2×Q8—412no—
714C2×Q8—68no—
715C2×Q8C23×D316yes—
716C2×Q8C23×D312yes—
717C2×Q8C23×D3112yes—
718C2×Q8C23×D311yescharacteristic
719C2×D4—312no—
720C2×D4—36no—
721C2×D4—31no—
722C2×D4—33no—
723C2×D4—36no—
724C2×D4—36no—
725C2×D4—36no—
726C2×D4—312no—
727C2×D4—33no—
728C2×D4—312no—
729C2×D4—36no—
730C2×D4—324no—
731C2×D4—612no—
732C2×D4—624no—
733C2×D4—624no—
734C2×D4—612no—
735C2×D4—1224no—
736C2×D4C23×D313yes—
737C22×C4—36no—
738C22×C4—36no—
739C22×C4—36no—
740C22×C4—312no—
741C22×C4—36no—
742C22×C4—36no—
743C22×C4—32no—
744C22×C4—36no—
745C22×C4—36no—
746C22×C4—34no—
747C22×C4—36no—
748C22×C4—312no—
749C22×C4—324no—
750C22×C4—624no—
751C22×C4—1212no—
752C22×C4—1224no—
753C22×C4C23×D313yes—
754C22×C4C23×D313yes—
755C22×C4C23×D3112yes—
756C22×C4C23×D313yes—
757C4⋊C4—33no—
758C4⋊C4—36no—
759C4⋊C4—312no—
760C4⋊C4—31no—
761C4⋊C4—324no—
762C4⋊C4—31no—
763C4⋊C4—36no—
764C4⋊C4—34no—
765C4⋊C4—33no—
766C4⋊C4—36no—
767C4⋊C4—32no—
768C4⋊C4—36no—
769C4⋊C4—312no—
770C4⋊C4—34no—
771C4⋊C4C23×D316yes—
772C4⋊C4C23×D3112yes—
773C4⋊C4C23×D313yes—
774C4⋊C4C23×D312yes—
775C4⋊C4C23×D316yes—
776C4⋊C4C23×D3112yes—
777C4⋊C4C23×D312yes—
778C4⋊C4C23×D313yes—
779C4⋊C4C23×D3112yes—
780C4⋊C4C23×D3112yes—
781C22⋊C4—36no—
782C22⋊C4—32no—
783C22⋊C4—312no—
784C22⋊C4—36no—
785C22⋊C4—36no—
786C22⋊C4—312no—
787C22⋊C4—36no—
788C22⋊C4—312no—
789C22⋊C4—312no—
790C22⋊C4—324no—
791C22⋊C4—36no—
792C22⋊C4—36no—
793C22⋊C4—34no—
794C22⋊C4—312no—
795C22⋊C4—312no—
796C22⋊C4—312no—
797C22⋊C4C23×D316yes—
798C22⋊C4C23×D3112yes—
799C42—36no—
800C42—32no—
801C42—36no—
802C42—312no—
803C42—312no—
804C42C23×D313yes—
805C42C23×D3112yes—
806C42C23×D311yescharacteristic
807C42C23×D313yes—
808C42C23×D313yes—
809C22×C3—23no—
810C22×C3—23no—
811C22×C3C22×#4116yes—
812C22×C3C2611yescharacteristic
813C2×D3—22no—
814C2×D3—22no—
815C2×D3—26no—
816C2×D3—26no—
817C2×D3—26no—
818C2×D3—26no—
819C2×D3—26no—
820C2×D3—26no—
821C2×D3—424no—
822C2×D3—812no—
823C2×D3C2×H(5,𝔽2)14yes—
824C3×C4—212no—
825C3×C4—23no—
826C3×C4—23no—
827C3×C4—24no—
828C3×C4—21no—
829C3×C4C22×#4116yes—
830C3×C4C22×#4112yes—
831C3×C4C2×H(5,𝔽2)12yes—
832Dic3—26no—
833Dic3—22no—
834Dic3—22no—
835Dic3—26no—
836Dic3—22no—
837C23—32no—
838C23—36no—
839C23—36no—
840C23—612no—
841C23—612no—
842C23—612no—
843C23—126no—
844C23—126no—
845C23—126no—
846C23C24×D313yes—
847Q8—212no—
848Q8—412no—
849Q8—42no—
850Q8—612no—
851Q8—62no—
852Q8C2×#23914yescomplemented
853D4—34no—
854D4—612no—
855D4—624no—
856D4—612no—
857D4—624no—
858D4—66no—
859D4—612no—
860D4—612no—
861D4—66no—
862D4—1224no—
863D4—126no—
864D4—1212no—
865D4C2×#239112yescomplemented
866C2×C4—26no—
867C2×C4—32no—
868C2×C4—36no—
869C2×C4—32no—
870C2×C4—36no—
871C2×C4—32no—
872C2×C4—412no—
873C2×C4—43no—
874C2×C4—624no—
875C2×C4—612no—
876C2×C4—64no—
877C2×C4—612no—
878C2×C4—612no—
879C2×C4—612no—
880C2×C4—612no—
881C2×C4—612no—
882C2×C4—1212no—
883C2×C4—1224no—
884C2×C4—126no—
885C2×C4—124no—
886C2×C4—126no—
887C2×C4C2×#239112yescomplemented
888C2×C4C24×D314yes—
889C2×C4C24×D313yes—
890C2×C4C24×D3112yes—
891C2×C4C24×D311yescharacteristic
892C2×C4C24×D313yes—
893C2×C4C24×D313yes—
894C2×C4C24×D311yescharacteristic
895C2×C4C24×D311yescharacteristic
896C2×C3—26no—
897C2×C3C23×#4111yescharacteristic
898C2×C3C22×H(5,𝔽2)11yescharacteristic
899C2×C32−1+611yescharacteristic
900D3—24no—
901D3—46no—
902D3—46no—
903C22—23no—
904C22—23no—
905C22—34no—
906C22—62no—
907C22—62no—
908C22—66no—
909C22—66no—
910C22—66no—
911C22—66no—
912C22—66no—
913C22—66no—
914C22—1224no—
915C22—2412no—
916C22C22×#23916yes—
917C22C25×D311yescharacteristic
918C4—23no—
919C4—212no—
920C4—21no—
921C4—23no—
922C4—24no—
923C4—62no—
924C4—62no—
925C4—66no—
926C4—66no—
927C4—62no—
928C4C22×#23912yes—
929C4C22×#23916yes—
930C4D3×H(5,𝔽2)12yes—
931C3#6298511yescharacteristic, complemented, Sylow
932C2—26no—
933C2—64no—
934C2—126no—
935C2—126no—
936C2C23×#23911yescharacteristic
937C2C2×D3×H(5,𝔽2)11yescharacteristic
938C2#8757111yescharacteristic
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC3×#3503C2
hypercenter#3503D3
hypocenterC3#62985
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. C3×#3503C2semidirect
2. #87043C2semidirect
3. #87023C2semidirect
4. #87017C2semidirect
5. #86929C2semidirect
6. #86751C2semidirect
7. D4×#239C2semidirect
8. #86597C2semidirect
9. #86596C2semidirect
10. #86276C2semidirect
11. #86259C2semidirect
12. C2×#5726C2semidirect
13. #86205C2semidirect
14. #85900C2semidirect
15. D3×#520C2semidirect
16. #41×D12C2semidirect
17. C4×#1009C2semidirect
21. C22×#239C22semidirect
22. C3×Q82C22semidirect
23. C3×#557C22semidirect
24. C3×#554C22semidirect
25. C3×D4×Q8C22semidirect
26. C3×#544C22semidirect
27. C3×#533C22semidirect
28. C2×C3×C4⋊Q8C22semidirect
32. #5817C22semidirect
33. C2×#946C22semidirect
34. #5734C22semidirect
35. #5734C22semidirect
36. #5733C22semidirect
37. #5733C22semidirect
38. #5732C22semidirect
39. #5730C22semidirect
40. #5730C22semidirect
41. #5730C22semidirect
42. #5728C22semidirect
43. #5726C22semidirect
44. #5726C22semidirect
45. #5726C22semidirect
46. #5726C22semidirect
47. #5726C22semidirect
48. #5726C22semidirect
49. #5726C22semidirect
50. #5725C22semidirect
51. #5725C22semidirect
52. #5697C22semidirect
53. #5695C22semidirect
54. #5695C22semidirect
55. #5695C22semidirect
56. #5694C22semidirect
57. #5694C22semidirect
58. #5691C22semidirect
59. #5645C22semidirect
60. #5644C22semidirect
61. #5642C22semidirect
62. #5637C22semidirect
63. #5637C22semidirect
64. #5630C22semidirect
65. #5630C22semidirect
66. #5627C22semidirect
67. #5627C22semidirect
68. #5585C22semidirect
69. #5584C22semidirect
70. #5580C22semidirect
71. #5580C22semidirect
72. #5577C22semidirect
73. #5577C22semidirect
74. #5577C22semidirect
75. #5576C22semidirect
76. #5576C22semidirect
77. Q8×D12C22semidirect
78. #5574C22semidirect
79. #5574C22semidirect
80. C4×#239C22semidirect
81. C4×#239C22semidirect
82. C4×D3×Q8C22semidirect
83. #5555C22semidirect
84. #5554C22semidirect
85. #5554C22semidirect
86. D4×D12C22semidirect
87. D4×D12C22semidirect
88. #5546C22semidirect
89. #5545C22semidirect
90. C4×D3×D4C22semidirect
91. C4×D3×D4C22semidirect
92. #5525C22semidirect
93. #5524C22semidirect
94. #5524C22semidirect
95. #5523C22semidirect
96. #5523C22semidirect
97. #5521C22semidirect
98. D3×#117C22semidirect
99. #5514C22semidirect
100. #5510C22semidirect
101. C2×#895C22semidirect
102. C2×#894C22semidirect
103. #5504C22semidirect
104. C2×D3×C4⋊C4C22semidirect
105. #5477C22semidirect
106. C4×#235C22semidirect
107. C2×C4×D12C22semidirect
108. C2×C4×D12C22semidirect
115. #3503D3semidirect
288. Q82C2×D3semidirect
289. #557C2×D3semidirect
297. #554C2×D3semidirect
311. D4×Q8C2×D3semidirect
329. #544C2×D3semidirect
338. #533C2×D3semidirect
342. C2×C4⋊Q8C2×D3semidirect
376. C3×#41#41semidirect
654. C3×Q8C2×#41semidirect
655. C3×D4C2×#41semidirect
659. C2×C3×C4C2×#41semidirect
686. D12H(5,𝔽2)semidirect
710. #41#239semidirect
852. Q8C2×#239semidirect
865. D4C2×#239semidirect
887. C2×C4C2×#239semidirect
931. C3#62985semidirect

Maximal subgroups

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

subgroupindex
C3×#35032
#870432
#870232
#870172
#869292
#867512
D4×#2392
#865972
#865962
#862762
#862592
C2×#57262
#862052
#859002
D3×#5202
#41×D122
C4×#10092
#629853