Finite Group Databasebeta

← D3×#4751 #11857653

Subgroups — D3×#4751 #11857653

Order 1152.

1587 conjugacy classes of subgroups.

The subgroup lattice has 845 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C211yesmaximal, characteristic
2D32×M16C212yesmaximal, complemented
3#10592450C211yesmaximal, characteristic, complemented
4C3×#4751C211yesmaximal, characteristic, complemented
5C3×D3×#101C211yesmaximal, characteristic, complemented
6#10591640C211yesmaximal, characteristic, complemented
7#10591637C211yesmaximal, characteristic, complemented
8D3×#836C211yesmaximal, characteristic, complemented
9#10591010C212yesmaximal, complemented
10#10591007C212yesmaximal, complemented
11D3×#823C212yesmaximal, complemented
12D3×#413—31nomaximal
13C2×#4751—31nomaximal
14C2×#3832C2211yescharacteristic
15C2×C3×#239C2211yescharacteristic
16C2×C3×D3×Q8C2211yescharacteristic
17D3×#239—22no—
18D3×#239—22no—
19D3×#239—22no—
20D3×#239—22no—
21C2×D3×D12C412yes—
22C2×D3×D12C2211yescharacteristic
23C2×C4×D32C412yes—
24C2×C4×D32C2211yescharacteristic
25C2×#3799C412yes—
26C2×#3799C2211yescharacteristic
27C2×#3796C412yes—
28C2×#3796C2211yescharacteristic
29M16×C3⋊D3C2212yescomplemented
30C3×D3×M16C2212yes—
31C3×D3×M16C2212yescomplemented
32#63818C2212yescomplemented
33D3×#208C2212yes—
34D3×#208C2212yescomplemented
35#63791—22no—
36D3×ΓL(1,𝔽25)—22no—
37D3×ΓL(1,𝔽25)—22no—
38D32×C8—22no—
39C32×#101C2211yescharacteristic, complemented
40#63663C2211yescharacteristic, complemented
41#63650C2212yescomplemented
42C3×#836C2211yescharacteristic, complemented
43C3×#836C2211yescharacteristic, complemented
44C3×#824C2212yescomplemented
45C3×#823C2212yescomplemented
46#63560C2212yescomplemented
47#63559C2212yescomplemented
48#63558C2212yescomplemented
49C2×D3×#41—31no—
50C22×#239—31no—
51C2×D3×M16—32no—
52C2×D3×M16—32no—
53C3×#413—31no—
54C2×C3×#101—31no—
55#5237—31no—
56C2×#836—31no—
57#5132—32no—
58C2×#823—32no—
59#4751—31no—
60#4751—32no—
61#4751—31no—
62#4751—31no—
63#4751—31no—
64#4751—31no—
65#4751—32no—
66#4751—61no—
67#4751D311yescharacteristic, direct product factor
68D3×#101—31no—
69D3×#101D311yescharacteristic, complemented
70#4745—32no—
71D3×#100—32no—
72C22×D32C2×C412yes—
73C22×D32C2×C411yescharacteristic
74C2×C32×Q8C2311yescharacteristic
75#3832—22no—
76#3832—22no—
77C2×C4⋊(C3⋊D3)C2×C412yes—
78C2×C4⋊(C3⋊D3)C2311yescharacteristic
79C2×C4×C3⋊D3C2×C412yes—
80C2×C4×C3⋊D3C2311yescharacteristic
81C3×#239—22no—
82C3×#239—22no—
83C3×D3×Q8—22no—
84C3×D3×Q8—22no—
85C2×C3×D12C2×C412yes—
86C2×C3×D12C2311yescharacteristic
87C2×C3×C4×D3C2×C412yes—
88C2×C3×C4×D3C2×C412yes—
89C2×C3×C4×D3C2311yescharacteristic
90C2×C3×C4×D3C2311yescharacteristic
91C2×C3×Dic6C2×C412yes—
92C2×C3×Dic6C2311yescharacteristic
93C2×#626C2×C412yes—
94C2×#626C2×C412yes—
95C2×#626C2×C412yes—
96C2×#624C2×C412yes—
97C2×#624C2×C411yescharacteristic
98C2×D3×Dic3C2×C412yes—
99C2×D3×Dic3C2×C411yescharacteristic
100C2×D3×Dic3C2×C411yescharacteristic
101D3×D12—24no—
102D3×D12—24no—
103D3×D12—22no—
104D3×D12—22no—
105C4×D32—22no—
106C4×D32—22no—
107C4×D32—22no—
108C4×D32—22no—
109C4×D32D412yes—
110C4×D32D412yes—
111C4×D32D412yes—
112C4×D32D412yes—
113#3799—22no—
114#3799—22no—
115#3799—24no—
116#3799—24no—
117#3796—22no—
118#3796—22no—
119#3796—24no—
120#3796—24no—
121C32×M16C2312yes—
122#3748C2312yes—
123#3743—22no—
124C8×C3⋊D3—22no—
125C3×#208C2312yes—
126C3×#208C2312yes—
127C3×ΓL(1,𝔽25)—22no—
128C3×ΓL(1,𝔽25)—22no—
129C3×D3×C8—22no—
130C3×D3×C8—22no—
131#3712—22no—
132#3711—22no—
133#3711—22no—
134#3710—22no—
135D3×C3⋊C8—22no—
136D3×C3⋊C8—22no—
137C2×#413—91noSylow
138C2×C3×#41—31no—
139C22×C3×Q8—31no—
140D3×#41—62no—
141D3×#41—62no—
142D3×#41—62no—
143D3×#41—62no—
144C2×#239—31no—
145C2×#239—31no—
146C2×#239—32no—
147C2×#239—31no—
148C2×#239—32no—
149C2×#239—31no—
150C2×#239—61no—
151C2×#239—62no—
152C2×#239—62no—
153C2×#239—62no—
154C2×#239—62no—
155C2×#239C2×D311yescharacteristic
156C2×D3×Q8C2×D311yescharacteristic
157C2×#237—32no—
158C2×#237—31no—
159C2×D3×D4—32no—
160C2×D3×D4—31no—
161C2×#235—32no—
162C2×#235—31no—
163C22×D12—32no—
164C22×D12—31no—
165C22×C4×D3—31no—
166C22×C4×D3—31no—
167C22×C4×D3—32no—
168C22×C4×D3—32no—
169C2×C3×M16—32no—
170C2×C3×M16—32no—
171C2×#208—32no—
172C2×#208—32no—
173D3×M16—32no—
174D3×M16—32no—
175D3×M16—32no—
176D3×M16—32no—
177D3×M16—32no—
178D3×M16—32no—
179D3×M16—62no—
180D3×M16—62no—
181D3×M16—62no—
182D3×M16—62no—
183D3×M16—62no—
184D3×M16C2×D312yes—
185D3×M16C2×D312yescomplemented
186C2×ΓL(1,𝔽25)—62no—
187C2×ΓL(1,𝔽25)—62no—
188C2×D3×C8—62no—
189C2×D3×C8—62no—
190C3×#101—21no—
191C3×#101—31no—
192C3×#101—31no—
193C3×#101—32no—
194C3×#101C2×D311yescharacteristic, complemented
195C3×#101C2×D311yescharacteristic, complemented
196C3×#100—32no—
197#836—31no—
198#836—31no—
199#836—32no—
200#836—61no—
201#836C2×D311yescharacteristic, complemented
202#836C2×D311yescharacteristic, complemented
203#833—32no—
204#824—32no—
205#824C2×D312yescomplemented
206#823—32no—
207#823—32no—
208#823—32no—
209#823—32no—
210#823—32no—
211#823—62no—
212#823C2×D312yescomplemented
213C22×C3⋊D3C22×C412yes—
214C22×C3⋊D3C22×C411yescharacteristic
215C22×C3×D3C22×C411yescharacteristic
216C22×C3×D3C22×C412yes—
217C22×C3×D3C22×C411yescharacteristic
218C2×D32—22no—
219C2×D32—22no—
220C2×D32—42no—
221C2×D32—44no—
222C2×D32C22⋊C412yes—
223C2×D32C22⋊C412yes—
224C32×Q8—22no—
225C2×C32×C4C22×C412yes—
226C2×C32×C4C2411yescharacteristic
227C2×C3⋊Dic3C22×C411yescharacteristic
228C4⋊(C3⋊D3)—24no—
229C4⋊(C3⋊D3)—22no—
230C4×C3⋊D3—22no—
231C4×C3⋊D3—22no—
232C4×C3⋊D3C2×D412yes—
233C4×C3⋊D3C2×D412yes—
234C2×C3×Dic3C22×C412yes—
235C2×C3×Dic3C22×C411yescharacteristic
236C2×C3×Dic3C22×C411yescharacteristic
237C3×D12—24no—
238C3×D12—22no—
239C3×C4×D3—22no—
240C3×C4×D3—22no—
241C3×C4×D3—22no—
242C3×C4×D3—22no—
243C3×C4×D3C2×D412yes—
244C3×C4×D3C2×D412yes—
245C3×C4×D3C2×D412yes—
246C3×C4×D3C2×D412yes—
247C3×Dic6—22no—
248C3×Dic6—24no—
249#626—24no—
250#626—24no—
251#626—24no—
252#624—22no—
253#624—22no—
254#624C22⋊C412yes—
255#624C22⋊C412yes—
256D3×Dic3—22no—
257D3×Dic3—22no—
258D3×Dic3C22⋊C412yes—
259D3×Dic3C22⋊C412yes—
260D3×Dic3C22⋊C411yescharacteristic
261D3×Dic3C22⋊C411yescharacteristic
262D3×Dic3C22⋊C411yescharacteristic
263D3×Dic3C22⋊C411yescharacteristic
264C32×C8—22no—
265C3⋊(C3⋊C8)—22no—
266C3×C3⋊C8—22no—
267C3×C3⋊C8—22no—
268C22×#41—91no—
269C22×M16—92no—
270#413—31no—
271#413—92no—
272#413—91no—
273#413—92no—
274#413—91no—
275#413—91no—
276C2×#101—31no—
277C2×#101—91no—
278C2×#100—92no—
279C23×D3—31no—
280C23×D3—31no—
281C23×D3—32no—
282C23×D3—32no—
283C3×#41—62no—
284C3×#41—62no—
285C2×C3×Q8—21no—
286C2×C3×Q8—32no—
287C2×C3×Q8—31no—
288C2×C3×Q8—62no—
289C2×C3×Q8—62no—
290C2×C3×Q8C22×D311yescharacteristic
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×D4—32no—
293C2×C3×D4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—32no—
297C22×C3×C4—32no—
298C2×#67—32no—
299C2×#67—32no—
300C2×#67—32no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—32no—
304#239—22no—
305#239—22no—
306#239—64no—
307#239—64no—
308#239—64no—
309#239—64no—
310#239—62no—
311#239—62no—
312#239—62no—
313#239—62no—
314#239—62no—
315#239—62no—
316#239—62no—
317#239—62no—
318#239—122no—
319#239—122no—
320D3×Q8—22no—
321D3×Q8—22no—
322#237—62no—
323#237—62no—
324#237—64no—
325#237—64no—
326D3×D4—64no—
327D3×D4—64no—
328D3×D4—62no—
329D3×D4—62no—
330#235—64no—
331#235—64no—
332#235—62no—
333#235—62no—
334C2×D12—32no—
335C2×D12—32no—
336C2×D12—32no—
337C2×D12—32no—
338C2×D12—32no—
339C2×D12—31no—
340C2×D12—31no—
341C2×D12—61no—
342C2×D12—62no—
343C2×D12—62no—
344C2×D12—62no—
345C2×D12—64no—
346C2×D12—64no—
347C2×D12C4×D312yes—
348C2×D12C22×D311yescharacteristic
349C2×C4×D3—31no—
350C2×C4×D3—31no—
351C2×C4×D3—31no—
352C2×C4×D3—31no—
353C2×C4×D3—31no—
354C2×C4×D3—31no—
355C2×C4×D3—32no—
356C2×C4×D3—32no—
357C2×C4×D3—32no—
358C2×C4×D3—32no—
359C2×C4×D3—32no—
360C2×C4×D3—32no—
361C2×C4×D3—32no—
362C2×C4×D3—32no—
363C2×C4×D3—32no—
364C2×C4×D3—32no—
365C2×C4×D3—32no—
366C2×C4×D3—32no—
367C2×C4×D3—32no—
368C2×C4×D3—61no—
369C2×C4×D3—62no—
370C2×C4×D3—62no—
371C2×C4×D3—62no—
372C2×C4×D3—62no—
373C2×C4×D3—62no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—62no—
378C2×C4×D3C4×D312yes—
379C2×C4×D3C4×D312yes—
380C2×C4×D3C22×D311yescharacteristic
381C2×C4×D3C22×D311yescharacteristic
382C2×Dic6C4×D312yes—
383C2×Dic6C22×D311yescharacteristic
384C3×M16—22no—
385C3×M16—32no—
386C3×M16—32no—
387C3×M16—62no—
388C3×M16—62no—
389C3×M16C22×D312yes—
390C3×M16C22×D312yes—
391C2×C3×C8—62no—
392C2×C3×C8—62no—
393#208—32no—
394#208—32no—
395#208—62no—
396#208—62no—
397#208—62no—
398#208C22×D312yes—
399#208C22×D312yes—
400C2×C3⋊C8—62no—
401C2×C3⋊C8—62no—
402ΓL(1,𝔽25)—22no—
403ΓL(1,𝔽25)—22no—
404ΓL(1,𝔽25)—62no—
405ΓL(1,𝔽25)—62no—
406ΓL(1,𝔽25)—62no—
407ΓL(1,𝔽25)—62no—
408ΓL(1,𝔽25)—62no—
409ΓL(1,𝔽25)—62no—
410ΓL(1,𝔽25)—122no—
411D3×C8—22no—
412D3×C8—22no—
413D3×C8—62no—
414D3×C8—62no—
415D3×C8—62no—
416D3×C8—62no—
417D3×C8—62no—
418D3×C8—62no—
419D3×C8—122no—
420C22×C32C23×C411yescharacteristic
421C2×C3⋊D3—22no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—42no—
424C2×C3⋊D3C2×C22⋊C412yes—
425C2×C3×D3—22no—
426C2×C3×D3—22no—
427C2×C3×D3—41no—
428C2×C3×D3—42no—
429C2×C3×D3C2×C22⋊C412yes—
430C2×C3×D3C2×C22⋊C411yescharacteristic
431C2×C3×D3C2×C22⋊C411yescharacteristic
432D32—24no—
433D32—42no—
434D32—44no—
435D32—44no—
436C32×C4—22no—
437C32×C4C22×D412yes—
438C3⋊Dic3C2×C22⋊C411yescharacteristic
439C3⋊Dic3C2×C22⋊C411yescharacteristic
440C3×Dic3—22no—
441C3×Dic3C2×C22⋊C411yescharacteristic
442C3×Dic3C2×C22⋊C411yescharacteristic
443C3×Dic3C2×C22⋊C412yes—
444C2×#41—31no—
445C2×#41—91no—
446C2×#41—92no—
447C2×#41—91no—
448C2×#41—92no—
449C2×#41—91no—
450C2×#41—182no—
451C2×#41—182no—
452C2×#41—182no—
453C2×#41—182no—
454C22×Q8—31no—
455C22×D4—91no—
456C22×D4—92no—
457C23×C4—91no—
458C23×C4—92no—
459C2×M16—32no—
460C2×M16—32no—
461C2×M16—92no—
462C2×M16—92no—
463C2×M16—92no—
464C2×M16—92no—
465C2×M16—182no—
466C2×M16—182no—
467C2×M16—182no—
468C22×C8—182no—
469#101—31no—
470#101—31no—
471#101—32no—
472#101—92no—
473#101—91no—
474#101D3211yescharacteristic, complemented
475#100—32no—
476#100—92no—
477#100—92no—
478#100—92no—
479C23×C3—31no—
480C23×C3—31no—
481C23×C3—32no—
482C22×D3—31no—
483C22×D3—31no—
484C22×D3—32no—
485C22×D3—32no—
486C22×D3—32no—
487C22×D3—32no—
488C22×D3—32no—
489C22×D3—32no—
490C22×D3—61no—
491C22×D3—62no—
492C22×D3—62no—
493C22×D3—62no—
494C22×D3—62no—
495C22×D3—62no—
496C22×D3—122no—
497C22×D3—124no—
498C22×D3—122no—
499C22×D3—124no—
500C22×D3C2×C4×D311yescharacteristic
501C22×D3C2×C4×D312yes—
502C22×D3C2×C4×D311yescharacteristic
503C3×Q8—22no—
504C3×Q8—22no—
505C3×Q8—42no—
506C3×Q8—64no—
507C3×Q8—62no—
508C3×D4—64no—
509C3×D4—62no—
510C2×C3×C4—21no—
511C2×C3×C4—22no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—32no—
515C2×C3×C4—32no—
516C2×C3×C4—32no—
517C2×C3×C4—32no—
518C2×C3×C4—32no—
519C2×C3×C4—62no—
520C2×C3×C4—62no—
521C2×C3×C4—62no—
522C2×C3×C4—62no—
523C2×C3×C4C2×C4×D312yes—
524C2×C3×C4C2×C4×D312yes—
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527#67—64no—
528#67—64no—
529#67—64no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—32no—
537C2×Dic3—32no—
538C2×Dic3—61no—
539C2×Dic3—62no—
540C2×Dic3—62no—
541C2×Dic3C2×C4×D312yes—
542C2×Dic3C2×C4×D311yescharacteristic
543C2×Dic3C2×C4×D311yescharacteristic
544D12—24no—
545D12—22no—
546D12—64no—
547D12—64no—
548D12—64no—
549D12—64no—
550D12—64no—
551D12—62no—
552D12—62no—
553D12—122no—
554D12—124no—
555C4×D3—22no—
556C4×D3—22no—
557C4×D3—22no—
558C4×D3—22no—
559C4×D3—31no—
560C4×D3—31no—
561C4×D3—31no—
562C4×D3—31no—
563C4×D3—32no—
564C4×D3—32no—
565C4×D3—32no—
566C4×D3—32no—
567C4×D3—32no—
568C4×D3—32no—
569C4×D3—32no—
570C4×D3—32no—
571C4×D3—32no—
572C4×D3—32no—
573C4×D3—62no—
574C4×D3—62no—
575C4×D3—62no—
576C4×D3—62no—
577C4×D3—62no—
578C4×D3—62no—
579C4×D3—62no—
580C4×D3—62no—
581C4×D3—62no—
582C4×D3—62no—
583C4×D3—62no—
584C4×D3—62no—
585C4×D3—122no—
586C4×D3—122no—
587C4×D3D3×D412yes—
588C4×D3D3×D412yes—
589C4×D3D3×D412yes—
590C4×D3D3×D412yes—
591Dic6—22no—
592Dic6—24no—
593C3×C8—22no—
594C3×C8—22no—
595C3×C8—42no—
596C3×C8—62no—
597C3×C8—62no—
598C3⋊C8—22no—
599C3⋊C8—22no—
600C3⋊C8—62no—
601C3⋊C8—62no—
602C3⋊C8—122no—
603C2×C32—21no—
604C2×C32C22×C22⋊C411yescharacteristic
605C3⋊D3—22no—
606C3⋊D3—42no—
607C3×D3—22no—
608C3×D3—21no—
609C3×D3—42no—
610C3×D3#41312yescomplemented
611C24—91no—
612C24—92no—
613#41—62no—
614#41—62no—
615#41—182no—
616#41—182no—
617#41—184no—
618#41—184no—
619#41—184no—
620#41—184no—
621#41—182no—
622#41—182no—
623#41—182no—
624#41—182no—
625C2×Q8—31no—
626C2×Q8—32no—
627C2×Q8—62no—
628C2×Q8—62no—
629C2×Q8C2×D3211yescharacteristic
630C2×D4—31no—
631C2×D4—32no—
632C2×D4—92no—
633C2×D4—92no—
634C2×D4—92no—
635C2×D4—91no—
636C2×D4—92no—
637C2×D4—182no—
638C2×D4—182no—
639C2×D4—184no—
640C2×D4—184no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—32no—
644C22×C4—32no—
645C22×C4—92no—
646C22×C4—92no—
647C22×C4—92no—
648C22×C4—92no—
649C22×C4—91no—
650C22×C4—92no—
651C22×C4—91no—
652C22×C4—91no—
653C22×C4—92no—
654C22×C4—91no—
655C22×C4—92no—
656C22×C4—182no—
657C22×C4—182no—
658C22×C4—182no—
659C22×C4—182no—
660M16—32no—
661M16—32no—
662M16—62no—
663M16—62no—
664M16—92no—
665M16—182no—
666M16—182no—
667M16—182no—
668M16—182no—
669M16C2×D3212yes—
670C2×C8—62no—
671C2×C8—62no—
672C2×C8—182no—
673C2×C8—182no—
674C2×C8—182no—
675C2×C8—182no—
676C22×C3—21no—
677C22×C3—31no—
678C22×C3—32no—
679C22×C3—31no—
680C22×C3—62no—
681C22×C3—62no—
682C22×C3—121no—
683C22×C3—122no—
684C22×C3C22×C4×D311yescharacteristic
685C22×C3C22×C4×D311yescharacteristic
686C2×D3—22no—
687C2×D3—22no—
688C2×D3—32no—
689C2×D3—32no—
690C2×D3—41no—
691C2×D3—42no—
692C2×D3—62no—
693C2×D3—64no—
694C2×D3—64no—
695C2×D3—62no—
696C2×D3—62no—
697C2×D3—122no—
698C2×D3—122no—
699C2×D3—122no—
700C2×D3—124no—
701C2×D3—124no—
702C2×D3—124no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—124no—
706C2×D3—122no—
707C2×D3—122no—
708C2×D3—241no—
709C2×D3—242no—
710C2×D3D3×C22⋊C411yescharacteristic
711C2×D3D3×C22⋊C412yes—
712C2×D3D3×C22⋊C411yescharacteristic
713C3×C4—22no—
714C3×C4—22no—
715C3×C4—22no—
716C3×C4—31no—
717C3×C4—31no—
718C3×C4—32no—
719C3×C4—42no—
720C3×C4—62no—
721C3×C4C2×D3×D412yes—
722C3×C4C2×D3×D412yes—
723Dic3—22no—
724Dic3—31no—
725Dic3—31no—
726Dic3—31no—
727Dic3—31no—
728Dic3—61no—
729Dic3—61no—
730Dic3D3×C22⋊C412yes—
731Dic3D3×C22⋊C411yescharacteristic
732Dic3D3×C22⋊C411yescharacteristic
733C32C2×#41311yescharacteristic, complemented, Sylow
734C23—31no—
735C23—31no—
736C23—32no—
737C23—92no—
738C23—92no—
739C23—91no—
740C23—92no—
741C23—182no—
742C23—182no—
743C23—362no—
744C23—364no—
745Q8—22no—
746Q8—64no—
747Q8—62no—
748D4—64no—
749D4—62no—
750D4—184no—
751D4—184no—
752D4—184no—
753D4—184no—
754D4—182no—
755C2×C4—31no—
756C2×C4—31no—
757C2×C4—32no—
758C2×C4—32no—
759C2×C4—32no—
760C2×C4—32no—
761C2×C4—32no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—92no—
767C2×C4—92no—
768C2×C4—91no—
769C2×C4—91no—
770C2×C4—91no—
771C2×C4—91no—
772C2×C4—92no—
773C2×C4—92no—
774C2×C4—91no—
775C2×C4—92no—
776C2×C4—92no—
777C2×C4—182no—
778C2×C4—182no—
779C2×C4—182no—
780C2×C4—182no—
781C2×C4—182no—
782C2×C4—182no—
783C2×C4C4×D3212yes—
784C2×C4C22×D3211yescharacteristic
785C8—22no—
786C8—62no—
787C8—62no—
788C8—182no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—32no—
793C2×C3—41no—
794C2×C3—62no—
795C2×C3—61no—
796C2×C3—122no—
797C2×C3C2×D3×C22⋊C411yescharacteristic
798C2×C3C2×D3×C22⋊C411yescharacteristic
799D3—21no—
800D3—22no—
801D3—42no—
802D3—62no—
803D3—62no—
804D3—122no—
805D3—122no—
806D3—122no—
807D3—242no—
808D3#475112yesdirect product factor
809C22—31no—
810C22—31no—
811C22—32no—
812C22—62no—
813C22—62no—
814C22—92no—
815C22—121no—
816C22—122no—
817C22—184no—
818C22—182no—
819C22—361no—
820C22—362no—
821C22—364no—
822C22—362no—
823C22—364no—
824C22C2×C4×D3211yescharacteristic
825C4—22no—
826C4—31no—
827C4—31no—
828C4—32no—
829C4—62no—
830C4—91no—
831C4—91no—
832C4D32×D412yes—
833C3—21no—
834C3C2×#475111yescharacteristic, complemented
835C3D3×#41311yescharacteristic, complemented
836C2—21no—
837C2—32no—
838C2—61no—
839C2—62no—
840C2—122no—
841C2—182no—
842C2—362no—
843C2D32×C22⋊C411yescharacteristic
subgroupG/H
centerC2D32×C22⋊C4
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC32×#101C22
socleC2×C32C22×C22⋊C4
prime radicalC2×D3×#239C2
cosocleC2×C32×C4C24
hypercenter#101D32
hypocenterC32C2×#413
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
2. D32×M16C2semidirect
3. #10592450C2semidirect
4. C3×#4751C2semidirect
5. C3×D3×#101C2semidirect
6. #10591640C2semidirect
7. #10591637C2semidirect
8. D3×#836C2semidirect
9. #10591010C2semidirect
10. #10591007C2semidirect
11. D3×#823C2semidirect
29. M16×C3⋊D3C22semidirect
31. C3×D3×M16C22semidirect
32. #63818C22semidirect
34. D3×#208C22semidirect
39. C32×#101C22semidirect
40. #63663C22semidirect
41. #63650C22semidirect
42. C3×#836C22semidirect
43. C3×#836C22semidirect
44. C3×#824C22semidirect
45. C3×#823C22semidirect
46. #63560C22semidirect
47. #63559C22semidirect
48. #63558C22semidirect
67. #4751D3direct (N × H)
69. D3×#101D3semidirect
185. D3×M16C2×D3semidirect
194. C3×#101C2×D3semidirect
195. C3×#101C2×D3semidirect
201. #836C2×D3semidirect
202. #836C2×D3semidirect
205. #824C2×D3semidirect
212. #823C2×D3semidirect
474. #101D32semidirect
610. C3×D3#413semidirect
733. C32C2×#413semidirect
808. D3#4751direct (N × H)
834. C3C2×#4751semidirect
835. C3D3×#413semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
D32×M162
#105924502
C3×#47512
C3×D3×#1012
#105916402
#105916372
D3×#8362
#105910102
#105910072
D3×#8232
D3×#4133
C2×#47513