Finite Group Databasebeta

← D3×#63808 #13167783

Subgroups — D3×#63808 #13167783

Order 1728.

1286 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#3799C212yesmaximal, complemented
2#11723654C211yesmaximal, characteristic, complemented
3#11723341C211yesmaximal, characteristic, complemented
4#11723337C211yesmaximal, characteristic, complemented
5D3×#3745C211yesmaximal, characteristic, complemented
6C3×#63808C211yesmaximal, characteristic, complemented
7C3×D3×Dic12C211yesmaximal, characteristic, complemented
8C3×D32×C8C211yesmaximal, characteristic, complemented
9#11722865C212yesmaximal, complemented
10#11722856C212yesmaximal, complemented
11D3×#3717C212yesmaximal, complemented
12D3×#919—31nomaximal
13C2×#63808—31nomaximal
14D3×#904—31nomaximal
15#89041C2212yescomplemented
16D3×C4⋊(C3⋊D3)C2212yes—
17#89022C2212yescomplemented
18#89018C2212yescomplemented
19C3×C4×D32C2211yescharacteristic
20C3×#3799C2212yescomplemented
21C3×D3×Dic6C2212yes—
22#88965—22no—
23#88962—22no—
24D3×#626—22no—
25D3×#624—22no—
26#88852C2211yescharacteristic, complemented
27C3×#3746C2211yescharacteristic, complemented
28C3×#3745C2211yescharacteristic, complemented
29C3×C8×C3⋊D3C2211yescharacteristic, complemented
30C32×Dic12C2211yescharacteristic, complemented
31C32×D3×C8C2211yescharacteristic
32C32×D3×C8C2211yescharacteristic, complemented
33#88811C2212yescomplemented
34#88797C2212yescomplemented
35#88795C2212yescomplemented
36#88791C2212yescomplemented
37C3×#3719C2212yescomplemented
38C3×#3717C2212yescomplemented
39C3×#3710C2211yescharacteristic, complemented
40C3×D3×C3⋊C8C2211yescharacteristic
41C3×D3×C3⋊C8C2211yescharacteristic, complemented
42D3×#239—32no—
43D3×#235—32no—
44C2×#3799—32no—
45#64128—31no—
46#64113—31no—
47C2×#3745—31no—
48C3×#919—31no—
49C3×D3×Q16—31no—
50C2×C3×Dic12—31no—
51C3×#904—31no—
52C2×C3×D3×C8—31no—
53C2×C3×D3×C8—31no—
54#63950—32no—
55#63949—32no—
56D3×#215—32no—
57C2×#3717—32no—
58#63829—32no—
59#63810—31no—
60#63808—32no—
61#63808—31no—
62#63808—31no—
63#63808—31no—
64#63808—31no—
65#63808—31no—
66#63808—32no—
67#63808—61no—
68#63808—61no—
69#63808D311yescharacteristic, direct product factor
70#63807—31no—
71#63806—32no—
72D3×Dic12D311yescharacteristic, complemented
73D3×D24—31no—
74D3×D24—31no—
75D3×D24—61no—
76D3×#204—32no—
77D32×C8D311yescharacteristic, complemented
78C2×D3×C3⋊D3—22no—
79C2×C3×D32D411yescharacteristic
80C4⋊(C3⋊(C3⋊D3))C2312yes—
81C3×C4⋊(C3⋊D3)C2312yes—
82C3×C4×C3⋊D3C2311yescharacteristic
83C3×#634C2312yes—
84C32×C4×D3C2311yescharacteristic
85C32×C4×D3C2311yescharacteristic
86C32×Dic6C2312yes—
87#6295—22no—
88#6294—22no—
89#6292—22no—
90#6292—22no—
91#6291—22no—
92#6289—22no—
93#6289—22no—
94C3×#627—22no—
95C3×#626—22no—
96C3×#624—22no—
97C3×#624D411yescharacteristic
98C3×D3×Dic3—22no—
99C3×D3×Dic3D411yescharacteristic
100C3×D3×Dic3D411yescharacteristic
101C33×C8C2311yescharacteristic
102C3×C3⋊(C3⋊C8)C2311yescharacteristic
103C32×C3⋊C8C2311yescharacteristic
104C32×C3⋊C8C2311yescharacteristic
105D3×#135—91no—
106C2×#919—91no—
107C2×#904—91no—
108#3832—32no—
109#3828—32no—
110C2×C4⋊(C3⋊D3)—32no—
111C3×#239—32no—
112C3×D3×Q8—32no—
113C3×#235—32no—
114C2×C3×C4×D3—31no—
115C2×C3×C4×D3—31no—
116C2×C3×Dic6—32no—
117D3×#67—62no—
118C2×#626—62no—
119C2×#624—62no—
120#3804—62no—
121D3×D12—32no—
122D3×D12—32no—
123D3×D12—62no—
124D3×D12—62no—
125C4×D32—62no—
126C4×D32—62no—
127C4×D32C2×D311yescharacteristic
128#3799—32no—
129#3799—32no—
130#3799—32no—
131#3799—32no—
132#3799—32no—
133#3799—62no—
134#3799—62no—
135#3799—62no—
136#3799—62no—
137#3799—62no—
138#3799C2×D312yescomplemented
139#3798—62no—
140#3796—32no—
141#3796—62no—
142#3795—32no—
143D3×Dic6C2×D312yes—
144C32×Q16—31no—
145C2×C32×C8—31no—
146C2×C32×C8—31no—
147#3755—32no—
148#3746C2×D311yescharacteristic, complemented
149#3745—32no—
150#3745—31no—
151#3745—31no—
152#3745—31no—
153#3745—61no—
154#3745—61no—
155#3745—61no—
156#3745—121no—
157#3745C2×D311yescharacteristic, complemented
158#3744—32no—
159C8×C3⋊D3C2×D311yescharacteristic, complemented
160C3×#216—32no—
161C3×#215—32no—
162C2×C3×C3⋊C8—31no—
163C2×C3×C3⋊C8—31no—
164C3×Dic12—21no—
165C3×Dic12—32no—
166C3×Dic12—31no—
167C3×Dic12—31no—
168C3×Dic12—61no—
169C3×Dic12C2×D311yescharacteristic, complemented
170C3×Dic12C2×D311yescharacteristic, complemented
171C3×D24—31no—
172C3×D24—31no—
173C3×D24—61no—
174C3×#204—32no—
175C3×D3×C8—21no—
176C3×D3×C8—21no—
177C3×D3×C8—31no—
178C3×D3×C8—31no—
179C3×D3×C8—31no—
180C3×D3×C8—31no—
181C3×D3×C8—31no—
182C3×D3×C8—31no—
183C3×D3×C8—61no—
184C3×D3×C8C2×D311yescharacteristic
185C3×D3×C8C2×D311yescharacteristic
186C3×D3×C8C2×D311yescharacteristic, complemented
187C3×D3×C8C2×D311yescharacteristic, complemented
188#3719C2×D312yescomplemented
189#3717—32no—
190#3717—32no—
191#3717—32no—
192#3717—32no—
193#3717—32no—
194#3717—62no—
195#3717—62no—
196#3717C2×D312yescomplemented
197#3716—32no—
198#3715—32no—
199#3714—32no—
200#3714—32no—
201#3714—62no—
202#3710C2×D311yescharacteristic, complemented
203D3×C3⋊C8C2×D311yescharacteristic
204D3×C3⋊C8C2×D311yescharacteristic, complemented
205C2×C3⋊(C3⋊D3)—22no—
206C2×C3×C3⋊D3—22no—
207C2×C3×C3⋊D3C2×D411yescharacteristic
208C2×C32×D3C2×D411yescharacteristic
209C2×C32×D3C2×D411yescharacteristic
210D3×C3⋊D3—44no—
211C3×D32—22no—
212C33×C4C2411yescharacteristic
213C3×C3⋊Dic3—22no—
214C3×C3⋊Dic3C2×D411yescharacteristic
215C32×Dic3—22no—
216C32×Dic3C2×D411yescharacteristic
217C32×Dic3C2×D411yescharacteristic
218D3×#41—92no—
219C2×#239—92no—
220C2×#235—92no—
221C3×#135—91no—
222C2×C3×Q16—91no—
223C22×C3×C8—91no—
224#950—92no—
225C2×#215—92no—
226#919—31no—
227#919—91no—
228#919—92no—
229#919—91no—
230#919—91no—
231#919—92no—
232#919—91no—
233#919—181no—
234D3×Q16—31no—
235#916—92no—
236D3×SD16—92no—
237#912—91no—
238D3×D8—91no—
239C2×Dic12—31no—
240#904—31no—
241#904—92no—
242#904—91no—
243#904—91no—
244#904—91no—
245#904—92no—
246#904—91no—
247#904—181no—
248C2×D24—91no—
249C2×D24—91no—
250C2×D24—181no—
251C2×#204—92no—
252C2×D3×C8—31no—
253C2×D3×C8—31no—
254C22×C3⋊D3—62no—
255C22×C3×D3—31no—
256C22×C3×D3—31no—
257C2×D32—62no—
258C2×D32—62no—
259C2×D32—122no—
260C2×D32D1211yescharacteristic
261C32×Q8—32no—
262C2×C32×C4—31no—
263C2×C32×C4—31no—
264#638—62no—
265C4⋊(C3⋊D3)—32no—
266C4⋊(C3⋊D3)—32no—
267C4⋊(C3⋊D3)—32no—
268C4⋊(C3⋊D3)—62no—
269C4⋊(C3⋊D3)—62no—
270C4⋊(C3⋊D3)—62no—
271C4⋊(C3⋊D3)—62no—
272C4⋊(C3⋊D3)—62no—
273C4⋊(C3⋊D3)—122no—
274C4⋊(C3⋊D3)C22×D312yes—
275C4×C3⋊D3—62no—
276C4×C3⋊D3—62no—
277C4×C3⋊D3C22×D311yescharacteristic
278#634C22×D312yes—
279C3×#67—62no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—62no—
283C3×D12—32no—
284C3×D12—32no—
285C3×D12—62no—
286C3×D12—62no—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—31no—
290C3×C4×D3—31no—
291C3×C4×D3—31no—
292C3×C4×D3—31no—
293C3×C4×D3—31no—
294C3×C4×D3—31no—
295C3×C4×D3—61no—
296C3×C4×D3—62no—
297C3×C4×D3—62no—
298C3×C4×D3—62no—
299C3×C4×D3C22×D311yescharacteristic
300C3×C4×D3C22×D311yescharacteristic
301C3×C4×D3C22×D311yescharacteristic
302C3×C4×D3C22×D311yescharacteristic
303C3×Dic6—22no—
304C3×Dic6—32no—
305C3×Dic6—32no—
306C3×Dic6—62no—
307C3×Dic6—62no—
308C3×Dic6—62no—
309C3×Dic6C22×D312yes—
310C3×Dic6C22×D312yes—
311#627—22no—
312#626—22no—
313#626—62no—
314#626—62no—
315#626—62no—
316#626—62no—
317#626—62no—
318#626—62no—
319#626—62no—
320#626—62no—
321#626—122no—
322#626—122no—
323#626—122no—
324#625—62no—
325#624—22no—
326#624—62no—
327#624—62no—
328#624—62no—
329#624—62no—
330#624—62no—
331#624—122no—
332#624—122no—
333#624D1211yescharacteristic
334D3×Dic3—22no—
335D3×Dic3—62no—
336D3×Dic3—62no—
337D3×Dic3D1211yescharacteristic
338D3×Dic3D1211yescharacteristic
339C32×C8—21no—
340C32×C8—21no—
341C32×C8—21no—
342C32×C8—31no—
343C32×C8—31no—
344C32×C8—41no—
345C32×C8C22×D311yescharacteristic
346C32×C8C22×D311yescharacteristic
347C32×C8C22×D311yescharacteristic
348C3⋊(C3⋊C8)C22×D311yescharacteristic
349C3×C3⋊C8—21no—
350C3×C3⋊C8—21no—
351C3×C3⋊C8—31no—
352C3×C3⋊C8—31no—
353C3×C3⋊C8—61no—
354C3×C3⋊C8C22×D311yescharacteristic
355C3×C3⋊C8C22×D311yescharacteristic
356C3×C3⋊C8C22×D311yescharacteristic
357C3×C3⋊C8C22×D311yescharacteristic
358C2×#135—271noSylow
359C2×C33C22×D411yescharacteristic
360C3⋊(C3⋊D3)—42no—
361C3×C3⋊D3—21no—
362C3×C3⋊D3—42no—
363C32×D3—21no—
364C32×D3#13512yescomplemented
365C3×#41—92no—
366C2×C3×Q8—92no—
367C22×C3×C4—91no—
368C2×#67—182no—
369#239—32no—
370#239—92no—
371#239—92no—
372#239—92no—
373#239—92no—
374#239—182no—
375#239—182no—
376#239—182no—
377D3×Q8—32no—
378#237—92no—
379#237—182no—
380D3×D4—92no—
381D3×D4—182no—
382#235—32no—
383#235—92no—
384#235—92no—
385#235—92no—
386#235—92no—
387#235—182no—
388#235—182no—
389#235—182no—
390#235—182no—
391C2×D12—92no—
392C2×D12—92no—
393C2×D12—182no—
394C2×D12—182no—
395C2×C4×D3—31no—
396C2×C4×D3—31no—
397C2×C4×D3—182no—
398C2×C4×D3—182no—
399C2×C4×D3—182no—
400C2×Dic6—32no—
401C3×Q16—31no—
402C3×Q16—31no—
403C3×Q16—61no—
404C3×Q16—92no—
405C3×Q16—91no—
406C3×SD16—92no—
407C3×D8—91no—
408C2×C3×C8—31no—
409C2×C3×C8—31no—
410C2×C3×C8—31no—
411C2×C3×C8—31no—
412C2×C3×C8—61no—
413C2×C3×C8—61no—
414C2×C3×C8—91no—
415C2×C3×C8—91no—
416C2×C3×C8—91no—
417C2×C3×C8—91no—
418#216—32no—
419#215—32no—
420#215—92no—
421#215—92no—
422#215—92no—
423#215—92no—
424#215—182no—
425#214—92no—
426#213—92no—
427C2×C3⋊C8—31no—
428C2×C3⋊C8—31no—
429Dic12—32no—
430Dic12—31no—
431Dic12—31no—
432Dic12—61no—
433Dic12D3211yescharacteristic, complemented
434D24—31no—
435D24—31no—
436D24—61no—
437D24—92no—
438D24—92no—
439D24—91no—
440D24—91no—
441D24—91no—
442D24—181no—
443D24—181no—
444D24—181no—
445D24—182no—
446D24—361no—
447#204—32no—
448#204—92no—
449#204—92no—
450#204—92no—
451#204—92no—
452#204—182no—
453D3×C8—31no—
454D3×C8—31no—
455D3×C8—31no—
456D3×C8—31no—
457D3×C8—31no—
458D3×C8—31no—
459D3×C8—61no—
460D3×C8D3211yescharacteristic
461D3×C8D3211yescharacteristic, complemented
462C22×C32—31no—
463C22×C32—31no—
464C2×C3⋊D3—22no—
465C2×C3⋊D3—62no—
466C2×C3⋊D3—62no—
467C2×C3⋊D3—62no—
468C2×C3⋊D3—122no—
469C2×C3⋊D3—122no—
470C2×C3⋊D3—122no—
471C2×C3⋊D3—124no—
472C2×C3⋊D3—242no—
473C2×C3⋊D3C2×D1211yescharacteristic
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—31no—
477C2×C3×D3—31no—
478C2×C3×D3—61no—
479C2×C3×D3—62no—
480C2×C3×D3—62no—
481C2×C3×D3—62no—
482C2×C3×D3—62no—
483C2×C3×D3—122no—
484C2×C3×D3C2×D1211yescharacteristic
485C2×C3×D3C2×D1211yescharacteristic
486C2×C3×D3D3×D411yescharacteristic
487C2×C3×D3D3×D411yescharacteristic
488D32—22no—
489D32—124no—
490D32—124no—
491D32—244no—
492C32×C4—21no—
493C32×C4—21no—
494C32×C4—21no—
495C32×C4—31no—
496C32×C4—31no—
497C32×C4—41no—
498C32×C4—62no—
499C32×C4C23×D311yescharacteristic
500C32×C4C23×D311yescharacteristic
501C32×C4C23×D311yescharacteristic
502C3⋊Dic3—22no—
503C3⋊Dic3C2×D1211yescharacteristic
504C3×Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—21no—
507C3×Dic3—21no—
508C3×Dic3—31no—
509C3×Dic3—31no—
510C3×Dic3—42no—
511C3×Dic3—61no—
512C3×Dic3—62no—
513C3×Dic3—62no—
514C3×Dic3—122no—
515C3×Dic3C2×D1211yescharacteristic
516C3×Dic3C2×D1211yescharacteristic
517C3×Dic3D3×D411yescharacteristic
518C3×Dic3D3×D411yescharacteristic
519C2×#41—272no—
520#135—91no—
521#135—271no—
522#135—271no—
523#135—272no—
524#135—271no—
525#135—272no—
526C2×Q16—91no—
527C2×SD16—272no—
528C2×D8—271no—
529C22×C8—91no—
530C33C2×#13511yescharacteristic, complemented, Sylow
531C23×C3—91no—
532C22×D3—31no—
533C22×D3—31no—
534C22×D3—182no—
535C22×D3—182no—
536C22×D3—182no—
537C22×D3—362no—
538C3×Q8—32no—
539C3×Q8—32no—
540C3×Q8—62no—
541C3×Q8—92no—
542C3×Q8—182no—
543C3×D4—92no—
544C3×D4—182no—
545C2×C3×C4—31no—
546C2×C3×C4—31no—
547C2×C3×C4—31no—
548C2×C3×C4—31no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—91no—
552C2×C3×C4—91no—
553C2×C3×C4—91no—
554C2×C3×C4—91no—
555C2×C3×C4—182no—
556C2×C3×C4—182no—
557#67—62no—
558#67—182no—
559#67—182no—
560#67—182no—
561#67—182no—
562#67—182no—
563#67—182no—
564#67—362no—
565C2×Dic3—31no—
566C2×Dic3—31no—
567C2×Dic3—62no—
568C2×Dic3—182no—
569D12—32no—
570D12—32no—
571D12—62no—
572D12—62no—
573D12—92no—
574D12—92no—
575D12—92no—
576D12—182no—
577D12—182no—
578D12—182no—
579D12—182no—
580D12—182no—
581D12—182no—
582D12—182no—
583D12—182no—
584D12—182no—
585D12—362no—
586D12—362no—
587D12—362no—
588C4×D3—31no—
589C4×D3—31no—
590C4×D3—31no—
591C4×D3—31no—
592C4×D3—31no—
593C4×D3—31no—
594C4×D3—61no—
595C4×D3—62no—
596C4×D3—62no—
597C4×D3—62no—
598C4×D3—182no—
599C4×D3—182no—
600C4×D3—182no—
601C4×D3—182no—
602C4×D3—182no—
603C4×D3—182no—
604C4×D3—182no—
605C4×D3—182no—
606C4×D3—362no—
607C4×D3—362no—
608C4×D3C2×D3211yescharacteristic
609C4×D3C2×D3211yescharacteristic
610Dic6—32no—
611Dic6—32no—
612Dic6—62no—
613Dic6—62no—
614Dic6—62no—
615Dic6C2×D3212yes—
616C3×C8—21no—
617C3×C8—21no—
618C3×C8—21no—
619C3×C8—31no—
620C3×C8—31no—
621C3×C8—31no—
622C3×C8—31no—
623C3×C8—41no—
624C3×C8—61no—
625C3×C8—61no—
626C3×C8—91no—
627C3×C8C2×D3211yescharacteristic
628C3×C8C2×D3211yescharacteristic
629C3×C8C2×D3211yescharacteristic
630C3⋊C8—31no—
631C3⋊C8—31no—
632C3⋊C8—61no—
633C3⋊C8C2×D3211yescharacteristic
634C3⋊C8C2×D3211yescharacteristic
635C2×C32—21no—
636C2×C32—21no—
637C2×C32—21no—
638C2×C32—32no—
639C2×C32—41no—
640C2×C32—61no—
641C2×C32C22×D1211yescharacteristic
642C2×C32C2×D3×D411yescharacteristic
643C2×C32C2×D3×D411yescharacteristic
644C3⋊D3—21no—
645C3⋊D3—42no—
646C3⋊D3—122no—
647C3⋊D3—122no—
648C3⋊D3—122no—
649C3⋊D3—242no—
650C3⋊D3—242no—
651C3⋊D3—242no—
652C3⋊D3—482no—
653C3×D3—21no—
654C3×D3—21no—
655C3×D3—22no—
656C3×D3—41no—
657C3×D3—61no—
658C3×D3—61no—
659C3×D3—121no—
660C3×D3—122no—
661C3×D3—122no—
662C3×D3—242no—
663C3×D3#90412yescomplemented
664C3×D3#91912yescomplemented
665#41—92no—
666#41—272no—
667#41—272no—
668#41—272no—
669#41—542no—
670#41—542no—
671C2×Q8—92no—
672C2×D4—272no—
673C2×D4—542no—
674C22×C4—91no—
675C22×C4—542no—
676Q16—31no—
677Q16—92no—
678Q16—91no—
679SD16—92no—
680SD16—272no—
681SD16—272no—
682SD16—272no—
683D8—91no—
684D8—272no—
685D8—271no—
686C2×C8—31no—
687C2×C8—31no—
688C2×C8—91no—
689C2×C8—91no—
690C2×C8—91no—
691C2×C8—91no—
692C22×C3—31no—
693C22×C3—31no—
694C22×C3—31no—
695C22×C3—31no—
696C22×C3—61no—
697C22×C3—61no—
698C22×C3—91no—
699C22×C3—182no—
700C22×C3—182no—
701C2×D3—31no—
702C2×D3—31no—
703C2×D3—61no—
704C2×D3—62no—
705C2×D3—62no—
706C2×D3—62no—
707C2×D3—62no—
708C2×D3—122no—
709C2×D3—182no—
710C2×D3—182no—
711C2×D3—182no—
712C2×D3—362no—
713C2×D3—362no—
714C2×D3—362no—
715C2×D3—364no—
716C2×D3—364no—
717C2×D3—364no—
718C2×D3—722no—
719C2×D3—724no—
720C2×D3D3×D1211yescharacteristic
721C2×D3D3×D1211yescharacteristic
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—31no—
726C3×C4—31no—
727C3×C4—31no—
728C3×C4—31no—
729C3×C4—41no—
730C3×C4—61no—
731C3×C4—61no—
732C3×C4—62no—
733C3×C4—62no—
734C3×C4—91no—
735C3×C4—122no—
736C3×C4—182no—
737C3×C4C22×D3211yescharacteristic
738C3×C4C22×D3211yescharacteristic
739C3×C4C22×D3211yescharacteristic
740Dic3—22no—
741Dic3—31no—
742Dic3—31no—
743Dic3—61no—
744Dic3—62no—
745Dic3—62no—
746Dic3—122no—
747Dic3D3×D1211yescharacteristic
748Dic3D3×D1211yescharacteristic
749C32—21no—
750C32—21no—
751C32—21no—
752C32—41no—
753C32C2×#90411yescharacteristic, complemented
754C32C2×#91911yescharacteristic, complemented
755C32D3×#13511yescharacteristic, complemented
756C23—91no—
757C23—542no—
758Q8—32no—
759Q8—92no—
760Q8—182no—
761D4—92no—
762D4—182no—
763D4—272no—
764D4—542no—
765D4—542no—
766D4—542no—
767D4—542no—
768C2×C4—31no—
769C2×C4—31no—
770C2×C4—91no—
771C2×C4—91no—
772C2×C4—91no—
773C2×C4—91no—
774C2×C4—182no—
775C2×C4—182no—
776C2×C4—542no—
777C2×C4—542no—
778C2×C4—542no—
779C8—31no—
780C8—31no—
781C8—91no—
782C8D3311yescharacteristic
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—32no—
787C2×C3—32no—
788C2×C3—41no—
789C2×C3—62no—
790C2×C3—61no—
791C2×C3—61no—
792C2×C3—121no—
793C2×C3—181no—
794C2×C3—362no—
795C2×C3C2×D3×D1211yescharacteristic
796C2×C3C2×D3×D1211yescharacteristic
797C2×C3D32×D411yescharacteristic
798D3—21no—
799D3—61no—
800D3—61no—
801D3—121no—
802D3—122no—
803D3—122no—
804D3—242no—
805D3—362no—
806D3—362no—
807D3—362no—
808D3—722no—
809D3—722no—
810D3—722no—
811D3—1442no—
812D3#6380812yesdirect product factor
813C22—31no—
814C22—31no—
815C22—91no—
816C22—182no—
817C22—182no—
818C22—542no—
819C22—1084no—
820C4—31no—
821C4—31no—
822C4—62no—
823C4—91no—
824C4—182no—
825C4C2×D3311yescharacteristic
826C3—21no—
827C3—21no—
828C3—21no—
829C3—41no—
830C3D3×#90411yescharacteristic, complemented
831C3C2×#6380811yescharacteristic, complemented
832C3D3×#91911yescharacteristic, complemented
833C2—32no—
834C2—61no—
835C2—181no—
836C2—362no—
837C2—1082no—
838C2D32×D1211yescharacteristic
subgroupG/H
centerC2D32×D12
commutator, cosocleC33×C4C24
FrattiniC4C2×D33
FittingC33×C8C23
socleC2×C33C22×D4
hypercenterC8D33
hypocenterC33C2×#135
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
1. D3×#3799C2semidirect
2. #11723654C2semidirect
3. #11723341C2semidirect
4. #11723337C2semidirect
5. D3×#3745C2semidirect
6. C3×#63808C2semidirect
7. C3×D3×Dic12C2semidirect
8. C3×D32×C8C2semidirect
9. #11722865C2semidirect
10. #11722856C2semidirect
11. D3×#3717C2semidirect
15. #89041C22semidirect
17. #89022C22semidirect
18. #89018C22semidirect
20. C3×#3799C22semidirect
26. #88852C22semidirect
27. C3×#3746C22semidirect
28. C3×#3745C22semidirect
29. C3×C8×C3⋊D3C22semidirect
30. C32×Dic12C22semidirect
32. C32×D3×C8C22semidirect
33. #88811C22semidirect
34. #88797C22semidirect
35. #88795C22semidirect
36. #88791C22semidirect
37. C3×#3719C22semidirect
38. C3×#3717C22semidirect
39. C3×#3710C22semidirect
41. C3×D3×C3⋊C8C22semidirect
69. #63808D3direct (N × H)
72. D3×Dic12D3semidirect
77. D32×C8D3semidirect
138. #3799C2×D3semidirect
148. #3746C2×D3semidirect
157. #3745C2×D3semidirect
159. C8×C3⋊D3C2×D3semidirect
169. C3×Dic12C2×D3semidirect
170. C3×Dic12C2×D3semidirect
186. C3×D3×C8C2×D3semidirect
187. C3×D3×C8C2×D3semidirect
188. #3719C2×D3semidirect
196. #3717C2×D3semidirect
202. #3710C2×D3semidirect
204. D3×C3⋊C8C2×D3semidirect
364. C32×D3#135semidirect
433. Dic12D32semidirect
461. D3×C8D32semidirect
530. C33C2×#135semidirect
663. C3×D3#904semidirect
664. C3×D3#919semidirect
753. C32C2×#904semidirect
754. C32C2×#919semidirect
755. C32D3×#135semidirect
812. D3#63808direct (N × H)
830. C3D3×#904semidirect
831. C3C2×#63808semidirect
832. C3D3×#919semidirect

Maximal subgroups

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

subgroupindex
D3×#37992
#117236542
#117233412
#117233372
D3×#37452
C3×#638082
C3×D3×Dic122
C3×D32×C82
#117228652
#117228562
D3×#37172
D3×#9193
C2×#638083
D3×#9043