Finite Group Databasebeta

← D3×#63814 #13170482

Subgroups — D3×#63814 #13170482

Order 1728.

1276 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#235C211yesmaximal, characteristic
2#11723657C211yesmaximal, characteristic, complemented
3#11723352C211yesmaximal, characteristic, complemented
4#11723349C211yesmaximal, characteristic, complemented
5D3×#3748C211yesmaximal, characteristic, complemented
6C3×#63814C211yesmaximal, characteristic, complemented
7C2×C3×D3×C3⋊C8C211yesmaximal, characteristic, complemented
8#11722822C212yesmaximal, complemented
9#11722821C212yesmaximal, complemented
10D3×#3711C212yesmaximal, complemented
11D32×C3⋊C8C212yesmaximal, complemented
12D3×#948—31nomaximal
13C2×#63814—31nomaximal
14D3×#901—31nomaximal
15C3×#3828C2211yescharacteristic
16C32×#235C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C3×D3×#67C412yes—
19C3×#3804C412yes—
20C3×D3×D12C411yescharacteristic
21C3×C4×D32C2212yes—
22C3×#3799C411yescharacteristic
23C3×#3798C2212yes—
24C3×#3795C411yescharacteristic
25C3×D3×Dic6C411yescharacteristic
26#88855C2211yescharacteristic, complemented
27C3×#3748C2211yescharacteristic, complemented
28C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
29C2×C32×C3⋊C8C2211yescharacteristic, complemented
30#88809C2212yescomplemented
31#88808C2212yescomplemented
32#88787C2212yescomplemented
33#88786C2212yescomplemented
34#88786C2212yescomplemented
35C3⋊D3×C3⋊C8C2212yescomplemented
36D3×C3⋊(C3⋊C8)C2212yes—
37D3×C3⋊(C3⋊C8)C2212yescomplemented
38C3×#3711C2212yescomplemented
39C3×D3×C3⋊C8C2211yescharacteristic
40C3×D3×C3⋊C8C2211yescharacteristic
41C3×D3×C3⋊C8C2212yescomplemented
42C3×D3×C3⋊C8C2211yescharacteristic, complemented
43C3×D3×C3⋊C8C2211yescharacteristic, complemented
44C3×D3×#41—31no—
45C2×C3×#235—31no—
46D3×#235D311yescharacteristic
47#64157—31no—
48C2×#3748—31no—
49#64110—31no—
50C3×#948—31no—
51C22×C3×C3⋊C8—31no—
52C3×#901—31no—
53C2×C3×D3×C8—31no—
54C2×#3711—32no—
55#63817—31no—
56#63815—31no—
57#63815—32no—
58#63814—31no—
59#63814—31no—
60#63814—31no—
61#63814—31no—
62#63814—31no—
63#63814—32no—
64#63814—32no—
65#63814—32no—
66#63814—61no—
67#63814—61no—
68#63814D311yescharacteristic, direct product factor
69D3×#208—31no—
70D3×#208—31no—
71D3×#208—32no—
72D3×#208—61no—
73C2×D3×C3⋊C8—32no—
74C2×D3×C3⋊C8—32no—
75C2×D3×C3⋊C8D311yescharacteristic, complemented
76#63804—32no—
77#63803—32no—
78D3×ΓL(1,𝔽25)—32no—
79D32×C8—32no—
80C22×C32×D3C2×C411yescharacteristic
81C2×C3×D32C2×C412yes—
82C2×C33×C4C2311yescharacteristic
83C3×#638C2×C412yes—
84C3×C4⋊(C3⋊D3)C2×C411yescharacteristic
85C3×C4×C3⋊D3C2312yes—
86C3×#634C2×C411yescharacteristic
87C32×#67C2×C412yes—
88C2×C32×Dic3C2×C411yescharacteristic
89C32×D12C2×C411yescharacteristic
90C32×C4×D3C2×C411yescharacteristic
91C32×C4×D3C2×C411yescharacteristic
92C32×C4×D3C2311yescharacteristic
93C32×C4×D3C2312yes—
94C32×C4×D3C2311yescharacteristic
95C32×Dic6C2×C411yescharacteristic
96C3×#627C2×C412yes—
97C3×#626C2×C412yes—
98C3×#626C2×C412yes—
99C3×#625C2×C412yes—
100C3×#624C2×C412yes—
101C3×D3×Dic3C2×C412yes—
102C3×D3×Dic3C2×C412yes—
103C3⋊(C3⋊(C3⋊C8))C2312yes—
104C3×C3⋊(C3⋊C8)C2311yescharacteristic
105C3×C3⋊(C3⋊C8)C2311yescharacteristic
106C3×C3⋊(C3⋊C8)C2312yes—
107C32×C3⋊C8C2311yescharacteristic
108C32×C3⋊C8C2311yescharacteristic
109C2×#948—91no—
110D3×#131—91no—
111C2×#901—91no—
112C32×#41—31no—
113C22×C32×C4—31no—
114#3828C2×D311yescharacteristic
115C2×C3×#67—32no—
116C3×#239—31no—
117C3×D3×Q8—31no—
118C3×#237—32no—
119C3×#237—31no—
120C3×D3×D4—32no—
121C3×D3×D4—31no—
122C3×#235—21no—
123C3×#235—31no—
124C3×#235—31no—
125C3×#235—32no—
126C3×#235—31no—
127C3×#235—32no—
128C3×#235—32no—
129C3×#235—31no—
130C3×#235—61no—
131C3×#235C2×D311yescharacteristic
132C3×#235C2×D311yescharacteristic
133C2×C3×D12—31no—
134C2×C3×C4×D3—21no—
135C2×C3×C4×D3—32no—
136C2×C3×C4×D3—32no—
137C2×C3×C4×D3C2×D311yescharacteristic
138C2×C3×C4×D3C2×D311yescharacteristic
139C2×C3×Dic6—31no—
140D3×#67Dic312yes—
141#3804Dic312yes—
142D3×D12Dic311yescharacteristic
143C4×D32C2×D312yes—
144#3799Dic311yescharacteristic
145#3798C2×D312yes—
146#3795Dic311yescharacteristic
147D3×Dic6Dic311yescharacteristic
148C2×C32×C8—31no—
149#3748—31no—
150#3748—31no—
151#3748—31no—
152#3748—32no—
153#3748—32no—
154#3748—61no—
155#3748—61no—
156#3748—61no—
157#3748—121no—
158#3748C2×D311yescharacteristic, complemented
159C2×C3⋊(C3⋊C8)—32no—
160C2×C3⋊(C3⋊C8)—32no—
161C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
162#3743—32no—
163C8×C3⋊D3—32no—
164C3×#208—31no—
165C3×#208—31no—
166C3×#208—32no—
167C3×#208—61no—
168C2×C3×C3⋊C8—21no—
169C2×C3×C3⋊C8—31no—
170C2×C3×C3⋊C8—31no—
171C2×C3×C3⋊C8—31no—
172C2×C3×C3⋊C8—31no—
173C2×C3×C3⋊C8—31no—
174C2×C3×C3⋊C8—31no—
175C2×C3×C3⋊C8—32no—
176C2×C3×C3⋊C8—61no—
177C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
178C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
179C3×ΓL(1,𝔽25)—32no—
180C3×D3×C8—31no—
181C3×D3×C8—31no—
182C3×D3×C8—31no—
183C3×D3×C8—31no—
184C3×D3×C8—32no—
185#3712—32no—
186#3711—32no—
187#3711—32no—
188#3711—32no—
189#3711—32no—
190#3711—32no—
191#3711—32no—
192#3711—32no—
193#3711—32no—
194#3711—62no—
195#3711—62no—
196#3711—62no—
197#3711C2×D312yescomplemented
198#3710—32no—
199D3×C3⋊C8—32no—
200D3×C3⋊C8—32no—
201D3×C3⋊C8—32no—
202D3×C3⋊C8—32no—
203D3×C3⋊C8—32no—
204D3×C3⋊C8—32no—
205D3×C3⋊C8—32no—
206D3×C3⋊C8—32no—
207D3×C3⋊C8—62no—
208D3×C3⋊C8—62no—
209D3×C3⋊C8—62no—
210D3×C3⋊C8C2×D311yescharacteristic
211D3×C3⋊C8C2×D311yescharacteristic
212D3×C3⋊C8C2×D312yescomplemented
213D3×C3⋊C8C2×D311yescharacteristic, complemented
214D3×C3⋊C8C2×D311yescharacteristic, complemented
215C22×C33C22×C411yescharacteristic
216C2×C3×C3⋊D3C22×C412yes—
217C2×C32×D3—22no—
218C2×C32×D3C22×C412yes—
219C2×C32×D3C22×C411yescharacteristic
220C2×C32×D3C22×C411yescharacteristic
221C3×D32—24no—
222C33×C4C22×C411yescharacteristic
223C33×C4C2411yescharacteristic
224C3×C3⋊Dic3C22×C412yes—
225C32×Dic3C22×C411yescharacteristic
226C32×Dic3C22×C412yes—
227C32×Dic3C22×C411yescharacteristic
228C2×C3×#41—91no—
229D3×#41—31no—
230C2×#235—31no—
231C3×#131—91no—
232C22×C3×C8—91no—
233#948—31no—
234#948—92no—
235#948—91no—
236#948—92no—
237#948—91no—
238#948—91no—
239#948—91no—
240#948—181no—
241C2×#208—92no—
242C2×#208—91no—
243C2×#208—91no—
244C2×#208—181no—
245C22×C3⋊C8—31no—
246C22×C3⋊C8—92no—
247#907—92no—
248#907—91no—
249D3×M16—92no—
250D3×M16—91no—
251#901—31no—
252#901—92no—
253#901—92no—
254#901—92no—
255#901—91no—
256#901—91no—
257#901—91no—
258#901—91no—
259#901—181no—
260C2×ΓL(1,𝔽25)—92no—
261C2×D3×C8—31no—
262C2×D3×C8—92no—
263C2×D3×C8—92no—
264C23×C32—31no—
265C22×C3×D3—21no—
266C22×C3×D3—32no—
267C22×C3×D3—32no—
268C22×C3×D3C4×D311yescharacteristic
269C22×C3×D3C2×Dic311yescharacteristic
270C2×D32C2×Dic312yes—
271C32×Q8—31no—
272C32×D4—32no—
273C32×D4—31no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—31no—
278C2×C32×C4—31no—
279C2×C32×C4—31no—
280C2×C32×C4—31no—
281C2×C32×C4—31no—
282C2×C32×C4—32no—
283C2×C32×C4—41no—
284C2×C32×C4C22×D311yescharacteristic
285C2×C32×C4C22×D311yescharacteristic
286C2×C32×C4C22×D311yescharacteristic
287#638C2×Dic312yes—
288C4⋊(C3⋊D3)C2×Dic311yescharacteristic
289C4×C3⋊D3C22×D312yes—
290#634C2×Dic311yescharacteristic
291C3×#67—22no—
292C3×#67—32no—
293C3×#67—32no—
294C3×#67—32no—
295C3×#67—32no—
296C3×#67—32no—
297C3×#67—32no—
298C3×#67—62no—
299C3×#67C4×D312yes—
300C3×#67C2×Dic312yes—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—32no—
303C2×C3×Dic3—32no—
304C2×C3×Dic3C4×D311yescharacteristic
305C2×C3×Dic3C2×Dic311yescharacteristic
306C3×D12—21no—
307C3×D12—32no—
308C3×D12—32no—
309C3×D12—31no—
310C3×D12—31no—
311C3×D12—61no—
312C3×D12C4×D311yescharacteristic
313C3×D12C2×Dic311yescharacteristic
314C3×C4×D3—21no—
315C3×C4×D3—21no—
316C3×C4×D3—21no—
317C3×C4×D3—22no—
318C3×C4×D3—21no—
319C3×C4×D3—32no—
320C3×C4×D3—32no—
321C3×C4×D3—32no—
322C3×C4×D3—32no—
323C3×C4×D3—32no—
324C3×C4×D3—32no—
325C3×C4×D3—62no—
326C3×C4×D3C4×D311yescharacteristic
327C3×C4×D3C4×D311yescharacteristic
328C3×C4×D3C2×Dic311yescharacteristic
329C3×C4×D3C2×Dic311yescharacteristic
330C3×C4×D3C22×D311yescharacteristic
331C3×C4×D3C22×D312yes—
332C3×C4×D3C22×D311yescharacteristic
333C3×C4×D3C22×D311yescharacteristic
334C3×C4×D3C22×D312yes—
335C3×C4×D3C22×D311yescharacteristic
336C3×Dic6—21no—
337C3×Dic6—31no—
338C3×Dic6—31no—
339C3×Dic6—32no—
340C3×Dic6—32no—
341C3×Dic6—61no—
342C3×Dic6C4×D311yescharacteristic
343C3×Dic6C2×Dic311yescharacteristic
344#627C2×Dic312yes—
345#626C2×Dic312yes—
346#626C2×Dic312yes—
347#625C2×Dic312yes—
348#624C2×Dic312yes—
349D3×Dic3C2×Dic312yes—
350D3×Dic3C2×Dic312yes—
351C32×C8—31no—
352C32×C8—31no—
353C3⋊(C3⋊C8)—32no—
354C3⋊(C3⋊C8)—32no—
355C3⋊(C3⋊C8)—32no—
356C3⋊(C3⋊C8)—62no—
357C3⋊(C3⋊C8)—62no—
358C3⋊(C3⋊C8)—62no—
359C3⋊(C3⋊C8)—122no—
360C3⋊(C3⋊C8)C22×D311yescharacteristic
361C3⋊(C3⋊C8)C22×D312yes—
362C3⋊(C3⋊C8)C22×D311yescharacteristic
363C3×C3⋊C8—21no—
364C3×C3⋊C8—21no—
365C3×C3⋊C8—31no—
366C3×C3⋊C8—31no—
367C3×C3⋊C8—32no—
368C3×C3⋊C8—32no—
369C3×C3⋊C8—31no—
370C3×C3⋊C8—31no—
371C3×C3⋊C8—61no—
372C3×C3⋊C8—62no—
373C3×C3⋊C8—61no—
374C3×C3⋊C8C22×D311yescharacteristic
375C3×C3⋊C8C22×D311yescharacteristic
376C3×C3⋊C8C22×D311yescharacteristic
377C3×C3⋊C8C22×D311yescharacteristic
378C2×#131—271noSylow
379C2×C33—21no—
380C2×C33C23×C411yescharacteristic
381C3×C3⋊D3—22no—
382C32×D3—22no—
383C32×D3—21no—
384C32×D3#13112yescomplemented
385C3×#41—31no—
386C3×#41—31no—
387C3×#41—61no—
388C3×#41—92no—
389C3×#41—92no—
390C3×#41—91no—
391C3×#41—91no—
392C3×#41—91no—
393C2×C3×Q8—91no—
394C2×C3×D4—91no—
395C2×C3×D4—92no—
396C22×C3×C4—31no—
397C22×C3×C4—31no—
398C22×C3×C4—61no—
399C22×C3×C4—92no—
400C2×#67—32no—
401#239—31no—
402D3×Q8—31no—
403#237—32no—
404#237—31no—
405D3×D4—32no—
406D3×D4—31no—
407#235—31no—
408#235—31no—
409#235—32no—
410#235—31no—
411#235—32no—
412#235—32no—
413#235—31no—
414#235—61no—
415#235D3211yescharacteristic
416C2×D12—31no—
417C2×C4×D3—32no—
418C2×C4×D3—32no—
419C2×C4×D3D3211yescharacteristic
420C2×Dic6—31no—
421C3×M16—92no—
422C3×M16—91no—
423C2×C3×C8—31no—
424C2×C3×C8—31no—
425C2×C3×C8—61no—
426C2×C3×C8—91no—
427C2×C3×C8—92no—
428C2×C3×C8—91no—
429C2×C3×C8—91no—
430C2×C3×C8—91no—
431C2×C3×C8—91no—
432#208—31no—
433#208—31no—
434#208—32no—
435#208—61no—
436#208—92no—
437#208—92no—
438#208—92no—
439#208—92no—
440#208—92no—
441#208—91no—
442#208—91no—
443#208—91no—
444#208—92no—
445#208—182no—
446#208—182no—
447#208—181no—
448#208—181no—
449#208—181no—
450#208—361no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—31no—
455C2×C3⋊C8—31no—
456C2×C3⋊C8—31no—
457C2×C3⋊C8—32no—
458C2×C3⋊C8—61no—
459C2×C3⋊C8—92no—
460C2×C3⋊C8—92no—
461C2×C3⋊C8—92no—
462C2×C3⋊C8—92no—
463C2×C3⋊C8—92no—
464C2×C3⋊C8—92no—
465C2×C3⋊C8—182no—
466C2×C3⋊C8—182no—
467C2×C3⋊C8D3211yescharacteristic, complemented
468ΓL(1,𝔽25)—32no—
469ΓL(1,𝔽25)—92no—
470ΓL(1,𝔽25)—92no—
471ΓL(1,𝔽25)—92no—
472ΓL(1,𝔽25)—92no—
473ΓL(1,𝔽25)—92no—
474ΓL(1,𝔽25)—92no—
475ΓL(1,𝔽25)—182no—
476D3×C8—31no—
477D3×C8—31no—
478D3×C8—31no—
479D3×C8—31no—
480D3×C8—32no—
481D3×C8—92no—
482D3×C8—92no—
483D3×C8—92no—
484D3×C8—92no—
485D3×C8—92no—
486D3×C8—92no—
487D3×C8—182no—
488C22×C32—21no—
489C22×C32—21no—
490C22×C32—21no—
491C22×C32—31no—
492C22×C32—32no—
493C22×C32—31no—
494C22×C32—41no—
495C22×C32—62no—
496C22×C32C2×C4×D311yescharacteristic
497C22×C32C2×C4×D311yescharacteristic
498C22×C32C22×Dic311yescharacteristic
499C2×C3⋊D3C22×Dic312yes—
500C2×C3×D3—22no—
501C2×C3×D3—22no—
502C2×C3×D3—21no—
503C2×C3×D3—21no—
504C2×C3×D3—22no—
505C2×C3×D3—32no—
506C2×C3×D3—32no—
507C2×C3×D3—42no—
508C2×C3×D3—62no—
509C2×C3×D3—64no—
510C2×C3×D3—64no—
511C2×C3×D3C2×C4×D312yes—
512C2×C3×D3C2×C4×D311yescharacteristic
513C2×C3×D3C2×C4×D311yescharacteristic
514C2×C3×D3C22×Dic312yes—
515C2×C3×D3C22×Dic311yescharacteristic
516C2×C3×D3C22×Dic311yescharacteristic
517D32—24no—
518C32×C4—21no—
519C32×C4—21no—
520C32×C4—21no—
521C32×C4—21no—
522C32×C4—21no—
523C32×C4—21no—
524C32×C4—31no—
525C32×C4—32no—
526C32×C4—31no—
527C32×C4—41no—
528C32×C4—41no—
529C32×C4C2×C4×D311yescharacteristic
530C32×C4C2×C4×D311yescharacteristic
531C32×C4C22×Dic311yescharacteristic
532C32×C4C23×D311yescharacteristic
533C32×C4C23×D311yescharacteristic
534C32×C4C23×D311yescharacteristic
535C3⋊Dic3C22×Dic312yes—
536C3×Dic3—22no—
537C3×Dic3—21no—
538C3×Dic3—21no—
539C3×Dic3—32no—
540C3×Dic3—32no—
541C3×Dic3—62no—
542C3×Dic3C2×C4×D311yescharacteristic
543C3×Dic3C2×C4×D312yes—
544C3×Dic3C2×C4×D311yescharacteristic
545C3×Dic3C22×Dic311yescharacteristic
546C3×Dic3C22×Dic312yes—
547C3×Dic3C22×Dic311yescharacteristic
548C2×#41—91no—
549#131—91no—
550#131—271no—
551#131—272no—
552#131—272no—
553#131—271no—
554#131—271no—
555C2×M16—272no—
556C2×M16—271no—
557C22×C8—91no—
558C22×C8—272no—
559C33C2×#13111yescharacteristic, complemented, Sylow
560C23×C3—31no—
561C23×C3—31no—
562C23×C3—61no—
563C23×C3—92no—
564C22×D3—32no—
565C22×D3—32no—
566C22×D3D3×Dic311yescharacteristic
567C3×Q8—31no—
568C3×Q8—31no—
569C3×Q8—61no—
570C3×Q8—92no—
571C3×Q8—91no—
572C3×D4—32no—
573C3×D4—32no—
574C3×D4—31no—
575C3×D4—31no—
576C3×D4—61no—
577C3×D4—62no—
578C3×D4—92no—
579C3×D4—92no—
580C3×D4—92no—
581C3×D4—92no—
582C3×D4—91no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—31no—
587C2×C3×C4—31no—
588C2×C3×C4—31no—
589C2×C3×C4—31no—
590C2×C3×C4—32no—
591C2×C3×C4—31no—
592C2×C3×C4—32no—
593C2×C3×C4—31no—
594C2×C3×C4—31no—
595C2×C3×C4—31no—
596C2×C3×C4—31no—
597C2×C3×C4—31no—
598C2×C3×C4—41no—
599C2×C3×C4—61no—
600C2×C3×C4—62no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—92no—
606C2×C3×C4—92no—
607C2×C3×C4—92no—
608C2×C3×C4—92no—
609C2×C3×C4C2×D3211yescharacteristic
610C2×C3×C4C2×D3211yescharacteristic
611C2×C3×C4C2×D3211yescharacteristic
612#67—32no—
613#67—32no—
614#67—32no—
615#67—32no—
616#67—32no—
617#67—32no—
618#67—62no—
619#67D3×Dic312yes—
620C2×Dic3—32no—
621C2×Dic3—32no—
622C2×Dic3D3×Dic311yescharacteristic
623D12—32no—
624D12—32no—
625D12—31no—
626D12—31no—
627D12—61no—
628D12D3×Dic311yescharacteristic
629C4×D3—32no—
630C4×D3—32no—
631C4×D3—32no—
632C4×D3—32no—
633C4×D3—32no—
634C4×D3—32no—
635C4×D3—62no—
636C4×D3D3×Dic311yescharacteristic
637C4×D3D3×Dic311yescharacteristic
638C4×D3C2×D3211yescharacteristic
639C4×D3C2×D3211yescharacteristic
640C4×D3C2×D3212yes—
641Dic6—31no—
642Dic6—31no—
643Dic6—32no—
644Dic6—32no—
645Dic6—61no—
646Dic6D3×Dic311yescharacteristic
647C3×C8—31no—
648C3×C8—31no—
649C3×C8—31no—
650C3×C8—31no—
651C3×C8—61no—
652C3×C8—61no—
653C3×C8—91no—
654C3×C8—92no—
655C3×C8—91no—
656C3⋊C8—31no—
657C3⋊C8—31no—
658C3⋊C8—32no—
659C3⋊C8—31no—
660C3⋊C8—31no—
661C3⋊C8—32no—
662C3⋊C8—61no—
663C3⋊C8—61no—
664C3⋊C8—62no—
665C3⋊C8—92no—
666C3⋊C8—92no—
667C3⋊C8—92no—
668C3⋊C8—182no—
669C3⋊C8—182no—
670C3⋊C8—182no—
671C3⋊C8—362no—
672C3⋊C8C2×D3211yescharacteristic
673C3⋊C8C2×D3211yescharacteristic
674C2×C32—21no—
675C2×C32—21no—
676C2×C32—21no—
677C2×C32—21no—
678C2×C32—21no—
679C2×C32—21no—
680C2×C32—32no—
681C2×C32—41no—
682C2×C32—41no—
683C2×C32—41no—
684C2×C32—41no—
685C2×C32—62no—
686C2×C32—61no—
687C2×C32—81no—
688C2×C32C22×C4×D311yescharacteristic
689C2×C32C22×C4×D311yescharacteristic
690C2×C32C23×Dic311yescharacteristic
691C3⋊D3—22no—
692C3×D3—21no—
693C3×D3—22no—
694C3×D3—22no—
695C3×D3—21no—
696C3×D3—22no—
697C3×D3—42no—
698C3×D3—41no—
699C3×D3—62no—
700C3×D3—62no—
701C3×D3—122no—
702C3×D3#90112yescomplemented
703C3×D3#94812yescomplemented
704#41—31no—
705#41—92no—
706#41—92no—
707#41—91no—
708#41—91no—
709#41—91no—
710C2×Q8—91no—
711C2×D4—91no—
712C2×D4—92no—
713C22×C4—31no—
714C22×C4—92no—
715M16—92no—
716M16—91no—
717M16—272no—
718M16—272no—
719M16—272no—
720M16—272no—
721M16—271no—
722C2×C8—31no—
723C2×C8—91no—
724C2×C8—91no—
725C2×C8—91no—
726C2×C8—91no—
727C2×C8—92no—
728C2×C8—91no—
729C2×C8—272no—
730C2×C8—272no—
731C2×C8—272no—
732C2×C8—272no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—31no—
737C22×C3—31no—
738C22×C3—31no—
739C22×C3—32no—
740C22×C3—32no—
741C22×C3—31no—
742C22×C3—41no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—62no—
746C22×C3—62no—
747C22×C3—62no—
748C22×C3—92no—
749C22×C3—122no—
750C22×C3—184no—
751C22×C3C4×D3211yescharacteristic
752C22×C3C2×D3×Dic311yescharacteristic
753C22×C3C2×D3×Dic311yescharacteristic
754C2×D3—22no—
755C2×D3—32no—
756C2×D3—32no—
757C2×D3—62no—
758C2×D3—64no—
759C2×D3—64no—
760C2×D3C2×D3×Dic312yes—
761C2×D3C2×D3×Dic311yescharacteristic
762C2×D3C2×D3×Dic311yescharacteristic
763C3×C4—21no—
764C3×C4—21no—
765C3×C4—21no—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—31no—
770C3×C4—31no—
771C3×C4—32no—
772C3×C4—31no—
773C3×C4—32no—
774C3×C4—31no—
775C3×C4—41no—
776C3×C4—41no—
777C3×C4—61no—
778C3×C4—61no—
779C3×C4—62no—
780C3×C4—92no—
781C3×C4C4×D3211yescharacteristic
782C3×C4C2×D3×Dic311yescharacteristic
783C3×C4C2×D3×Dic311yescharacteristic
784C3×C4C22×D3211yescharacteristic
785C3×C4C22×D3211yescharacteristic
786C3×C4C22×D3211yescharacteristic
787Dic3—32no—
788Dic3—32no—
789Dic3—62no—
790Dic3C2×D3×Dic311yescharacteristic
791Dic3C2×D3×Dic312yes—
792Dic3C2×D3×Dic311yescharacteristic
793C32—21no—
794C32—21no—
795C32—21no—
796C32—41no—
797C32C2×#90111yescharacteristic, complemented
798C32D3×#13111yescharacteristic, complemented
799C32C2×#94811yescharacteristic, complemented
800C23—31no—
801C23—92no—
802Q8—31no—
803Q8—92no—
804Q8—91no—
805D4—32no—
806D4—31no—
807D4—92no—
808D4—92no—
809D4—92no—
810D4—92no—
811D4—91no—
812C2×C4—31no—
813C2×C4—31no—
814C2×C4—31no—
815C2×C4—32no—
816C2×C4—31no—
817C2×C4—31no—
818C2×C4—92no—
819C2×C4—92no—
820C2×C4—92no—
821C2×C4—92no—
822C2×C4D3311yescharacteristic
823C8—31no—
824C8—31no—
825C8—91no—
826C8—91no—
827C8—92no—
828C8—272no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—32no—
836C2×C3—32no—
837C2×C3—41no—
838C2×C3—41no—
839C2×C3—41no—
840C2×C3—41no—
841C2×C3—62no—
842C2×C3—61no—
843C2×C3—62no—
844C2×C3—61no—
845C2×C3—62no—
846C2×C3—81no—
847C2×C3—121no—
848C2×C3—122no—
849C2×C3—182no—
850C2×C3C2×C4×D3211yescharacteristic
851C2×C3C22×D3×Dic311yescharacteristic
852C2×C3C22×D3×Dic311yescharacteristic
853D3—22no—
854D3—21no—
855D3—62no—
856D3—62no—
857D3—122no—
858D3#6381412yesdirect product factor
859C22—31no—
860C22—31no—
861C22—32no—
862C22—62no—
863C22—92no—
864C22—184no—
865C22D32×Dic311yescharacteristic
866C4—31no—
867C4—31no—
868C4—32no—
869C4—92no—
870C4D32×Dic311yescharacteristic
871C4C2×D3311yescharacteristic
872C3—21no—
873C3—21no—
874C3—21no—
875C3—41no—
876C3D3×#90111yescharacteristic, complemented
877C3C2×#6381411yescharacteristic, complemented
878C3D3×#94811yescharacteristic, complemented
879C2—21no—
880C2—32no—
881C2—61no—
882C2—62no—
883C2—182no—
884C2C2×D32×Dic311yescharacteristic
subgroupG/H
center, FrattiniC4C2×D33
commutator, socleC2×C33C23×C4
FittingC2×C33×C4C23
prime radicalC3×D3×#235C2
cosocleC33×C4C24
hypercenterC2×C4D33
hypocenterC33C2×#131
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723657C2semidirect
3. #11723352C2semidirect
4. #11723349C2semidirect
5. D3×#3748C2semidirect
6. C3×#63814C2semidirect
7. C2×C3×D3×C3⋊C8C2semidirect
8. #11722822C2semidirect
9. #11722821C2semidirect
10. D3×#3711C2semidirect
11. D32×C3⋊C8C2semidirect
26. #88855C22semidirect
27. C3×#3748C22semidirect
28. C2×C3×C3⋊(C3⋊C8)C22semidirect
29. C2×C32×C3⋊C8C22semidirect
30. #88809C22semidirect
31. #88808C22semidirect
32. #88787C22semidirect
33. #88786C22semidirect
34. #88786C22semidirect
35. C3⋊D3×C3⋊C8C22semidirect
37. D3×C3⋊(C3⋊C8)C22semidirect
38. C3×#3711C22semidirect
41. C3×D3×C3⋊C8C22semidirect
42. C3×D3×C3⋊C8C22semidirect
43. C3×D3×C3⋊C8C22semidirect
68. #63814D3direct (N × H)
75. C2×D3×C3⋊C8D3semidirect
158. #3748C2×D3semidirect
161. C2×C3⋊(C3⋊C8)C2×D3semidirect
177. C2×C3×C3⋊C8C2×D3semidirect
178. C2×C3×C3⋊C8C2×D3semidirect
197. #3711C2×D3semidirect
212. D3×C3⋊C8C2×D3semidirect
213. D3×C3⋊C8C2×D3semidirect
214. D3×C3⋊C8C2×D3semidirect
384. C32×D3#131semidirect
467. C2×C3⋊C8D32semidirect
559. C33C2×#131semidirect
702. C3×D3#901semidirect
703. C3×D3#948semidirect
797. C32C2×#901semidirect
798. C32D3×#131semidirect
799. C32C2×#948semidirect
858. D3#63814direct (N × H)
876. C3D3×#901semidirect
877. C3C2×#63814semidirect
878. C3D3×#948semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#2352
#117236572
#117233522
#117233492
D3×#37482
C3×#638142
C2×C3×D3×C3⋊C82
#117228222
#117228212
D3×#37112
D32×C3⋊C82
D3×#9483
C2×#638143
D3×#9013