Finite Group Databasebeta

← C3×#10595459 #13175056

Subgroups — C3×#10595459 #13175056

Order 1728.

1392 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#41×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×#64306C211yesmaximal, characteristic, complemented
3C32×#950C212yesmaximal, complemented
4C3×#63950C212yesmaximal, complemented
5C3×#63944C211yesmaximal, characteristic, complemented
6C3×#63940C211yesmaximal, characteristic, complemented
7C3×#63936C212yesmaximal, complemented
8C3×#63930C211yesmaximal, characteristic, complemented
9C3×#63926C211yesmaximal, characteristic, complemented
10C3×#63829C212yesmaximal, complemented
11C2×C3×#3710C211yesmaximal, characteristic, complemented
12C3×D3×#135—32nomaximal
13#10595459C311yesmaximal, characteristic, direct product factor
14C33×#41C2211yescharacteristic, complemented
15C3×#3832C2211yescharacteristic, complemented
16C3×Q8×C3⋊D3C2211yescharacteristic
17C3×#3830—21no—
18C3×#3830C2211yescharacteristic, complemented
19C3×D4×C3⋊D3—21no—
20C3×D4×C3⋊D3C2211yescharacteristic
21C3×#3828—21no—
22C3×#3828C2211yescharacteristic, complemented
23C2×C3×C4×C3⋊D3—21no—
24C2×C3×C4×C3⋊D3C2211yescharacteristic
25C32×#235C2212yescomplemented
26C3×#3811—21no—
27C3×#3805—21no—
28C3×#3802C2211yescharacteristic
29C3×C4×D32—21no—
30C3×#3798—21no—
31C3×#3797C2211yescharacteristic
32C3×#3796C2212yescomplemented
33C32×#216C2212yescomplemented
34C32×#215C2212yescomplemented
35C32×#214C2212yescomplemented
36C32×#213C2212yescomplemented
37C2×C32×C3⋊C8C2212yescomplemented
38C3×#3719C2212yescomplemented
39C3×#3717C2212yescomplemented
40C3×#3716C2212yescomplemented
41C3×#3714C2212yescomplemented
42C3×#3710C2211yescharacteristic
43C3×#3710C2211yescharacteristic
44C3×#3710C2212yescomplemented
45#41×C3⋊D3C2×C311yescharacteristic, complemented
46C3×D3×#41—32no—
47C3×D3×#41—32no—
48C3×D3×#41—61no—
49#64306C2×C311yescharacteristic, complemented
50C32×#135—32no—
51C3×#950—22no—
52C3×#950—32no—
53C3×#950D312yescomplemented
54C3×#950C2×C312yescomplemented
55C3×#919—32no—
56C3×D3×Q16—32no—
57C3×#916—32no—
58C3×#916—32no—
59C3×D3×SD16—32no—
60C3×D3×SD16—32no—
61C3×#912—32no—
62C3×D3×D8—32no—
63C3×#904—32no—
64C2×C3×D3×C8—32no—
65#63950C2×C312yescomplemented
66#63944C2×C311yescharacteristic, complemented
67#63940C2×C311yescharacteristic, complemented
68#63936C2×C312yescomplemented
69#63930C2×C311yescharacteristic, complemented
70#63926C2×C311yescharacteristic, complemented
71#63829C2×C312yescomplemented
72C2×#3710C2×C311yescharacteristic, complemented
73C22×C3×C3⋊D3—21no—
74C22×C3×C3⋊D3D411yescharacteristic
75C2×C3×D32—21no—
76C33×Q8C2311yescharacteristic
77C33×D4—21no—
78C33×D4C2311yescharacteristic
79C2×C33×C4—21no—
80C2×C33×C4C2311yescharacteristic
81C3×#638—21no—
82C3×#638—21no—
83C3×#638—21no—
84C2×C3×C3⋊Dic3—21no—
85C2×C3×C3⋊Dic3D411yescharacteristic
86C3×C4⋊(C3⋊D3)—21no—
87C3×C4⋊(C3⋊D3)C2311yescharacteristic
88C3×C4×C3⋊D3—21no—
89C3×C4×C3⋊D3—21no—
90C3×C4×C3⋊D3—21no—
91C3×C4×C3⋊D3D411yescharacteristic
92C3×C4×C3⋊D3D411yescharacteristic
93C3×C4×C3⋊D3C2311yescharacteristic
94C3×C4×C3⋊D3C2311yescharacteristic
95C3×#634—21no—
96C3×#634C2311yescharacteristic
97C32×#67—22no—
98C32×D12C2312yes—
99C32×C4×D3—22no—
100C32×Dic6C2312yes—
101C3×#627—21no—
102C3×#626—22no—
103C3×#625—21no—
104C3×#624—21no—
105C3×D3×Dic3—22no—
106C32×C3⋊C8C2312yes—
107C32×C3⋊C8C2312yes—
108C2×C3×#135—91no—
109D3×#135—32no—
110C32×#41—21no—
111C32×#41—22no—
112C32×#41—32no—
113C32×#41—41no—
114C32×#41C2×D312yescomplemented
115C32×#41C22×C311yescharacteristic, complemented
116#3832C22×C311yescharacteristic, complemented
117Q8×C3⋊D3C22×C311yescharacteristic
118#3830—21no—
119#3830C22×C311yescharacteristic, complemented
120D4×C3⋊D3—21no—
121D4×C3⋊D3C22×C311yescharacteristic
122#3828—21no—
123#3828C22×C311yescharacteristic, complemented
124C2×C4×C3⋊D3—21no—
125C2×C4×C3⋊D3C22×C311yescharacteristic
126C3×#239—32no—
127C3×#239—32no—
128C3×#239—61no—
129C3×D3×Q8—32no—
130C3×D3×Q8—32no—
131C3×D3×Q8—61no—
132C3×#237—32no—
133C3×#237—32no—
134C3×#237—62no—
135C3×#237—62no—
136C3×#237—61no—
137C3×#237—62no—
138C3×D3×D4—32no—
139C3×D3×D4—32no—
140C3×D3×D4—62no—
141C3×D3×D4—62no—
142C3×D3×D4—61no—
143C3×D3×D4—62no—
144C3×#235—22no—
145C3×#235—32no—
146C3×#235—62no—
147C3×#235—62no—
148C3×#235—61no—
149C3×#235—62no—
150C3×#235C2×D312yescomplemented
151C3×#235C22×C312yescomplemented
152C2×C3×C4×D3—32no—
153C2×C3×C4×D3—62no—
154C2×C3×C4×D3—62no—
155C2×C3×C4×D3—61no—
156C2×C3×C4×D3—62no—
157#3811—21no—
158#3805—21no—
159#3802C22×C311yescharacteristic
160C4×D32—21no—
161#3798—21no—
162#3797C22×C311yescharacteristic
163#3796C22×C312yescomplemented
164C32×Q16—32no—
165C32×SD16—32no—
166C32×SD16—32no—
167C32×D8—32no—
168C2×C32×C8—32no—
169C3×#216—22no—
170C3×#216—32no—
171C3×#216C2×D312yescomplemented
172C3×#216C22×C312yescomplemented
173C3×#215—22no—
174C3×#215—32no—
175C3×#215C2×D312yescomplemented
176C3×#215C22×C312yescomplemented
177C3×#214—22no—
178C3×#214—32no—
179C3×#214C2×D312yescomplemented
180C3×#214C22×C312yescomplemented
181C3×#213—22no—
182C3×#213—32no—
183C3×#213C2×D312yescomplemented
184C3×#213C22×C312yescomplemented
185C2×C3×C3⋊C8—22no—
186C2×C3×C3⋊C8C2×D312yescomplemented
187C2×C3×C3⋊C8C22×C312yescomplemented
188C3×Dic12—32no—
189C3×D24—32no—
190C3×#204—32no—
191C3×#204—32no—
192C3×D3×C8—32no—
193C3×D3×C8—32no—
194C3×D3×C8—32no—
195C3×D3×C8—32no—
196#3719C22×C312yescomplemented
197#3717C22×C312yescomplemented
198#3716C22×C312yescomplemented
199#3714C22×C312yescomplemented
200#3710C22×C311yescharacteristic
201#3710C22×C311yescharacteristic
202#3710C22×C312yescomplemented
203C22×C33—21no—
204C22×C33C2×D411yescharacteristic
205C2×C3×C3⋊D3—22no—
206C2×C3×C3⋊D3—21no—
207C2×C3×C3⋊D3—42no—
208C2×C3×C3⋊D3C2×D411yescharacteristic
209C2×C3×C3⋊D3C2×D411yescharacteristic
210C2×C32×D3—22no—
211C3×D32—42no—
212C33×C4—21no—
213C33×C4C2×D411yescharacteristic
214C33×C4C2411yescharacteristic
215C3×C3⋊Dic3—21no—
216C3×C3⋊Dic3C2×D411yescharacteristic
217C3×C3⋊Dic3C2×D411yescharacteristic
218C32×Dic3—22no—
219C2×C3×#41—91no—
220C2×C3×#41—91no—
221D3×#41—32no—
222D3×#41—32no—
223D3×#41—61no—
224C3×#135—32no—
225C3×#135—32no—
226C3×#135—62no—
227C3×#135—92no—
228C3×#135—92no—
229C3×#135—92no—
230C2×C3×Q16—91no—
231C2×C3×SD16—91no—
232C2×C3×SD16—91no—
233C2×C3×D8—91no—
234C22×C3×C8—91no—
235#950—32no—
236#950C3×D312yescomplemented
237#919—32no—
238D3×Q16—32no—
239#916—32no—
240#916—32no—
241D3×SD16—32no—
242D3×SD16—32no—
243#912—32no—
244D3×D8—32no—
245#904—32no—
246C2×D3×C8—32no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3C3×D411yescharacteristic
249C22×C3×D3—32no—
250C22×C3×D3—61no—
251C22×C3×D3—62no—
252C22×C3×D3—62no—
253C22×C3×D3—62no—
254C2×D32—21no—
255C32×Q8—21no—
256C32×Q8—22no—
257C32×Q8—32no—
258C32×Q8—41no—
259C32×Q8C22×D312yes—
260C32×Q8C23×C311yescharacteristic
261C32×D4—21no—
262C32×D4—22no—
263C32×D4—22no—
264C32×D4—21no—
265C32×D4—22no—
266C32×D4—32no—
267C32×D4—41no—
268C32×D4—42no—
269C32×D4—42no—
270C32×D4—62no—
271C32×D4C22×D312yes—
272C32×D4C23×C311yescharacteristic
273C2×C32×C4—21no—
274C2×C32×C4—22no—
275C2×C32×C4—22no—
276C2×C32×C4—21no—
277C2×C32×C4—22no—
278C2×C32×C4—41no—
279C2×C32×C4—42no—
280C2×C32×C4—42no—
281C2×C32×C4—62no—
282C2×C32×C4C22×D312yes—
283C2×C32×C4C23×C311yescharacteristic
284#638—21no—
285#638—21no—
286#638—21no—
287C2×C3⋊Dic3—21no—
288C2×C3⋊Dic3C3×D411yescharacteristic
289C4⋊(C3⋊D3)—21no—
290C4⋊(C3⋊D3)C23×C311yescharacteristic
291C4×C3⋊D3—21no—
292C4×C3⋊D3—21no—
293C4×C3⋊D3—21no—
294C4×C3⋊D3C3×D411yescharacteristic
295C4×C3⋊D3C3×D411yescharacteristic
296C4×C3⋊D3C23×C311yescharacteristic
297C4×C3⋊D3C23×C311yescharacteristic
298#634—21no—
299#634C23×C311yescharacteristic
300C3×#67—22no—
301C3×#67—22no—
302C3×#67—42no—
303C3×#67—62no—
304C3×#67—62no—
305C3×#67—62no—
306C3×#67—62no—
307C3×#67—62no—
308C3×#67—62no—
309C3×#67—62no—
310C3×#67—62no—
311C2×C3×Dic3—32no—
312C2×C3×Dic3—61no—
313C2×C3×Dic3—62no—
314C2×C3×Dic3—62no—
315C2×C3×Dic3—62no—
316C3×D12—22no—
317C3×D12—32no—
318C3×D12—61no—
319C3×D12—62no—
320C3×D12—62no—
321C3×D12—62no—
322C3×D12C22×D312yes—
323C3×D12C23×C312yes—
324C3×C4×D3—22no—
325C3×C4×D3—22no—
326C3×C4×D3—32no—
327C3×C4×D3—32no—
328C3×C4×D3—32no—
329C3×C4×D3—32no—
330C3×C4×D3—42no—
331C3×C4×D3—61no—
332C3×C4×D3—61no—
333C3×C4×D3—61no—
334C3×C4×D3—61no—
335C3×C4×D3—62no—
336C3×C4×D3—62no—
337C3×C4×D3—62no—
338C3×C4×D3—62no—
339C3×C4×D3—62no—
340C3×C4×D3—62no—
341C3×C4×D3—62no—
342C3×C4×D3—62no—
343C3×Dic6—22no—
344C3×Dic6—32no—
345C3×Dic6—61no—
346C3×Dic6—62no—
347C3×Dic6—62no—
348C3×Dic6—62no—
349C3×Dic6C22×D312yes—
350C3×Dic6C23×C312yes—
351#627—21no—
352#626—22no—
353#625—21no—
354#624—21no—
355D3×Dic3—22no—
356C32×C8—32no—
357C32×C8—32no—
358C3×C3⋊C8—22no—
359C3×C3⋊C8—22no—
360C3×C3⋊C8C22×D312yes—
361C3×C3⋊C8C22×D312yes—
362C3×C3⋊C8C23×C312yes—
363C3×C3⋊C8C23×C312yes—
364C2×#135—91noSylow
365C2×C33—21no—
366C2×C33—41no—
367C2×C33C22×D411yescharacteristic
368C3×C3⋊D3—21no—
369C3×C3⋊D3—41no—
370C3×C3⋊D3#13512yescomplemented
371C32×D3—42no—
372C3×#41—21no—
373C3×#41—22no—
374C3×#41—32no—
375C3×#41—32no—
376C3×#41—41no—
377C3×#41—62no—
378C3×#41—92no—
379C3×#41—91no—
380C3×#41—91no—
381C3×#41—91no—
382C3×#41—181no—
383C3×#41—181no—
384C3×#41—181no—
385C3×#41—181no—
386C3×#41D3211yescharacteristic, complemented
387C3×#41C2×C3×D312yescomplemented
388C2×C3×Q8—91no—
389C2×C3×Q8—91no—
390C2×C3×D4—91no—
391C2×C3×D4—91no—
392C2×C3×D4—181no—
393C2×C3×D4—181no—
394C22×C3×C4—91no—
395C22×C3×C4—181no—
396C22×C3×C4—181no—
397#239—32no—
398#239—32no—
399#239—61no—
400D3×Q8—32no—
401D3×Q8—32no—
402D3×Q8—61no—
403#237—32no—
404#237—32no—
405#237—61no—
406#237—62no—
407#237—62no—
408#237—62no—
409D3×D4—32no—
410D3×D4—32no—
411D3×D4—61no—
412D3×D4—62no—
413D3×D4—62no—
414D3×D4—62no—
415#235—32no—
416#235—61no—
417#235—62no—
418#235—62no—
419#235—62no—
420#235C2×C3×D312yescomplemented
421C2×C4×D3—32no—
422C2×C4×D3—61no—
423C2×C4×D3—62no—
424C2×C4×D3—62no—
425C2×C4×D3—62no—
426C3×Q16—32no—
427C3×Q16—32no—
428C3×Q16—62no—
429C3×Q16—92no—
430C3×SD16—32no—
431C3×SD16—32no—
432C3×SD16—32no—
433C3×SD16—32no—
434C3×SD16—62no—
435C3×SD16—62no—
436C3×SD16—92no—
437C3×SD16—92no—
438C3×D8—32no—
439C3×D8—32no—
440C3×D8—62no—
441C3×D8—92no—
442C2×C3×C8—32no—
443C2×C3×C8—32no—
444C2×C3×C8—62no—
445C2×C3×C8—91no—
446C2×C3×C8—91no—
447C2×C3×C8—92no—
448#216—32no—
449#216C2×C3×D312yescomplemented
450#215—32no—
451#215C2×C3×D312yescomplemented
452#214—32no—
453#214C2×C3×D312yescomplemented
454#213—32no—
455#213C2×C3×D312yescomplemented
456C2×C3⋊C8C2×C3×D312yescomplemented
457Dic12—32no—
458D24—32no—
459#204—32no—
460#204—32no—
461D3×C8—32no—
462D3×C8—32no—
463D3×C8—32no—
464D3×C8—32no—
465C22×C32—21no—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—21no—
469C22×C32—22no—
470C22×C32—41no—
471C22×C32—42no—
472C22×C32—42no—
473C22×C32—62no—
474C22×C32D3×D412yes—
475C22×C32C2×C3×D411yescharacteristic
476C2×C3⋊D3—21no—
477C2×C3⋊D3—22no—
478C2×C3⋊D3—42no—
479C2×C3⋊D3C2×C3×D411yescharacteristic
480C2×C3⋊D3C2×C3×D411yescharacteristic
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—32no—
484C2×C3×D3—32no—
485C2×C3×D3—42no—
486C2×C3×D3—61no—
487C2×C3×D3—61no—
488C2×C3×D3—64no—
489C2×C3×D3—62no—
490C2×C3×D3—62no—
491C2×C3×D3—122no—
492C2×C3×D3—124no—
493C2×C3×D3—124no—
494C2×C3×D3—124no—
495D32—42no—
496C32×C4—21no—
497C32×C4—22no—
498C32×C4—22no—
499C32×C4—21no—
500C32×C4—22no—
501C32×C4—21no—
502C32×C4—22no—
503C32×C4—41no—
504C32×C4—41no—
505C32×C4—42no—
506C32×C4—42no—
507C32×C4—62no—
508C32×C4D3×D412yes—
509C32×C4C2×C3×D411yescharacteristic
510C32×C4C23×D312yes—
511C32×C4C24×C311yescharacteristic
512C3⋊Dic3—21no—
513C3⋊Dic3C2×C3×D411yescharacteristic
514C3⋊Dic3C2×C3×D411yescharacteristic
515C3×Dic3—22no—
516C3×Dic3—22no—
517C3×Dic3—32no—
518C3×Dic3—32no—
519C3×Dic3—42no—
520C3×Dic3—61no—
521C3×Dic3—61no—
522C3×Dic3—62no—
523C3×Dic3—62no—
524C2×#41—91no—
525C2×#41—91no—
526#135—32no—
527#135—92no—
528#135—92no—
529#135—92no—
530C2×Q16—91no—
531C2×SD16—91no—
532C2×SD16—91no—
533C2×D8—91no—
534C22×C8—91no—
535C33C2×#13511yescharacteristic, complemented, Sylow
536C23×C3—91no—
537C23×C3—181no—
538C23×C3—181no—
539C22×D3—32no—
540C22×D3—61no—
541C22×D3—62no—
542C22×D3—62no—
543C22×D3—62no—
544C3×Q8—21no—
545C3×Q8—22no—
546C3×Q8—32no—
547C3×Q8—32no—
548C3×Q8—41no—
549C3×Q8—62no—
550C3×Q8—91no—
551C3×Q8—181no—
552C3×Q8—181no—
553C3×Q8C2×D3211yescharacteristic
554C3×Q8C22×C3×D312yes—
555C3×D4—22no—
556C3×D4—21no—
557C3×D4—22no—
558C3×D4—21no—
559C3×D4—22no—
560C3×D4—32no—
561C3×D4—32no—
562C3×D4—42no—
563C3×D4—42no—
564C3×D4—41no—
565C3×D4—62no—
566C3×D4—62no—
567C3×D4—62no—
568C3×D4—91no—
569C3×D4—122no—
570C3×D4—181no—
571C3×D4—182no—
572C3×D4—181no—
573C3×D4—181no—
574C3×D4—181no—
575C3×D4—181no—
576C3×D4C2×D3211yescharacteristic
577C3×D4C22×C3×D312yes—
578C2×C3×C4—22no—
579C2×C3×C4—21no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—21no—
583C2×C3×C4—42no—
584C2×C3×C4—42no—
585C2×C3×C4—41no—
586C2×C3×C4—62no—
587C2×C3×C4—62no—
588C2×C3×C4—91no—
589C2×C3×C4—91no—
590C2×C3×C4—91no—
591C2×C3×C4—91no—
592C2×C3×C4—91no—
593C2×C3×C4—122no—
594C2×C3×C4—181no—
595C2×C3×C4—181no—
596C2×C3×C4—181no—
597C2×C3×C4—182no—
598C2×C3×C4—181no—
599C2×C3×C4—181no—
600C2×C3×C4C2×D3211yescharacteristic
601C2×C3×C4C22×C3×D312yes—
602#67—22no—
603#67—62no—
604#67—62no—
605#67—62no—
606#67—62no—
607#67—62no—
608#67—62no—
609#67—62no—
610#67—62no—
611C2×Dic3—32no—
612C2×Dic3—61no—
613C2×Dic3—62no—
614C2×Dic3—62no—
615C2×Dic3—62no—
616D12—32no—
617D12—61no—
618D12—62no—
619D12—62no—
620D12—62no—
621D12C22×C3×D312yes—
622C4×D3—22no—
623C4×D3—32no—
624C4×D3—32no—
625C4×D3—32no—
626C4×D3—32no—
627C4×D3—61no—
628C4×D3—61no—
629C4×D3—61no—
630C4×D3—61no—
631C4×D3—62no—
632C4×D3—62no—
633C4×D3—62no—
634C4×D3—62no—
635C4×D3—62no—
636C4×D3—62no—
637C4×D3—62no—
638C4×D3—62no—
639Dic6—32no—
640Dic6—61no—
641Dic6—62no—
642Dic6—62no—
643Dic6—62no—
644Dic6C22×C3×D312yes—
645C3×C8—32no—
646C3×C8—32no—
647C3×C8—32no—
648C3×C8—32no—
649C3×C8—62no—
650C3×C8—62no—
651C3⋊C8C22×C3×D312yes—
652C3⋊C8C22×C3×D312yes—
653C2×C32—21no—
654C2×C32—22no—
655C2×C32—21no—
656C2×C32—22no—
657C2×C32—41no—
658C2×C32—41no—
659C2×C32—42no—
660C2×C32—41no—
661C2×C32—42no—
662C2×C32—42no—
663C2×C32—81no—
664C2×C32—82no—
665C2×C32—82no—
666C2×C32—122no—
667C2×C32C2×D3×D412yes—
668C2×C32C22×C3×D411yescharacteristic
669C3⋊D3—21no—
670C3⋊D3—41no—
671C3⋊D3C3×#13512yescomplemented
672C3×D3—34no—
673C3×D3—42no—
674C3×D3—42no—
675C3×D3—62no—
676C3×D3—62no—
677C3×D3—82no—
678C3×D3—121no—
679C3×D3—122no—
680C3×D3—122no—
681#41—32no—
682#41—92no—
683#41—91no—
684#41—91no—
685#41—91no—
686#41—181no—
687#41—181no—
688#41—181no—
689#41—181no—
690#41C3×D3211yescharacteristic, complemented
691C2×Q8—91no—
692C2×Q8—91no—
693C2×D4—91no—
694C2×D4—91no—
695C2×D4—181no—
696C2×D4—181no—
697C22×C4—91no—
698C22×C4—181no—
699C22×C4—181no—
700Q16—32no—
701Q16—92no—
702SD16—32no—
703SD16—32no—
704SD16—92no—
705SD16—92no—
706D8—32no—
707D8—92no—
708C2×C8—32no—
709C2×C8—91no—
710C2×C8—91no—
711C2×C8—92no—
712C22×C3—22no—
713C22×C3—21no—
714C22×C3—22no—
715C22×C3—21no—
716C22×C3—22no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—41no—
720C22×C3—62no—
721C22×C3—62no—
722C22×C3—91no—
723C22×C3—91no—
724C22×C3—122no—
725C22×C3—182no—
726C22×C3—181no—
727C22×C3—362no—
728C22×C3—362no—
729C22×C3#381111yescharacteristic
730C22×C3C3×D3×D412yes—
731C2×D3—22no—
732C2×D3—32no—
733C2×D3—32no—
734C2×D3—61no—
735C2×D3—61no—
736C2×D3—64no—
737C2×D3—62no—
738C2×D3—62no—
739C2×D3—122no—
740C2×D3—124no—
741C2×D3—124no—
742C2×D3—124no—
743C3×C4—22no—
744C3×C4—21no—
745C3×C4—22no—
746C3×C4—22no—
747C3×C4—21no—
748C3×C4—21no—
749C3×C4—22no—
750C3×C4—42no—
751C3×C4—42no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—62no—
755C3×C4—62no—
756C3×C4—91no—
757C3×C4—91no—
758C3×C4—122no—
759C3×C4—181no—
760C3×C4#381111yescharacteristic
761C3×C4C3×D3×D412yes—
762C3×C4C22×D3211yescharacteristic
763C3×C4C23×C3×D312yes—
764Dic3—22no—
765Dic3—32no—
766Dic3—32no—
767Dic3—61no—
768Dic3—61no—
769Dic3—62no—
770Dic3—62no—
771C32—22no—
772C32—21no—
773C32—41no—
774C32D3×#13512yescomplemented
775C32C2×C3×#13511yescharacteristic, complemented
776C23—91no—
777C23—181no—
778C23—181no—
779Q8—32no—
780Q8—91no—
781Q8—181no—
782Q8—181no—
783Q8C2×C3×D3211yescharacteristic
784D4—21no—
785D4—32no—
786D4—62no—
787D4—91no—
788D4—181no—
789D4—182no—
790D4—181no—
791D4—181no—
792D4—181no—
793D4—181no—
794D4C2×C3×D3211yescharacteristic
795C2×C4—21no—
796C2×C4—62no—
797C2×C4—91no—
798C2×C4—91no—
799C2×C4—91no—
800C2×C4—91no—
801C2×C4—91no—
802C2×C4—181no—
803C2×C4—181no—
804C2×C4—181no—
805C2×C4—182no—
806C2×C4—181no—
807C2×C4—181no—
808C2×C4C2×C3×D3211yescharacteristic
809C8—32no—
810C8—32no—
811C2×C3—22no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—22no—
815C2×C3—41no—
816C2×C3—42no—
817C2×C3—42no—
818C2×C3—42no—
819C2×C3—41no—
820C2×C3—41no—
821C2×C3—81no—
822C2×C3—82no—
823C2×C3—82no—
824C2×C3—92no—
825C2×C3—122no—
826C2×C3—122no—
827C2×C3—181no—
828C2×C3—242no—
829C2×C3—361no—
830C2×C3C2×#381111yescharacteristic
831C2×C3C2×C3×D3×D412yes—
832D3—34no—
833D3—42no—
834D3—62no—
835D3—62no—
836D3—121no—
837D3—122no—
838D3—122no—
839C22—21no—
840C22—62no—
841C22—91no—
842C22—91no—
843C22—182no—
844C22—181no—
845C22—362no—
846C22—362no—
847C22C3×#381111yescharacteristic
848C4—21no—
849C4—62no—
850C4—91no—
851C4—91no—
852C4—181no—
853C4C3×#381111yescharacteristic
854C4C22×C3×D3211yescharacteristic
855C3—21no—
856C3—22no—
857C3—41no—
858C3#1059545911yescharacteristic, direct product factor
859C3C3×D3×#13512yescomplemented
860C2—21no—
861C2—41no—
862C2—92no—
863C2—122no—
864C2—181no—
865C2—361no—
866C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC3×C4#3811
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×#41C22
socleC2×C33C22×D4
hypercenterC3×#41D32
hypocenterC32C2×C3×#135
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×#41

Complements

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

NH ≅ G/Ntype
1. C3×#41×C3⋊D3C2semidirect
2. C3×#64306C2semidirect
3. C32×#950C2semidirect
4. C3×#63950C2semidirect
5. C3×#63944C2semidirect
6. C3×#63940C2semidirect
7. C3×#63936C2semidirect
8. C3×#63930C2semidirect
9. C3×#63926C2semidirect
10. C3×#63829C2semidirect
11. C2×C3×#3710C2semidirect
13. #10595459C3direct (N × H)
14. C33×#41C22semidirect
15. C3×#3832C22semidirect
18. C3×#3830C22semidirect
22. C3×#3828C22semidirect
25. C32×#235C22semidirect
32. C3×#3796C22semidirect
33. C32×#216C22semidirect
34. C32×#215C22semidirect
35. C32×#214C22semidirect
36. C32×#213C22semidirect
37. C2×C32×C3⋊C8C22semidirect
38. C3×#3719C22semidirect
39. C3×#3717C22semidirect
40. C3×#3716C22semidirect
41. C3×#3714C22semidirect
44. C3×#3710C22semidirect
45. #41×C3⋊D3C2×C3semidirect
49. #64306C2×C3semidirect
53. C3×#950D3semidirect
54. C3×#950C2×C3semidirect
65. #63950C2×C3semidirect
66. #63944C2×C3semidirect
67. #63940C2×C3semidirect
68. #63936C2×C3semidirect
69. #63930C2×C3semidirect
70. #63926C2×C3semidirect
71. #63829C2×C3semidirect
72. C2×#3710C2×C3semidirect
114. C32×#41C2×D3semidirect
115. C32×#41C22×C3semidirect
116. #3832C22×C3semidirect
119. #3830C22×C3semidirect
123. #3828C22×C3semidirect
150. C3×#235C2×D3semidirect
151. C3×#235C22×C3semidirect
163. #3796C22×C3semidirect
171. C3×#216C2×D3semidirect
172. C3×#216C22×C3semidirect
175. C3×#215C2×D3semidirect
176. C3×#215C22×C3semidirect
179. C3×#214C2×D3semidirect
180. C3×#214C22×C3semidirect
183. C3×#213C2×D3semidirect
184. C3×#213C22×C3semidirect
186. C2×C3×C3⋊C8C2×D3semidirect
187. C2×C3×C3⋊C8C22×C3semidirect
196. #3719C22×C3semidirect
197. #3717C22×C3semidirect
198. #3716C22×C3semidirect
199. #3714C22×C3semidirect
202. #3710C22×C3semidirect
236. #950C3×D3semidirect
370. C3×C3⋊D3#135semidirect
386. C3×#41D32semidirect
387. C3×#41C2×C3×D3semidirect
420. #235C2×C3×D3semidirect
449. #216C2×C3×D3semidirect
451. #215C2×C3×D3semidirect
453. #214C2×C3×D3semidirect
455. #213C2×C3×D3semidirect
456. C2×C3⋊C8C2×C3×D3semidirect
535. C33C2×#135semidirect
671. C3⋊D3C3×#135semidirect
690. #41C3×D32semidirect
774. C32D3×#135semidirect
775. C32C2×C3×#135semidirect
858. C3#10595459direct (N × H)
859. C3C3×D3×#135semidirect

Maximal subgroups

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

subgroupindex
C3×#41×C3⋊D32
C3×#643062
C32×#9502
C3×#639502
C3×#639442
C3×#639402
C3×#639362
C3×#639302
C3×#639262
C3×#638292
C2×C3×#37102
C3×D3×#1353
#105954593