Finite Group Databasebeta

← C3×#10595465 #13175062

Subgroups — C3×#10595465 #13175062

Order 1728.

1300 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#1010C211yesmaximal, characteristic, complemented
2C3×#64297C211yesmaximal, characteristic, complemented
3C3×#64159C211yesmaximal, characteristic, complemented
4C32×#951C211yesmaximal, characteristic, complemented
5C3×#63948C212yesmaximal, complemented
6C3×D3×#216C212yesmaximal, complemented
7C3×#63935C212yesmaximal, complemented
8C3×#63929C212yesmaximal, complemented
9C2×C3×#3718C211yesmaximal, characteristic, complemented
10C3×#63833C211yesmaximal, characteristic, complemented
11C3×#63815C211yesmaximal, characteristic, complemented
12C3×#5838—31nomaximal
13C3×#5779—31nomaximal
14#10595465C311yesmaximal, characteristic, direct product factor
15C33×#41C2211yescharacteristic
16C3×#3828C2211yescharacteristic
17C32×D3×Q8C2212yes—
18C32×#237—22no—
19C32×#237C2212yes—
20C32×#235—21no—
21C32×#235C2211yescharacteristic
22C2×C32×Dic6—21no—
23C2×C32×Dic6C2211yescharacteristic
24C2×C32×Dic6C2211yescharacteristic
25C3×#3804—22no—
26C3×#3799C2212yes—
27C3×#3797—21no—
28C3×#3796—21no—
29C3×D3×Dic6C2212yes—
30C3×#3756C2211yescharacteristic
31C3×#3755C2211yescharacteristic
32C3×#3754C2211yescharacteristic
33C3×#3753C2211yescharacteristic
34C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
35C32×#216C2212yes—
36C32×#214C2212yes—
37C32×#208C2211yescharacteristic
38C3×#3719C2212yes—
39C3×#3718C2212yes—
40C3×#3718C2212yes—
41C3×#3717C2212yes—
42C3×#3711C2212yes—
43C3×D3×C3⋊C8C2212yes—
44C32×2−1+4—31no—
45C3×#1010—21no—
46C3×#1010—31no—
47C3×#1010D311yescharacteristic, complemented
48C3×#1010C2×C311yescharacteristic, complemented
49C3×#1007—31no—
50#64297C2×C311yescharacteristic, complemented
51C32×#137—31no—
52#64159C2×C311yescharacteristic, complemented
53C3×#951—21no—
54C3×#951—32no—
55C3×#951D311yescharacteristic, complemented
56C3×#951C2×C311yescharacteristic, complemented
57C3×#950—31no—
58C3×#950—31no—
59C3×#950—32no—
60C3×#950—61no—
61C3×#948—31no—
62C2×C3×#216—31no—
63C2×C3×#216—31no—
64C2×C3×#216—32no—
65C3×#942—32no—
66C3×#942—31no—
67C3×#918—32no—
68C3×D3×Q16—32no—
69C3×#916—32no—
70C3×#915—32no—
71C3×#909—31no—
72C3×#907—31no—
73#63948C2×C312yescomplemented
74D3×#216C2×C312yescomplemented
75#63935C2×C312yescomplemented
76#63929C2×C312yescomplemented
77C2×#3718C2×C311yescharacteristic, complemented
78#63833C2×C311yescharacteristic, complemented
79#63815C2×C311yescharacteristic, complemented
80C33×Q8C2311yescharacteristic
81C33×D4—21no—
82C33×D4C2311yescharacteristic
83C2×C33×C4—21no—
84C2×C33×C4C2311yescharacteristic
85C3×#638—21no—
86C3×C4⋊(C3⋊D3)C2311yescharacteristic
87C3×C4×C3⋊D3—21no—
88C3×#634C2311yescharacteristic
89C32×#67—22no—
90C32×#67D412yes—
91C2×C32×Dic3—21no—
92C2×C32×Dic3—21no—
93C2×C32×Dic3—22no—
94C32×D12D411yescharacteristic
95C32×C4×D3—22no—
96C32×C4×D3C2312yes—
97C32×Dic6—21no—
98C32×Dic6—21no—
99C32×Dic6—22no—
100C32×Dic6D411yescharacteristic
101C32×Dic6C2312yes—
102C32×Dic6C2312yes—
103C3×#627—22no—
104C3×#626—22no—
105C3×#624—22no—
106C3×D3×Dic3—22no—
107C3×C3⋊(C3⋊C8)C2311yescharacteristic
108C3×C3⋊(C3⋊C8)C2311yescharacteristic
109C32×C3⋊C8C2312yes—
110C3×#578—91no—
111#5838—31no—
112#5779—31no—
113C32×#41—21no—
114C32×#41—21no—
115C32×#41—21no—
116C32×#41—31no—
117C32×#41—32no—
118C32×#41—41no—
119C32×#41—61no—
120C32×#41—62no—
121C32×#41C2×D311yescharacteristic
122C32×#41C2×D311yescharacteristic
123C32×#41C22×C311yescharacteristic
124C2×C32×Q8—32no—
125C2×C32×Q8—31no—
126C2×C32×Q8—31no—
127C2×C32×Q8—61no—
128#3828C22×C311yescharacteristic
129C3×#239—32no—
130C3×#239—61no—
131C3×D3×Q8—22no—
132C3×D3×Q8—32no—
133C3×D3×Q8—61no—
134C3×D3×Q8—61no—
135C3×D3×Q8C2×D312yes—
136C3×D3×Q8C22×C312yes—
137C3×#237—24no—
138C3×#237—22no—
139C3×#237—22no—
140C3×#237—22no—
141C3×#237—61no—
142C3×#237—62no—
143C3×#237C2×D312yes—
144C3×#237C22×C312yes—
145C3×#235—22no—
146C3×#235—21no—
147C3×#235—21no—
148C3×#235—21no—
149C3×#235—31no—
150C3×#235—31no—
151C3×#235—32no—
152C3×#235—62no—
153C3×#235—61no—
154C3×#235C2×D311yescharacteristic
155C3×#235C22×C311yescharacteristic
156C2×C3×Dic6—22no—
157C2×C3×Dic6—21no—
158C2×C3×Dic6—21no—
159C2×C3×Dic6—21no—
160C2×C3×Dic6—21no—
161C2×C3×Dic6—32no—
162C2×C3×Dic6C2×D311yescharacteristic
163C2×C3×Dic6C2×D311yescharacteristic
164C2×C3×Dic6C22×C311yescharacteristic
165C2×C3×Dic6C22×C311yescharacteristic
166#3804—22no—
167#3799C22×C312yes—
168#3797—21no—
169#3796—21no—
170D3×Dic6C22×C312yes—
171C32×Q16—32no—
172C32×SD16—32no—
173C32×M16—31no—
174#3756C22×C311yescharacteristic
175#3755C22×C311yescharacteristic
176#3754C22×C311yescharacteristic
177#3753C22×C311yescharacteristic
178C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
179C3×#216—22no—
180C3×#216—31no—
181C3×#216—31no—
182C3×#216—32no—
183C3×#216—32no—
184C3×#216—32no—
185C3×#216—32no—
186C3×#216—32no—
187C3×#216—61no—
188C3×#216C2×D312yes—
189C3×#216C22×C312yes—
190C3×#215—31no—
191C3×#215—31no—
192C3×#215—32no—
193C3×#215—61no—
194C3×#214—22no—
195C3×#214—31no—
196C3×#214—31no—
197C3×#214—61no—
198C3×#214C2×D312yes—
199C3×#214C22×C312yes—
200C3×#213—31no—
201C3×#213—31no—
202C3×#213—61no—
203C3×#208—21no—
204C3×#208—32no—
205C3×#208C2×D311yescharacteristic
206C3×#208C22×C311yescharacteristic
207C2×C3×C3⋊C8—31no—
208C2×C3×C3⋊C8—31no—
209C2×C3×C3⋊C8—32no—
210C2×C3×C3⋊C8—61no—
211C3×Dic12—32no—
212C3×#204—32no—
213C3×ΓL(1,𝔽25)—32no—
214C3×D3×C8—32no—
215#3719C22×C312yes—
216#3718C22×C312yes—
217#3718C22×C312yes—
218#3717C22×C312yes—
219#3711C22×C312yes—
220D3×C3⋊C8C22×C312yes—
221C22×C33—21no—
222C22×C33C2×D411yescharacteristic
223C2×C3×C3⋊D3—21no—
224C2×C32×D3C2×D412yes—
225C33×C4—21no—
226C33×C4C2×D411yescharacteristic
227C33×C4C2411yescharacteristic
228C3×C3⋊Dic3—21no—
229C32×Dic3—22no—
230C32×Dic3—22no—
231C32×Dic3C2×D412yes—
232C3×2−1+4—31no—
233C3×2−1+4—31no—
234C3×2−1+4—61no—
235C3×2−1+4—91no—
236#1010—31no—
237#1010C3×D311yescharacteristic, complemented
238#1007—31no—
239C3×#137—31no—
240C3×#137—31no—
241C3×#137—61no—
242C3×#137—91no—
243C3×#137—92no—
244C3×#137—92no—
245C3×#135—92no—
246C3×#135—91no—
247C2×C3×Q16—92no—
248C2×C3×Q16—91no—
249C3×#131—91no—
250#951—32no—
251#951C3×D311yescharacteristic, complemented
252#950—31no—
253#950—31no—
254#950—32no—
255#950—61no—
256#948—31no—
257C2×#216—31no—
258C2×#216—31no—
259C2×#216—32no—
260#942—32no—
261#942—31no—
262#918—32no—
263D3×Q16—32no—
264#916—32no—
265#915—32no—
266#909—31no—
267#907—31no—
268C32×Q8—21no—
269C32×Q8—21no—
270C32×Q8—21no—
271C32×Q8—31no—
272C32×Q8—32no—
273C32×Q8—32no—
274C32×Q8—41no—
275C32×Q8—62no—
276C32×Q8—61no—
277C32×Q8—61no—
278C32×Q8C22×D311yescharacteristic
279C32×Q8C22×D311yescharacteristic
280C32×Q8C23×C311yescharacteristic
281C32×D4—21no—
282C32×D4—22no—
283C32×D4—21no—
284C32×D4—21no—
285C32×D4—21no—
286C32×D4—21no—
287C32×D4—21no—
288C32×D4—32no—
289C32×D4—31no—
290C32×D4—41no—
291C32×D4—41no—
292C32×D4—41no—
293C32×D4—42no—
294C32×D4—62no—
295C32×D4C22×D311yescharacteristic
296C32×D4C22×D311yescharacteristic
297C32×D4C23×C311yescharacteristic
298C2×C32×C4—21no—
299C2×C32×C4—22no—
300C2×C32×C4—21no—
301C2×C32×C4—21no—
302C2×C32×C4—21no—
303C2×C32×C4—21no—
304C2×C32×C4—21no—
305C2×C32×C4—32no—
306C2×C32×C4—41no—
307C2×C32×C4—41no—
308C2×C32×C4—41no—
309C2×C32×C4—42no—
310C2×C32×C4—62no—
311C2×C32×C4—62no—
312C2×C32×C4—61no—
313C2×C32×C4—61no—
314C2×C32×C4C22×D311yescharacteristic
315C2×C32×C4C22×D311yescharacteristic
316C2×C32×C4C23×C311yescharacteristic
317#638—21no—
318C4⋊(C3⋊D3)C23×C311yescharacteristic
319C4×C3⋊D3—21no—
320#634C23×C311yescharacteristic
321C3×#67—24no—
322C3×#67—22no—
323C3×#67—22no—
324C3×#67—22no—
325C3×#67—62no—
326C3×#67—61no—
327C3×#67—61no—
328C3×#67—121no—
329C3×#67#6712yes—
330C3×#67C3×D412yes—
331C2×C3×Dic3—22no—
332C2×C3×Dic3—24no—
333C2×C3×Dic3—21no—
334C2×C3×Dic3—21no—
335C2×C3×Dic3—21no—
336C2×C3×Dic3—21no—
337C2×C3×Dic3—22no—
338C2×C3×Dic3—22no—
339C2×C3×Dic3—41no—
340C2×C3×Dic3—62no—
341C3×D12—21no—
342C3×D12—31no—
343C3×D12—31no—
344C3×D12—61no—
345C3×D12—62no—
346C3×D12#6711yescharacteristic
347C3×D12C3×D411yescharacteristic
348C3×C4×D3—24no—
349C3×C4×D3—22no—
350C3×C4×D3—22no—
351C3×C4×D3—22no—
352C3×C4×D3—62no—
353C3×C4×D3—62no—
354C3×C4×D3—61no—
355C3×C4×D3—61no—
356C3×C4×D3—62no—
357C3×C4×D3—121no—
358C3×C4×D3C22×D312yes—
359C3×C4×D3C23×C312yes—
360C3×Dic6—22no—
361C3×Dic6—24no—
362C3×Dic6—21no—
363C3×Dic6—21no—
364C3×Dic6—21no—
365C3×Dic6—21no—
366C3×Dic6—22no—
367C3×Dic6—22no—
368C3×Dic6—21no—
369C3×Dic6—22no—
370C3×Dic6—22no—
371C3×Dic6—31no—
372C3×Dic6—31no—
373C3×Dic6—41no—
374C3×Dic6—61no—
375C3×Dic6—62no—
376C3×Dic6—62no—
377C3×Dic6#6711yescharacteristic
378C3×Dic6C3×D411yescharacteristic
379C3×Dic6C22×D312yes—
380C3×Dic6C22×D312yes—
381C3×Dic6C23×C312yes—
382C3×Dic6C23×C312yes—
383#627—22no—
384#626—22no—
385#624—22no—
386D3×Dic3—22no—
387C32×C8—32no—
388C3⋊(C3⋊C8)C23×C311yescharacteristic
389C3⋊(C3⋊C8)C23×C311yescharacteristic
390C3×C3⋊C8—22no—
391C3×C3⋊C8—31no—
392C3×C3⋊C8—31no—
393C3×C3⋊C8—31no—
394C3×C3⋊C8—31no—
395C3×C3⋊C8—61no—
396C3×C3⋊C8—61no—
397C3×C3⋊C8C22×D312yes—
398C3×C3⋊C8C23×C312yes—
399#578—91noSylow
400C2×C33—21no—
401C2×C33—41no—
402C2×C33C22×D411yescharacteristic
403C3×C3⋊D3—41no—
404C32×D3—22no—
405C3×#41—21no—
406C3×#41—21no—
407C3×#41—21no—
408C3×#41—31no—
409C3×#41—31no—
410C3×#41—32no—
411C3×#41—32no—
412C3×#41—41no—
413C3×#41—61no—
414C3×#41—62no—
415C3×#41—61no—
416C3×#41—61no—
417C3×#41—62no—
418C3×#41—62no—
419C3×#41—62no—
420C3×#41—64no—
421C3×#41—92no—
422C3×#41—91no—
423C3×#41—182no—
424C3×#41—181no—
425C3×#41D3211yescharacteristic
426C3×#41C2×C3×D311yescharacteristic
427C3×#41C2×C3×D311yescharacteristic
428C2×C3×Q8—32no—
429C2×C3×Q8—32no—
430C2×C3×Q8—31no—
431C2×C3×Q8—31no—
432C2×C3×Q8—31no—
433C2×C3×Q8—31no—
434C2×C3×Q8—61no—
435C2×C3×Q8—61no—
436C2×C3×Q8—62no—
437C2×C3×Q8—61no—
438C2×C3×Q8—61no—
439C2×C3×Q8—62no—
440C2×C3×Q8—92no—
441C2×C3×Q8—181no—
442#239—32no—
443#239—61no—
444D3×Q8—32no—
445D3×Q8—61no—
446D3×Q8—61no—
447D3×Q8C2×C3×D312yes—
448#237—22no—
449#237—61no—
450#237—62no—
451#237C2×C3×D312yes—
452#235—21no—
453#235—31no—
454#235—31no—
455#235—32no—
456#235—61no—
457#235—62no—
458#235C2×C3×D311yescharacteristic
459C2×Dic6—21no—
460C2×Dic6—32no—
461C2×Dic6C2×C3×D311yescharacteristic
462C2×Dic6C2×C3×D311yescharacteristic
463C3×Q16—32no—
464C3×Q16—32no—
465C3×Q16—62no—
466C3×Q16—92no—
467C3×Q16—92no—
468C3×Q16—92no—
469C3×Q16—91no—
470C3×SD16—32no—
471C3×SD16—32no—
472C3×SD16—62no—
473C3×SD16—92no—
474C3×SD16—91no—
475C3×SD16—91no—
476C3×D8—91no—
477C3×M16—31no—
478C3×M16—31no—
479C3×M16—61no—
480C3×M16—92no—
481C2×C3×C8—92no—
482C2×C3×C8—91no—
483#216—31no—
484#216—31no—
485#216—32no—
486#216—32no—
487#216—32no—
488#216—32no—
489#216—32no—
490#216—61no—
491#216C2×C3×D312yes—
492#215—31no—
493#215—31no—
494#215—32no—
495#215—61no—
496#214—31no—
497#214—31no—
498#214—61no—
499#214C2×C3×D312yes—
500#213—31no—
501#213—31no—
502#213—61no—
503#208—32no—
504#208C2×C3×D311yescharacteristic
505C2×C3⋊C8—31no—
506C2×C3⋊C8—31no—
507C2×C3⋊C8—32no—
508C2×C3⋊C8—61no—
509Dic12—32no—
510#204—32no—
511ΓL(1,𝔽25)—32no—
512D3×C8—32no—
513C22×C32—21no—
514C22×C32—22no—
515C22×C32—21no—
516C22×C32—21no—
517C22×C32—21no—
518C22×C32—21no—
519C22×C32—21no—
520C22×C32—32no—
521C22×C32—41no—
522C22×C32—41no—
523C22×C32—41no—
524C22×C32—42no—
525C22×C32D3×D411yescharacteristic
526C22×C32C2×#6711yescharacteristic
527C22×C32C2×C3×D411yescharacteristic
528C2×C3⋊D3—21no—
529C2×C3×D3—22no—
530C2×C3×D3—61no—
531C2×C3×D3—61no—
532C2×C3×D3—121no—
533C2×C3×D3C2×#6712yes—
534C2×C3×D3C2×C3×D412yes—
535C32×C4—21no—
536C32×C4—22no—
537C32×C4—21no—
538C32×C4—21no—
539C32×C4—21no—
540C32×C4—21no—
541C32×C4—21no—
542C32×C4—21no—
543C32×C4—21no—
544C32×C4—21no—
545C32×C4—32no—
546C32×C4—41no—
547C32×C4—41no—
548C32×C4—41no—
549C32×C4—41no—
550C32×C4—42no—
551C32×C4—62no—
552C32×C4—62no—
553C32×C4D3×D411yescharacteristic
554C32×C4C2×#6711yescharacteristic
555C32×C4C2×C3×D411yescharacteristic
556C32×C4C23×D311yescharacteristic
557C32×C4C23×D311yescharacteristic
558C32×C4C24×C311yescharacteristic
559C3⋊Dic3—21no—
560C3×Dic3—24no—
561C3×Dic3—22no—
562C3×Dic3—22no—
563C3×Dic3—22no—
564C3×Dic3—22no—
565C3×Dic3—22no—
566C3×Dic3—42no—
567C3×Dic3—61no—
568C3×Dic3—61no—
569C3×Dic3—121no—
570C3×Dic3C2×#6712yes—
571C3×Dic3C2×C3×D412yes—
5722−1+4—31no—
5732−1+4—91no—
574#137—31no—
575#137—91no—
576#137—92no—
577#137—92no—
578#135—92no—
579#135—91no—
580C2×Q16—92no—
581C2×Q16—91no—
582#131—91no—
583C33#57811yescharacteristic, complemented, Sylow
584C3×Q8—21no—
585C3×Q8—21no—
586C3×Q8—21no—
587C3×Q8—31no—
588C3×Q8—31no—
589C3×Q8—32no—
590C3×Q8—32no—
591C3×Q8—32no—
592C3×Q8—32no—
593C3×Q8—41no—
594C3×Q8—61no—
595C3×Q8—62no—
596C3×Q8—62no—
597C3×Q8—62no—
598C3×Q8—62no—
599C3×Q8—64no—
600C3×Q8—62no—
601C3×Q8—61no—
602C3×Q8—61no—
603C3×Q8—61no—
604C3×Q8—61no—
605C3×Q8—91no—
606C3×Q8—121no—
607C3×Q8—182no—
608C3×Q8C2×D3211yescharacteristic
609C3×Q8C22×C3×D311yescharacteristic
610C3×Q8C22×C3×D311yescharacteristic
611C3×D4—22no—
612C3×D4—21no—
613C3×D4—21no—
614C3×D4—21no—
615C3×D4—21no—
616C3×D4—21no—
617C3×D4—21no—
618C3×D4—32no—
619C3×D4—32no—
620C3×D4—31no—
621C3×D4—31no—
622C3×D4—41no—
623C3×D4—41no—
624C3×D4—42no—
625C3×D4—41no—
626C3×D4—61no—
627C3×D4—62no—
628C3×D4—62no—
629C3×D4—62no—
630C3×D4—64no—
631C3×D4—91no—
632C3×D4—182no—
633C3×D4—181no—
634C3×D4C2×D3211yescharacteristic
635C3×D4C22×C3×D311yescharacteristic
636C3×D4C22×C3×D311yescharacteristic
637C2×C3×C4—22no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—32no—
645C2×C3×C4—32no—
646C2×C3×C4—41no—
647C2×C3×C4—41no—
648C2×C3×C4—42no—
649C2×C3×C4—41no—
650C2×C3×C4—62no—
651C2×C3×C4—62no—
652C2×C3×C4—62no—
653C2×C3×C4—64no—
654C2×C3×C4—62no—
655C2×C3×C4—62no—
656C2×C3×C4—64no—
657C2×C3×C4—62no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—121no—
663C2×C3×C4—182no—
664C2×C3×C4—182no—
665C2×C3×C4—181no—
666C2×C3×C4C2×D3211yescharacteristic
667C2×C3×C4C22×C3×D311yescharacteristic
668C2×C3×C4C22×C3×D311yescharacteristic
669#67—22no—
670#67—62no—
671#67—61no—
672#67—61no—
673#67—121no—
674#67C3×#6712yes—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—22no—
678C2×Dic3—62no—
679D12—31no—
680D12—31no—
681D12—61no—
682D12—62no—
683D12C3×#6711yescharacteristic
684C4×D3—22no—
685C4×D3—62no—
686C4×D3—62no—
687C4×D3—61no—
688C4×D3—61no—
689C4×D3—62no—
690C4×D3—121no—
691C4×D3C22×C3×D312yes—
692Dic6—21no—
693Dic6—21no—
694Dic6—22no—
695Dic6—31no—
696Dic6—31no—
697Dic6—61no—
698Dic6—62no—
699Dic6—62no—
700Dic6C3×#6711yescharacteristic
701Dic6C22×C3×D312yes—
702Dic6C22×C3×D312yes—
703C3×C8—32no—
704C3×C8—32no—
705C3×C8—62no—
706C3×C8—91no—
707C3×C8—91no—
708C3⋊C8—31no—
709C3⋊C8—31no—
710C3⋊C8—31no—
711C3⋊C8—31no—
712C3⋊C8—61no—
713C3⋊C8—61no—
714C3⋊C8C22×C3×D312yes—
715C2×C32—21no—
716C2×C32—21no—
717C2×C32—21no—
718C2×C32—21no—
719C2×C32—21no—
720C2×C32—21no—
721C2×C32—41no—
722C2×C32—41no—
723C2×C32—41no—
724C2×C32—41no—
725C2×C32—41no—
726C2×C32—42no—
727C2×C32—41no—
728C2×C32—41no—
729C2×C32—62no—
730C2×C32—81no—
731C2×C32—81no—
732C2×C32—81no—
733C2×C32—82no—
734C2×C32C2×D3×D411yescharacteristic
735C2×C32C22×#6711yescharacteristic
736C2×C32C22×C3×D411yescharacteristic
737C3⋊D3—41no—
738C3×D3—22no—
739C3×D3—22no—
740C3×D3—42no—
741C3×D3—121no—
742C3×D3—121no—
743C3×D3—241no—
744#41—31no—
745#41—32no—
746#41—61no—
747#41—62no—
748#41—92no—
749#41—91no—
750#41—182no—
751#41—181no—
752#41C3×D3211yescharacteristic
753C2×Q8—32no—
754C2×Q8—31no—
755C2×Q8—31no—
756C2×Q8—61no—
757C2×Q8—92no—
758C2×Q8—181no—
759Q16—32no—
760Q16—92no—
761Q16—92no—
762Q16—92no—
763Q16—91no—
764SD16—32no—
765SD16—92no—
766SD16—91no—
767SD16—91no—
768D8—91no—
769M16—31no—
770M16—92no—
771C2×C8—92no—
772C2×C8—91no—
773C22×C3—22no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—21no—
778C22×C3—21no—
779C22×C3—21no—
780C22×C3—32no—
781C22×C3—32no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—42no—
785C22×C3—41no—
786C22×C3—62no—
787C22×C3—181no—
788C22×C3D3×#6711yescharacteristic
789C22×C3C3×D3×D411yescharacteristic
790C22×C3C2×C3×#6711yescharacteristic
791C2×D3—61no—
792C2×D3—61no—
793C2×D3—121no—
794C2×D3C2×C3×#6712yes—
795C3×C4—22no—
796C3×C4—21no—
797C3×C4—21no—
798C3×C4—21no—
799C3×C4—21no—
800C3×C4—21no—
801C3×C4—21no—
802C3×C4—21no—
803C3×C4—21no—
804C3×C4—21no—
805C3×C4—32no—
806C3×C4—32no—
807C3×C4—41no—
808C3×C4—41no—
809C3×C4—42no—
810C3×C4—41no—
811C3×C4—41no—
812C3×C4—62no—
813C3×C4—64no—
814C3×C4—62no—
815C3×C4—62no—
816C3×C4—62no—
817C3×C4—62no—
818C3×C4—122no—
819C3×C4—181no—
820C3×C4D3×#6711yescharacteristic
821C3×C4C3×D3×D411yescharacteristic
822C3×C4C2×C3×#6711yescharacteristic
823C3×C4C22×D3211yescharacteristic
824C3×C4C23×C3×D311yescharacteristic
825C3×C4C23×C3×D311yescharacteristic
826Dic3—22no—
827Dic3—22no—
828Dic3—61no—
829Dic3—61no—
830Dic3—121no—
831Dic3C2×C3×#6712yes—
832C32—21no—
833C32—21no—
834C32—21no—
835C32—41no—
836C32#577911yescharacteristic, complemented
837C32#583811yescharacteristic, complemented
838C32C3×#57811yescharacteristic, complemented
839Q8—31no—
840Q8—32no—
841Q8—32no—
842Q8—62no—
843Q8—61no—
844Q8—61no—
845Q8—91no—
846Q8—182no—
847Q8C2×C3×D3211yescharacteristic
848D4—21no—
849D4—32no—
850D4—31no—
851D4—62no—
852D4—91no—
853D4—182no—
854D4—181no—
855D4C2×C3×D3211yescharacteristic
856C2×C4—21no—
857C2×C4—32no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—182no—
863C2×C4—182no—
864C2×C4—181no—
865C2×C4C2×C3×D3211yescharacteristic
866C8—32no—
867C8—91no—
868C8—91no—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—41no—
876C2×C3—41no—
877C2×C3—41no—
878C2×C3—42no—
879C2×C3—41no—
880C2×C3—41no—
881C2×C3—41no—
882C2×C3—41no—
883C2×C3—62no—
884C2×C3—62no—
885C2×C3—81no—
886C2×C3—81no—
887C2×C3—81no—
888C2×C3—82no—
889C2×C3—122no—
890C2×C3—361no—
891C2×C3C2×D3×#6711yescharacteristic
892C2×C3C2×C3×D3×D411yescharacteristic
893C2×C3C22×C3×#6711yescharacteristic
894D3—22no—
895D3—121no—
896D3—121no—
897D3—241no—
898C22—21no—
899C22—32no—
900C22—181no—
901C22C3×D3×#6711yescharacteristic
902C4—21no—
903C4—32no—
904C4—62no—
905C4—62no—
906C4—181no—
907C4C3×D3×#6711yescharacteristic
908C4C22×C3×D3211yescharacteristic
909C3—21no—
910C3—21no—
911C3—21no—
912C3—41no—
913C3#1059546511yescharacteristic, direct product factor
914C3C3×#577911yescharacteristic, complemented
915C3C3×#583811yescharacteristic, complemented
916C2—21no—
917C2—41no—
918C2—62no—
919C2—361no—
920C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC2×C3C2×D3×#67
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×#41C22
socleC2×C33C22×D4
hypercenterC3×#41D32
hypocenterC32C3×#578
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#41

Complements

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

NH ≅ G/Ntype
1. C32×#1010C2semidirect
2. C3×#64297C2semidirect
3. C3×#64159C2semidirect
4. C32×#951C2semidirect
5. C3×#63948C2semidirect
6. C3×D3×#216C2semidirect
7. C3×#63935C2semidirect
8. C3×#63929C2semidirect
9. C2×C3×#3718C2semidirect
10. C3×#63833C2semidirect
11. C3×#63815C2semidirect
14. #10595465C3direct (N × H)
47. C3×#1010D3semidirect
48. C3×#1010C2×C3semidirect
50. #64297C2×C3semidirect
52. #64159C2×C3semidirect
55. C3×#951D3semidirect
56. C3×#951C2×C3semidirect
73. #63948C2×C3semidirect
74. D3×#216C2×C3semidirect
75. #63935C2×C3semidirect
76. #63929C2×C3semidirect
77. C2×#3718C2×C3semidirect
78. #63833C2×C3semidirect
79. #63815C2×C3semidirect
237. #1010C3×D3semidirect
251. #951C3×D3semidirect
583. C33#578semidirect
836. C32#5779semidirect
837. C32#5838semidirect
838. C32C3×#578semidirect
913. C3#10595465direct (N × H)
914. C3C3×#5779semidirect
915. C3C3×#5838semidirect

Maximal subgroups

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

subgroupindex
C32×#10102
C3×#642972
C3×#641592
C32×#9512
C3×#639482
C3×D3×#2162
C3×#639352
C3×#639292
C2×C3×#37182
C3×#638332
C3×#638152
C3×#58383
C3×#57793
#105954653