Finite Group Databasebeta

← C3×#10595473 #13175070

Subgroups — C3×#10595473 #13175070

Order 1728.

1360 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64366C211yesmaximal, characteristic, complemented
2C3×#64297C211yesmaximal, characteristic, complemented
3C32×#951C211yesmaximal, characteristic, complemented
4C32×#950C211yesmaximal, characteristic, complemented
5C3×#63950C212yesmaximal, complemented
6C3×#63945C212yesmaximal, complemented
7C3×#63937C212yesmaximal, complemented
8C3×#63930C212yesmaximal, complemented
9C2×C3×#3717C211yesmaximal, characteristic, complemented
10C3×#63825C211yesmaximal, characteristic, complemented
11C3×#63817C211yesmaximal, characteristic, complemented
12C3×#5778—31nomaximal
13C3×#5770—31nomaximal
14#10595473C311yesmaximal, characteristic, direct product factor
15C33×#41C2211yescharacteristic
16C3×#3832C2212yes—
17C3×D4×C3⋊D3—22no—
18C3×D4×C3⋊D3C2212yes—
19C3×#3828—21no—
20C3×#3828C2211yescharacteristic
21C2×C3×C4⋊(C3⋊D3)—21no—
22C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
23C32×#235C2211yescharacteristic, complemented
24C2×C32×Dic6C2211yescharacteristic, complemented
25C3×#3804—22no—
26C3×#3799—21no—
27C3×#3797C2212yescomplemented
28C3×#3796C2212yescomplemented
29C3×D3×Dic6—21no—
30C32×#216C2211yescharacteristic, complemented
31C32×#216C2212yescomplemented
32C32×#215C2211yescharacteristic, complemented
33C32×#214C2211yescharacteristic, complemented
34C32×#214C2212yescomplemented
35C32×#213C2211yescharacteristic, complemented
36C32×#208C2211yescharacteristic, complemented
37C2×C32×C3⋊C8C2211yescharacteristic, complemented
38C3×#3717C2212yescomplemented
39C3×#3717C2212yescomplemented
40C3×#3717C2212yescomplemented
41C3×#3714C2212yescomplemented
42C3×#3712C2212yescomplemented
43C3×#3710C2212yescomplemented
44#64366C2×C311yescharacteristic, complemented
45C3×#1010—31no—
46C3×#1009—31no—
47C3×#1009—31no—
48C3×#1009—61no—
49C3×#1007—31no—
50#64297C2×C311yescharacteristic, complemented
51C32×#137—31no—
52C32×#135—31no—
53C3×#951—21no—
54C3×#951D311yescharacteristic, complemented
55C3×#951C2×C311yescharacteristic, complemented
56C3×#950—21no—
57C3×#950D311yescharacteristic, complemented
58C3×#950C2×C311yescharacteristic, complemented
59C3×#949—31no—
60C2×C3×#215—31no—
61C3×#919—32no—
62C3×#918—32no—
63C3×#918—32no—
64C3×#916—32no—
65C3×#914—32no—
66C3×D3×SD16—32no—
67C3×D3×SD16—32no—
68C3×#911—32no—
69C3×#908—31no—
70C3×#907—31no—
71C2×C3×#204—31no—
72C3×#901—31no—
73#63950C2×C312yescomplemented
74#63945C2×C312yescomplemented
75#63937C2×C312yescomplemented
76#63930C2×C312yescomplemented
77C2×#3717C2×C311yescharacteristic, complemented
78#63825C2×C311yescharacteristic, complemented
79#63817C2×C311yescharacteristic, complemented
80C22×C3×C3⋊D3—21no—
81C22×C3×C3⋊D3—22no—
82C33×Q8C2311yescharacteristic
83C33×D4—21no—
84C33×D4C2311yescharacteristic
85C2×C33×C4—21no—
86C2×C33×C4C2311yescharacteristic
87C3×#638—22no—
88C3×#638D412yes—
89C3×C4⋊(C3⋊D3)—22no—
90C3×C4⋊(C3⋊D3)—21no—
91C3×C4⋊(C3⋊D3)D411yescharacteristic
92C3×C4⋊(C3⋊D3)C2312yes—
93C3×C4×C3⋊D3—22no—
94C3×C4×C3⋊D3C2312yes—
95C3×#634D411yescharacteristic
96C32×#67—21no—
97C2×C32×Dic3—21no—
98C32×D12C2311yescharacteristic
99C32×C4×D3—21no—
100C32×Dic6—21no—
101C32×Dic6C2312yes—
102C32×Dic6C2311yescharacteristic
103C3×#627—22no—
104C3×#626—22no—
105C3×#624—22no—
106C3×D3×Dic3—22no—
107C32×C3⋊C8C2311yescharacteristic
108C32×C3⋊C8C2312yes—
109C32×C3⋊C8C2311yescharacteristic
110C3×#577—91no—
111#5778—31no—
112#5770—31no—
113C32×#41—21no—
114C32×#41—21no—
115C32×#41—21no—
116C32×#41—31no—
117C32×#41—41no—
118C32×#41C2×D311yescharacteristic
119C32×#41C2×D311yescharacteristic
120C32×#41C22×C311yescharacteristic
121C2×C32×Q8—31no—
122#3832C22×C312yes—
123D4×C3⋊D3—22no—
124D4×C3⋊D3C22×C312yes—
125#3828—21no—
126#3828C22×C311yescharacteristic
127C2×C4⋊(C3⋊D3)—21no—
128C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
129C3×#239—32no—
130C3×#239—32no—
131C3×#239—32no—
132C3×#239—61no—
133C3×#239—62no—
134C3×D3×Q8—32no—
135C3×D3×Q8—32no—
136C3×D3×Q8—61no—
137C3×#237—32no—
138C3×#237—62no—
139C3×D3×D4—32no—
140C3×D3×D4—32no—
141C3×D3×D4—62no—
142C3×D3×D4—62no—
143C3×D3×D4—62no—
144C3×D3×D4—64no—
145C3×#235—21no—
146C3×#235—31no—
147C3×#235—31no—
148C3×#235—61no—
149C3×#235—61no—
150C3×#235—61no—
151C3×#235—62no—
152C3×#235—61no—
153C3×#235—62no—
154C3×#235C2×D311yescharacteristic, complemented
155C3×#235C22×C311yescharacteristic, complemented
156C2×C3×D12—31no—
157C2×C3×D12—31no—
158C2×C3×D12—61no—
159C2×C3×D12—61no—
160C2×C3×D12—61no—
161C2×C3×D12—62no—
162C2×C3×Dic6—21no—
163C2×C3×Dic6—61no—
164C2×C3×Dic6C2×D311yescharacteristic, complemented
165C2×C3×Dic6C22×C311yescharacteristic, complemented
166#3804—22no—
167#3799—21no—
168#3797C22×C312yescomplemented
169#3796C22×C312yescomplemented
170D3×Dic6—21no—
171C32×Q16—31no—
172C32×Q16—32no—
173C32×SD16—31no—
174C32×SD16—31no—
175C32×SD16—32no—
176C32×D8—31no—
177C32×M16—31no—
178C2×C32×C8—31no—
179C3×#216—21no—
180C3×#216—22no—
181C3×#216C2×D312yescomplemented
182C3×#216C2×D311yescharacteristic, complemented
183C3×#216C22×C311yescharacteristic, complemented
184C3×#216C22×C312yescomplemented
185C3×#215—21no—
186C3×#215—32no—
187C3×#215—32no—
188C3×#215—32no—
189C3×#215C2×D311yescharacteristic, complemented
190C3×#215C22×C311yescharacteristic, complemented
191C3×#214—21no—
192C3×#214—22no—
193C3×#214C2×D312yescomplemented
194C3×#214C2×D311yescharacteristic, complemented
195C3×#214C22×C311yescharacteristic, complemented
196C3×#214C22×C312yescomplemented
197C3×#213—21no—
198C3×#213—32no—
199C3×#213C2×D311yescharacteristic, complemented
200C3×#213C22×C311yescharacteristic, complemented
201C3×#208—21no—
202C3×#208C2×D311yescharacteristic, complemented
203C3×#208C22×C311yescharacteristic, complemented
204C2×C3×C3⋊C8—21no—
205C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
206C2×C3×C3⋊C8C22×C311yescharacteristic, complemented
207C3×D24—32no—
208C3×#204—32no—
209C3×#204—32no—
210C3×#204—32no—
211C3×ΓL(1,𝔽25)—32no—
212C3×ΓL(1,𝔽25)—32no—
213C3×D3×C8—32no—
214C3×D3×C8—32no—
215#3717C22×C312yescomplemented
216#3717C22×C312yescomplemented
217#3717C22×C312yescomplemented
218#3714C22×C312yescomplemented
219#3712C22×C312yescomplemented
220#3710C22×C312yescomplemented
221C22×C33—21no—
222C22×C33C2×D411yescharacteristic
223C2×C3×C3⋊D3—22no—
224C2×C3×C3⋊D3—82no—
225C2×C3×C3⋊D3—81no—
226C2×C3×C3⋊D3C2×D412yes—
227C2×C32×D3—21no—
228C33×C4—21no—
229C33×C4C2×D411yescharacteristic
230C33×C4C2411yescharacteristic
231C3×C3⋊Dic3C2×D412yes—
232C32×Dic3—22no—
233C32×Dic3—21no—
234C3×2−1+4—91no—
235C3×H(5,𝔽2)—91no—
236#1010—31no—
237#1009—31no—
238#1009—31no—
239#1009—61no—
240#1007—31no—
241C3×#137—31no—
242C3×#137—31no—
243C3×#137—61no—
244C3×#137—92no—
245C3×AGL(1,ℤ/8)—91no—
246C3×AGL(1,ℤ/8)—92no—
247C3×#135—31no—
248C3×#135—31no—
249C3×#135—61no—
250C3×#135—92no—
251C2×C3×SD16—91no—
252C2×C3×SD16—92no—
253C3×#131—91no—
254#951C3×D311yescharacteristic, complemented
255#950C3×D311yescharacteristic, complemented
256#949—31no—
257C2×#215—31no—
258#919—32no—
259#918—32no—
260#918—32no—
261#916—32no—
262#914—32no—
263D3×SD16—32no—
264D3×SD16—32no—
265#911—32no—
266#908—31no—
267#907—31no—
268C2×#204—31no—
269#901—31no—
270C22×C3⋊D3—21no—
271C22×C3⋊D3—22no—
272C22×C3×D3—62no—
273C22×C3×D3—62no—
274C22×C3×D3—64no—
275C22×C3×D3—62no—
276C22×C3×D3—61no—
277C22×C3×D3—61no—
278C32×Q8—21no—
279C32×Q8—21no—
280C32×Q8—21no—
281C32×Q8—31no—
282C32×Q8—32no—
283C32×Q8—41no—
284C32×Q8—61no—
285C32×Q8C22×D311yescharacteristic
286C32×Q8C22×D311yescharacteristic
287C32×Q8C23×C311yescharacteristic
288C32×D4—21no—
289C32×D4—22no—
290C32×D4—21no—
291C32×D4—21no—
292C32×D4—21no—
293C32×D4—21no—
294C32×D4—21no—
295C32×D4—31no—
296C32×D4—41no—
297C32×D4—41no—
298C32×D4—41no—
299C32×D4—42no—
300C32×D4—61no—
301C32×D4C22×D311yescharacteristic
302C32×D4C22×D311yescharacteristic
303C32×D4C23×C311yescharacteristic
304C2×C32×C4—21no—
305C2×C32×C4—22no—
306C2×C32×C4—21no—
307C2×C32×C4—21no—
308C2×C32×C4—21no—
309C2×C32×C4—21no—
310C2×C32×C4—21no—
311C2×C32×C4—41no—
312C2×C32×C4—41no—
313C2×C32×C4—41no—
314C2×C32×C4—42no—
315C2×C32×C4—61no—
316C2×C32×C4—61no—
317C2×C32×C4C22×D311yescharacteristic
318C2×C32×C4C22×D311yescharacteristic
319C2×C32×C4C23×C311yescharacteristic
320#638—22no—
321#638C3×D412yes—
322C4⋊(C3⋊D3)—22no—
323C4⋊(C3⋊D3)—21no—
324C4⋊(C3⋊D3)C3×D411yescharacteristic
325C4⋊(C3⋊D3)C23×C312yes—
326C4×C3⋊D3—22no—
327C4×C3⋊D3C23×C312yes—
328#634C3×D411yescharacteristic
329C3×#67—21no—
330C3×#67—21no—
331C3×#67—32no—
332C3×#67—32no—
333C3×#67—41no—
334C3×#67—62no—
335C3×#67—62no—
336C3×#67—62no—
337C3×#67—62no—
338C3×#67—64no—
339C2×C3×Dic3—21no—
340C2×C3×Dic3—21no—
341C2×C3×Dic3—41no—
342C2×C3×Dic3—62no—
343C3×D12—21no—
344C3×D12—31no—
345C3×D12—31no—
346C3×D12—32no—
347C3×D12—32no—
348C3×D12—61no—
349C3×D12—62no—
350C3×D12—62no—
351C3×D12—62no—
352C3×D12—62no—
353C3×D12—64no—
354C3×D12—62no—
355C3×D12—61no—
356C3×D12—61no—
357C3×D12C22×D311yescharacteristic
358C3×D12C23×C311yescharacteristic
359C3×C4×D3—21no—
360C3×C4×D3—21no—
361C3×C4×D3—32no—
362C3×C4×D3—32no—
363C3×C4×D3—41no—
364C3×C4×D3—62no—
365C3×C4×D3—62no—
366C3×C4×D3—62no—
367C3×C4×D3—62no—
368C3×C4×D3—62no—
369C3×C4×D3—62no—
370C3×C4×D3—64no—
371C3×Dic6—21no—
372C3×Dic6—21no—
373C3×Dic6—22no—
374C3×Dic6—21no—
375C3×Dic6—31no—
376C3×Dic6—31no—
377C3×Dic6—41no—
378C3×Dic6—61no—
379C3×Dic6—62no—
380C3×Dic6—62no—
381C3×Dic6C22×D312yes—
382C3×Dic6C22×D311yescharacteristic
383C3×Dic6C23×C312yes—
384C3×Dic6C23×C311yescharacteristic
385#627—22no—
386#626—22no—
387#624—22no—
388D3×Dic3—22no—
389C32×C8—31no—
390C32×C8—32no—
391C32×C8—31no—
392C3×C3⋊C8—21no—
393C3×C3⋊C8—21no—
394C3×C3⋊C8—22no—
395C3×C3⋊C8C22×D311yescharacteristic
396C3×C3⋊C8C22×D312yes—
397C3×C3⋊C8C22×D311yescharacteristic
398C3×C3⋊C8C23×C311yescharacteristic
399C3×C3⋊C8C23×C312yes—
400C3×C3⋊C8C23×C311yescharacteristic
401#577—91noSylow
402C2×C33—21no—
403C2×C33—41no—
404C2×C33C22×D411yescharacteristic
405C3×C3⋊D3—22no—
406C3×C3⋊D3—42no—
407C32×D3—41no—
408C3×#41—21no—
409C3×#41—21no—
410C3×#41—21no—
411C3×#41—31no—
412C3×#41—31no—
413C3×#41—41no—
414C3×#41—61no—
415C3×#41—91no—
416C3×#41—92no—
417C3×#41—92no—
418C3×#41—181no—
419C3×#41—182no—
420C3×#41—181no—
421C3×#41D3211yescharacteristic
422C3×#41C2×C3×D311yescharacteristic
423C3×#41C2×C3×D311yescharacteristic
424C2×C3×Q8—31no—
425C2×C3×Q8—31no—
426C2×C3×Q8—61no—
427C2×C3×Q8—92no—
428C2×C3×Q8—181no—
429C2×C3×D4—92no—
430C2×C3×D4—91no—
431C2×C3×D4—181no—
432C2×C3×D4—182no—
433#239—32no—
434#239—32no—
435#239—32no—
436#239—62no—
437#239—61no—
438D3×Q8—32no—
439D3×Q8—32no—
440D3×Q8—61no—
441#237—32no—
442#237—62no—
443D3×D4—32no—
444D3×D4—32no—
445D3×D4—62no—
446D3×D4—62no—
447D3×D4—62no—
448D3×D4—64no—
449#235—31no—
450#235—31no—
451#235—61no—
452#235—61no—
453#235—61no—
454#235—61no—
455#235—62no—
456#235—62no—
457#235C2×C3×D311yescharacteristic, complemented
458C2×D12—31no—
459C2×D12—31no—
460C2×D12—61no—
461C2×D12—61no—
462C2×D12—61no—
463C2×D12—62no—
464C2×Dic6—61no—
465C2×Dic6C2×C3×D311yescharacteristic, complemented
466C3×Q16—31no—
467C3×Q16—32no—
468C3×Q16—31no—
469C3×Q16—32no—
470C3×Q16—61no—
471C3×Q16—62no—
472C3×SD16—31no—
473C3×SD16—31no—
474C3×SD16—31no—
475C3×SD16—32no—
476C3×SD16—31no—
477C3×SD16—32no—
478C3×SD16—61no—
479C3×SD16—62no—
480C3×SD16—61no—
481C3×SD16—92no—
482C3×SD16—92no—
483C3×SD16—92no—
484C3×D8—31no—
485C3×D8—31no—
486C3×D8—61no—
487C3×D8—92no—
488C3×M16—31no—
489C3×M16—31no—
490C3×M16—61no—
491C3×M16—92no—
492C2×C3×C8—31no—
493C2×C3×C8—31no—
494C2×C3×C8—61no—
495C2×C3×C8—92no—
496#216C2×C3×D312yescomplemented
497#216C2×C3×D311yescharacteristic, complemented
498#215—32no—
499#215—32no—
500#215—32no—
501#215C2×C3×D311yescharacteristic, complemented
502#214C2×C3×D312yescomplemented
503#214C2×C3×D311yescharacteristic, complemented
504#213—32no—
505#213C2×C3×D311yescharacteristic, complemented
506#208C2×C3×D311yescharacteristic, complemented
507C2×C3⋊C8C2×C3×D311yescharacteristic, complemented
508D24—32no—
509#204—32no—
510#204—32no—
511#204—32no—
512ΓL(1,𝔽25)—32no—
513ΓL(1,𝔽25)—32no—
514D3×C8—32no—
515D3×C8—32no—
516C22×C32—21no—
517C22×C32—22no—
518C22×C32—21no—
519C22×C32—21no—
520C22×C32—21no—
521C22×C32—21no—
522C22×C32—21no—
523C22×C32—41no—
524C22×C32—41no—
525C22×C32—41no—
526C22×C32—42no—
527C22×C32—61no—
528C22×C32D3×D411yescharacteristic
529C22×C32D3×D411yescharacteristic
530C22×C32C2×C3×D411yescharacteristic
531C2×C3⋊D3—22no—
532C2×C3⋊D3—82no—
533C2×C3⋊D3—81no—
534C2×C3⋊D3C2×C3×D412yes—
535C2×C3×D3—21no—
536C2×C3×D3—21no—
537C2×C3×D3—32no—
538C2×C3×D3—32no—
539C2×C3×D3—41no—
540C2×C3×D3—62no—
541C2×C3×D3—64no—
542C2×C3×D3—62no—
543C2×C3×D3—62no—
544C2×C3×D3—242no—
545C2×C3×D3—242no—
546C2×C3×D3—241no—
547C2×C3×D3—241no—
548C2×C3×D3—242no—
549C2×C3×D3—244no—
550C32×C4—21no—
551C32×C4—22no—
552C32×C4—21no—
553C32×C4—21no—
554C32×C4—21no—
555C32×C4—21no—
556C32×C4—21no—
557C32×C4—21no—
558C32×C4—21no—
559C32×C4—21no—
560C32×C4—41no—
561C32×C4—41no—
562C32×C4—41no—
563C32×C4—41no—
564C32×C4—42no—
565C32×C4—61no—
566C32×C4—62no—
567C32×C4D3×D411yescharacteristic
568C32×C4D3×D411yescharacteristic
569C32×C4C2×C3×D411yescharacteristic
570C32×C4C23×D311yescharacteristic
571C32×C4C23×D311yescharacteristic
572C32×C4C24×C311yescharacteristic
573C3⋊Dic3C2×C3×D412yes—
574C3×Dic3—22no—
575C3×Dic3—21no—
576C3×Dic3—22no—
577C3×Dic3—21no—
578C3×Dic3—32no—
579C3×Dic3—32no—
580C3×Dic3—42no—
581C3×Dic3—41no—
582C3×Dic3—62no—
5832−1+4—91no—
584H(5,𝔽2)—91no—
585#137—31no—
586#137—92no—
587AGL(1,ℤ/8)—91no—
588AGL(1,ℤ/8)—92no—
589#135—31no—
590#135—92no—
591C2×SD16—91no—
592C2×SD16—92no—
593#131—91no—
594C33#57711yescharacteristic, complemented, Sylow
595C23×C3—182no—
596C23×C3—181no—
597C22×D3—62no—
598C22×D3—62no—
599C22×D3—64no—
600C22×D3—62no—
601C22×D3—61no—
602C22×D3—61no—
603C3×Q8—21no—
604C3×Q8—21no—
605C3×Q8—21no—
606C3×Q8—32no—
607C3×Q8—31no—
608C3×Q8—31no—
609C3×Q8—32no—
610C3×Q8—41no—
611C3×Q8—62no—
612C3×Q8—61no—
613C3×Q8—61no—
614C3×Q8—61no—
615C3×Q8—91no—
616C3×Q8—121no—
617C3×Q8—182no—
618C3×Q8C2×D3211yescharacteristic
619C3×Q8C22×C3×D311yescharacteristic
620C3×Q8C22×C3×D311yescharacteristic
621C3×D4—22no—
622C3×D4—21no—
623C3×D4—21no—
624C3×D4—21no—
625C3×D4—21no—
626C3×D4—21no—
627C3×D4—21no—
628C3×D4—31no—
629C3×D4—31no—
630C3×D4—41no—
631C3×D4—41no—
632C3×D4—42no—
633C3×D4—41no—
634C3×D4—61no—
635C3×D4—61no—
636C3×D4—61no—
637C3×D4—92no—
638C3×D4—92no—
639C3×D4—91no—
640C3×D4—121no—
641C3×D4—182no—
642C3×D4—182no—
643C3×D4—182no—
644C3×D4—181no—
645C3×D4C2×D3211yescharacteristic
646C3×D4C22×C3×D311yescharacteristic
647C3×D4C22×C3×D311yescharacteristic
648C2×C3×C4—22no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—42no—
658C2×C3×C4—41no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—92no—
664C2×C3×C4—121no—
665C2×C3×C4—121no—
666C2×C3×C4—182no—
667C2×C3×C4—182no—
668C2×C3×C4—182no—
669C2×C3×C4C2×D3211yescharacteristic
670C2×C3×C4C22×C3×D311yescharacteristic
671C2×C3×C4C22×C3×D311yescharacteristic
672#67—21no—
673#67—32no—
674#67—32no—
675#67—62no—
676#67—62no—
677#67—62no—
678#67—62no—
679#67—64no—
680C2×Dic3—21no—
681C2×Dic3—62no—
682D12—32no—
683D12—32no—
684D12—31no—
685D12—31no—
686D12—61no—
687D12—62no—
688D12—62no—
689D12—62no—
690D12—62no—
691D12—64no—
692D12—62no—
693D12—61no—
694D12—61no—
695D12C22×C3×D311yescharacteristic
696C4×D3—21no—
697C4×D3—32no—
698C4×D3—32no—
699C4×D3—62no—
700C4×D3—62no—
701C4×D3—62no—
702C4×D3—62no—
703C4×D3—62no—
704C4×D3—62no—
705C4×D3—64no—
706Dic6—21no—
707Dic6—31no—
708Dic6—31no—
709Dic6—61no—
710Dic6—62no—
711Dic6—62no—
712Dic6C22×C3×D312yes—
713Dic6C22×C3×D311yescharacteristic
714C3×C8—31no—
715C3×C8—31no—
716C3×C8—32no—
717C3×C8—31no—
718C3×C8—32no—
719C3×C8—31no—
720C3×C8—61no—
721C3×C8—61no—
722C3×C8—62no—
723C3⋊C8C22×C3×D311yescharacteristic
724C3⋊C8C22×C3×D312yes—
725C3⋊C8C22×C3×D311yescharacteristic
726C2×C32—21no—
727C2×C32—21no—
728C2×C32—21no—
729C2×C32—21no—
730C2×C32—21no—
731C2×C32—21no—
732C2×C32—41no—
733C2×C32—41no—
734C2×C32—41no—
735C2×C32—41no—
736C2×C32—41no—
737C2×C32—42no—
738C2×C32—41no—
739C2×C32—41no—
740C2×C32—81no—
741C2×C32—81no—
742C2×C32—81no—
743C2×C32—82no—
744C2×C32—121no—
745C2×C32C2×D3×D411yescharacteristic
746C2×C32C2×D3×D411yescharacteristic
747C2×C32C22×C3×D411yescharacteristic
748C3⋊D3—22no—
749C3⋊D3—42no—
750C3×D3—41no—
751C3×D3—41no—
752C3×D3—62no—
753C3×D3—62no—
754C3×D3—81no—
755C3×D3—122no—
756C3×D3—124no—
757C3×D3—122no—
758C3×D3—122no—
759#41—31no—
760#41—91no—
761#41—92no—
762#41—92no—
763#41—181no—
764#41—182no—
765#41—181no—
766#41C3×D3211yescharacteristic
767C2×Q8—31no—
768C2×Q8—92no—
769C2×Q8—181no—
770C2×D4—92no—
771C2×D4—91no—
772C2×D4—181no—
773C2×D4—182no—
774Q16—31no—
775Q16—32no—
776SD16—31no—
777SD16—31no—
778SD16—32no—
779SD16—92no—
780SD16—92no—
781SD16—92no—
782D8—31no—
783D8—92no—
784M16—31no—
785M16—92no—
786C2×C8—31no—
787C2×C8—92no—
788C22×C3—22no—
789C22×C3—21no—
790C22×C3—21no—
791C22×C3—21no—
792C22×C3—21no—
793C22×C3—21no—
794C22×C3—21no—
795C22×C3—41no—
796C22×C3—41no—
797C22×C3—42no—
798C22×C3—41no—
799C22×C3—61no—
800C22×C3—61no—
801C22×C3—92no—
802C22×C3—121no—
803C22×C3—182no—
804C22×C3—721no—
805C22×C3—722no—
806C22×C3#381111yescharacteristic
807C22×C3C3×D3×D411yescharacteristic
808C22×C3C3×D3×D411yescharacteristic
809C2×D3—21no—
810C2×D3—32no—
811C2×D3—32no—
812C2×D3—62no—
813C2×D3—64no—
814C2×D3—62no—
815C2×D3—62no—
816C2×D3—242no—
817C2×D3—242no—
818C2×D3—241no—
819C2×D3—241no—
820C2×D3—242no—
821C2×D3—244no—
822C3×C4—22no—
823C3×C4—21no—
824C3×C4—21no—
825C3×C4—21no—
826C3×C4—21no—
827C3×C4—21no—
828C3×C4—21no—
829C3×C4—21no—
830C3×C4—21no—
831C3×C4—21no—
832C3×C4—41no—
833C3×C4—41no—
834C3×C4—42no—
835C3×C4—41no—
836C3×C4—41no—
837C3×C4—61no—
838C3×C4—62no—
839C3×C4—61no—
840C3×C4—62no—
841C3×C4—92no—
842C3×C4—121no—
843C3×C4—122no—
844C3×C4#381111yescharacteristic
845C3×C4C3×D3×D411yescharacteristic
846C3×C4C3×D3×D411yescharacteristic
847C3×C4C22×D3211yescharacteristic
848C3×C4C23×C3×D311yescharacteristic
849C3×C4C23×C3×D311yescharacteristic
850Dic3—22no—
851Dic3—21no—
852Dic3—32no—
853Dic3—32no—
854Dic3—62no—
855C32—21no—
856C32—21no—
857C32—21no—
858C32—41no—
859C32#577011yescharacteristic, complemented
860C32#577811yescharacteristic, complemented
861C32C3×#57711yescharacteristic, complemented
862C23—182no—
863C23—181no—
864Q8—32no—
865Q8—31no—
866Q8—61no—
867Q8—91no—
868Q8—182no—
869Q8C2×C3×D3211yescharacteristic
870D4—21no—
871D4—31no—
872D4—61no—
873D4—92no—
874D4—92no—
875D4—91no—
876D4—182no—
877D4—182no—
878D4—182no—
879D4—181no—
880D4C2×C3×D3211yescharacteristic
881C2×C4—21no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—92no—
885C2×C4—182no—
886C2×C4—182no—
887C2×C4—182no—
888C2×C4C2×C3×D3211yescharacteristic
889C8—31no—
890C8—31no—
891C8—32no—
892C2×C3—21no—
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—41no—
899C2×C3—41no—
900C2×C3—41no—
901C2×C3—42no—
902C2×C3—41no—
903C2×C3—41no—
904C2×C3—41no—
905C2×C3—41no—
906C2×C3—81no—
907C2×C3—81no—
908C2×C3—81no—
909C2×C3—82no—
910C2×C3—121no—
911C2×C3—121no—
912C2×C3—182no—
913C2×C3—241no—
914C2×C3—362no—
915C2×C3C2×#381111yescharacteristic
916C2×C3C2×C3×D3×D411yescharacteristic
917C2×C3C2×C3×D3×D411yescharacteristic
918D3—41no—
919D3—62no—
920D3—62no—
921D3—122no—
922D3—124no—
923D3—122no—
924D3—122no—
925C22—21no—
926C22—61no—
927C22—92no—
928C22—182no—
929C22—721no—
930C22—722no—
931C22C3×#381111yescharacteristic
932C4—21no—
933C4—61no—
934C4—62no—
935C4—92no—
936C4C3×#381111yescharacteristic
937C4C22×C3×D3211yescharacteristic
938C3—21no—
939C3—21no—
940C3—21no—
941C3—41no—
942C3#1059547311yescharacteristic, direct product factor
943C3C3×#577011yescharacteristic, complemented
944C3C3×#577811yescharacteristic, complemented
945C2—21no—
946C2—41no—
947C2—121no—
948C2—182no—
949C2—362no—
950C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC2×C3C2×#3811
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×#41C22
socleC2×C33C22×D4
hypercenterC3×#41D32
hypocenterC32C3×#577
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. C3×#64366C2semidirect
2. C3×#64297C2semidirect
3. C32×#951C2semidirect
4. C32×#950C2semidirect
5. C3×#63950C2semidirect
6. C3×#63945C2semidirect
7. C3×#63937C2semidirect
8. C3×#63930C2semidirect
9. C2×C3×#3717C2semidirect
10. C3×#63825C2semidirect
11. C3×#63817C2semidirect
14. #10595473C3direct (N × H)
23. C32×#235C22semidirect
24. C2×C32×Dic6C22semidirect
27. C3×#3797C22semidirect
28. C3×#3796C22semidirect
30. C32×#216C22semidirect
31. C32×#216C22semidirect
32. C32×#215C22semidirect
33. C32×#214C22semidirect
34. C32×#214C22semidirect
35. C32×#213C22semidirect
36. C32×#208C22semidirect
37. C2×C32×C3⋊C8C22semidirect
38. C3×#3717C22semidirect
39. C3×#3717C22semidirect
40. C3×#3717C22semidirect
41. C3×#3714C22semidirect
42. C3×#3712C22semidirect
43. C3×#3710C22semidirect
44. #64366C2×C3semidirect
50. #64297C2×C3semidirect
54. C3×#951D3semidirect
55. C3×#951C2×C3semidirect
57. C3×#950D3semidirect
58. C3×#950C2×C3semidirect
73. #63950C2×C3semidirect
74. #63945C2×C3semidirect
75. #63937C2×C3semidirect
76. #63930C2×C3semidirect
77. C2×#3717C2×C3semidirect
78. #63825C2×C3semidirect
79. #63817C2×C3semidirect
154. C3×#235C2×D3semidirect
155. C3×#235C22×C3semidirect
164. C2×C3×Dic6C2×D3semidirect
165. C2×C3×Dic6C22×C3semidirect
168. #3797C22×C3semidirect
169. #3796C22×C3semidirect
181. C3×#216C2×D3semidirect
182. C3×#216C2×D3semidirect
183. C3×#216C22×C3semidirect
184. C3×#216C22×C3semidirect
189. C3×#215C2×D3semidirect
190. C3×#215C22×C3semidirect
193. C3×#214C2×D3semidirect
194. C3×#214C2×D3semidirect
195. C3×#214C22×C3semidirect
196. C3×#214C22×C3semidirect
199. C3×#213C2×D3semidirect
200. C3×#213C22×C3semidirect
202. C3×#208C2×D3semidirect
203. C3×#208C22×C3semidirect
205. C2×C3×C3⋊C8C2×D3semidirect
206. C2×C3×C3⋊C8C22×C3semidirect
215. #3717C22×C3semidirect
216. #3717C22×C3semidirect
217. #3717C22×C3semidirect
218. #3714C22×C3semidirect
219. #3712C22×C3semidirect
220. #3710C22×C3semidirect
254. #951C3×D3semidirect
255. #950C3×D3semidirect
457. #235C2×C3×D3semidirect
465. C2×Dic6C2×C3×D3semidirect
496. #216C2×C3×D3semidirect
497. #216C2×C3×D3semidirect
501. #215C2×C3×D3semidirect
502. #214C2×C3×D3semidirect
503. #214C2×C3×D3semidirect
505. #213C2×C3×D3semidirect
506. #208C2×C3×D3semidirect
507. C2×C3⋊C8C2×C3×D3semidirect
594. C33#577semidirect
859. C32#5770semidirect
860. C32#5778semidirect
861. C32C3×#577semidirect
942. C3#10595473direct (N × H)
943. C3C3×#5770semidirect
944. C3C3×#5778semidirect

Maximal subgroups

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

subgroupindex
C3×#643662
C3×#642972
C32×#9512
C32×#9502
C3×#639502
C3×#639452
C3×#639372
C3×#639302
C2×C3×#37172
C3×#638252
C3×#638172
C3×#57783
C3×#57703
#105954733