Finite Group Databasebeta

← C3×#10595471 #13175068

Subgroups — C3×#10595471 #13175068

Order 1728.

1380 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#41×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#3796C211yesmaximal, characteristic, complemented
3C32×#951C211yesmaximal, characteristic, complemented
4C32×#949C211yesmaximal, characteristic, complemented
5C3×#63951C212yesmaximal, complemented
6C3×#63950C212yesmaximal, complemented
7C3×#63937C212yesmaximal, complemented
8C3×#63936C212yesmaximal, complemented
9C3×#63833C211yesmaximal, characteristic, complemented
10C3×#63830C211yesmaximal, characteristic, complemented
11C3×#63818C211yesmaximal, characteristic, complemented
12C3×#5777—31nomaximal
13C3×#5773—31nomaximal
14#10595471C311yesmaximal, characteristic, direct product factor
15C33×#41C2211yescharacteristic
16C3×#3832C2211yescharacteristic, complemented
17C3×Q8×C3⋊D3C2211yescharacteristic, complemented
18C3×#3830—21no—
19C3×#3830C2211yescharacteristic, complemented
20C3×D4×C3⋊D3—21no—
21C3×D4×C3⋊D3C2211yescharacteristic, complemented
22C3×#3828—21no—
23C3×#3828C2211yescharacteristic
24C2×C3×C4×C3⋊D3—21no—
25C2×C3×C4×C3⋊D3C2211yescharacteristic
26C2×C32×D12C2211yescharacteristic, complemented
27C2×C32×Dic6C2211yescharacteristic, complemented
28C2×C3×#626—21no—
29C2×C3×D3×Dic3—21no—
30C3×#3796—21no—
31C3×#3796—21no—
32C3×#3796C2212yes—
33C3×#3796C2212yescomplemented
34C32×#216C2212yescomplemented
35C32×#215C2212yescomplemented
36C32×#214C2212yescomplemented
37C32×#213C2212yescomplemented
38C32×#208C2211yescharacteristic, complemented
39C32×#208C2211yescharacteristic, complemented
40C3×#3719C2212yescomplemented
41C3×#3717C2212yescomplemented
42C3×#3716C2212yescomplemented
43C3×#3714C2212yescomplemented
44C3×#3712C2212yescomplemented
45C3×#3710C2212yescomplemented
46#41×C3⋊D3C2×C311yescharacteristic, complemented
47C3×D3×#41—31no—
48C3×D3×#41—31no—
49C3×D3×#41—61no—
50C2×C3×#239—31no—
51C2×C3×#237—31no—
52C2×#3796C2×C311yescharacteristic, complemented
53C32×#137—31no—
54C32×AGL(1,ℤ/8)—31no—
55C3×#951—21no—
56C3×#951D311yescharacteristic, complemented
57C3×#951C2×C311yescharacteristic, complemented
58C3×#949—21no—
59C3×#949D311yescharacteristic, complemented
60C3×#949C2×C311yescharacteristic, complemented
61C3×#942—31no—
62C3×#932—31no—
63C3×#919—32no—
64C3×#918—32no—
65C3×#916—32no—
66C3×#916—32no—
67C3×#915—32no—
68C3×#914—32no—
69C3×#912—32no—
70C3×#911—32no—
71C3×#909—31no—
72C3×#908—31no—
73C3×D3×M16—31no—
74C3×D3×M16—31no—
75#63951C2×C312yescomplemented
76#63950C2×C312yescomplemented
77#63937C2×C312yescomplemented
78#63936C2×C312yescomplemented
79#63833C2×C311yescharacteristic, complemented
80#63830C2×C311yescharacteristic, complemented
81#63818C2×C311yescharacteristic, complemented
82C22×C3×C3⋊D3—21no—
83C22×C3×C3⋊D3D411yescharacteristic
84C22×C32×D3—21no—
85C33×Q8C2311yescharacteristic
86C33×D4—21no—
87C33×D4C2311yescharacteristic
88C2×C33×C4—21no—
89C2×C33×C4C2311yescharacteristic
90C3×#638—21no—
91C3×#638—21no—
92C3×#638—21no—
93C2×C3×C3⋊Dic3—21no—
94C2×C3×C3⋊Dic3D411yescharacteristic
95C3×C4⋊(C3⋊D3)—21no—
96C3×C4⋊(C3⋊D3)C2311yescharacteristic
97C3×C4×C3⋊D3—21no—
98C3×C4×C3⋊D3—21no—
99C3×C4×C3⋊D3—21no—
100C3×C4×C3⋊D3D411yescharacteristic
101C3×C4×C3⋊D3D411yescharacteristic
102C3×C4×C3⋊D3C2311yescharacteristic
103C3×C4×C3⋊D3C2311yescharacteristic
104C3×#634—21no—
105C3×#634C2311yescharacteristic
106C2×C32×Dic3—21no—
107C32×D12—21no—
108C32×D12C2312yes—
109C32×Dic6—21no—
110C32×Dic6C2312yes—
111C3×#626—22no—
112C3×#626—22no—
113C3×D3×Dic3—22no—
114C3×D3×Dic3—22no—
115C32×C3⋊C8C2312yes—
116C32×C3⋊C8C2312yes—
117C3×#575—91no—
118#5777—31no—
119#5773—31no—
120C32×#41—21no—
121C32×#41—21no—
122C32×#41—21no—
123C32×#41—41no—
124C32×#41C2×D311yescharacteristic
125C32×#41C2×D311yescharacteristic
126C32×#41C22×C311yescharacteristic
127C2×C32×Q8—31no—
128C2×C32×D4—31no—
129#3832C22×C311yescharacteristic, complemented
130Q8×C3⋊D3C22×C311yescharacteristic, complemented
131#3830—21no—
132#3830C22×C311yescharacteristic, complemented
133D4×C3⋊D3—21no—
134D4×C3⋊D3C22×C311yescharacteristic, complemented
135#3828—21no—
136#3828C22×C311yescharacteristic
137C2×C4×C3⋊D3—21no—
138C2×C4×C3⋊D3C22×C311yescharacteristic
139C2×C3×#67—61no—
140C22×C3×Dic3—61no—
141C3×#239—31no—
142C3×#239—31no—
143C3×#239—32no—
144C3×#239—32no—
145C3×#239—61no—
146C3×#239—61no—
147C3×#239—61no—
148C3×D3×Q8—31no—
149C3×D3×Q8—31no—
150C3×D3×Q8—61no—
151C3×#237—31no—
152C3×#237—31no—
153C3×#237—32no—
154C3×#237—32no—
155C3×#237—61no—
156C3×#237—61no—
157C3×#237—61no—
158C3×#237—61no—
159C3×#237—61no—
160C3×#237—62no—
161C3×D3×D4—31no—
162C3×D3×D4—31no—
163C3×D3×D4—61no—
164C3×D3×D4—61no—
165C3×D3×D4—61no—
166C3×D3×D4—62no—
167C3×#235—31no—
168C3×#235—31no—
169C3×#235—61no—
170C3×#235—61no—
171C3×#235—61no—
172C3×#235—62no—
173C2×C3×D12—21no—
174C2×C3×D12—61no—
175C2×C3×D12C2×D311yescharacteristic, complemented
176C2×C3×D12C22×C311yescharacteristic, complemented
177C2×C3×C4×D3—31no—
178C2×C3×C4×D3—31no—
179C2×C3×C4×D3—61no—
180C2×C3×C4×D3—61no—
181C2×C3×C4×D3—61no—
182C2×C3×C4×D3—61no—
183C2×C3×C4×D3—62no—
184C2×C3×Dic6—21no—
185C2×C3×Dic6C2×D311yescharacteristic, complemented
186C2×C3×Dic6C22×C311yescharacteristic, complemented
187C2×#626—21no—
188C2×D3×Dic3—21no—
189#3796—21no—
190#3796—21no—
191#3796C22×C312yes—
192#3796C22×C312yescomplemented
193C32×Q16—32no—
194C32×SD16—32no—
195C32×SD16—32no—
196C32×D8—32no—
197C32×M16—31no—
198C32×M16—31no—
199C3×#216—22no—
200C3×#216—32no—
201C3×#216C2×D312yescomplemented
202C3×#216C22×C312yescomplemented
203C3×#215—22no—
204C3×#215—32no—
205C3×#215C2×D312yescomplemented
206C3×#215C22×C312yescomplemented
207C3×#214—22no—
208C3×#214—32no—
209C3×#214C2×D312yescomplemented
210C3×#214C22×C312yescomplemented
211C3×#213—22no—
212C3×#213—32no—
213C3×#213C2×D312yescomplemented
214C3×#213C22×C312yescomplemented
215C3×#208—21no—
216C3×#208—21no—
217C3×#208C2×D311yescharacteristic, complemented
218C3×#208C2×D311yescharacteristic, complemented
219C3×#208C22×C311yescharacteristic, complemented
220C3×#208C22×C311yescharacteristic, complemented
221C3×Dic12—32no—
222C3×D24—32no—
223C3×#204—32no—
224C3×#204—32no—
225C3×ΓL(1,𝔽25)—32no—
226C3×ΓL(1,𝔽25)—32no—
227C3×D3×C8—32no—
228C3×D3×C8—32no—
229#3719C22×C312yescomplemented
230#3717C22×C312yescomplemented
231#3716C22×C312yescomplemented
232#3714C22×C312yescomplemented
233#3712C22×C312yescomplemented
234#3710C22×C312yescomplemented
235C22×C33—21no—
236C22×C33C2×D411yescharacteristic
237C2×C3×C3⋊D3—21no—
238C2×C3×C3⋊D3—41no—
239C2×C3×C3⋊D3—42no—
240C2×C3×C3⋊D3C2×D411yescharacteristic
241C2×C3×C3⋊D3C2×D411yescharacteristic
242C2×C32×D3—22no—
243C2×C32×D3—42no—
244C33×C4—21no—
245C33×C4C2×D411yescharacteristic
246C33×C4C2411yescharacteristic
247C3×C3⋊Dic3—21no—
248C3×C3⋊Dic3C2×D411yescharacteristic
249C3×C3⋊Dic3C2×D411yescharacteristic
250C32×Dic3—22no—
251C2×C3×#41—91no—
252C2×C3×#41—91no—
253D3×#41—31no—
254D3×#41—31no—
255D3×#41—61no—
256C2×#239—31no—
257C2×#237—31no—
258C3×#137—31no—
259C3×#137—31no—
260C3×#137—61no—
261C3×#137—91no—
262C3×#137—92no—
263C3×AGL(1,ℤ/8)—31no—
264C3×AGL(1,ℤ/8)—31no—
265C3×AGL(1,ℤ/8)—61no—
266C3×AGL(1,ℤ/8)—91no—
267C3×AGL(1,ℤ/8)—92no—
268C3×#135—92no—
269C3×#135—92no—
270C2×C3×M16—91no—
271#951C3×D311yescharacteristic, complemented
272#949C3×D311yescharacteristic, complemented
273#942—31no—
274#932—31no—
275#919—32no—
276#918—32no—
277#916—32no—
278#916—32no—
279#915—32no—
280#914—32no—
281#912—32no—
282#911—32no—
283#909—31no—
284#908—31no—
285D3×M16—31no—
286D3×M16—31no—
287C23×C32—61no—
288C22×C3⋊D3—21no—
289C22×C3⋊D3C3×D411yescharacteristic
290C22×C3×D3—21no—
291C22×C3×D3—21no—
292C22×C3×D3—31no—
293C22×C3×D3—31no—
294C22×C3×D3—41no—
295C22×C3×D3—61no—
296C22×C3×D3—61no—
297C22×C3×D3—61no—
298C22×C3×D3—62no—
299C32×Q8—21no—
300C32×Q8—21no—
301C32×Q8—21no—
302C32×Q8—32no—
303C32×Q8—41no—
304C32×Q8—61no—
305C32×Q8C22×D311yescharacteristic
306C32×Q8C22×D311yescharacteristic
307C32×Q8C23×C311yescharacteristic
308C32×D4—21no—
309C32×D4—22no—
310C32×D4—21no—
311C32×D4—21no—
312C32×D4—21no—
313C32×D4—21no—
314C32×D4—21no—
315C32×D4—32no—
316C32×D4—41no—
317C32×D4—41no—
318C32×D4—41no—
319C32×D4—42no—
320C32×D4—61no—
321C32×D4C22×D311yescharacteristic
322C32×D4C22×D311yescharacteristic
323C32×D4C23×C311yescharacteristic
324C2×C32×C4—21no—
325C2×C32×C4—22no—
326C2×C32×C4—21no—
327C2×C32×C4—21no—
328C2×C32×C4—21no—
329C2×C32×C4—21no—
330C2×C32×C4—21no—
331C2×C32×C4—41no—
332C2×C32×C4—41no—
333C2×C32×C4—41no—
334C2×C32×C4—42no—
335C2×C32×C4—61no—
336C2×C32×C4C22×D311yescharacteristic
337C2×C32×C4C22×D311yescharacteristic
338C2×C32×C4C23×C311yescharacteristic
339#638—21no—
340#638—21no—
341#638—21no—
342C2×C3⋊Dic3—21no—
343C2×C3⋊Dic3C3×D411yescharacteristic
344C4⋊(C3⋊D3)—21no—
345C4⋊(C3⋊D3)C23×C311yescharacteristic
346C4×C3⋊D3—21no—
347C4×C3⋊D3—21no—
348C4×C3⋊D3—21no—
349C4×C3⋊D3C3×D411yescharacteristic
350C4×C3⋊D3C3×D411yescharacteristic
351C4×C3⋊D3C23×C311yescharacteristic
352C4×C3⋊D3C23×C311yescharacteristic
353#634—21no—
354#634C23×C311yescharacteristic
355C3×#67—62no—
356C3×#67—62no—
357C3×#67—61no—
358C3×#67—61no—
359C3×#67—61no—
360C3×#67—61no—
361C3×#67—62no—
362C3×#67—62no—
363C3×#67—62no—
364C3×#67—61no—
365C3×#67—61no—
366C2×C3×Dic3—21no—
367C2×C3×Dic3—21no—
368C2×C3×Dic3—31no—
369C2×C3×Dic3—31no—
370C2×C3×Dic3—41no—
371C2×C3×Dic3—61no—
372C2×C3×Dic3—62no—
373C2×C3×Dic3—62no—
374C2×C3×Dic3—61no—
375C2×C3×Dic3—61no—
376C2×C3×Dic3—62no—
377C3×D12—21no—
378C3×D12—21no—
379C3×D12—22no—
380C3×D12—31no—
381C3×D12—31no—
382C3×D12—41no—
383C3×D12—61no—
384C3×D12—61no—
385C3×D12—61no—
386C3×D12—62no—
387C3×D12—62no—
388C3×D12—62no—
389C3×D12C22×D312yes—
390C3×D12C23×C312yes—
391C3×C4×D3—31no—
392C3×C4×D3—31no—
393C3×C4×D3—31no—
394C3×C4×D3—31no—
395C3×C4×D3—31no—
396C3×C4×D3—31no—
397C3×C4×D3—31no—
398C3×C4×D3—31no—
399C3×C4×D3—61no—
400C3×C4×D3—61no—
401C3×C4×D3—61no—
402C3×C4×D3—61no—
403C3×C4×D3—61no—
404C3×C4×D3—61no—
405C3×C4×D3—62no—
406C3×C4×D3—62no—
407C3×C4×D3—61no—
408C3×C4×D3—61no—
409C3×C4×D3—62no—
410C3×C4×D3—62no—
411C3×C4×D3—62no—
412C3×C4×D3—61no—
413C3×C4×D3—61no—
414C3×Dic6—21no—
415C3×Dic6—21no—
416C3×Dic6—22no—
417C3×Dic6—31no—
418C3×Dic6—31no—
419C3×Dic6—41no—
420C3×Dic6—61no—
421C3×Dic6—61no—
422C3×Dic6—61no—
423C3×Dic6—62no—
424C3×Dic6C22×D312yes—
425C3×Dic6C23×C312yes—
426#626—22no—
427#626—22no—
428D3×Dic3—22no—
429D3×Dic3—22no—
430C32×C8—32no—
431C32×C8—32no—
432C3×C3⋊C8—22no—
433C3×C3⋊C8—22no—
434C3×C3⋊C8C22×D312yes—
435C3×C3⋊C8C22×D312yes—
436C3×C3⋊C8C23×C312yes—
437C3×C3⋊C8C23×C312yes—
438#575—91noSylow
439C2×C33—21no—
440C2×C33—41no—
441C2×C33C22×D411yescharacteristic
442C3×C3⋊D3—21no—
443C3×C3⋊D3—21no—
444C3×C3⋊D3—41no—
445C32×D3—42no—
446C3×#41—21no—
447C3×#41—21no—
448C3×#41—21no—
449C3×#41—41no—
450C3×#41—92no—
451C3×#41—92no—
452C3×#41—91no—
453C3×#41—91no—
454C3×#41—91no—
455C3×#41—181no—
456C3×#41—181no—
457C3×#41—181no—
458C3×#41—181no—
459C3×#41D3211yescharacteristic
460C3×#41C2×C3×D311yescharacteristic
461C3×#41C2×C3×D311yescharacteristic
462C2×C3×Q8—31no—
463C2×C3×Q8—31no—
464C2×C3×Q8—61no—
465C2×C3×Q8—91no—
466C2×C3×D4—31no—
467C2×C3×D4—31no—
468C2×C3×D4—61no—
469C2×C3×D4—91no—
470C2×C3×D4—181no—
471C2×C3×D4—181no—
472C22×C3×C4—91no—
473C22×C3×C4—181no—
474C22×C3×C4—181no—
475C2×#67—61no—
476C22×Dic3—61no—
477#239—31no—
478#239—31no—
479#239—32no—
480#239—32no—
481#239—61no—
482#239—61no—
483#239—61no—
484D3×Q8—31no—
485D3×Q8—31no—
486D3×Q8—61no—
487#237—31no—
488#237—31no—
489#237—32no—
490#237—32no—
491#237—61no—
492#237—61no—
493#237—61no—
494#237—61no—
495#237—61no—
496#237—62no—
497D3×D4—31no—
498D3×D4—31no—
499D3×D4—61no—
500D3×D4—61no—
501D3×D4—61no—
502D3×D4—62no—
503#235—31no—
504#235—31no—
505#235—61no—
506#235—61no—
507#235—61no—
508#235—62no—
509C2×D12—61no—
510C2×D12C2×C3×D311yescharacteristic, complemented
511C2×C4×D3—31no—
512C2×C4×D3—31no—
513C2×C4×D3—61no—
514C2×C4×D3—61no—
515C2×C4×D3—61no—
516C2×C4×D3—61no—
517C2×C4×D3—62no—
518C2×Dic6C2×C3×D311yescharacteristic, complemented
519C3×Q16—32no—
520C3×Q16—32no—
521C3×Q16—62no—
522C3×Q16—92no—
523C3×SD16—32no—
524C3×SD16—32no—
525C3×SD16—32no—
526C3×SD16—32no—
527C3×SD16—62no—
528C3×SD16—62no—
529C3×SD16—92no—
530C3×SD16—92no—
531C3×D8—32no—
532C3×D8—32no—
533C3×D8—62no—
534C3×D8—92no—
535C3×M16—31no—
536C3×M16—31no—
537C3×M16—31no—
538C3×M16—31no—
539C3×M16—61no—
540C3×M16—61no—
541C3×M16—92no—
542C2×C3×C8—92no—
543#216—32no—
544#216C2×C3×D312yescomplemented
545#215—32no—
546#215C2×C3×D312yescomplemented
547#214—32no—
548#214C2×C3×D312yescomplemented
549#213—32no—
550#213C2×C3×D312yescomplemented
551#208C2×C3×D311yescharacteristic, complemented
552#208C2×C3×D311yescharacteristic, complemented
553Dic12—32no—
554D24—32no—
555#204—32no—
556#204—32no—
557ΓL(1,𝔽25)—32no—
558ΓL(1,𝔽25)—32no—
559D3×C8—32no—
560D3×C8—32no—
561C22×C32—21no—
562C22×C32—22no—
563C22×C32—21no—
564C22×C32—21no—
565C22×C32—21no—
566C22×C32—21no—
567C22×C32—21no—
568C22×C32—41no—
569C22×C32—41no—
570C22×C32—41no—
571C22×C32—42no—
572C22×C32—62no—
573C22×C32—122no—
574C22×C32D3×D411yescharacteristic
575C22×C32D3×D411yescharacteristic
576C22×C32C2×C3×D411yescharacteristic
577C2×C3⋊D3—21no—
578C2×C3⋊D3—41no—
579C2×C3⋊D3—42no—
580C2×C3⋊D3C2×C3×D411yescharacteristic
581C2×C3⋊D3C2×C3×D411yescharacteristic
582C2×C3×D3—22no—
583C2×C3×D3—22no—
584C2×C3×D3—31no—
585C2×C3×D3—31no—
586C2×C3×D3—31no—
587C2×C3×D3—31no—
588C2×C3×D3—42no—
589C2×C3×D3—42no—
590C2×C3×D3—42no—
591C2×C3×D3—61no—
592C2×C3×D3—61no—
593C2×C3×D3—62no—
594C2×C3×D3—61no—
595C2×C3×D3—61no—
596C2×C3×D3—82no—
597C2×C3×D3—121no—
598C2×C3×D3—121no—
599C2×C3×D3—122no—
600C2×C3×D3—124no—
601C2×C3×D3—122no—
602C2×C3×D3—122no—
603C32×C4—21no—
604C32×C4—22no—
605C32×C4—21no—
606C32×C4—21no—
607C32×C4—21no—
608C32×C4—21no—
609C32×C4—21no—
610C32×C4—21no—
611C32×C4—21no—
612C32×C4—21no—
613C32×C4—41no—
614C32×C4—41no—
615C32×C4—41no—
616C32×C4—41no—
617C32×C4—42no—
618C32×C4—62no—
619C32×C4D3×D411yescharacteristic
620C32×C4D3×D411yescharacteristic
621C32×C4C2×C3×D411yescharacteristic
622C32×C4C23×D311yescharacteristic
623C32×C4C23×D311yescharacteristic
624C32×C4C24×C311yescharacteristic
625C3⋊Dic3—21no—
626C3⋊Dic3C2×C3×D411yescharacteristic
627C3⋊Dic3C2×C3×D411yescharacteristic
628C3×Dic3—22no—
629C3×Dic3—22no—
630C3×Dic3—31no—
631C3×Dic3—31no—
632C3×Dic3—31no—
633C3×Dic3—31no—
634C3×Dic3—42no—
635C3×Dic3—61no—
636C3×Dic3—61no—
637C3×Dic3—62no—
638C3×Dic3—61no—
639C3×Dic3—61no—
640C2×#41—91no—
641C2×#41—91no—
642#137—31no—
643#137—91no—
644#137—92no—
645AGL(1,ℤ/8)—31no—
646AGL(1,ℤ/8)—91no—
647AGL(1,ℤ/8)—92no—
648#135—92no—
649#135—92no—
650C2×M16—91no—
651C33#57511yescharacteristic, complemented, Sylow
652C23×C3—61no—
653C23×C3—61no—
654C23×C3—91no—
655C23×C3—121no—
656C23×C3—181no—
657C22×D3—21no—
658C22×D3—31no—
659C22×D3—31no—
660C22×D3—61no—
661C22×D3—61no—
662C22×D3—61no—
663C22×D3—62no—
664C3×Q8—21no—
665C3×Q8—21no—
666C3×Q8—21no—
667C3×Q8—32no—
668C3×Q8—32no—
669C3×Q8—41no—
670C3×Q8—62no—
671C3×Q8—61no—
672C3×Q8—61no—
673C3×Q8—91no—
674C3×Q8—121no—
675C3×Q8—181no—
676C3×Q8C2×D3211yescharacteristic
677C3×Q8C22×C3×D311yescharacteristic
678C3×Q8C22×C3×D311yescharacteristic
679C3×D4—22no—
680C3×D4—21no—
681C3×D4—21no—
682C3×D4—21no—
683C3×D4—21no—
684C3×D4—21no—
685C3×D4—21no—
686C3×D4—32no—
687C3×D4—32no—
688C3×D4—41no—
689C3×D4—41no—
690C3×D4—42no—
691C3×D4—41no—
692C3×D4—62no—
693C3×D4—61no—
694C3×D4—61no—
695C3×D4—91no—
696C3×D4—121no—
697C3×D4—181no—
698C3×D4—182no—
699C3×D4—182no—
700C3×D4—181no—
701C3×D4—181no—
702C3×D4—181no—
703C3×D4C2×D3211yescharacteristic
704C3×D4C22×C3×D311yescharacteristic
705C3×D4C22×C3×D311yescharacteristic
706C2×C3×C4—22no—
707C2×C3×C4—21no—
708C2×C3×C4—21no—
709C2×C3×C4—21no—
710C2×C3×C4—21no—
711C2×C3×C4—21no—
712C2×C3×C4—21no—
713C2×C3×C4—41no—
714C2×C3×C4—41no—
715C2×C3×C4—42no—
716C2×C3×C4—41no—
717C2×C3×C4—61no—
718C2×C3×C4—61no—
719C2×C3×C4—91no—
720C2×C3×C4—91no—
721C2×C3×C4—91no—
722C2×C3×C4—91no—
723C2×C3×C4—91no—
724C2×C3×C4—121no—
725C2×C3×C4—181no—
726C2×C3×C4—181no—
727C2×C3×C4—182no—
728C2×C3×C4—182no—
729C2×C3×C4—181no—
730C2×C3×C4—181no—
731C2×C3×C4C2×D3211yescharacteristic
732C2×C3×C4C22×C3×D311yescharacteristic
733C2×C3×C4C22×C3×D311yescharacteristic
734#67—62no—
735#67—62no—
736#67—61no—
737#67—61no—
738#67—61no—
739#67—61no—
740#67—62no—
741#67—62no—
742#67—62no—
743#67—61no—
744#67—61no—
745C2×Dic3—21no—
746C2×Dic3—31no—
747C2×Dic3—31no—
748C2×Dic3—61no—
749C2×Dic3—62no—
750C2×Dic3—62no—
751C2×Dic3—61no—
752C2×Dic3—61no—
753C2×Dic3—62no—
754D12—21no—
755D12—31no—
756D12—31no—
757D12—61no—
758D12—61no—
759D12—61no—
760D12—62no—
761D12—62no—
762D12—62no—
763D12C22×C3×D312yes—
764C4×D3—31no—
765C4×D3—31no—
766C4×D3—31no—
767C4×D3—31no—
768C4×D3—31no—
769C4×D3—31no—
770C4×D3—31no—
771C4×D3—31no—
772C4×D3—61no—
773C4×D3—61no—
774C4×D3—61no—
775C4×D3—61no—
776C4×D3—61no—
777C4×D3—61no—
778C4×D3—62no—
779C4×D3—62no—
780C4×D3—61no—
781C4×D3—61no—
782C4×D3—62no—
783C4×D3—62no—
784C4×D3—62no—
785C4×D3—61no—
786C4×D3—61no—
787Dic6—21no—
788Dic6—31no—
789Dic6—31no—
790Dic6—61no—
791Dic6—61no—
792Dic6—61no—
793Dic6—62no—
794Dic6C22×C3×D312yes—
795C3×C8—32no—
796C3×C8—32no—
797C3×C8—32no—
798C3×C8—32no—
799C3×C8—62no—
800C3×C8—62no—
801C3⋊C8C22×C3×D312yes—
802C3⋊C8C22×C3×D312yes—
803C2×C32—21no—
804C2×C32—21no—
805C2×C32—21no—
806C2×C32—21no—
807C2×C32—21no—
808C2×C32—21no—
809C2×C32—41no—
810C2×C32—41no—
811C2×C32—41no—
812C2×C32—41no—
813C2×C32—41no—
814C2×C32—42no—
815C2×C32—41no—
816C2×C32—41no—
817C2×C32—81no—
818C2×C32—81no—
819C2×C32—81no—
820C2×C32—82no—
821C2×C32—122no—
822C2×C32C2×D3×D411yescharacteristic
823C2×C32C2×D3×D411yescharacteristic
824C2×C32C22×C3×D411yescharacteristic
825C3⋊D3—21no—
826C3⋊D3—21no—
827C3⋊D3—41no—
828C3×D3—42no—
829C3×D3—42no—
830C3×D3—62no—
831C3×D3—61no—
832C3×D3—61no—
833C3×D3—61no—
834C3×D3—61no—
835C3×D3—82no—
836C3×D3—121no—
837C3×D3—122no—
838C3×D3—121no—
839C3×D3—121no—
840#41—92no—
841#41—92no—
842#41—91no—
843#41—91no—
844#41—91no—
845#41—181no—
846#41—181no—
847#41—181no—
848#41—181no—
849#41C3×D3211yescharacteristic
850C2×Q8—31no—
851C2×Q8—91no—
852C2×D4—31no—
853C2×D4—91no—
854C2×D4—181no—
855C2×D4—181no—
856C22×C4—91no—
857C22×C4—181no—
858C22×C4—181no—
859Q16—32no—
860Q16—92no—
861SD16—32no—
862SD16—32no—
863SD16—92no—
864SD16—92no—
865D8—32no—
866D8—92no—
867M16—31no—
868M16—31no—
869M16—92no—
870C2×C8—92no—
871C22×C3—22no—
872C22×C3—21no—
873C22×C3—21no—
874C22×C3—21no—
875C22×C3—21no—
876C22×C3—21no—
877C22×C3—21no—
878C22×C3—41no—
879C22×C3—41no—
880C22×C3—42no—
881C22×C3—41no—
882C22×C3—62no—
883C22×C3—62no—
884C22×C3—91no—
885C22×C3—91no—
886C22×C3—122no—
887C22×C3—122no—
888C22×C3—122no—
889C22×C3—181no—
890C22×C3—242no—
891C22×C3—361no—
892C22×C3—362no—
893C22×C3#381111yescharacteristic
894C22×C3C3×D3×D411yescharacteristic
895C22×C3C3×D3×D411yescharacteristic
896C2×D3—22no—
897C2×D3—31no—
898C2×D3—31no—
899C2×D3—31no—
900C2×D3—31no—
901C2×D3—42no—
902C2×D3—61no—
903C2×D3—61no—
904C2×D3—62no—
905C2×D3—61no—
906C2×D3—61no—
907C2×D3—121no—
908C2×D3—121no—
909C2×D3—122no—
910C2×D3—124no—
911C2×D3—122no—
912C2×D3—122no—
913C3×C4—22no—
914C3×C4—21no—
915C3×C4—21no—
916C3×C4—21no—
917C3×C4—21no—
918C3×C4—21no—
919C3×C4—21no—
920C3×C4—21no—
921C3×C4—21no—
922C3×C4—21no—
923C3×C4—41no—
924C3×C4—41no—
925C3×C4—42no—
926C3×C4—41no—
927C3×C4—41no—
928C3×C4—62no—
929C3×C4—62no—
930C3×C4—91no—
931C3×C4—91no—
932C3×C4—122no—
933C3×C4—181no—
934C3×C4#381111yescharacteristic
935C3×C4C3×D3×D411yescharacteristic
936C3×C4C3×D3×D411yescharacteristic
937C3×C4C22×D3211yescharacteristic
938C3×C4C23×C3×D311yescharacteristic
939C3×C4C23×C3×D311yescharacteristic
940Dic3—22no—
941Dic3—31no—
942Dic3—31no—
943Dic3—31no—
944Dic3—31no—
945Dic3—61no—
946Dic3—61no—
947Dic3—62no—
948Dic3—61no—
949Dic3—61no—
950C32—21no—
951C32—21no—
952C32—21no—
953C32—41no—
954C32#577311yescharacteristic, complemented
955C32#577711yescharacteristic, complemented
956C32C3×#57511yescharacteristic, complemented
957C23—61no—
958C23—91no—
959C23—181no—
960Q8—32no—
961Q8—61no—
962Q8—91no—
963Q8—181no—
964Q8C2×C3×D3211yescharacteristic
965D4—21no—
966D4—32no—
967D4—61no—
968D4—91no—
969D4—181no—
970D4—182no—
971D4—182no—
972D4—181no—
973D4—181no—
974D4—181no—
975D4C2×C3×D3211yescharacteristic
976C2×C4—21no—
977C2×C4—61no—
978C2×C4—91no—
979C2×C4—91no—
980C2×C4—91no—
981C2×C4—91no—
982C2×C4—91no—
983C2×C4—181no—
984C2×C4—181no—
985C2×C4—182no—
986C2×C4—182no—
987C2×C4—181no—
988C2×C4—181no—
989C2×C4C2×C3×D3211yescharacteristic
990C8—32no—
991C8—32no—
992C2×C3—21no—
993C2×C3—21no—
994C2×C3—21no—
995C2×C3—21no—
996C2×C3—21no—
997C2×C3—21no—
998C2×C3—41no—
999C2×C3—41no—
1000C2×C3—41no—
1001C2×C3—42no—
1002C2×C3—41no—
1003C2×C3—41no—
1004C2×C3—41no—
1005C2×C3—41no—
1006C2×C3—81no—
1007C2×C3—81no—
1008C2×C3—81no—
1009C2×C3—82no—
1010C2×C3—122no—
1011C2×C3—122no—
1012C2×C3—181no—
1013C2×C3—181no—
1014C2×C3—242no—
1015C2×C3—361no—
1016C2×C3C2×#381111yescharacteristic
1017C2×C3C2×C3×D3×D411yescharacteristic
1018C2×C3C2×C3×D3×D411yescharacteristic
1019D3—42no—
1020D3—62no—
1021D3—61no—
1022D3—61no—
1023D3—61no—
1024D3—61no—
1025D3—121no—
1026D3—122no—
1027D3—121no—
1028D3—121no—
1029C22—21no—
1030C22—62no—
1031C22—91no—
1032C22—91no—
1033C22—122no—
1034C22—181no—
1035C22—361no—
1036C22—362no—
1037C22C3×#381111yescharacteristic
1038C4—21no—
1039C4—62no—
1040C4—91no—
1041C4—91no—
1042C4—181no—
1043C4C3×#381111yescharacteristic
1044C4C22×C3×D3211yescharacteristic
1045C3—21no—
1046C3—21no—
1047C3—21no—
1048C3—41no—
1049C3#1059547111yescharacteristic, direct product factor
1050C3C3×#577311yescharacteristic, complemented
1051C3C3×#577711yescharacteristic, complemented
1052C2—21no—
1053C2—41no—
1054C2—122no—
1055C2—181no—
1056C2—181no—
1057C2—361no—
1058C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC2×C3C2×#3811
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×#41C22
socleC2×C33C22×D4
hypercenterC3×#41D32
hypocenterC32C3×#575
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×#41×C3⋊D3C2semidirect
2. C2×C3×#3796C2semidirect
3. C32×#951C2semidirect
4. C32×#949C2semidirect
5. C3×#63951C2semidirect
6. C3×#63950C2semidirect
7. C3×#63937C2semidirect
8. C3×#63936C2semidirect
9. C3×#63833C2semidirect
10. C3×#63830C2semidirect
11. C3×#63818C2semidirect
14. #10595471C3direct (N × H)
16. C3×#3832C22semidirect
17. C3×Q8×C3⋊D3C22semidirect
19. C3×#3830C22semidirect
21. C3×D4×C3⋊D3C22semidirect
26. C2×C32×D12C22semidirect
27. C2×C32×Dic6C22semidirect
33. C3×#3796C22semidirect
34. C32×#216C22semidirect
35. C32×#215C22semidirect
36. C32×#214C22semidirect
37. C32×#213C22semidirect
38. C32×#208C22semidirect
39. C32×#208C22semidirect
40. C3×#3719C22semidirect
41. C3×#3717C22semidirect
42. C3×#3716C22semidirect
43. C3×#3714C22semidirect
44. C3×#3712C22semidirect
45. C3×#3710C22semidirect
46. #41×C3⋊D3C2×C3semidirect
52. C2×#3796C2×C3semidirect
56. C3×#951D3semidirect
57. C3×#951C2×C3semidirect
59. C3×#949D3semidirect
60. C3×#949C2×C3semidirect
75. #63951C2×C3semidirect
76. #63950C2×C3semidirect
77. #63937C2×C3semidirect
78. #63936C2×C3semidirect
79. #63833C2×C3semidirect
80. #63830C2×C3semidirect
81. #63818C2×C3semidirect
129. #3832C22×C3semidirect
130. Q8×C3⋊D3C22×C3semidirect
132. #3830C22×C3semidirect
134. D4×C3⋊D3C22×C3semidirect
175. C2×C3×D12C2×D3semidirect
176. C2×C3×D12C22×C3semidirect
185. C2×C3×Dic6C2×D3semidirect
186. C2×C3×Dic6C22×C3semidirect
192. #3796C22×C3semidirect
201. C3×#216C2×D3semidirect
202. C3×#216C22×C3semidirect
205. C3×#215C2×D3semidirect
206. C3×#215C22×C3semidirect
209. C3×#214C2×D3semidirect
210. C3×#214C22×C3semidirect
213. C3×#213C2×D3semidirect
214. C3×#213C22×C3semidirect
217. C3×#208C2×D3semidirect
218. C3×#208C2×D3semidirect
219. C3×#208C22×C3semidirect
220. C3×#208C22×C3semidirect
229. #3719C22×C3semidirect
230. #3717C22×C3semidirect
231. #3716C22×C3semidirect
232. #3714C22×C3semidirect
233. #3712C22×C3semidirect
234. #3710C22×C3semidirect
271. #951C3×D3semidirect
272. #949C3×D3semidirect
510. C2×D12C2×C3×D3semidirect
518. C2×Dic6C2×C3×D3semidirect
544. #216C2×C3×D3semidirect
546. #215C2×C3×D3semidirect
548. #214C2×C3×D3semidirect
550. #213C2×C3×D3semidirect
551. #208C2×C3×D3semidirect
552. #208C2×C3×D3semidirect
651. C33#575semidirect
954. C32#5773semidirect
955. C32#5777semidirect
956. C32C3×#575semidirect
1049. C3#10595471direct (N × H)
1050. C3C3×#5773semidirect
1051. C3C3×#5777semidirect

Maximal subgroups

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

subgroupindex
C3×#41×C3⋊D32
C2×C3×#37962
C32×#9512
C32×#9492
C3×#639512
C3×#639502
C3×#639372
C3×#639362
C3×#638332
C3×#638302
C3×#638182
C3×#57773
C3×#57733
#105954713