Finite Group Databasebeta

← C3×#10595469 #13175066

Subgroups — C3×#10595469 #13175066

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
1C32×D3×#41C211yesmaximal, characteristic, complemented
2C2×C3×#3795C211yesmaximal, characteristic, complemented
3C3×#64160C211yesmaximal, characteristic, complemented
4C32×#949C211yesmaximal, characteristic, complemented
5C3×#63947C212yesmaximal, complemented
6C3×#63946C212yesmaximal, complemented
7C3×#63933C212yesmaximal, complemented
8C3×#63932C212yesmaximal, complemented
9C3×#63831C211yesmaximal, characteristic, complemented
10C3×#63823C211yesmaximal, characteristic, complemented
11C3×D3×#208C211yesmaximal, characteristic, complemented
12C3×#5822—31nomaximal
13C3×#5773—31nomaximal
14#10595469C311yesmaximal, characteristic, direct product factor
15C33×#41C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic, complemented
17C32×#239C2211yescharacteristic, complemented
18C32×D3×Q8C2211yescharacteristic, complemented
19C32×#237—21no—
20C32×#237C2211yescharacteristic, complemented
21C32×D3×D4—21no—
22C32×D3×D4C2211yescharacteristic, complemented
23C32×#235—21no—
24C32×#235C2211yescharacteristic
25C2×C32×D12C2211yescharacteristic, complemented
26C2×C32×C4×D3—21no—
27C2×C32×C4×D3C2211yescharacteristic
28C2×C3×#625—21no—
29C2×C3×D3×Dic3—21no—
30C3×#3795—21no—
31C3×#3795—21no—
32C3×#3795C2212yes—
33C3×#3795C2212yescomplemented
34C3×#3756C2212yescomplemented
35C3×#3754C2212yescomplemented
36C3×#3748C2211yescharacteristic, complemented
37C32×#215C2212yescomplemented
38C32×#213C2212yescomplemented
39C32×#208C2211yescharacteristic, complemented
40C3×#3719C2212yescomplemented
41C3×#3716C2212yescomplemented
42C3×#3715C2212yescomplemented
43C3×#3713C2212yescomplemented
44C3×#3711C2212yescomplemented
45C3×D3×C3⋊C8C2212yescomplemented
46C2×C32×#41—31no—
47C3×D3×#41—21no—
48C3×D3×#41D311yescharacteristic, complemented
49C3×D3×#41C2×C311yescharacteristic, complemented
50C2×C3×#237—31no—
51C2×C3×#235—31no—
52C2×#3795C2×C311yescharacteristic, complemented
53C32×AGL(1,ℤ/8)—31no—
54#64160C2×C311yescharacteristic, complemented
55C3×#951—31no—
56C3×#951—31no—
57C3×#951—31no—
58C3×#951—61no—
59C3×#950—32no—
60C3×#950—32no—
61C3×#949—21no—
62C3×#949—31no—
63C3×#949D311yescharacteristic, complemented
64C3×#949C2×C311yescharacteristic, complemented
65C3×#942—32no—
66C3×#932—31no—
67C3×#932—32no—
68C2×C3×#208—31no—
69C3×#916—32no—
70C3×#915—32no—
71C3×#912—32no—
72C3×#911—32no—
73C3×#909—31no—
74C3×D3×M16—31no—
75#63947C2×C312yescomplemented
76#63946C2×C312yescomplemented
77#63933C2×C312yescomplemented
78#63932C2×C312yescomplemented
79#63831C2×C311yescharacteristic, complemented
80#63823C2×C311yescharacteristic, complemented
81D3×#208C2×C311yescharacteristic, complemented
82C22×C32×D3—21no—
83C22×C32×D3—21no—
84C22×C32×D3D411yescharacteristic
85C33×Q8C2311yescharacteristic
86C33×D4—21no—
87C33×D4C2311yescharacteristic
88C2×C33×C4—21no—
89C2×C33×C4C2311yescharacteristic
90C2×C3×C3⋊Dic3—21no—
91C3×#634—21no—
92C3×#634C2312yes—
93C32×#67—21no—
94C32×#67—21no—
95C32×#67—21no—
96C2×C32×Dic3—21no—
97C2×C32×Dic3D411yescharacteristic
98C32×D12—21no—
99C32×D12—21no—
100C32×D12C2312yes—
101C32×D12C2311yescharacteristic
102C32×C4×D3—21no—
103C32×C4×D3—21no—
104C32×C4×D3—21no—
105C32×C4×D3D411yescharacteristic
106C32×C4×D3D411yescharacteristic
107C32×C4×D3C2311yescharacteristic
108C32×C4×D3C2311yescharacteristic
109C32×Dic6—21no—
110C32×Dic6C2311yescharacteristic
111C3×#625—22no—
112C3×#625—22no—
113C3×D3×Dic3—22no—
114C3×D3×Dic3—22no—
115C3×C3⋊(C3⋊C8)C2312yes—
116C32×C3⋊C8C2312yes—
117C3×#575—91no—
118#5822—31no—
119#5773—31no—
120C32×#41—21no—
121C32×#41—21no—
122C32×#41—21no—
123C32×#41—31no—
124C32×#41—31no—
125C32×#41—31no—
126C32×#41—41no—
127C32×#41—61no—
128C32×#41—61no—
129C32×#41C2×D311yescharacteristic
130C32×#41C2×D311yescharacteristic
131C32×#41C22×C311yescharacteristic
132C2×C32×Q8—31no—
133C2×C32×D4—31no—
134C2×C32×D4—31no—
135C2×C32×D4—61no—
136C22×C32×C4—31no—
137C22×C32×C4—61no—
138C2×#634C22×C311yescharacteristic, complemented
139C2×C3×#67—61no—
140C2×C3×#67—61no—
141C22×C3×Dic3—61no—
142C3×#239—21no—
143C3×#239C2×D311yescharacteristic, complemented
144C3×#239C22×C311yescharacteristic, complemented
145C3×D3×Q8—21no—
146C3×D3×Q8C2×D311yescharacteristic, complemented
147C3×D3×Q8C22×C311yescharacteristic, complemented
148C3×#237—22no—
149C3×#237—21no—
150C3×#237—21no—
151C3×#237—21no—
152C3×#237—32no—
153C3×#237—32no—
154C3×#237—61no—
155C3×#237—61no—
156C3×#237C2×D311yescharacteristic, complemented
157C3×#237C22×C311yescharacteristic, complemented
158C3×D3×D4—22no—
159C3×D3×D4—21no—
160C3×D3×D4—21no—
161C3×D3×D4—21no—
162C3×D3×D4C2×D311yescharacteristic, complemented
163C3×D3×D4C22×C311yescharacteristic, complemented
164C3×#235—22no—
165C3×#235—21no—
166C3×#235—21no—
167C3×#235—21no—
168C3×#235—32no—
169C3×#235—32no—
170C3×#235—61no—
171C3×#235—61no—
172C3×#235C2×D311yescharacteristic
173C3×#235C22×C311yescharacteristic
174C2×C3×D12—21no—
175C2×C3×D12C2×D311yescharacteristic, complemented
176C2×C3×D12C22×C311yescharacteristic, complemented
177C2×C3×C4×D3—22no—
178C2×C3×C4×D3—21no—
179C2×C3×C4×D3—21no—
180C2×C3×C4×D3—21no—
181C2×C3×C4×D3—61no—
182C2×C3×C4×D3C2×D311yescharacteristic
183C2×C3×C4×D3C22×C311yescharacteristic
184C2×C3×Dic6—31no—
185C2×C3×Dic6—31no—
186C2×C3×Dic6—61no—
187C2×#625—21no—
188C2×D3×Dic3—21no—
189#3795—21no—
190#3795—21no—
191#3795C22×C312yes—
192#3795C22×C312yescomplemented
193C32×SD16—32no—
194C32×D8—32no—
195C32×M16—31no—
196#3756C22×C312yescomplemented
197#3754C22×C312yescomplemented
198#3748C22×C311yescharacteristic, complemented
199C3×#216—32no—
200C3×#216—32no—
201C3×#216—32no—
202C3×#216—62no—
203C3×#215—22no—
204C3×#215—32no—
205C3×#215C2×D312yescomplemented
206C3×#215C22×C312yescomplemented
207C3×#214—32no—
208C3×#214—32no—
209C3×#214—32no—
210C3×#214—32no—
211C3×#214—62no—
212C3×#213—22no—
213C3×#213—32no—
214C3×#213—32no—
215C3×#213C2×D312yescomplemented
216C3×#213C22×C312yescomplemented
217C3×#208—21no—
218C3×#208—31no—
219C3×#208—31no—
220C3×#208—32no—
221C3×#208—61no—
222C3×#208C2×D311yescharacteristic, complemented
223C3×#208C22×C311yescharacteristic, complemented
224C2×C3×C3⋊C8—32no—
225C3×Dic12—32no—
226C3×#204—32no—
227C3×ΓL(1,𝔽25)—32no—
228C3×D3×C8—32no—
229#3719C22×C312yescomplemented
230#3716C22×C312yescomplemented
231#3715C22×C312yescomplemented
232#3713C22×C312yescomplemented
233#3711C22×C312yescomplemented
234D3×C3⋊C8C22×C312yescomplemented
235C22×C33—21no—
236C22×C33C2×D411yescharacteristic
237C2×C32×D3—21no—
238C2×C32×D3—22no—
239C2×C32×D3—41no—
240C2×C32×D3—42no—
241C2×C32×D3—42no—
242C2×C32×D3C2×D411yescharacteristic
243C2×C32×D3C2×D411yescharacteristic
244C33×C4—21no—
245C33×C4C2×D411yescharacteristic
246C33×C4C2411yescharacteristic
247C3×C3⋊Dic3—22no—
248C32×Dic3—21no—
249C32×Dic3C2×D411yescharacteristic
250C32×Dic3C2×D411yescharacteristic
251C2×C3×#41—31no—
252C2×C3×#41—31no—
253C2×C3×#41—61no—
254C2×C3×#41—91no—
255D3×#41C3×D311yescharacteristic, complemented
256C2×#237—31no—
257C2×#235—31no—
258C3×#137—91no—
259C3×#137—92no—
260C3×#137—91no—
261C3×AGL(1,ℤ/8)—31no—
262C3×AGL(1,ℤ/8)—31no—
263C3×AGL(1,ℤ/8)—61no—
264C3×AGL(1,ℤ/8)—92no—
265C3×AGL(1,ℤ/8)—91no—
266C3×#135—92no—
267C3×#135—92no—
268C2×C3×M16—91no—
269#951—31no—
270#951—31no—
271#951—31no—
272#951—61no—
273#950—32no—
274#950—32no—
275#949—31no—
276#949C3×D311yescharacteristic, complemented
277#942—32no—
278#932—31no—
279#932—32no—
280C2×#208—31no—
281#916—32no—
282#915—32no—
283#912—32no—
284#911—32no—
285#909—31no—
286D3×M16—31no—
287C23×C32—31no—
288C23×C32—61no—
289C23×C32—61no—
290C22×C3×D3—22no—
291C22×C3×D3—21no—
292C22×C3×D3—21no—
293C22×C3×D3—21no—
294C22×C3×D3—21no—
295C22×C3×D3—21no—
296C22×C3×D3—41no—
297C22×C3×D3#6711yescharacteristic
298C22×C3×D3C3×D411yescharacteristic
299C32×Q8—21no—
300C32×Q8—21no—
301C32×Q8—21no—
302C32×Q8—31no—
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—31no—
316C32×D4—32no—
317C32×D4—41no—
318C32×D4—41no—
319C32×D4—41no—
320C32×D4—42no—
321C32×D4—61no—
322C32×D4—61no—
323C32×D4—61no—
324C32×D4—61no—
325C32×D4—61no—
326C32×D4C22×D311yescharacteristic
327C32×D4C22×D311yescharacteristic
328C32×D4C23×C311yescharacteristic
329C2×C32×C4—21no—
330C2×C32×C4—22no—
331C2×C32×C4—21no—
332C2×C32×C4—21no—
333C2×C32×C4—21no—
334C2×C32×C4—21no—
335C2×C32×C4—21no—
336C2×C32×C4—31no—
337C2×C32×C4—31no—
338C2×C32×C4—31no—
339C2×C32×C4—31no—
340C2×C32×C4—31no—
341C2×C32×C4—41no—
342C2×C32×C4—41no—
343C2×C32×C4—41no—
344C2×C32×C4—42no—
345C2×C32×C4—61no—
346C2×C32×C4—61no—
347C2×C32×C4—61no—
348C2×C32×C4—61no—
349C2×C32×C4C22×D311yescharacteristic
350C2×C32×C4C22×D311yescharacteristic
351C2×C32×C4C23×C311yescharacteristic
352C2×C3⋊Dic3—21no—
353#634—21no—
354#634C23×C312yes—
355C3×#67—22no—
356C3×#67—22no—
357C3×#67—22no—
358C3×#67—21no—
359C3×#67—21no—
360C3×#67—21no—
361C3×#67—21no—
362C3×#67—21no—
363C3×#67—21no—
364C3×#67—62no—
365C3×#67—62no—
366C3×#67—62no—
367C3×#67—62no—
368C2×C3×Dic3—22no—
369C2×C3×Dic3—21no—
370C2×C3×Dic3—21no—
371C2×C3×Dic3—21no—
372C2×C3×Dic3—61no—
373C2×C3×Dic3—61no—
374C2×C3×Dic3—62no—
375C2×C3×Dic3—62no—
376C2×C3×Dic3—121no—
377C2×C3×Dic3#6711yescharacteristic
378C2×C3×Dic3C3×D411yescharacteristic
379C3×D12—22no—
380C3×D12—21no—
381C3×D12—21no—
382C3×D12—21no—
383C3×D12—21no—
384C3×D12—21no—
385C3×D12—22no—
386C3×D12—41no—
387C3×D12C22×D311yescharacteristic
388C3×D12C22×D312yes—
389C3×D12C23×C311yescharacteristic
390C3×D12C23×C312yes—
391C3×C4×D3—22no—
392C3×C4×D3—22no—
393C3×C4×D3—22no—
394C3×C4×D3—21no—
395C3×C4×D3—21no—
396C3×C4×D3—21no—
397C3×C4×D3—21no—
398C3×C4×D3—21no—
399C3×C4×D3—21no—
400C3×C4×D3—21no—
401C3×C4×D3—21no—
402C3×C4×D3—21no—
403C3×C4×D3—21no—
404C3×C4×D3—62no—
405C3×C4×D3—62no—
406C3×C4×D3#6711yescharacteristic
407C3×C4×D3#6711yescharacteristic
408C3×C4×D3C3×D411yescharacteristic
409C3×C4×D3C3×D411yescharacteristic
410C3×C4×D3C22×D311yescharacteristic
411C3×C4×D3C22×D311yescharacteristic
412C3×C4×D3C23×C311yescharacteristic
413C3×C4×D3C23×C311yescharacteristic
414C3×Dic6—22no—
415C3×Dic6—21no—
416C3×Dic6—21no—
417C3×Dic6—21no—
418C3×Dic6—32no—
419C3×Dic6—32no—
420C3×Dic6—62no—
421C3×Dic6—61no—
422C3×Dic6—61no—
423C3×Dic6—121no—
424C3×Dic6C22×D311yescharacteristic
425C3×Dic6C23×C311yescharacteristic
426#625—22no—
427#625—22no—
428D3×Dic3—22no—
429D3×Dic3—22no—
430C32×C8—32no—
431C3⋊(C3⋊C8)C23×C312yes—
432C3×C3⋊C8—22no—
433C3×C3⋊C8—32no—
434C3×C3⋊C8—32no—
435C3×C3⋊C8—62no—
436C3×C3⋊C8C22×D312yes—
437C3×C3⋊C8C23×C312yes—
438#575—91noSylow
439C2×C33—21no—
440C2×C33—41no—
441C2×C33C22×D411yescharacteristic
442C32×D3—21no—
443C32×D3—21no—
444C32×D3—41no—
445C32×D3—42no—
446C3×#41—21no—
447C3×#41—21no—
448C3×#41—21no—
449C3×#41—31no—
450C3×#41—31no—
451C3×#41—31no—
452C3×#41—31no—
453C3×#41—31no—
454C3×#41—31no—
455C3×#41—41no—
456C3×#41—61no—
457C3×#41—61no—
458C3×#41—61no—
459C3×#41—61no—
460C3×#41—61no—
461C3×#41—62no—
462C3×#41—61no—
463C3×#41—61no—
464C3×#41—62no—
465C3×#41—92no—
466C3×#41—92no—
467C3×#41—181no—
468C3×#41—181no—
469C3×#41D3211yescharacteristic
470C3×#41C2×C3×D311yescharacteristic
471C3×#41C2×C3×D311yescharacteristic
472C2×C3×Q8—31no—
473C2×C3×Q8—31no—
474C2×C3×Q8—61no—
475C2×C3×Q8—91no—
476C2×C3×D4—31no—
477C2×C3×D4—31no—
478C2×C3×D4—31no—
479C2×C3×D4—31no—
480C2×C3×D4—61no—
481C2×C3×D4—61no—
482C2×C3×D4—61no—
483C2×C3×D4—61no—
484C2×C3×D4—62no—
485C2×C3×D4—181no—
486C22×C3×C4—31no—
487C22×C3×C4—31no—
488C22×C3×C4—61no—
489C22×C3×C4—61no—
490C22×C3×C4—61no—
491C22×C3×C4—62no—
492C22×C3×C4—181no—
493C2×#67—61no—
494C2×#67—61no—
495C22×Dic3—61no—
496#239C2×C3×D311yescharacteristic, complemented
497D3×Q8C2×C3×D311yescharacteristic, complemented
498#237—21no—
499#237—32no—
500#237—32no—
501#237—61no—
502#237—61no—
503#237C2×C3×D311yescharacteristic, complemented
504D3×D4—21no—
505D3×D4C2×C3×D311yescharacteristic, complemented
506#235—21no—
507#235—32no—
508#235—32no—
509#235—61no—
510#235—61no—
511#235C2×C3×D311yescharacteristic
512C2×D12C2×C3×D311yescharacteristic, complemented
513C2×C4×D3—21no—
514C2×C4×D3—61no—
515C2×C4×D3C2×C3×D311yescharacteristic
516C2×Dic6—31no—
517C2×Dic6—31no—
518C2×Dic6—61no—
519C3×Q16—92no—
520C3×Q16—92no—
521C3×SD16—32no—
522C3×SD16—32no—
523C3×SD16—62no—
524C3×SD16—92no—
525C3×SD16—92no—
526C3×SD16—92no—
527C3×D8—32no—
528C3×D8—32no—
529C3×D8—62no—
530C3×D8—92no—
531C3×M16—31no—
532C3×M16—31no—
533C3×M16—61no—
534C3×M16—92no—
535C3×M16—91no—
536C2×C3×C8—92no—
537#216—32no—
538#216—32no—
539#216—32no—
540#216—62no—
541#215—32no—
542#215C2×C3×D312yescomplemented
543#214—32no—
544#214—32no—
545#214—32no—
546#214—32no—
547#214—62no—
548#213—32no—
549#213—32no—
550#213C2×C3×D312yescomplemented
551#208—31no—
552#208—31no—
553#208—32no—
554#208—61no—
555#208C2×C3×D311yescharacteristic, complemented
556C2×C3⋊C8—32no—
557Dic12—32no—
558#204—32no—
559ΓL(1,𝔽25)—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—31no—
569C22×C32—31no—
570C22×C32—41no—
571C22×C32—41no—
572C22×C32—41no—
573C22×C32—42no—
574C22×C32—61no—
575C22×C32—62no—
576C22×C32—121no—
577C22×C32—122no—
578C22×C32—122no—
579C22×C32D3×D411yescharacteristic
580C22×C32C2×#6711yescharacteristic
581C22×C32C2×C3×D411yescharacteristic
582C2×C3×D3—22no—
583C2×C3×D3—22no—
584C2×C3×D3—21no—
585C2×C3×D3—22no—
586C2×C3×D3—21no—
587C2×C3×D3—21no—
588C2×C3×D3—21no—
589C2×C3×D3—42no—
590C2×C3×D3—41no—
591C2×C3×D3—41no—
592C2×C3×D3—42no—
593C2×C3×D3—44no—
594C2×C3×D3—42no—
595C2×C3×D3—42no—
596C2×C3×D3—42no—
597C2×C3×D3—42no—
598C2×C3×D3—82no—
599C2×C3×D3C2×#6711yescharacteristic
600C2×C3×D3C2×#6711yescharacteristic
601C2×C3×D3C2×C3×D411yescharacteristic
602C2×C3×D3C2×C3×D411yescharacteristic
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—31no—
614C32×C4—31no—
615C32×C4—41no—
616C32×C4—41no—
617C32×C4—41no—
618C32×C4—41no—
619C32×C4—42no—
620C32×C4—61no—
621C32×C4D3×D411yescharacteristic
622C32×C4C2×#6711yescharacteristic
623C32×C4C2×C3×D411yescharacteristic
624C32×C4C23×D311yescharacteristic
625C32×C4C23×D311yescharacteristic
626C32×C4C24×C311yescharacteristic
627C3⋊Dic3—22no—
628C3×Dic3—22no—
629C3×Dic3—21no—
630C3×Dic3—21no—
631C3×Dic3—21no—
632C3×Dic3—21no—
633C3×Dic3—62no—
634C3×Dic3—62no—
635C3×Dic3—122no—
636C3×Dic3C2×#6711yescharacteristic
637C3×Dic3C2×#6711yescharacteristic
638C3×Dic3C2×C3×D411yescharacteristic
639C3×Dic3C2×C3×D411yescharacteristic
640C2×#41—31no—
641C2×#41—91no—
642#137—91no—
643#137—92no—
644#137—91no—
645AGL(1,ℤ/8)—31no—
646AGL(1,ℤ/8)—92no—
647AGL(1,ℤ/8)—91no—
648#135—92no—
649#135—92no—
650C2×M16—91no—
651C33#57511yescharacteristic, complemented, Sylow
652C23×C3—31no—
653C23×C3—31no—
654C23×C3—61no—
655C23×C3—61no—
656C23×C3—61no—
657C23×C3—62no—
658C23×C3—61no—
659C23×C3—61no—
660C23×C3—121no—
661C22×D3—21no—
662C22×D3—21no—
663C22×D3C3×#6711yescharacteristic
664C3×Q8—21no—
665C3×Q8—21no—
666C3×Q8—21no—
667C3×Q8—31no—
668C3×Q8—31no—
669C3×Q8—41no—
670C3×Q8—61no—
671C3×Q8—61no—
672C3×Q8—61no—
673C3×Q8—62no—
674C3×Q8—92no—
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—31no—
688C3×D4—31no—
689C3×D4—32no—
690C3×D4—41no—
691C3×D4—41no—
692C3×D4—42no—
693C3×D4—41no—
694C3×D4—61no—
695C3×D4—62no—
696C3×D4—61no—
697C3×D4—61no—
698C3×D4—62no—
699C3×D4—61no—
700C3×D4—61no—
701C3×D4—61no—
702C3×D4—61no—
703C3×D4—62no—
704C3×D4—62no—
705C3×D4—62no—
706C3×D4—61no—
707C3×D4—61no—
708C3×D4—61no—
709C3×D4—61no—
710C3×D4—121no—
711C3×D4—182no—
712C3×D4—182no—
713C3×D4C2×D3211yescharacteristic
714C3×D4C22×C3×D311yescharacteristic
715C3×D4C22×C3×D311yescharacteristic
716C2×C3×C4—22no—
717C2×C3×C4—21no—
718C2×C3×C4—21no—
719C2×C3×C4—21no—
720C2×C3×C4—21no—
721C2×C3×C4—21no—
722C2×C3×C4—21no—
723C2×C3×C4—31no—
724C2×C3×C4—31no—
725C2×C3×C4—31no—
726C2×C3×C4—31no—
727C2×C3×C4—31no—
728C2×C3×C4—31no—
729C2×C3×C4—31no—
730C2×C3×C4—31no—
731C2×C3×C4—31no—
732C2×C3×C4—31no—
733C2×C3×C4—41no—
734C2×C3×C4—41no—
735C2×C3×C4—42no—
736C2×C3×C4—41no—
737C2×C3×C4—61no—
738C2×C3×C4—61no—
739C2×C3×C4—61no—
740C2×C3×C4—61no—
741C2×C3×C4—61no—
742C2×C3×C4—61no—
743C2×C3×C4—61no—
744C2×C3×C4—61no—
745C2×C3×C4—61no—
746C2×C3×C4—62no—
747C2×C3×C4—62no—
748C2×C3×C4—62no—
749C2×C3×C4—61no—
750C2×C3×C4—61no—
751C2×C3×C4—62no—
752C2×C3×C4—61no—
753C2×C3×C4—61no—
754C2×C3×C4—182no—
755C2×C3×C4—182no—
756C2×C3×C4—181no—
757C2×C3×C4C2×D3211yescharacteristic
758C2×C3×C4C22×C3×D311yescharacteristic
759C2×C3×C4C22×C3×D311yescharacteristic
760#67—21no—
761#67—21no—
762#67—21no—
763#67—62no—
764#67—62no—
765#67—62no—
766#67—62no—
767C2×Dic3—21no—
768C2×Dic3—61no—
769C2×Dic3—61no—
770C2×Dic3—62no—
771C2×Dic3—62no—
772C2×Dic3—121no—
773C2×Dic3C3×#6711yescharacteristic
774D12—21no—
775D12—21no—
776D12C22×C3×D311yescharacteristic
777D12C22×C3×D312yes—
778C4×D3—21no—
779C4×D3—21no—
780C4×D3—21no—
781C4×D3—62no—
782C4×D3—62no—
783C4×D3C3×#6711yescharacteristic
784C4×D3C3×#6711yescharacteristic
785C4×D3C22×C3×D311yescharacteristic
786C4×D3C22×C3×D311yescharacteristic
787Dic6—21no—
788Dic6—32no—
789Dic6—32no—
790Dic6—62no—
791Dic6—61no—
792Dic6—61no—
793Dic6—121no—
794Dic6C22×C3×D311yescharacteristic
795C3×C8—32no—
796C3×C8—32no—
797C3×C8—62no—
798C3×C8—92no—
799C3⋊C8—32no—
800C3⋊C8—32no—
801C3⋊C8—62no—
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—61no—
818C2×C32—61no—
819C2×C32—81no—
820C2×C32—81no—
821C2×C32—81no—
822C2×C32—82no—
823C2×C32—121no—
824C2×C32—122no—
825C2×C32C2×D3×D411yescharacteristic
826C2×C32C22×#6711yescharacteristic
827C2×C32C22×C3×D411yescharacteristic
828C3×D3—22no—
829C3×D3—21no—
830C3×D3—21no—
831C3×D3—21no—
832C3×D3—21no—
833C3×D3—41no—
834C3×D3—42no—
835C3×D3—42no—
836C3×D3—41no—
837C3×D3—42no—
838C3×D3—41no—
839C3×D3—82no—
840#41—31no—
841#41—31no—
842#41—31no—
843#41—61no—
844#41—61no—
845#41—92no—
846#41—92no—
847#41—181no—
848#41—181no—
849#41C3×D3211yescharacteristic
850C2×Q8—31no—
851C2×Q8—91no—
852C2×D4—31no—
853C2×D4—31no—
854C2×D4—61no—
855C2×D4—181no—
856C22×C4—31no—
857C22×C4—61no—
858C22×C4—181no—
859Q16—92no—
860Q16—92no—
861SD16—32no—
862SD16—92no—
863SD16—92no—
864SD16—92no—
865D8—32no—
866D8—92no—
867M16—31no—
868M16—92no—
869M16—91no—
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—31no—
879C22×C3—31no—
880C22×C3—31no—
881C22×C3—31no—
882C22×C3—41no—
883C22×C3—41no—
884C22×C3—42no—
885C22×C3—41no—
886C22×C3—61no—
887C22×C3—61no—
888C22×C3—62no—
889C22×C3—61no—
890C22×C3—62no—
891C22×C3—61no—
892C22×C3—62no—
893C22×C3—122no—
894C22×C3—121no—
895C22×C3—121no—
896C22×C3—122no—
897C22×C3—122no—
898C22×C3—122no—
899C22×C3—124no—
900C22×C3—122no—
901C22×C3—122no—
902C22×C3—242no—
903C22×C3D3×#6711yescharacteristic
904C22×C3C3×D3×D411yescharacteristic
905C22×C3C2×C3×#6711yescharacteristic
906C2×D3—22no—
907C2×D3—21no—
908C2×D3—41no—
909C2×D3—42no—
910C2×D3—42no—
911C2×D3C2×C3×#6711yescharacteristic
912C2×D3C2×C3×#6711yescharacteristic
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—31no—
924C3×C4—31no—
925C3×C4—31no—
926C3×C4—31no—
927C3×C4—41no—
928C3×C4—41no—
929C3×C4—42no—
930C3×C4—41no—
931C3×C4—41no—
932C3×C4—61no—
933C3×C4—61no—
934C3×C4—62no—
935C3×C4—61no—
936C3×C4—61no—
937C3×C4—182no—
938C3×C4D3×#6711yescharacteristic
939C3×C4C3×D3×D411yescharacteristic
940C3×C4C2×C3×#6711yescharacteristic
941C3×C4C22×D3211yescharacteristic
942C3×C4C23×C3×D311yescharacteristic
943C3×C4C23×C3×D311yescharacteristic
944Dic3—21no—
945Dic3—62no—
946Dic3—62no—
947Dic3—122no—
948Dic3C2×C3×#6711yescharacteristic
949Dic3C2×C3×#6711yescharacteristic
950C32—21no—
951C32—21no—
952C32—21no—
953C32—41no—
954C32#577311yescharacteristic, complemented
955C32#582211yescharacteristic, complemented
956C32C3×#57511yescharacteristic, complemented
957C23—31no—
958C23—61no—
959C23—61no—
960Q8—31no—
961Q8—61no—
962Q8—92no—
963Q8—181no—
964Q8C2×C3×D3211yescharacteristic
965D4—21no—
966D4—32no—
967D4—31no—
968D4—61no—
969D4—61no—
970D4—61no—
971D4—61no—
972D4—61no—
973D4—182no—
974D4—182no—
975D4C2×C3×D3211yescharacteristic
976C2×C4—21no—
977C2×C4—31no—
978C2×C4—31no—
979C2×C4—31no—
980C2×C4—31no—
981C2×C4—31no—
982C2×C4—61no—
983C2×C4—61no—
984C2×C4—61no—
985C2×C4—61no—
986C2×C4—182no—
987C2×C4—182no—
988C2×C4—181no—
989C2×C4C2×C3×D3211yescharacteristic
990C8—32no—
991C8—92no—
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—62no—
1007C2×C3—61no—
1008C2×C3—61no—
1009C2×C3—61no—
1010C2×C3—61no—
1011C2×C3—81no—
1012C2×C3—81no—
1013C2×C3—81no—
1014C2×C3—82no—
1015C2×C3—121no—
1016C2×C3—122no—
1017C2×C3—121no—
1018C2×C3—122no—
1019C2×C3—121no—
1020C2×C3—122no—
1021C2×C3—242no—
1022C2×C3C2×D3×#6711yescharacteristic
1023C2×C3C2×C3×D3×D411yescharacteristic
1024C2×C3C22×C3×#6711yescharacteristic
1025D3—21no—
1026D3—21no—
1027D3—42no—
1028D3—41no—
1029C22—21no—
1030C22—31no—
1031C22—31no—
1032C22—61no—
1033C22—62no—
1034C22—121no—
1035C22—122no—
1036C22—122no—
1037C22C3×D3×#6711yescharacteristic
1038C4—21no—
1039C4—31no—
1040C4—31no—
1041C4—61no—
1042C4—182no—
1043C4C3×D3×#6711yescharacteristic
1044C4C22×C3×D3211yescharacteristic
1045C3—21no—
1046C3—21no—
1047C3—21no—
1048C3—41no—
1049C3#1059546911yescharacteristic, direct product factor
1050C3C3×#577311yescharacteristic, complemented
1051C3C3×#582211yescharacteristic, complemented
1052C2—21no—
1053C2—41no—
1054C2—61no—
1055C2—61no—
1056C2—121no—
1057C2—122no—
1058C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC2×C3C2×D3×#67
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. C32×D3×#41C2semidirect
2. C2×C3×#3795C2semidirect
3. C3×#64160C2semidirect
4. C32×#949C2semidirect
5. C3×#63947C2semidirect
6. C3×#63946C2semidirect
7. C3×#63933C2semidirect
8. C3×#63932C2semidirect
9. C3×#63831C2semidirect
10. C3×#63823C2semidirect
11. C3×D3×#208C2semidirect
14. #10595469C3direct (N × H)
16. C2×C3×#634C22semidirect
17. C32×#239C22semidirect
18. C32×D3×Q8C22semidirect
20. C32×#237C22semidirect
22. C32×D3×D4C22semidirect
25. C2×C32×D12C22semidirect
33. C3×#3795C22semidirect
34. C3×#3756C22semidirect
35. C3×#3754C22semidirect
36. C3×#3748C22semidirect
37. C32×#215C22semidirect
38. C32×#213C22semidirect
39. C32×#208C22semidirect
40. C3×#3719C22semidirect
41. C3×#3716C22semidirect
42. C3×#3715C22semidirect
43. C3×#3713C22semidirect
44. C3×#3711C22semidirect
45. C3×D3×C3⋊C8C22semidirect
48. C3×D3×#41D3semidirect
49. C3×D3×#41C2×C3semidirect
52. C2×#3795C2×C3semidirect
54. #64160C2×C3semidirect
63. C3×#949D3semidirect
64. C3×#949C2×C3semidirect
75. #63947C2×C3semidirect
76. #63946C2×C3semidirect
77. #63933C2×C3semidirect
78. #63932C2×C3semidirect
79. #63831C2×C3semidirect
80. #63823C2×C3semidirect
81. D3×#208C2×C3semidirect
138. C2×#634C22×C3semidirect
143. C3×#239C2×D3semidirect
144. C3×#239C22×C3semidirect
146. C3×D3×Q8C2×D3semidirect
147. C3×D3×Q8C22×C3semidirect
156. C3×#237C2×D3semidirect
157. C3×#237C22×C3semidirect
162. C3×D3×D4C2×D3semidirect
163. C3×D3×D4C22×C3semidirect
175. C2×C3×D12C2×D3semidirect
176. C2×C3×D12C22×C3semidirect
192. #3795C22×C3semidirect
196. #3756C22×C3semidirect
197. #3754C22×C3semidirect
198. #3748C22×C3semidirect
205. C3×#215C2×D3semidirect
206. C3×#215C22×C3semidirect
215. C3×#213C2×D3semidirect
216. C3×#213C22×C3semidirect
222. C3×#208C2×D3semidirect
223. C3×#208C22×C3semidirect
229. #3719C22×C3semidirect
230. #3716C22×C3semidirect
231. #3715C22×C3semidirect
232. #3713C22×C3semidirect
233. #3711C22×C3semidirect
234. D3×C3⋊C8C22×C3semidirect
255. D3×#41C3×D3semidirect
276. #949C3×D3semidirect
496. #239C2×C3×D3semidirect
497. D3×Q8C2×C3×D3semidirect
503. #237C2×C3×D3semidirect
505. D3×D4C2×C3×D3semidirect
512. C2×D12C2×C3×D3semidirect
542. #215C2×C3×D3semidirect
550. #213C2×C3×D3semidirect
555. #208C2×C3×D3semidirect
651. C33#575semidirect
954. C32#5773semidirect
955. C32#5822semidirect
956. C32C3×#575semidirect
1049. C3#10595469direct (N × H)
1050. C3C3×#5773semidirect
1051. C3C3×#5822semidirect

Maximal subgroups

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

subgroupindex
C32×D3×#412
C2×C3×#37952
C3×#641602
C32×#9492
C3×#639472
C3×#639462
C3×#639332
C3×#639322
C3×#638312
C3×#638232
C3×D3×#2082
C3×#58223
C3×#57733
#105954693