Finite Group Databasebeta

← C3×#10595470 #13175067

Subgroups — C3×#10595470 #13175067

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×#3799C211yesmaximal, characteristic, complemented
3C3×#64158C211yesmaximal, characteristic, complemented
4C32×#951C211yesmaximal, characteristic, complemented
5C3×#63949C212yesmaximal, complemented
6C3×#63948C212yesmaximal, complemented
7C3×#63935C212yesmaximal, complemented
8C3×#63934C212yesmaximal, complemented
9C3×#63827C211yesmaximal, characteristic, complemented
10C3×#63825C211yesmaximal, characteristic, complemented
11C3×D3×#208C211yesmaximal, characteristic, complemented
12C3×#5822—31nomaximal
13C3×#5777—31nomaximal
14#10595470C311yesmaximal, characteristic, direct product factor
15C33×#41C2211yescharacteristic
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, 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×C4×D3—21no—
26C2×C32×C4×D3C2211yescharacteristic
27C2×C32×Dic6C2211yescharacteristic, complemented
28C2×C3×#626—21no—
29C2×C3×#624—21no—
30C3×#3799—21no—
31C3×#3799—21no—
32C3×#3799C2212yes—
33C3×#3799C2212yescomplemented
34C3×#3755C2212yescomplemented
35C3×#3753C2212yescomplemented
36C3×#3748C2211yescharacteristic, complemented
37C32×#216C2212yescomplemented
38C32×#214C2212yescomplemented
39C32×#208C2211yescharacteristic, complemented
40C3×#3718C2212yescomplemented
41C3×#3717C2212yescomplemented
42C3×#3715C2212yescomplemented
43C3×#3714C2212yescomplemented
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×#239—31no—
51C2×C3×#235—31no—
52C2×#3799C2×C311yescharacteristic, complemented
53C32×#137—31no—
54#64158C2×C311yescharacteristic, complemented
55C3×#951—21no—
56C3×#951—31no—
57C3×#951D311yescharacteristic, complemented
58C3×#951C2×C311yescharacteristic, complemented
59C3×#950—32no—
60C3×#950—32no—
61C3×#949—31no—
62C3×#949—31no—
63C3×#949—31no—
64C3×#949—61no—
65C3×#942—31no—
66C3×#942—32no—
67C3×#932—32no—
68C2×C3×#208—31no—
69C3×#919—32no—
70C3×#918—32no—
71C3×#916—32no—
72C3×#914—32no—
73C3×#908—31no—
74C3×D3×M16—31no—
75#63949C2×C312yescomplemented
76#63948C2×C312yescomplemented
77#63935C2×C312yescomplemented
78#63934C2×C312yescomplemented
79#63827C2×C311yescharacteristic, complemented
80#63825C2×C311yescharacteristic, complemented
81D3×#208C2×C311yescharacteristic, complemented
82C22×C3×C3⋊D3—21no—
83C22×C32×D3—21no—
84C22×C32×D3D411yescharacteristic
85C33×Q8C2311yescharacteristic
86C33×D4—21no—
87C33×D4C2311yescharacteristic
88C2×C33×C4—21no—
89C2×C33×C4C2311yescharacteristic
90C3×C4⋊(C3⋊D3)—21no—
91C3×C4⋊(C3⋊D3)C2312yes—
92C32×#67—21no—
93C32×#67—21no—
94C32×#67—21no—
95C2×C32×Dic3—21no—
96C2×C32×Dic3—21no—
97C2×C32×Dic3D411yescharacteristic
98C32×D12—21no—
99C32×D12C2311yescharacteristic
100C32×C4×D3—21no—
101C32×C4×D3—21no—
102C32×C4×D3—21no—
103C32×C4×D3D411yescharacteristic
104C32×C4×D3D411yescharacteristic
105C32×C4×D3C2311yescharacteristic
106C32×C4×D3C2311yescharacteristic
107C32×Dic6—21no—
108C32×Dic6—21no—
109C32×Dic6C2312yes—
110C32×Dic6C2311yescharacteristic
111C3×#626—22no—
112C3×#626—22no—
113C3×#624—22no—
114C3×#624—22no—
115C3×C3⋊(C3⋊C8)C2312yes—
116C32×C3⋊C8C2312yes—
117C3×#575—91no—
118#5822—31no—
119#5777—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×Q8—31no—
134C2×C32×D4—31no—
135C2×C32×D4—61no—
136C22×C32×C4—31no—
137C22×C32×C4—61no—
138C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
139C2×C3×#67—61no—
140C3×#239—21no—
141C3×#239—32no—
142C3×#239—32no—
143C3×#239—61no—
144C3×#239—61no—
145C3×#239C2×D311yescharacteristic, complemented
146C3×#239C22×C311yescharacteristic, complemented
147C3×D3×Q8—21no—
148C3×D3×Q8C2×D311yescharacteristic, complemented
149C3×D3×Q8C22×C311yescharacteristic, complemented
150C3×#237—22no—
151C3×#237—21no—
152C3×#237—21no—
153C3×#237—21no—
154C3×#237C2×D311yescharacteristic, complemented
155C3×#237C22×C311yescharacteristic, complemented
156C3×D3×D4—22no—
157C3×D3×D4—21no—
158C3×D3×D4—21no—
159C3×D3×D4—21no—
160C3×D3×D4C2×D311yescharacteristic, complemented
161C3×D3×D4C22×C311yescharacteristic, complemented
162C3×#235—22no—
163C3×#235—21no—
164C3×#235—21no—
165C3×#235—21no—
166C3×#235—32no—
167C3×#235—32no—
168C3×#235—61no—
169C3×#235—61no—
170C3×#235C2×D311yescharacteristic
171C3×#235C22×C311yescharacteristic
172C2×C3×D12—31no—
173C2×C3×D12—31no—
174C2×C3×D12—61no—
175C2×C3×D12—61no—
176C2×C3×C4×D3—22no—
177C2×C3×C4×D3—21no—
178C2×C3×C4×D3—21no—
179C2×C3×C4×D3—21no—
180C2×C3×C4×D3—61no—
181C2×C3×C4×D3—61no—
182C2×C3×C4×D3C2×D311yescharacteristic
183C2×C3×C4×D3C22×C311yescharacteristic
184C2×C3×Dic6—21no—
185C2×C3×Dic6C2×D311yescharacteristic, complemented
186C2×C3×Dic6C22×C311yescharacteristic, complemented
187C2×#626—21no—
188C2×#624—21no—
189#3799—21no—
190#3799—21no—
191#3799C22×C312yes—
192#3799C22×C312yescomplemented
193C32×Q16—32no—
194C32×SD16—32no—
195C32×M16—31no—
196#3755C22×C312yescomplemented
197#3753C22×C312yescomplemented
198#3748C22×C311yescharacteristic, complemented
199C3×#216—22no—
200C3×#216—32no—
201C3×#216—32no—
202C3×#216C2×D312yescomplemented
203C3×#216C22×C312yescomplemented
204C3×#215—32no—
205C3×#215—32no—
206C3×#215—32no—
207C3×#215—32no—
208C3×#215—62no—
209C3×#214—22no—
210C3×#214—32no—
211C3×#214C2×D312yescomplemented
212C3×#214C22×C312yescomplemented
213C3×#213—32no—
214C3×#213—32no—
215C3×#213—32no—
216C3×#213—62no—
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×D24—32no—
226C3×#204—32no—
227C3×ΓL(1,𝔽25)—32no—
228C3×D3×C8—32no—
229#3718C22×C312yescomplemented
230#3717C22×C312yescomplemented
231#3715C22×C312yescomplemented
232#3714C22×C312yescomplemented
233#3711C22×C312yescomplemented
234D3×C3⋊C8C22×C312yescomplemented
235C22×C33—21no—
236C22×C33C2×D411yescharacteristic
237C2×C3×C3⋊D3—22no—
238C2×C3×C3⋊D3—42no—
239C2×C32×D3—21no—
240C2×C32×D3—41no—
241C2×C32×D3—42no—
242C2×C32×D3C2×D411yescharacteristic
243C2×C32×D3C2×D411yescharacteristic
244C33×C4—21no—
245C33×C4C2×D411yescharacteristic
246C33×C4C2411yescharacteristic
247C32×Dic3—21no—
248C32×Dic3—22no—
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×#239—31no—
257C2×#235—31no—
258C3×#137—31no—
259C3×#137—31no—
260C3×#137—61no—
261C3×#137—92no—
262C3×#137—91no—
263C3×AGL(1,ℤ/8)—91no—
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#951C3×D311yescharacteristic, complemented
271#950—32no—
272#950—32no—
273#949—31no—
274#949—31no—
275#949—31no—
276#949—61no—
277#942—31no—
278#942—32no—
279#932—32no—
280C2×#208—31no—
281#919—32no—
282#918—32no—
283#916—32no—
284#914—32no—
285#908—31no—
286D3×M16—31no—
287C23×C32—31no—
288C23×C32—61no—
289C22×C3⋊D3—21no—
290C22×C3×D3—22no—
291C22×C3×D3—21no—
292C22×C3×D3—21no—
293C22×C3×D3—21no—
294C22×C3×D3—61no—
295C22×C3×D3—61no—
296C22×C3×D3—121no—
297C22×C3×D3#6711yescharacteristic
298C22×C3×D3C3×D411yescharacteristic
299C32×Q8—21no—
300C32×Q8—21no—
301C32×Q8—21no—
302C32×Q8—31no—
303C32×Q8—32no—
304C32×Q8—41no—
305C32×Q8—61no—
306C32×Q8—61no—
307C32×Q8C22×D311yescharacteristic
308C32×Q8C22×D311yescharacteristic
309C32×Q8C23×C311yescharacteristic
310C32×D4—21no—
311C32×D4—22no—
312C32×D4—21no—
313C32×D4—21no—
314C32×D4—21no—
315C32×D4—21no—
316C32×D4—21no—
317C32×D4—31no—
318C32×D4—41no—
319C32×D4—41no—
320C32×D4—41no—
321C32×D4—42no—
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×C4—61no—
350C2×C32×C4C22×D311yescharacteristic
351C2×C32×C4C22×D311yescharacteristic
352C2×C32×C4C23×C311yescharacteristic
353C4⋊(C3⋊D3)—21no—
354C4⋊(C3⋊D3)C23×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—
366C2×C3×Dic3—22no—
367C2×C3×Dic3—21no—
368C2×C3×Dic3—21no—
369C2×C3×Dic3—21no—
370C2×C3×Dic3—21no—
371C2×C3×Dic3—21no—
372C2×C3×Dic3—41no—
373C2×C3×Dic3#6711yescharacteristic
374C2×C3×Dic3C3×D411yescharacteristic
375C3×D12—22no—
376C3×D12—21no—
377C3×D12—21no—
378C3×D12—21no—
379C3×D12—32no—
380C3×D12—32no—
381C3×D12—62no—
382C3×D12—62no—
383C3×D12—62no—
384C3×D12—61no—
385C3×D12—61no—
386C3×D12—121no—
387C3×D12C22×D311yescharacteristic
388C3×D12C23×C311yescharacteristic
389C3×C4×D3—22no—
390C3×C4×D3—22no—
391C3×C4×D3—22no—
392C3×C4×D3—21no—
393C3×C4×D3—21no—
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—62no—
403C3×C4×D3—62no—
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—21no—
419C3×Dic6—21no—
420C3×Dic6—22no—
421C3×Dic6—41no—
422C3×Dic6C22×D311yescharacteristic
423C3×Dic6C22×D312yes—
424C3×Dic6C23×C312yes—
425C3×Dic6C23×C311yescharacteristic
426#626—22no—
427#626—22no—
428#624—22no—
429#624—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
442C3×C3⋊D3—42no—
443C32×D3—21no—
444C32×D3—21no—
445C32×D3—41no—
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—31no—
475C2×C3×Q8—31no—
476C2×C3×Q8—61no—
477C2×C3×Q8—61no—
478C2×C3×D4—31no—
479C2×C3×D4—31no—
480C2×C3×D4—61no—
481C2×C3×D4—61no—
482C2×C3×D4—61no—
483C2×C3×D4—62no—
484C2×C3×D4—91no—
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—
494#239—32no—
495#239—32no—
496#239—61no—
497#239—61no—
498#239C2×C3×D311yescharacteristic, complemented
499D3×Q8C2×C3×D311yescharacteristic, complemented
500#237—21no—
501#237C2×C3×D311yescharacteristic, complemented
502D3×D4—21no—
503D3×D4C2×C3×D311yescharacteristic, complemented
504#235—21no—
505#235—32no—
506#235—32no—
507#235—61no—
508#235—61no—
509#235C2×C3×D311yescharacteristic
510C2×D12—31no—
511C2×D12—31no—
512C2×D12—61no—
513C2×D12—61no—
514C2×C4×D3—21no—
515C2×C4×D3—61no—
516C2×C4×D3—61no—
517C2×C4×D3C2×C3×D311yescharacteristic
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—62no—
526C3×SD16—92no—
527C3×SD16—92no—
528C3×SD16—92no—
529C3×D8—92no—
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#216C2×C3×D312yescomplemented
540#215—32no—
541#215—32no—
542#215—32no—
543#215—32no—
544#215—62no—
545#214—32no—
546#214C2×C3×D312yescomplemented
547#213—32no—
548#213—32no—
549#213—32no—
550#213—62no—
551#208—31no—
552#208—31no—
553#208—32no—
554#208—61no—
555#208C2×C3×D311yescharacteristic, complemented
556C2×C3⋊C8—32no—
557D24—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—121no—
576C22×C32—122no—
577C22×C32D3×D411yescharacteristic
578C22×C32C2×#6711yescharacteristic
579C22×C32C2×C3×D411yescharacteristic
580C2×C3⋊D3—22no—
581C2×C3⋊D3—42no—
582C2×C3×D3—22no—
583C2×C3×D3—21no—
584C2×C3×D3—21no—
585C2×C3×D3—21no—
586C2×C3×D3—21no—
587C2×C3×D3—41no—
588C2×C3×D3—41no—
589C2×C3×D3—42no—
590C2×C3×D3—44no—
591C2×C3×D3—42no—
592C2×C3×D3—42no—
593C2×C3×D3—62no—
594C2×C3×D3—62no—
595C2×C3×D3—122no—
596C2×C3×D3—122no—
597C2×C3×D3—122no—
598C2×C3×D3—242no—
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×C4—62no—
622C32×C4D3×D411yescharacteristic
623C32×C4C2×#6711yescharacteristic
624C32×C4C2×C3×D411yescharacteristic
625C32×C4C23×D311yescharacteristic
626C32×C4C23×D311yescharacteristic
627C32×C4C24×C311yescharacteristic
628C3×Dic3—22no—
629C3×Dic3—22no—
630C3×Dic3—21no—
631C3×Dic3—22no—
632C3×Dic3—21no—
633C3×Dic3—21no—
634C3×Dic3—21no—
635C3×Dic3—42no—
636C3×Dic3C2×#6711yescharacteristic
637C3×Dic3C2×#6711yescharacteristic
638C3×Dic3C2×C3×D411yescharacteristic
639C3×Dic3C2×C3×D411yescharacteristic
640C2×#41—31no—
641C2×#41—91no—
642#137—31no—
643#137—92no—
644#137—91no—
645AGL(1,ℤ/8)—91no—
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—181no—
659C22×D3—21no—
660C22×D3—61no—
661C22×D3—61no—
662C22×D3—121no—
663C22×D3C3×#6711yescharacteristic
664C3×Q8—21no—
665C3×Q8—21no—
666C3×Q8—21no—
667C3×Q8—32no—
668C3×Q8—31no—
669C3×Q8—31no—
670C3×Q8—32no—
671C3×Q8—41no—
672C3×Q8—61no—
673C3×Q8—62no—
674C3×Q8—61no—
675C3×Q8—61no—
676C3×Q8—62no—
677C3×Q8—61no—
678C3×Q8—61no—
679C3×Q8—121no—
680C3×Q8C2×D3211yescharacteristic
681C3×Q8C22×C3×D311yescharacteristic
682C3×Q8C22×C3×D311yescharacteristic
683C3×D4—22no—
684C3×D4—21no—
685C3×D4—21no—
686C3×D4—21no—
687C3×D4—21no—
688C3×D4—21no—
689C3×D4—21no—
690C3×D4—31no—
691C3×D4—31no—
692C3×D4—41no—
693C3×D4—41no—
694C3×D4—42no—
695C3×D4—41no—
696C3×D4—61no—
697C3×D4—61no—
698C3×D4—61no—
699C3×D4—62no—
700C3×D4—61no—
701C3×D4—61no—
702C3×D4—61no—
703C3×D4—61no—
704C3×D4—62no—
705C3×D4—62no—
706C3×D4—62no—
707C3×D4—61no—
708C3×D4—61no—
709C3×D4—92no—
710C3×D4—182no—
711C3×D4—182no—
712C3×D4—181no—
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—61no—
755C2×C3×C4—61no—
756C2×C3×C4—121no—
757C2×C3×C4—182no—
758C2×C3×C4—182no—
759C2×C3×C4C2×D3211yescharacteristic
760C2×C3×C4C22×C3×D311yescharacteristic
761C2×C3×C4C22×C3×D311yescharacteristic
762#67—21no—
763#67—21no—
764#67—21no—
765#67—62no—
766#67—62no—
767C2×Dic3—21no—
768C2×Dic3—21no—
769C2×Dic3C3×#6711yescharacteristic
770D12—21no—
771D12—32no—
772D12—32no—
773D12—62no—
774D12—62no—
775D12—62no—
776D12—61no—
777D12—61no—
778D12—121no—
779D12C22×C3×D311yescharacteristic
780C4×D3—21no—
781C4×D3—21no—
782C4×D3—21no—
783C4×D3—62no—
784C4×D3—62no—
785C4×D3—62no—
786C4×D3—62no—
787C4×D3C3×#6711yescharacteristic
788C4×D3C3×#6711yescharacteristic
789C4×D3C22×C3×D311yescharacteristic
790C4×D3C22×C3×D311yescharacteristic
791Dic6—21no—
792Dic6—21no—
793Dic6C22×C3×D311yescharacteristic
794Dic6C22×C3×D312yes—
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×C32C2×D3×D411yescharacteristic
825C2×C32C22×#6711yescharacteristic
826C2×C32C22×C3×D411yescharacteristic
827C3⋊D3—42no—
828C3×D3—22no—
829C3×D3—21no—
830C3×D3—21no—
831C3×D3—21no—
832C3×D3—21no—
833C3×D3—41no—
834C3×D3—42no—
835C3×D3—41no—
836C3×D3—41no—
837C3×D3—122no—
838C3×D3—122no—
839C3×D3—242no—
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—31no—
852C2×D4—31no—
853C2×D4—61no—
854C2×D4—91no—
855C2×D4—181no—
856C22×C4—31no—
857C22×C4—61no—
858C22×C4—181no—
859Q16—32no—
860Q16—92no—
861SD16—32no—
862SD16—92no—
863SD16—92no—
864SD16—92no—
865D8—92no—
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—61no—
891C22×C3—121no—
892C22×C3—121no—
893C22×C3—122no—
894C22×C3—124no—
895C22×C3—122no—
896C22×C3—122no—
897C22×C3—182no—
898C22×C3—362no—
899C22×C3D3×#6711yescharacteristic
900C22×C3C3×D3×D411yescharacteristic
901C22×C3C2×C3×#6711yescharacteristic
902C2×D3—21no—
903C2×D3—41no—
904C2×D3—42no—
905C2×D3—62no—
906C2×D3—62no—
907C2×D3—122no—
908C2×D3—122no—
909C2×D3—122no—
910C2×D3—242no—
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—62no—
937C3×C4—61no—
938C3×C4—62no—
939C3×C4—122no—
940C3×C4D3×#6711yescharacteristic
941C3×C4C3×D3×D411yescharacteristic
942C3×C4C2×C3×#6711yescharacteristic
943C3×C4C22×D3211yescharacteristic
944C3×C4C23×C3×D311yescharacteristic
945C3×C4C23×C3×D311yescharacteristic
946Dic3—22no—
947Dic3—21no—
948Dic3C2×C3×#6711yescharacteristic
949Dic3C2×C3×#6711yescharacteristic
950C32—21no—
951C32—21no—
952C32—21no—
953C32—41no—
954C32#577711yescharacteristic, complemented
955C32#582211yescharacteristic, complemented
956C32C3×#57511yescharacteristic, complemented
957C23—31no—
958C23—61no—
959C23—181no—
960Q8—32no—
961Q8—31no—
962Q8—61no—
963Q8—61no—
964Q8C2×C3×D3211yescharacteristic
965D4—21no—
966D4—31no—
967D4—61no—
968D4—61no—
969D4—61no—
970D4—61no—
971D4—92no—
972D4—182no—
973D4—182no—
974D4—181no—
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—61no—
987C2×C4—182no—
988C2×C4—182no—
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—121no—
1019C2×C3—362no—
1020C2×C3C2×D3×#6711yescharacteristic
1021C2×C3C2×C3×D3×D411yescharacteristic
1022C2×C3C22×C3×#6711yescharacteristic
1023D3—21no—
1024D3—21no—
1025D3—41no—
1026D3—122no—
1027D3—122no—
1028D3—242no—
1029C22—21no—
1030C22—31no—
1031C22—31no—
1032C22—61no—
1033C22—121no—
1034C22—122no—
1035C22—182no—
1036C22—362no—
1037C22C3×D3×#6711yescharacteristic
1038C4—21no—
1039C4—31no—
1040C4—31no—
1041C4—61no—
1042C4—62no—
1043C4C3×D3×#6711yescharacteristic
1044C4C22×C3×D3211yescharacteristic
1045C3—21no—
1046C3—21no—
1047C3—21no—
1048C3—41no—
1049C3#1059547011yescharacteristic, direct product factor
1050C3C3×#577711yescharacteristic, complemented
1051C3C3×#582211yescharacteristic, complemented
1052C2—21no—
1053C2—41no—
1054C2—61no—
1055C2—61no—
1056C2—121no—
1057C2—362no—
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×#3799C2semidirect
3. C3×#64158C2semidirect
4. C32×#951C2semidirect
5. C3×#63949C2semidirect
6. C3×#63948C2semidirect
7. C3×#63935C2semidirect
8. C3×#63934C2semidirect
9. C3×#63827C2semidirect
10. C3×#63825C2semidirect
11. C3×D3×#208C2semidirect
14. #10595470C3direct (N × H)
16. C2×C3×C4⋊(C3⋊D3)C22semidirect
17. C32×#239C22semidirect
18. C32×D3×Q8C22semidirect
20. C32×#237C22semidirect
22. C32×D3×D4C22semidirect
27. C2×C32×Dic6C22semidirect
33. C3×#3799C22semidirect
34. C3×#3755C22semidirect
35. C3×#3753C22semidirect
36. C3×#3748C22semidirect
37. C32×#216C22semidirect
38. C32×#214C22semidirect
39. C32×#208C22semidirect
40. C3×#3718C22semidirect
41. C3×#3717C22semidirect
42. C3×#3715C22semidirect
43. C3×#3714C22semidirect
44. C3×#3711C22semidirect
45. C3×D3×C3⋊C8C22semidirect
48. C3×D3×#41D3semidirect
49. C3×D3×#41C2×C3semidirect
52. C2×#3799C2×C3semidirect
54. #64158C2×C3semidirect
57. C3×#951D3semidirect
58. C3×#951C2×C3semidirect
75. #63949C2×C3semidirect
76. #63948C2×C3semidirect
77. #63935C2×C3semidirect
78. #63934C2×C3semidirect
79. #63827C2×C3semidirect
80. #63825C2×C3semidirect
81. D3×#208C2×C3semidirect
138. C2×C4⋊(C3⋊D3)C22×C3semidirect
145. C3×#239C2×D3semidirect
146. C3×#239C22×C3semidirect
148. C3×D3×Q8C2×D3semidirect
149. C3×D3×Q8C22×C3semidirect
154. C3×#237C2×D3semidirect
155. C3×#237C22×C3semidirect
160. C3×D3×D4C2×D3semidirect
161. C3×D3×D4C22×C3semidirect
185. C2×C3×Dic6C2×D3semidirect
186. C2×C3×Dic6C22×C3semidirect
192. #3799C22×C3semidirect
196. #3755C22×C3semidirect
197. #3753C22×C3semidirect
198. #3748C22×C3semidirect
202. C3×#216C2×D3semidirect
203. C3×#216C22×C3semidirect
211. C3×#214C2×D3semidirect
212. C3×#214C22×C3semidirect
222. C3×#208C2×D3semidirect
223. C3×#208C22×C3semidirect
229. #3718C22×C3semidirect
230. #3717C22×C3semidirect
231. #3715C22×C3semidirect
232. #3714C22×C3semidirect
233. #3711C22×C3semidirect
234. D3×C3⋊C8C22×C3semidirect
255. D3×#41C3×D3semidirect
270. #951C3×D3semidirect
498. #239C2×C3×D3semidirect
499. D3×Q8C2×C3×D3semidirect
501. #237C2×C3×D3semidirect
503. D3×D4C2×C3×D3semidirect
518. C2×Dic6C2×C3×D3semidirect
539. #216C2×C3×D3semidirect
546. #214C2×C3×D3semidirect
555. #208C2×C3×D3semidirect
651. C33#575semidirect
954. C32#5777semidirect
955. C32#5822semidirect
956. C32C3×#575semidirect
1049. C3#10595470direct (N × H)
1050. C3C3×#5777semidirect
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×#37992
C3×#641582
C32×#9512
C3×#639492
C3×#639482
C3×#639352
C3×#639342
C3×#638272
C3×#638252
C3×D3×#2082
C3×#58223
C3×#57773
#105954703