Finite Group Databasebeta

← C3×#10595235 #13174799

Subgroups — C3×#10595235 #13174799

Order 1728.

1810 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×D3×D4C211yesmaximal, characteristic, complemented
2C2×C3×#3799C211yesmaximal, characteristic, complemented
3C3×#64149C211yesmaximal, characteristic, complemented
4C32×#936C211yesmaximal, characteristic, complemented
5C3×#63977C214yesmaximal, complemented
6C3×#63958C214yesmaximal, complemented
7C3×#63911C211yesmaximal, characteristic, complemented
8C3×#63863C211yesmaximal, characteristic, complemented
9C3×#63855C211yesmaximal, characteristic, complemented
10C3×#5805—31nomaximal
11C3×#5674—31nomaximal
12#10595235C311yesmaximal, characteristic, direct product factor
13C23×C32×D3C2212yes—
14C2×C33×D4C2211yescharacteristic
15C2×C3×#638C2214yescomplemented
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
17C2×C32×#67C2212yes—
18C32×D3×D4—24no—
19C2×C32×D12C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×C32×Dic6C2211yescharacteristic, complemented
22C2×C3×#626C2212yes—
23C2×C3×#626C2214yescomplemented
24C2×C3×#624C2212yescomplemented
25C3×#3799—24no—
26C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
27C32×#217C2214yescomplemented
28C32×C4×Dic3C2211yescharacteristic, complemented
29C3×Dic3⋊Dic3C2212yescomplemented
30C3×(C2×D3)⋊Dic3C2212yes—
31C3×(C2×D3)⋊Dic3C2214yescomplemented
32C22×C32×D4—31no—
33C2×C3×#239—31no—
34C2×C3×D3×D4—21no—
35C2×C3×D3×D4D311yescharacteristic, complemented
36C2×C3×D3×D4C2×C311yescharacteristic, complemented
37C2×C3×#235—31no—
38C2×#3799C2×C311yescharacteristic, complemented
39C32×#124—31no—
40#64149C2×C311yescharacteristic, complemented
41C3×#953—34no—
42C3×#947—31no—
43C3×#940—31no—
44C3×#940—31no—
45C3×#940—31no—
46C3×#940—61no—
47C3×#938—34no—
48C3×#936—21no—
49C3×#936—31no—
50C3×#936D311yescharacteristic, complemented
51C3×#936C2×C311yescharacteristic, complemented
52C3×#926—31no—
53C3×#884—34no—
54C3×#882—34no—
55C3×#874—31no—
56C3×#872—31no—
57#63977C2×C314yescomplemented
58#63958C2×C314yescomplemented
59#63911C2×C311yescharacteristic, complemented
60#63863C2×C311yescharacteristic, complemented
61#63855C2×C311yescharacteristic, complemented
62C23×C33C2312yes—
63C22×C3×C3⋊D3C2312yes—
64C22×C32×D3—24no—
65C22×C32×D3—44no—
66C22×C32×D3C2312yes—
67C22×C32×D3C2311yescharacteristic
68C33×D4—22no—
69C2×C33×C4C2311yescharacteristic
70C3×#638—44no—
71C2×C3×C3⋊Dic3C2312yes—
72C3×C4⋊(C3⋊D3)—22no—
73C32×#67—24no—
74C2×C32×Dic3C2312yes—
75C2×C32×Dic3C2312yes—
76C2×C32×Dic3C2311yescharacteristic
77C32×D12—22no—
78C32×C4×D3D414yescomplemented
79C32×Dic6—22no—
80C3×#626—24no—
81C3×#626—44no—
82C3×#624—24no—
83C3×#535—91no—
84#5805—31no—
85#5674—31no—
86C24×C32—32no—
87C23×C3×D3—22no—
88C23×C3×D3C2×D312yes—
89C23×C3×D3C22×C312yes—
90C2×C32×Q8—31no—
91C2×C32×D4—21no—
92C2×C32×D4—21no—
93C2×C32×D4—21no—
94C2×C32×D4—32no—
95C2×C32×D4—31no—
96C2×C32×D4—41no—
97C2×C32×D4—64no—
98C2×C32×D4C2×D311yescharacteristic
99C2×C32×D4C2×D311yescharacteristic
100C2×C32×D4C22×C311yescharacteristic
101C22×C32×C4—31no—
102C2×#638C22×C314yescomplemented
103C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
104C2×C3×#67—22no—
105C2×C3×#67—34no—
106C2×C3×#67—34no—
107C2×C3×#67—32no—
108C2×C3×#67—34no—
109C2×C3×#67—64no—
110C2×C3×#67C2×D312yes—
111C2×C3×#67C22×C312yes—
112C3×#239—64no—
113C3×D3×D4—28no—
114C3×D3×D4—24no—
115C3×D3×D4—24no—
116C3×#235—64no—
117C2×C3×D12—21no—
118C2×C3×D12—32no—
119C2×C3×D12—31no—
120C2×C3×D12—31no—
121C2×C3×D12—34no—
122C2×C3×D12—61no—
123C2×C3×D12C2×D311yescharacteristic
124C2×C3×D12C22×C311yescharacteristic
125C2×C3×C4×D3—21no—
126C2×C3×C4×D3—32no—
127C2×C3×C4×D3—32no—
128C2×C3×C4×D3C2×D311yescharacteristic
129C2×C3×C4×D3C22×C311yescharacteristic
130C2×C3×Dic6—21no—
131C2×C3×Dic6C2×D311yescharacteristic, complemented
132C2×C3×Dic6C22×C311yescharacteristic, complemented
133C2×#626C22×C312yes—
134C2×#626C22×C314yescomplemented
135C2×#624C22×C312yescomplemented
136#3799—24no—
137C32×C22⋊C4—34no—
138C32×C42—31no—
139C4×C3⋊Dic3C22×C311yescharacteristic, complemented
140C3×#217—24no—
141C3×#217—32no—
142C3×#217—34no—
143C3×#217C2×D314yescomplemented
144C3×#217C22×C314yescomplemented
145C3×(C2×D3)⋊C4—32no—
146C3×(C2×D3)⋊C4—34no—
147C3×C4⋊Dic3—32no—
148C3×Dic3⋊C4—32no—
149C3×C4×Dic3—21no—
150C3×C4×Dic3—31no—
151C3×C4×Dic3—31no—
152C3×C4×Dic3—61no—
153C3×C4×Dic3C2×D311yescharacteristic, complemented
154C3×C4×Dic3C22×C311yescharacteristic, complemented
155Dic3⋊Dic3C22×C312yescomplemented
156(C2×D3)⋊Dic3C22×C312yes—
157(C2×D3)⋊Dic3C22×C314yescomplemented
158C22×C33—22no—
159C22×C33—24no—
160C22×C33C2411yescharacteristic
161C2×C3×C3⋊D3—22no—
162C2×C3×C3⋊D3—24no—
163C2×C32×D3—22no—
164C2×C32×D3—22no—
165C2×C32×D3—24no—
166C2×C32×D3—48no—
167C2×C32×D3C2×D412yes—
168C33×C4C2×D412yes—
169C3×C3⋊Dic3—22no—
170C32×Dic3—22no—
171C32×Dic3—22no—
172C32×Dic3C2×D412yes—
173C2×C3×#41—91no—
174C22×C3×D4—31no—
175C22×C3×D4—31no—
176C22×C3×D4—61no—
177C2×#239—31no—
178C2×D3×D4C3×D311yescharacteristic, complemented
179C2×#235—31no—
180C3×#127—91no—
181C3×#127—91no—
182C3×#124—31no—
183C3×#124—31no—
184C3×#124—61no—
185C3×#124—91no—
186C3×#121—94no—
187C3×#120—94no—
188C3×#117—91no—
189#953—34no—
190#947—31no—
191#940—31no—
192#940—31no—
193#940—31no—
194#940—61no—
195#938—34no—
196#936—31no—
197#936C3×D311yescharacteristic, complemented
198#926—31no—
199#884—34no—
200#882—34no—
201#874—31no—
202#872—31no—
203C23×C32—22no—
204C23×C32—22no—
205C23×C32—22no—
206C23×C32—31no—
207C23×C32—32no—
208C23×C32—42no—
209C23×C32—64no—
210C23×C32—124no—
211C23×C32C22×D312yes—
212C23×C32C22×D312yes—
213C23×C32C23×C312yes—
214C22×C3⋊D3C23×C312yes—
215C22×C3×D3—28no—
216C22×C3×D3—24no—
217C22×C3×D3—24no—
218C22×C3×D3—21no—
219C22×C3×D3—22no—
220C22×C3×D3—32no—
221C22×C3×D3—32no—
222C22×C3×D3—44no—
223C22×C3×D3—44no—
224C22×C3×D3—48no—
225C22×C3×D3—62no—
226C22×C3×D3C22×D312yes—
227C22×C3×D3C22×D311yescharacteristic
228C22×C3×D3C23×C312yes—
229C22×C3×D3C23×C311yescharacteristic
230C32×Q8—62no—
231C32×D4—22no—
232C32×D4—24no—
233C32×D4—22no—
234C32×D4—22no—
235C32×D4—42no—
236C32×D4—42no—
237C32×D4—44no—
238C32×D4—64no—
239C32×D4—62no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—31no—
244C2×C32×C4—34no—
245C2×C32×C4—32no—
246C2×C32×C4—32no—
247C2×C32×C4—41no—
248C2×C32×C4C22×D311yescharacteristic
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C23×C311yescharacteristic
251#638—44no—
252C2×C3⋊Dic3C23×C312yes—
253C4⋊(C3⋊D3)—22no—
254C3×#67—28no—
255C3×#67—24no—
256C3×#67—24no—
257C3×#67—64no—
258C3×#67—124no—
259C3×#67—124no—
260C3×#67—124no—
261C3×#67—128no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—22no—
264C2×C3×Dic3—22no—
265C2×C3×Dic3—32no—
266C2×C3×Dic3—32no—
267C2×C3×Dic3—62no—
268C2×C3×Dic3C22×D312yes—
269C2×C3×Dic3C22×D312yes—
270C2×C3×Dic3C22×D311yescharacteristic
271C2×C3×Dic3C23×C312yes—
272C2×C3×Dic3C23×C312yes—
273C2×C3×Dic3C23×C311yescharacteristic
274C3×D12—24no—
275C3×D12—22no—
276C3×D12—22no—
277C3×D12—64no—
278C3×D12—62no—
279C3×D12—62no—
280C3×D12—122no—
281C3×D12—124no—
282C3×C4×D3—24no—
283C3×C4×D3—64no—
284C3×C4×D3—64no—
285C3×C4×D3#6714yescomplemented
286C3×C4×D3C3×D414yescomplemented
287C3×Dic6—22no—
288C3×Dic6—22no—
289C3×Dic6—42no—
290#626—24no—
291#626—44no—
292#624—24no—
293#535—91noSylow
294C2×C33—42no—
295C2×C33C22×D411yescharacteristic
296C2×C33H(5,𝔽2)12yes—
297C3×C3⋊D3—42no—
298C32×D3—22no—
299C32×D3—42no—
300C24×C3—32no—
301C24×C3—32no—
302C24×C3—62no—
303C23×D3C2×C3×D312yes—
304C3×#41—184no—
305C2×C3×Q8—31no—
306C2×C3×Q8—31no—
307C2×C3×Q8—61no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—32no—
312C2×C3×D4—32no—
313C2×C3×D4—31no—
314C2×C3×D4—31no—
315C2×C3×D4—41no—
316C2×C3×D4—61no—
317C2×C3×D4—62no—
318C2×C3×D4—64no—
319C2×C3×D4—64no—
320C2×C3×D4—68no—
321C2×C3×D4—92no—
322C2×C3×D4—94no—
323C2×C3×D4—94no—
324C2×C3×D4—91no—
325C2×C3×D4D3211yescharacteristic
326C2×C3×D4C2×C3×D311yescharacteristic
327C2×C3×D4C2×C3×D311yescharacteristic
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—61no—
331C22×C3×C4—92no—
332C2×#67—34no—
333C2×#67—34no—
334C2×#67—32no—
335C2×#67—34no—
336C2×#67—64no—
337C2×#67C2×C3×D312yes—
338#239—64no—
339D3×D4—24no—
340#235—64no—
341C2×D12—32no—
342C2×D12—31no—
343C2×D12—31no—
344C2×D12—34no—
345C2×D12—61no—
346C2×D12C2×C3×D311yescharacteristic
347C2×C4×D3—32no—
348C2×C4×D3—32no—
349C2×C4×D3C2×C3×D311yescharacteristic
350C2×Dic6C2×C3×D311yescharacteristic, complemented
351C3×C4⋊C4—92no—
352C3×C22⋊C4—34no—
353C3×C22⋊C4—34no—
354C3×C22⋊C4—64no—
355C3×C22⋊C4—92no—
356C3×C22⋊C4—94no—
357C3×C42—31no—
358C3×C42—31no—
359C3×C42—61no—
360C3×C42—91no—
361#217—32no—
362#217—34no—
363#217C2×C3×D314yescomplemented
364(C2×D3)⋊C4—32no—
365(C2×D3)⋊C4—34no—
366C4⋊Dic3—32no—
367Dic3⋊C4—32no—
368C4×Dic3—31no—
369C4×Dic3—31no—
370C4×Dic3—61no—
371C4×Dic3C2×C3×D311yescharacteristic, complemented
372C22×C32—22no—
373C22×C32—24no—
374C22×C32—24no—
375C22×C32—24no—
376C22×C32—22no—
377C22×C32—22no—
378C22×C32—24no—
379C22×C32—21no—
380C22×C32—21no—
381C22×C32—21no—
382C22×C32—32no—
383C22×C32—41no—
384C22×C32—42no—
385C22×C32—42no—
386C22×C32—44no—
387C22×C32—44no—
388C22×C32—44no—
389C22×C32—44no—
390C22×C32—62no—
391C22×C32—62no—
392C22×C32—64no—
393C22×C32—84no—
394C22×C32—128no—
395C22×C32C23×D311yescharacteristic
396C22×C32C23×D311yescharacteristic
397C22×C32C24×C311yescharacteristic
398C2×C3⋊D3—22no—
399C2×C3⋊D3—24no—
400C2×C3×D3—24no—
401C2×C3×D3—22no—
402C2×C3×D3—22no—
403C2×C3×D3—24no—
404C2×C3×D3—24no—
405C2×C3×D3—22no—
406C2×C3×D3—22no—
407C2×C3×D3—24no—
408C2×C3×D3—22no—
409C2×C3×D3—44no—
410C2×C3×D3—416no—
411C2×C3×D3—48no—
412C2×C3×D3—48no—
413C2×C3×D3—62no—
414C2×C3×D3—64no—
415C2×C3×D3—64no—
416C2×C3×D3—62no—
417C2×C3×D3—122no—
418C2×C3×D3—124no—
419C2×C3×D3C2×#6712yes—
420C2×C3×D3C2×C3×D412yes—
421C32×C4—22no—
422C32×C4—22no—
423C32×C4—22no—
424C32×C4—32no—
425C32×C4—42no—
426C32×C4—62no—
427C32×C4—62no—
428C32×C4D3×D412yes—
429C32×C4C2×#6712yes—
430C32×C4C2×C3×D412yes—
431C3⋊Dic3—22no—
432C3×Dic3—22no—
433C3×Dic3—22no—
434C3×Dic3—22no—
435C3×Dic3—22no—
436C3×Dic3—22no—
437C3×Dic3—42no—
438C3×Dic3—42no—
439C3×Dic3—64no—
440C3×Dic3—62no—
441C3×Dic3—62no—
442C3×Dic3C2×#6712yes—
443C3×Dic3C2×C3×D412yes—
444C2×#41—91no—
445C22×D4—31no—
446#127—91no—
447#127—91no—
448#124—31no—
449#124—91no—
450#121—94no—
451#120—94no—
452#117—91no—
453C33#53511yescharacteristic, complemented, Sylow
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—31no—
458C23×C3—31no—
459C23×C3—32no—
460C23×C3—32no—
461C23×C3—42no—
462C23×C3—61no—
463C23×C3—62no—
464C23×C3—64no—
465C23×C3—64no—
466C23×C3—68no—
467C23×C3—92no—
468C23×C3—124no—
469C23×C3—124no—
470C23×C3—128no—
471C23×C3C2×D3212yes—
472C23×C3C22×C3×D312yes—
473C23×C3C22×C3×D312yes—
474C22×D3—24no—
475C22×D3—32no—
476C22×D3—32no—
477C22×D3—44no—
478C22×D3—62no—
479C22×D3C22×C3×D312yes—
480C22×D3C22×C3×D311yescharacteristic
481C3×Q8—62no—
482C3×Q8—62no—
483C3×Q8—122no—
484C3×D4—24no—
485C3×D4—22no—
486C3×D4—22no—
487C3×D4—22no—
488C3×D4—42no—
489C3×D4—42no—
490C3×D4—44no—
491C3×D4—64no—
492C3×D4—64no—
493C3×D4—64no—
494C3×D4—68no—
495C3×D4—62no—
496C3×D4—62no—
497C3×D4—184no—
498C3×D4—182no—
499C3×D4—364no—
500C3×D4—364no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—34no—
507C2×C3×C4—34no—
508C2×C3×C4—32no—
509C2×C3×C4—32no—
510C2×C3×C4—32no—
511C2×C3×C4—32no—
512C2×C3×C4—41no—
513C2×C3×C4—64no—
514C2×C3×C4—61no—
515C2×C3×C4—62no—
516C2×C3×C4—62no—
517C2×C3×C4—92no—
518C2×C3×C4—184no—
519C2×C3×C4C2×D3211yescharacteristic
520C2×C3×C4C22×C3×D311yescharacteristic
521C2×C3×C4C22×C3×D311yescharacteristic
522#67—24no—
523#67—64no—
524#67—124no—
525#67—124no—
526#67—124no—
527#67—128no—
528C2×Dic3—32no—
529C2×Dic3—32no—
530C2×Dic3—62no—
531C2×Dic3C22×C3×D312yes—
532C2×Dic3C22×C3×D312yes—
533C2×Dic3C22×C3×D311yescharacteristic
534D12—22no—
535D12—64no—
536D12—62no—
537D12—62no—
538D12—122no—
539D12—124no—
540C4×D3—64no—
541C4×D3—64no—
542C4×D3C3×#6714yescomplemented
543Dic6—22no—
544C2×C32—22no—
545C2×C32—21no—
546C2×C32—21no—
547C2×C32—22no—
548C2×C32—22no—
549C2×C32—21no—
550C2×C32—41no—
551C2×C32—42no—
552C2×C32—42no—
553C2×C32—44no—
554C2×C32—42no—
555C2×C32—42no—
556C2×C32—62no—
557C2×C32—82no—
558C2×C32—82no—
559C2×C32—84no—
560C2×C32—122no—
561C2×C32C2×D3×D411yescharacteristic
562C2×C32#100412yes—
563C2×C32#100912yes—
564C2×C32C22×#6711yescharacteristic
565C2×C32C22×C3×D411yescharacteristic
566C2×C32C3×H(5,𝔽2)12yes—
567C3⋊D3—42no—
568C3×D3—24no—
569C3×D3—22no—
570C3×D3—22no—
571C3×D3—44no—
572C3×D3—42no—
573C3×D3—42no—
574C3×D3—122no—
575C3×D3—122no—
576C3×D3—242no—
577C24—32no—
578#41—184no—
579C2×Q8—31no—
580C2×D4—32no—
581C2×D4—31no—
582C2×D4—64no—
583C2×D4—92no—
584C2×D4—94no—
585C2×D4—94no—
586C2×D4—91no—
587C2×D4C3×D3211yescharacteristic
588C22×C4—31no—
589C22×C4—92no—
590C4⋊C4—92no—
591C22⋊C4—34no—
592C22⋊C4—92no—
593C22⋊C4—94no—
594C42—31no—
595C42—91no—
596C22×C3—24no—
597C22×C3—24no—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—24no—
601C22×C3—24no—
602C22×C3—22no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—32no—
607C22×C3—32no—
608C22×C3—44no—
609C22×C3—44no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3—44no—
613C22×C3—44no—
614C22×C3—41no—
615C22×C3—62no—
616C22×C3—64no—
617C22×C3—64no—
618C22×C3—62no—
619C22×C3—62no—
620C22×C3—64no—
621C22×C3—62no—
622C22×C3—62no—
623C22×C3—64no—
624C22×C3—84no—
625C22×C3—124no—
626C22×C3—1216no—
627C22×C3—128no—
628C22×C3—128no—
629C22×C3—184no—
630C22×C3—182no—
631C22×C3C22×D3211yescharacteristic
632C22×C3C23×C3×D311yescharacteristic
633C22×C3C23×C3×D311yescharacteristic
634C2×D3—22no—
635C2×D3—24no—
636C2×D3—22no—
637C2×D3—48no—
638C2×D3—62no—
639C2×D3—64no—
640C2×D3—64no—
641C2×D3—62no—
642C2×D3—122no—
643C2×D3—124no—
644C2×D3C2×C3×#6712yes—
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—32no—
649C3×C4—32no—
650C3×C4—42no—
651C3×C4—62no—
652C3×C4—62no—
653C3×C4—62no—
654C3×C4—62no—
655C3×C4—62no—
656C3×C4—122no—
657C3×C4—122no—
658C3×C4—182no—
659C3×C4D3×#6712yes—
660C3×C4C3×D3×D412yes—
661C3×C4C2×C3×#6712yes—
662Dic3—22no—
663Dic3—22no—
664Dic3—64no—
665Dic3—62no—
666Dic3—62no—
667Dic3C2×C3×#6712yes—
668C32—21no—
669C32—21no—
670C32—21no—
671C32—41no—
672C32#567411yescharacteristic, complemented
673C32#580511yescharacteristic, complemented
674C32C3×#53511yescharacteristic, complemented
675C23—31no—
676C23—32no—
677C23—64no—
678C23—92no—
679C23—124no—
680C23C2×C3×D3212yes—
681Q8—62no—
682D4—22no—
683D4—64no—
684D4—62no—
685D4—184no—
686D4—182no—
687D4—364no—
688D4—364no—
689C2×C4—31no—
690C2×C4—34no—
691C2×C4—32no—
692C2×C4—32no—
693C2×C4—92no—
694C2×C4—184no—
695C2×C4C2×C3×D3211yescharacteristic
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—22no—
700C2×C3—22no—
701C2×C3—22no—
702C2×C3—44no—
703C2×C3—42no—
704C2×C3—42no—
705C2×C3—42no—
706C2×C3—41no—
707C2×C3—42no—
708C2×C3—64no—
709C2×C3—62no—
710C2×C3—62no—
711C2×C3—82no—
712C2×C3—82no—
713C2×C3—84no—
714C2×C3—124no—
715C2×C3—122no—
716C2×C3—122no—
717C2×C3—362no—
718C2×C3#6431412yes—
719C2×C3C2×D3×#6711yescharacteristic
720C2×C3C2×C3×D3×D411yescharacteristic
721C2×C3C3×#100412yes—
722C2×C3C3×#100912yes—
723C2×C3C22×C3×#6711yescharacteristic
724D3—22no—
725D3—42no—
726D3—122no—
727D3—122no—
728D3—242no—
729C22—22no—
730C22—24no—
731C22—32no—
732C22—62no—
733C22—62no—
734C22—64no—
735C22—128no—
736C22—182no—
737C22—184no—
738C22C22×C3×D3211yescharacteristic
739C4—32no—
740C4—62no—
741C4—62no—
742C4—182no—
743C4C3×D3×#6712yes—
744C3—21no—
745C3—21no—
746C3—21no—
747C3—41no—
748C3#1059523511yescharacteristic, direct product factor
749C3C3×#567411yescharacteristic, complemented
750C3C3×#580511yescharacteristic, complemented
751C2—42no—
752C2—62no—
753C2—122no—
754C2—362no—
755C2C3×#6431412yes—
756C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#535
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×D3×D4C2semidirect
2. C2×C3×#3799C2semidirect
3. C3×#64149C2semidirect
4. C32×#936C2semidirect
5. C3×#63977C2semidirect
6. C3×#63958C2semidirect
7. C3×#63911C2semidirect
8. C3×#63863C2semidirect
9. C3×#63855C2semidirect
12. #10595235C3direct (N × H)
15. C2×C3×#638C22semidirect
16. C2×C3×C4⋊(C3⋊D3)C22semidirect
21. C2×C32×Dic6C22semidirect
23. C2×C3×#626C22semidirect
24. C2×C3×#624C22semidirect
26. C3×C4×C3⋊Dic3C22semidirect
27. C32×#217C22semidirect
28. C32×C4×Dic3C22semidirect
29. C3×Dic3⋊Dic3C22semidirect
31. C3×(C2×D3)⋊Dic3C22semidirect
35. C2×C3×D3×D4D3semidirect
36. C2×C3×D3×D4C2×C3semidirect
38. C2×#3799C2×C3semidirect
40. #64149C2×C3semidirect
50. C3×#936D3semidirect
51. C3×#936C2×C3semidirect
57. #63977C2×C3semidirect
58. #63958C2×C3semidirect
59. #63911C2×C3semidirect
60. #63863C2×C3semidirect
61. #63855C2×C3semidirect
78. C32×C4×D3D4semidirect
102. C2×#638C22×C3semidirect
103. C2×C4⋊(C3⋊D3)C22×C3semidirect
131. C2×C3×Dic6C2×D3semidirect
132. C2×C3×Dic6C22×C3semidirect
134. C2×#626C22×C3semidirect
135. C2×#624C22×C3semidirect
139. C4×C3⋊Dic3C22×C3semidirect
143. C3×#217C2×D3semidirect
144. C3×#217C22×C3semidirect
153. C3×C4×Dic3C2×D3semidirect
154. C3×C4×Dic3C22×C3semidirect
155. Dic3⋊Dic3C22×C3semidirect
157. (C2×D3)⋊Dic3C22×C3semidirect
178. C2×D3×D4C3×D3semidirect
197. #936C3×D3semidirect
285. C3×C4×D3#67semidirect
286. C3×C4×D3C3×D4semidirect
350. C2×Dic6C2×C3×D3semidirect
363. #217C2×C3×D3semidirect
371. C4×Dic3C2×C3×D3semidirect
453. C33#535semidirect
542. C4×D3C3×#67semidirect
672. C32#5674semidirect
673. C32#5805semidirect
674. C32C3×#535semidirect
748. C3#10595235direct (N × H)
749. C3C3×#5674semidirect
750. C3C3×#5805semidirect

Maximal subgroups

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

subgroupindex
C2×C32×D3×D42
C2×C3×#37992
C3×#641492
C32×#9362
C3×#639772
C3×#639582
C3×#639112
C3×#638632
C3×#638552
C3×#58053
C3×#56743
#105952353