Finite Group Databasebeta

← C3×#83913 #11864656

Subgroups — C3×#83913 #11864656

Order 1152.

1557 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C2×C32×#135C211yesmaximal, characteristic, complemented
3C3×#5833C211yesmaximal, characteristic, complemented
4C2×C3×#951C211yesmaximal, characteristic, complemented
5C3×#5232C211yesmaximal, characteristic, complemented
6C3×#5186C212yesmaximal, complemented
7C3×#5173C212yesmaximal, complemented
8C3×#5170C212yesmaximal, complemented
9C3×#5158C212yesmaximal, complemented
10C3×#5110C211yesmaximal, characteristic, complemented
11C2×C3×#816C211yesmaximal, characteristic, complemented
12C3×#3013—31nomaximal
13#83913C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C2×C32×#41C2211yescharacteristic
16C3×#1010—24no—
17C3×#1010—24no—
18C2×C3×D3×Q8C2212yes—
19C2×C3×#237—22no—
20C2×C3×#237C2212yes—
21C2×C3×#235—21no—
22C2×C3×#235C2211yescharacteristic
23C22×C3×Dic6—21no—
24C22×C3×Dic6C2211yescharacteristic
25C32×#135—24no—
26C2×C32×Q16C2211yescharacteristic
27C2×C32×SD16C2211yescharacteristic
28C2×C32×SD16C2211yescharacteristic
29C2×C32×D8C2211yescharacteristic
30C22×C32×C8C2211yescharacteristic
31C3×#951—24no—
32C3×#946C2212yes—
33C2×C3×#216C2212yes—
34C3×#939—22no—
35C3×#938C2212yes—
36C2×C3×#214C2212yes—
37C3×#930—21no—
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C3×#924—21no—
40C2×C3×#208C2211yescharacteristic
41C3×#835C2212yes—
42C3×#832C2212yes—
43C3×(C2×D3)⋊C8C2212yes—
44C3×(C2×D3)⋊C8C2212yes—
45C3×#816C2212yes—
46C3×#816C2212yes—
47C2×C3×2−1+4—31no—
48C2×#1010C2×C311yescharacteristic, complemented
49C2×C3×#137—31no—
50C2×C3×#135—21no—
51C2×C3×#135D311yescharacteristic, complemented
52C2×C3×#135C2×C311yescharacteristic, complemented
53C3×#537—31no—
54#5833C2×C311yescharacteristic, complemented
55C2×#951C2×C311yescharacteristic, complemented
56C3×#452—32no—
57C3×#451—32no—
58C3×#449—32no—
59C3×#448—32no—
60C3×#417—31no—
61C2×C3×#103—31no—
62C3×#408—31no—
63#5232C2×C311yescharacteristic, complemented
64#5186C2×C312yescomplemented
65#5173C2×C312yescomplemented
66#5170C2×C312yescomplemented
67#5158C2×C312yescomplemented
68#5110C2×C311yescharacteristic, complemented
69C2×#816C2×C311yescharacteristic, complemented
70C32×#41—22no—
71C32×#41—22no—
72C32×#41—22no—
73C32×#41D414yescomplemented
74C2×C32×Q8C2311yescharacteristic
75C2×C32×Q8C2311yescharacteristic
76C2×C32×D4—21no—
77C2×C32×D4—21no—
78C2×C32×D4C2311yescharacteristic
79C2×C32×D4C2311yescharacteristic
80C22×C32×C4—21no—
81C22×C32×C4—21no—
82C22×C32×C4C2311yescharacteristic
83C2×C3×#67—22no—
84C2×C3×#67—22no—
85C2×C3×#67D412yes—
86C22×C3×Dic3—21no—
87C22×C3×Dic3—22no—
88C22×C3×Dic3—21no—
89C3×D3×Q8—24no—
90C3×D3×Q8—24no—
91C3×#237—216no—
92C3×#237—24no—
93C3×#237—24no—
94C3×#235—28no—
95C3×#235—22no—
96C3×#235—22no—
97C2×C3×D12D411yescharacteristic
98C2×C3×C4×D3—22no—
99C2×C3×C4×D3C2312yes—
100C2×C3×Dic6—28no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6—22no—
103C2×C3×Dic6—22no—
104C2×C3×Dic6D411yescharacteristic
105C2×C3×Dic6D414yescomplemented
106C2×C3×Dic6C2312yes—
107C32×Q16—22no—
108C32×SD16—22no—
109C32×SD16—22no—
110C32×D8—22no—
111C2×C32×C8—22no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C3×#217—22no—
115C3×#216—24no—
116C3×#214—24no—
117C3×(C2×D3)⋊C4—22no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3C2312yes—
120C3×Dic3⋊C4—22no—
121C3×#208—22no—
122C2×C3×C3⋊C8C2312yes—
123#3013—31noSylow
124C3×2−1+4—64no—
125C3×2−1+4—64no—
126C2×C3×#41—21no—
127C2×C3×#41—21no—
128C2×C3×#41—31no—
129C2×C3×#41—32no—
130C2×C3×#41—61no—
131C2×C3×#41—62no—
132C2×C3×#41C2×D311yescharacteristic
133C2×C3×#41C2×D311yescharacteristic
134C2×C3×#41C22×C311yescharacteristic
135C2×C3×#41C22×C311yescharacteristic
136C22×C3×Q8—32no—
137C22×C3×Q8—31no—
138C22×C3×Q8—61no—
139#1010—24no—
140#1010—24no—
141C2×D3×Q8C22×C312yes—
142C2×#237—22no—
143C2×#237C22×C312yes—
144C2×#235—21no—
145C2×#235C22×C311yescharacteristic
146C22×Dic6—21no—
147C22×Dic6C22×C311yescharacteristic
148C3×#137—64no—
149C3×#135—28no—
150C3×#135—24no—
151C3×#135—24no—
152C2×C3×Q16—21no—
153C2×C3×Q16—32no—
154C2×C3×Q16C2×D311yescharacteristic
155C2×C3×Q16C22×C311yescharacteristic
156C2×C3×SD16—21no—
157C2×C3×SD16—21no—
158C2×C3×SD16—32no—
159C2×C3×SD16C2×D311yescharacteristic
160C2×C3×SD16C2×D311yescharacteristic
161C2×C3×SD16C22×C311yescharacteristic
162C2×C3×SD16C22×C311yescharacteristic
163C2×C3×D8—21no—
164C2×C3×D8C2×D311yescharacteristic
165C2×C3×D8C22×C311yescharacteristic
166C2×C3×M16—31no—
167C22×C3×C8—21no—
168C22×C3×C8C2×D311yescharacteristic
169C22×C3×C8C22×C311yescharacteristic
170C3×C22⋊Q8—32no—
171C3×C22⋊Q8—61no—
172C3×#121—32no—
173C3×#121—61no—
174C3×#121—62no—
175C2×C3×C4⋊C4—31no—
176#951—24no—
177#946C22×C312yes—
178C2×#216C22×C312yes—
179#939—22no—
180#938C22×C312yes—
181C2×#214C22×C312yes—
182#930—21no—
183C2×C4⋊Dic3C22×C311yescharacteristic
184#924—21no—
185C2×#208C22×C311yescharacteristic
186C3×#103—32no—
187C3×#103—32no—
188C3×#103—32no—
189C3×#102—32no—
190C3×C22⋊C8—32no—
191C3×C22⋊C8—32no—
192#835C22×C312yes—
193#832C22×C312yes—
194(C2×D3)⋊C8C22×C312yes—
195(C2×D3)⋊C8C22×C312yes—
196#816C22×C312yes—
197#816C22×C312yes—
198C23×C32—21no—
199C23×C32—21no—
200C23×C32C2×D411yescharacteristic
201C22×C3×D3C2×D412yes—
202C32×Q8—21no—
203C32×Q8—21no—
204C32×Q8—21no—
205C32×Q8C2×D412yes—
206C32×D4—21no—
207C32×D4—24no—
208C32×D4—21no—
209C32×D4—21no—
210C32×D4—42no—
211C32×D4C2×D412yes—
212C2×C32×C4—21no—
213C2×C32×C4—24no—
214C2×C32×C4—21no—
215C2×C32×C4—42no—
216C2×C32×C4C2×D411yescharacteristic
217C2×C32×C4C2×D412yes—
218C2×C32×C4C2×D412yes—
219C2×C32×C4C2411yescharacteristic
220C3×#67—28no—
221C3×#67—24no—
222C3×#67—82no—
223C2×C3×Dic3—28no—
224C2×C3×Dic3—24no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—81no—
228C2×C3×Dic3C2×D412yes—
229C3×D12—22no—
230C3×C4×D3—28no—
231C3×C4×D3—22no—
232C3×C4×D3—22no—
233C3×Dic6—28no—
234C3×Dic6—22no—
235C3×Dic6—24no—
236C3×Dic6—22no—
237C3×Dic6C2×D414yes—
238C32×C8—21no—
239C32×C8—21no—
240C3×C3⋊C8—22no—
241C2×2−1+4—31no—
242C2×#137—31no—
243C2×#135C3×D311yescharacteristic, complemented
244#537—31no—
245#452—32no—
246#451—32no—
247#449—32no—
248#448—32no—
249#417—31no—
250C2×#103—31no—
251#408—31no—
252C3×#41—22no—
253C3×#41—22no—
254C3×#41—24no—
255C3×#41—22no—
256C3×#41—22no—
257C3×#41—22no—
258C3×#41—22no—
259C3×#41—24no—
260C3×#41—42no—
261C3×#41—42no—
262C3×#41—68no—
263C3×#41—64no—
264C3×#41—616no—
265C3×#41—64no—
266C3×#41—62no—
267C3×#41—62no—
268C3×#41#6714yescomplemented
269C3×#41C3×D414yescomplemented
270C2×C3×Q8—21no—
271C2×C3×Q8—21no—
272C2×C3×Q8—31no—
273C2×C3×Q8—34no—
274C2×C3×Q8—32no—
275C2×C3×Q8—62no—
276C2×C3×Q8—68no—
277C2×C3×Q8—64no—
278C2×C3×Q8—64no—
279C2×C3×Q8—61no—
280C2×C3×Q8—62no—
281C2×C3×Q8C22×D311yescharacteristic
282C2×C3×Q8C22×D311yescharacteristic
283C2×C3×Q8C23×C311yescharacteristic
284C2×C3×Q8C23×C311yescharacteristic
285C2×C3×D4—21no—
286C2×C3×D4—21no—
287C2×C3×D4—21no—
288C2×C3×D4—21no—
289C2×C3×D4—21no—
290C2×C3×D4—21no—
291C2×C3×D4—32no—
292C2×C3×D4—31no—
293C2×C3×D4—41no—
294C2×C3×D4—41no—
295C2×C3×D4—62no—
296C2×C3×D4—62no—
297C2×C3×D4C22×D311yescharacteristic
298C2×C3×D4C22×D311yescharacteristic
299C2×C3×D4C23×C311yescharacteristic
300C2×C3×D4C23×C311yescharacteristic
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—32no—
307C22×C3×C4—41no—
308C22×C3×C4—41no—
309C22×C3×C4—62no—
310C22×C3×C4—62no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C23×C311yescharacteristic
315C2×#67—22no—
316C2×#67—22no—
317C2×#67C3×D412yes—
318C22×Dic3—21no—
319C22×Dic3—22no—
320C22×Dic3—21no—
321D3×Q8—24no—
322D3×Q8—24no—
323#237—216no—
324#237—24no—
325#237—24no—
326#235—28no—
327#235—22no—
328#235—22no—
329C2×D12C3×D411yescharacteristic
330C2×C4×D3—22no—
331C2×C4×D3C23×C312yes—
332C2×Dic6—28no—
333C2×Dic6—21no—
334C2×Dic6—22no—
335C2×Dic6—22no—
336C2×Dic6C3×D411yescharacteristic
337C2×Dic6C3×D414yescomplemented
338C2×Dic6C23×C312yes—
339C3×Q16—24no—
340C3×Q16—22no—
341C3×Q16—22no—
342C3×Q16—64no—
343C3×SD16—24no—
344C3×SD16—24no—
345C3×SD16—22no—
346C3×SD16—22no—
347C3×SD16—22no—
348C3×SD16—22no—
349C3×SD16—64no—
350C3×D8—24no—
351C3×D8—22no—
352C3×D8—22no—
353C3×M16—62no—
354C2×C3×C8—24no—
355C2×C3×C8—22no—
356C2×C3×C8—22no—
357C2×C3×C8—21no—
358C2×C3×C8—21no—
359C2×C3×C8—32no—
360C2×C3×C8C22×D311yescharacteristic
361C2×C3×C8C22×D311yescharacteristic
362C2×C3×C8C23×C311yescharacteristic
363C2×C3×C8C23×C311yescharacteristic
364C3×C4⋊C4—32no—
365C3×C4⋊C4—62no—
366C3×C4⋊C4—61no—
367C3×C22⋊C4—62no—
368C3×C22⋊C4—62no—
369#217—22no—
370#216—24no—
371#214—24no—
372(C2×D3)⋊C4—22no—
373C4⋊Dic3—21no—
374C4⋊Dic3C23×C312yes—
375Dic3⋊C4—22no—
376#208—22no—
377C2×C3⋊C8C23×C312yes—
378C22×C32—21no—
379C22×C32—21no—
380C22×C32—22no—
381C22×C32—41no—
382C22×C32—41no—
383C22×C32—41no—
384C22×C32—41no—
385C22×C32—41no—
386C22×C32#12012yes—
387C22×C32C22×D411yescharacteristic
388C2×C3×D3—22no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C32×C4—22no—
392C32×C4—41no—
393C32×C4#12012yes—
394C32×C4C22×D411yescharacteristic
395C32×C4C22×D411yescharacteristic
396C3×Dic3—22no—
397C3×Dic3—24no—
398C3×Dic3—42no—
3992−1+4—64no—
4002−1+4—64no—
401C2×#41—31no—
402C2×#41—32no—
403C2×#41—61no—
404C2×#41—62no—
405C2×#41C2×C3×D311yescharacteristic
406C2×#41C2×C3×D311yescharacteristic
407C22×Q8—32no—
408C22×Q8—31no—
409C22×Q8—61no—
410#137—64no—
411#135—24no—
412C2×Q16—32no—
413C2×Q16C2×C3×D311yescharacteristic
414C2×SD16—32no—
415C2×SD16C2×C3×D311yescharacteristic
416C2×SD16C2×C3×D311yescharacteristic
417C2×D8C2×C3×D311yescharacteristic
418C2×M16—31no—
419C22×C8C2×C3×D311yescharacteristic
420C22⋊Q8—32no—
421C22⋊Q8—61no—
422#121—32no—
423#121—61no—
424#121—62no—
425C2×C4⋊C4—31no—
426#103—32no—
427#103—32no—
428#103—32no—
429#102—32no—
430C22⋊C8—32no—
431C22⋊C8—32no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—32no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3D3×D411yescharacteristic
441C23×C3C2×C3×D411yescharacteristic
442C22×D3C2×C3×D412yes—
443C3×Q8—21no—
444C3×Q8—21no—
445C3×Q8—22no—
446C3×Q8—21no—
447C3×Q8—21no—
448C3×Q8—21no—
449C3×Q8—21no—
450C3×Q8—22no—
451C3×Q8—34no—
452C3×Q8—41no—
453C3×Q8—41no—
454C3×Q8—68no—
455C3×Q8—62no—
456C3×Q8—64no—
457C3×Q8—62no—
458C3×Q8C2×#6712yes—
459C3×Q8C2×C3×D412yes—
460C3×D4—24no—
461C3×D4—24no—
462C3×D4—22no—
463C3×D4—21no—
464C3×D4—21no—
465C3×D4—21no—
466C3×D4—21no—
467C3×D4—21no—
468C3×D4—21no—
469C3×D4—22no—
470C3×D4—41no—
471C3×D4—41no—
472C3×D4—44no—
473C3×D4—44no—
474C3×D4—42no—
475C3×D4—42no—
476C3×D4—68no—
477C3×D4—64no—
478C3×D4—62no—
479C3×D4—242no—
480C3×D4C2×#6712yes—
481C3×D4C2×C3×D412yes—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—24no—
485C2×C3×C4—24no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—32no—
493C2×C3×C4—44no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—44no—
497C2×C3×C4—42no—
498C2×C3×C4—42no—
499C2×C3×C4—68no—
500C2×C3×C4—68no—
501C2×C3×C4—64no—
502C2×C3×C4—62no—
503C2×C3×C4—62no—
504C2×C3×C4—62no—
505C2×C3×C4—62no—
506C2×C3×C4—241no—
507C2×C3×C4D3×D411yescharacteristic
508C2×C3×C4D3×D412yes—
509C2×C3×C4C2×#6712yes—
510C2×C3×C4C2×C3×D411yescharacteristic
511C2×C3×C4C2×C3×D412yes—
512C2×C3×C4C2×C3×D412yes—
513C2×C3×C4C23×D311yescharacteristic
514C2×C3×C4C24×C311yescharacteristic
515#67—28no—
516#67—24no—
517#67—82no—
518C2×Dic3—28no—
519C2×Dic3—24no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—81no—
523C2×Dic3C2×C3×D412yes—
524D12—22no—
525C4×D3—28no—
526C4×D3—22no—
527C4×D3—22no—
528Dic6—28no—
529Dic6—22no—
530Dic6—24no—
531Dic6—22no—
532Dic6C2×C3×D414yes—
533C3×C8—22no—
534C3×C8—22no—
535C3×C8—21no—
536C3×C8—21no—
537C3×C8—21no—
538C3×C8—21no—
539C3×C8—62no—
540C3⋊C8—22no—
541C2×C32—22no—
542C2×C32—42no—
543C2×C32—81no—
544C2×C32C2×#12011yescharacteristic
545C2×C32#57711yescharacteristic
546C2×C32#57811yescharacteristic
547C3×D3—42no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—68no—
552#41—64no—
553#41—616no—
554#41—64no—
555#41—62no—
556#41—62no—
557#41C3×#6714yescomplemented
558C2×Q8—31no—
559C2×Q8—32no—
560C2×Q8—34no—
561C2×Q8—62no—
562C2×Q8—68no—
563C2×Q8—64no—
564C2×Q8—64no—
565C2×Q8—61no—
566C2×Q8—62no—
567C2×Q8C22×C3×D311yescharacteristic
568C2×Q8C22×C3×D311yescharacteristic
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—32no—
572C2×D4—31no—
573C2×D4—62no—
574C2×D4—62no—
575C2×D4C22×C3×D311yescharacteristic
576C2×D4C22×C3×D311yescharacteristic
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—32no—
580C22×C4—62no—
581C22×C4—62no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4C22×C3×D311yescharacteristic
585Q16—22no—
586Q16—64no—
587SD16—22no—
588SD16—22no—
589SD16—64no—
590D8—22no—
591M16—62no—
592C2×C8—22no—
593C2×C8—32no—
594C2×C8C22×C3×D311yescharacteristic
595C2×C8C22×C3×D311yescharacteristic
596C4⋊C4—32no—
597C4⋊C4—62no—
598C4⋊C4—61no—
599C22⋊C4—62no—
600C22⋊C4—62no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—21no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—62no—
624C22×C3—62no—
625C22×C3—62no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3#93712yes—
631C22×C3C3×#12012yes—
632C22×C3C2×D3×D411yescharacteristic
633C22×C3C22×C3×D411yescharacteristic
634C2×D3—22no—
635C2×D3—22no—
636C2×D3—22no—
637C3×C4—22no—
638C3×C4—22no—
639C3×C4—22no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—42no—
643C3×C4—42no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—62no—
647C3×C4—64no—
648C3×C4—122no—
649C3×C4#93712yes—
650C3×C4C3×#12012yes—
651C3×C4C2×D3×D411yescharacteristic
652C3×C4C22×#6711yescharacteristic
653C3×C4C22×C3×D411yescharacteristic
654C3×C4C22×C3×D411yescharacteristic
655Dic3—22no—
656Dic3—24no—
657Dic3—42no—
658C32#301311yescharacteristic, complemented, Sylow
659C23—21no—
660C23—21no—
661C23—32no—
662C23C3×D3×D411yescharacteristic
663Q8—21no—
664Q8—21no—
665Q8—21no—
666Q8—34no—
667Q8—68no—
668Q8—62no—
669Q8—64no—
670Q8—62no—
671Q8C2×C3×#6712yes—
672D4—24no—
673D4—21no—
674D4—21no—
675D4—21no—
676D4—42no—
677D4—68no—
678D4—64no—
679D4—62no—
680D4—242no—
681D4C2×C3×#6712yes—
682C2×C4—21no—
683C2×C4—24no—
684C2×C4—21no—
685C2×C4—32no—
686C2×C4—42no—
687C2×C4—68no—
688C2×C4—68no—
689C2×C4—64no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—241no—
695C2×C4C3×D3×D411yescharacteristic
696C2×C4C3×D3×D412yes—
697C2×C4C2×C3×#6712yes—
698C2×C4C23×C3×D311yescharacteristic
699C8—21no—
700C8—21no—
701C8—62no—
702C2×C3—22no—
703C2×C3—22no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—42no—
708C2×C3—42no—
709C2×C3—42no—
710C2×C3—82no—
711C2×C3—82no—
712C2×C3—81no—
713C2×C3—81no—
714C2×C3—122no—
715C2×C3#577011yescharacteristic
716C2×C3#577111yescharacteristic
717C2×C3C2×#93711yescharacteristic
718C2×C3C2×C3×#12011yescharacteristic
719C2×C3C3×#57711yescharacteristic
720C2×C3C3×#57811yescharacteristic
721D3—42no—
722C22—21no—
723C22—21no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—62no—
731C22—62no—
732C22—62no—
733C22C3×#93712yes—
734C22C2×C3×D3×D411yescharacteristic
735C4—22no—
736C4—41no—
737C4—62no—
738C4—64no—
739C4—122no—
740C4C3×#93712yes—
741C4C2×C3×D3×D411yescharacteristic
742C4C22×C3×#6711yescharacteristic
743C3—21no—
744C3#8391311yescharacteristic, direct product factor
745C3C3×#301311yescharacteristic, complemented
746C2—22no—
747C2—42no—
748C2—81no—
749C2—122no—
750C2C3×#577011yescharacteristic
751C2C3×#577111yescharacteristic
752C2C2×C3×#93711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#135C2
socleC22×C32C22×D4
hypercenterC2×C3×#135D3
hypocenterC3C3×#3013
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#135

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C2×C32×#135C2semidirect
3. C3×#5833C2semidirect
4. C2×C3×#951C2semidirect
5. C3×#5232C2semidirect
6. C3×#5186C2semidirect
7. C3×#5173C2semidirect
8. C3×#5170C2semidirect
9. C3×#5158C2semidirect
10. C3×#5110C2semidirect
11. C2×C3×#816C2semidirect
13. #83913C3direct (N × H)
48. C2×#1010C2×C3semidirect
51. C2×C3×#135D3semidirect
52. C2×C3×#135C2×C3semidirect
54. #5833C2×C3semidirect
55. C2×#951C2×C3semidirect
63. #5232C2×C3semidirect
64. #5186C2×C3semidirect
65. #5173C2×C3semidirect
66. #5170C2×C3semidirect
67. #5158C2×C3semidirect
68. #5110C2×C3semidirect
69. C2×#816C2×C3semidirect
73. C32×#41D4semidirect
105. C2×C3×Dic6D4semidirect
243. C2×#135C3×D3semidirect
268. C3×#41#67semidirect
269. C3×#41C3×D4semidirect
337. C2×Dic6C3×D4semidirect
557. #41C3×#67semidirect
658. C32#3013semidirect
744. C3#83913direct (N × H)
745. C3C3×#3013semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×C32×#1352
C3×#58332
C2×C3×#9512
C3×#52322
C3×#51862
C3×#51732
C3×#51702
C3×#51582
C3×#51102
C2×C3×#8162
C3×#30133
#839133