Finite Group Databasebeta

← C3×#80147 #11864172

Subgroups — C3×#80147 #11864172

Order 1152.

1602 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic
2C2×C3×#915C212yesmaximal, complemented
3C3×D3×C22⋊Q8C211yesmaximal, characteristic, complemented
4C32×#450C211yesmaximal, characteristic, complemented
5C3×#5218C211yesmaximal, characteristic, complemented
6C3×#5173C212yesmaximal, complemented
7C3×#5050C211yesmaximal, characteristic, complemented
8C3×#4783C212yesmaximal, complemented
9C3×#4771C212yesmaximal, complemented
10C3×#4739C211yesmaximal, characteristic, complemented
11C3×#4726C211yesmaximal, characteristic, complemented
12C3×#3007—31nomaximal
13#80147C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2211yescharacteristic
15C22×C3×#67—21no—
16C23×C3×Dic3—21no—
17C2×C3×D3×Q8C2211yescharacteristic, complemented
18C2×C3×#237—28no—
19C2×C3×#237—21no—
20C2×C3×#237—21no—
21C2×C3×#237C2212yes—
22C2×C3×#237C2212yes—
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic
25C2×C32×SD16C2212yescomplemented
26C32×C22⋊Q8C2211yescharacteristic
27C3×#946C2211yescharacteristic, complemented
28C2×C3×#216C2212yescomplemented
29C2×C3×#214C2212yescomplemented
30C3×#924C2211yescharacteristic
31C3×#915—28no—
32C2×C3×Dic12C2212yescomplemented
33C2×C3×ΓL(1,𝔽25)C2212yescomplemented
34C3×#897C2211yescharacteristic, complemented
35C3×#896—21no—
36C3×D3×C4⋊C4—21no—
37C3×D3×C4⋊C4C2211yescharacteristic, complemented
38C3×D3×C22⋊C4—21no—
39C3×#878—21no—
40C32×#102C2212yescomplemented
41C32×C22⋊C8C2211yescharacteristic
42C3×#832C2212yescomplemented
43C3×#830C2211yescharacteristic
44C3×(C2×D3)⋊C8C2212yescomplemented
45C3×#816C2212yescomplemented
46C3×#810C2212yescomplemented
47C22×C3×#41—31no—
48C22×#237C2×C311yescharacteristic
49C2×C3×#137—32no—
50C2×C3×C22⋊Q8—31no—
51C2×#915C2×C312yescomplemented
52D3×C22⋊Q8C2×C311yescharacteristic, complemented
53C3×#452—32no—
54C3×#452—32no—
55C3×#451—31no—
56C3×#451—31no—
57C3×#450—21no—
58C3×#450—31no—
59C3×#450D311yescharacteristic, complemented
60C3×#450C2×C311yescharacteristic, complemented
61C3×#417—32no—
62C3×#407—31no—
63#5218C2×C311yescharacteristic, complemented
64#5173C2×C312yescomplemented
65#5050C2×C311yescharacteristic, complemented
66#4783C2×C312yescomplemented
67#4771C2×C312yescomplemented
68#4739C2×C311yescharacteristic, complemented
69#4726C2×C311yescharacteristic, complemented
70C24×C32—21no—
71C23×C3×D3D411yescharacteristic
72C2×C32×Q8C2311yescharacteristic
73C2×C32×D4—24no—
74C2×C32×D4—21no—
75C2×C32×D4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C2×C3×#67—28no—
78C2×C3×#67—22no—
79C2×C3×#67—22no—
80C22×C3×Dic3—28no—
81C22×C3×Dic3—21no—
82C22×C3×Dic3—22no—
83C22×C3×Dic3—22no—
84C22×C3×Dic3D411yescharacteristic
85C3×D3×Q8—24no—
86C3×#237—28no—
87C3×#237—28no—
88C3×#237—24no—
89C3×#237—24no—
90C3×#237—24no—
91C3×#237D418yes—
92C2×C3×C4×D3—24no—
93C2×C3×C4×D3—21no—
94C2×C3×C4×D3—21no—
95C2×C3×C4×D3D411yescharacteristic
96C2×C3×C4×D3D411yescharacteristic
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6—21no—
100C2×C3×Dic6—24no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2312yes—
104C32×SD16—24no—
105C2×C32×C8C2312yes—
106C32×C4⋊C4—21no—
107C32×C4⋊C4C2311yescharacteristic
108C32×C22⋊C4—21no—
109C3×#217—21no—
110C3×#216—24no—
111C3×#214—24no—
112C3×(C2×D3)⋊C4—21no—
113C3×(C2×D3)⋊C4—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C2×C3×C3⋊C8C2312yes—
120C3×Dic12—24no—
121C3×ΓL(1,𝔽25)—24no—
122#3007—31noSylow
123C2×C3×#41—32no—
124C2×C3×#41—32no—
125C2×C3×#41—61no—
126C2×C3×#41—61no—
127C2×C3×#41—68no—
128C22×C3×Q8—31no—
129C22×C3×Q8—31no—
130C22×C3×D4—21no—
131C22×C3×D4—61no—
132C22×C3×D4C2×D311yescharacteristic
133C22×C3×D4C22×C311yescharacteristic
134C23×C3×C4—31no—
135C23×C3×C4—61no—
136C22×#67—21no—
137C23×Dic3—21no—
138C2×D3×Q8C22×C311yescharacteristic, complemented
139C2×#237—28no—
140C2×#237—21no—
141C2×#237—21no—
142C2×#237C22×C312yes—
143C2×#237C22×C312yes—
144C22×C4×D3C22×C311yescharacteristic
145C22×Dic6C22×C311yescharacteristic
146C3×#137—68no—
147C2×C3×Q16—32no—
148C2×C3×Q16—32no—
149C2×C3×SD16—22no—
150C2×C3×SD16—32no—
151C2×C3×SD16C2×D312yescomplemented
152C2×C3×SD16C22×C312yescomplemented
153C2×C3×M16—32no—
154C3×C22⋊Q8—21no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—61no—
159C3×C22⋊Q8—61no—
160C3×C22⋊Q8C2×D311yescharacteristic
161C3×C22⋊Q8C22×C311yescharacteristic
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—61no—
164C2×C3×C22⋊C4—61no—
165#946C22×C311yescharacteristic, complemented
166C2×#216C22×C312yescomplemented
167C2×#214C22×C312yescomplemented
168#924C22×C311yescharacteristic
169#915—28no—
170C2×Dic12C22×C312yescomplemented
171C2×ΓL(1,𝔽25)C22×C312yescomplemented
172#897C22×C311yescharacteristic, complemented
173#896—21no—
174D3×C4⋊C4—21no—
175D3×C4⋊C4C22×C311yescharacteristic, complemented
176D3×C22⋊C4—21no—
177#878—21no—
178C3×#103—32no—
179C3×#103—32no—
180C3×#102—22no—
181C3×#102—32no—
182C3×#102C2×D312yescomplemented
183C3×#102C22×C312yescomplemented
184C3×C22⋊C8—21no—
185C3×C22⋊C8—31no—
186C3×C22⋊C8—32no—
187C3×C22⋊C8C2×D311yescharacteristic
188C3×C22⋊C8C22×C311yescharacteristic
189#832C22×C312yescomplemented
190#830C22×C311yescharacteristic
191(C2×D3)⋊C8C22×C312yescomplemented
192#816C22×C312yescomplemented
193#810C22×C312yescomplemented
194C23×C32—24no—
195C23×C32—22no—
196C23×C32—42no—
197C23×C32—42no—
198C23×C32C2×D411yescharacteristic
199C22×C3×D3—22no—
200C22×C3×D3—22no—
201C22×C3×D3—41no—
202C22×C3×D3C2×D411yescharacteristic
203C22×C3×D3C2×D411yescharacteristic
204C32×Q8—22no—
205C32×D4—24no—
206C32×D4—22no—
207C32×D4C2×D414yes—
208C2×C32×C4—22no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4C2×D411yescharacteristic
212C2×C32×C4C2411yescharacteristic
213C3×#67—28no—
214C3×#67—28no—
215C2×C3×Dic3—24no—
216C2×C3×Dic3—28no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—28no—
220C2×C3×Dic3—21no—
221C2×C3×Dic3—21no—
222C2×C3×Dic3C2×D411yescharacteristic
223C2×C3×Dic3C2×D411yescharacteristic
224C3×C4×D3—22no—
225C3×C4×D3—22no—
226C3×C4×D3—22no—
227C3×C4×D3—42no—
228C3×C4×D3—42no—
229C3×C4×D3C2×D414yes—
230C3×Dic6—24no—
231C3×Dic6—22no—
232C3×Dic6—22no—
233C3×Dic6—42no—
234C3×Dic6C2×D414yes—
235C32×C8—22no—
236C3×C3⋊C8—22no—
237C22×#41—31no—
238C2×#137—32no—
239C2×C22⋊Q8—31no—
240#452—32no—
241#452—32no—
242#451—31no—
243#451—31no—
244#450—31no—
245#450C3×D311yescharacteristic, complemented
246#417—32no—
247#407—31no—
248C24×C3—21no—
249C24×C3—21no—
250C24×C3—31no—
251C24×C3—41no—
252C23×D3C3×D411yescharacteristic
253C3×#41—38no—
254C3×#41—64no—
255C3×#41—64no—
256C3×#41—68no—
257C3×#41—68no—
258C3×#41—64no—
259C2×C3×Q8—21no—
260C2×C3×Q8—32no—
261C2×C3×Q8—31no—
262C2×C3×Q8—61no—
263C2×C3×Q8—64no—
264C2×C3×Q8—64no—
265C2×C3×Q8—61no—
266C2×C3×Q8C22×D311yescharacteristic
267C2×C3×Q8C23×C311yescharacteristic
268C2×C3×D4—24no—
269C2×C3×D4—24no—
270C2×C3×D4—21no—
271C2×C3×D4—21no—
272C2×C3×D4—22no—
273C2×C3×D4—41no—
274C2×C3×D4—44no—
275C2×C3×D4—62no—
276C2×C3×D4—62no—
277C2×C3×D4—68no—
278C2×C3×D4C22×D312yes—
279C2×C3×D4C23×C312yes—
280C22×C3×C4—21no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—64no—
287C22×C3×C4—61no—
288C22×C3×C4—61no—
289C22×C3×C4—62no—
290C22×C3×C4—62no—
291C22×C3×C4—68no—
292C22×C3×C4—61no—
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C23×C311yescharacteristic
295C2×#67—28no—
296C2×#67—22no—
297C2×#67—22no—
298C22×Dic3—28no—
299C22×Dic3—21no—
300C22×Dic3—22no—
301C22×Dic3—22no—
302C22×Dic3C3×D411yescharacteristic
303D3×Q8—24no—
304#237—28no—
305#237—28no—
306#237—24no—
307#237—24no—
308#237—24no—
309#237C3×D418yes—
310C2×C4×D3—24no—
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3C3×D411yescharacteristic
314C2×C4×D3C3×D411yescharacteristic
315C2×C4×D3C23×C311yescharacteristic
316C2×C4×D3C23×C311yescharacteristic
317C2×Dic6—21no—
318C2×Dic6—24no—
319C2×Dic6—21no—
320C2×Dic6C23×C311yescharacteristic
321C2×Dic6C23×C312yes—
322C3×Q16—64no—
323C3×Q16—64no—
324C3×SD16—24no—
325C3×SD16—24no—
326C3×SD16—44no—
327C3×SD16—64no—
328C3×M16—64no—
329C2×C3×C8—22no—
330C2×C3×C8—32no—
331C2×C3×C8C22×D312yes—
332C2×C3×C8C23×C312yes—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—41no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C23×C311yescharacteristic
344C3×C22⋊C4—21no—
345C3×C22⋊C4—21no—
346C3×C22⋊C4—41no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350#217—21no—
351#216—24no—
352#214—24no—
353(C2×D3)⋊C4—21no—
354(C2×D3)⋊C4—21no—
355C4⋊Dic3—21no—
356C4⋊Dic3C23×C311yescharacteristic
357Dic3⋊C4—21no—
358Dic3⋊C4—21no—
359Dic3⋊C4—21no—
360C2×C3⋊C8C23×C312yes—
361Dic12—24no—
362ΓL(1,𝔽25)—24no—
363C22×C32—21no—
364C22×C32—21no—
365C22×C32—24no—
366C22×C32—48no—
367C22×C32—42no—
368C22×C32—42no—
369C22×C32#13712yescomplemented
370C22×C32C22×D411yescharacteristic
371C2×C3×D3—21no—
372C2×C3×D3—21no—
373C2×C3×D3—21no—
374C2×C3×D3—21no—
375C2×C3×D3—21no—
376C2×C3×D3—44no—
377C2×C3×D3#12012yes—
378C32×C4—21no—
379C32×C4—41no—
380C32×C4—41no—
381C32×C4C22×D412yes—
382C3×Dic3—24no—
383C3×Dic3—21no—
384C3×Dic3—41no—
385C3×Dic3—41no—
386C3×Dic3#12012yes—
387C2×#41—32no—
388C2×#41—32no—
389C2×#41—61no—
390C2×#41—61no—
391C2×#41—68no—
392C22×Q8—31no—
393C22×Q8—31no—
394C22×D4—61no—
395C22×D4C2×C3×D311yescharacteristic
396C23×C4—31no—
397C23×C4—61no—
398#137—68no—
399C2×Q16—32no—
400C2×Q16—32no—
401C2×SD16—32no—
402C2×SD16C2×C3×D312yescomplemented
403C2×M16—32no—
404C22⋊Q8—31no—
405C22⋊Q8—31no—
406C22⋊Q8—31no—
407C22⋊Q8—61no—
408C22⋊Q8—61no—
409C22⋊Q8C2×C3×D311yescharacteristic
410C2×C4⋊C4—31no—
411C2×C4⋊C4—61no—
412C2×C22⋊C4—61no—
413#103—32no—
414#103—32no—
415#102—32no—
416#102C2×C3×D312yescomplemented
417C22⋊C8—31no—
418C22⋊C8—32no—
419C22⋊C8C2×C3×D311yescharacteristic
420C23×C3—24no—
421C23×C3—24no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—21no—
425C23×C3—31no—
426C23×C3—31no—
427C23×C3—42no—
428C23×C3—44no—
429C23×C3—42no—
430C23×C3—42no—
431C23×C3—42no—
432C23×C3—42no—
433C23×C3—62no—
434C23×C3—62no—
435C23×C3—82no—
436C23×C3—82no—
437C23×C3—121no—
438C23×C3D3×D411yescharacteristic
439C23×C3C2×C3×D411yescharacteristic
440C22×D3—22no—
441C22×D3—22no—
442C22×D3—41no—
443C22×D3C2×C3×D411yescharacteristic
444C22×D3C2×C3×D411yescharacteristic
445C3×Q8—22no—
446C3×Q8—22no—
447C3×Q8—34no—
448C3×Q8—42no—
449C3×Q8—64no—
450C3×Q8—62no—
451C3×Q8—62no—
452C3×Q8—122no—
453C3×D4—24no—
454C3×D4—24no—
455C3×D4—22no—
456C3×D4—22no—
457C3×D4—24no—
458C3×D4—42no—
459C3×D4—44no—
460C3×D4—68no—
461C3×D4—68no—
462C3×D4D3×D414yes—
463C3×D4C2×C3×D414yes—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—31no—
473C2×C3×C4—34no—
474C2×C3×C4—31no—
475C2×C3×C4—42no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—62no—
479C2×C3×C4—62no—
480C2×C3×C4—62no—
481C2×C3×C4—68no—
482C2×C3×C4—64no—
483C2×C3×C4—68no—
484C2×C3×C4—62no—
485C2×C3×C4—62no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—122no—
489C2×C3×C4—122no—
490C2×C3×C4D3×D411yescharacteristic
491C2×C3×C4C2×C3×D411yescharacteristic
492C2×C3×C4C23×D311yescharacteristic
493C2×C3×C4C24×C311yescharacteristic
494#67—28no—
495#67—28no—
496C2×Dic3—24no—
497C2×Dic3—28no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—28no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3C2×C3×D411yescharacteristic
504C2×Dic3C2×C3×D411yescharacteristic
505C4×D3—22no—
506C4×D3—22no—
507C4×D3—22no—
508C4×D3—42no—
509C4×D3—42no—
510C4×D3C2×C3×D414yes—
511Dic6—24no—
512Dic6—22no—
513Dic6—22no—
514Dic6—42no—
515Dic6C2×C3×D414yes—
516C3×C8—22no—
517C3×C8—22no—
518C3×C8—42no—
519C3×C8—62no—
520C3⋊C8—22no—
521C2×C32—22no—
522C2×C32—44no—
523C2×C32C2×#12011yescharacteristic
524C2×C32C2×#13711yescharacteristic
525C2×C32#57511yescharacteristic
526C3×D3—22no—
527C3×D3—41no—
528C24—21no—
529C24—31no—
530#41—38no—
531#41—64no—
532#41—64no—
533#41—68no—
534#41—68no—
535#41—64no—
536C2×Q8—32no—
537C2×Q8—31no—
538C2×Q8—61no—
539C2×Q8—64no—
540C2×Q8—64no—
541C2×Q8—61no—
542C2×Q8C22×C3×D311yescharacteristic
543C2×D4—24no—
544C2×D4—21no—
545C2×D4—62no—
546C2×D4—62no—
547C2×D4—68no—
548C2×D4C22×C3×D312yes—
549C22×C4—31no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—64no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—68no—
560C22×C4—61no—
561C22×C4C22×C3×D311yescharacteristic
562Q16—64no—
563Q16—64no—
564SD16—24no—
565SD16—64no—
566M16—64no—
567C2×C8—32no—
568C2×C8C22×C3×D312yes—
569C4⋊C4—21no—
570C4⋊C4—31no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4C22×C3×D311yescharacteristic
576C22⋊C4—21no—
577C22⋊C4—61no—
578C22⋊C4—61no—
579C22⋊C4—61no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—24no—
585C22×C3—24no—
586C22×C3—22no—
587C22×C3—21no—
588C22×C3—32no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—44no—
592C22×C3—48no—
593C22×C3—48no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—61no—
599C22×C3—61no—
600C22×C3—61no—
601C22×C3—61no—
602C22×C3—61no—
603C22×C3—82no—
604C22×C3—82no—
605C22×C3—88no—
606C22×C3—124no—
607C22×C3#91512yescomplemented
608C22×C3C3×#13712yescomplemented
609C22×C3C2×D3×D411yescharacteristic
610C22×C3C22×C3×D411yescharacteristic
611C2×D3—21no—
612C2×D3—21no—
613C2×D3—21no—
614C2×D3—21no—
615C2×D3—21no—
616C2×D3—44no—
617C2×D3C3×#12012yes—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—22no—
621C3×C4—32no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—61no—
628C3×C4—64no—
629C3×C4—81no—
630C3×C4—81no—
631C3×C4—121no—
632C3×C4—121no—
633C3×C4C2×D3×D412yes—
634C3×C4C22×C3×D412yes—
635Dic3—24no—
636Dic3—21no—
637Dic3—41no—
638Dic3—41no—
639Dic3C3×#12012yes—
640C32#300711yescharacteristic, complemented, Sylow
641C23—24no—
642C23—22no—
643C23—31no—
644C23—31no—
645C23—42no—
646C23—42no—
647C23—62no—
648C23—62no—
649C23—121no—
650C23C3×D3×D411yescharacteristic
651Q8—22no—
652Q8—34no—
653Q8—64no—
654Q8—62no—
655Q8—62no—
656Q8—122no—
657D4—24no—
658D4—22no—
659D4—68no—
660D4—68no—
661D4C3×D3×D414yes—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—31no—
666C2×C4—34no—
667C2×C4—31no—
668C2×C4—62no—
669C2×C4—62no—
670C2×C4—62no—
671C2×C4—68no—
672C2×C4—64no—
673C2×C4—68no—
674C2×C4—62no—
675C2×C4—62no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—122no—
679C2×C4—122no—
680C2×C4C3×D3×D411yescharacteristic
681C2×C4C23×C3×D311yescharacteristic
682C8—22no—
683C8—62no—
684C2×C3—22no—
685C2×C3—22no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—42no—
690C2×C3—44no—
691C2×C3—44no—
692C2×C3—62no—
693C2×C3—84no—
694C2×C3—121no—
695C2×C3D3×#12011yescharacteristic
696C2×C3C2×#91511yescharacteristic
697C2×C3#577311yescharacteristic
698C2×C3C2×C3×#12011yescharacteristic
699C2×C3C2×C3×#13711yescharacteristic
700C2×C3C3×#57511yescharacteristic
701D3—22no—
702D3—41no—
703C22—21no—
704C22—21no—
705C22—24no—
706C22—32no—
707C22—48no—
708C22—42no—
709C22—42no—
710C22—61no—
711C22—61no—
712C22—61no—
713C22—61no—
714C22—61no—
715C22—124no—
716C22C3×#91512yescomplemented
717C22C2×C3×D3×D411yescharacteristic
718C4—21no—
719C4—32no—
720C4—41no—
721C4—41no—
722C4—61no—
723C4—64no—
724C4—121no—
725C4—121no—
726C4C2×C3×D3×D412yes—
727C3—21no—
728C3#8014711yescharacteristic, direct product factor
729C3C3×#300711yescharacteristic, complemented
730C2—22no—
731C2—44no—
732C2—62no—
733C2—121no—
734C2C3×D3×#12011yescharacteristic
735C2C2×C3×#91511yescharacteristic
736C2C3×#577311yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#450C2
socleC22×C32C22×D4
prime radicalC22×C3×#237C2
hypercenterC3×#450D3
hypocenterC3C3×#3007
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#450

Complements

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

NH ≅ G/Ntype
2. C2×C3×#915C2semidirect
3. C3×D3×C22⋊Q8C2semidirect
4. C32×#450C2semidirect
5. C3×#5218C2semidirect
6. C3×#5173C2semidirect
7. C3×#5050C2semidirect
8. C3×#4783C2semidirect
9. C3×#4771C2semidirect
10. C3×#4739C2semidirect
11. C3×#4726C2semidirect
13. #80147C3direct (N × H)
17. C2×C3×D3×Q8C22semidirect
25. C2×C32×SD16C22semidirect
27. C3×#946C22semidirect
28. C2×C3×#216C22semidirect
29. C2×C3×#214C22semidirect
32. C2×C3×Dic12C22semidirect
33. C2×C3×ΓL(1,𝔽25)C22semidirect
34. C3×#897C22semidirect
37. C3×D3×C4⋊C4C22semidirect
40. C32×#102C22semidirect
42. C3×#832C22semidirect
44. C3×(C2×D3)⋊C8C22semidirect
45. C3×#816C22semidirect
46. C3×#810C22semidirect
51. C2×#915C2×C3semidirect
52. D3×C22⋊Q8C2×C3semidirect
59. C3×#450D3semidirect
60. C3×#450C2×C3semidirect
63. #5218C2×C3semidirect
64. #5173C2×C3semidirect
65. #5050C2×C3semidirect
66. #4783C2×C3semidirect
67. #4771C2×C3semidirect
68. #4739C2×C3semidirect
69. #4726C2×C3semidirect
138. C2×D3×Q8C22×C3semidirect
151. C2×C3×SD16C2×D3semidirect
152. C2×C3×SD16C22×C3semidirect
165. #946C22×C3semidirect
166. C2×#216C22×C3semidirect
167. C2×#214C22×C3semidirect
170. C2×Dic12C22×C3semidirect
171. C2×ΓL(1,𝔽25)C22×C3semidirect
172. #897C22×C3semidirect
175. D3×C4⋊C4C22×C3semidirect
182. C3×#102C2×D3semidirect
183. C3×#102C22×C3semidirect
189. #832C22×C3semidirect
191. (C2×D3)⋊C8C22×C3semidirect
192. #816C22×C3semidirect
193. #810C22×C3semidirect
245. #450C3×D3semidirect
369. C22×C32#137semidirect
402. C2×SD16C2×C3×D3semidirect
416. #102C2×C3×D3semidirect
607. C22×C3#915semidirect
608. C22×C3C3×#137semidirect
640. C32#3007semidirect
716. C22C3×#915semidirect
728. C3#80147direct (N × H)
729. C3C3×#3007semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C2×C3×#9152
C3×D3×C22⋊Q82
C32×#4502
C3×#52182
C3×#51732
C3×#50502
C3×#47832
C3×#47712
C3×#47392
C3×#47262
C3×#30073
#801473