Finite Group Databasebeta

← C3×#79569 #11895314

Subgroups — C3×#79569 #11895314

Order 1152.

791 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
1C3×#5559C211yesmaximal, characteristic, complemented
2C3×#5539C211yesmaximal, characteristic, complemented
3C32×C4×D8C211yesmaximal, characteristic, complemented
4C3×#5153C211yesmaximal, characteristic, complemented
5C3×#5150C211yesmaximal, characteristic
6C3×#5016C211yesmaximal, characteristic, complemented
7C3×#5009C211yesmaximal, characteristic, complemented
8C3×#4891C211yesmaximal, characteristic, complemented
9C3×#4875C211yesmaximal, characteristic, complemented
10C3×#4768C211yesmaximal, characteristic, complemented
11C3×#4760C211yesmaximal, characteristic, complemented
12C3×#4758C211yesmaximal, characteristic, complemented
13C3×#4756C211yesmaximal, characteristic, complemented
14C3×#4697C211yesmaximal, characteristic, complemented
15C3×C8×Dic6C211yesmaximal, characteristic, complemented
16C3×#3361—31nomaximal
17#79569C311yesmaximal, characteristic, direct product factor
18C2×C32×D8C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C3×#940C2211yescharacteristic
22C3×#936C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C3×#929—21no—
28C3×C4×#67—21no—
29C3×#924—21no—
30C2×C3×Dic3⋊C4—21no—
31C3×#893C2211yescharacteristic
32C3×#890C2211yescharacteristic
33C3×#888C2211yescharacteristic
34C3×#887C2211yescharacteristic
35C3×#885—21no—
36C3×#883—21no—
37C3×#878—21no—
38C3×#878—21no—
39C3×#875C2211yescharacteristic
40C3×#870C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C32×#107C2211yescharacteristic
43C32×#102C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×C4×C8C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55C3×C8×Dic3C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#559—31no—
62C3×#554—31no—
63#5559C2×C311yescharacteristic, complemented
64#5539C2×C311yescharacteristic, complemented
65C3×#488—31no—
66C3×#488—31no—
67C3×#486—31no—
68C3×#478—31no—
69C3×#478—31no—
70C3×#477—31no—
71C3×#463—31no—
72C3×#463—31no—
73C3×#459—31no—
74C3×C8×Q8—31no—
75C3×C4×SD16—31no—
76C3×C4×D8—21no—
77C3×C4×D8—31no—
78C3×C4×D8D311yescharacteristic, complemented
79C3×C4×D8C2×C311yescharacteristic, complemented
80#5153C2×C311yescharacteristic, complemented
81#5150C2×C311yescharacteristic
82#5016C2×C311yescharacteristic, complemented
83#5009C2×C311yescharacteristic, complemented
84#4891C2×C311yescharacteristic, complemented
85#4875C2×C311yescharacteristic, complemented
86#4768C2×C311yescharacteristic, complemented
87#4760C2×C311yescharacteristic, complemented
88#4758C2×C311yescharacteristic, complemented
89#4756C2×C311yescharacteristic, complemented
90#4697C2×C311yescharacteristic, complemented
91C8×Dic6C2×C311yescharacteristic, complemented
92C2×C32×D4C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C22×C32×C4—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C22×C3×Dic3—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6D411yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C32×D8—22no—
106C2×C32×C8C2311yescharacteristic
107C2×C32×C8C2311yescharacteristic
108C32×C4⋊C4C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111C32×C22⋊C4—21no—
112C32×C42C2311yescharacteristic
113C3×#217—21no—
114C3×#217—21no—
115C3×#217—21no—
116C3×#217—21no—
117C3×#214—22no—
118C3×#213—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3361—31noSylow
139C2×C3×SD16—31no—
140C2×C3×D8—21no—
141C2×C3×D8—31no—
142C2×C3×D8C2×D311yescharacteristic
143C2×C3×D8C22×C311yescharacteristic
144C3×C4⋊Q8—31no—
145C3×#127—31no—
146C3×#125—31no—
147C3×#125—31no—
148C3×#124—31no—
149C3×#124—31no—
150C3×#124—61no—
151C3×#123—61no—
152C3×#123—61no—
153C3×C22⋊Q8—61no—
154C3×C22⋊Q8—61no—
155C3×C22⋊Q8—61no—
156C3×C4×Q8—31no—
157C3×C4×Q8—31no—
158C3×C4×D4—21no—
159C3×C4×D4—21no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C3×C4×D4—31no—
163C3×C4×D4—61no—
164C3×C4×D4C2×D311yescharacteristic
165C3×C4×D4C2×D311yescharacteristic
166C3×C4×D4C22×C311yescharacteristic
167C3×C4×D4C22×C311yescharacteristic
168C2×C3×C4⋊C4—61no—
169#940C22×C311yescharacteristic
170#936C22×C311yescharacteristic
171D4×Dic3C22×C311yescharacteristic
172D4×Dic3C22×C311yescharacteristic
173C2×#214C22×C311yescharacteristic
174C2×#213C22×C311yescharacteristic
175#929—21no—
176C4×#67—21no—
177#924—21no—
178C2×Dic3⋊C4—21no—
179#893C22×C311yescharacteristic
180#890C22×C311yescharacteristic
181#888C22×C311yescharacteristic
182#887C22×C311yescharacteristic
183#885—21no—
184#883—21no—
185#878—21no—
186#878—21no—
187#875C22×C311yescharacteristic
188#870C22×C311yescharacteristic
189C4×Dic6C22×C311yescharacteristic
190C3×#107—21no—
191C3×#107—31no—
192C3×#107C2×D311yescharacteristic
193C3×#107C22×C311yescharacteristic
194C3×#106—31no—
195C3×C4⋊C8—31no—
196C3×C4⋊C8—31no—
197C3×C4⋊C8—31no—
198C3×#103—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#102—21no—
202C3×#102—21no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102C2×D311yescharacteristic
209C3×#102C2×D311yescharacteristic
210C3×#102C22×C311yescharacteristic
211C3×#102C22×C311yescharacteristic
212C3×C4×C8—21no—
213C3×C4×C8—31no—
214C3×C4×C8—31no—
215C3×C4×C8C2×D311yescharacteristic
216C3×C4×C8C22×C311yescharacteristic
217#832C22×C311yescharacteristic
218#832C22×C311yescharacteristic
219#821C22×C311yescharacteristic
220#821C22×C311yescharacteristic
221#816C22×C311yescharacteristic
222#816C22×C311yescharacteristic
223Dic3⋊C8C22×C311yescharacteristic
224Dic3⋊C8C22×C311yescharacteristic
225C8×Dic3C22×C311yescharacteristic
226C8×Dic3C22×C311yescharacteristic
227#810C22×C311yescharacteristic
228#809C22×C311yescharacteristic
229#808C22×C311yescharacteristic
230#807C22×C311yescharacteristic
231C4⋊(C3⋊C8)C22×C311yescharacteristic
232C23×C32—21no—
233C23×C32—21no—
234C22×C3×D3—21no—
235C32×D4—21no—
236C32×D4—21no—
237C32×D4—21no—
238C32×D4#4112yes—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—81no—
242C2×C32×C4—81no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C3×#67—42no—
247C3×#67—81no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—42no—
252C2×C3×Dic3—81no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—21no—
258C3×D12—21no—
259C3×C4×D3—81no—
260C3×Dic6—22no—
261C3×Dic6—21no—
262C3×Dic6—21no—
263C3×Dic6—81no—
264C32×C8—21no—
265C32×C8—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268#559—31no—
269#554—31no—
270#488—31no—
271#488—31no—
272#486—31no—
273#478—31no—
274#478—31no—
275#477—31no—
276#463—31no—
277#463—31no—
278#459—31no—
279C8×Q8—31no—
280C4×SD16—31no—
281C4×D8—31no—
282C4×D8C3×D311yescharacteristic, complemented
283C2×C3×Q8—31no—
284C2×C3×Q8—31no—
285C2×C3×Q8—61no—
286C2×C3×D4—21no—
287C2×C3×D4—21no—
288C2×C3×D4—31no—
289C2×C3×D4—61no—
290C2×C3×D4—61no—
291C2×C3×D4C22×D311yescharacteristic
292C2×C3×D4C22×D311yescharacteristic
293C2×C3×D4C23×C311yescharacteristic
294C2×C3×D4C23×C311yescharacteristic
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—41no—
300C22×C3×C4—41no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C2×#67—21no—
305C2×#67—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C2×D12C23×C311yescharacteristic
309C2×C4×D3—21no—
310C2×Dic6—21no—
311C2×Dic6C3×D411yescharacteristic
312C2×Dic6C23×C311yescharacteristic
313C3×SD16—62no—
314C3×D8—24no—
315C3×D8—22no—
316C3×D8—22no—
317C3×D8—62no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—31no—
321C2×C3×C8—31no—
322C2×C3×C8C22×D311yescharacteristic
323C2×C3×C8C22×D311yescharacteristic
324C2×C3×C8C23×C311yescharacteristic
325C2×C3×C8C23×C311yescharacteristic
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C4⋊C4C23×C311yescharacteristic
342C3×C4⋊C4C23×C311yescharacteristic
343C3×C22⋊C4—21no—
344C3×C22⋊C4—21no—
345C3×C22⋊C4—21no—
346C3×C22⋊C4—21no—
347C3×C22⋊C4—41no—
348C3×C22⋊C4—41no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C42—21no—
357C3×C42—31no—
358C3×C42—31no—
359C3×C42—61no—
360C3×C42C22×D311yescharacteristic
361C3×C42C23×C311yescharacteristic
362#217—21no—
363#217—21no—
364#217—21no—
365#217—21no—
366#214—22no—
367#213—22no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371C4⋊Dic3—21no—
372C4⋊Dic3C3×D411yescharacteristic
373C4⋊Dic3C23×C311yescharacteristic
374C4⋊Dic3C23×C311yescharacteristic
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4C3×D411yescharacteristic
381Dic3⋊C4C3×D411yescharacteristic
382C4×Dic3—21no—
383C4×Dic3C23×C311yescharacteristic
384C4×Dic3C23×C311yescharacteristic
385C2×C3⋊C8C23×C311yescharacteristic
386C2×C3⋊C8C23×C311yescharacteristic
387C22×C32—22no—
388C22×C32—41no—
389C22×C32—41no—
390C22×C32—41no—
391C22×C32—41no—
392C22×C32—41no—
393C22×C32C22×D411yescharacteristic
394C2×C3×D3—41no—
395C2×C3×D3—41no—
396C2×C3×D3—41no—
397C32×C4—21no—
398C32×C4—21no—
399C32×C4—41no—
400C32×C4—41no—
401C32×C4C2×#4111yescharacteristic
402C32×C42−1+411yescharacteristic
403C3×Dic3—21no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C3×Dic3#13512yes—
410C2×SD16—31no—
411C2×D8—31no—
412C2×D8C2×C3×D311yescharacteristic
413C4⋊Q8—31no—
414#127—31no—
415#125—31no—
416#125—31no—
417#124—31no—
418#124—31no—
419#124—61no—
420#123—61no—
421#123—61no—
422C22⋊Q8—61no—
423C22⋊Q8—61no—
424C22⋊Q8—61no—
425C4×Q8—31no—
426C4×Q8—31no—
427C4×D4—31no—
428C4×D4—31no—
429C4×D4—31no—
430C4×D4—61no—
431C4×D4C2×C3×D311yescharacteristic
432C4×D4C2×C3×D311yescharacteristic
433C2×C4⋊C4—61no—
434#107—31no—
435#107C2×C3×D311yescharacteristic
436#106—31no—
437C4⋊C8—31no—
438C4⋊C8—31no—
439C4⋊C8—31no—
440#103—31no—
441#103—31no—
442#103—31no—
443#102—31no—
444#102—31no—
445#102—31no—
446#102—31no—
447#102—31no—
448#102C2×C3×D311yescharacteristic
449#102C2×C3×D311yescharacteristic
450C4×C8—31no—
451C4×C8—31no—
452C4×C8C2×C3×D311yescharacteristic
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—61no—
460C22×D3—21no—
461C3×Q8—62no—
462C3×Q8—61no—
463C3×Q8—61no—
464C3×Q8—241no—
465C3×D4—22no—
466C3×D4—21no—
467C3×D4—21no—
468C3×D4—21no—
469C3×D4—21no—
470C3×D4—21no—
471C3×D4—21no—
472C3×D4—22no—
473C3×D4—41no—
474C3×D4—41no—
475C3×D4—61no—
476C3×D4—61no—
477C3×D4—122no—
478C3×D4—241no—
479C3×D4#23512yes—
480C3×D4C3×#4112yes—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—81no—
498C2×C3×C4—81no—
499C2×C3×C4—81no—
500C2×C3×C4—81no—
501C2×C3×C4—82no—
502C2×C3×C4—82no—
503C2×C3×C4—122no—
504C2×C3×C4—241no—
505C2×C3×C4—241no—
506C2×C3×C4D3×D411yescharacteristic
507C2×C3×C4D3×D411yescharacteristic
508C2×C3×C4C2×C3×D411yescharacteristic
509C2×C3×C4C2×C3×D411yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C24×C311yescharacteristic
512#67—42no—
513#67—81no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—42no—
518C2×Dic3—81no—
519C2×Dic3C2×C3×D411yescharacteristic
520C2×Dic3C2×C3×D411yescharacteristic
521C2×Dic3C2×C3×D411yescharacteristic
522C2×Dic3C2×C3×D411yescharacteristic
523D12—21no—
524D12—21no—
525C4×D3—81no—
526Dic6—22no—
527Dic6—21no—
528Dic6—21no—
529Dic6—81no—
530C3×C8—22no—
531C3×C8—21no—
532C3×C8—21no—
533C3×C8—21no—
534C3×C8—21no—
535C3×C8—41no—
536C3×C8—61no—
537C3×C8—61no—
538C3⋊C8—21no—
539C3⋊C8—21no—
540C2×C32—42no—
541C2×C32—81no—
542C2×C32#54811yescharacteristic
543C2×C32C2×#13511yescharacteristic
544C2×C32#57611yescharacteristic
545C3×D3—81no—
546C2×Q8—31no—
547C2×Q8—31no—
548C2×Q8—61no—
549C2×D4—31no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4C22×C3×D311yescharacteristic
553C2×D4C22×C3×D311yescharacteristic
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559SD16—62no—
560D8—22no—
561D8—62no—
562C2×C8—31no—
563C2×C8—31no—
564C2×C8C22×C3×D311yescharacteristic
565C2×C8C22×C3×D311yescharacteristic
566C4⋊C4—31no—
567C4⋊C4—31no—
568C4⋊C4—31no—
569C4⋊C4—31no—
570C4⋊C4—31no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4—61no—
576C4⋊C4—61no—
577C4⋊C4C22×C3×D311yescharacteristic
578C4⋊C4C22×C3×D311yescharacteristic
579C22⋊C4—21no—
580C22⋊C4—21no—
581C22⋊C4—61no—
582C22⋊C4—61no—
583C22⋊C4—61no—
584C22⋊C4—61no—
585C22⋊C4—61no—
586C22⋊C4—61no—
587C22⋊C4—61no—
588C42—31no—
589C42—31no—
590C42—61no—
591C42C22×C3×D311yescharacteristic
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—21no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3—121no—
612C22×C3—121no—
613C22×C3—121no—
614C22×C3C2×D3×D411yescharacteristic
615C22×C3C22×C3×D411yescharacteristic
616C2×D3—41no—
617C2×D3—41no—
618C2×D3—41no—
619C3×C4—22no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—32no—
627C3×C4—41no—
628C3×C4—41no—
629C3×C4—41no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—61no—
633C3×C4—61no—
634C3×C4—61no—
635C3×C4—81no—
636C3×C4—81no—
637C3×C4—121no—
638C3×C4—121no—
639C3×C4—121no—
640C3×C4C2×#23511yescharacteristic
641C3×C4#101011yescharacteristic
642C3×C4C2×C3×#4111yescharacteristic
643C3×C4C3×2−1+411yescharacteristic
644Dic3—21no—
645Dic3—21no—
646Dic3—21no—
647Dic3—41no—
648Dic3—41no—
649Dic3—41no—
650Dic3C3×#13512yes—
651C32#336111yescharacteristic, complemented, Sylow
652C23—21no—
653C23—21no—
654C23—61no—
655Q8—62no—
656Q8—61no—
657Q8—61no—
658Q8—241no—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—61no—
663D4—61no—
664D4—122no—
665D4—241no—
666D4C3×#23512yes—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—31no—
670C2×C4—31no—
671C2×C4—31no—
672C2×C4—31no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—81no—
677C2×C4—81no—
678C2×C4—122no—
679C2×C4—241no—
680C2×C4—241no—
681C2×C4C3×D3×D411yescharacteristic
682C2×C4C3×D3×D411yescharacteristic
683C2×C4C23×C3×D311yescharacteristic
684C8—21no—
685C8—21no—
686C8—61no—
687C8—61no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—42no—
692C2×C3—42no—
693C2×C3—82no—
694C2×C3—82no—
695C2×C3—81no—
696C2×C3—81no—
697C2×C3—241no—
698C2×C3#555211yescharacteristic
699C2×C3#575711yescharacteristic
700C2×C3D3×#13511yescharacteristic
701C2×C3C3×#54811yescharacteristic
702C2×C3C2×C3×#13511yescharacteristic
703C2×C3C3×#57611yescharacteristic
704D3—81no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—121no—
712C22—121no—
713C22—121no—
714C22C2×C3×D3×D411yescharacteristic
715C4—21no—
716C4—21no—
717C4—32no—
718C4—41no—
719C4—41no—
720C4—61no—
721C4—61no—
722C4—61no—
723C4—121no—
724C4—121no—
725C4—121no—
726C4C2×C3×#23511yescharacteristic
727C4C3×#101011yescharacteristic
728C3—21no—
729C3#7956911yescharacteristic, direct product factor
730C3C3×#336111yescharacteristic, complemented
731C2—42no—
732C2—81no—
733C2—241no—
734C2C3×#555211yescharacteristic
735C2C3×#575711yescharacteristic
736C2C3×D3×#13511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×D8C2
socleC22×C32C22×D4
prime radicalC3×#5150C2
hypercenterC3×C4×D8D3
hypocenterC3C3×#3361
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×D8

Complements

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

NH ≅ G/Ntype
1. C3×#5559C2semidirect
2. C3×#5539C2semidirect
3. C32×C4×D8C2semidirect
4. C3×#5153C2semidirect
6. C3×#5016C2semidirect
7. C3×#5009C2semidirect
8. C3×#4891C2semidirect
9. C3×#4875C2semidirect
10. C3×#4768C2semidirect
11. C3×#4760C2semidirect
12. C3×#4758C2semidirect
13. C3×#4756C2semidirect
14. C3×#4697C2semidirect
15. C3×C8×Dic6C2semidirect
17. #79569C3direct (N × H)
63. #5559C2×C3semidirect
64. #5539C2×C3semidirect
78. C3×C4×D8D3semidirect
79. C3×C4×D8C2×C3semidirect
80. #5153C2×C3semidirect
82. #5016C2×C3semidirect
83. #5009C2×C3semidirect
84. #4891C2×C3semidirect
85. #4875C2×C3semidirect
86. #4768C2×C3semidirect
87. #4760C2×C3semidirect
88. #4758C2×C3semidirect
89. #4756C2×C3semidirect
90. #4697C2×C3semidirect
91. C8×Dic6C2×C3semidirect
282. C4×D8C3×D3semidirect
651. C32#3361semidirect
729. C3#79569direct (N × H)
730. C3C3×#3361semidirect

Maximal subgroups

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

subgroupindex
C3×#55592
C3×#55392
C32×C4×D82
C3×#51532
C3×#51502
C3×#50162
C3×#50092
C3×#48912
C3×#48752
C3×#47682
C3×#47602
C3×#47582
C3×#47562
C3×#46972
C3×C8×Dic62
C3×#33613
#795693