Finite Group Databasebeta

← C3×#81153 #11895934

Subgroups — C3×#81153 #11895934

Order 1152.

815 conjugacy classes of subgroups.

The subgroup lattice has 743 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5685C211yesmaximal, characteristic, complemented
2C3×#5553C211yesmaximal, characteristic
3C32×#478C211yesmaximal, characteristic, complemented
4C3×#5067C211yesmaximal, characteristic, complemented
5C3×#5018C211yesmaximal, characteristic, complemented
6C3×#4890C211yesmaximal, characteristic, complemented
7C3×#4889C211yesmaximal, characteristic, complemented
8C3×#4871C211yesmaximal, characteristic, complemented
9C3×#4852C211yesmaximal, characteristic, complemented
10C3×#4848C211yesmaximal, characteristic, complemented
11C3×#4828C211yesmaximal, characteristic, complemented
12C3×#4764C211yesmaximal, characteristic, complemented
13C3×#4762C211yesmaximal, characteristic, complemented
14C3×#4762C211yesmaximal, characteristic, complemented
15C3×#4760C211yesmaximal, characteristic, complemented
16C3×#3368—31nomaximal
17#81153C311yesmaximal, characteristic, direct product factor
18C2×C3×#235—21no—
19C32×#125C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C3×#940C2211yescharacteristic
22C3×#940C2211yescharacteristic
23C2×C3×#214C2211yescharacteristic
24C3×#930—21no—
25C2×C3×#204C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C3×#893C2211yescharacteristic
28C3×#893C2211yescharacteristic
29C3×#890C2211yescharacteristic
30C3×#889—21no—
31C3×#889—21no—
32C3×#888—21no—
33C3×#888C2211yescharacteristic
34C3×#887—21no—
35C3×#887C2211yescharacteristic
36C3×#887C2211yescharacteristic
37C3×#884—21no—
38C3×#884—21no—
39C3×#874C2211yescharacteristic
40C3×C4×Dic6C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C32×#107C2211yescharacteristic
43C32×#106C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×#102C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#815C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#809C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×#557—31no—
62C3×#550—31no—
63#5685C2×C311yescharacteristic, complemented
64#5553C2×C311yescharacteristic
65C3×#490—31no—
66C3×#490—31no—
67C3×#486—31no—
68C3×#478—21no—
69C3×#478—31no—
70C3×#478D311yescharacteristic, complemented
71C3×#478C2×C311yescharacteristic, complemented
72C3×#474—31no—
73C3×#460—31no—
74C3×#460—31no—
75C3×#460—31no—
76C3×#446—31no—
77C3×#440—31no—
78C3×#440—31no—
79C3×C4×SD16—31no—
80#5067C2×C311yescharacteristic, complemented
81#5018C2×C311yescharacteristic, complemented
82#4890C2×C311yescharacteristic, complemented
83#4889C2×C311yescharacteristic, complemented
84#4871C2×C311yescharacteristic, complemented
85#4852C2×C311yescharacteristic, complemented
86#4848C2×C311yescharacteristic, complemented
87#4828C2×C311yescharacteristic, complemented
88#4764C2×C311yescharacteristic, complemented
89#4762C2×C311yescharacteristic, complemented
90#4762C2×C311yescharacteristic, complemented
91#4760C2×C311yescharacteristic, complemented
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C3×#235—44no—
99C2×C3×D12—21no—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×Dic6—21no—
106C2×C3×Dic6D411yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4—21no—
111C32×C4⋊C4—21no—
112C32×C4⋊C4C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C32×C42C2311yescharacteristic
117C3×#214—22no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3D411yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4D411yescharacteristic
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×#204—22no—
138C3×#204—22no—
139#3368—31noSylow
140C2×C3×#41—61no—
141C2×#235—21no—
142C2×C3×SD16—31no—
143C2×C3×SD16—31no—
144C2×C3×SD16—31no—
145C3×C4⋊Q8—31no—
146C3×C4⋊Q8—61no—
147C3×#127—31no—
148C3×#127—31no—
149C3×#127—31no—
150C3×#125—21no—
151C3×#125—31no—
152C3×#125—61no—
153C3×#125—61no—
154C3×#125C2×D311yescharacteristic
155C3×#125C22×C311yescharacteristic
156C3×#121—61no—
157C3×#121—61no—
158C3×#121—61no—
159C3×C4×Q8—31no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—61no—
164C3×C4×D4—21no—
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C3×C4×D4C2×D311yescharacteristic
168C3×C4×D4C22×C311yescharacteristic
169#940C22×C311yescharacteristic
170#940C22×C311yescharacteristic
171C2×#214C22×C311yescharacteristic
172#930—21no—
173C2×#204C22×C311yescharacteristic
174C2×#204C22×C311yescharacteristic
175#893C22×C311yescharacteristic
176#893C22×C311yescharacteristic
177#890C22×C311yescharacteristic
178#889—21no—
179#889—21no—
180#888—21no—
181#888C22×C311yescharacteristic
182#887—21no—
183#887C22×C311yescharacteristic
184#887C22×C311yescharacteristic
185#884—21no—
186#884—21no—
187#874C22×C311yescharacteristic
188C4×Dic6C22×C311yescharacteristic
189C4×Dic6C22×C311yescharacteristic
190C3×#107—21no—
191C3×#107—31no—
192C3×#107C2×D311yescharacteristic
193C3×#107C22×C311yescharacteristic
194C3×#106—21no—
195C3×#106C2×D311yescharacteristic
196C3×#106C22×C311yescharacteristic
197C3×C4⋊C8—21no—
198C3×C4⋊C8—31no—
199C3×C4⋊C8—31no—
200C3×C4⋊C8C2×D311yescharacteristic
201C3×C4⋊C8C22×C311yescharacteristic
202C3×#103—31no—
203C3×#102—21no—
204C3×#102—21no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102C2×D311yescharacteristic
213C3×#102C2×D311yescharacteristic
214C3×#102C22×C311yescharacteristic
215C3×#102C22×C311yescharacteristic
216C3×#97—31no—
217C3×#97—31no—
218C3×C4×C8—31no—
219#832C22×C311yescharacteristic
220#821C22×C311yescharacteristic
221#821C22×C311yescharacteristic
222#815C22×C311yescharacteristic
223Dic3⋊C8C22×C311yescharacteristic
224Dic3⋊C8C22×C311yescharacteristic
225C8×Dic3C22×C311yescharacteristic
226#810C22×C311yescharacteristic
227#809C22×C311yescharacteristic
228#809C22×C311yescharacteristic
229#809C22×C311yescharacteristic
230#809C22×C311yescharacteristic
231#807C22×C311yescharacteristic
232#803C22×C311yescharacteristic
233C23×C32—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C32×D4—21no—
237C32×D4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—42no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C3×#67—42no—
246C3×#67—42no—
247C3×#67—81no—
248C3×#67—81no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×D12—21no—
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—42no—
260C3×D12—81no—
261C3×C4×D3—42no—
262C3×C4×D3—42no—
263C3×Dic6—21no—
264C3×Dic6—22no—
265C3×Dic6—42no—
266C3×Dic6#4112yescomplemented
267C32×C8—21no—
268C32×C8—21no—
269C3×C3⋊C8—21no—
270C3×C3⋊C8—21no—
271#557—31no—
272#550—31no—
273#490—31no—
274#490—31no—
275#486—31no—
276#478—31no—
277#478C3×D311yescharacteristic, complemented
278#474—31no—
279#460—31no—
280#460—31no—
281#460—31no—
282#446—31no—
283#440—31no—
284#440—31no—
285C4×SD16—31no—
286C3×#41—124no—
287C2×C3×Q8—31no—
288C2×C3×Q8—31no—
289C2×C3×Q8—61no—
290C2×C3×D4—21no—
291C2×C3×D4—31no—
292C2×C3×D4—31no—
293C2×C3×D4—61no—
294C2×C3×D4—61no—
295C2×C3×D4—61no—
296C2×C3×D4—61no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C2×C3×D4C22×D311yescharacteristic
300C2×C3×D4C23×C311yescharacteristic
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—41no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C2×#67—21no—
307C2×#67—21no—
308C2×#67—21no—
309C2×#67—21no—
310#235—44no—
311C2×D12—21no—
312C2×D12—21no—
313C2×D12C23×C311yescharacteristic
314C2×D12C23×C311yescharacteristic
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×Dic6—21no—
318C2×Dic6C3×D411yescharacteristic
319C2×Dic6C23×C311yescharacteristic
320C3×SD16—62no—
321C3×SD16—62no—
322C3×SD16—62no—
323C2×C3×C8—21no—
324C2×C3×C8—21no—
325C2×C3×C8—31no—
326C2×C3×C8—31no—
327C2×C3×C8C22×D311yescharacteristic
328C2×C3×C8C22×D311yescharacteristic
329C2×C3×C8C23×C311yescharacteristic
330C2×C3×C8C23×C311yescharacteristic
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—41no—
343C3×C4⋊C4—41no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C23×C311yescharacteristic
354C3×C4⋊C4C23×C311yescharacteristic
355C3×C4⋊C4C23×C311yescharacteristic
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—41no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C42—21no—
362C3×C42—31no—
363C3×C42—31no—
364C3×C42—61no—
365C3×C42—61no—
366C3×C42—61no—
367C3×C42C22×D311yescharacteristic
368C3×C42C23×C311yescharacteristic
369#214—22no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372C4⋊Dic3—21no—
373C4⋊Dic3C3×D411yescharacteristic
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×Dic3—21no—
384C4×Dic3—21no—
385C4×Dic3C23×C311yescharacteristic
386C4×Dic3C23×C311yescharacteristic
387C2×C3⋊C8C23×C311yescharacteristic
388C2×C3⋊C8C23×C311yescharacteristic
389#204—22no—
390#204—22no—
391C22×C32—41no—
392C22×C32—41no—
393C22×C32—41no—
394C22×C32C22×D411yescharacteristic
395C2×C3×D3—41no—
396C2×C3×D3—41no—
397C2×C3×D3—41no—
398C2×C3×D3—41no—
399C2×C3×D3—41no—
400C2×C3×D3—41no—
401C32×C4—21no—
402C32×C4—21no—
403C32×C4—41no—
404C32×C4—41no—
405C32×C4—41no—
406C32×C4C2×#4111yescharacteristic
407C32×C42−1+411yescharacteristic
408C3×Dic3—22no—
409C3×Dic3—21no—
410C3×Dic3—21no—
411C3×Dic3—21no—
412C3×Dic3—41no—
413C3×Dic3AGL(1,ℤ/8)12yes—
414C2×#41—61no—
415C2×SD16—31no—
416C2×SD16—31no—
417C2×SD16—31no—
418C4⋊Q8—31no—
419C4⋊Q8—61no—
420#127—31no—
421#127—31no—
422#127—31no—
423#125—31no—
424#125—61no—
425#125—61no—
426#125C2×C3×D311yescharacteristic
427#121—61no—
428#121—61no—
429#121—61no—
430C4×Q8—31no—
431C4×Q8—31no—
432C4×Q8—31no—
433C4×Q8—31no—
434C4×Q8—61no—
435C4×D4—31no—
436C4×D4—31no—
437C4×D4C2×C3×D311yescharacteristic
438#107—31no—
439#107C2×C3×D311yescharacteristic
440#106C2×C3×D311yescharacteristic
441C4⋊C8—31no—
442C4⋊C8—31no—
443C4⋊C8C2×C3×D311yescharacteristic
444#103—31no—
445#102—31no—
446#102—31no—
447#102—31no—
448#102—31no—
449#102—31no—
450#102—31no—
451#102—31no—
452#102C2×C3×D311yescharacteristic
453#102C2×C3×D311yescharacteristic
454#97—31no—
455#97—31no—
456C4×C8—31no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—41no—
460C23×C3—61no—
461C23×C3—61no—
462C22×D3—21no—
463C22×D3—21no—
464C3×Q8—32no—
465C3×Q8—62no—
466C3×Q8—61no—
467C3×Q8—122no—
468C3×D4—22no—
469C3×D4—21no—
470C3×D4—21no—
471C3×D4—21no—
472C3×D4—21no—
473C3×D4—41no—
474C3×D4—61no—
475C3×D4—61no—
476C3×D4—61no—
477C3×D4—61no—
478C3×D4—122no—
479C3×D4—122no—
480C3×D4—122no—
481C3×D4—241no—
482C3×D4—241no—
483C3×D4—241no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—42no—
501C2×C3×C4—42no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—82no—
505C2×C3×C4—122no—
506C2×C3×C4—122no—
507C2×C3×C4D3×D411yescharacteristic
508C2×C3×C4D3×D411yescharacteristic
509C2×C3×C4C2×C3×D411yescharacteristic
510C2×C3×C4C2×C3×D411yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512C2×C3×C4C24×C311yescharacteristic
513#67—42no—
514#67—42no—
515#67—81no—
516#67—81no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3C2×C3×D411yescharacteristic
520C2×Dic3C2×C3×D411yescharacteristic
521C2×Dic3C2×C3×D411yescharacteristic
522C2×Dic3C2×C3×D411yescharacteristic
523D12—21no—
524D12—21no—
525D12—21no—
526D12—21no—
527D12—42no—
528D12—81no—
529C4×D3—42no—
530C4×D3—42no—
531Dic6—21no—
532Dic6—22no—
533Dic6—42no—
534Dic6C3×#4112yescomplemented
535C3×C8—21no—
536C3×C8—21no—
537C3×C8—21no—
538C3×C8—21no—
539C3×C8—41no—
540C3×C8—41no—
541C3×C8—61no—
542C3×C8—61no—
543C3⋊C8—21no—
544C3⋊C8—21no—
545C2×C32—81no—
546C2×C32#54811yescharacteristic
547C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
548C2×C32#57711yescharacteristic
549C3×D3—81no—
550C3×D3—81no—
551#41—124no—
552C2×Q8—31no—
553C2×Q8—31no—
554C2×Q8—61no—
555C2×D4—31no—
556C2×D4—31no—
557C2×D4—61no—
558C2×D4—61no—
559C2×D4—61no—
560C2×D4—61no—
561C2×D4—61no—
562C2×D4—61no—
563C2×D4C22×C3×D311yescharacteristic
564C22×C4—21no—
565C22×C4—61no—
566C22×C4—61no—
567SD16—62no—
568SD16—62no—
569SD16—62no—
570C2×C8—31no—
571C2×C8—31no—
572C2×C8C22×C3×D311yescharacteristic
573C2×C8C22×C3×D311yescharacteristic
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—31no—
577C4⋊C4—31no—
578C4⋊C4—31no—
579C4⋊C4—31no—
580C4⋊C4—61no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4C22×C3×D311yescharacteristic
587C4⋊C4C22×C3×D311yescharacteristic
588C4⋊C4C22×C3×D311yescharacteristic
589C22⋊C4—21no—
590C22⋊C4—61no—
591C22⋊C4—61no—
592C42—31no—
593C42—31no—
594C42—61no—
595C42—61no—
596C42—61no—
597C42C22×C3×D311yescharacteristic
598C22×C3—21no—
599C22×C3—42no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3—121no—
609C22×C3—121no—
610C22×C3—121no—
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—
619C2×D3—41no—
620C2×D3—41no—
621C2×D3—41no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—32no—
629C3×C4—41no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—41no—
634C3×C4—41no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—62no—
638C3×C4—61no—
639C3×C4—61no—
640C3×C4—61no—
641C3×C4—81no—
642C3×C4—81no—
643C3×C4—81no—
644C3×C4—121no—
645C3×C4#100711yescharacteristic
646C3×C4D3×#4111yescharacteristic
647C3×C4C2×C3×#4111yescharacteristic
648C3×C4C3×2−1+411yescharacteristic
649Dic3—21no—
650Dic3—21no—
651Dic3—21no—
652Dic3—22no—
653Dic3—41no—
654Dic3C3×AGL(1,ℤ/8)12yes—
655C32#336811yescharacteristic, complemented, Sylow
656C23—21no—
657C23—61no—
658C23—61no—
659Q8—32no—
660Q8—62no—
661Q8—61no—
662Q8—122no—
663D4—21no—
664D4—21no—
665D4—61no—
666D4—61no—
667D4—61no—
668D4—61no—
669D4—122no—
670D4—122no—
671D4—122no—
672D4—241no—
673D4—241no—
674D4—241no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—31no—
681C2×C4—31no—
682C2×C4—42no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—122no—
686C2×C4—122no—
687C2×C4C3×D3×D411yescharacteristic
688C2×C4C3×D3×D411yescharacteristic
689C2×C4C23×C3×D311yescharacteristic
690C8—21no—
691C8—21no—
692C8—61no—
693C8—61no—
694C2×C3—21no—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—82no—
698C2×C3—81no—
699C2×C3—81no—
700C2×C3—241no—
701C2×C3—241no—
702C2×C3#563311yescharacteristic
703C2×C3#577011yescharacteristic
704C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
705C2×C3C3×#54811yescharacteristic
706C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
707C2×C3C3×#57711yescharacteristic
708D3—81no—
709D3—81no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—121no—
714C22—121no—
715C22—121no—
716C22—121no—
717C22—121no—
718C22—121no—
719C22C2×C3×D3×D411yescharacteristic
720C4—21no—
721C4—21no—
722C4—32no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—61no—
727C4—61no—
728C4—61no—
729C4—62no—
730C4—121no—
731C4C3×#100711yescharacteristic
732C4C3×D3×#4111yescharacteristic
733C3—21no—
734C3#8115311yescharacteristic, direct product factor
735C3C3×#336811yescharacteristic, complemented
736C2—81no—
737C2—241no—
738C2—241no—
739C2C3×#563311yescharacteristic
740C2C3×#577011yescharacteristic
741C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#478C2
socleC22×C32C22×D4
prime radicalC3×#5553C2
hypercenterC3×#478D3
hypocenterC3C3×#3368
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#478

Complements

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

NH ≅ G/Ntype
1. C3×#5685C2semidirect
3. C32×#478C2semidirect
4. C3×#5067C2semidirect
5. C3×#5018C2semidirect
6. C3×#4890C2semidirect
7. C3×#4889C2semidirect
8. C3×#4871C2semidirect
9. C3×#4852C2semidirect
10. C3×#4848C2semidirect
11. C3×#4828C2semidirect
12. C3×#4764C2semidirect
13. C3×#4762C2semidirect
14. C3×#4762C2semidirect
15. C3×#4760C2semidirect
17. #81153C3direct (N × H)
63. #5685C2×C3semidirect
70. C3×#478D3semidirect
71. C3×#478C2×C3semidirect
80. #5067C2×C3semidirect
81. #5018C2×C3semidirect
82. #4890C2×C3semidirect
83. #4889C2×C3semidirect
84. #4871C2×C3semidirect
85. #4852C2×C3semidirect
86. #4848C2×C3semidirect
87. #4828C2×C3semidirect
88. #4764C2×C3semidirect
89. #4762C2×C3semidirect
90. #4762C2×C3semidirect
91. #4760C2×C3semidirect
266. C3×Dic6#41semidirect
277. #478C3×D3semidirect
534. Dic6C3×#41semidirect
655. C32#3368semidirect
734. C3#81153direct (N × H)
735. C3C3×#3368semidirect

Maximal subgroups

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

subgroupindex
C3×#56852
C3×#55532
C32×#4782
C3×#50672
C3×#50182
C3×#48902
C3×#48892
C3×#48712
C3×#48522
C3×#48482
C3×#48282
C3×#47642
C3×#47622
C3×#47602
C3×#33683
#811533