Finite Group Databasebeta

← C3×#81709 #11895916

Subgroups — C3×#81709 #11895916

Order 1152.

819 conjugacy classes of subgroups.

The subgroup lattice has 749 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5718C211yesmaximal, characteristic
2C3×#5685C211yesmaximal, characteristic, complemented
3C32×#490C211yesmaximal, characteristic, complemented
4C3×#5075C211yesmaximal, characteristic, complemented
5C3×#5066C211yesmaximal, characteristic, complemented
6C3×#4766C211yesmaximal, characteristic, complemented
7C3×#4764C211yesmaximal, characteristic, complemented
8C3×#4762C211yesmaximal, characteristic, complemented
9C3×#4762C211yesmaximal, characteristic, complemented
10C3×#4760C211yesmaximal, characteristic, complemented
11C3×#4759C211yesmaximal, characteristic, complemented
12C3×#4758C211yesmaximal, characteristic, complemented
13C3×#4757C211yesmaximal, characteristic, complemented
14C3×#4710C211yesmaximal, characteristic, complemented
15C3×#4701C211yesmaximal, characteristic, complemented
16C3×#3368—31nomaximal
17#81709C311yesmaximal, characteristic, direct product factor
18C2×C3×#237—21no—
19C32×#127C2211yescharacteristic
20C32×#125C2211yescharacteristic
21C3×#940C2211yescharacteristic
22C3×#940C2211yescharacteristic
23C3×#939—21no—
24C3×#939—21no—
25C3×#938—21no—
26C3×D4×Dic3C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C2×C3×#204C2211yescharacteristic
31C3×#890C2211yescharacteristic
32C3×#889—21no—
33C3×#889—21no—
34C3×#888—21no—
35C3×#888C2211yescharacteristic
36C3×#887—21no—
37C3×#887C2211yescharacteristic
38C3×#887C2211yescharacteristic
39C3×C4×D12C2211yescharacteristic
40C3×C4×Dic6C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C32×#102C2211yescharacteristic
43C32×#102C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×#97C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#818C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×C8×Dic3C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#557—31no—
62C3×#550—31no—
63#5718C2×C311yescharacteristic
64#5685C2×C311yescharacteristic, complemented
65C3×#490—21no—
66C3×#490—31no—
67C3×#490D311yescharacteristic, complemented
68C3×#490C2×C311yescharacteristic, complemented
69C3×#486—31no—
70C3×#478—31no—
71C3×#478—31no—
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#5075C2×C311yescharacteristic, complemented
81#5066C2×C311yescharacteristic, complemented
82#4766C2×C311yescharacteristic, complemented
83#4764C2×C311yescharacteristic, complemented
84#4762C2×C311yescharacteristic, complemented
85#4762C2×C311yescharacteristic, complemented
86#4760C2×C311yescharacteristic, complemented
87#4759C2×C311yescharacteristic, complemented
88#4758C2×C311yescharacteristic, complemented
89#4757C2×C311yescharacteristic, complemented
90#4710C2×C311yescharacteristic, complemented
91#4701C2×C311yescharacteristic, complemented
92C2×C32×D4—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C3×#237—44no—
103C2×C3×D12C2311yescharacteristic
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×C42C2311yescharacteristic
115C3×#217—21no—
116C3×#217—21no—
117C3×#214—22no—
118C3×#214—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3D411yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×#204—22no—
139#3368—31noSylow
140C2×C3×#41—61no—
141C2×#237—21no—
142C2×C3×SD16—31no—
143C2×C3×SD16—31no—
144C2×C3×SD16—31no—
145C3×C4⋊Q8—31no—
146C3×C4⋊Q8—61no—
147C3×#127—21no—
148C3×#127—31no—
149C3×#127—31no—
150C3×#127C2×D311yescharacteristic
151C3×#127C22×C311yescharacteristic
152C3×#125—21no—
153C3×#125—31no—
154C3×#125—61no—
155C3×#125—61no—
156C3×#125C2×D311yescharacteristic
157C3×#125C22×C311yescharacteristic
158C3×#121—61no—
159C3×#121—61no—
160C3×#121—61no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—31no—
164C3×C4×Q8—31no—
165C3×C4×Q8—61no—
166C3×C4×D4—31no—
167C3×C4×D4—31no—
168C3×C4×D4—31no—
169#940C22×C311yescharacteristic
170#940C22×C311yescharacteristic
171#939—21no—
172#939—21no—
173#938—21no—
174D4×Dic3C22×C311yescharacteristic
175D4×Dic3C22×C311yescharacteristic
176C2×#214C22×C311yescharacteristic
177C2×#214C22×C311yescharacteristic
178C2×#204C22×C311yescharacteristic
179#890C22×C311yescharacteristic
180#889—21no—
181#889—21no—
182#888—21no—
183#888C22×C311yescharacteristic
184#887—21no—
185#887C22×C311yescharacteristic
186#887C22×C311yescharacteristic
187C4×D12C22×C311yescharacteristic
188C4×Dic6C22×C311yescharacteristic
189C4×Dic6C22×C311yescharacteristic
190C3×#107—31no—
191C3×#107—31no—
192C3×#106—31no—
193C3×C4⋊C8—31no—
194C3×C4⋊C8—31no—
195C3×C4⋊C8—31no—
196C3×#103—31no—
197C3×#102—21no—
198C3×#102—21no—
199C3×#102—21no—
200C3×#102—21no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102C2×D311yescharacteristic
207C3×#102C2×D311yescharacteristic
208C3×#102C2×D311yescharacteristic
209C3×#102C2×D311yescharacteristic
210C3×#102C22×C311yescharacteristic
211C3×#102C22×C311yescharacteristic
212C3×#102C22×C311yescharacteristic
213C3×#102C22×C311yescharacteristic
214C3×#97—21no—
215C3×#97—31no—
216C3×#97C2×D311yescharacteristic
217C3×#97C22×C311yescharacteristic
218C3×C4×C8—31no—
219#832C22×C311yescharacteristic
220#832C22×C311yescharacteristic
221#821C22×C311yescharacteristic
222#818C22×C311yescharacteristic
223#816C22×C311yescharacteristic
224#815C22×C311yescharacteristic
225Dic3⋊C8C22×C311yescharacteristic
226Dic3⋊C8C22×C311yescharacteristic
227C8×Dic3C22×C311yescharacteristic
228#809C22×C311yescharacteristic
229#809C22×C311yescharacteristic
230#808C22×C311yescharacteristic
231#807C22×C311yescharacteristic
232C4⋊(C3⋊C8)C22×C311yescharacteristic
233C23×C32—21no—
234C23×C32—21no—
235C22×C3×D3—21no—
236C32×D4—21no—
237C32×D4—21no—
238C32×D4—21no—
239C32×D4—21no—
240C32×D4—42no—
241C32×D4—81no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C3×#67—42no—
248C3×#67—42no—
249C3×#67—81no—
250C3×#67—81no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—42no—
255C2×C3×Dic3—42no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12—21no—
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#490C3×D311yescharacteristic, complemented
275#486—31no—
276#478—31no—
277#478—31no—
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—21no—
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—31no—
297C2×C3×D4—41no—
298C2×C3×D4—41no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C2×C3×D4—61no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C23×C311yescharacteristic
306C2×C3×D4C23×C311yescharacteristic
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C2×#67—21no—
311C2×#67—21no—
312C2×#67—21no—
313C2×#67—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316#237—44no—
317C2×D12C23×C311yescharacteristic
318C2×C4×D3—21no—
319C2×Dic6—21no—
320C2×Dic6C3×D411yescharacteristic
321C2×Dic6C23×C311yescharacteristic
322C3×SD16—62no—
323C3×SD16—62no—
324C3×SD16—62no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—31no—
328C2×C3×C8—31no—
329C2×C3×C8C22×D311yescharacteristic
330C2×C3×C8C22×D311yescharacteristic
331C2×C3×C8C23×C311yescharacteristic
332C2×C3×C8C23×C311yescharacteristic
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—41no—
345C3×C4⋊C4—41no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C23×C311yescharacteristic
355C3×C4⋊C4C23×C311yescharacteristic
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C42—21no—
360C3×C42—31no—
361C3×C42—31no—
362C3×C42—61no—
363C3×C42—61no—
364C3×C42—61no—
365C3×C42C22×D311yescharacteristic
366C3×C42C23×C311yescharacteristic
367#217—21no—
368#217—21no—
369#214—22no—
370#214—22no—
371(C2×D3)⋊C4—21no—
372C4⋊Dic3—21no—
373C4⋊Dic3C3×D411yescharacteristic
374C4⋊Dic3C23×C311yescharacteristic
375C4⋊Dic3C23×C311yescharacteristic
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4C3×D411yescharacteristic
382Dic3⋊C4C3×D411yescharacteristic
383C4×Dic3—21no—
384C4×Dic3—21no—
385C4×Dic3—21no—
386C4×Dic3C23×C311yescharacteristic
387C4×Dic3C23×C311yescharacteristic
388C2×C3⋊C8C23×C311yescharacteristic
389C2×C3⋊C8C23×C311yescharacteristic
390#204—22no—
391C22×C32—41no—
392C22×C32—41no—
393C22×C32—41no—
394C22×C32—41no—
395C22×C32—41no—
396C22×C32—41no—
397C22×C32C22×D411yescharacteristic
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×C4C2×#4111yescharacteristic
406C32×C42−1+411yescharacteristic
407C3×Dic3—22no—
408C3×Dic3—21no—
409C3×Dic3—21no—
410C3×Dic3—21no—
411C3×Dic3—41no—
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#127C2×C3×D311yescharacteristic
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×D4—31no—
438#107—31no—
439#107—31no—
440#106—31no—
441C4⋊C8—31no—
442C4⋊C8—31no—
443C4⋊C8—31no—
444#103—31no—
445#102—31no—
446#102—31no—
447#102—31no—
448#102—31no—
449#102—31no—
450#102C2×C3×D311yescharacteristic
451#102C2×C3×D311yescharacteristic
452#102C2×C3×D311yescharacteristic
453#102C2×C3×D311yescharacteristic
454#97—31no—
455#97C2×C3×D311yescharacteristic
456C4×C8—31no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—61no—
464C22×D3—21no—
465C3×Q8—32no—
466C3×Q8—62no—
467C3×Q8—61no—
468C3×Q8—122no—
469C3×D4—21no—
470C3×D4—21no—
471C3×D4—21no—
472C3×D4—21no—
473C3×D4—21no—
474C3×D4—21no—
475C3×D4—21no—
476C3×D4—21no—
477C3×D4—41no—
478C3×D4—41no—
479C3×D4—41no—
480C3×D4—41no—
481C3×D4—42no—
482C3×D4—42no—
483C3×D4—61no—
484C3×D4—61no—
485C3×D4—82no—
486C3×D4—81no—
487C3×D4—81no—
488C3×D4—82no—
489C3×D4—122no—
490C3×D4—122no—
491C3×D4—241no—
492C3×D4—241no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—122no—
510C2×C3×C4—122no—
511C2×C3×C4—122no—
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4C2×C3×D411yescharacteristic
515C2×C3×C4C2×C3×D411yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C24×C311yescharacteristic
518#67—42no—
519#67—42no—
520#67—81no—
521#67—81no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—42no—
526C2×Dic3—42no—
527C2×Dic3C2×C3×D411yescharacteristic
528C2×Dic3C2×C3×D411yescharacteristic
529C2×Dic3C2×C3×D411yescharacteristic
530C2×Dic3C2×C3×D411yescharacteristic
531D12—21no—
532D12—21no—
533C4×D3—42no—
534Dic6—21no—
535Dic6—22no—
536Dic6—42no—
537Dic6C3×#4112yescomplemented
538C3×C8—21no—
539C3×C8—21no—
540C3×C8—21no—
541C3×C8—21no—
542C3×C8—41no—
543C3×C8—41no—
544C3×C8—61no—
545C3×C8—61no—
546C3⋊C8—21no—
547C3⋊C8—21no—
548C2×C32—81no—
549C2×C32—81no—
550C2×C32#54811yescharacteristic
551C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
552C2×C32#57711yescharacteristic
553C3×D3—81no—
554#41—124no—
555C2×Q8—31no—
556C2×Q8—31no—
557C2×Q8—61no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—31no—
561C2×D4—61no—
562C2×D4—61no—
563C2×D4—61no—
564C2×D4—61no—
565C2×D4C22×C3×D311yescharacteristic
566C2×D4C22×C3×D311yescharacteristic
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570SD16—62no—
571SD16—62no—
572SD16—62no—
573C2×C8—31no—
574C2×C8—31no—
575C2×C8C22×C3×D311yescharacteristic
576C2×C8C22×C3×D311yescharacteristic
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—31no—
582C4⋊C4—31no—
583C4⋊C4—31no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4C22×C3×D311yescharacteristic
591C4⋊C4C22×C3×D311yescharacteristic
592C22⋊C4—61no—
593C22⋊C4—61no—
594C22⋊C4—61no—
595C42—31no—
596C42—31no—
597C42—61no—
598C42—61no—
599C42—61no—
600C42C22×C3×D311yescharacteristic
601C22×C3—21no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—41no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—81no—
615C22×C3—81no—
616C22×C3—81no—
617C22×C3—81no—
618C22×C3—81no—
619C22×C3—81no—
620C22×C3—121no—
621C22×C3—121no—
622C22×C3—121no—
623C22×C3C2×D3×D411yescharacteristic
624C22×C3C22×C3×D411yescharacteristic
625C2×D3—41no—
626C2×D3—41no—
627C2×D3—41no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—32no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—62no—
642C3×C4—61no—
643C3×C4—61no—
644C3×C4—61no—
645C3×C4—81no—
646C3×C4—81no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4D3×#4111yescharacteristic
650C3×C4#101011yescharacteristic
651C3×C4C2×C3×#4111yescharacteristic
652C3×C4C3×2−1+411yescharacteristic
653Dic3—21no—
654Dic3—21no—
655Dic3—21no—
656Dic3—22no—
657Dic3—41no—
658Dic3—41no—
659Dic3C3×AGL(1,ℤ/8)12yes—
660C32#336811yescharacteristic, complemented, Sylow
661C23—21no—
662C23—21no—
663C23—61no—
664Q8—32no—
665Q8—62no—
666Q8—61no—
667Q8—122no—
668D4—21no—
669D4—21no—
670D4—21no—
671D4—21no—
672D4—42no—
673D4—61no—
674D4—61no—
675D4—81no—
676D4—122no—
677D4—122no—
678D4—241no—
679D4—241no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—31no—
683C2×C4—31no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—122no—
690C2×C4—122no—
691C2×C4—122no—
692C2×C4C3×D3×D411yescharacteristic
693C2×C4C3×D3×D411yescharacteristic
694C2×C4C23×C3×D311yescharacteristic
695C8—21no—
696C8—21no—
697C8—61no—
698C8—61no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—81no—
703C2×C3—81no—
704C2×C3—81no—
705C2×C3—81no—
706C2×C3—161no—
707C2×C3—161no—
708C2×C3—241no—
709C2×C3#567711yescharacteristic
710C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
711C2×C3#577511yescharacteristic
712C2×C3C3×#54811yescharacteristic
713C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
714C2×C3C3×#57711yescharacteristic
715D3—81no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—121no—
723C22—121no—
724C22—121no—
725C22C2×C3×D3×D411yescharacteristic
726C4—21no—
727C4—21no—
728C4—32no—
729C4—41no—
730C4—41no—
731C4—61no—
732C4—61no—
733C4—61no—
734C4—62no—
735C4—121no—
736C4—121no—
737C4C3×D3×#4111yescharacteristic
738C4C3×#101011yescharacteristic
739C3—21no—
740C3#8170911yescharacteristic, direct product factor
741C3C3×#336811yescharacteristic, complemented
742C2—81no—
743C2—81no—
744C2—241no—
745C2C3×#567711yescharacteristic
746C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
747C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#490C2
socleC22×C32C22×D4
prime radicalC3×#5718C2
hypercenterC3×#490D3
hypocenterC3C3×#3368
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#490

Complements

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

NH ≅ G/Ntype
2. C3×#5685C2semidirect
3. C32×#490C2semidirect
4. C3×#5075C2semidirect
5. C3×#5066C2semidirect
6. C3×#4766C2semidirect
7. C3×#4764C2semidirect
8. C3×#4762C2semidirect
9. C3×#4762C2semidirect
10. C3×#4760C2semidirect
11. C3×#4759C2semidirect
12. C3×#4758C2semidirect
13. C3×#4757C2semidirect
14. C3×#4710C2semidirect
15. C3×#4701C2semidirect
17. #81709C3direct (N × H)
64. #5685C2×C3semidirect
67. C3×#490D3semidirect
68. C3×#490C2×C3semidirect
80. #5075C2×C3semidirect
81. #5066C2×C3semidirect
82. #4766C2×C3semidirect
83. #4764C2×C3semidirect
84. #4762C2×C3semidirect
85. #4762C2×C3semidirect
86. #4760C2×C3semidirect
87. #4759C2×C3semidirect
88. #4758C2×C3semidirect
89. #4757C2×C3semidirect
90. #4710C2×C3semidirect
91. #4701C2×C3semidirect
266. C3×Dic6#41semidirect
274. #490C3×D3semidirect
537. Dic6C3×#41semidirect
660. C32#3368semidirect
740. C3#81709direct (N × H)
741. C3C3×#3368semidirect

Maximal subgroups

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

subgroupindex
C3×#57182
C3×#56852
C32×#4902
C3×#50752
C3×#50662
C3×#47662
C3×#47642
C3×#47622
C3×#47602
C3×#47592
C3×#47582
C3×#47572
C3×#47102
C3×#47012
C3×#33683
#817093