Finite Group Databasebeta

← C3×#79751 #11895827

Subgroups — C3×#79751 #11895827

Order 1152.

804 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5568C211yesmaximal, characteristic, complemented
2C3×D4×Dic6C211yesmaximal, characteristic, complemented
3C32×#440C211yesmaximal, characteristic, complemented
4C3×#5165C211yesmaximal, characteristic
5C3×#5162C211yesmaximal, characteristic, complemented
6C3×#5021C211yesmaximal, characteristic, complemented
7C3×#5016C211yesmaximal, characteristic
8C3×#4890C211yesmaximal, characteristic, complemented
9C3×#4875C211yesmaximal, characteristic, complemented
10C3×#4794C211yesmaximal, characteristic, complemented
11C3×#4792C211yesmaximal, characteristic, complemented
12C3×#4757C211yesmaximal, characteristic, complemented
13C3×#4756C211yesmaximal, characteristic
14C3×#4714C211yesmaximal, characteristic, complemented
15C3×#4701C211yesmaximal, characteristic, complemented
16C3×#3367—31nomaximal
17#79751C311yesmaximal, characteristic, direct product factor
18C22×C3×Dic6—21no—
19C2×C32×SD16C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C3×#944C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28C3×#924—21no—
29C3×#898—21no—
30C3×#896—21no—
31C3×#893C2211yescharacteristic
32C3×#888C2211yescharacteristic
33C3×#888C2211yescharacteristic
34C3×#887C2211yescharacteristic
35C3×#878—21no—
36C3×#878—21no—
37C3×#876—21no—
38C3×#875C2211yescharacteristic
39C3×#872—21no—
40C3×#869C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C32×#107C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×#97C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×C8×Dic3C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#807C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#556—31no—
62C3×D4×Q8—31no—
63#5568C2×C311yescharacteristic, complemented
64D4×Dic6C2×C311yescharacteristic, complemented
65C3×#489—31no—
66C3×#489—31no—
67C3×#487—31no—
68C3×#477—31no—
69C3×#477—31no—
70C3×#474—31no—
71C3×#463—31no—
72C3×#463—31no—
73C3×#461—31no—
74C3×#446—31no—
75C3×#440—21no—
76C3×#440—31no—
77C3×#440D311yescharacteristic, complemented
78C3×#440C2×C311yescharacteristic, complemented
79C3×C4×D8—31no—
80#5165C2×C311yescharacteristic
81#5162C2×C311yescharacteristic, complemented
82#5021C2×C311yescharacteristic, complemented
83#5016C2×C311yescharacteristic
84#4890C2×C311yescharacteristic, complemented
85#4875C2×C311yescharacteristic, complemented
86#4794C2×C311yescharacteristic, complemented
87#4792C2×C311yescharacteristic, complemented
88#4757C2×C311yescharacteristic, complemented
89#4756C2×C311yescharacteristic
90#4714C2×C311yescharacteristic, complemented
91#4701C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×Dic6—21no—
100C2×C3×Dic6—21no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6—44no—
103C2×C3×Dic6D411yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C32×SD16—22no—
106C2×C32×C8C2311yescharacteristic
107C2×C32×C8C2311yescharacteristic
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C32×C42—21no—
113C32×C42C2311yescharacteristic
114C3×#217—21no—
115C3×#217—21no—
116C3×#214—22no—
117C3×#213—22no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3D411yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4D411yescharacteristic
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139#3367—31noSylow
140C22×C3×Q8—61no—
141C22×Dic6—21no—
142C2×C3×SD16—21no—
143C2×C3×SD16—31no—
144C2×C3×SD16C2×D311yescharacteristic
145C2×C3×SD16C22×C311yescharacteristic
146C2×C3×D8—31no—
147C3×C4⋊Q8—31no—
148C3×C4⋊Q8—31no—
149C3×C4⋊Q8—31no—
150C3×C4⋊Q8—31no—
151C3×#126—61no—
152C3×#126—61no—
153C3×#124—31no—
154C3×#124—31no—
155C3×C22⋊Q8—61no—
156C3×C22⋊Q8—61no—
157C3×C22⋊Q8—61no—
158C3×C22⋊Q8—61no—
159C3×C4×Q8—21no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×Q8C2×D311yescharacteristic
163C3×C4×Q8C22×C311yescharacteristic
164C3×C4×D4—21no—
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C3×C4×D4—31no—
168C3×C4×D4C2×D311yescharacteristic
169C3×C4×D4C22×C311yescharacteristic
170C3×#117—61no—
171#947C22×C311yescharacteristic
172#944C22×C311yescharacteristic
173D4×Dic3C22×C311yescharacteristic
174D4×Dic3C22×C311yescharacteristic
175C2×#214C22×C311yescharacteristic
176C2×#213C22×C311yescharacteristic
177#924—21no—
178#898—21no—
179#896—21no—
180#893C22×C311yescharacteristic
181#888C22×C311yescharacteristic
182#888C22×C311yescharacteristic
183#887C22×C311yescharacteristic
184#878—21no—
185#878—21no—
186#876—21no—
187#875C22×C311yescharacteristic
188#872—21no—
189#869C22×C311yescharacteristic
190C4×Dic6C22×C311yescharacteristic
191C3×#107—21no—
192C3×#107—31no—
193C3×#107—31no—
194C3×#107C2×D311yescharacteristic
195C3×#107C22×C311yescharacteristic
196C3×C4⋊C8—31no—
197C3×C4⋊C8—31no—
198C3×C4⋊C8—31no—
199C3×#103—21no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103C2×D311yescharacteristic
206C3×#103C22×C311yescharacteristic
207C3×#102—21no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102C2×D311yescharacteristic
212C3×#102C22×C311yescharacteristic
213C3×#97—21no—
214C3×#97—31no—
215C3×#97C2×D311yescharacteristic
216C3×#97C22×C311yescharacteristic
217C3×C4×C8—31no—
218#835C22×C311yescharacteristic
219#835C22×C311yescharacteristic
220#821C22×C311yescharacteristic
221#821C22×C311yescharacteristic
222#816C22×C311yescharacteristic
223#816C22×C311yescharacteristic
224#815C22×C311yescharacteristic
225Dic3⋊C8C22×C311yescharacteristic
226Dic3⋊C8C22×C311yescharacteristic
227C8×Dic3C22×C311yescharacteristic
228#810C22×C311yescharacteristic
229#809C22×C311yescharacteristic
230#807C22×C311yescharacteristic
231#807C22×C311yescharacteristic
232C4⋊(C3⋊C8)C22×C311yescharacteristic
233C23×C32—21no—
234C22×C3×D3—21no—
235C32×Q8—21no—
236C32×Q8—21no—
237C32×D4—21no—
238C32×D4#4112yes—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—42no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—42no—
250C2×C3×Dic3—42no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×D12—21no—
256C3×D12—21no—
257C3×C4×D3—42no—
258C3×Dic6—22no—
259C3×Dic6—21no—
260C3×Dic6—21no—
261C3×Dic6—42no—
262C3×Dic6—42no—
263C3×Dic6—42no—
264C32×C8—21no—
265C32×C8—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268#556—31no—
269D4×Q8—31no—
270#489—31no—
271#489—31no—
272#487—31no—
273#477—31no—
274#477—31no—
275#474—31no—
276#463—31no—
277#463—31no—
278#461—31no—
279#446—31no—
280#440—31no—
281#440C3×D311yescharacteristic, complemented
282C4×D8—31no—
283C2×C3×Q8—21no—
284C2×C3×Q8—31no—
285C2×C3×Q8—31no—
286C2×C3×Q8—61no—
287C2×C3×Q8—61no—
288C2×C3×Q8—61no—
289C2×C3×Q8—124no—
290C2×C3×Q8C22×D311yescharacteristic
291C2×C3×Q8C23×C311yescharacteristic
292C2×C3×D4—21no—
293C2×C3×D4—31no—
294C2×C3×D4C22×D311yescharacteristic
295C2×C3×D4C23×C311yescharacteristic
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—41no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C2×D12C23×C311yescharacteristic
305C2×C4×D3—21no—
306C2×Dic6—21no—
307C2×Dic6—21no—
308C2×Dic6—21no—
309C2×Dic6—44no—
310C2×Dic6C3×D411yescharacteristic
311C2×Dic6C23×C311yescharacteristic
312C3×SD16—24no—
313C3×SD16—22no—
314C3×SD16—22no—
315C3×SD16—62no—
316C3×D8—62no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—31no—
320C2×C3×C8—31no—
321C2×C3×C8C22×D311yescharacteristic
322C2×C3×C8C22×D311yescharacteristic
323C2×C3×C8C23×C311yescharacteristic
324C2×C3×C8C23×C311yescharacteristic
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—41no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C23×C311yescharacteristic
344C3×C4⋊C4C23×C311yescharacteristic
345C3×C22⋊C4—21no—
346C3×C22⋊C4—21no—
347C3×C22⋊C4—41no—
348C3×C22⋊C4—61no—
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×C42—21no—
356C3×C42—21no—
357C3×C42—21no—
358C3×C42—31no—
359C3×C42—31no—
360C3×C42—41no—
361C3×C42—61no—
362C3×C42C22×D311yescharacteristic
363C3×C42C23×C311yescharacteristic
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—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373C4⋊Dic3—21no—
374C4⋊Dic3C3×D411yescharacteristic
375C4⋊Dic3C23×C311yescharacteristic
376C4⋊Dic3C23×C311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4C3×D411yescharacteristic
383Dic3⋊C4C3×D411yescharacteristic
384C4×Dic3—21no—
385C4×Dic3C23×C311yescharacteristic
386C4×Dic3C23×C311yescharacteristic
387C2×C3⋊C8C23×C311yescharacteristic
388C2×C3⋊C8C23×C311yescharacteristic
389C22×C32—22no—
390C22×C32—41no—
391C22×C32—41no—
392C22×C32C22×D411yescharacteristic
393C2×C3×D3—41no—
394C2×C3×D3—41no—
395C2×C3×D3—41no—
396C32×C4—21no—
397C32×C4—21no—
398C32×C4—41no—
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×Dic3AGL(1,ℤ/8)12yes—
410C22×Q8—61no—
411C2×SD16—31no—
412C2×SD16C2×C3×D311yescharacteristic
413C2×D8—31no—
414C4⋊Q8—31no—
415C4⋊Q8—31no—
416C4⋊Q8—31no—
417C4⋊Q8—31no—
418#126—61no—
419#126—61no—
420#124—31no—
421#124—31no—
422C22⋊Q8—61no—
423C22⋊Q8—61no—
424C22⋊Q8—61no—
425C22⋊Q8—61no—
426C4×Q8—31no—
427C4×Q8—31no—
428C4×Q8C2×C3×D311yescharacteristic
429C4×D4—31no—
430C4×D4—31no—
431C4×D4—31no—
432C4×D4C2×C3×D311yescharacteristic
433#117—61no—
434#107—31no—
435#107—31no—
436#107C2×C3×D311yescharacteristic
437C4⋊C8—31no—
438C4⋊C8—31no—
439C4⋊C8—31no—
440#103—31no—
441#103—31no—
442#103—31no—
443#103—31no—
444#103—31no—
445#103C2×C3×D311yescharacteristic
446#102—31no—
447#102—31no—
448#102—31no—
449#102C2×C3×D311yescharacteristic
450#97—31no—
451#97C2×C3×D311yescharacteristic
452C4×C8—31no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—41no—
456C23×C3—61no—
457C22×D3—21no—
458C3×Q8—22no—
459C3×Q8—21no—
460C3×Q8—21no—
461C3×Q8—21no—
462C3×Q8—21no—
463C3×Q8—41no—
464C3×Q8—62no—
465C3×Q8—61no—
466C3×Q8—61no—
467C3×Q8—122no—
468C3×Q8—122no—
469C3×Q8—122no—
470C3×D4—21no—
471C3×D4—21no—
472C3×D4—22no—
473C3×D4—41no—
474C3×D4—61no—
475C3×D4—61no—
476C3×D4#23512yes—
477C3×D4C3×#4112yes—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
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—31no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—42no—
495C2×C3×C4—42no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—82no—
500C2×C3×C4—122no—
501C2×C3×C4—122no—
502C2×C3×C4—122no—
503C2×C3×C4D3×D411yescharacteristic
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4C2×C3×D411yescharacteristic
506C2×C3×C4C2×C3×D411yescharacteristic
507C2×C3×C4C23×D311yescharacteristic
508C2×C3×C4C24×C311yescharacteristic
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—42no—
513C2×Dic3—42no—
514C2×Dic3C2×C3×D411yescharacteristic
515C2×Dic3C2×C3×D411yescharacteristic
516C2×Dic3C2×C3×D411yescharacteristic
517C2×Dic3C2×C3×D411yescharacteristic
518D12—21no—
519D12—21no—
520C4×D3—42no—
521Dic6—22no—
522Dic6—21no—
523Dic6—21no—
524Dic6—42no—
525Dic6—42no—
526Dic6—42no—
527C3×C8—22no—
528C3×C8—21no—
529C3×C8—21no—
530C3×C8—21no—
531C3×C8—21no—
532C3×C8—41no—
533C3×C8—61no—
534C3×C8—61no—
535C3⋊C8—21no—
536C3⋊C8—21no—
537C2×C32—42no—
538C2×C32#54811yescharacteristic
539C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
540C2×C32#57811yescharacteristic
541C3×D3—81no—
542C2×Q8—31no—
543C2×Q8—31no—
544C2×Q8—61no—
545C2×Q8—61no—
546C2×Q8—61no—
547C2×Q8—124no—
548C2×Q8C22×C3×D311yescharacteristic
549C2×D4—31no—
550C2×D4C22×C3×D311yescharacteristic
551C22×C4—21no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555SD16—22no—
556SD16—62no—
557D8—62no—
558C2×C8—31no—
559C2×C8—31no—
560C2×C8C22×C3×D311yescharacteristic
561C2×C8C22×C3×D311yescharacteristic
562C4⋊C4—21no—
563C4⋊C4—31no—
564C4⋊C4—31no—
565C4⋊C4—31no—
566C4⋊C4—31no—
567C4⋊C4—31no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4—61no—
574C4⋊C4C22×C3×D311yescharacteristic
575C4⋊C4C22×C3×D311yescharacteristic
576C22⋊C4—21no—
577C22⋊C4—61no—
578C22⋊C4—61no—
579C22⋊C4—61no—
580C22⋊C4—61no—
581C22⋊C4—61no—
582C22⋊C4—61no—
583C22⋊C4—61no—
584C42—21no—
585C42—31no—
586C42—31no—
587C42—61no—
588C42C22×C3×D311yescharacteristic
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—21no—
592C22×C3—42no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—81no—
598C22×C3—81no—
599C22×C3—121no—
600C22×C3—121no—
601C22×C3—121no—
602C22×C3C2×D3×D411yescharacteristic
603C22×C3C22×C3×D411yescharacteristic
604C2×D3—41no—
605C2×D3—41no—
606C2×D3—41no—
607C3×C4—21no—
608C3×C4—21no—
609C3×C4—21no—
610C3×C4—21no—
611C3×C4—21no—
612C3×C4—21no—
613C3×C4—32no—
614C3×C4—41no—
615C3×C4—41no—
616C3×C4—42no—
617C3×C4—41no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—61no—
624C3×C4—61no—
625C3×C4—61no—
626C3×C4—81no—
627C3×C4—81no—
628C3×C4—121no—
629C3×C4—121no—
630C3×C4—121no—
631C3×C4C2×#23511yescharacteristic
632C3×C4#101011yescharacteristic
633C3×C4C2×C3×#4111yescharacteristic
634C3×C4C3×2−1+411yescharacteristic
635Dic3—21no—
636Dic3—21no—
637Dic3—21no—
638Dic3—41no—
639Dic3—41no—
640Dic3—41no—
641Dic3C3×AGL(1,ℤ/8)12yes—
642C32#336711yescharacteristic, complemented, Sylow
643C23—21no—
644C23—61no—
645Q8—21no—
646Q8—21no—
647Q8—62no—
648Q8—61no—
649Q8—61no—
650Q8—122no—
651Q8—122no—
652Q8—122no—
653D4—21no—
654D4—61no—
655D4—61no—
656D4C3×#23512yes—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—31no—
661C2×C4—31no—
662C2×C4—31no—
663C2×C4—31no—
664C2×C4—42no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—122no—
669C2×C4—122no—
670C2×C4—122no—
671C2×C4C3×D3×D411yescharacteristic
672C2×C4C3×D3×D411yescharacteristic
673C2×C4C23×C3×D311yescharacteristic
674C8—21no—
675C8—21no—
676C8—61no—
677C8—61no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—42no—
682C2×C3—42no—
683C2×C3—82no—
684C2×C3—241no—
685C2×C3#555211yescharacteristic
686C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
687C2×C3#577911yescharacteristic
688C2×C3C3×#54811yescharacteristic
689C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
690C2×C3C3×#57811yescharacteristic
691D3—81no—
692C22—22no—
693C22—41no—
694C22—41no—
695C22—121no—
696C22—121no—
697C22—121no—
698C22C2×C3×D3×D411yescharacteristic
699C4—21no—
700C4—21no—
701C4—32no—
702C4—41no—
703C4—41no—
704C4—41no—
705C4—61no—
706C4—61no—
707C4—61no—
708C4—121no—
709C4—121no—
710C4—121no—
711C4C2×C3×#23511yescharacteristic
712C4C3×#101011yescharacteristic
713C3—21no—
714C3#7975111yescharacteristic, direct product factor
715C3C3×#336711yescharacteristic, complemented
716C2—42no—
717C2—241no—
718C2C3×#555211yescharacteristic
719C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
720C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#440C2
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC3×#440D3
hypocenterC3C3×#3367
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#440

Complements

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

NH ≅ G/Ntype
1. C3×#5568C2semidirect
2. C3×D4×Dic6C2semidirect
3. C32×#440C2semidirect
5. C3×#5162C2semidirect
6. C3×#5021C2semidirect
8. C3×#4890C2semidirect
9. C3×#4875C2semidirect
10. C3×#4794C2semidirect
11. C3×#4792C2semidirect
12. C3×#4757C2semidirect
14. C3×#4714C2semidirect
15. C3×#4701C2semidirect
17. #79751C3direct (N × H)
63. #5568C2×C3semidirect
64. D4×Dic6C2×C3semidirect
77. C3×#440D3semidirect
78. C3×#440C2×C3semidirect
81. #5162C2×C3semidirect
82. #5021C2×C3semidirect
84. #4890C2×C3semidirect
85. #4875C2×C3semidirect
86. #4794C2×C3semidirect
87. #4792C2×C3semidirect
88. #4757C2×C3semidirect
90. #4714C2×C3semidirect
91. #4701C2×C3semidirect
281. #440C3×D3semidirect
642. C32#3367semidirect
714. C3#79751direct (N × H)
715. C3C3×#3367semidirect

Maximal subgroups

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

subgroupindex
C3×#55682
C3×D4×Dic62
C32×#4402
C3×#51652
C3×#51622
C3×#50212
C3×#50162
C3×#48902
C3×#48752
C3×#47942
C3×#47922
C3×#47572
C3×#47562
C3×#47142
C3×#47012
C3×#33673
#797513