Finite Group Databasebeta

← C3×#80518 #11895809

Subgroups — C3×#80518 #11895809

Order 1152.

806 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5671C211yesmaximal, characteristic, complemented
2C3×D4×Dic6C211yesmaximal, characteristic, complemented
3C32×#463C211yesmaximal, characteristic
4C3×#5164C211yesmaximal, characteristic, complemented
5C3×#5162C211yesmaximal, characteristic, complemented
6C3×#5153C211yesmaximal, characteristic
7C3×Dic3×D8C211yesmaximal, characteristic
8C3×#5055C211yesmaximal, characteristic, complemented
9C3×#5018C211yesmaximal, characteristic, complemented
10C3×#4850C211yesmaximal, characteristic, complemented
11C3×#4828C211yesmaximal, characteristic, complemented
12C3×#4793C211yesmaximal, characteristic, complemented
13C3×#4792C211yesmaximal, characteristic, complemented
14C3×#4765C211yesmaximal, characteristic, complemented
15C3×#4759C211yesmaximal, characteristic, complemented
16C3×#3367—31nomaximal
17#80518C311yesmaximal, characteristic, direct product factor
18C22×C3×Dic6—21no—
19C2×C32×SD16C2211yescharacteristic
20C2×C32×D8C2211yescharacteristic
21C32×#124C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×#944C2211yescharacteristic
25C3×#936C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic
28C3×D4×Dic3C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C3×#924—21no—
31C3×#888C2211yescharacteristic
32C3×#888C2211yescharacteristic
33C3×#879—21no—
34C3×#879—21no—
35C3×#878—21no—
36C3×#878—21no—
37C3×#878—21no—
38C3×#877—21no—
39C3×#869C2211yescharacteristic
40C3×C4×Dic6C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C32×C4⋊C8C2211yescharacteristic
43C32×#103C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#818C2211yescharacteristic
51C3×#818C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#815C2211yescharacteristic
55C3×Dic3⋊C8C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57C3×C8×Dic3C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×#556—31no—
62C3×D4×Q8—31no—
63#5671C2×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—21no—
72C3×#463—31no—
73C3×#463D311yescharacteristic
74C3×#463C2×C311yescharacteristic
75C3×#461—31no—
76C3×#446—31no—
77C3×#440—31no—
78C3×#440—31no—
79C3×C4×D8—31no—
80#5164C2×C311yescharacteristic, complemented
81#5162C2×C311yescharacteristic, complemented
82#5153C2×C311yescharacteristic
83Dic3×D8C2×C311yescharacteristic
84#5055C2×C311yescharacteristic, complemented
85#5018C2×C311yescharacteristic, complemented
86#4850C2×C311yescharacteristic, complemented
87#4828C2×C311yescharacteristic, complemented
88#4793C2×C311yescharacteristic, complemented
89#4792C2×C311yescharacteristic, complemented
90#4765C2×C311yescharacteristic, complemented
91#4759C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—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—
106C32×D8—22no—
107C2×C32×C8C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111C32×C22⋊C4—21no—
112C32×C22⋊C4—21no—
113C32×C42C2311yescharacteristic
114C3×#217—21no—
115C3×#217—21no—
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#214—22no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3D411yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
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×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—21no—
147C2×C3×D8C2×D311yescharacteristic
148C2×C3×D8C22×C311yescharacteristic
149C3×C4⋊Q8—31no—
150C3×C4⋊Q8—31no—
151C3×C4⋊Q8—31no—
152C3×C4⋊Q8—31no—
153C3×#126—61no—
154C3×#126—61no—
155C3×#124—21no—
156C3×#124—31no—
157C3×#124C2×D311yescharacteristic
158C3×#124C22×C311yescharacteristic
159C3×C22⋊Q8—61no—
160C3×C22⋊Q8—61no—
161C3×C22⋊Q8—61no—
162C3×C22⋊Q8—61no—
163C3×C4×Q8—31no—
164C3×C4×Q8—31no—
165C3×C4×Q8—31no—
166C3×C4×D4—21no—
167C3×C4×D4—31no—
168C3×C4×D4—31no—
169C3×C4×D4—31no—
170C3×C4×D4C2×D311yescharacteristic
171C3×C4×D4C22×C311yescharacteristic
172C3×#117—61no—
173Q8×Dic3C22×C311yescharacteristic
174#944C22×C311yescharacteristic
175#936C22×C311yescharacteristic
176D4×Dic3C22×C311yescharacteristic
177D4×Dic3C22×C311yescharacteristic
178D4×Dic3C22×C311yescharacteristic
179C2×#214C22×C311yescharacteristic
180#924—21no—
181#888C22×C311yescharacteristic
182#888C22×C311yescharacteristic
183#879—21no—
184#879—21no—
185#878—21no—
186#878—21no—
187#878—21no—
188#877—21no—
189#869C22×C311yescharacteristic
190C4×Dic6C22×C311yescharacteristic
191C4×Dic6C22×C311yescharacteristic
192C3×#107—31no—
193C3×#107—31no—
194C3×#107—31no—
195C3×C4⋊C8—21no—
196C3×C4⋊C8—31no—
197C3×C4⋊C8—31no—
198C3×C4⋊C8C2×D311yescharacteristic
199C3×C4⋊C8C22×C311yescharacteristic
200C3×#103—21no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103C2×D311yescharacteristic
207C3×#103C22×C311yescharacteristic
208C3×#102—21no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102C2×D311yescharacteristic
213C3×#102C22×C311yescharacteristic
214C3×#97—31no—
215C3×#97—31no—
216C3×C4×C8—31no—
217#835C22×C311yescharacteristic
218#835C22×C311yescharacteristic
219#832C22×C311yescharacteristic
220#832C22×C311yescharacteristic
221#832C22×C311yescharacteristic
222#818C22×C311yescharacteristic
223#818C22×C311yescharacteristic
224#816C22×C311yescharacteristic
225#816C22×C311yescharacteristic
226#815C22×C311yescharacteristic
227Dic3⋊C8C22×C311yescharacteristic
228Dic3⋊C8C22×C311yescharacteristic
229C8×Dic3C22×C311yescharacteristic
230#810C22×C311yescharacteristic
231#807C22×C311yescharacteristic
232#803C22×C311yescharacteristic
233C23×C32—21no—
234C23×C32—21no—
235C32×Q8—21no—
236C32×Q8—21no—
237C32×D4—21no—
238C32×D4—21no—
239C32×D4—21no—
240C32×D4#4112yes—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—42no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—42no—
252C2×C3×Dic3—42no—
253C2×C3×Dic3—42no—
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
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#463C3×D311yescharacteristic
278#461—31no—
279#446—31no—
280#440—31no—
281#440—31no—
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—21no—
294C2×C3×D4C22×D311yescharacteristic
295C2×C3×D4C22×D311yescharacteristic
296C2×C3×D4C23×C311yescharacteristic
297C2×C3×D4C23×C311yescharacteristic
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—41no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C2×Dic6—21no—
308C2×Dic6—21no—
309C2×Dic6—21no—
310C2×Dic6—44no—
311C2×Dic6C3×D411yescharacteristic
312C2×Dic6C23×C311yescharacteristic
313C3×SD16—22no—
314C3×SD16—22no—
315C3×SD16—42no—
316C3×SD16—62no—
317C3×D8—22no—
318C3×D8—22no—
319C3×D8—42no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8—31no—
323C2×C3×C8—31no—
324C2×C3×C8C22×D311yescharacteristic
325C2×C3×C8C22×D311yescharacteristic
326C2×C3×C8C23×C311yescharacteristic
327C2×C3×C8C23×C311yescharacteristic
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—31no—
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⋊C4—61no—
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C23×C311yescharacteristic
344C3×C22⋊C4—21no—
345C3×C22⋊C4—21no—
346C3×C22⋊C4—21no—
347C3×C22⋊C4—21no—
348C3×C22⋊C4—21no—
349C3×C22⋊C4—21no—
350C3×C22⋊C4—41no—
351C3×C22⋊C4—41no—
352C3×C22⋊C4—41no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C42—21no—
359C3×C42—31no—
360C3×C42—31no—
361C3×C42—61no—
362C3×C42—61no—
363C3×C42C22×D311yescharacteristic
364C3×C42C23×C311yescharacteristic
365#217—21no—
366#217—21no—
367#217—21no—
368#217—21no—
369#217—21no—
370#214—22no—
371C4⋊Dic3—21no—
372C4⋊Dic3—21no—
373C4⋊Dic3C3×D411yescharacteristic
374C4⋊Dic3C23×C311yescharacteristic
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×Dic3—21no—
386C4×Dic3C23×C311yescharacteristic
387C4×Dic3C23×C311yescharacteristic
388C2×C3⋊C8C23×C311yescharacteristic
389C2×C3⋊C8C23×C311yescharacteristic
390C22×C32—22no—
391C22×C32—41no—
392C22×C32—41no—
393C22×C32—41no—
394C22×C32—41no—
395C22×C32—41no—
396C22×C32C22×D411yescharacteristic
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—41no—
410C3×Dic3AGL(1,ℤ/8)12yes—
411C22×Q8—61no—
412C2×SD16—31no—
413C2×SD16C2×C3×D311yescharacteristic
414C2×D8C2×C3×D311yescharacteristic
415C4⋊Q8—31no—
416C4⋊Q8—31no—
417C4⋊Q8—31no—
418C4⋊Q8—31no—
419#126—61no—
420#126—61no—
421#124—31no—
422#124C2×C3×D311yescharacteristic
423C22⋊Q8—61no—
424C22⋊Q8—61no—
425C22⋊Q8—61no—
426C22⋊Q8—61no—
427C4×Q8—31no—
428C4×Q8—31no—
429C4×Q8—31no—
430C4×D4—31no—
431C4×D4—31no—
432C4×D4—31no—
433C4×D4C2×C3×D311yescharacteristic
434#117—61no—
435#107—31no—
436#107—31no—
437#107—31no—
438C4⋊C8—31no—
439C4⋊C8—31no—
440C4⋊C8C2×C3×D311yescharacteristic
441#103—31no—
442#103—31no—
443#103—31no—
444#103—31no—
445#103—31no—
446#103C2×C3×D311yescharacteristic
447#102—31no—
448#102—31no—
449#102—31no—
450#102C2×C3×D311yescharacteristic
451#97—31no—
452#97—31no—
453C4×C8—31no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—41no—
459C23×C3—41no—
460C3×Q8—21no—
461C3×Q8—21no—
462C3×Q8—21no—
463C3×Q8—21no—
464C3×Q8—41no—
465C3×Q8—41no—
466C3×Q8—62no—
467C3×Q8—61no—
468C3×Q8—61no—
469C3×Q8—122no—
470C3×Q8—122no—
471C3×Q8—122no—
472C3×D4—21no—
473C3×D4—21no—
474C3×D4—21no—
475C3×D4—21no—
476C3×D4—21no—
477C3×D4—21no—
478C3×D4—22no—
479C3×D4—41no—
480C3×D4—41no—
481C3×D4—41no—
482C3×D4#23712yes—
483C3×D4C3×#4112yes—
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—31no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—42no—
498C2×C3×C4—42no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—82no—
504C2×C3×C4—122no—
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
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—42no—
518C2×Dic3—42no—
519C2×Dic3—42no—
520C2×Dic3C2×C3×D411yescharacteristic
521C2×Dic3C2×C3×D411yescharacteristic
522C2×Dic3C2×C3×D411yescharacteristic
523C2×Dic3C2×C3×D411yescharacteristic
524Dic6—22no—
525Dic6—21no—
526Dic6—21no—
527Dic6—42no—
528Dic6—42no—
529Dic6—42no—
530C3×C8—21no—
531C3×C8—21no—
532C3×C8—21no—
533C3×C8—21no—
534C3×C8—41no—
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×AGL(1,ℤ/8)11yescharacteristic
544C2×C32#57811yescharacteristic
545C2×Q8—31no—
546C2×Q8—31no—
547C2×Q8—61no—
548C2×Q8—61no—
549C2×Q8—61no—
550C2×Q8—124no—
551C2×Q8C22×C3×D311yescharacteristic
552C2×D4C22×C3×D311yescharacteristic
553C2×D4C22×C3×D311yescharacteristic
554C22×C4—21no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558SD16—22no—
559SD16—62no—
560D8—22no—
561C2×C8—31no—
562C2×C8—31no—
563C2×C8C22×C3×D311yescharacteristic
564C2×C8C22×C3×D311yescharacteristic
565C4⋊C4—31no—
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⋊C4—61no—
578C4⋊C4C22×C3×D311yescharacteristic
579C22⋊C4—21no—
580C22⋊C4—21no—
581C22⋊C4—21no—
582C22⋊C4—61no—
583C22⋊C4—61no—
584C22⋊C4—61no—
585C22⋊C4—61no—
586C22⋊C4—61no—
587C42—31no—
588C42—31no—
589C42—61no—
590C42—61no—
591C42C22×C3×D311yescharacteristic
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—21no—
595C22×C3—42no—
596C22×C3—41no—
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—81no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3C2×D3×D411yescharacteristic
612C22×C3C22×C3×D411yescharacteristic
613C3×C4—21no—
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—21no—
619C3×C4—32no—
620C3×C4—41no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—61no—
627C3×C4—61no—
628C3×C4—61no—
629C3×C4—81no—
630C3×C4—81no—
631C3×C4—121no—
632C3×C4—121no—
633C3×C4—121no—
634C3×C4—121no—
635C3×C4C2×#23711yescharacteristic
636C3×C4#101011yescharacteristic
637C3×C4C2×C3×#4111yescharacteristic
638C3×C4C3×2−1+411yescharacteristic
639Dic3—21no—
640Dic3—21no—
641Dic3—21no—
642Dic3—41no—
643Dic3—41no—
644Dic3—41no—
645Dic3—41no—
646Dic3C3×AGL(1,ℤ/8)12yes—
647C32#336711yescharacteristic, complemented, Sylow
648C23—21no—
649C23—21no—
650Q8—21no—
651Q8—21no—
652Q8—62no—
653Q8—61no—
654Q8—61no—
655Q8—122no—
656Q8—122no—
657Q8—122no—
658D4—21no—
659D4—21no—
660D4—21no—
661D4C3×#23712yes—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—31no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—42no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—122no—
674C2×C4—122no—
675C2×C4—122no—
676C2×C4C3×D3×D411yescharacteristic
677C2×C4C3×D3×D411yescharacteristic
678C2×C4C23×C3×D311yescharacteristic
679C8—21no—
680C8—21no—
681C8—61no—
682C8—61no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—42no—
687C2×C3—42no—
688C2×C3—82no—
689C2×C3—81no—
690C2×C3—81no—
691C2×C3—161no—
692C2×C3#559811yescharacteristic
693C2×C3#577111yescharacteristic
694C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
695C2×C3C3×#54811yescharacteristic
696C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
697C2×C3C3×#57811yescharacteristic
698C22—22no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22C2×C3×D3×D411yescharacteristic
705C4—21no—
706C4—21no—
707C4—32no—
708C4—41no—
709C4—41no—
710C4—61no—
711C4—61no—
712C4—61no—
713C4—121no—
714C4—121no—
715C4—121no—
716C4—121no—
717C4C2×C3×#23711yescharacteristic
718C4C3×#101011yescharacteristic
719C3—21no—
720C3#8051811yescharacteristic, direct product factor
721C3C3×#336711yescharacteristic, complemented
722C2—42no—
723C2—81no—
724C2C3×#559811yescharacteristic
725C2C3×#577111yescharacteristic
726C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#463C2
socleC22×C32C22×D4
prime radicalC2×C32×D8C22
hypercenterC3×#463D3
hypocenterC3C3×#3367
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#463

Complements

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

NH ≅ G/Ntype
1. C3×#5671C2semidirect
2. C3×D4×Dic6C2semidirect
4. C3×#5164C2semidirect
5. C3×#5162C2semidirect
8. C3×#5055C2semidirect
9. C3×#5018C2semidirect
10. C3×#4850C2semidirect
11. C3×#4828C2semidirect
12. C3×#4793C2semidirect
13. C3×#4792C2semidirect
14. C3×#4765C2semidirect
15. C3×#4759C2semidirect
17. #80518C3direct (N × H)
63. #5671C2×C3semidirect
64. D4×Dic6C2×C3semidirect
80. #5164C2×C3semidirect
81. #5162C2×C3semidirect
84. #5055C2×C3semidirect
85. #5018C2×C3semidirect
86. #4850C2×C3semidirect
87. #4828C2×C3semidirect
88. #4793C2×C3semidirect
89. #4792C2×C3semidirect
90. #4765C2×C3semidirect
91. #4759C2×C3semidirect
647. C32#3367semidirect
720. C3#80518direct (N × H)
721. C3C3×#3367semidirect

Maximal subgroups

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

subgroupindex
C3×#56712
C3×D4×Dic62
C32×#4632
C3×#51642
C3×#51622
C3×#51532
C3×Dic3×D82
C3×#50552
C3×#50182
C3×#48502
C3×#48282
C3×#47932
C3×#47922
C3×#47652
C3×#47592
C3×#33673
#805183