Finite Group Databasebeta

← C3×#81348 #11870548

Subgroups — C3×#81348 #11870548

Order 1152.

845 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5600C211yesmaximal, characteristic, complemented
2C3×#5522C211yesmaximal, characteristic, complemented
3C32×#482C211yesmaximal, characteristic, complemented
4C3×#5037C211yesmaximal, characteristic
5C3×#4996C211yesmaximal, characteristic, complemented
6C3×#4891C211yesmaximal, characteristic, complemented
7C3×#4873C211yesmaximal, characteristic, complemented
8C3×#4857C211yesmaximal, characteristic, complemented
9C3×#4852C211yesmaximal, characteristic, complemented
10C3×#4787C211yesmaximal, characteristic, complemented
11C3×#4767C211yesmaximal, characteristic, complemented
12C3×#4758C211yesmaximal, characteristic, complemented
13C3×#4756C211yesmaximal, characteristic, complemented
14C3×#4733C211yesmaximal, characteristic, complemented
15C3×#4718C211yesmaximal, characteristic, complemented
16C3×#3102—31nomaximal
17#81348C311yesmaximal, characteristic, direct product factor
18C2×C3×#235C2211yescharacteristic
19C32×#121C2211yescharacteristic
20C32×#117C2211yescharacteristic
21C3×#936C2211yescharacteristic
22C3×#935—21no—
23C3×D4×Dic3—21no—
24C3×D4×Dic3C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C3×#924C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×Dic12C2211yescharacteristic
30C2×C3×#204C2211yescharacteristic
31C3×#893C2211yescharacteristic
32C3×#893C2211yescharacteristic
33C3×#890C2211yescharacteristic
34C3×#887C2211yescharacteristic
35C3×#887C2211yescharacteristic
36C3×#887C2211yescharacteristic
37C3×#67⋊C4—21no—
38C3×#67⋊C4—21no—
39C3×#879—21no—
40C3×#877—21no—
41C3×#872—21no—
42C3×C42×D3—21no—
43C32×#107C2211yescharacteristic
44C32×#106C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×#102C2211yescharacteristic
47C32×C22⋊C8C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#529—31no—
62C3×C4×#41—31no—
63#5600C2×C311yescharacteristic, complemented
64#5522C2×C311yescharacteristic, complemented
65C3×#485—31no—
66C3×#482—21no—
67C3×#482D311yescharacteristic, complemented
68C3×#482C2×C311yescharacteristic, complemented
69C3×#479—31no—
70C3×#478—31no—
71C3×#464—31no—
72C3×#463—31no—
73C3×#452—31no—
74C3×#449—31no—
75C3×C4×Q16—31no—
76C3×C4×SD16—31no—
77C3×C4×SD16—31no—
78C3×C4×D8—31no—
79C3×#431—31no—
80#5037C2×C311yescharacteristic
81#4996C2×C311yescharacteristic, complemented
82#4891C2×C311yescharacteristic, complemented
83#4873C2×C311yescharacteristic, complemented
84#4857C2×C311yescharacteristic, complemented
85#4852C2×C311yescharacteristic, complemented
86#4787C2×C311yescharacteristic, complemented
87#4767C2×C311yescharacteristic, complemented
88#4758C2×C311yescharacteristic, complemented
89#4756C2×C311yescharacteristic, complemented
90#4733C2×C311yescharacteristic, complemented
91#4718C2×C311yescharacteristic, complemented
92C2×C32×D4—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3D411yescharacteristic
98C22×C3×Dic3D411yescharacteristic
99C3×#235—22no—
100C3×#235—22no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C32×C8C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113C32×C22⋊C4—21no—
114C32×C42—21no—
115C3×#217—21no—
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#214—22no—
120C3×#213—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3D411yescharacteristic
134C3×C4×Dic3D411yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×Dic12—22no—
140C3×#204—22no—
141#3102—31noSylow
142C2×C3×#41—31no—
143C2×#235C22×C311yescharacteristic
144C2×C3×Q16—31no—
145C2×C3×SD16—31no—
146C2×C3×SD16—31no—
147C2×C3×D8—31no—
148C3×#126—61no—
149C3×#125—31no—
150C3×#124—31no—
151C3×#123—61no—
152C3×C22⋊Q8—31no—
153C3×#121—21no—
154C3×#121C2×D311yescharacteristic
155C3×#121C22×C311yescharacteristic
156C3×C4×Q8—31no—
157C3×C4×Q8—31no—
158C3×C4×Q8—31no—
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C3×C4×D4—61no—
163C3×C4×D4—61no—
164C3×C4×D4—61no—
165C3×#117—21no—
166C3×#117—61no—
167C3×#117—61no—
168C3×#117C2×D311yescharacteristic
169C3×#117C22×C311yescharacteristic
170C2×C3×C42—31no—
171C2×C3×C42—61no—
172#936C22×C311yescharacteristic
173#935—21no—
174D4×Dic3—21no—
175D4×Dic3C22×C311yescharacteristic
176C2×#214C22×C311yescharacteristic
177C2×#213C22×C311yescharacteristic
178#924C22×C311yescharacteristic
179C2×C4×Dic3C22×C311yescharacteristic
180C2×Dic12C22×C311yescharacteristic
181C2×#204C22×C311yescharacteristic
182#893C22×C311yescharacteristic
183#893C22×C311yescharacteristic
184#890C22×C311yescharacteristic
185#887C22×C311yescharacteristic
186#887C22×C311yescharacteristic
187#887C22×C311yescharacteristic
188#67⋊C4—21no—
189#67⋊C4—21no—
190#879—21no—
191#877—21no—
192#872—21no—
193C42×D3—21no—
194C3×#107—21no—
195C3×#107—31no—
196C3×#107C2×D311yescharacteristic
197C3×#107C22×C311yescharacteristic
198C3×#106—21no—
199C3×#106—31no—
200C3×#106C2×D311yescharacteristic
201C3×#106C22×C311yescharacteristic
202C3×C4⋊C8—31no—
203C3×C4⋊C8—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#102—21no—
209C3×#102—21no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102C2×D311yescharacteristic
213C3×#102C2×D311yescharacteristic
214C3×#102C22×C311yescharacteristic
215C3×#102C22×C311yescharacteristic
216C3×C22⋊C8—21no—
217C3×C22⋊C8—31no—
218C3×C22⋊C8C2×D311yescharacteristic
219C3×C22⋊C8C22×C311yescharacteristic
220C3×C4×C8—31no—
221C3×C4×C8—31no—
222#830C22×C311yescharacteristic
223#821C22×C311yescharacteristic
224#816C22×C311yescharacteristic
225Dic3⋊C8C22×C311yescharacteristic
226Dic3⋊C8C22×C311yescharacteristic
227C8×Dic3C22×C311yescharacteristic
228C8×Dic3C22×C311yescharacteristic
229#810C22×C311yescharacteristic
230#810C22×C311yescharacteristic
231#810C22×C311yescharacteristic
232#809C22×C311yescharacteristic
233#808C22×C311yescharacteristic
234#807C22×C311yescharacteristic
235C23×C32—21no—
236C23×C32C2×D411yescharacteristic
237C22×C3×D3—21no—
238C32×D4—21no—
239C32×D4—21no—
240C32×D4—42no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C3×#67—24no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—22no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—41no—
254C2×C3×Dic3—42no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12#4112yes—
261C3×C4×D3—24no—
262C3×C4×D3—42no—
263C3×C4×D3—42no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6#4112yes—
268C32×C8—21no—
269C32×C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#529—31no—
273C4×#41—31no—
274#485—31no—
275#482C3×D311yescharacteristic, complemented
276#479—31no—
277#478—31no—
278#464—31no—
279#463—31no—
280#452—31no—
281#449—31no—
282C4×Q16—31no—
283C4×SD16—31no—
284C4×SD16—31no—
285C4×D8—31no—
286#431—31no—
287C3×#41—62no—
288C3×#41—62no—
289C2×C3×Q8—31no—
290C2×C3×Q8—31no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4—31no—
295C2×C3×D4—41no—
296C2×C3×D4—61no—
297C2×C3×D4C22×D311yescharacteristic
298C2×C3×D4C23×C311yescharacteristic
299C22×C3×C4—21no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C23×C311yescharacteristic
308C2×#67—21no—
309C22×Dic3—21no—
310C22×Dic3C3×D411yescharacteristic
311C22×Dic3C3×D411yescharacteristic
312#235—22no—
313#235—22no—
314C2×D12C23×C311yescharacteristic
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×Dic6C23×C311yescharacteristic
319C2×Dic6C23×C311yescharacteristic
320C3×Q16—62no—
321C3×SD16—62no—
322C3×SD16—62no—
323C3×D8—62no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8—31no—
327C2×C3×C8—31no—
328C2×C3×C8C22×D311yescharacteristic
329C2×C3×C8C22×D311yescharacteristic
330C2×C3×C8C23×C311yescharacteristic
331C2×C3×C8C23×C311yescharacteristic
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—31no—
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⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C23×C311yescharacteristic
346C3×C4⋊C4C23×C311yescharacteristic
347C3×C4⋊C4C23×C311yescharacteristic
348C3×C22⋊C4—21no—
349C3×C22⋊C4—21no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—41no—
353C3×C22⋊C4—41no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C42—21no—
361C3×C42—21no—
362C3×C42—31no—
363C3×C42—31no—
364C3×C42—31no—
365C3×C42—31no—
366C3×C42—41no—
367C3×C42—61no—
368C3×C42—61no—
369C3×C42—61no—
370#217—21no—
371#217—21no—
372#217—21no—
373#217—21no—
374#214—22no—
375#213—22no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378C4⋊Dic3—21no—
379C4⋊Dic3C23×C311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3—21no—
388C4×Dic3C3×D411yescharacteristic
389C4×Dic3C3×D411yescharacteristic
390C4×Dic3C23×C311yescharacteristic
391C4×Dic3C23×C311yescharacteristic
392C2×C3⋊C8C23×C311yescharacteristic
393C2×C3⋊C8C23×C311yescharacteristic
394Dic12—22no—
395#204—22no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—41no—
400C22×C32—41no—
401C22×C32—41no—
402C22×C32C22×D411yescharacteristic
403C2×C3×D3—22no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C32×C4—21no—
407C32×C4—41no—
408C32×C4—41no—
409C32×C4—41no—
410C32×C4C2×#4111yescharacteristic
411C32×C4C2×#4111yescharacteristic
412C3×Dic3—22no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—41no—
417C3×Dic3—41no—
418C3×Dic3#13512yes—
419C2×#41—31no—
420C2×Q16—31no—
421C2×SD16—31no—
422C2×SD16—31no—
423C2×D8—31no—
424#126—61no—
425#125—31no—
426#124—31no—
427#123—61no—
428C22⋊Q8—31no—
429#121C2×C3×D311yescharacteristic
430C4×Q8—31no—
431C4×Q8—31no—
432C4×Q8—31no—
433C4×D4—31no—
434C4×D4—31no—
435C4×D4—31no—
436C4×D4—61no—
437C4×D4—61no—
438C4×D4—61no—
439#117—61no—
440#117—61no—
441#117C2×C3×D311yescharacteristic
442C2×C42—31no—
443C2×C42—61no—
444#107—31no—
445#107C2×C3×D311yescharacteristic
446#106—31no—
447#106C2×C3×D311yescharacteristic
448C4⋊C8—31no—
449C4⋊C8—31no—
450#103—31no—
451#103—31no—
452#103—31no—
453#103—31no—
454#102—31no—
455#102—31no—
456#102C2×C3×D311yescharacteristic
457#102C2×C3×D311yescharacteristic
458C22⋊C8—31no—
459C22⋊C8C2×C3×D311yescharacteristic
460C4×C8—31no—
461C4×C8—31no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—41no—
466C23×C3—61no—
467C23×C3D3×D411yescharacteristic
468C23×C3C2×C3×D411yescharacteristic
469C22×D3—21no—
470C3×Q8—32no—
471C3×Q8—61no—
472C3×Q8—61no—
473C3×Q8—61no—
474C3×D4—21no—
475C3×D4—21no—
476C3×D4—21no—
477C3×D4—21no—
478C3×D4—32no—
479C3×D4—41no—
480C3×D4—41no—
481C3×D4—42no—
482C3×D4—42no—
483C3×D4—64no—
484C3×D4—61no—
485C3×D4—82no—
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—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—64no—
508C2×C3×C4—62no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—122no—
513C2×C3×C4—122no—
514C2×C3×C4—122no—
515C2×C3×C4—121no—
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4C2×C3×D411yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519C2×C3×C4C24×C311yescharacteristic
520#67—24no—
521C2×Dic3—21no—
522C2×Dic3—22no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—41no—
526C2×Dic3—42no—
527C2×Dic3C2×C3×D411yescharacteristic
528C2×Dic3C2×C3×D411yescharacteristic
529C2×Dic3C2×C3×D411yescharacteristic
530C2×Dic3C2×C3×D411yescharacteristic
531D12—21no—
532D12C3×#4112yes—
533C4×D3—24no—
534C4×D3—42no—
535C4×D3—42no—
536Dic6—21no—
537Dic6—21no—
538Dic6—21no—
539Dic6C3×#4112yes—
540C3×C8—21no—
541C3×C8—21no—
542C3×C8—21no—
543C3×C8—21no—
544C3×C8—41no—
545C3×C8—41no—
546C3×C8—61no—
547C3×C8—61no—
548C3⋊C8—21no—
549C3⋊C8—21no—
550C2×C32—41no—
551C2×C32—81no—
552C2×C32#52511yescharacteristic
553C2×C32C2×#13511yescharacteristic
554C2×C32#57511yescharacteristic
555C3×D3—42no—
556#41—62no—
557#41—62no—
558C2×Q8—31no—
559C2×Q8—31no—
560C2×D4—21no—
561C2×D4—31no—
562C2×D4—61no—
563C2×D4C22×C3×D311yescharacteristic
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4C22×C3×D311yescharacteristic
571Q16—62no—
572SD16—62no—
573SD16—62no—
574D8—62no—
575C2×C8—31no—
576C2×C8—31no—
577C2×C8C22×C3×D311yescharacteristic
578C2×C8C22×C3×D311yescharacteristic
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—21no—
591C22⋊C4—61no—
592C22⋊C4—61no—
593C22⋊C4—61no—
594C22⋊C4—61no—
595C22⋊C4—61no—
596C22⋊C4—61no—
597C42—21no—
598C42—31no—
599C42—31no—
600C42—31no—
601C42—31no—
602C42—61no—
603C42—61no—
604C42—61no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—62no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3—121no—
626C22×C3—121no—
627C22×C3C2×D3×D411yescharacteristic
628C22×C3C22×C3×D411yescharacteristic
629C2×D3—22no—
630C2×D3—41no—
631C2×D3—41no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—32no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—62no—
645C3×C4—61no—
646C3×C4—61no—
647C3×C4—61no—
648C3×C4—81no—
649C3×C4—81no—
650C3×C4—81no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4D3×#4111yescharacteristic
654C3×C4D3×#4111yescharacteristic
655C3×C4C2×C3×#4111yescharacteristic
656C3×C4C2×C3×#4111yescharacteristic
657Dic3—21no—
658Dic3—21no—
659Dic3—21no—
660Dic3—22no—
661Dic3—41no—
662Dic3—41no—
663Dic3C3×#13512yes—
664C32#310211yescharacteristic, complemented, Sylow
665C23—21no—
666C23—61no—
667C23C3×D3×D411yescharacteristic
668Q8—32no—
669Q8—61no—
670Q8—61no—
671Q8—61no—
672D4—21no—
673D4—21no—
674D4—32no—
675D4—42no—
676D4—64no—
677D4—61no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—31no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—31no—
687C2×C4—64no—
688C2×C4—62no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—122no—
693C2×C4—122no—
694C2×C4—122no—
695C2×C4—121no—
696C2×C4C3×D3×D411yescharacteristic
697C2×C4C23×C3×D311yescharacteristic
698C8—21no—
699C8—21no—
700C8—61no—
701C8—61no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—41no—
706C2×C3—41no—
707C2×C3—81no—
708C2×C3—81no—
709C2×C3—81no—
710C2×C3—122no—
711C2×C3—161no—
712C2×C3#565611yescharacteristic
713C2×C3D3×#13511yescharacteristic
714C2×C3#577311yescharacteristic
715C2×C3C3×#52511yescharacteristic
716C2×C3C2×C3×#13511yescharacteristic
717C2×C3C3×#57511yescharacteristic
718D3—42no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—62no—
726C22—121no—
727C22—121no—
728C22C2×C3×D3×D411yescharacteristic
729C4—21no—
730C4—32no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—61no—
735C4—61no—
736C4—61no—
737C4—62no—
738C4—121no—
739C4—121no—
740C4C3×D3×#4111yescharacteristic
741C4C3×D3×#4111yescharacteristic
742C3—21no—
743C3#8134811yescharacteristic, direct product factor
744C3C3×#310211yescharacteristic, complemented
745C2—41no—
746C2—81no—
747C2—122no—
748C2C3×#565611yescharacteristic
749C2C3×D3×#13511yescharacteristic
750C2C3×#577311yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#482C2
socleC22×C32C22×D4
prime radicalC3×#5037C2
hypercenterC3×#482D3
hypocenterC3C3×#3102
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#482

Complements

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

NH ≅ G/Ntype
1. C3×#5600C2semidirect
2. C3×#5522C2semidirect
3. C32×#482C2semidirect
5. C3×#4996C2semidirect
6. C3×#4891C2semidirect
7. C3×#4873C2semidirect
8. C3×#4857C2semidirect
9. C3×#4852C2semidirect
10. C3×#4787C2semidirect
11. C3×#4767C2semidirect
12. C3×#4758C2semidirect
13. C3×#4756C2semidirect
14. C3×#4733C2semidirect
15. C3×#4718C2semidirect
17. #81348C3direct (N × H)
63. #5600C2×C3semidirect
64. #5522C2×C3semidirect
67. C3×#482D3semidirect
68. C3×#482C2×C3semidirect
81. #4996C2×C3semidirect
82. #4891C2×C3semidirect
83. #4873C2×C3semidirect
84. #4857C2×C3semidirect
85. #4852C2×C3semidirect
86. #4787C2×C3semidirect
87. #4767C2×C3semidirect
88. #4758C2×C3semidirect
89. #4756C2×C3semidirect
90. #4733C2×C3semidirect
91. #4718C2×C3semidirect
275. #482C3×D3semidirect
664. C32#3102semidirect
743. C3#81348direct (N × H)
744. C3C3×#3102semidirect

Maximal subgroups

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

subgroupindex
C3×#56002
C3×#55222
C32×#4822
C3×#50372
C3×#49962
C3×#48912
C3×#48732
C3×#48572
C3×#48522
C3×#47872
C3×#47672
C3×#47582
C3×#47562
C3×#47332
C3×#47182
C3×#31023
#813483