Finite Group Databasebeta

← C3×#81498 #11872789

Subgroups — C3×#81498 #11872789

Order 1152.

836 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×#5625C211yesmaximal, characteristic, complemented
2C3×#5521C211yesmaximal, characteristic
3C32×#485C211yesmaximal, characteristic, complemented
4C3×#5046C211yesmaximal, characteristic
5C3×#4996C211yesmaximal, characteristic, complemented
6C3×#4891C211yesmaximal, characteristic, complemented
7C3×#4889C211yesmaximal, characteristic, complemented
8C3×#4871C211yesmaximal, characteristic, complemented
9C3×#4852C211yesmaximal, characteristic, complemented
10C3×#4818C211yesmaximal, characteristic, complemented
11C3×#4818C211yesmaximal, characteristic, complemented
12C3×#4817C211yesmaximal, characteristic, complemented
13C3×#4788C211yesmaximal, characteristic, complemented
14C3×#4731C211yesmaximal, characteristic
15C3×#4720C211yesmaximal, characteristic, complemented
16C3×#3123—31nomaximal
17#81498C311yesmaximal, characteristic, direct product factor
18C22×C3×D12C2211yescharacteristic
19C32×C22⋊Q8C2211yescharacteristic
20C32×#117C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic, complemented
22C3×#944C2211yescharacteristic, complemented
23C2×C3×#215C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic
29C3×#893C2211yescharacteristic
30C3×#893C2211yescharacteristic
31C3×#893C2211yescharacteristic
32C3×#893C2211yescharacteristic
33C3×#890—21no—
34C3×#890C2211yescharacteristic, complemented
35C3×#889—21no—
36C3×#887C2211yescharacteristic, complemented
37C3×D3×C22⋊C4—21no—
38C3×D3×C22⋊C4—21no—
39C3×#879—21no—
40C3×#879—21no—
41C3×C4×D12—21no—
42C3×C4×D12—21no—
43C32×#107C2211yescharacteristic, complemented
44C32×#106C2211yescharacteristic, complemented
45C32×#103C2211yescharacteristic, complemented
46C32×#103C2211yescharacteristic, complemented
47C32×C22⋊C8C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#815C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C8×Dic3C2211yescharacteristic, complemented
55C3×#810C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic, complemented
60C3×#807C2211yescharacteristic, complemented
61C3×#541—31no—
62C3×#518—31no—
63#5625C2×C311yescharacteristic, complemented
64#5521C2×C311yescharacteristic
65C3×#485—21no—
66C3×#485—31no—
67C3×#485D311yescharacteristic, complemented
68C3×#485C2×C311yescharacteristic, complemented
69C3×#478—31no—
70C3×#478—31no—
71C3×#461—31no—
72C3×#461—31no—
73C3×#450—31no—
74C3×#450—31no—
75C3×#440—31no—
76C3×#440—31no—
77C3×C4×SD16—31no—
78C3×C4×SD16—31no—
79C3×#433—31no—
80#5046C2×C311yescharacteristic
81#4996C2×C311yescharacteristic, complemented
82#4891C2×C311yescharacteristic, complemented
83#4889C2×C311yescharacteristic, complemented
84#4871C2×C311yescharacteristic, complemented
85#4852C2×C311yescharacteristic, complemented
86#4818C2×C311yescharacteristic, complemented
87#4818C2×C311yescharacteristic, complemented
88#4817C2×C311yescharacteristic, complemented
89#4788C2×C311yescharacteristic, complemented
90#4731C2×C311yescharacteristic
91#4720C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×C3×D12—21no—
96C2×C3×D12—22no—
97C2×C3×D12—22no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×C32×C8C2311yescharacteristic
106C2×C32×C8C2311yescharacteristic
107C32×C4⋊C4—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C32×C22⋊C4—21no—
113C32×C42—21no—
114C3×#217—21no—
115C3×#217D411yescharacteristic
116C3×#217D411yescharacteristic
117C3×#215—22no—
118C3×#215—22no—
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⋊Dic3—21no—
125C3×C4⋊Dic3D411yescharacteristic
126C3×C4⋊Dic3D411yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×#204—22no—
140C3×#204—22no—
141#3123—31noSylow
142C22×C3×D4—31no—
143C22×D12C22×C311yescharacteristic
144C2×C3×SD16—31no—
145C2×C3×SD16—31no—
146C2×C3×SD16—31no—
147C2×C3×SD16—31no—
148C3×C4⋊Q8—31no—
149C3×#126—61no—
150C3×#126—61no—
151C3×#125—31no—
152C3×#125—61no—
153C3×#125—61no—
154C3×C22⋊Q8—21no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8C2×D311yescharacteristic
157C3×C22⋊Q8C22×C311yescharacteristic
158C3×C4×Q8—31no—
159C3×C4×Q8—31no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164C3×C4×D4—61no—
165C3×C4×D4—61no—
166C3×#117—21no—
167C3×#117—31no—
168C3×#117C2×D311yescharacteristic
169C3×#117C22×C311yescharacteristic
170C2×C3×C22⋊C4—61no—
171C2×C3×C22⋊C4—61no—
172Q8×Dic3C22×C311yescharacteristic, complemented
173#944C22×C311yescharacteristic, complemented
174C2×#215C22×C311yescharacteristic
175C2×#215C22×C311yescharacteristic
176#926C22×C311yescharacteristic
177#924C22×C311yescharacteristic
178C2×#204C22×C311yescharacteristic
179C2×#204C22×C311yescharacteristic
180#893C22×C311yescharacteristic
181#893C22×C311yescharacteristic
182#893C22×C311yescharacteristic
183#893C22×C311yescharacteristic
184#890—21no—
185#890C22×C311yescharacteristic, complemented
186#889—21no—
187#887C22×C311yescharacteristic, complemented
188D3×C22⋊C4—21no—
189D3×C22⋊C4—21no—
190#879—21no—
191#879—21no—
192C4×D12—21no—
193C4×D12—21no—
194C3×#107—21no—
195C3×#107—31no—
196C3×#107C2×D311yescharacteristic, complemented
197C3×#107C22×C311yescharacteristic, complemented
198C3×#106—21no—
199C3×#106—31no—
200C3×#106C2×D311yescharacteristic, complemented
201C3×#106C22×C311yescharacteristic, complemented
202C3×C4⋊C8—31no—
203C3×C4⋊C8—31no—
204C3×#103—21no—
205C3×#103—21no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103C2×D311yescharacteristic, complemented
209C3×#103C2×D311yescharacteristic, complemented
210C3×#103C22×C311yescharacteristic, complemented
211C3×#103C22×C311yescharacteristic, complemented
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×C22⋊C8—21no—
217C3×C22⋊C8—31no—
218C3×C22⋊C8C2×D311yescharacteristic
219C3×C22⋊C8C22×C311yescharacteristic
220C3×#97—31no—
221C3×C4×C8—31no—
222#830C22×C311yescharacteristic
223#821C22×C311yescharacteristic
224#821C22×C311yescharacteristic
225#815C22×C311yescharacteristic, complemented
226Dic3⋊C8C22×C311yescharacteristic, complemented
227Dic3⋊C8C22×C311yescharacteristic, complemented
228C8×Dic3C22×C311yescharacteristic, complemented
229#810C22×C311yescharacteristic, complemented
230#810C22×C311yescharacteristic, complemented
231#809C22×C311yescharacteristic
232#809C22×C311yescharacteristic
233#808C22×C311yescharacteristic, complemented
234#807C22×C311yescharacteristic, complemented
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—24no—
239C22×C3×D3—81no—
240C22×C3×D3—81no—
241C32×Q8—21no—
242C32×Q8—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—24no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12#4112yes—
261C3×D12#4112yes—
262C3×C4×D3—81no—
263C3×C4×D3—81no—
264C3×C4×D3—81no—
265C3×C4×D3—81no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C32×C8—21no—
269C32×C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#541—31no—
273#518—31no—
274#485—31no—
275#485C3×D311yescharacteristic, complemented
276#478—31no—
277#478—31no—
278#461—31no—
279#461—31no—
280#450—31no—
281#450—31no—
282#440—31no—
283#440—31no—
284C4×SD16—31no—
285C4×SD16—31no—
286#433—31no—
287C24×C3—61no—
288C23×D3—21no—
289C2×C3×Q8—21no—
290C2×C3×Q8—31no—
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×Q8C23×C311yescharacteristic
293C2×C3×D4—31no—
294C2×C3×D4—31no—
295C2×C3×D4—62no—
296C2×C3×D4—62no—
297C2×C3×D4—61no—
298C22×C3×C4—21no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C23×C311yescharacteristic
305C2×D12—21no—
306C2×D12—22no—
307C2×D12—22no—
308C2×D12C23×C311yescharacteristic
309C2×D12C23×C311yescharacteristic
310C2×C4×D3—21no—
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×Dic6C23×C311yescharacteristic
315C3×SD16—62no—
316C3×SD16—62no—
317C3×SD16—62no—
318C3×SD16—62no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—31no—
322C2×C3×C8—31no—
323C2×C3×C8C22×D311yescharacteristic
324C2×C3×C8C22×D311yescharacteristic
325C2×C3×C8C23×C311yescharacteristic
326C2×C3×C8C23×C311yescharacteristic
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—41no—
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⋊C4—61no—
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C23×C311yescharacteristic
347C3×C4⋊C4C23×C311yescharacteristic
348C3×C4⋊C4C23×C311yescharacteristic
349C3×C22⋊C4—21no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—21no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—41no—
356C3×C22⋊C4—41no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C42—21no—
363C3×C42—21no—
364C3×C42—31no—
365C3×C42—31no—
366C3×C42—41no—
367C3×C42—61no—
368C3×C42—61no—
369#217—21no—
370#217C3×D411yescharacteristic
371#217C3×D411yescharacteristic
372#215—22no—
373#215—22no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378C4⋊Dic3—21no—
379C4⋊Dic3—21no—
380C4⋊Dic3C3×D411yescharacteristic
381C4⋊Dic3C3×D411yescharacteristic
382C4⋊Dic3C23×C311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3C23×C311yescharacteristic
391C4×Dic3C23×C311yescharacteristic
392C2×C3⋊C8C23×C311yescharacteristic
393C2×C3⋊C8C23×C311yescharacteristic
394#204—22no—
395#204—22no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32C22×D411yescharacteristic
400C2×C3×D3—22no—
401C2×C3×D3—22no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—84no—
407C32×C4—21no—
408C32×C4—41no—
409C32×C4—41no—
410C32×C4—41no—
411C32×C4—41no—
412C32×C4C2×#4111yescharacteristic
413C32×C4C2×#4111yescharacteristic
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C22×D4—31no—
421C2×SD16—31no—
422C2×SD16—31no—
423C2×SD16—31no—
424C2×SD16—31no—
425C4⋊Q8—31no—
426#126—61no—
427#126—61no—
428#125—31no—
429#125—61no—
430#125—61no—
431C22⋊Q8—31no—
432C22⋊Q8C2×C3×D311yescharacteristic
433C4×Q8—31no—
434C4×Q8—31no—
435C4×D4—31no—
436C4×D4—31no—
437C4×D4—31no—
438C4×D4—31no—
439C4×D4—61no—
440C4×D4—61no—
441#117—31no—
442#117C2×C3×D311yescharacteristic
443C2×C22⋊C4—61no—
444C2×C22⋊C4—61no—
445#107—31no—
446#107C2×C3×D311yescharacteristic, complemented
447#106—31no—
448#106C2×C3×D311yescharacteristic, complemented
449C4⋊C8—31no—
450C4⋊C8—31no—
451#103—31no—
452#103—31no—
453#103C2×C3×D311yescharacteristic, complemented
454#103C2×C3×D311yescharacteristic, complemented
455#102—31no—
456#102—31no—
457#102—31no—
458#102—31no—
459C22⋊C8—31no—
460C22⋊C8C2×C3×D311yescharacteristic
461#97—31no—
462C4×C8—31no—
463C23×C3—21no—
464C23×C3—64no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3—241no—
468C23×C3—241no—
469C23×C3D3×D411yescharacteristic
470C23×C3C2×C3×D411yescharacteristic
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—24no—
474C22×D3—81no—
475C22×D3—81no—
476C3×Q8—21no—
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—41no—
481C3×Q8—41no—
482C3×Q8—61no—
483C3×Q8—61no—
484C3×D4—32no—
485C3×D4—32no—
486C3×D4—64no—
487C3×D4—61no—
488C3×D4—61no—
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—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—241no—
516C2×C3×C4—241no—
517C2×C3×C4—241no—
518C2×C3×C4—241no—
519C2×C3×C4D3×D411yescharacteristic
520C2×C3×C4C2×C3×D411yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C24×C311yescharacteristic
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3C2×C3×D411yescharacteristic
526C2×Dic3C2×C3×D411yescharacteristic
527C2×Dic3C2×C3×D411yescharacteristic
528C2×Dic3C2×C3×D411yescharacteristic
529D12—24no—
530D12—21no—
531D12—21no—
532D12C3×#4112yes—
533D12C3×#4112yes—
534C4×D3—81no—
535C4×D3—81no—
536C4×D3—81no—
537C4×D3—81no—
538Dic6—21no—
539Dic6—21no—
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#52511yescharacteristic
552C2×C32#57711yescharacteristic
553C2×C32#57711yescharacteristic
554C3×D3—42no—
555C3×D3—42no—
556C24—61no—
557C2×Q8—31no—
558C2×Q8C22×C3×D311yescharacteristic
559C2×D4—31no—
560C2×D4—31no—
561C2×D4—62no—
562C2×D4—62no—
563C2×D4—61no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4C22×C3×D311yescharacteristic
569SD16—62no—
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—31no—
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4C22×C3×D311yescharacteristic
589C4⋊C4C22×C3×D311yescharacteristic
590C4⋊C4C22×C3×D311yescharacteristic
591C22⋊C4—21no—
592C22⋊C4—21no—
593C22⋊C4—31no—
594C22⋊C4—31no—
595C22⋊C4—61no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C22⋊C4—61no—
599C22⋊C4—61no—
600C42—21no—
601C42—31no—
602C42—31no—
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—62no—
616C22×C3—62no—
617C22×C3—121no—
618C22×C3—121no—
619C22×C3—121no—
620C22×C3—121no—
621C22×C3—244no—
622C22×C3C2×D3×D411yescharacteristic
623C22×C3C22×C3×D411yescharacteristic
624C2×D3—22no—
625C2×D3—22no—
626C2×D3—41no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3—41no—
630C2×D3—84no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—61no—
647C3×C4—61no—
648C3×C4—81no—
649C3×C4—81no—
650C3×C4—81no—
651C3×C4—81no—
652C3×C4—121no—
653C3×C4—121no—
654C3×C4D3×#4111yescharacteristic
655C3×C4D3×#4111yescharacteristic
656C3×C4C2×C3×#4111yescharacteristic
657C3×C4C2×C3×#4111yescharacteristic
658Dic3—21no—
659Dic3—21no—
660Dic3—21no—
661Dic3—21no—
662Dic3—41no—
663Dic3—41no—
664C32#312311yescharacteristic, complemented, Sylow
665C23—64no—
666C23—61no—
667C23—61no—
668C23—241no—
669C23—241no—
670C23C3×D3×D411yescharacteristic
671Q8—21no—
672Q8—21no—
673Q8—61no—
674Q8—61no—
675D4—32no—
676D4—32no—
677D4—64no—
678D4—61no—
679D4—61no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—31no—
687C2×C4—31no—
688C2×C4—31no—
689C2×C4—31no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—241no—
693C2×C4—241no—
694C2×C4—241no—
695C2×C4—241no—
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—122no—
709C2×C3—122no—
710C2×C3#565611yescharacteristic
711C2×C3#577011yescharacteristic
712C2×C3#577811yescharacteristic
713C2×C3C3×#52511yescharacteristic
714C2×C3C3×#57711yescharacteristic
715C2×C3C3×#57711yescharacteristic
716D3—42no—
717D3—42no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—62no—
722C22—62no—
723C22—121no—
724C22—121no—
725C22—121no—
726C22—121no—
727C22—244no—
728C22C2×C3×D3×D411yescharacteristic
729C4—21no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—61no—
735C4—61no—
736C4—61no—
737C4—61no—
738C4—121no—
739C4—121no—
740C4C3×D3×#4111yescharacteristic
741C4C3×D3×#4111yescharacteristic
742C3—21no—
743C3#8149811yescharacteristic, direct product factor
744C3C3×#312311yescharacteristic, complemented
745C2—41no—
746C2—122no—
747C2—122no—
748C2C3×#565611yescharacteristic
749C2C3×#577011yescharacteristic
750C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#485C2
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
hypercenterC3×#485D3
hypocenterC3C3×#3123
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#485

Complements

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

NH ≅ G/Ntype
1. C3×#5625C2semidirect
3. C32×#485C2semidirect
5. C3×#4996C2semidirect
6. C3×#4891C2semidirect
7. C3×#4889C2semidirect
8. C3×#4871C2semidirect
9. C3×#4852C2semidirect
10. C3×#4818C2semidirect
11. C3×#4818C2semidirect
12. C3×#4817C2semidirect
13. C3×#4788C2semidirect
15. C3×#4720C2semidirect
17. #81498C3direct (N × H)
21. C3×Q8×Dic3C22semidirect
22. C3×#944C22semidirect
34. C3×#890C22semidirect
36. C3×#887C22semidirect
43. C32×#107C22semidirect
44. C32×#106C22semidirect
45. C32×#103C22semidirect
46. C32×#103C22semidirect
51. C3×#815C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C8×Dic3C22semidirect
55. C3×#810C22semidirect
56. C3×#810C22semidirect
59. C3×#808C22semidirect
60. C3×#807C22semidirect
63. #5625C2×C3semidirect
67. C3×#485D3semidirect
68. C3×#485C2×C3semidirect
81. #4996C2×C3semidirect
82. #4891C2×C3semidirect
83. #4889C2×C3semidirect
84. #4871C2×C3semidirect
85. #4852C2×C3semidirect
86. #4818C2×C3semidirect
87. #4818C2×C3semidirect
88. #4817C2×C3semidirect
89. #4788C2×C3semidirect
91. #4720C2×C3semidirect
172. Q8×Dic3C22×C3semidirect
173. #944C22×C3semidirect
185. #890C22×C3semidirect
187. #887C22×C3semidirect
196. C3×#107C2×D3semidirect
197. C3×#107C22×C3semidirect
200. C3×#106C2×D3semidirect
201. C3×#106C22×C3semidirect
208. C3×#103C2×D3semidirect
209. C3×#103C2×D3semidirect
210. C3×#103C22×C3semidirect
211. C3×#103C22×C3semidirect
225. #815C22×C3semidirect
226. Dic3⋊C8C22×C3semidirect
227. Dic3⋊C8C22×C3semidirect
228. C8×Dic3C22×C3semidirect
229. #810C22×C3semidirect
230. #810C22×C3semidirect
233. #808C22×C3semidirect
234. #807C22×C3semidirect
275. #485C3×D3semidirect
446. #107C2×C3×D3semidirect
448. #106C2×C3×D3semidirect
453. #103C2×C3×D3semidirect
454. #103C2×C3×D3semidirect
664. C32#3123semidirect
743. C3#81498direct (N × H)
744. C3C3×#3123semidirect

Maximal subgroups

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

subgroupindex
C3×#56252
C3×#55212
C32×#4852
C3×#50462
C3×#49962
C3×#48912
C3×#48892
C3×#48712
C3×#48522
C3×#48182
C3×#48172
C3×#47882
C3×#47312
C3×#47202
C3×#31233
#814983