Finite Group Databasebeta

← C3×#81401 #11889186

Subgroups — C3×#81401 #11889186

Order 1152.

857 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5612C211yesmaximal, characteristic
2C3×#5533C211yesmaximal, characteristic, complemented
3C32×#482C211yesmaximal, characteristic, complemented
4C3×#5041C211yesmaximal, characteristic, complemented
5C3×#5002C211yesmaximal, characteristic, complemented
6C3×#4889C211yesmaximal, characteristic, complemented
7C3×#4888C211yesmaximal, characteristic, complemented
8C3×#4870C211yesmaximal, characteristic, complemented
9C3×#4867C211yesmaximal, characteristic, complemented
10C3×#4776C211yesmaximal, characteristic, complemented
11C3×#4770C211yesmaximal, characteristic, complemented
12C3×#4767C211yesmaximal, characteristic, complemented
13C3×#4765C211yesmaximal, characteristic, complemented
14C3×#4733C211yesmaximal, characteristic, complemented
15C3×#4730C211yesmaximal, characteristic, complemented
16C3×#3311—31nomaximal
17#81401C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×D4C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C32×#121C2211yescharacteristic
21C32×#117C2211yescharacteristic, complemented
22C3×#938—21no—
23C3×#937—21no—
24C3×#936C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C3×C4×#67C2211yescharacteristic
27C3×#924C2211yescharacteristic, complemented
28C22×C3×C3⋊C8C2211yescharacteristic, complemented
29C2×C3×Dic12C2211yescharacteristic, complemented
30C2×C3×#204C2211yescharacteristic
31C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
32C3×#897C2211yescharacteristic
33C3×#897C2211yescharacteristic
34C3×#893C2211yescharacteristic
35C3×#892C2211yescharacteristic
36C3×#888C2211yescharacteristic, complemented
37C3×#887C2211yescharacteristic, complemented
38C3×#885—21no—
39C3×#883—21no—
40C3×D3×C22⋊C4—21no—
41C3×#879—21no—
42C3×#876—21no—
43C3×C4×Dic6—21no—
44C32×#107C2211yescharacteristic, complemented
45C32×#106C2211yescharacteristic, complemented
46C32×#102C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C32×C22⋊C8C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#816C2211yescharacteristic, complemented
53C3×#815C2211yescharacteristic, complemented
54C3×Dic3⋊C8C2211yescharacteristic, complemented
55C3×#810C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic
59C3×#809C2211yescharacteristic
60C3×#808C2211yescharacteristic, complemented
61C3×#556—31no—
62C3×#546—31no—
63#5612C2×C311yescharacteristic
64#5533C2×C311yescharacteristic, complemented
65C3×#489—31no—
66C3×#485—31no—
67C3×#482—21no—
68C3×#482D311yescharacteristic, complemented
69C3×#482C2×C311yescharacteristic, complemented
70C3×#476—31no—
71C3×#470—31no—
72C3×#465—31no—
73C3×#464—31no—
74C3×#452—31no—
75C3×#450—31no—
76C3×#440—31no—
77C3×#435—31no—
78C3×#418—31no—
79C3×#416—31no—
80#5041C2×C311yescharacteristic, complemented
81#5002C2×C311yescharacteristic, complemented
82#4889C2×C311yescharacteristic, complemented
83#4888C2×C311yescharacteristic, complemented
84#4870C2×C311yescharacteristic, complemented
85#4867C2×C311yescharacteristic, complemented
86#4776C2×C311yescharacteristic, complemented
87#4770C2×C311yescharacteristic, complemented
88#4767C2×C311yescharacteristic, complemented
89#4765C2×C311yescharacteristic, complemented
90#4733C2×C311yescharacteristic, complemented
91#4730C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67D411yescharacteristic
99C3×D3×D4—22no—
100C3×D3×D4—41no—
101C3×#235—22no—
102C3×#235—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6—21no—
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C32×C22⋊C4—21no—
117C32×C42—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217D411yescharacteristic
122C3×#214—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4D411yescharacteristic
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8—41no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×Dic12—41no—
142C3×#204—22no—
143C3×ΓL(1,𝔽25)—41no—
144#3311—31noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×D3×D4C22×C311yescharacteristic
148C2×#235C22×C311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C2×C3×SD16—31no—
152C2×C3×M16—31no—
153C22×C3×C8—31no—
154C3×C4⋊Q8—31no—
155C3×#126—61no—
156C3×#126—61no—
157C3×#124—31no—
158C3×#124—61no—
159C3×#123—61no—
160C3×C22⋊Q8—31no—
161C3×C22⋊Q8—31no—
162C3×C22⋊Q8—31no—
163C3×#121—21no—
164C3×#121—61no—
165C3×#121C2×D311yescharacteristic
166C3×#121C22×C311yescharacteristic
167C3×#120—61no—
168C3×C4×Q8—31no—
169C3×C4×Q8—61no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172C3×#117—21no—
173C3×#117—31no—
174C3×#117C2×D311yescharacteristic, complemented
175C3×#117C22×C311yescharacteristic, complemented
176C2×C3×C22⋊C4—61no—
177#938—21no—
178#937—21no—
179#936C22×C311yescharacteristic
180C2×#214C22×C311yescharacteristic
181C4×#67C22×C311yescharacteristic
182#924C22×C311yescharacteristic, complemented
183C22×C3⋊C8C22×C311yescharacteristic, complemented
184C2×Dic12C22×C311yescharacteristic, complemented
185C2×#204C22×C311yescharacteristic
186C2×ΓL(1,𝔽25)C22×C311yescharacteristic
187#897C22×C311yescharacteristic
188#897C22×C311yescharacteristic
189#893C22×C311yescharacteristic
190#892C22×C311yescharacteristic
191#888C22×C311yescharacteristic, complemented
192#887C22×C311yescharacteristic, complemented
193#885—21no—
194#883—21no—
195D3×C22⋊C4—21no—
196#879—21no—
197#876—21no—
198C4×Dic6—21no—
199C3×#107—21no—
200C3×#107C2×D311yescharacteristic, complemented
201C3×#107C22×C311yescharacteristic, complemented
202C3×#106—21no—
203C3×#106—31no—
204C3×#106C2×D311yescharacteristic, complemented
205C3×#106C22×C311yescharacteristic, complemented
206C3×C4⋊C8—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#102—21no—
212C3×#102—21no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102C2×D311yescharacteristic
218C3×#102C2×D311yescharacteristic
219C3×#102C22×C311yescharacteristic
220C3×#102C22×C311yescharacteristic
221C3×C22⋊C8—21no—
222C3×C22⋊C8—31no—
223C3×C22⋊C8C2×D311yescharacteristic, complemented
224C3×C22⋊C8C22×C311yescharacteristic, complemented
225C3×#97—31no—
226#832C22×C311yescharacteristic
227#821C22×C311yescharacteristic
228(C2×D3)⋊C8C22×C311yescharacteristic
229#816C22×C311yescharacteristic, complemented
230#815C22×C311yescharacteristic, complemented
231Dic3⋊C8C22×C311yescharacteristic, complemented
232#810C22×C311yescharacteristic, complemented
233#810C22×C311yescharacteristic, complemented
234#810C22×C311yescharacteristic, complemented
235#809C22×C311yescharacteristic
236#809C22×C311yescharacteristic
237#808C22×C311yescharacteristic, complemented
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4—21no—
247C32×D4—81no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C3×#67—41no—
256C3×#67—42no—
257C3×#67—42no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—42no—
269C3×C4×D3—81no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—42no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—31no—
280#546—31no—
281#489—31no—
282#485—31no—
283#482C3×D311yescharacteristic, complemented
284#476—31no—
285#470—31no—
286#465—31no—
287#464—31no—
288#452—31no—
289#450—31no—
290#440—31no—
291#435—31no—
292#418—31no—
293#416—31no—
294C24×C3—61no—
295C23×D3—21no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×Q8—61no—
301C2×C3×D4—21no—
302C2×C3×D4—21no—
303C2×C3×D4—21no—
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—41no—
307C2×C3×D4—61no—
308C2×C3×D4—62no—
309C2×C3×D4—61no—
310C2×C3×D4—121no—
311C2×C3×D4C22×D311yescharacteristic
312C2×C3×D4C23×C311yescharacteristic
313C22×C3×C4—21no—
314C22×C3×C4—31no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C23×C311yescharacteristic
319C2×#67—21no—
320C2×#67—21no—
321C2×#67C3×D411yescharacteristic
322D3×D4—22no—
323D3×D4—41no—
324#235—22no—
325#235—41no—
326C2×D12C23×C311yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3—21no—
329C2×C4×D3C23×C311yescharacteristic
330C2×Dic6—21no—
331C2×Dic6C23×C311yescharacteristic
332C2×Dic6C23×C311yescharacteristic
333C3×Q16—121no—
334C3×SD16—62no—
335C3×SD16—121no—
336C3×M16—121no—
337C2×C3×C8—21no—
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8—121no—
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C23×C311yescharacteristic
345C2×C3×C8C23×C311yescharacteristic
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C23×C311yescharacteristic
360C3×C4⋊C4C23×C311yescharacteristic
361C3×C4⋊C4C23×C311yescharacteristic
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—31no—
368C3×C22⋊C4—41no—
369C3×C22⋊C4—41no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C42—21no—
378C3×C42—21no—
379C3×C42—31no—
380C3×C42—41no—
381C3×C42—61no—
382C3×C42—61no—
383#217—21no—
384#217—21no—
385#217—21no—
386#217C3×D411yescharacteristic
387#214—41no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4C3×D411yescharacteristic
393C4⋊Dic3—21no—
394C4⋊Dic3—21no—
395C4⋊Dic3C23×C311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4C3×D411yescharacteristic
400C4×Dic3—21no—
401C4×Dic3—21no—
402C4×Dic3C23×C311yescharacteristic
403C2×C3⋊C8—41no—
404C2×C3⋊C8C23×C311yescharacteristic
405C2×C3⋊C8C23×C311yescharacteristic
406Dic12—41no—
407#204—22no—
408ΓL(1,𝔽25)—41no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32C22×D411yescharacteristic
416C2×C3×D3—21no—
417C2×C3×D3—22no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—84no—
423C32×C4—21no—
424C32×C4—41no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—31no—
436C22×D4—31no—
437C2×Q16—31no—
438C2×SD16—31no—
439C2×SD16—31no—
440C2×M16—31no—
441C22×C8—31no—
442C4⋊Q8—31no—
443#126—61no—
444#126—61no—
445#124—31no—
446#124—61no—
447#123—61no—
448C22⋊Q8—31no—
449C22⋊Q8—31no—
450C22⋊Q8—31no—
451#121—61no—
452#121C2×C3×D311yescharacteristic
453#120—61no—
454C4×Q8—31no—
455C4×Q8—61no—
456C4×D4—31no—
457C4×D4—31no—
458#117—31no—
459#117C2×C3×D311yescharacteristic, complemented
460C2×C22⋊C4—61no—
461#107C2×C3×D311yescharacteristic, complemented
462#106—31no—
463#106C2×C3×D311yescharacteristic, complemented
464C4⋊C8—31no—
465#103—31no—
466#103—31no—
467#103—31no—
468#103—31no—
469#102—31no—
470#102—31no—
471#102—31no—
472#102—31no—
473#102C2×C3×D311yescharacteristic
474#102C2×C3×D311yescharacteristic
475C22⋊C8—31no—
476C22⋊C8C2×C3×D311yescharacteristic, complemented
477#97—31no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—31no—
482C23×C3—41no—
483C23×C3—61no—
484C23×C3—122no—
485C23×C3—122no—
486C23×C3—241no—
487C23×C3D3×D411yescharacteristic
488C23×C3C2×C3×D411yescharacteristic
489C22×D3—21no—
490C22×D3—42no—
491C22×D3—42no—
492C22×D3—81no—
493C22×D3C2×C3×D411yescharacteristic
494C3×Q8—61no—
495C3×Q8—61no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×Q8—122no—
499C3×D4—21no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—32no—
504C3×D4—41no—
505C3×D4—41no—
506C3×D4—61no—
507C3×D4—81no—
508C3×D4—81no—
509C3×D4—82no—
510C3×D4—121no—
511C3×D4—122no—
512C3×D4—122no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—31no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—122no—
539C2×C3×C4—241no—
540C2×C3×C4D3×D411yescharacteristic
541C2×C3×C4C2×C3×D411yescharacteristic
542C2×C3×C4C23×D311yescharacteristic
543C2×C3×C4C24×C311yescharacteristic
544#67—41no—
545#67—42no—
546#67—42no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3C2×C3×D411yescharacteristic
551C2×Dic3C2×C3×D411yescharacteristic
552C2×Dic3C2×C3×D411yescharacteristic
553D12—21no—
554D12C3×#4112yes—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—42no—
558C4×D3—81no—
559Dic6—21no—
560Dic6—21no—
561Dic6—21no—
562Dic6—21no—
563Dic6—42no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—21no—
567C3×C8—21no—
568C3×C8—41no—
569C3×C8—41no—
570C3×C8—61no—
571C3×C8—61no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C2×C32—41no—
575C2×C32—81no—
576C2×C32#54611yescharacteristic
577C2×C32#57511yescharacteristic
578C2×C32#57711yescharacteristic
579C3×D3—41no—
580C3×D3—42no—
581C24—61no—
582#41—62no—
583#41—121no—
584C2×Q8—31no—
585C2×Q8—31no—
586C2×Q8—61no—
587C2×D4—21no—
588C2×D4—31no—
589C2×D4—31no—
590C2×D4—61no—
591C2×D4—62no—
592C2×D4—61no—
593C2×D4—121no—
594C2×D4C22×C3×D311yescharacteristic
595C22×C4—31no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4C22×C3×D311yescharacteristic
599Q16—121no—
600SD16—62no—
601SD16—121no—
602M16—121no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8—121no—
606C2×C8C22×C3×D311yescharacteristic
607C2×C8C22×C3×D311yescharacteristic
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4C22×C3×D311yescharacteristic
616C4⋊C4C22×C3×D311yescharacteristic
617C4⋊C4C22×C3×D311yescharacteristic
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—31no—
621C22⋊C4—31no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C42—21no—
630C42—31no—
631C42—61no—
632C42—61no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—61no—
650C22×C3—62no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—244no—
659C22×C3C2×D3×D411yescharacteristic
660C22×C3C22×C3×D411yescharacteristic
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—22no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—84no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—81no—
683C3×C4—81no—
684C3×C4—81no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4D3×#4111yescharacteristic
689C3×C4#100911yescharacteristic
690C3×C4C2×C3×#4111yescharacteristic
691C3×C4C3×H(5,𝔽2)11yescharacteristic
692Dic3—21no—
693Dic3—21no—
694Dic3—21no—
695Dic3—41no—
696Dic3—41no—
697Dic3—41no—
698C32#331111yescharacteristic, complemented, Sylow
699C23—21no—
700C23—31no—
701C23—61no—
702C23—122no—
703C23—122no—
704C23—241no—
705C23C3×D3×D411yescharacteristic
706Q8—61no—
707Q8—61no—
708Q8—61no—
709Q8—61no—
710Q8—122no—
711D4—21no—
712D4—21no—
713D4—32no—
714D4—61no—
715D4—81no—
716D4—121no—
717D4—122no—
718D4—122no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—122no—
733C2×C4—241no—
734C2×C4C3×D3×D411yescharacteristic
735C2×C4C23×C3×D311yescharacteristic
736C8—21no—
737C8—21no—
738C8—61no—
739C8—61no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—41no—
744C2×C3—41no—
745C2×C3—81no—
746C2×C3—81no—
747C2×C3—81no—
748C2×C3—121no—
749C2×C3—122no—
750C2×C3—161no—
751C2×C3#565411yescharacteristic
752C2×C3#576811yescharacteristic
753C2×C3#577511yescharacteristic
754C2×C3C3×#54611yescharacteristic
755C2×C3C3×#57511yescharacteristic
756C2×C3C3×#57711yescharacteristic
757D3—41no—
758D3—42no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—61no—
766C22—61no—
767C22—61no—
768C22—62no—
769C22—121no—
770C22—121no—
771C22—244no—
772C22C2×C3×D3×D411yescharacteristic
773C4—21no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—61no—
778C4—61no—
779C4—61no—
780C4—121no—
781C4—121no—
782C4—121no—
783C4C3×D3×#4111yescharacteristic
784C4C3×#100911yescharacteristic
785C3—21no—
786C3#8140111yescharacteristic, direct product factor
787C3C3×#331111yescharacteristic, complemented
788C2—41no—
789C2—81no—
790C2—121no—
791C2—122no—
792C2C3×#565411yescharacteristic
793C2C3×#576811yescharacteristic
794C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#482C2
socleC22×C32C22×D4
prime radicalC3×#5612C2
hypercenterC3×#482D3
hypocenterC3C3×#3311
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
2. C3×#5533C2semidirect
3. C32×#482C2semidirect
4. C3×#5041C2semidirect
5. C3×#5002C2semidirect
6. C3×#4889C2semidirect
7. C3×#4888C2semidirect
8. C3×#4870C2semidirect
9. C3×#4867C2semidirect
10. C3×#4776C2semidirect
11. C3×#4770C2semidirect
12. C3×#4767C2semidirect
13. C3×#4765C2semidirect
14. C3×#4733C2semidirect
15. C3×#4730C2semidirect
17. #81401C3direct (N × H)
21. C32×#117C22semidirect
27. C3×#924C22semidirect
28. C22×C3×C3⋊C8C22semidirect
29. C2×C3×Dic12C22semidirect
36. C3×#888C22semidirect
37. C3×#887C22semidirect
44. C32×#107C22semidirect
45. C32×#106C22semidirect
48. C32×C22⋊C8C22semidirect
52. C3×#816C22semidirect
53. C3×#815C22semidirect
54. C3×Dic3⋊C8C22semidirect
55. C3×#810C22semidirect
56. C3×#810C22semidirect
57. C3×#810C22semidirect
60. C3×#808C22semidirect
64. #5533C2×C3semidirect
68. C3×#482D3semidirect
69. C3×#482C2×C3semidirect
80. #5041C2×C3semidirect
81. #5002C2×C3semidirect
82. #4889C2×C3semidirect
83. #4888C2×C3semidirect
84. #4870C2×C3semidirect
85. #4867C2×C3semidirect
86. #4776C2×C3semidirect
87. #4770C2×C3semidirect
88. #4767C2×C3semidirect
89. #4765C2×C3semidirect
90. #4733C2×C3semidirect
91. #4730C2×C3semidirect
174. C3×#117C2×D3semidirect
175. C3×#117C22×C3semidirect
182. #924C22×C3semidirect
183. C22×C3⋊C8C22×C3semidirect
184. C2×Dic12C22×C3semidirect
191. #888C22×C3semidirect
192. #887C22×C3semidirect
200. C3×#107C2×D3semidirect
201. C3×#107C22×C3semidirect
204. C3×#106C2×D3semidirect
205. C3×#106C22×C3semidirect
223. C3×C22⋊C8C2×D3semidirect
224. C3×C22⋊C8C22×C3semidirect
229. #816C22×C3semidirect
230. #815C22×C3semidirect
231. Dic3⋊C8C22×C3semidirect
232. #810C22×C3semidirect
233. #810C22×C3semidirect
234. #810C22×C3semidirect
237. #808C22×C3semidirect
283. #482C3×D3semidirect
459. #117C2×C3×D3semidirect
461. #107C2×C3×D3semidirect
463. #106C2×C3×D3semidirect
476. C22⋊C8C2×C3×D3semidirect
698. C32#3311semidirect
786. C3#81401direct (N × H)
787. C3C3×#3311semidirect

Maximal subgroups

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

subgroupindex
C3×#56122
C3×#55332
C32×#4822
C3×#50412
C3×#50022
C3×#48892
C3×#48882
C3×#48702
C3×#48672
C3×#47762
C3×#47702
C3×#47672
C3×#47652
C3×#47332
C3×#47302
C3×#33113
#814013