Finite Group Databasebeta

← C3×#78994 #11865144

Subgroups — C3×#78994 #11865144

Order 1152.

1549 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5964C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3C2×C3×#908C211yesmaximal, characteristic, complemented
4C3×#5525C211yesmaximal, characteristic, complemented
5C32×#421C211yesmaximal, characteristic, complemented
6C3×#5132C211yesmaximal, characteristic, complemented
7C3×#5005C211yesmaximal, characteristic, complemented
8C3×#4827C214yesmaximal, complemented
9C3×#4822C214yesmaximal, complemented
10C3×#3021—31nomaximal
11#78994C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C3×#1010—21no—
14C3×#1010C2212yescomplemented
15C3×#1009—21no—
16C3×#1009C2212yescomplemented
17C3×D3×#41—22no—
18C3×D3×#41—22no—
19C3×#1007—21no—
20C3×#1004—21no—
21C3×#1004—22no—
22C2×C3×#235—22no—
23C2×C3×#235C2211yescharacteristic
24C2×C3×#235C2211yescharacteristic
25C22×C3×D12C2211yescharacteristic, complemented
26C2×C32×M16C2211yescharacteristic, complemented
27C32×#117C2211yescharacteristic, complemented
28C3×#949—22no—
29C3×#949C2214yescomplemented
30C2×C3×#215—21no—
31C2×C3×#213—21no—
32C2×C3×#208C2211yescharacteristic, complemented
33C3×#908—22no—
34C3×#908C2214yescomplemented
35C2×C3×D24—21no—
36C2×C3×#204—21no—
37C3×#895—22no—
38C3×#882—22no—
39C3×#875C2212yescomplemented
40C3×#874C2212yescomplemented
41C32×#104C2214yescomplemented
42C3×#824C2212yescomplemented
43C3×#823C2212yescomplemented
44C3×#805C2214yescomplemented
45C3×#585—31no—
46#5964C2×C311yescharacteristic, complemented
47C2×C3×AGL(1,ℤ/8)—31no—
48C2×C3×AGL(1,ℤ/8)—31no—
49C3×#535—31no—
50C2×#949C2×C311yescharacteristic, complemented
51C2×#908C2×C311yescharacteristic, complemented
52#5525C2×C311yescharacteristic, complemented
53C3×#454—34no—
54C3×#453—34no—
55C3×#421—21no—
56C3×#421—31no—
57C3×#421D311yescharacteristic, complemented
58C3×#421C2×C311yescharacteristic, complemented
59C3×#413—31no—
60#5132C2×C311yescharacteristic, complemented
61#5005C2×C311yescharacteristic, complemented
62#4827C2×C314yescomplemented
63#4822C2×C314yescomplemented
64C23×C3×D3—21no—
65C32×#41—21no—
66C32×#41—21no—
67C32×#41D412yescomplemented
68C32×#41C2312yes—
69C2×C32×Q8D411yescharacteristic, complemented
70C2×C32×D4—21no—
71C2×C32×D4D411yescharacteristic, complemented
72C22×C32×C4—21no—
73C22×C32×C4C2311yescharacteristic
74C2×C3×#67—24no—
75C2×C3×#67—21no—
76C2×C3×#67D412yes—
77C3×#239—22no—
78C3×#239—22no—
79C3×D3×Q8—22no—
80C3×D3×Q8—22no—
81C3×#237—24no—
82C3×#237—22no—
83C3×#237—22no—
84C3×#237—24no—
85C3×D3×D4—24no—
86C3×D3×D4—22no—
87C3×D3×D4—24no—
88C3×D3×D4—22no—
89C3×#235—24no—
90C3×#235—24no—
91C3×#235—21no—
92C3×#235—21no—
93C3×#235—21no—
94C3×#235—21no—
95C3×#235—21no—
96C3×#235—21no—
97C3×#235—22no—
98C3×#235—22no—
99C3×#235D412yescomplemented
100C3×#235C2312yes—
101C2×C3×D12—22no—
102C2×C3×D12—21no—
103C2×C3×D12—21no—
104C2×C3×D12—21no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12—24no—
108C2×C3×D12D411yescharacteristic, complemented
109C2×C3×D12C2312yes—
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—24no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3D412yes—
114C2×C3×Dic6—22no—
115C2×C3×Dic6D411yescharacteristic, complemented
116C2×C3×Dic6C2311yescharacteristic
117C32×M16—21no—
118C32×M16C2312yes—
119C2×C32×C8—21no—
120C32×C4⋊C4—21no—
121C32×C22⋊C4—21no—
122C32×C42C2312yes—
123C3×#215—24no—
124C3×#213—24no—
125C3×(C2×D3)⋊C4—24no—
126C3×#208—21no—
127C3×#208C2312yes—
128C2×C3×C3⋊C8—21no—
129C3×D24—24no—
130C3×#204—24no—
131#3021—31noSylow
132C3×2−1+4—32no—
133C3×2−1+4—61no—
134C3×2−1+4—61no—
135C3×H(5,𝔽2)—32no—
136C3×H(5,𝔽2)—62no—
137C3×H(5,𝔽2)—61no—
138C3×H(5,𝔽2)—61no—
139C2×C3×#41—21no—
140C2×C3×#41—31no—
141C2×C3×#41—31no—
142C2×C3×#41—62no—
143C2×C3×#41—62no—
144C2×C3×#41—62no—
145C2×C3×#41C2×D311yescharacteristic
146C2×C3×#41C22×C311yescharacteristic
147C22×C3×D4—31no—
148#1010—21no—
149#1010C22×C312yescomplemented
150#1009—21no—
151#1009C22×C312yescomplemented
152D3×#41—22no—
153D3×#41—22no—
154#1007—21no—
155#1004—21no—
156#1004—22no—
157C2×#235—22no—
158C2×#235C22×C311yescharacteristic
159C2×#235C22×C311yescharacteristic
160C22×D12C22×C311yescharacteristic, complemented
161C3×AGL(1,ℤ/8)—34no—
162C3×AGL(1,ℤ/8)—34no—
163C3×AGL(1,ℤ/8)—62no—
164C3×AGL(1,ℤ/8)—62no—
165C2×C3×SD16—61no—
166C2×C3×SD16—61no—
167C2×C3×D8—61no—
168C2×C3×D8—61no—
169C2×C3×M16—21no—
170C2×C3×M16—31no—
171C2×C3×M16C2×D311yescharacteristic, complemented
172C2×C3×M16C22×C311yescharacteristic, complemented
173C3×#127—32no—
174C3×#124—32no—
175C3×#121—62no—
176C3×#120—62no—
177C3×#117—21no—
178C3×#117C2×D311yescharacteristic, complemented
179C3×#117C22×C311yescharacteristic, complemented
180#949—22no—
181#949C22×C314yescomplemented
182C2×#215—21no—
183C2×#213—21no—
184C2×#208C22×C311yescharacteristic, complemented
185#908—22no—
186#908C22×C314yescomplemented
187C2×D24—21no—
188C2×#204—21no—
189#895—22no—
190#882—22no—
191#875C22×C312yescomplemented
192#874C22×C312yescomplemented
193C3×#104—24no—
194C3×#104—34no—
195C3×#104C2×D314yescomplemented
196C3×#104C22×C314yescomplemented
197C3×#101—32no—
198C3×#100—32no—
199#824C22×C312yescomplemented
200#823C22×C312yescomplemented
201#805C22×C314yescomplemented
202C23×C32—21no—
203C23×C32C2×D411yescharacteristic
204C22×C3×D3—24no—
205C22×C3×D3—21no—
206C22×C3×D3—22no—
207C22×C3×D3—41no—
208C22×C3×D3—41no—
209C22×C3×D3—82no—
210C22×C3×D3C2×D412yes—
211C32×Q8—21no—
212C32×Q8C2×D412yes—
213C32×D4—22no—
214C32×D4—22no—
215C32×D4—21no—
216C32×D4C2×D412yes—
217C2×C32×C4—21no—
218C2×C32×C4—22no—
219C2×C32×C4—22no—
220C2×C32×C4—22no—
221C2×C32×C4C2×D411yescharacteristic
222C2×C32×C4C2×D411yescharacteristic
223C2×C32×C4C2×D411yescharacteristic
224C2×C32×C4C2×D411yescharacteristic
225C2×C32×C4C2×D411yescharacteristic
226C2×C32×C4C2411yescharacteristic
227C3×#67—24no—
228C3×#67—24no—
229C3×#67—22no—
230C3×#67—22no—
231C3×#67—22no—
232C3×#67—22no—
233C2×C3×Dic3—24no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3C2×D412yes—
236C3×D12—24no—
237C3×D12—21no—
238C3×D12—21no—
239C3×D12—21no—
240C3×D12—22no—
241C3×D12—22no—
242C3×D12—41no—
243C3×D12—41no—
244C3×D12—84no—
245C3×D12C2×D412yes—
246C3×C4×D3—24no—
247C3×C4×D3—24no—
248C3×C4×D3—22no—
249C3×C4×D3—22no—
250C3×C4×D3—22no—
251C3×C4×D3—22no—
252C3×Dic6—24no—
253C3×Dic6—21no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6C2×D412yes—
257C32×C8—22no—
258C3×C3⋊C8—22no—
259#585—31no—
260C2×AGL(1,ℤ/8)—31no—
261C2×AGL(1,ℤ/8)—31no—
262#535—31no—
263#454—34no—
264#453—34no—
265#421—31no—
266#421C3×D311yescharacteristic, complemented
267#413—31no—
268C24×C3—61no—
269C23×D3—21no—
270C3×#41—21no—
271C3×#41—21no—
272C3×#41—21no—
273C3×#41—21no—
274C3×#41—22no—
275C3×#41—22no—
276C3×#41—32no—
277C3×#41—32no—
278C3×#41—41no—
279C3×#41—41no—
280C3×#41—62no—
281C3×#41—62no—
282C3×#41—64no—
283C3×#41—64no—
284C3×#41—64no—
285C3×#41—64no—
286C3×#41—62no—
287C3×#41—62no—
288C3×#41—62no—
289C3×#41—62no—
290C3×#41—61no—
291C3×#41—61no—
292C3×#41—61no—
293C3×#41—61no—
294C3×#41—61no—
295C3×#41—61no—
296C3×#41D1212yescomplemented
297C3×#41C3×D412yescomplemented
298C3×#41C22×D312yes—
299C3×#41C23×C312yes—
300C2×C3×Q8—21no—
301C2×C3×Q8—31no—
302C2×C3×Q8—31no—
303C2×C3×Q8—62no—
304C2×C3×Q8—62no—
305C2×C3×Q8—62no—
306C2×C3×Q8D1211yescharacteristic, complemented
307C2×C3×Q8C3×D411yescharacteristic, complemented
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—32no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—32no—
315C2×C3×D4—41no—
316C2×C3×D4—62no—
317C2×C3×D4—64no—
318C2×C3×D4—64no—
319C2×C3×D4—64no—
320C2×C3×D4—62no—
321C2×C3×D4—64no—
322C2×C3×D4—61no—
323C2×C3×D4—62no—
324C2×C3×D4—61no—
325C2×C3×D4—61no—
326C2×C3×D4—61no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C2×C3×D4D1211yescharacteristic, complemented
330C2×C3×D4C3×D411yescharacteristic, complemented
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—32no—
335C22×C3×C4—41no—
336C22×C3×C4—64no—
337C22×C3×C4—61no—
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C23×C311yescharacteristic
340C2×#67—24no—
341C2×#67—21no—
342C2×#67C3×D412yes—
343#239—22no—
344#239—22no—
345D3×Q8—22no—
346D3×Q8—22no—
347#237—24no—
348#237—22no—
349#237—22no—
350#237—24no—
351D3×D4—24no—
352D3×D4—22no—
353D3×D4—24no—
354D3×D4—22no—
355#235—24no—
356#235—24no—
357#235—21no—
358#235—21no—
359#235—21no—
360#235—21no—
361#235—21no—
362#235—21no—
363#235—22no—
364#235—22no—
365#235C3×D412yescomplemented
366#235C23×C312yes—
367C2×D12—22no—
368C2×D12—21no—
369C2×D12—21no—
370C2×D12—21no—
371C2×D12—21no—
372C2×D12—21no—
373C2×D12—24no—
374C2×D12C3×D411yescharacteristic, complemented
375C2×D12C23×C312yes—
376C2×D12C23×C311yescharacteristic
377C2×C4×D3—24no—
378C2×C4×D3—21no—
379C2×C4×D3C3×D412yes—
380C2×Dic6—22no—
381C2×Dic6C3×D411yescharacteristic, complemented
382C2×Dic6C23×C311yescharacteristic
383C3×SD16—64no—
384C3×SD16—64no—
385C3×D8—64no—
386C3×D8—64no—
387C3×M16—21no—
388C3×M16—21no—
389C3×M16—22no—
390C3×M16—32no—
391C3×M16—41no—
392C3×M16—61no—
393C3×M16C22×D312yes—
394C3×M16C23×C312yes—
395C2×C3×C8—21no—
396C2×C3×C8—21no—
397C2×C3×C8—41no—
398C2×C3×C8—61no—
399C3×C4⋊C4—21no—
400C3×C4⋊C4—21no—
401C3×C4⋊C4—41no—
402C3×C22⋊C4—21no—
403C3×C22⋊C4—21no—
404C3×C22⋊C4—41no—
405C3×C22⋊C4—64no—
406C3×C42—22no—
407C3×C42C22×D312yes—
408C3×C42C23×C312yes—
409#215—24no—
410#213—24no—
411(C2×D3)⋊C4—24no—
412#208—21no—
413#208C23×C312yes—
414C2×C3⋊C8—21no—
415D24—24no—
416#204—24no—
417C22×C32—22no—
418C22×C32—41no—
419C22×C32—81no—
420C22×C32#12011yescharacteristic
421C22×C32#12011yescharacteristic
422C22×C32C22×D411yescharacteristic
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—42no—
426C2×C3×D3—44no—
427C2×C3×D3—42no—
428C2×C3×D3—81no—
429C2×C3×D3—84no—
430C2×C3×D3—82no—
431C2×C3×D3—82no—
432C32×C4—22no—
433C32×C4—42no—
434C32×C4#12011yescharacteristic
435C32×C4#12011yescharacteristic
436C32×C4C22×D411yescharacteristic
437C32×C4C22×D411yescharacteristic
438C3×Dic3—22no—
439C3×Dic3—22no—
4402−1+4—32no—
4412−1+4—61no—
4422−1+4—61no—
443H(5,𝔽2)—32no—
444H(5,𝔽2)—62no—
445H(5,𝔽2)—61no—
446H(5,𝔽2)—61no—
447C2×#41—31no—
448C2×#41—31no—
449C2×#41—62no—
450C2×#41—62no—
451C2×#41—62no—
452C2×#41C2×C3×D311yescharacteristic
453C22×D4—31no—
454AGL(1,ℤ/8)—34no—
455AGL(1,ℤ/8)—34no—
456AGL(1,ℤ/8)—62no—
457AGL(1,ℤ/8)—62no—
458C2×SD16—61no—
459C2×SD16—61no—
460C2×D8—61no—
461C2×D8—61no—
462C2×M16—31no—
463C2×M16C2×C3×D311yescharacteristic, complemented
464#127—32no—
465#124—32no—
466#121—62no—
467#120—62no—
468#117C2×C3×D311yescharacteristic, complemented
469#104—34no—
470#104C2×C3×D314yescomplemented
471#101—32no—
472#100—32no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—32no—
477C23×C3—41no—
478C23×C3—64no—
479C23×C3—61no—
480C23×C3—62no—
481C23×C3—121no—
482C23×C3—121no—
483C23×C3—242no—
484C23×C3D3×D411yescharacteristic
485C23×C3C2×C3×D411yescharacteristic
486C22×D3—24no—
487C22×D3—21no—
488C22×D3—22no—
489C22×D3—41no—
490C22×D3—41no—
491C22×D3—82no—
492C22×D3C2×C3×D412yes—
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—22no—
496C3×Q8—32no—
497C3×Q8—41no—
498C3×Q8—64no—
499C3×Q8—61no—
500C3×Q8—61no—
501C3×Q8—61no—
502C3×Q8C2×D1212yes—
503C3×Q8C2×C3×D412yes—
504C3×D4—22no—
505C3×D4—22no—
506C3×D4—22no—
507C3×D4—22no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—22no—
511C3×D4—32no—
512C3×D4—41no—
513C3×D4—42no—
514C3×D4—42no—
515C3×D4—64no—
516C3×D4—64no—
517C3×D4—64no—
518C3×D4—62no—
519C3×D4—62no—
520C3×D4—62no—
521C3×D4—62no—
522C3×D4—61no—
523C3×D4—61no—
524C3×D4—62no—
525C3×D4—61no—
526C3×D4—62no—
527C3×D4—121no—
528C3×D4—121no—
529C3×D4—244no—
530C3×D4C2×D1212yes—
531C3×D4C2×C3×D412yes—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—32no—
547C2×C3×C4—42no—
548C2×C3×C4—42no—
549C2×C3×C4—41no—
550C2×C3×C4—42no—
551C2×C3×C4—64no—
552C2×C3×C4—64no—
553C2×C3×C4—64no—
554C2×C3×C4—61no—
555C2×C3×C4—62no—
556C2×C3×C4—62no—
557C2×C3×C4—62no—
558C2×C3×C4—62no—
559C2×C3×C4C2×D1211yescharacteristic
560C2×C3×C4C2×D1211yescharacteristic
561C2×C3×C4D3×D411yescharacteristic
562C2×C3×C4D3×D411yescharacteristic
563C2×C3×C4D3×D411yescharacteristic
564C2×C3×C4C2×C3×D411yescharacteristic
565C2×C3×C4C2×C3×D411yescharacteristic
566C2×C3×C4C2×C3×D411yescharacteristic
567C2×C3×C4C2×C3×D411yescharacteristic
568C2×C3×C4C2×C3×D411yescharacteristic
569C2×C3×C4C23×D311yescharacteristic
570C2×C3×C4C24×C311yescharacteristic
571#67—24no—
572#67—24no—
573#67—22no—
574#67—22no—
575#67—22no—
576#67—22no—
577C2×Dic3—24no—
578C2×Dic3—21no—
579C2×Dic3C2×C3×D412yes—
580D12—24no—
581D12—21no—
582D12—21no—
583D12—21no—
584D12—22no—
585D12—22no—
586D12—41no—
587D12—41no—
588D12—84no—
589D12C2×C3×D412yes—
590C4×D3—24no—
591C4×D3—24no—
592C4×D3—22no—
593C4×D3—22no—
594C4×D3—22no—
595C4×D3—22no—
596Dic6—24no—
597Dic6—21no—
598Dic6—21no—
599Dic6—21no—
600Dic6C2×C3×D412yes—
601C3×C8—22no—
602C3×C8—22no—
603C3×C8—42no—
604C3×C8—62no—
605C3⋊C8—22no—
606C2×C32—21no—
607C2×C32—21no—
608C2×C32—21no—
609C2×C32—42no—
610C2×C32C2×#12011yescharacteristic
611C3×D3—42no—
612C3×D3—42no—
613C3×D3—82no—
614C24—61no—
615#41—21no—
616#41—21no—
617#41—32no—
618#41—32no—
619#41—62no—
620#41—62no—
621#41—64no—
622#41—64no—
623#41—64no—
624#41—64no—
625#41—62no—
626#41—62no—
627#41—62no—
628#41—62no—
629#41—61no—
630#41—61no—
631#41—61no—
632#41—61no—
633#41—61no—
634#41—61no—
635#41C3×D1212yescomplemented
636#41C22×C3×D312yes—
637C2×Q8—31no—
638C2×Q8—31no—
639C2×Q8—62no—
640C2×Q8—62no—
641C2×Q8—62no—
642C2×Q8C3×D1211yescharacteristic, complemented
643C2×D4—21no—
644C2×D4—32no—
645C2×D4—31no—
646C2×D4—32no—
647C2×D4—31no—
648C2×D4—62no—
649C2×D4—64no—
650C2×D4—64no—
651C2×D4—64no—
652C2×D4—62no—
653C2×D4—64no—
654C2×D4—61no—
655C2×D4—62no—
656C2×D4—61no—
657C2×D4—61no—
658C2×D4—61no—
659C2×D4—61no—
660C2×D4—61no—
661C2×D4C3×D1211yescharacteristic, complemented
662C22×C4—21no—
663C22×C4—32no—
664C22×C4—64no—
665C22×C4—61no—
666C22×C4C22×C3×D311yescharacteristic
667SD16—64no—
668SD16—64no—
669D8—64no—
670D8—64no—
671M16—21no—
672M16—32no—
673M16—61no—
674M16C22×C3×D312yes—
675C2×C8—21no—
676C2×C8—61no—
677C4⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—64no—
680C42C22×C3×D312yes—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—42no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—62no—
690C22×C3—62no—
691C22×C3—81no—
692C22×C3—81no—
693C22×C3—81no—
694C22×C3—82no—
695C22×C3—122no—
696C22×C3—124no—
697C22×C3—122no—
698C22×C3—241no—
699C22×C3—242no—
700C22×C3—242no—
701C22×C3—244no—
702C22×C3#88211yescharacteristic
703C22×C3#88211yescharacteristic
704C22×C3C3×#12011yescharacteristic
705C22×C3C3×#12011yescharacteristic
706C22×C3C2×D3×D411yescharacteristic
707C22×C3C22×C3×D411yescharacteristic
708C2×D3—22no—
709C2×D3—22no—
710C2×D3—42no—
711C2×D3—44no—
712C2×D3—42no—
713C2×D3—81no—
714C2×D3—84no—
715C2×D3—82no—
716C2×D3—82no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—42no—
724C3×C4—42no—
725C3×C4—42no—
726C3×C4—62no—
727C3×C4—62no—
728C3×C4—82no—
729C3×C4#88211yescharacteristic
730C3×C4#88211yescharacteristic
731C3×C4C3×#12011yescharacteristic
732C3×C4C3×#12011yescharacteristic
733C3×C4C22×D1211yescharacteristic
734C3×C4C2×D3×D411yescharacteristic
735C3×C4C22×C3×D411yescharacteristic
736C3×C4C22×C3×D411yescharacteristic
737Dic3—22no—
738Dic3—22no—
739C32#302111yescharacteristic, complemented, Sylow
740C23—21no—
741C23—32no—
742C23—64no—
743C23—61no—
744C23—62no—
745C23—121no—
746C23—121no—
747C23—242no—
748C23C3×D3×D411yescharacteristic
749Q8—21no—
750Q8—32no—
751Q8—64no—
752Q8—61no—
753Q8—61no—
754Q8—61no—
755Q8C2×C3×D1212yes—
756D4—22no—
757D4—22no—
758D4—21no—
759D4—32no—
760D4—64no—
761D4—64no—
762D4—64no—
763D4—62no—
764D4—62no—
765D4—62no—
766D4—62no—
767D4—61no—
768D4—61no—
769D4—62no—
770D4—61no—
771D4—62no—
772D4—121no—
773D4—121no—
774D4—244no—
775D4C2×C3×D1212yes—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—32no—
781C2×C4—64no—
782C2×C4—64no—
783C2×C4—64no—
784C2×C4—61no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4C2×C3×D1211yescharacteristic
790C2×C4C2×C3×D1211yescharacteristic
791C2×C4C3×D3×D411yescharacteristic
792C2×C4C3×D3×D411yescharacteristic
793C2×C4C3×D3×D411yescharacteristic
794C2×C4C23×C3×D311yescharacteristic
795C8—22no—
796C8—62no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—41no—
805C2×C3—41no—
806C2×C3—41no—
807C2×C3—42no—
808C2×C3—42no—
809C2×C3—82no—
810C2×C3—122no—
811C2×C3—122no—
812C2×C3—242no—
813C2×C3C2×#88211yescharacteristic
814C2×C3C2×C3×#12011yescharacteristic
815D3—42no—
816D3—42no—
817D3—82no—
818C22—22no—
819C22—41no—
820C22—62no—
821C22—62no—
822C22—81no—
823C22—122no—
824C22—124no—
825C22—122no—
826C22—241no—
827C22—242no—
828C22—242no—
829C22—244no—
830C22C3×#88211yescharacteristic
831C22C3×#88211yescharacteristic
832C22C2×C3×D3×D411yescharacteristic
833C4—22no—
834C4—42no—
835C4—62no—
836C4—62no—
837C4C3×#88211yescharacteristic
838C4C3×#88211yescharacteristic
839C4C22×C3×D1211yescharacteristic
840C4C2×C3×D3×D411yescharacteristic
841C3—21no—
842C3#7899411yescharacteristic, direct product factor
843C3C3×#302111yescharacteristic, complemented
844C2—21no—
845C2—21no—
846C2—21no—
847C2—42no—
848C2—122no—
849C2—122no—
850C2—242no—
851C2C2×C3×#88211yescharacteristic
subgroupG/H
centerC2×C3C2×#882
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#421C2
socleC2×C32C2×#120
hypercenterC3×#421D3
hypocenterC3C3×#3021
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#421

Complements

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

NH ≅ G/Ntype
1. C3×#5964C2semidirect
2. C2×C3×#949C2semidirect
3. C2×C3×#908C2semidirect
4. C3×#5525C2semidirect
5. C32×#421C2semidirect
6. C3×#5132C2semidirect
7. C3×#5005C2semidirect
8. C3×#4827C2semidirect
9. C3×#4822C2semidirect
11. #78994C3direct (N × H)
14. C3×#1010C22semidirect
16. C3×#1009C22semidirect
25. C22×C3×D12C22semidirect
26. C2×C32×M16C22semidirect
27. C32×#117C22semidirect
29. C3×#949C22semidirect
32. C2×C3×#208C22semidirect
34. C3×#908C22semidirect
39. C3×#875C22semidirect
40. C3×#874C22semidirect
41. C32×#104C22semidirect
42. C3×#824C22semidirect
43. C3×#823C22semidirect
44. C3×#805C22semidirect
46. #5964C2×C3semidirect
50. C2×#949C2×C3semidirect
51. C2×#908C2×C3semidirect
52. #5525C2×C3semidirect
57. C3×#421D3semidirect
58. C3×#421C2×C3semidirect
60. #5132C2×C3semidirect
61. #5005C2×C3semidirect
62. #4827C2×C3semidirect
63. #4822C2×C3semidirect
67. C32×#41D4semidirect
69. C2×C32×Q8D4semidirect
71. C2×C32×D4D4semidirect
99. C3×#235D4semidirect
108. C2×C3×D12D4semidirect
115. C2×C3×Dic6D4semidirect
149. #1010C22×C3semidirect
151. #1009C22×C3semidirect
160. C22×D12C22×C3semidirect
171. C2×C3×M16C2×D3semidirect
172. C2×C3×M16C22×C3semidirect
178. C3×#117C2×D3semidirect
179. C3×#117C22×C3semidirect
181. #949C22×C3semidirect
184. C2×#208C22×C3semidirect
186. #908C22×C3semidirect
191. #875C22×C3semidirect
192. #874C22×C3semidirect
195. C3×#104C2×D3semidirect
196. C3×#104C22×C3semidirect
199. #824C22×C3semidirect
200. #823C22×C3semidirect
201. #805C22×C3semidirect
266. #421C3×D3semidirect
296. C3×#41D12semidirect
297. C3×#41C3×D4semidirect
306. C2×C3×Q8D12semidirect
307. C2×C3×Q8C3×D4semidirect
329. C2×C3×D4D12semidirect
330. C2×C3×D4C3×D4semidirect
365. #235C3×D4semidirect
374. C2×D12C3×D4semidirect
381. C2×Dic6C3×D4semidirect
463. C2×M16C2×C3×D3semidirect
468. #117C2×C3×D3semidirect
470. #104C2×C3×D3semidirect
635. #41C3×D12semidirect
642. C2×Q8C3×D12semidirect
661. C2×D4C3×D12semidirect
739. C32#3021semidirect
842. C3#78994direct (N × H)
843. C3C3×#3021semidirect

Maximal subgroups

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

subgroupindex
C3×#59642
C2×C3×#9492
C2×C3×#9082
C3×#55252
C32×#4212
C3×#51322
C3×#50052
C3×#48272
C3×#48222
C3×#30213
#789943