Finite Group Databasebeta

← C3×#78719 #11868012

Subgroups — C3×#78719 #11868012

Order 1152.

979 conjugacy classes of subgroups.

The subgroup lattice has 769 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5822C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic, complemented
3C3×#5748C211yesmaximal, characteristic, complemented
4C2×C3×#907C211yesmaximal, characteristic, complemented
5C32×#413C211yesmaximal, characteristic, complemented
6C3×#5132C211yesmaximal, characteristic, complemented
7C2×C3×#822C211yesmaximal, characteristic, complemented
8C3×#4755C212yesmaximal, complemented
9C3×#4754C212yesmaximal, complemented
10C3×#4749C212yesmaximal, complemented
11C3×#4748C212yesmaximal, complemented
12C3×#3067—31nomaximal
13#78719C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C3×#235C2211yescharacteristic
17C2×C32×M16C2211yescharacteristic
18C2×C32×M16C2211yescharacteristic
19C3×#951—21no—
20C3×#950—22no—
21C3×#950—21no—
22C3×#950—21no—
23C3×#950—21no—
24C3×#950—21no—
25C3×#949—21no—
26C2×C3×#216C2211yescharacteristic, complemented
27C3×#942C2212yes—
28C2×C3×#215C2211yescharacteristic, complemented
29C2×C3×#214C2211yescharacteristic, complemented
30C3×#932C2212yes—
31C2×C3×#213C2211yescharacteristic, complemented
32C2×C3×#208C2211yescharacteristic
33C22×C3×C3⋊C8C2211yescharacteristic
34C3×#909—21no—
35C3×#909C2212yes—
36C3×#908—21no—
37C3×#908C2212yes—
38C3×#907—21no—
39C3×#907—21no—
40C3×#907C2212yes—
41C3×#907C2212yes—
42C3×#904—22no—
43C2×C3×ΓL(1,𝔽25)—21no—
44C2×C3×D3×C8—21no—
45C32×#101C2212yescomplemented
46C32×#100C2212yescomplemented
47C3×#824C2212yescomplemented
48C3×#823C2212yescomplemented
49C3×#822C2212yescomplemented
50C3×#822C2212yescomplemented
51C3×#575—31no—
52C3×#575—31no—
53C2×C3×#135—31no—
54C2×C3×#131—31no—
55#5822C2×C311yescharacteristic, complemented
56C2×#950C2×C311yescharacteristic, complemented
57#5748C2×C311yescharacteristic, complemented
58C2×#907C2×C311yescharacteristic, complemented
59C3×#473—32no—
60C3×#472—32no—
61C3×#471—32no—
62C3×#471—32no—
63C2×C3×#108—31no—
64C3×#413—21no—
65C3×#413—31no—
66C3×#413D311yescharacteristic, complemented
67C3×#413C2×C311yescharacteristic, complemented
68#5132C2×C311yescharacteristic, complemented
69C2×#822C2×C311yescharacteristic, complemented
70#4755C2×C312yescomplemented
71#4754C2×C312yescomplemented
72#4749C2×C312yescomplemented
73#4748C2×C312yescomplemented
74C32×#41—21no—
75C32×#41—21no—
76C32×#41—21no—
77C32×#41—21no—
78C2×C32×Q8C2311yescharacteristic
79C2×C32×D4—21no—
80C2×C32×D4C2311yescharacteristic
81C22×C32×C4—21no—
82C22×C32×C4C2311yescharacteristic
83C2×C3×#67—21no—
84C2×C3×#67—21no—
85C3×#235—21no—
86C3×#235—21no—
87C3×#235—21no—
88C3×#235—21no—
89C3×#235—21no—
90C3×#235—21no—
91C3×#235D412yes—
92C3×#235C2312yes—
93C2×C3×D12D411yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×C4×D3—21no—
97C2×C3×Dic6D411yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C32×M16—21no—
100C32×M16—21no—
101C32×M16C2312yes—
102C32×M16C2312yes—
103C2×C32×C8—21no—
104C2×C32×C8—21no—
105C3×#216—22no—
106C3×#216—21no—
107C3×#216—21no—
108C3×#215—22no—
109C3×#215—21no—
110C3×#215—21no—
111C3×#214—22no—
112C3×#214—21no—
113C3×#214—21no—
114C3×#213—22no—
115C3×#213—21no—
116C3×#213—21no—
117C3×#208—21no—
118C3×#208C2312yes—
119C2×C3×C3⋊C8—21no—
120C2×C3×C3⋊C8D411yescharacteristic
121C2×C3×C3⋊C8D411yescharacteristic
122C2×C3×C3⋊C8D411yescharacteristic
123C2×C3×C3⋊C8D411yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C3×Dic12—22no—
127C3×D24—22no—
128C3×#204—22no—
129C3×#204—22no—
130C3×ΓL(1,𝔽25)—22no—
131C3×ΓL(1,𝔽25)—22no—
132C3×D3×C8—22no—
133C3×D3×C8—22no—
134#3067—31noSylow
135C2×C3×#41—21no—
136C2×C3×#41—31no—
137C2×C3×#41—31no—
138C2×C3×#41C2×D311yescharacteristic
139C2×C3×#41C22×C311yescharacteristic
140C2×#235C22×C311yescharacteristic
141C2×#235C22×C311yescharacteristic
142C3×#137—32no—
143C3×#137—32no—
144C3×#137—61no—
145C3×#137—61no—
146C3×AGL(1,ℤ/8)—32no—
147C3×AGL(1,ℤ/8)—32no—
148C3×AGL(1,ℤ/8)—61no—
149C3×AGL(1,ℤ/8)—61no—
150C3×#135—62no—
151C3×#135—61no—
152C3×#135—61no—
153C3×#135—61no—
154C3×#135—61no—
155C3×#135—62no—
156C2×C3×Q16—31no—
157C2×C3×SD16—31no—
158C2×C3×SD16—31no—
159C2×C3×D8—31no—
160C3×#131—32no—
161C3×#131—32no—
162C3×#131—61no—
163C3×#131—61no—
164C2×C3×M16—21no—
165C2×C3×M16—21no—
166C2×C3×M16—31no—
167C2×C3×M16—61no—
168C2×C3×M16C2×D311yescharacteristic
169C2×C3×M16C2×D311yescharacteristic
170C2×C3×M16C22×C311yescharacteristic
171C2×C3×M16C22×C311yescharacteristic
172C22×C3×C8—31no—
173C22×C3×C8—61no—
174#951—21no—
175#950—22no—
176#950—21no—
177#950—21no—
178#950—21no—
179#950—21no—
180#949—21no—
181C2×#216C22×C311yescharacteristic, complemented
182#942C22×C312yes—
183C2×#215C22×C311yescharacteristic, complemented
184C2×#214C22×C311yescharacteristic, complemented
185#932C22×C312yes—
186C2×#213C22×C311yescharacteristic, complemented
187C2×#208C22×C311yescharacteristic
188C22×C3⋊C8C22×C311yescharacteristic
189#909—21no—
190#909C22×C312yes—
191#908—21no—
192#908C22×C312yes—
193#907—21no—
194#907—21no—
195#907C22×C312yes—
196#907C22×C312yes—
197#904—22no—
198C2×ΓL(1,𝔽25)—21no—
199C2×D3×C8—21no—
200C3×#108—32no—
201C3×#108—32no—
202C3×#101—22no—
203C3×#101—32no—
204C3×#101C2×D312yescomplemented
205C3×#101C22×C312yescomplemented
206C3×#100—22no—
207C3×#100—32no—
208C3×#100C2×D312yescomplemented
209C3×#100C22×C312yescomplemented
210#824C22×C312yescomplemented
211#823C22×C312yescomplemented
212#822C22×C312yescomplemented
213#822C22×C312yescomplemented
214C23×C32—21no—
215C23×C32#4111yescharacteristic
216C22×C3×D3—21no—
217C22×C3×D3—21no—
218C32×Q8—21no—
219C32×Q8—21no—
220C32×D4—21no—
221C32×D4—21no—
222C32×D4—41no—
223C32×D4—41no—
224C2×C32×C4—21no—
225C2×C32×C4—41no—
226C2×C32×C4—41no—
227C2×C32×C4C2×D411yescharacteristic
228C2×C32×C4C2×D411yescharacteristic
229C2×C32×C4C2×D411yescharacteristic
230C2×C32×C4C2×D411yescharacteristic
231C2×C32×C4#4111yescharacteristic
232C2×C32×C4C2411yescharacteristic
233C3×#67—22no—
234C3×#67—22no—
235C3×#67—41no—
236C3×#67—41no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—21no—
239C3×D12—21no—
240C3×D12—21no—
241C3×D12—21no—
242C3×D12C2×D412yes—
243C3×C4×D3—22no—
244C3×C4×D3—22no—
245C3×C4×D3—41no—
246C3×C4×D3—41no—
247C3×Dic6—21no—
248C3×Dic6—21no—
249C3×Dic6—21no—
250C3×Dic6C2×D412yes—
251C32×C8—22no—
252C32×C8—22no—
253C3×C3⋊C8—22no—
254C3×C3⋊C8C2×D411yescharacteristic
255C3×C3⋊C8C2×D411yescharacteristic
256C3×C3⋊C8C2×D411yescharacteristic
257C3×C3⋊C8C2×D411yescharacteristic
258#575—31no—
259#575—31no—
260C2×#135—31no—
261C2×#131—31no—
262#473—32no—
263#472—32no—
264#471—32no—
265#471—32no—
266C2×#108—31no—
267#413—31no—
268#413C3×D311yescharacteristic, complemented
269C3×#41—21no—
270C3×#41—21no—
271C3×#41—21no—
272C3×#41—21no—
273C3×#41—21no—
274C3×#41—21no—
275C3×#41—21no—
276C3×#41—21no—
277C3×#41—32no—
278C3×#41—32no—
279C3×#41—41no—
280C3×#41—41no—
281C3×#41—41no—
282C3×#41—41no—
283C3×#41—61no—
284C3×#41—61no—
285C3×#41—61no—
286C3×#41—61no—
287C3×#41—61no—
288C3×#41—61no—
289C2×C3×Q8—21no—
290C2×C3×Q8—31no—
291C2×C3×Q8—31no—
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×Q8C23×C311yescharacteristic
294C2×C3×D4—22no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—31no—
299C2×C3×D4—31no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C23×C311yescharacteristic
304C22×C3×C4—22no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C23×C311yescharacteristic
312C2×#67—21no—
313C2×#67—21no—
314#235—21no—
315#235—21no—
316#235—21no—
317#235—21no—
318#235—21no—
319#235—21no—
320#235C3×D412yes—
321#235C23×C312yes—
322C2×D12C3×D411yescharacteristic
323C2×D12C23×C311yescharacteristic
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×Dic6C3×D411yescharacteristic
327C2×Dic6C23×C311yescharacteristic
328C3×Q16—62no—
329C3×Q16—61no—
330C3×Q16—61no—
331C3×Q16—62no—
332C3×SD16—62no—
333C3×SD16—62no—
334C3×SD16—61no—
335C3×SD16—61no—
336C3×SD16—61no—
337C3×SD16—61no—
338C3×SD16—62no—
339C3×SD16—62no—
340C3×D8—62no—
341C3×D8—61no—
342C3×D8—61no—
343C3×D8—62no—
344C3×M16—21no—
345C3×M16—21no—
346C3×M16—21no—
347C3×M16—21no—
348C3×M16—22no—
349C3×M16—22no—
350C3×M16—32no—
351C3×M16—41no—
352C3×M16—41no—
353C3×M16—62no—
354C3×M16—62no—
355C3×M16—61no—
356C3×M16C22×D312yes—
357C3×M16C22×D312yes—
358C3×M16C23×C312yes—
359C3×M16C23×C312yes—
360C2×C3×C8—21no—
361C2×C3×C8—21no—
362C2×C3×C8—21no—
363C2×C3×C8—21no—
364C2×C3×C8—31no—
365C2×C3×C8—31no—
366C2×C3×C8—31no—
367C2×C3×C8—31no—
368C2×C3×C8—31no—
369C2×C3×C8—31no—
370C2×C3×C8—41no—
371C2×C3×C8—41no—
372C2×C3×C8—62no—
373C2×C3×C8—62no—
374C2×C3×C8—61no—
375#216—22no—
376#216—21no—
377#216—21no—
378#215—22no—
379#215—21no—
380#215—21no—
381#214—22no—
382#214—21no—
383#214—21no—
384#213—22no—
385#213—21no—
386#213—21no—
387#208—21no—
388#208C23×C312yes—
389C2×C3⋊C8—21no—
390C2×C3⋊C8C3×D411yescharacteristic
391C2×C3⋊C8C3×D411yescharacteristic
392C2×C3⋊C8C3×D411yescharacteristic
393C2×C3⋊C8C3×D411yescharacteristic
394C2×C3⋊C8C23×C311yescharacteristic
395C2×C3⋊C8C23×C311yescharacteristic
396Dic12—22no—
397D24—22no—
398#204—22no—
399#204—22no—
400ΓL(1,𝔽25)—22no—
401ΓL(1,𝔽25)—22no—
402D3×C8—22no—
403D3×C8—22no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32—81no—
407C22×C32#12111yescharacteristic
408C22×C32#12111yescharacteristic
409C22×C32C2×#4111yescharacteristic
410C2×C3×D3—22no—
411C2×C3×D3—42no—
412C2×C3×D3—41no—
413C2×C3×D3—81no—
414C32×C4—41no—
415C32×C4#12111yescharacteristic
416C32×C4#12111yescharacteristic
417C32×C4C22×D411yescharacteristic
418C32×C4C22×D411yescharacteristic
419C3×Dic3—22no—
420C3×Dic3—41no—
421C2×#41—31no—
422C2×#41—31no—
423C2×#41C2×C3×D311yescharacteristic
424#137—32no—
425#137—32no—
426#137—61no—
427#137—61no—
428AGL(1,ℤ/8)—32no—
429AGL(1,ℤ/8)—32no—
430AGL(1,ℤ/8)—61no—
431AGL(1,ℤ/8)—61no—
432#135—62no—
433#135—61no—
434#135—61no—
435#135—61no—
436#135—61no—
437#135—62no—
438C2×Q16—31no—
439C2×SD16—31no—
440C2×SD16—31no—
441C2×D8—31no—
442#131—32no—
443#131—32no—
444#131—61no—
445#131—61no—
446C2×M16—31no—
447C2×M16—61no—
448C2×M16C2×C3×D311yescharacteristic
449C2×M16C2×C3×D311yescharacteristic
450C22×C8—31no—
451C22×C8—61no—
452#108—32no—
453#108—32no—
454#101—32no—
455#101C2×C3×D312yescomplemented
456#100—32no—
457#100C2×C3×D312yescomplemented
458C23×C3—22no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—61no—
463C23×C3—61no—
464C23×C3#23511yescharacteristic
465C23×C3C3×#4111yescharacteristic
466C22×D3—21no—
467C22×D3—21no—
468C3×Q8—21no—
469C3×Q8—21no—
470C3×Q8—21no—
471C3×Q8—21no—
472C3×Q8—32no—
473C3×Q8—41no—
474C3×Q8—41no—
475C3×Q8—61no—
476C3×Q8—61no—
477C3×Q8—61no—
478C3×D4—21no—
479C3×D4—21no—
480C3×D4—21no—
481C3×D4—21no—
482C3×D4—32no—
483C3×D4—41no—
484C3×D4—41no—
485C3×D4—42no—
486C3×D4—42no—
487C3×D4—41no—
488C3×D4—41no—
489C3×D4—41no—
490C3×D4—41no—
491C3×D4—62no—
492C3×D4—62no—
493C3×D4—61no—
494C3×D4—61no—
495C3×D4—61no—
496C3×D4—121no—
497C3×D4—121no—
498C2×C3×C4—22no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—42no—
508C2×C3×C4—42no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—61no—
514C2×C3×C4—62no—
515C2×C3×C4—62no—
516C2×C3×C4—61no—
517C2×C3×C4—121no—
518C2×C3×C4—121no—
519C2×C3×C4#23511yescharacteristic
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4C2×C3×D411yescharacteristic
525C2×C3×C4C2×C3×D411yescharacteristic
526C2×C3×C4C2×C3×D411yescharacteristic
527C2×C3×C4C2×C3×D411yescharacteristic
528C2×C3×C4C3×#4111yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C24×C311yescharacteristic
531#67—22no—
532#67—22no—
533#67—41no—
534#67—41no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537D12—21no—
538D12—21no—
539D12—21no—
540D12C2×C3×D412yes—
541C4×D3—22no—
542C4×D3—22no—
543C4×D3—41no—
544C4×D3—41no—
545Dic6—21no—
546Dic6—21no—
547Dic6—21no—
548Dic6C2×C3×D412yes—
549C3×C8—22no—
550C3×C8—22no—
551C3×C8—22no—
552C3×C8—22no—
553C3×C8—31no—
554C3×C8—31no—
555C3×C8—31no—
556C3×C8—31no—
557C3×C8—42no—
558C3×C8—42no—
559C3×C8—62no—
560C3⋊C8—22no—
561C3⋊C8C2×C3×D411yescharacteristic
562C3⋊C8C2×C3×D411yescharacteristic
563C3⋊C8C2×C3×D411yescharacteristic
564C3⋊C8C2×C3×D411yescharacteristic
565C2×C32—21no—
566C2×C32—21no—
567C2×C32—21no—
568C2×C32—81no—
569C2×C32C2×#12111yescharacteristic
570C3×D3—42no—
571C3×D3—81no—
572#41—21no—
573#41—21no—
574#41—21no—
575#41—21no—
576#41—32no—
577#41—32no—
578#41—61no—
579#41—61no—
580#41—61no—
581#41—61no—
582#41—61no—
583#41—61no—
584C2×Q8—31no—
585C2×Q8—31no—
586C2×Q8C22×C3×D311yescharacteristic
587C2×D4—21no—
588C2×D4—31no—
589C2×D4—31no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4C22×C3×D311yescharacteristic
593C22×C4—21no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4C22×C3×D311yescharacteristic
597Q16—62no—
598Q16—61no—
599Q16—61no—
600Q16—62no—
601SD16—62no—
602SD16—62no—
603SD16—61no—
604SD16—61no—
605SD16—61no—
606SD16—61no—
607SD16—62no—
608SD16—62no—
609D8—62no—
610D8—61no—
611D8—61no—
612D8—62no—
613M16—21no—
614M16—21no—
615M16—32no—
616M16—62no—
617M16—62no—
618M16—61no—
619M16C22×C3×D312yes—
620M16C22×C3×D312yes—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—31no—
624C2×C8—31no—
625C2×C8—31no—
626C2×C8—31no—
627C2×C8—31no—
628C2×C8—31no—
629C2×C8—62no—
630C2×C8—62no—
631C2×C8—61no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—42no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—62no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—81no—
644C22×C3—82no—
645C22×C3—122no—
646C22×C3—121no—
647C22×C3—241no—
648C22×C3#88411yescharacteristic
649C22×C3#88411yescharacteristic
650C22×C3C3×#12111yescharacteristic
651C22×C3C3×#12111yescharacteristic
652C22×C3C2×#23511yescharacteristic
653C22×C3C2×C3×#4111yescharacteristic
654C2×D3—22no—
655C2×D3—42no—
656C2×D3—41no—
657C2×D3—81no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—42no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—62no—
666C3×C4—121no—
667C3×C4#88411yescharacteristic
668C3×C4#88411yescharacteristic
669C3×C4C3×#12111yescharacteristic
670C3×C4C3×#12111yescharacteristic
671C3×C4C2×D3×D411yescharacteristic
672C3×C4C2×D3×D411yescharacteristic
673C3×C4C22×C3×D411yescharacteristic
674C3×C4C22×C3×D411yescharacteristic
675Dic3—22no—
676Dic3—41no—
677C32#306711yescharacteristic, complemented, Sylow
678C23—21no—
679C23—61no—
680C23—61no—
681C23C3×#23511yescharacteristic
682Q8—21no—
683Q8—21no—
684Q8—32no—
685Q8—61no—
686Q8—61no—
687Q8—61no—
688D4—21no—
689D4—21no—
690D4—32no—
691D4—41no—
692D4—41no—
693D4—62no—
694D4—62no—
695D4—61no—
696D4—61no—
697D4—61no—
698D4—121no—
699D4—121no—
700C2×C4—21no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—61no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—61no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4C3×#23511yescharacteristic
710C2×C4C3×D3×D411yescharacteristic
711C2×C4C3×D3×D411yescharacteristic
712C2×C4C3×D3×D411yescharacteristic
713C2×C4C3×D3×D411yescharacteristic
714C2×C4C23×C3×D311yescharacteristic
715C8—22no—
716C8—22no—
717C8—31no—
718C8—31no—
719C8—31no—
720C8—31no—
721C8—62no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—41no—
730C2×C3—41no—
731C2×C3—41no—
732C2×C3—82no—
733C2×C3—81no—
734C2×C3—81no—
735C2×C3—122no—
736C2×C3—241no—
737C2×C3C2×#88411yescharacteristic
738C2×C3C2×C3×#12111yescharacteristic
739D3—42no—
740D3—81no—
741C22—41no—
742C22—41no—
743C22—62no—
744C22—81no—
745C22—122no—
746C22—121no—
747C22—241no—
748C22C3×#88411yescharacteristic
749C22C3×#88411yescharacteristic
750C22C2×C3×#23511yescharacteristic
751C4—41no—
752C4—62no—
753C4—121no—
754C4C3×#88411yescharacteristic
755C4C3×#88411yescharacteristic
756C4C2×C3×D3×D411yescharacteristic
757C4C2×C3×D3×D411yescharacteristic
758C3—21no—
759C3#7871911yescharacteristic, direct product factor
760C3C3×#306711yescharacteristic, complemented
761C2—21no—
762C2—21no—
763C2—21no—
764C2—81no—
765C2—122no—
766C2—241no—
767C2C2×C3×#88411yescharacteristic
subgroupG/H
centerC3×C4#884
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#413C2
socleC2×C32C2×#121
hypercenterC3×#413D3
hypocenterC3C3×#3067
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#413

Complements

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

NH ≅ G/Ntype
1. C3×#5822C2semidirect
2. C2×C3×#950C2semidirect
3. C3×#5748C2semidirect
4. C2×C3×#907C2semidirect
5. C32×#413C2semidirect
6. C3×#5132C2semidirect
7. C2×C3×#822C2semidirect
8. C3×#4755C2semidirect
9. C3×#4754C2semidirect
10. C3×#4749C2semidirect
11. C3×#4748C2semidirect
13. #78719C3direct (N × H)
26. C2×C3×#216C22semidirect
28. C2×C3×#215C22semidirect
29. C2×C3×#214C22semidirect
31. C2×C3×#213C22semidirect
45. C32×#101C22semidirect
46. C32×#100C22semidirect
47. C3×#824C22semidirect
48. C3×#823C22semidirect
49. C3×#822C22semidirect
50. C3×#822C22semidirect
55. #5822C2×C3semidirect
56. C2×#950C2×C3semidirect
57. #5748C2×C3semidirect
58. C2×#907C2×C3semidirect
66. C3×#413D3semidirect
67. C3×#413C2×C3semidirect
68. #5132C2×C3semidirect
69. C2×#822C2×C3semidirect
70. #4755C2×C3semidirect
71. #4754C2×C3semidirect
72. #4749C2×C3semidirect
73. #4748C2×C3semidirect
181. C2×#216C22×C3semidirect
183. C2×#215C22×C3semidirect
184. C2×#214C22×C3semidirect
186. C2×#213C22×C3semidirect
204. C3×#101C2×D3semidirect
205. C3×#101C22×C3semidirect
208. C3×#100C2×D3semidirect
209. C3×#100C22×C3semidirect
210. #824C22×C3semidirect
211. #823C22×C3semidirect
212. #822C22×C3semidirect
213. #822C22×C3semidirect
268. #413C3×D3semidirect
455. #101C2×C3×D3semidirect
457. #100C2×C3×D3semidirect
677. C32#3067semidirect
759. C3#78719direct (N × H)
760. C3C3×#3067semidirect

Maximal subgroups

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

subgroupindex
C3×#58222
C2×C3×#9502
C3×#57482
C2×C3×#9072
C32×#4132
C3×#51322
C2×C3×#8222
C3×#47552
C3×#47542
C3×#47492
C3×#47482
C3×#30673
#787193