Finite Group Databasebeta

← C3×#30430 #10649037

Subgroups — C3×#30430 #10649037

Order 768.

878 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3061C211yesmaximal, characteristic, complemented
2C3×#3060C211yesmaximal, characteristic, complemented
3C3×#3013C211yesmaximal, characteristic, complemented
4C3×#3013C211yesmaximal, characteristic, complemented
5C3×#2097C211yesmaximal, characteristic, complemented
6C3×#2079C211yesmaximal, characteristic, complemented
7C3×#2078C211yesmaximal, characteristic, complemented
8C3×#2040C211yesmaximal, characteristic, complemented
9C3×#2040C211yesmaximal, characteristic, complemented
10C3×#2007C211yesmaximal, characteristic, complemented
11C3×#1908C211yesmaximal, characteristic, complemented
12C3×#1908C211yesmaximal, characteristic, complemented
13C3×#1876C211yesmaximal, characteristic, complemented
14C3×#1876C211yesmaximal, characteristic, complemented
15C3×#1793C211yesmaximal, characteristic, complemented
16#30430C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×2−1+4C2211yescharacteristic
18C2×C3×#137C2211yescharacteristic
19C2×C3×#137C2211yescharacteristic
20C2×C3×#135C2211yescharacteristic
21C2×C3×#135C2211yescharacteristic
22C2×C3×#131C2211yescharacteristic
23C2×C3×#131C2211yescharacteristic
24C3×#537C2211yescharacteristic
25C3×#537C2211yescharacteristic
26C3×#537C2211yescharacteristic
27C3×#470—21no—
28C3×#469—21no—
29C3×#468—21no—
30C3×#468—21no—
31C3×#467—21no—
32C3×#466—21no—
33C3×#465—21no—
34C3×#465—21no—
35C3×#452—21no—
36C3×#452—21no—
37C3×#451—21no—
38C3×#451—21no—
39C3×#449—21no—
40C3×#449—21no—
41C3×#448—21no—
42C3×#448—21no—
43C2×C3×#107C2211yescharacteristic
44C2×C3×#106C2211yescharacteristic
45C2×C3×#104C2211yescharacteristic
46C2×C3×#104C2211yescharacteristic
47C2×C3×#104C2211yescharacteristic
48C2×C3×#104C2211yescharacteristic
49C3×#417C2211yescharacteristic
50C3×#417C2211yescharacteristic
51C3×#417C2211yescharacteristic
52C3×#417C2211yescharacteristic
53C3×#417C2211yescharacteristic
54C3×#417C2211yescharacteristic
55C2×C3×#103C2211yescharacteristic
56C2×C3×#103C2211yescharacteristic
57C2×C3×#101C2211yescharacteristic
58C3×#408C2211yescharacteristic
59C3×#408C2211yescharacteristic
60C3×#391C2211yescharacteristic
61C3×#382C2211yescharacteristic
62C3×#343C2211yescharacteristic
63C3×#343C2211yescharacteristic
64C3×#343C2211yescharacteristic
65C3×#341C2211yescharacteristic
66C3×#341C2211yescharacteristic
67C3×#336C2211yescharacteristic
68#3061C2×C311yescharacteristic, complemented
69#3060C2×C311yescharacteristic, complemented
70#3013C2×C311yescharacteristic, complemented
71#3013C2×C311yescharacteristic, complemented
72#2097C2×C311yescharacteristic, complemented
73#2079C2×C311yescharacteristic, complemented
74#2078C2×C311yescharacteristic, complemented
75#2040C2×C311yescharacteristic, complemented
76#2040C2×C311yescharacteristic, complemented
77#2007C2×C311yescharacteristic, complemented
78#1908C2×C311yescharacteristic, complemented
79#1908C2×C311yescharacteristic, complemented
80#1876C2×C311yescharacteristic, complemented
81#1876C2×C311yescharacteristic, complemented
82#1793C2×C311yescharacteristic, complemented
83C3×2−1+4—22no—
84C3×2−1+4—41no—
85C3×2−1+4—41no—
86C3×2−1+4—41no—
87C2×C3×#41—21no—
88C2×C3×#41—21no—
89C2×C3×#41—41no—
90C2×C3×#41C2311yescharacteristic
91C2×C3×#41C2311yescharacteristic
92C2×C3×#41C2311yescharacteristic
93C2×C3×#41C2311yescharacteristic
94C22×C3×Q8—21no—
95C22×C3×Q8—21no—
96C22×C3×Q8C2311yescharacteristic
97C3×#137—22no—
98C3×#137—22no—
99C3×#137—41no—
100C3×#137—41no—
101C3×#135—41no—
102C3×#135—41no—
103C3×#135—41no—
104C3×#135—41no—
105C2×C3×Q16—21no—
106C2×C3×Q16—21no—
107C2×C3×Q16D411yescharacteristic
108C2×C3×Q16D411yescharacteristic
109C2×C3×SD16—21no—
110C2×C3×SD16—21no—
111C2×C3×SD16D411yescharacteristic
112C2×C3×SD16D411yescharacteristic
113C2×C3×SD16D411yescharacteristic
114C2×C3×SD16D411yescharacteristic
115C2×C3×D8D411yescharacteristic
116C2×C3×D8D411yescharacteristic
117C3×#131—41no—
118C3×#131—41no—
119C3×#131—41no—
120C3×#131—41no—
121C2×C3×M16—21no—
122C2×C3×M16—21no—
123C2×C3×M16C2311yescharacteristic
124C2×C3×M16C2311yescharacteristic
125C2×C3×M16C2311yescharacteristic
126C2×C3×M16C2311yescharacteristic
127C22×C3×C8—21no—
128C22×C3×C8—21no—
129C22×C3×C8C2311yescharacteristic
130C22×C3×C8C2311yescharacteristic
131C3×C22⋊Q8—21no—
132C3×C22⋊Q8—21no—
133C3×C22⋊Q8—21no—
134C3×C22⋊Q8—21no—
135C3×C22⋊Q8—21no—
136C3×C22⋊Q8—21no—
137C3×#121—21no—
138C3×#121—21no—
139C3×#121—21no—
140C3×#121—21no—
141C3×#121—21no—
142C3×#121—21no—
143C3×#121—41no—
144C3×#121—41no—
145C3×#121—41no—
146C2×C3×C4⋊C4C2311yescharacteristic
147C2×C3×C4⋊C4C2311yescharacteristic
148C2×C3×C4⋊C4C2311yescharacteristic
149C2×C3×C42C2311yescharacteristic
150C3×#107—21no—
151C3×#107—21no—
152C3×#106—21no—
153C3×#106—21no—
154C3×#104—41no—
155C3×#104—41no—
156C3×#104—41no—
157C3×#104—41no—
158C3×#103—21no—
159C3×#103—21no—
160C3×#103—21no—
161C3×#103—21no—
162C3×#103—21no—
163C3×#103—21no—
164C3×#103—21no—
165C3×#103—21no—
166C3×#103—21no—
167C3×#103—21no—
168C3×#102—21no—
169C3×#102—21no—
170C3×#102—21no—
171C3×#102—21no—
172C3×#102—21no—
173C3×#102—21no—
174C3×#101—41no—
175C3×C22⋊C8—21no—
176C3×C22⋊C8—21no—
177C3×C22⋊C8—21no—
178C3×C22⋊C8—21no—
179C3×#95—41no—
180C3×#95—41no—
181C2×2−1+4C22×C311yescharacteristic
182C2×#137C22×C311yescharacteristic
183C2×#137C22×C311yescharacteristic
184C2×#135C22×C311yescharacteristic
185C2×#135C22×C311yescharacteristic
186C2×#131C22×C311yescharacteristic
187C2×#131C22×C311yescharacteristic
188#537C22×C311yescharacteristic
189#537C22×C311yescharacteristic
190#537C22×C311yescharacteristic
191#470—21no—
192#469—21no—
193#468—21no—
194#468—21no—
195#467—21no—
196#466—21no—
197#465—21no—
198#465—21no—
199#452—21no—
200#452—21no—
201#451—21no—
202#451—21no—
203#449—21no—
204#449—21no—
205#448—21no—
206#448—21no—
207C2×#107C22×C311yescharacteristic
208C2×#106C22×C311yescharacteristic
209C2×#104C22×C311yescharacteristic
210C2×#104C22×C311yescharacteristic
211C2×#104C22×C311yescharacteristic
212C2×#104C22×C311yescharacteristic
213#417C22×C311yescharacteristic
214#417C22×C311yescharacteristic
215#417C22×C311yescharacteristic
216#417C22×C311yescharacteristic
217#417C22×C311yescharacteristic
218#417C22×C311yescharacteristic
219C2×#103C22×C311yescharacteristic
220C2×#103C22×C311yescharacteristic
221C2×#101C22×C311yescharacteristic
222#408C22×C311yescharacteristic
223#408C22×C311yescharacteristic
224#391C22×C311yescharacteristic
225#382C22×C311yescharacteristic
226#343C22×C311yescharacteristic
227#343C22×C311yescharacteristic
228#343C22×C311yescharacteristic
229#341C22×C311yescharacteristic
230#341C22×C311yescharacteristic
231#336C22×C311yescharacteristic
232C3×#41—21no—
233C3×#41—21no—
234C3×#41—21no—
235C3×#41—21no—
236C3×#41—21no—
237C3×#41—21no—
238C3×#41—21no—
239C3×#41—21no—
240C3×#41—21no—
241C3×#41—21no—
242C3×#41—21no—
243C3×#41—21no—
244C3×#41—21no—
245C3×#41—21no—
246C3×#41—21no—
247C3×#41—21no—
248C3×#41—44no—
249C3×#41—42no—
250C3×#41—42no—
251C3×#41—42no—
252C3×#41—42no—
253C3×#41—44no—
254C2×C3×Q8—21no—
255C2×C3×Q8—21no—
256C2×C3×Q8—21no—
257C2×C3×Q8—21no—
258C2×C3×Q8—21no—
259C2×C3×Q8—41no—
260C2×C3×Q8—42no—
261C2×C3×Q8—42no—
262C2×C3×Q8—42no—
263C2×C3×Q8—42no—
264C2×C3×Q8C2×D411yescharacteristic
265C2×C3×Q8C2×D411yescharacteristic
266C2×C3×Q8C2×D411yescharacteristic
267C2×C3×Q8C2×D411yescharacteristic
268C2×C3×Q8#4112yes—
269C2×C3×D4—21no—
270C2×C3×D4—21no—
271C2×C3×D4—21no—
272C2×C3×D4—21no—
273C2×C3×D4—41no—
274C2×C3×D4—41no—
275C2×C3×D4—41no—
276C2×C3×D4—41no—
277C2×C3×D4C2×D411yescharacteristic
278C2×C3×D4C2×D411yescharacteristic
279C2×C3×D4C2×D411yescharacteristic
280C2×C3×D4C2×D411yescharacteristic
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—41no—
291C22×C3×C4—41no—
292C22×C3×C4C2411yescharacteristic
293C3×Q16—41no—
294C3×Q16—41no—
295C3×Q16—42no—
296C3×Q16—42no—
297C3×SD16—41no—
298C3×SD16—41no—
299C3×SD16—41no—
300C3×SD16—41no—
301C3×SD16—42no—
302C3×SD16—42no—
303C3×D8—41no—
304C3×D8—41no—
305C3×M16—21no—
306C3×M16—21no—
307C3×M16—21no—
308C3×M16—21no—
309C3×M16—21no—
310C3×M16—21no—
311C3×M16—21no—
312C3×M16—21no—
313C3×M16—42no—
314C3×M16—42no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C2×C3×C8—42no—
324C2×C3×C8—42no—
325C2×C3×C8C2×D411yescharacteristic
326C2×C3×C8C2×D411yescharacteristic
327C2×C3×C8C2×D411yescharacteristic
328C2×C3×C8C2×D411yescharacteristic
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—41no—
336C3×C4⋊C4—41no—
337C3×C4⋊C4—41no—
338C3×C22⋊C4—41no—
339C3×C22⋊C4—41no—
340C3×C22⋊C4—41no—
341C3×C22⋊C4—41no—
342C3×C22⋊C4—41no—
343C3×C22⋊C4—41no—
344C3×C42—21no—
345C3×C42—21no—
3462−1+4—22no—
3472−1+4—41no—
3482−1+4—41no—
3492−1+4—41no—
350C2×#41—21no—
351C2×#41—21no—
352C2×#41—41no—
353C2×#41C23×C311yescharacteristic
354C2×#41C23×C311yescharacteristic
355C2×#41C23×C311yescharacteristic
356C2×#41C23×C311yescharacteristic
357C22×Q8—21no—
358C22×Q8—21no—
359C22×Q8C23×C311yescharacteristic
360#137—22no—
361#137—22no—
362#137—41no—
363#137—41no—
364#135—41no—
365#135—41no—
366#135—41no—
367#135—41no—
368C2×Q16—21no—
369C2×Q16—21no—
370C2×Q16C3×D411yescharacteristic
371C2×Q16C3×D411yescharacteristic
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16C3×D411yescharacteristic
375C2×SD16C3×D411yescharacteristic
376C2×SD16C3×D411yescharacteristic
377C2×SD16C3×D411yescharacteristic
378C2×D8C3×D411yescharacteristic
379C2×D8C3×D411yescharacteristic
380#131—41no—
381#131—41no—
382#131—41no—
383#131—41no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16C23×C311yescharacteristic
387C2×M16C23×C311yescharacteristic
388C2×M16C23×C311yescharacteristic
389C2×M16C23×C311yescharacteristic
390C22×C8—21no—
391C22×C8—21no—
392C22×C8C23×C311yescharacteristic
393C22×C8C23×C311yescharacteristic
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400#121—21no—
401#121—21no—
402#121—21no—
403#121—21no—
404#121—21no—
405#121—21no—
406#121—41no—
407#121—41no—
408#121—41no—
409C2×C4⋊C4C23×C311yescharacteristic
410C2×C4⋊C4C23×C311yescharacteristic
411C2×C4⋊C4C23×C311yescharacteristic
412C2×C42C23×C311yescharacteristic
413#107—21no—
414#107—21no—
415#106—21no—
416#106—21no—
417#104—41no—
418#104—41no—
419#104—41no—
420#104—41no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—21no—
427#103—21no—
428#103—21no—
429#103—21no—
430#103—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#101—41no—
438C22⋊C8—21no—
439C22⋊C8—21no—
440C22⋊C8—21no—
441C22⋊C8—21no—
442#95—41no—
443#95—41no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3H(5,𝔽2)11yescharacteristic
449C3×Q8—21no—
450C3×Q8—21no—
451C3×Q8—21no—
452C3×Q8—21no—
453C3×Q8—22no—
454C3×Q8—22no—
455C3×Q8—21no—
456C3×Q8—21no—
457C3×Q8—21no—
458C3×Q8—21no—
459C3×Q8—44no—
460C3×Q8—41no—
461C3×Q8—41no—
462C3×D4—21no—
463C3×D4—21no—
464C3×D4—21no—
465C3×D4—21no—
466C3×D4—21no—
467C3×D4—21no—
468C3×D4—21no—
469C3×D4—21no—
470C3×D4—44no—
471C3×D4—41no—
472C3×D4—41no—
473C3×D4—41no—
474C3×D4—41no—
475C3×D4—41no—
476C3×D4—41no—
477C3×D4—41no—
478C3×D4—41no—
479C3×D4—161no—
480C3×D4—161no—
481C3×D4—161no—
482C2×C3×C4—22no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—44no—
488C2×C3×C4—44no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—81no—
506C2×C3×C4—81no—
507C2×C3×C4—81no—
508C2×C3×C4C22×D411yescharacteristic
509C2×C3×C4C22×D411yescharacteristic
510C2×C3×C4C2×#4111yescharacteristic
511C2×C3×C4H(5,𝔽2)11yescharacteristic
512C2×C3×C4H(5,𝔽2)11yescharacteristic
513C2×C3×C4H(5,𝔽2)11yescharacteristic
514C3×C8—21no—
515C3×C8—21no—
516C3×C8—21no—
517C3×C8—21no—
518C3×C8—41no—
519C3×C8—41no—
520C3×C8—41no—
521C3×C8—41no—
522#41—21no—
523#41—21no—
524#41—21no—
525#41—21no—
526#41—21no—
527#41—21no—
528#41—21no—
529#41—21no—
530#41—21no—
531#41—21no—
532#41—21no—
533#41—21no—
534#41—21no—
535#41—21no—
536#41—21no—
537#41—21no—
538#41—44no—
539#41—42no—
540#41—42no—
541#41—42no—
542#41—42no—
543#41—44no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—41no—
550C2×Q8—42no—
551C2×Q8—42no—
552C2×Q8—42no—
553C2×Q8—42no—
554C2×Q8C2×C3×D411yescharacteristic
555C2×Q8C2×C3×D411yescharacteristic
556C2×Q8C2×C3×D411yescharacteristic
557C2×Q8C2×C3×D411yescharacteristic
558C2×Q8C3×#4112yes—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4C2×C3×D411yescharacteristic
568C2×D4C2×C3×D411yescharacteristic
569C2×D4C2×C3×D411yescharacteristic
570C2×D4C2×C3×D411yescharacteristic
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4C24×C311yescharacteristic
583Q16—41no—
584Q16—41no—
585Q16—42no—
586Q16—42no—
587SD16—41no—
588SD16—41no—
589SD16—41no—
590SD16—41no—
591SD16—42no—
592SD16—42no—
593D8—41no—
594D8—41no—
595M16—21no—
596M16—21no—
597M16—21no—
598M16—21no—
599M16—21no—
600M16—21no—
601M16—21no—
602M16—21no—
603M16—42no—
604M16—42no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—42no—
614C2×C8—42no—
615C2×C8C2×C3×D411yescharacteristic
616C2×C8C2×C3×D411yescharacteristic
617C2×C8C2×C3×D411yescharacteristic
618C2×C8C2×C3×D411yescharacteristic
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—41no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C22⋊C4—41no—
629C22⋊C4—41no—
630C22⋊C4—41no—
631C22⋊C4—41no—
632C22⋊C4—41no—
633C22⋊C4—41no—
634C42—21no—
635C42—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—41no—
639C22×C3—41no—
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—41no—
650C22×C3#53811yescharacteristic
651C22×C3D4211yescharacteristic
652C22×C3#56011yescharacteristic
653C3×C4—42no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—81no—
659C3×C4—81no—
660C3×C4—81no—
661C3×C4—81no—
662C3×C4#53411yescharacteristic
663C3×C4#53411yescharacteristic
664C3×C4#54611yescharacteristic
665C3×C4#54611yescharacteristic
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23C3×H(5,𝔽2)11yescharacteristic
671Q8—21no—
672Q8—21no—
673Q8—21no—
674Q8—21no—
675Q8—22no—
676Q8—22no—
677Q8—21no—
678Q8—21no—
679Q8—21no—
680Q8—21no—
681Q8—44no—
682Q8—41no—
683Q8—41no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—21no—
690D4—21no—
691D4—21no—
692D4—44no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—161no—
702D4—161no—
703D4—161no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4C22×C3×D411yescharacteristic
731C2×C4C22×C3×D411yescharacteristic
732C2×C4C2×C3×#4111yescharacteristic
733C2×C4C3×H(5,𝔽2)11yescharacteristic
734C2×C4C3×H(5,𝔽2)11yescharacteristic
735C2×C4C3×H(5,𝔽2)11yescharacteristic
736C8—21no—
737C8—21no—
738C8—21no—
739C8—21no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—41no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—81no—
747C2×C3—81no—
748C2×C3—81no—
749C2×C3—81no—
750C2×C3#266811yescharacteristic
751C2×C3#328911yescharacteristic
752C2×C3#329011yescharacteristic
753C22—21no—
754C22—21no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22C3×#53811yescharacteristic
768C22C3×D4211yescharacteristic
769C22C3×#56011yescharacteristic
770C4—42no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—81no—
776C4—81no—
777C4—81no—
778C4—81no—
779C4C3×#53411yescharacteristic
780C4C3×#53411yescharacteristic
781C4C3×#54611yescharacteristic
782C4C3×#54611yescharacteristic
783C3#3043011yescharacteristic, direct product factor, Sylow
784C2—21no—
785C2—21no—
786C2—81no—
787C2—81no—
788C2—81no—
789C2—81no—
790C2C3×#266811yescharacteristic
791C2C3×#328911yescharacteristic
792C2C3×#329011yescharacteristic
subgroupG/H
center, socleC22×C3D42
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3061C2semidirect
2. C3×#3060C2semidirect
3. C3×#3013C2semidirect
4. C3×#3013C2semidirect
5. C3×#2097C2semidirect
6. C3×#2079C2semidirect
7. C3×#2078C2semidirect
8. C3×#2040C2semidirect
9. C3×#2040C2semidirect
10. C3×#2007C2semidirect
11. C3×#1908C2semidirect
12. C3×#1908C2semidirect
13. C3×#1876C2semidirect
14. C3×#1876C2semidirect
15. C3×#1793C2semidirect
16. #30430C3direct (N × H)
68. #3061C2×C3semidirect
69. #3060C2×C3semidirect
70. #3013C2×C3semidirect
71. #3013C2×C3semidirect
72. #2097C2×C3semidirect
73. #2079C2×C3semidirect
74. #2078C2×C3semidirect
75. #2040C2×C3semidirect
76. #2040C2×C3semidirect
77. #2007C2×C3semidirect
78. #1908C2×C3semidirect
79. #1908C2×C3semidirect
80. #1876C2×C3semidirect
81. #1876C2×C3semidirect
82. #1793C2×C3semidirect
783. C3#30430direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#30612
C3×#30602
C3×#30132
C3×#20972
C3×#20792
C3×#20782
C3×#20402
C3×#20072
C3×#19082
C3×#18762
C3×#17932
#304303