Finite Group Databasebeta

← C3×#30479 #10649086

Subgroups — C3×#30479 #10649086

Order 768.

1024 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3155C211yesmaximal, characteristic, complemented
2C2×C3×#471C211yesmaximal, characteristic, complemented
3C3×#3062C211yesmaximal, characteristic, complemented
4C2×C3×#454C211yesmaximal, characteristic, complemented
5C3×#3013C211yesmaximal, characteristic, complemented
6C3×#3010C211yesmaximal, characteristic, complemented
7C3×#2051C211yesmaximal, characteristic, complemented
8C3×#2037C211yesmaximal, characteristic, complemented
9C3×#2018C211yesmaximal, characteristic, complemented
10C3×#2012C211yesmaximal, characteristic, complemented
11C3×#2006C211yesmaximal, characteristic, complemented
12C3×#2004C211yesmaximal, characteristic, complemented
13C3×#1930C211yesmaximal, characteristic, complemented
14C3×#1929C211yesmaximal, characteristic, complemented
15C3×#1876C211yesmaximal, characteristic, complemented
16#30479C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×2−1+4C2211yescharacteristic
18C2×C3×#137C2211yescharacteristic
19C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
20C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
21C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
22C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
23C2×C3×#135C2211yescharacteristic
24C22×C3×SD16C2211yescharacteristic
25C22×C3×D8C2211yescharacteristic
26C2×C3×#131C2211yescharacteristic
27C3×#537C2211yescharacteristic
28C3×#535C2211yescharacteristic
29C3×#535C2211yescharacteristic
30C2×C3×#124C2211yescharacteristic
31C3×#496—21no—
32C3×#496—21no—
33C3×#495—21no—
34C3×#493—21no—
35C3×#471—24no—
36C3×#469—21no—
37C3×#468—21no—
38C3×#466—21no—
39C3×#465—21no—
40C3×#454—24no—
41C3×#452—21no—
42C3×#451—21no—
43C3×#449—21no—
44C3×#449—21no—
45C3×#449—21no—
46C3×#448—21no—
47C3×#448—21no—
48C3×#448—21no—
49C2×C3×#108C2211yescharacteristic
50C3×#428C2211yescharacteristic
51C2×C3×#104C2211yescharacteristic
52C2×C3×#104C2211yescharacteristic
53C2×C3×#104C2211yescharacteristic
54C3×#419C2211yescharacteristic
55C3×#417C2211yescharacteristic
56C3×#416C2211yescharacteristic
57C2×C3×#103C2211yescharacteristic
58C2×C3×#102C2211yescharacteristic
59C2×C3×#101C2211yescharacteristic
60C2×C3×#100C2211yescharacteristic
61C2×C3×#100C2211yescharacteristic
62C3×#408C2211yescharacteristic
63C3×#408C2211yescharacteristic
64C3×#405C2211yescharacteristic
65C3×#390C2211yescharacteristic
66C3×#343C2211yescharacteristic
67C3×#341C2211yescharacteristic
68C3×#339C2211yescharacteristic
69C3×#336C2211yescharacteristic
70#3155C2×C311yescharacteristic, complemented
71C2×#471C2×C311yescharacteristic, complemented
72#3062C2×C311yescharacteristic, complemented
73C2×#454C2×C311yescharacteristic, complemented
74#3013C2×C311yescharacteristic, complemented
75#3010C2×C311yescharacteristic, complemented
76#2051C2×C311yescharacteristic, complemented
77#2037C2×C311yescharacteristic, complemented
78#2018C2×C311yescharacteristic, complemented
79#2012C2×C311yescharacteristic, complemented
80#2006C2×C311yescharacteristic, complemented
81#2004C2×C311yescharacteristic, complemented
82#1930C2×C311yescharacteristic, complemented
83#1929C2×C311yescharacteristic, complemented
84#1876C2×C311yescharacteristic, complemented
85C3×2−1+4—22no—
86C3×2−1+4—41no—
87C3×2−1+4—41no—
88C3×2−1+4—41no—
89C2×C3×#41—21no—
90C2×C3×#41—21no—
91C2×C3×#41—41no—
92C2×C3×#41C2311yescharacteristic
93C2×C3×#41C2311yescharacteristic
94C2×C3×#41C2311yescharacteristic
95C22×C3×Q8—21no—
96C22×C3×Q8—21no—
97C22×C3×Q8C2311yescharacteristic
98C22×C3×D4C2311yescharacteristic
99C22×C3×D4C2311yescharacteristic
100C3×#137—22no—
101C3×#137—41no—
102C3×AGL(1,ℤ/8)—22no—
103C3×AGL(1,ℤ/8)—22no—
104C3×AGL(1,ℤ/8)—22no—
105C3×AGL(1,ℤ/8)—41no—
106C3×AGL(1,ℤ/8)—41no—
107C3×AGL(1,ℤ/8)—41no—
108C3×AGL(1,ℤ/8)—41no—
109C3×AGL(1,ℤ/8)—41no—
110C3×#135—41no—
111C3×#135—41no—
112C2×C3×Q16—21no—
113C2×C3×Q16D411yescharacteristic
114C2×C3×SD16—22no—
115C2×C3×SD16—21no—
116C2×C3×SD16—21no—
117C2×C3×SD16—21no—
118C2×C3×SD16—21no—
119C2×C3×SD16—21no—
120C2×C3×SD16—21no—
121C2×C3×SD16—21no—
122C2×C3×SD16—41no—
123C2×C3×SD16D411yescharacteristic
124C2×C3×SD16D411yescharacteristic
125C2×C3×D8—21no—
126C2×C3×D8—21no—
127C2×C3×D8—21no—
128C2×C3×D8—21no—
129C2×C3×D8—21no—
130C2×C3×D8—21no—
131C2×C3×D8—41no—
132C2×C3×D8—41no—
133C2×C3×D8D411yescharacteristic
134C3×#131—22no—
135C3×#131—41no—
136C2×C3×M16—21no—
137C2×C3×M16C2311yescharacteristic
138C2×C3×M16C2311yescharacteristic
139C2×C3×M16C2311yescharacteristic
140C2×C3×M16C2311yescharacteristic
141C22×C3×C8—21no—
142C22×C3×C8C2311yescharacteristic
143C22×C3×C8C2311yescharacteristic
144C3×#127—21no—
145C3×#127—21no—
146C3×#124—22no—
147C3×#124—21no—
148C3×#124—21no—
149C3×#124—41no—
150C3×C22⋊Q8—21no—
151C3×C22⋊Q8—21no—
152C3×#121—21no—
153C3×#121—21no—
154C3×#121—21no—
155C3×#121—21no—
156C3×#121—21no—
157C3×#121—21no—
158C3×#121—41no—
159C3×#120—41no—
160C3×#120—41no—
161C3×#117C2311yescharacteristic
162C2×C3×C4⋊C4C2311yescharacteristic
163C2×C3×C22⋊C4—41no—
164C2×C3×C22⋊C4—41no—
165C2×C3×C42C2311yescharacteristic
166C3×#108—22no—
167C3×#107—21no—
168C3×#106—21no—
169C3×#104—22no—
170C3×#104—22no—
171C3×#104—41no—
172C3×#103—21no—
173C3×#103—21no—
174C3×#103—21no—
175C3×#103—21no—
176C3×#103—21no—
177C3×#103D411yescharacteristic
178C3×#103D411yescharacteristic
179C3×#102—21no—
180C3×#102—21no—
181C3×#102—21no—
182C3×#102D411yescharacteristic
183C3×#102D411yescharacteristic
184C3×#101D414yescomplemented
185C3×#100—22no—
186C3×#100—41no—
187C3×C22⋊C8—21no—
188C3×C22⋊C8—21no—
189C3×C22⋊C8—21no—
190C3×C22⋊C8—21no—
191C3×#97—21no—
192C3×C4×C8—21no—
193C2×2−1+4C22×C311yescharacteristic
194C2×#137C22×C311yescharacteristic
195C2×AGL(1,ℤ/8)C22×C311yescharacteristic
196C2×AGL(1,ℤ/8)C22×C311yescharacteristic
197C2×AGL(1,ℤ/8)C22×C311yescharacteristic
198C2×AGL(1,ℤ/8)C22×C311yescharacteristic
199C2×#135C22×C311yescharacteristic
200C22×SD16C22×C311yescharacteristic
201C22×D8C22×C311yescharacteristic
202C2×#131C22×C311yescharacteristic
203#537C22×C311yescharacteristic
204#535C22×C311yescharacteristic
205#535C22×C311yescharacteristic
206C2×#124C22×C311yescharacteristic
207#496—21no—
208#496—21no—
209#495—21no—
210#493—21no—
211#471—24no—
212#469—21no—
213#468—21no—
214#466—21no—
215#465—21no—
216#454—24no—
217#452—21no—
218#451—21no—
219#449—21no—
220#449—21no—
221#449—21no—
222#448—21no—
223#448—21no—
224#448—21no—
225C2×#108C22×C311yescharacteristic
226#428C22×C311yescharacteristic
227C2×#104C22×C311yescharacteristic
228C2×#104C22×C311yescharacteristic
229C2×#104C22×C311yescharacteristic
230#419C22×C311yescharacteristic
231#417C22×C311yescharacteristic
232#416C22×C311yescharacteristic
233C2×#103C22×C311yescharacteristic
234C2×#102C22×C311yescharacteristic
235C2×#101C22×C311yescharacteristic
236C2×#100C22×C311yescharacteristic
237C2×#100C22×C311yescharacteristic
238#408C22×C311yescharacteristic
239#408C22×C311yescharacteristic
240#405C22×C311yescharacteristic
241#390C22×C311yescharacteristic
242#343C22×C311yescharacteristic
243#341C22×C311yescharacteristic
244#339C22×C311yescharacteristic
245#336C22×C311yescharacteristic
246C24×C3—21no—
247C24×C3—21no—
248C3×#41—21no—
249C3×#41—21no—
250C3×#41—21no—
251C3×#41—21no—
252C3×#41—21no—
253C3×#41—21no—
254C3×#41—21no—
255C3×#41—21no—
256C3×#41—21no—
257C3×#41—21no—
258C3×#41—21no—
259C3×#41—21no—
260C3×#41—44no—
261C3×#41—42no—
262C3×#41—42no—
263C3×#41—42no—
264C3×#41—42no—
265C3×#41—44no—
266C2×C3×Q8—21no—
267C2×C3×Q8—21no—
268C2×C3×Q8—21no—
269C2×C3×Q8—21no—
270C2×C3×Q8—21no—
271C2×C3×Q8—41no—
272C2×C3×Q8—42no—
273C2×C3×Q8—42no—
274C2×C3×Q8—42no—
275C2×C3×Q8—42no—
276C2×C3×Q8C2×D412yes—
277C2×C3×Q8C2×D411yescharacteristic
278C2×C3×Q8C2×D411yescharacteristic
279C2×C3×Q8C2×D411yescharacteristic
280C2×C3×D4—21no—
281C2×C3×D4—21no—
282C2×C3×D4—21no—
283C2×C3×D4—21no—
284C2×C3×D4—21no—
285C2×C3×D4—21no—
286C2×C3×D4—21no—
287C2×C3×D4—21no—
288C2×C3×D4—21no—
289C2×C3×D4—21no—
290C2×C3×D4—21no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—41no—
296C2×C3×D4—41no—
297C2×C3×D4—41no—
298C2×C3×D4—41no—
299C2×C3×D4—41no—
300C2×C3×D4—41no—
301C2×C3×D4C2×D411yescharacteristic
302C2×C3×D4C2×D411yescharacteristic
303C2×C3×D4C2×D411yescharacteristic
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—41no—
311C22×C3×C4—41no—
312C22×C3×C4C2411yescharacteristic
313C3×Q16—41no—
314C3×Q16—42no—
315C3×SD16—41no—
316C3×SD16—41no—
317C3×SD16—42no—
318C3×SD16—42no—
319C3×SD16—42no—
320C3×SD16—42no—
321C3×SD16—42no—
322C3×SD16—42no—
323C3×SD16—42no—
324C3×D8—41no—
325C3×D8—42no—
326C3×D8—42no—
327C3×D8—42no—
328C3×D8—42no—
329C3×D8—42no—
330C3×D8—42no—
331C3×M16—21no—
332C3×M16—21no—
333C3×M16—21no—
334C3×M16—21no—
335C3×M16—21no—
336C3×M16—21no—
337C3×M16—42no—
338C3×M16C2×D412yes—
339C3×M16C2×D412yes—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—21no—
343C2×C3×C8—21no—
344C2×C3×C8—21no—
345C2×C3×C8—21no—
346C2×C3×C8—21no—
347C2×C3×C8—21no—
348C2×C3×C8—42no—
349C2×C3×C8C2×D411yescharacteristic
350C2×C3×C8C2×D411yescharacteristic
351C2×C3×C8C2×D411yescharacteristic
352C2×C3×C8C2×D411yescharacteristic
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—41no—
356C3×C4⋊C4C2×D411yescharacteristic
357C3×C4⋊C4C2×D411yescharacteristic
358C3×C22⋊C4—21no—
359C3×C22⋊C4—41no—
360C3×C22⋊C4—41no—
361C3×C22⋊C4—41no—
362C3×C22⋊C4—41no—
363C3×C22⋊C4—41no—
364C3×C22⋊C4—41no—
365C3×C22⋊C4—44no—
366C3×C22⋊C4—82no—
367C3×C42—21no—
368C3×C42—21no—
369C3×C42—21no—
3702−1+4—22no—
3712−1+4—41no—
3722−1+4—41no—
3732−1+4—41no—
374C2×#41—21no—
375C2×#41—21no—
376C2×#41—41no—
377C2×#41C23×C311yescharacteristic
378C2×#41C23×C311yescharacteristic
379C2×#41C23×C311yescharacteristic
380C22×Q8—21no—
381C22×Q8—21no—
382C22×Q8C23×C311yescharacteristic
383C22×D4C23×C311yescharacteristic
384C22×D4C23×C311yescharacteristic
385#137—22no—
386#137—41no—
387AGL(1,ℤ/8)—22no—
388AGL(1,ℤ/8)—22no—
389AGL(1,ℤ/8)—22no—
390AGL(1,ℤ/8)—41no—
391AGL(1,ℤ/8)—41no—
392AGL(1,ℤ/8)—41no—
393AGL(1,ℤ/8)—41no—
394AGL(1,ℤ/8)—41no—
395#135—41no—
396#135—41no—
397C2×Q16—21no—
398C2×Q16C3×D411yescharacteristic
399C2×SD16—22no—
400C2×SD16—21no—
401C2×SD16—21no—
402C2×SD16—21no—
403C2×SD16—21no—
404C2×SD16—21no—
405C2×SD16—21no—
406C2×SD16—21no—
407C2×SD16—41no—
408C2×SD16C3×D411yescharacteristic
409C2×SD16C3×D411yescharacteristic
410C2×D8—21no—
411C2×D8—21no—
412C2×D8—21no—
413C2×D8—21no—
414C2×D8—21no—
415C2×D8—21no—
416C2×D8—41no—
417C2×D8—41no—
418C2×D8C3×D411yescharacteristic
419#131—22no—
420#131—41no—
421C2×M16—21no—
422C2×M16C23×C311yescharacteristic
423C2×M16C23×C311yescharacteristic
424C2×M16C23×C311yescharacteristic
425C2×M16C23×C311yescharacteristic
426C22×C8—21no—
427C22×C8C23×C311yescharacteristic
428C22×C8C23×C311yescharacteristic
429#127—21no—
430#127—21no—
431#124—22no—
432#124—21no—
433#124—21no—
434#124—41no—
435C22⋊Q8—21no—
436C22⋊Q8—21no—
437#121—21no—
438#121—21no—
439#121—21no—
440#121—21no—
441#121—21no—
442#121—21no—
443#121—41no—
444#120—41no—
445#120—41no—
446#117C23×C311yescharacteristic
447C2×C4⋊C4C23×C311yescharacteristic
448C2×C22⋊C4—41no—
449C2×C22⋊C4—41no—
450C2×C42C23×C311yescharacteristic
451#108—22no—
452#107—21no—
453#106—21no—
454#104—22no—
455#104—22no—
456#104—41no—
457#103—21no—
458#103—21no—
459#103—21no—
460#103—21no—
461#103—21no—
462#103C3×D411yescharacteristic
463#103C3×D411yescharacteristic
464#102—21no—
465#102—21no—
466#102—21no—
467#102C3×D411yescharacteristic
468#102C3×D411yescharacteristic
469#101C3×D414yescomplemented
470#100—22no—
471#100—41no—
472C22⋊C8—21no—
473C22⋊C8—21no—
474C22⋊C8—21no—
475C22⋊C8—21no—
476#97—21no—
477C4×C8—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—81no—
488C23×C3—81no—
489C23×C3—81no—
490C23×C3—81no—
491C23×C3H(5,𝔽2)11yescharacteristic
492C3×Q8—21no—
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—21no—
496C3×Q8—22no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—22no—
500C3×Q8—44no—
501C3×Q8—41no—
502C3×Q8—41no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—44no—
510C3×D4—41no—
511C3×D4—41no—
512C3×D4—41no—
513C3×D4—41no—
514C3×D4—41no—
515C3×D4—41no—
516C3×D4—41no—
517C3×D4—41no—
518C3×D4—41no—
519C3×D4—41no—
520C3×D4—41no—
521C3×D4—41no—
522C3×D4—41no—
523C3×D4—41no—
524C3×D4—161no—
525C3×D4—161no—
526C3×D4—161no—
527C3×D4—161no—
528C3×D4—161no—
529C2×C3×C4—22no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—44no—
536C2×C3×C4—44no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—81no—
550C2×C3×C4C22×D411yescharacteristic
551C2×C3×C4C22×D411yescharacteristic
552C2×C3×C4C22×D411yescharacteristic
553C2×C3×C4H(5,𝔽2)11yescharacteristic
554C2×C3×C4H(5,𝔽2)11yescharacteristic
555C2×C3×C4H(5,𝔽2)11yescharacteristic
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—22no—
561C3×C8—22no—
562C3×C8—41no—
563C3×C8—41no—
564C24—21no—
565C24—21no—
566#41—21no—
567#41—21no—
568#41—21no—
569#41—21no—
570#41—21no—
571#41—21no—
572#41—21no—
573#41—21no—
574#41—21no—
575#41—21no—
576#41—21no—
577#41—21no—
578#41—44no—
579#41—42no—
580#41—42no—
581#41—42no—
582#41—42no—
583#41—44no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—41no—
590C2×Q8—42no—
591C2×Q8—42no—
592C2×Q8—42no—
593C2×Q8—42no—
594C2×Q8C2×C3×D412yes—
595C2×Q8C2×C3×D411yescharacteristic
596C2×Q8C2×C3×D411yescharacteristic
597C2×Q8C2×C3×D411yescharacteristic
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—41no—
616C2×D4—41no—
617C2×D4—41no—
618C2×D4—41no—
619C2×D4C2×C3×D411yescharacteristic
620C2×D4C2×C3×D411yescharacteristic
621C2×D4C2×C3×D411yescharacteristic
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4C24×C311yescharacteristic
631Q16—41no—
632Q16—42no—
633SD16—41no—
634SD16—41no—
635SD16—42no—
636SD16—42no—
637SD16—42no—
638SD16—42no—
639SD16—42no—
640SD16—42no—
641SD16—42no—
642D8—41no—
643D8—42no—
644D8—42no—
645D8—42no—
646D8—42no—
647D8—42no—
648D8—42no—
649M16—21no—
650M16—21no—
651M16—21no—
652M16—21no—
653M16—21no—
654M16—21no—
655M16—42no—
656M16C2×C3×D412yes—
657M16C2×C3×D412yes—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—42no—
667C2×C8C2×C3×D411yescharacteristic
668C2×C8C2×C3×D411yescharacteristic
669C2×C8C2×C3×D411yescharacteristic
670C2×C8C2×C3×D411yescharacteristic
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—41no—
674C4⋊C4C2×C3×D411yescharacteristic
675C4⋊C4C2×C3×D411yescharacteristic
676C22⋊C4—21no—
677C22⋊C4—41no—
678C22⋊C4—41no—
679C22⋊C4—41no—
680C22⋊C4—41no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C22⋊C4—44no—
684C22⋊C4—82no—
685C42—21no—
686C42—21no—
687C42—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—82no—
700C22×C3—82no—
701C22×C3—81no—
702C22×C3—81no—
703C22×C3—81no—
704C22×C3—81no—
705C22×C3—81no—
706C22×C3—81no—
707C22×C3—161no—
708C22×C3—161no—
709C22×C3#53511yescharacteristic
710C22×C3D4211yescharacteristic
711C22×C3#56011yescharacteristic
712C3×C4—42no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—81no—
719C3×C4—81no—
720C3×C4#53411yescharacteristic
721C3×C4#53511yescharacteristic
722C3×C4D4211yescharacteristic
723C3×C4D4211yescharacteristic
724C23—21no—
725C23—21no—
726C23—21no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—81no—
734C23—81no—
735C23—81no—
736C23—81no—
737C23C3×H(5,𝔽2)11yescharacteristic
738Q8—21no—
739Q8—21no—
740Q8—21no—
741Q8—21no—
742Q8—22no—
743Q8—21no—
744Q8—21no—
745Q8—22no—
746Q8—44no—
747Q8—41no—
748Q8—41no—
749D4—21no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—44no—
756D4—41no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—161no—
771D4—161no—
772D4—161no—
773D4—161no—
774D4—161no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—81no—
796C2×C4C22×C3×D411yescharacteristic
797C2×C4C22×C3×D411yescharacteristic
798C2×C4C22×C3×D411yescharacteristic
799C2×C4C3×H(5,𝔽2)11yescharacteristic
800C2×C4C3×H(5,𝔽2)11yescharacteristic
801C2×C4C3×H(5,𝔽2)11yescharacteristic
802C8—21no—
803C8—21no—
804C8—21no—
805C8—21no—
806C8—22no—
807C8—22no—
808C8—41no—
809C8—41no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—81no—
813C2×C3—81no—
814C2×C3—81no—
815C2×C3—161no—
816C2×C3—161no—
817C2×C3#266911yescharacteristic
818C2×C3#328811yescharacteristic
819C2×C3#329011yescharacteristic
820C22—21no—
821C22—21no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—82no—
832C22—82no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—161no—
840C22—161no—
841C22C3×#53511yescharacteristic
842C22C3×D4211yescharacteristic
843C22C3×#56011yescharacteristic
844C4—42no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—81no—
851C4—81no—
852C4C3×#53411yescharacteristic
853C4C3×#53511yescharacteristic
854C4C3×D4211yescharacteristic
855C4C3×D4211yescharacteristic
856C3#3047911yescharacteristic, direct product factor, Sylow
857C2—21no—
858C2—21no—
859C2—81no—
860C2—81no—
861C2—81no—
862C2—161no—
863C2—161no—
864C2C3×#266911yescharacteristic
865C2C3×#328811yescharacteristic
866C2C3×#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×#3155C2semidirect
2. C2×C3×#471C2semidirect
3. C3×#3062C2semidirect
4. C2×C3×#454C2semidirect
5. C3×#3013C2semidirect
6. C3×#3010C2semidirect
7. C3×#2051C2semidirect
8. C3×#2037C2semidirect
9. C3×#2018C2semidirect
10. C3×#2012C2semidirect
11. C3×#2006C2semidirect
12. C3×#2004C2semidirect
13. C3×#1930C2semidirect
14. C3×#1929C2semidirect
15. C3×#1876C2semidirect
16. #30479C3direct (N × H)
70. #3155C2×C3semidirect
71. C2×#471C2×C3semidirect
72. #3062C2×C3semidirect
73. C2×#454C2×C3semidirect
74. #3013C2×C3semidirect
75. #3010C2×C3semidirect
76. #2051C2×C3semidirect
77. #2037C2×C3semidirect
78. #2018C2×C3semidirect
79. #2012C2×C3semidirect
80. #2006C2×C3semidirect
81. #2004C2×C3semidirect
82. #1930C2×C3semidirect
83. #1929C2×C3semidirect
84. #1876C2×C3semidirect
184. C3×#101D4semidirect
469. #101C3×D4semidirect
856. C3#30479direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#31552
C2×C3×#4712
C3×#30622
C2×C3×#4542
C3×#30132
C3×#30102
C3×#20512
C3×#20372
C3×#20182
C3×#20122
C3×#20062
C3×#20042
C3×#19302
C3×#19292
C3×#18762
#304793