Finite Group Databasebeta

← C3×#87206 #11918967

Subgroups — C3×#87206 #11918967

Order 1152.

2977 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5968C211yesmaximal, characteristic, complemented
2C3×#5966C211yesmaximal, characteristic, complemented
3C32×#577C211yesmaximal, characteristic, complemented
4C3×#5838C211yesmaximal, characteristic, complemented
5C3×#5835C211yesmaximal, characteristic, complemented
6C3×#5779C213yesmaximal, complemented
7C3×#5777C213yesmaximal, complemented
8C3×#5774C213yesmaximal, complemented
9C3×#5773C213yesmaximal, complemented
10C3×#5770C213yesmaximal, complemented
11C3×D3×#135C213yesmaximal, complemented
12C3×#5762C213yesmaximal, complemented
13C2×C3×#916C213yesmaximal, complemented
14C3×#5751C211yesmaximal, characteristic, complemented
15C3×D3×#131C211yesmaximal, characteristic, complemented
16C3×#3584—31nomaximal
17#87206C311yesmaximal, characteristic, direct product factor
18C32×2−1+4C2211yescharacteristic, complemented
19C32×H(5,𝔽2)C2211yescharacteristic, complemented
20C3×#1010—21no—
21C3×#1010C2213yescomplemented
22C3×#1010C2211yescharacteristic, complemented
23C3×#1009—23no—
24C3×#1009C2213yescomplemented
25C3×#1009C2211yescharacteristic, complemented
26C3×D3×#41—21no—
27C3×D3×#41—23no—
28C3×D3×#41C2211yescharacteristic
29C3×D3×#41C2213yescomplemented
30C3×D3×#41C2213yescomplemented
31C3×#1007—21no—
32C3×#1007C2213yescomplemented
33C2×C3×#239—21no—
34C2×C3×#239C2213yescomplemented
35C3×#1004—23no—
36C3×#1004C2213yescomplemented
37C2×C3×#237—23no—
38C2×C3×#237C2213yescomplemented
39C32×#137C2213yescomplemented
40C32×AGL(1,ℤ/8)C2213yescomplemented
41C32×#135C2213yescomplemented
42C2×C32×SD16C2213yescomplemented
43C32×#131C2211yescharacteristic, complemented
44C3×#951C2213yescomplemented
45C3×#950C2213yescomplemented
46C3×#950C2213yescomplemented
47C3×#949C2213yescomplemented
48C3×#948C2211yescharacteristic, complemented
49C2×C3×#216C2213yescomplemented
50C3×#942C2213yescomplemented
51C3×#932C2213yescomplemented
52C2×C3×#213C2213yescomplemented
53C3×#919C2213yescomplemented
54C3×#918C2216yescomplemented
55C3×D3×Q16C2213yescomplemented
56C3×#916C2213yescomplemented
57C3×#916C2216yescomplemented
58C3×#916C2216yescomplemented
59C3×#916C2216yescomplemented
60C3×#916C2211yescharacteristic, complemented
61C3×#915C2216yescomplemented
62C3×#914C2216yescomplemented
63C3×D3×SD16C2213yescomplemented
64C3×D3×SD16C2213yescomplemented
65C3×#912C2213yescomplemented
66C3×#911C2216yescomplemented
67C3×D3×D8C2213yescomplemented
68C3×#909C2213yescomplemented
69C3×#908C2213yescomplemented
70C3×#907C2213yescomplemented
71C3×D3×M16C2213yescomplemented
72C3×#904C2213yescomplemented
73C2×C3×#204C2213yescomplemented
74C3×#901C2213yescomplemented
75C2×C3×D3×C8C2213yescomplemented
76C3×#585—31no—
77C3×#585—31no—
78#5968C2×C311yescharacteristic, complemented
79#5966C2×C311yescharacteristic, complemented
80C3×#578—31no—
81C3×#578—33no—
82C3×#577—21no—
83C3×#577—33no—
84C3×#577—33no—
85C3×#577—31no—
86C3×#577D311yescharacteristic, complemented
87C3×#577C2×C311yescharacteristic, complemented
88C3×#576—31no—
89C3×#576—33no—
90C3×#575—33no—
91C3×#575—33no—
92C2×C3×#135—33no—
93C2×C3×#135—33no—
94C2×C3×#131—31no—
95#5838C2×C311yescharacteristic, complemented
96#5835C2×C311yescharacteristic, complemented
97#5779C2×C313yescomplemented
98#5777C2×C313yescomplemented
99#5774C2×C313yescomplemented
100#5773C2×C313yescomplemented
101#5770C2×C313yescomplemented
102D3×#135C2×C313yescomplemented
103#5762C2×C313yescomplemented
104C2×#916C2×C313yescomplemented
105#5751C2×C311yescharacteristic, complemented
106D3×#131C2×C311yescharacteristic, complemented
107C32×#41—21no—
108C32×#41—23no—
109C32×#41C2313yes—
110C32×#41C2313yes—
111C32×#41C2311yescharacteristic
112C2×C32×Q8—21no—
113C2×C32×Q8C2313yes—
114C2×C32×D4—23no—
115C2×C32×D4C2313yes—
116C2×C3×#67—23no—
117C2×C3×#67—26no—
118C22×C3×Dic3—23no—
119C3×#239—21no—
120C3×#239—23no—
121C3×#239—23no—
122C3×#239—23no—
123C3×#239D411yescharacteristic
124C3×#239C2316yes—
125C3×#239C2313yes—
126C3×#239C2311yescharacteristic
127C3×D3×Q8—21no—
128C3×D3×Q8—23no—
129C3×D3×Q8D411yescharacteristic
130C3×D3×Q8C2313yes—
131C3×D3×Q8C2313yes—
132C3×#237—23no—
133C3×#237—26no—
134C3×#237—23no—
135C3×#237—23no—
136C3×#237—23no—
137C3×#237—23no—
138C3×#237—23no—
139C3×#237D413yes—
140C3×#237C2316yes—
141C3×#237C2311yescharacteristic
142C3×#237C2313yes—
143C3×D3×D4—23no—
144C3×D3×D4—23no—
145C3×D3×D4—23no—
146C3×D3×D4—26no—
147C3×D3×D4—23no—
148C3×D3×D4D413yes—
149C3×D3×D4C2313yes—
150C3×D3×D4C2313yes—
151C3×#235—26no—
152C3×#235—23no—
153C3×#235—23no—
154C3×#235—23no—
155C3×#235—23no—
156C3×#235C2313yes—
157C3×#235C2313yes—
158C3×#235C2313yes—
159C2×C3×D12—23no—
160C2×C3×D12—23no—
161C2×C3×D12C2313yes—
162C2×C3×C4×D3—23no—
163C2×C3×C4×D3—23no—
164C2×C3×C4×D3—23no—
165C2×C3×C4×D3C2313yes—
166C2×C3×Dic6—23no—
167C2×C3×Dic6C2313yes—
168C32×Q16C2313yes—
169C32×SD16C2311yescharacteristic
170C32×SD16C2313yes—
171C32×SD16C2316yes—
172C32×D8C2313yes—
173C32×M16C2313yes—
174C2×C32×C8C2313yes—
175C3×#216C2316yes—
176C3×#216C2313yes—
177C3×#216C2311yescharacteristic
178C3×#215C2313yes—
179C3×#215C2313yes—
180C3×#214C2313yes—
181C3×#214C2313yes—
182C3×#213C2311yescharacteristic
183C3×#213C2313yes—
184C3×#213C2316yes—
185C3×#208C2313yes—
186C2×C3×C3⋊C8C2313yes—
187C3×Dic12C2313yes—
188C3×D24C2313yes—
189C3×#204C2313yes—
190C3×#204C2316yes—
191C3×#204C2311yescharacteristic
192C3×ΓL(1,𝔽25)C2316yes—
193C3×D3×C8C2311yescharacteristic
194C3×D3×C8C2313yes—
195C3×D3×C8C2313yes—
196C3×D3×C8C2313yes—
197#3584—31noSylow
198C3×2−1+4—21no—
199C3×2−1+4—33no—
200C3×2−1+4—31no—
201C3×2−1+4—33no—
202C3×2−1+4—61no—
203C3×2−1+4—61no—
204C3×2−1+4C2×D311yescharacteristic, complemented
205C3×2−1+4C22×C311yescharacteristic, complemented
206C3×H(5,𝔽2)—21no—
207C3×H(5,𝔽2)—33no—
208C3×H(5,𝔽2)—31no—
209C3×H(5,𝔽2)—33no—
210C3×H(5,𝔽2)—63no—
211C3×H(5,𝔽2)—63no—
212C3×H(5,𝔽2)C2×D311yescharacteristic, complemented
213C3×H(5,𝔽2)C22×C311yescharacteristic, complemented
214C2×C3×#41—31no—
215C2×C3×#41—33no—
216C2×C3×#41—33no—
217C2×C3×#41—33no—
218C2×C3×#41—33no—
219C2×C3×#41—63no—
220C2×C3×#41—61no—
221C2×C3×#41—61no—
222C2×C3×#41—63no—
223#1010—21no—
224#1010C22×C313yescomplemented
225#1010C22×C311yescharacteristic, complemented
226#1009—23no—
227#1009C22×C313yescomplemented
228#1009C22×C311yescharacteristic, complemented
229D3×#41—21no—
230D3×#41—23no—
231D3×#41C22×C311yescharacteristic
232D3×#41C22×C313yescomplemented
233D3×#41C22×C313yescomplemented
234#1007—21no—
235#1007C22×C313yescomplemented
236C2×#239—21no—
237C2×#239C22×C313yescomplemented
238#1004—23no—
239#1004C22×C313yescomplemented
240C2×#237—23no—
241C2×#237C22×C313yescomplemented
242C3×#137—23no—
243C3×#137—33no—
244C3×#137—33no—
245C3×#137—36no—
246C3×#137—36no—
247C3×#137—33no—
248C3×#137C2×D313yescomplemented
249C3×#137C22×C313yescomplemented
250C3×AGL(1,ℤ/8)—23no—
251C3×AGL(1,ℤ/8)—33no—
252C3×AGL(1,ℤ/8)—33no—
253C3×AGL(1,ℤ/8)—36no—
254C3×AGL(1,ℤ/8)—36no—
255C3×AGL(1,ℤ/8)—33no—
256C3×AGL(1,ℤ/8)C2×D313yescomplemented
257C3×AGL(1,ℤ/8)C22×C313yescomplemented
258C3×#135—23no—
259C3×#135—33no—
260C3×#135—33no—
261C3×#135—33no—
262C3×#135—31no—
263C3×#135—33no—
264C3×#135—36no—
265C3×#135—36no—
266C3×#135—36no—
267C3×#135—33no—
268C3×#135—33no—
269C3×#135C2×D313yescomplemented
270C3×#135C22×C313yescomplemented
271C2×C3×Q16—33no—
272C2×C3×Q16—33no—
273C2×C3×SD16—23no—
274C2×C3×SD16—33no—
275C2×C3×SD16—33no—
276C2×C3×SD16—33no—
277C2×C3×SD16C2×D313yescomplemented
278C2×C3×SD16C22×C313yescomplemented
279C2×C3×D8—33no—
280C2×C3×D8—33no—
281C3×#131—21no—
282C3×#131—31no—
283C3×#131—33no—
284C3×#131—33no—
285C3×#131C2×D311yescharacteristic, complemented
286C3×#131C22×C311yescharacteristic, complemented
287C2×C3×M16—33no—
288C22×C3×C8—33no—
289#951C22×C313yescomplemented
290#950C22×C313yescomplemented
291#950C22×C313yescomplemented
292#949C22×C313yescomplemented
293#948C22×C311yescharacteristic, complemented
294C2×#216C22×C313yescomplemented
295#942C22×C313yescomplemented
296#932C22×C313yescomplemented
297C2×#213C22×C313yescomplemented
298#919C22×C313yescomplemented
299#918C22×C316yescomplemented
300D3×Q16C22×C313yescomplemented
301#916C22×C313yescomplemented
302#916C22×C316yescomplemented
303#916C22×C316yescomplemented
304#916C22×C316yescomplemented
305#916C22×C311yescharacteristic, complemented
306#915C22×C316yescomplemented
307#914C22×C316yescomplemented
308D3×SD16C22×C313yescomplemented
309D3×SD16C22×C313yescomplemented
310#912C22×C313yescomplemented
311#911C22×C316yescomplemented
312D3×D8C22×C313yescomplemented
313#909C22×C313yescomplemented
314#908C22×C313yescomplemented
315#907C22×C313yescomplemented
316D3×M16C22×C313yescomplemented
317#904C22×C313yescomplemented
318C2×#204C22×C313yescomplemented
319#901C22×C313yescomplemented
320C2×D3×C8C22×C313yescomplemented
321C23×C32—23no—
322C22×C3×D3—23no—
323C22×C3×D3—23no—
324C22×C3×D3—23no—
325C22×C3×D3C2×D413yes—
326C32×Q8—23no—
327C32×Q8C2×D411yescharacteristic
328C32×Q8C2411yescharacteristic
329C32×Q8C2413yes—
330C32×D4—23no—
331C32×D4—23no—
332C32×D4—23no—
333C32×D4C2×D413yes—
334C32×D4C2413yes—
335C32×D4C2411yescharacteristic
336C2×C32×C4—23no—
337C2×C32×C4—23no—
338C2×C32×C4—23no—
339C2×C32×C4C2413yes—
340C3×#67—23no—
341C3×#67—23no—
342C3×#67—21no—
343C3×#67—26no—
344C3×#67—23no—
345C3×#67—23no—
346C3×#67—23no—
347C3×#67C2×D416yes—
348C2×C3×Dic3—23no—
349C2×C3×Dic3—26no—
350C2×C3×Dic3—21no—
351C2×C3×Dic3—23no—
352C2×C3×Dic3C2×D413yes—
353C3×D12—26no—
354C3×D12—23no—
355C3×D12—21no—
356C3×D12—23no—
357C3×D12C2×D413yes—
358C3×D12C2413yes—
359C3×D12C2411yescharacteristic
360C3×C4×D3—23no—
361C3×C4×D3—23no—
362C3×C4×D3—23no—
363C3×C4×D3—23no—
364C3×C4×D3—21no—
365C3×C4×D3—23no—
366C3×C4×D3—26no—
367C3×C4×D3C2×D413yes—
368C3×C4×D3C2×D413yes—
369C3×C4×D3C2411yescharacteristic
370C3×C4×D3C2413yes—
371C3×Dic6—23no—
372C3×Dic6—23no—
373C3×Dic6—23no—
374C3×Dic6C2×D413yes—
375C3×Dic6C2413yes—
376C3×Dic6C2411yescharacteristic
377C32×C8C2411yescharacteristic
378C32×C8C2413yes—
379C3×C3⋊C8C2411yescharacteristic
380C3×C3⋊C8C2413yes—
381#585—31no—
382#585—31no—
383#578—31no—
384#578—33no—
385#577—33no—
386#577—33no—
387#577—31no—
388#577C3×D311yescharacteristic, complemented
389#576—31no—
390#576—33no—
391#575—33no—
392#575—33no—
393C2×#135—33no—
394C2×#135—33no—
395C2×#131—31no—
396C3×#41—21no—
397C3×#41—21no—
398C3×#41—23no—
399C3×#41—23no—
400C3×#41—21no—
401C3×#41—23no—
402C3×#41—23no—
403C3×#41—31no—
404C3×#41—33no—
405C3×#41—33no—
406C3×#41—31no—
407C3×#41—33no—
408C3×#41—36no—
409C3×#41—33no—
410C3×#41—31no—
411C3×#41—36no—
412C3×#41—33no—
413C3×#41—33no—
414C3×#41—43no—
415C3×#41—41no—
416C3×#41—63no—
417C3×#41—63no—
418C3×#41—66no—
419C3×#41—63no—
420C3×#41—63no—
421C3×#41—63no—
422C3×#41—63no—
423C3×#41—63no—
424C3×#41—63no—
425C3×#41—63no—
426C3×#41—63no—
427C3×#41—66no—
428C3×#41—63no—
429C3×#41—63no—
430C3×#41—61no—
431C3×#41—63no—
432C3×#41C22×D313yes—
433C3×#41C22×D313yes—
434C3×#41C22×D311yescharacteristic
435C3×#41C23×C313yes—
436C3×#41C23×C313yes—
437C3×#41C23×C311yescharacteristic
438C2×C3×Q8—21no—
439C2×C3×Q8—21no—
440C2×C3×Q8—23no—
441C2×C3×Q8—31no—
442C2×C3×Q8—33no—
443C2×C3×Q8—33no—
444C2×C3×Q8—33no—
445C2×C3×Q8—41no—
446C2×C3×Q8—63no—
447C2×C3×Q8—63no—
448C2×C3×Q8—61no—
449C2×C3×Q8C22×D313yes—
450C2×C3×Q8C23×C313yes—
451C2×C3×D4—23no—
452C2×C3×D4—23no—
453C2×C3×D4—23no—
454C2×C3×D4—33no—
455C2×C3×D4—33no—
456C2×C3×D4—33no—
457C2×C3×D4—33no—
458C2×C3×D4—43no—
459C2×C3×D4—63no—
460C2×C3×D4—63no—
461C2×C3×D4—66no—
462C2×C3×D4—63no—
463C2×C3×D4—63no—
464C2×C3×D4—63no—
465C2×C3×D4—66no—
466C2×C3×D4—63no—
467C2×C3×D4—63no—
468C2×C3×D4C22×D313yes—
469C2×C3×D4C23×C313yes—
470C22×C3×C4—33no—
471C22×C3×C4—63no—
472C22×C3×C4—63no—
473C22×C3×C4—63no—
474C22×C3×C4—63no—
475C2×#67—23no—
476C2×#67—26no—
477C22×Dic3—23no—
478#239—21no—
479#239—23no—
480#239—23no—
481#239—23no—
482#239C3×D411yescharacteristic
483#239C23×C316yes—
484#239C23×C313yes—
485#239C23×C311yescharacteristic
486D3×Q8—21no—
487D3×Q8—23no—
488D3×Q8C3×D411yescharacteristic
489D3×Q8C23×C313yes—
490D3×Q8C23×C313yes—
491#237—23no—
492#237—26no—
493#237—23no—
494#237—23no—
495#237—23no—
496#237—23no—
497#237—23no—
498#237C3×D413yes—
499#237C23×C316yes—
500#237C23×C311yescharacteristic
501#237C23×C313yes—
502D3×D4—23no—
503D3×D4—23no—
504D3×D4—23no—
505D3×D4—26no—
506D3×D4—23no—
507D3×D4C3×D413yes—
508D3×D4C23×C313yes—
509D3×D4C23×C313yes—
510#235—26no—
511#235—23no—
512#235—23no—
513#235—23no—
514#235—23no—
515#235C23×C313yes—
516#235C23×C313yes—
517#235C23×C313yes—
518C2×D12—23no—
519C2×D12—23no—
520C2×D12C23×C313yes—
521C2×C4×D3—23no—
522C2×C4×D3—23no—
523C2×C4×D3—23no—
524C2×C4×D3C23×C313yes—
525C2×Dic6—23no—
526C2×Dic6C23×C313yes—
527C3×Q16—23no—
528C3×Q16—31no—
529C3×Q16—33no—
530C3×Q16—36no—
531C3×Q16—33no—
532C3×Q16C22×D313yes—
533C3×Q16C23×C313yes—
534C3×SD16—23no—
535C3×SD16—26no—
536C3×SD16—21no—
537C3×SD16—33no—
538C3×SD16—33no—
539C3×SD16—33no—
540C3×SD16—33no—
541C3×SD16—33no—
542C3×SD16—31no—
543C3×SD16—36no—
544C3×SD16C22×D311yescharacteristic
545C3×SD16C22×D313yes—
546C3×SD16C22×D316yes—
547C3×SD16C23×C311yescharacteristic
548C3×SD16C23×C313yes—
549C3×SD16C23×C316yes—
550C3×D8—23no—
551C3×D8—33no—
552C3×D8—31no—
553C3×D8—36no—
554C3×D8—33no—
555C3×D8C22×D313yes—
556C3×D8C23×C313yes—
557C3×M16—23no—
558C3×M16—33no—
559C3×M16—36no—
560C3×M16C22×D313yes—
561C3×M16C23×C313yes—
562C2×C3×C8—23no—
563C2×C3×C8—33no—
564C2×C3×C8—31no—
565C2×C3×C8—33no—
566C2×C3×C8—33no—
567C2×C3×C8—33no—
568C2×C3×C8C22×D313yes—
569C2×C3×C8C23×C313yes—
570#216C23×C316yes—
571#216C23×C313yes—
572#216C23×C311yescharacteristic
573#215C23×C313yes—
574#215C23×C313yes—
575#214C23×C313yes—
576#214C23×C313yes—
577#213C23×C311yescharacteristic
578#213C23×C313yes—
579#213C23×C316yes—
580#208C23×C313yes—
581C2×C3⋊C8C23×C313yes—
582Dic12C23×C313yes—
583D24C23×C313yes—
584#204C23×C313yes—
585#204C23×C316yes—
586#204C23×C311yescharacteristic
587ΓL(1,𝔽25)C23×C316yes—
588D3×C8C23×C311yescharacteristic
589D3×C8C23×C313yes—
590D3×C8C23×C313yes—
591D3×C8C23×C313yes—
592C22×C32—23no—
593C22×C32—21no—
594C22×C32—83no—
595C22×C32C22×D413yes—
596C2×C3×D3—23no—
597C2×C3×D3—21no—
598C2×C3×D3—43no—
599C2×C3×D3—83no—
600C2×C3×D3—83no—
601C2×C3×D3—83no—
602C2×C3×D3C22×D413yes—
603C2×C3×D3C22×D411yescharacteristic
604C32×C4—21no—
605C32×C4—23no—
606C32×C4C22×D413yes—
607C32×C4C2511yescharacteristic
608C3×Dic3—21no—
609C3×Dic3—23no—
610C3×Dic3C22×D413yes—
611C3×Dic3C22×D411yescharacteristic
6122−1+4—33no—
6132−1+4—31no—
6142−1+4—33no—
6152−1+4—61no—
6162−1+4—61no—
6172−1+4C2×C3×D311yescharacteristic, complemented
618H(5,𝔽2)—33no—
619H(5,𝔽2)—31no—
620H(5,𝔽2)—33no—
621H(5,𝔽2)—63no—
622H(5,𝔽2)—63no—
623H(5,𝔽2)C2×C3×D311yescharacteristic, complemented
624C2×#41—31no—
625C2×#41—33no—
626C2×#41—33no—
627C2×#41—33no—
628C2×#41—33no—
629C2×#41—63no—
630C2×#41—61no—
631C2×#41—61no—
632C2×#41—63no—
633#137—33no—
634#137—33no—
635#137—36no—
636#137—36no—
637#137—33no—
638#137C2×C3×D313yescomplemented
639AGL(1,ℤ/8)—33no—
640AGL(1,ℤ/8)—33no—
641AGL(1,ℤ/8)—36no—
642AGL(1,ℤ/8)—36no—
643AGL(1,ℤ/8)—33no—
644AGL(1,ℤ/8)C2×C3×D313yescomplemented
645#135—33no—
646#135—33no—
647#135—33no—
648#135—31no—
649#135—33no—
650#135—36no—
651#135—36no—
652#135—36no—
653#135—33no—
654#135—33no—
655#135C2×C3×D313yescomplemented
656C2×Q16—33no—
657C2×Q16—33no—
658C2×SD16—33no—
659C2×SD16—33no—
660C2×SD16—33no—
661C2×SD16C2×C3×D313yescomplemented
662C2×D8—33no—
663C2×D8—33no—
664#131—31no—
665#131—33no—
666#131—33no—
667#131C2×C3×D311yescharacteristic, complemented
668C2×M16—33no—
669C22×C8—33no—
670C23×C3—23no—
671C23×C3—23no—
672C23×C3—33no—
673C23×C3—43no—
674C23×C3—63no—
675C23×C3—63no—
676C23×C3—63no—
677C22×D3—23no—
678C22×D3—23no—
679C22×D3—23no—
680C22×D3C2×C3×D413yes—
681C3×Q8—23no—
682C3×Q8—23no—
683C3×Q8—23no—
684C3×Q8—21no—
685C3×Q8—21no—
686C3×Q8—33no—
687C3×Q8—33no—
688C3×Q8—31no—
689C3×Q8—43no—
690C3×Q8—63no—
691C3×Q8—63no—
692C3×Q8—63no—
693C3×Q8D3×D411yescharacteristic
694C3×Q8C2×C3×D411yescharacteristic
695C3×Q8C23×D311yescharacteristic
696C3×Q8C23×D313yes—
697C3×Q8C24×C311yescharacteristic
698C3×Q8C24×C313yes—
699C3×D4—23no—
700C3×D4—23no—
701C3×D4—23no—
702C3×D4—23no—
703C3×D4—23no—
704C3×D4—23no—
705C3×D4—21no—
706C3×D4—23no—
707C3×D4—23no—
708C3×D4—36no—
709C3×D4—33no—
710C3×D4—33no—
711C3×D4—31no—
712C3×D4—43no—
713C3×D4—43no—
714C3×D4—43no—
715C3×D4—61no—
716C3×D4—63no—
717C3×D4—66no—
718C3×D4—63no—
719C3×D4—63no—
720C3×D4—61no—
721C3×D4—63no—
722C3×D4—66no—
723C3×D4—63no—
724C3×D4—63no—
725C3×D4—63no—
726C3×D4D3×D413yes—
727C3×D4C2×C3×D413yes—
728C3×D4C23×D313yes—
729C3×D4C23×D311yescharacteristic
730C3×D4C24×C313yes—
731C3×D4C24×C311yescharacteristic
732C2×C3×C4—23no—
733C2×C3×C4—23no—
734C2×C3×C4—23no—
735C2×C3×C4—23no—
736C2×C3×C4—23no—
737C2×C3×C4—23no—
738C2×C3×C4—23no—
739C2×C3×C4—33no—
740C2×C3×C4—33no—
741C2×C3×C4—33no—
742C2×C3×C4—31no—
743C2×C3×C4—33no—
744C2×C3×C4—43no—
745C2×C3×C4—43no—
746C2×C3×C4—43no—
747C2×C3×C4—61no—
748C2×C3×C4—63no—
749C2×C3×C4—66no—
750C2×C3×C4—63no—
751C2×C3×C4—63no—
752C2×C3×C4—61no—
753C2×C3×C4—63no—
754C2×C3×C4—66no—
755C2×C3×C4—63no—
756C2×C3×C4—63no—
757C2×C3×C4—63no—
758C2×C3×C4C23×D313yes—
759C2×C3×C4C24×C313yes—
760#67—23no—
761#67—23no—
762#67—21no—
763#67—26no—
764#67—23no—
765#67—23no—
766#67—23no—
767#67C2×C3×D416yes—
768C2×Dic3—23no—
769C2×Dic3—26no—
770C2×Dic3—21no—
771C2×Dic3—23no—
772C2×Dic3C2×C3×D413yes—
773D12—26no—
774D12—23no—
775D12—21no—
776D12—23no—
777D12C2×C3×D413yes—
778D12C24×C313yes—
779D12C24×C311yescharacteristic
780C4×D3—23no—
781C4×D3—23no—
782C4×D3—23no—
783C4×D3—23no—
784C4×D3—21no—
785C4×D3—23no—
786C4×D3—26no—
787C4×D3C2×C3×D413yes—
788C4×D3C2×C3×D413yes—
789C4×D3C24×C311yescharacteristic
790C4×D3C24×C313yes—
791Dic6—23no—
792Dic6—23no—
793Dic6—23no—
794Dic6C2×C3×D413yes—
795Dic6C24×C313yes—
796Dic6C24×C311yescharacteristic
797C3×C8—21no—
798C3×C8—23no—
799C3×C8—31no—
800C3×C8—33no—
801C3×C8C23×D311yescharacteristic
802C3×C8C23×D313yes—
803C3×C8C24×C311yescharacteristic
804C3×C8C24×C313yes—
805C3⋊C8C24×C311yescharacteristic
806C3⋊C8C24×C313yes—
807C2×C32—23no—
808C2×C32—41no—
809C2×C32—43no—
810C2×C32C23×D411yescharacteristic
811C3×D3—21no—
812C3×D3—23no—
813C3×D3—43no—
814C3×D3—41no—
815#41—21no—
816#41—23no—
817#41—31no—
818#41—33no—
819#41—33no—
820#41—31no—
821#41—33no—
822#41—36no—
823#41—33no—
824#41—31no—
825#41—36no—
826#41—33no—
827#41—33no—
828#41—63no—
829#41—63no—
830#41—66no—
831#41—63no—
832#41—63no—
833#41—63no—
834#41—63no—
835#41—63no—
836#41—63no—
837#41—63no—
838#41—63no—
839#41—66no—
840#41—63no—
841#41—63no—
842#41—61no—
843#41—63no—
844#41C22×C3×D313yes—
845#41C22×C3×D313yes—
846#41C22×C3×D311yescharacteristic
847C2×Q8—21no—
848C2×Q8—31no—
849C2×Q8—33no—
850C2×Q8—33no—
851C2×Q8—33no—
852C2×Q8—63no—
853C2×Q8—63no—
854C2×Q8—61no—
855C2×Q8C22×C3×D313yes—
856C2×D4—23no—
857C2×D4—33no—
858C2×D4—33no—
859C2×D4—33no—
860C2×D4—33no—
861C2×D4—63no—
862C2×D4—63no—
863C2×D4—66no—
864C2×D4—63no—
865C2×D4—63no—
866C2×D4—63no—
867C2×D4—66no—
868C2×D4—63no—
869C2×D4—63no—
870C2×D4C22×C3×D313yes—
871C22×C4—33no—
872C22×C4—63no—
873C22×C4—63no—
874C22×C4—63no—
875C22×C4—63no—
876Q16—31no—
877Q16—33no—
878Q16—36no—
879Q16—33no—
880Q16C22×C3×D313yes—
881SD16—33no—
882SD16—33no—
883SD16—33no—
884SD16—33no—
885SD16—31no—
886SD16—33no—
887SD16—36no—
888SD16C22×C3×D311yescharacteristic
889SD16C22×C3×D313yes—
890SD16C22×C3×D316yes—
891D8—33no—
892D8—31no—
893D8—36no—
894D8—33no—
895D8C22×C3×D313yes—
896M16—33no—
897M16—36no—
898M16C22×C3×D313yes—
899C2×C8—33no—
900C2×C8—31no—
901C2×C8—33no—
902C2×C8—33no—
903C2×C8—33no—
904C2×C8C22×C3×D313yes—
905C22×C3—21no—
906C22×C3—23no—
907C22×C3—23no—
908C22×C3—21no—
909C22×C3—23no—
910C22×C3—31no—
911C22×C3—33no—
912C22×C3—41no—
913C22×C3—43no—
914C22×C3—63no—
915C22×C3—61no—
916C22×C3—83no—
917C22×C3—83no—
918C22×C3—123no—
919C22×C3—163no—
920C22×C3—243no—
921C22×C3—243no—
922C22×C3—243no—
923C22×C3C2×D3×D413yes—
924C22×C3C22×C3×D413yes—
925C2×D3—23no—
926C2×D3—21no—
927C2×D3—43no—
928C2×D3—83no—
929C2×D3—83no—
930C2×D3—83no—
931C2×D3C22×C3×D413yes—
932C2×D3C22×C3×D411yescharacteristic
933C3×C4—21no—
934C3×C4—23no—
935C3×C4—21no—
936C3×C4—23no—
937C3×C4—23no—
938C3×C4—21no—
939C3×C4—31no—
940C3×C4—33no—
941C3×C4—41no—
942C3×C4—43no—
943C3×C4—61no—
944C3×C4—63no—
945C3×C4C2×D3×D413yes—
946C3×C4C22×C3×D413yes—
947C3×C4C24×D311yescharacteristic
948C3×C4C25×C311yescharacteristic
949Dic3—21no—
950Dic3—23no—
951Dic3C22×C3×D413yes—
952Dic3C22×C3×D411yescharacteristic
953C32#358411yescharacteristic, complemented, Sylow
954C23—23no—
955C23—33no—
956C23—63no—
957C23—63no—
958C23—63no—
959Q8—23no—
960Q8—33no—
961Q8—31no—
962Q8—33no—
963Q8—63no—
964Q8—63no—
965Q8—63no—
966Q8C3×D3×D411yescharacteristic
967Q8C23×C3×D311yescharacteristic
968Q8C23×C3×D313yes—
969D4—23no—
970D4—23no—
971D4—23no—
972D4—36no—
973D4—33no—
974D4—33no—
975D4—31no—
976D4—61no—
977D4—63no—
978D4—66no—
979D4—63no—
980D4—63no—
981D4—61no—
982D4—63no—
983D4—66no—
984D4—63no—
985D4—63no—
986D4—63no—
987D4C3×D3×D413yes—
988D4C23×C3×D313yes—
989D4C23×C3×D311yescharacteristic
990C2×C4—23no—
991C2×C4—23no—
992C2×C4—23no—
993C2×C4—33no—
994C2×C4—33no—
995C2×C4—33no—
996C2×C4—31no—
997C2×C4—33no—
998C2×C4—61no—
999C2×C4—63no—
1000C2×C4—66no—
1001C2×C4—63no—
1002C2×C4—63no—
1003C2×C4—61no—
1004C2×C4—63no—
1005C2×C4—66no—
1006C2×C4—63no—
1007C2×C4—63no—
1008C2×C4—63no—
1009C2×C4C23×C3×D313yes—
1010C8—31no—
1011C8—33no—
1012C8C23×C3×D311yescharacteristic
1013C8C23×C3×D313yes—
1014C2×C3—23no—
1015C2×C3—23no—
1016C2×C3—21no—
1017C2×C3—43no—
1018C2×C3—43no—
1019C2×C3—41no—
1020C2×C3—41no—
1021C2×C3—43no—
1022C2×C3—61no—
1023C2×C3—63no—
1024C2×C3—83no—
1025C2×C3—81no—
1026C2×C3—123no—
1027C2×C3—121no—
1028C2×C3C22×D3×D411yescharacteristic
1029C2×C3C23×C3×D411yescharacteristic
1030D3—21no—
1031D3—23no—
1032D3—43no—
1033D3—41no—
1034C22—21no—
1035C22—23no—
1036C22—31no—
1037C22—33no—
1038C22—63no—
1039C22—61no—
1040C22—83no—
1041C22—123no—
1042C22—243no—
1043C22—243no—
1044C22—243no—
1045C22C2×C3×D3×D413yes—
1046C4—21no—
1047C4—23no—
1048C4—31no—
1049C4—33no—
1050C4—61no—
1051C4—63no—
1052C4C2×C3×D3×D413yes—
1053C4C24×C3×D311yescharacteristic
1054C3—21no—
1055C3#8720611yescharacteristic, direct product factor
1056C3C3×#358411yescharacteristic, complemented
1057C2—23no—
1058C2—43no—
1059C2—41no—
1060C2—61no—
1061C2—63no—
1062C2—123no—
1063C2—121no—
1064C2C22×C3×D3×D411yescharacteristic
subgroupG/H
centerC2×C3C22×D3×D4
commutator, cosocleC3×C4C25×C3
FrattiniC4C24×C3×D3
FittingC32×#577C2
socleC2×C32C23×D4
hypercenterC3×#577D3
hypocenterC3C3×#3584
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C3×#41 ◁ C3×#577

Complements

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

NH ≅ G/Ntype
1. C3×#5968C2semidirect
2. C3×#5966C2semidirect
3. C32×#577C2semidirect
4. C3×#5838C2semidirect
5. C3×#5835C2semidirect
6. C3×#5779C2semidirect
7. C3×#5777C2semidirect
8. C3×#5774C2semidirect
9. C3×#5773C2semidirect
10. C3×#5770C2semidirect
11. C3×D3×#135C2semidirect
12. C3×#5762C2semidirect
13. C2×C3×#916C2semidirect
14. C3×#5751C2semidirect
15. C3×D3×#131C2semidirect
17. #87206C3direct (N × H)
18. C32×2−1+4C22semidirect
19. C32×H(5,𝔽2)C22semidirect
21. C3×#1010C22semidirect
22. C3×#1010C22semidirect
24. C3×#1009C22semidirect
25. C3×#1009C22semidirect
29. C3×D3×#41C22semidirect
30. C3×D3×#41C22semidirect
32. C3×#1007C22semidirect
34. C2×C3×#239C22semidirect
36. C3×#1004C22semidirect
38. C2×C3×#237C22semidirect
39. C32×#137C22semidirect
40. C32×AGL(1,ℤ/8)C22semidirect
41. C32×#135C22semidirect
42. C2×C32×SD16C22semidirect
43. C32×#131C22semidirect
44. C3×#951C22semidirect
45. C3×#950C22semidirect
46. C3×#950C22semidirect
47. C3×#949C22semidirect
48. C3×#948C22semidirect
49. C2×C3×#216C22semidirect
50. C3×#942C22semidirect
51. C3×#932C22semidirect
52. C2×C3×#213C22semidirect
53. C3×#919C22semidirect
54. C3×#918C22semidirect
55. C3×D3×Q16C22semidirect
56. C3×#916C22semidirect
57. C3×#916C22semidirect
58. C3×#916C22semidirect
59. C3×#916C22semidirect
60. C3×#916C22semidirect
61. C3×#915C22semidirect
62. C3×#914C22semidirect
63. C3×D3×SD16C22semidirect
64. C3×D3×SD16C22semidirect
65. C3×#912C22semidirect
66. C3×#911C22semidirect
67. C3×D3×D8C22semidirect
68. C3×#909C22semidirect
69. C3×#908C22semidirect
70. C3×#907C22semidirect
71. C3×D3×M16C22semidirect
72. C3×#904C22semidirect
73. C2×C3×#204C22semidirect
74. C3×#901C22semidirect
75. C2×C3×D3×C8C22semidirect
78. #5968C2×C3semidirect
79. #5966C2×C3semidirect
86. C3×#577D3semidirect
87. C3×#577C2×C3semidirect
95. #5838C2×C3semidirect
96. #5835C2×C3semidirect
97. #5779C2×C3semidirect
98. #5777C2×C3semidirect
99. #5774C2×C3semidirect
100. #5773C2×C3semidirect
101. #5770C2×C3semidirect
102. D3×#135C2×C3semidirect
103. #5762C2×C3semidirect
104. C2×#916C2×C3semidirect
105. #5751C2×C3semidirect
106. D3×#131C2×C3semidirect
204. C3×2−1+4C2×D3semidirect
205. C3×2−1+4C22×C3semidirect
212. C3×H(5,𝔽2)C2×D3semidirect
213. C3×H(5,𝔽2)C22×C3semidirect
224. #1010C22×C3semidirect
225. #1010C22×C3semidirect
227. #1009C22×C3semidirect
228. #1009C22×C3semidirect
232. D3×#41C22×C3semidirect
233. D3×#41C22×C3semidirect
235. #1007C22×C3semidirect
237. C2×#239C22×C3semidirect
239. #1004C22×C3semidirect
241. C2×#237C22×C3semidirect
248. C3×#137C2×D3semidirect
249. C3×#137C22×C3semidirect
256. C3×AGL(1,ℤ/8)C2×D3semidirect
257. C3×AGL(1,ℤ/8)C22×C3semidirect
269. C3×#135C2×D3semidirect
270. C3×#135C22×C3semidirect
277. C2×C3×SD16C2×D3semidirect
278. C2×C3×SD16C22×C3semidirect
285. C3×#131C2×D3semidirect
286. C3×#131C22×C3semidirect
289. #951C22×C3semidirect
290. #950C22×C3semidirect
291. #950C22×C3semidirect
292. #949C22×C3semidirect
293. #948C22×C3semidirect
294. C2×#216C22×C3semidirect
295. #942C22×C3semidirect
296. #932C22×C3semidirect
297. C2×#213C22×C3semidirect
298. #919C22×C3semidirect
299. #918C22×C3semidirect
300. D3×Q16C22×C3semidirect
301. #916C22×C3semidirect
302. #916C22×C3semidirect
303. #916C22×C3semidirect
304. #916C22×C3semidirect
305. #916C22×C3semidirect
306. #915C22×C3semidirect
307. #914C22×C3semidirect
308. D3×SD16C22×C3semidirect
309. D3×SD16C22×C3semidirect
310. #912C22×C3semidirect
311. #911C22×C3semidirect
312. D3×D8C22×C3semidirect
313. #909C22×C3semidirect
314. #908C22×C3semidirect
315. #907C22×C3semidirect
316. D3×M16C22×C3semidirect
317. #904C22×C3semidirect
318. C2×#204C22×C3semidirect
319. #901C22×C3semidirect
320. C2×D3×C8C22×C3semidirect
388. #577C3×D3semidirect
617. 2−1+4C2×C3×D3semidirect
623. H(5,𝔽2)C2×C3×D3semidirect
638. #137C2×C3×D3semidirect
644. AGL(1,ℤ/8)C2×C3×D3semidirect
655. #135C2×C3×D3semidirect
661. C2×SD16C2×C3×D3semidirect
667. #131C2×C3×D3semidirect
953. C32#3584semidirect
1055. C3#87206direct (N × H)
1056. C3C3×#3584semidirect

Maximal subgroups

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

subgroupindex
C3×#59682
C3×#59662
C32×#5772
C3×#58382
C3×#58352
C3×#57792
C3×#57772
C3×#57742
C3×#57732
C3×#57702
C3×D3×#1352
C3×#57622
C2×C3×#9162
C3×#57512
C3×D3×#1312
C3×#35843
#872063