Finite Group Databasebeta

← C3×#87204 #11919019

Subgroups — C3×#87204 #11919019

Order 1152.

3062 conjugacy classes of subgroups.

The subgroup lattice has 1079 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5966C211yesmaximal, characteristic, complemented
2C3×D3×H(5,𝔽2)C211yesmaximal, characteristic, complemented
3C32×#576C211yesmaximal, characteristic, complemented
4C3×#5836C211yesmaximal, characteristic, complemented
5C3×#5835C211yesmaximal, characteristic, complemented
6C3×#5775C213yesmaximal, complemented
7C3×#5774C213yesmaximal, complemented
8C3×#5773C213yesmaximal, complemented
9C3×D3×AGL(1,ℤ/8)C213yesmaximal, complemented
10C3×#5770C213yesmaximal, complemented
11C3×#5768C213yesmaximal, complemented
12C3×#5757C213yesmaximal, complemented
13C2×C3×#911C213yesmaximal, complemented
14C3×#5751C211yesmaximal, characteristic, complemented
15C3×#5750C211yesmaximal, characteristic, complemented
16C3×#3585—31nomaximal
17#87204C311yesmaximal, characteristic, direct product factor
18C32×H(5,𝔽2)C2211yescharacteristic, complemented
19C32×H(5,𝔽2)C2211yescharacteristic, complemented
20C3×#1010—21no—
21C3×#1010C2213yescomplemented
22C3×#1010C2211yescharacteristic, complemented
23C3×#1009—21no—
24C3×#1009C2213yescomplemented
25C3×#1009C2211yescharacteristic, complemented
26C3×D3×#41—21no—
27C3×D3×#41—21no—
28C3×D3×#41C2211yescharacteristic
29C3×D3×#41C2213yescomplemented
30C3×D3×#41C2213yescomplemented
31C3×#1004—23no—
32C3×#1004—23no—
33C3×#1004C2213yescomplemented
34C3×#1004C2213yescomplemented
35C2×C3×#237—23no—
36C2×C3×#237C2213yescomplemented
37C2×C3×D3×D4—23no—
38C2×C3×D3×D4C2213yescomplemented
39C32×AGL(1,ℤ/8)C2213yescomplemented
40C32×AGL(1,ℤ/8)C2213yescomplemented
41C32×#135C2213yescomplemented
42C2×C32×D8C2213yescomplemented
43C32×#131C2211yescharacteristic, complemented
44C3×#951C2213yescomplemented
45C3×#950C2213yescomplemented
46C3×#950C2213yescomplemented
47C3×#949C2213yescomplemented
48C3×#948C2211yescharacteristic, complemented
49C2×C3×#214C2213yescomplemented
50C3×#932C2213yescomplemented
51C3×#932C2213yescomplemented
52C2×C3×#213C2213yescomplemented
53C3×#918C2211yescharacteristic, complemented
54C3×#918C2213yescomplemented
55C3×#916C2216yescomplemented
56C3×#915C2213yescomplemented
57C3×#915C2213yescomplemented
58C3×#914C2213yescomplemented
59C3×#914C2213yescomplemented
60C3×D3×SD16C2216yescomplemented
61C3×#912C2216yescomplemented
62C3×#911C2213yescomplemented
63C3×#911C2216yescomplemented
64C3×#911C2216yescomplemented
65C3×#911C2216yescomplemented
66C3×#911C2213yescomplemented
67C3×D3×D8C2216yescomplemented
68C3×#909C2213yescomplemented
69C3×#908C2213yescomplemented
70C3×#907C2213yescomplemented
71C3×D3×M16C2213yescomplemented
72C3×#904C2213yescomplemented
73C2×C3×#204C2213yescomplemented
74C3×#901C2213yescomplemented
75C2×C3×ΓL(1,𝔽25)C2213yescomplemented
76C3×#585—31no—
77C2×C3×H(5,𝔽2)—31no—
78#5966C2×C311yescharacteristic, complemented
79D3×H(5,𝔽2)C2×C311yescharacteristic, complemented
80C3×#577—31no—
81C3×#577—33no—
82C3×#577—33no—
83C3×#577—31no—
84C3×#576—21no—
85C3×#576—31no—
86C3×#576—33no—
87C3×#576—33no—
88C3×#576D311yescharacteristic, complemented
89C3×#576C2×C311yescharacteristic, complemented
90C3×#575—33no—
91C3×#575—33no—
92C2×C3×AGL(1,ℤ/8)—33no—
93C2×C3×AGL(1,ℤ/8)—33no—
94C3×#568—31no—
95#5836C2×C311yescharacteristic, complemented
96#5835C2×C311yescharacteristic, complemented
97#5775C2×C313yescomplemented
98#5774C2×C313yescomplemented
99#5773C2×C313yescomplemented
100D3×AGL(1,ℤ/8)C2×C313yescomplemented
101#5770C2×C313yescomplemented
102#5768C2×C313yescomplemented
103#5757C2×C313yescomplemented
104C2×#911C2×C313yescomplemented
105#5751C2×C311yescharacteristic, complemented
106#5750C2×C311yescharacteristic, complemented
107C23×C3×D3—23no—
108C32×#41—21no—
109C32×#41—21no—
110C32×#41C2313yes—
111C32×#41C2311yescharacteristic
112C32×#41C2313yescomplemented
113C2×C32×D4—23no—
114C2×C32×D4—23no—
115C2×C32×D4C2313yes—
116C2×C32×D4C2313yescomplemented
117C2×C3×#67—23no—
118C2×C3×#67—26no—
119C2×C3×#67—26no—
120C2×C3×#67—23no—
121C22×C3×Dic3—23no—
122C3×#239—21no—
123C3×#239D411yescharacteristic
124C3×#239C2311yescharacteristic
125C3×#239C2313yes—
126C3×D3×Q8—21no—
127C3×D3×Q8D411yescharacteristic
128C3×D3×Q8C2311yescharacteristic
129C3×D3×Q8C2313yescomplemented
130C3×#237—23no—
131C3×#237—26no—
132C3×#237—23no—
133C3×#237—23no—
134C3×#237—23no—
135C3×#237—23no—
136C3×#237—23no—
137C3×#237—23no—
138C3×#237D413yes—
139C3×#237C2313yes—
140C3×#237C2313yes—
141C3×#237C2316yescomplemented
142C3×D3×D4—23no—
143C3×D3×D4—23no—
144C3×D3×D4—23no—
145C3×D3×D4—26no—
146C3×D3×D4—23no—
147C3×D3×D4—23no—
148C3×D3×D4—23no—
149C3×D3×D4—23no—
150C3×D3×D4D413yes—
151C3×D3×D4C2316yes—
152C3×D3×D4C2313yes—
153C3×D3×D4C2313yescomplemented
154C3×#235—23no—
155C3×#235—23no—
156C3×#235—23no—
157C3×#235—23no—
158C3×#235C2313yes—
159C3×#235C2313yes—
160C3×#235C2313yescomplemented
161C2×C3×D12—23no—
162C2×C3×D12C2313yes—
163C2×C3×C4×D3—23no—
164C2×C3×C4×D3—23no—
165C2×C3×C4×D3C2313yes—
166C2×C3×Dic6—23no—
167C2×C3×Dic6C2313yescomplemented
168C32×Q16C2311yescharacteristic, complemented
169C32×SD16C2313yescomplemented
170C32×SD16C2313yescomplemented
171C32×D8C2316yescomplemented
172C32×D8C2313yescomplemented
173C32×M16C2313yescomplemented
174C2×C32×C8C2313yescomplemented
175C3×#216C2311yescharacteristic, complemented
176C3×#216C2313yescomplemented
177C3×#215C2313yescomplemented
178C3×#215C2311yescharacteristic, complemented
179C3×#214C2313yescomplemented
180C3×#214C2316yescomplemented
181C3×#214C2313yescomplemented
182C3×#213C2313yescomplemented
183C3×#213C2316yescomplemented
184C3×#213C2313yescomplemented
185C3×#208C2313yescomplemented
186C2×C3×C3⋊C8C2313yescomplemented
187C3×Dic12C2313yescomplemented
188C3×D24C2313yescomplemented
189C3×#204C2313yescomplemented
190C3×#204C2316yescomplemented
191C3×#204C2311yescharacteristic, complemented
192C3×ΓL(1,𝔽25)C2311yescharacteristic
193C3×ΓL(1,𝔽25)C2313yes—
194C3×ΓL(1,𝔽25)C2313yescomplemented
195C3×ΓL(1,𝔽25)C2313yescomplemented
196C3×D3×C8C2316yescomplemented
197#3585—31noSylow
198C3×2−1+4—31no—
199C3×2−1+4—33no—
200C3×2−1+4—61no—
201C3×H(5,𝔽2)—21no—
202C3×H(5,𝔽2)—21no—
203C3×H(5,𝔽2)—33no—
204C3×H(5,𝔽2)—31no—
205C3×H(5,𝔽2)—33no—
206C3×H(5,𝔽2)—33no—
207C3×H(5,𝔽2)—63no—
208C3×H(5,𝔽2)—63no—
209C3×H(5,𝔽2)—61no—
210C3×H(5,𝔽2)C2×D311yescharacteristic, complemented
211C3×H(5,𝔽2)C2×D311yescharacteristic, complemented
212C3×H(5,𝔽2)C22×C311yescharacteristic, 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—63no—
219C2×C3×#41—61no—
220C2×C3×#41—61no—
221C22×C3×D4—33no—
222C22×C3×D4—63no—
223#1010—21no—
224#1010C22×C313yescomplemented
225#1010C22×C311yescharacteristic, complemented
226#1009—21no—
227#1009C22×C313yescomplemented
228#1009C22×C311yescharacteristic, complemented
229D3×#41—21no—
230D3×#41—21no—
231D3×#41C22×C311yescharacteristic
232D3×#41C22×C313yescomplemented
233D3×#41C22×C313yescomplemented
234#1004—23no—
235#1004—23no—
236#1004C22×C313yescomplemented
237#1004C22×C313yescomplemented
238C2×#237—23no—
239C2×#237C22×C313yescomplemented
240C2×D3×D4—23no—
241C2×D3×D4C22×C313yescomplemented
242C3×#137—33no—
243C3×#137—31no—
244C3×#137—33no—
245C3×#137—33no—
246C3×#137—33no—
247C3×#137—33no—
248C3×AGL(1,ℤ/8)—23no—
249C3×AGL(1,ℤ/8)—23no—
250C3×AGL(1,ℤ/8)—33no—
251C3×AGL(1,ℤ/8)—33no—
252C3×AGL(1,ℤ/8)—33no—
253C3×AGL(1,ℤ/8)—33no—
254C3×AGL(1,ℤ/8)—33no—
255C3×AGL(1,ℤ/8)—36no—
256C3×AGL(1,ℤ/8)—33no—
257C3×AGL(1,ℤ/8)—36no—
258C3×AGL(1,ℤ/8)—36no—
259C3×AGL(1,ℤ/8)—33no—
260C3×AGL(1,ℤ/8)—33no—
261C3×AGL(1,ℤ/8)C2×D313yescomplemented
262C3×AGL(1,ℤ/8)C2×D313yescomplemented
263C3×AGL(1,ℤ/8)C22×C313yescomplemented
264C3×AGL(1,ℤ/8)C22×C313yescomplemented
265C3×#135—23no—
266C3×#135—33no—
267C3×#135—33no—
268C3×#135—36no—
269C3×#135—36no—
270C3×#135—33no—
271C3×#135C2×D313yescomplemented
272C3×#135C22×C313yescomplemented
273C2×C3×SD16—33no—
274C2×C3×SD16—36no—
275C2×C3×SD16—33no—
276C2×C3×D8—23no—
277C2×C3×D8—33no—
278C2×C3×D8—36no—
279C2×C3×D8C2×D313yescomplemented
280C2×C3×D8C22×C313yescomplemented
281C3×#131—21no—
282C3×#131—31no—
283C3×#131—33no—
284C3×#131—33no—
285C3×#131C2×D311yescharacteristic, complemented
286C3×#131C22×C311yescharacteristic, complemented
287C2×C3×M16—33no—
288C2×C3×M16—33no—
289#951C22×C313yescomplemented
290#950C22×C313yescomplemented
291#950C22×C313yescomplemented
292#949C22×C313yescomplemented
293#948C22×C311yescharacteristic, complemented
294C2×#214C22×C313yescomplemented
295#932C22×C313yescomplemented
296#932C22×C313yescomplemented
297C2×#213C22×C313yescomplemented
298#918C22×C311yescharacteristic, complemented
299#918C22×C313yescomplemented
300#916C22×C316yescomplemented
301#915C22×C313yescomplemented
302#915C22×C313yescomplemented
303#914C22×C313yescomplemented
304#914C22×C313yescomplemented
305D3×SD16C22×C316yescomplemented
306#912C22×C316yescomplemented
307#911C22×C313yescomplemented
308#911C22×C316yescomplemented
309#911C22×C316yescomplemented
310#911C22×C316yescomplemented
311#911C22×C313yescomplemented
312D3×D8C22×C316yescomplemented
313#909C22×C313yescomplemented
314#908C22×C313yescomplemented
315#907C22×C313yescomplemented
316D3×M16C22×C313yescomplemented
317#904C22×C313yescomplemented
318C2×#204C22×C313yescomplemented
319#901C22×C313yescomplemented
320C2×ΓL(1,𝔽25)C22×C313yescomplemented
321C23×C32—23no—
322C23×C32—23no—
323C22×C3×D3—23no—
324C22×C3×D3—23no—
325C22×C3×D3—26no—
326C22×C3×D3—23no—
327C22×C3×D3—86no—
328C22×C3×D3C2×D413yes—
329C32×Q8C2×D411yescharacteristic
330C32×Q8C2411yescharacteristic
331C32×Q8C2411yescharacteristic
332C32×D4—23no—
333C32×D4—23no—
334C32×D4—23no—
335C32×D4—23no—
336C32×D4C2×D413yes—
337C32×D4C2413yes—
338C32×D4C2413yes—
339C2×C32×C4—23no—
340C2×C32×C4—23no—
341C2×C32×C4C2413yes—
342C3×#67—23no—
343C3×#67—23no—
344C3×#67—23no—
345C3×#67—23no—
346C3×#67—26no—
347C3×#67—26no—
348C3×#67—23no—
349C3×#67—23no—
350C3×#67C2×D416yes—
351C2×C3×Dic3—23no—
352C2×C3×Dic3—26no—
353C2×C3×Dic3—23no—
354C2×C3×Dic3—23no—
355C2×C3×Dic3C2×D413yes—
356C3×D12—23no—
357C3×D12—21no—
358C3×D12—23no—
359C3×D12C2×D413yes—
360C3×D12C2413yes—
361C3×D12C2411yescharacteristic
362C3×C4×D3—21no—
363C3×C4×D3—23no—
364C3×C4×D3—23no—
365C3×C4×D3—23no—
366C3×C4×D3—21no—
367C3×C4×D3—23no—
368C3×C4×D3C2×D413yes—
369C3×C4×D3C2×D413yes—
370C3×C4×D3C2413yes—
371C3×C4×D3C2411yescharacteristic
372C3×Dic6—23no—
373C3×Dic6—23no—
374C3×Dic6—21no—
375C3×Dic6C2×D413yes—
376C3×Dic6C2413yes—
377C3×Dic6C2411yescharacteristic
378C32×C8C2413yes—
379C32×C8C2411yescharacteristic
380C3×C3⋊C8C2413yes—
381C3×C3⋊C8C2411yescharacteristic
382#585—31no—
383C2×H(5,𝔽2)—31no—
384#577—31no—
385#577—33no—
386#577—33no—
387#577—31no—
388#576—31no—
389#576—33no—
390#576—33no—
391#576C3×D311yescharacteristic, complemented
392#575—33no—
393#575—33no—
394C2×AGL(1,ℤ/8)—33no—
395C2×AGL(1,ℤ/8)—33no—
396#568—31no—
397C24×C3—63no—
398C23×D3—23no—
399C3×#41—21no—
400C3×#41—21no—
401C3×#41—21no—
402C3×#41—21no—
403C3×#41—21no—
404C3×#41—23no—
405C3×#41—23no—
406C3×#41—31no—
407C3×#41—33no—
408C3×#41—33no—
409C3×#41—33no—
410C3×#41—31no—
411C3×#41—36no—
412C3×#41—33no—
413C3×#41—33no—
414C3×#41—33no—
415C3×#41—33no—
416C3×#41—41no—
417C3×#41—41no—
418C3×#41—63no—
419C3×#41—63no—
420C3×#41—63no—
421C3×#41—63no—
422C3×#41—63no—
423C3×#41—63no—
424C3×#41—63no—
425C3×#41—63no—
426C3×#41—66no—
427C3×#41—63no—
428C3×#41—63no—
429C3×#41—61no—
430C3×#41—63no—
431C3×#41C22×D313yes—
432C3×#41C22×D311yescharacteristic
433C3×#41C22×D313yescomplemented
434C3×#41C23×C313yes—
435C3×#41C23×C311yescharacteristic
436C3×#41C23×C313yescomplemented
437C2×C3×Q8—31no—
438C2×C3×Q8—33no—
439C2×C3×Q8—31no—
440C2×C3×Q8—33no—
441C2×C3×Q8—63no—
442C2×C3×Q8—61no—
443C2×C3×D4—23no—
444C2×C3×D4—23no—
445C2×C3×D4—23no—
446C2×C3×D4—23no—
447C2×C3×D4—23no—
448C2×C3×D4—23no—
449C2×C3×D4—33no—
450C2×C3×D4—33no—
451C2×C3×D4—36no—
452C2×C3×D4—33no—
453C2×C3×D4—33no—
454C2×C3×D4—43no—
455C2×C3×D4—43no—
456C2×C3×D4—63no—
457C2×C3×D4—63no—
458C2×C3×D4—63no—
459C2×C3×D4—63no—
460C2×C3×D4—66no—
461C2×C3×D4—63no—
462C2×C3×D4—63no—
463C2×C3×D4—63no—
464C2×C3×D4—63no—
465C2×C3×D4—66no—
466C2×C3×D4—66no—
467C2×C3×D4—63no—
468C2×C3×D4—63no—
469C2×C3×D4C22×D313yes—
470C2×C3×D4C22×D313yescomplemented
471C2×C3×D4C23×C313yes—
472C2×C3×D4C23×C313yescomplemented
473C22×C3×C4—33no—
474C22×C3×C4—63no—
475C22×C3×C4—63no—
476C22×C3×C4—63no—
477C2×#67—23no—
478C2×#67—26no—
479C2×#67—26no—
480C2×#67—23no—
481C22×Dic3—23no—
482#239—21no—
483#239C3×D411yescharacteristic
484#239C23×C311yescharacteristic
485#239C23×C313yes—
486D3×Q8—21no—
487D3×Q8C3×D411yescharacteristic
488D3×Q8C23×C311yescharacteristic
489D3×Q8C23×C313yescomplemented
490#237—23no—
491#237—26no—
492#237—23no—
493#237—23no—
494#237—23no—
495#237—23no—
496#237—23no—
497#237—23no—
498#237C3×D413yes—
499#237C23×C313yes—
500#237C23×C313yes—
501#237C23×C316yescomplemented
502D3×D4—23no—
503D3×D4—23no—
504D3×D4—23no—
505D3×D4—26no—
506D3×D4—23no—
507D3×D4—23no—
508D3×D4—23no—
509D3×D4—23no—
510D3×D4C3×D413yes—
511D3×D4C23×C316yes—
512D3×D4C23×C313yes—
513D3×D4C23×C313yescomplemented
514#235—23no—
515#235—23no—
516#235—23no—
517#235—23no—
518#235C23×C313yes—
519#235C23×C313yes—
520#235C23×C313yescomplemented
521C2×D12—23no—
522C2×D12C23×C313yes—
523C2×C4×D3—23no—
524C2×C4×D3—23no—
525C2×C4×D3C23×C313yes—
526C2×Dic6—23no—
527C2×Dic6C23×C313yescomplemented
528C3×Q16—21no—
529C3×Q16—33no—
530C3×Q16—31no—
531C3×Q16—33no—
532C3×Q16C22×D311yescharacteristic, complemented
533C3×Q16C23×C311yescharacteristic, complemented
534C3×SD16—23no—
535C3×SD16—23no—
536C3×SD16—33no—
537C3×SD16—31no—
538C3×SD16—33no—
539C3×SD16—36no—
540C3×SD16—33no—
541C3×SD16—36no—
542C3×SD16—33no—
543C3×SD16—31no—
544C3×SD16C22×D313yescomplemented
545C3×SD16C22×D313yescomplemented
546C3×SD16C23×C313yescomplemented
547C3×SD16C23×C313yescomplemented
548C3×D8—23no—
549C3×D8—26no—
550C3×D8—33no—
551C3×D8—36no—
552C3×D8—33no—
553C3×D8—33no—
554C3×D8C22×D316yescomplemented
555C3×D8C22×D313yescomplemented
556C3×D8C23×C316yescomplemented
557C3×D8C23×C313yescomplemented
558C3×M16—23no—
559C3×M16—33no—
560C3×M16—33no—
561C3×M16—31no—
562C3×M16—33no—
563C3×M16—33no—
564C3×M16C22×D313yescomplemented
565C3×M16C23×C313yescomplemented
566C2×C3×C8—23no—
567C2×C3×C8—33no—
568C2×C3×C8—36no—
569C2×C3×C8C22×D313yescomplemented
570C2×C3×C8C23×C313yescomplemented
571#216C23×C311yescharacteristic, complemented
572#216C23×C313yescomplemented
573#215C23×C313yescomplemented
574#215C23×C311yescharacteristic, complemented
575#214C23×C313yescomplemented
576#214C23×C316yescomplemented
577#214C23×C313yescomplemented
578#213C23×C313yescomplemented
579#213C23×C316yescomplemented
580#213C23×C313yescomplemented
581#208C23×C313yescomplemented
582C2×C3⋊C8C23×C313yescomplemented
583Dic12C23×C313yescomplemented
584D24C23×C313yescomplemented
585#204C23×C313yescomplemented
586#204C23×C316yescomplemented
587#204C23×C311yescharacteristic, complemented
588ΓL(1,𝔽25)C23×C311yescharacteristic
589ΓL(1,𝔽25)C23×C313yes—
590ΓL(1,𝔽25)C23×C313yescomplemented
591ΓL(1,𝔽25)C23×C313yescomplemented
592D3×C8C23×C316yescomplemented
593C22×C32—23no—
594C22×C32—23no—
595C22×C32—83no—
596C22×C32—83no—
597C22×C32C22×D413yes—
598C2×C3×D3—21no—
599C2×C3×D3—23no—
600C2×C3×D3—43no—
601C2×C3×D3—46no—
602C2×C3×D3—83no—
603C2×C3×D3—86no—
604C2×C3×D3—83no—
605C2×C3×D3C22×D411yescharacteristic
606C2×C3×D3C22×D413yes—
607C32×C4—21no—
608C32×C4—21no—
609C32×C4C22×D413yes—
610C32×C4C2511yescharacteristic
611C3×Dic3—23no—
612C3×Dic3—21no—
613C3×Dic3C22×D413yes—
614C3×Dic3C22×D411yescharacteristic
6152−1+4—31no—
6162−1+4—33no—
6172−1+4—61no—
618H(5,𝔽2)—33no—
619H(5,𝔽2)—31no—
620H(5,𝔽2)—33no—
621H(5,𝔽2)—33no—
622H(5,𝔽2)—63no—
623H(5,𝔽2)—63no—
624H(5,𝔽2)—61no—
625H(5,𝔽2)C2×C3×D311yescharacteristic, complemented
626H(5,𝔽2)C2×C3×D311yescharacteristic, complemented
627C2×#41—31no—
628C2×#41—33no—
629C2×#41—33no—
630C2×#41—33no—
631C2×#41—63no—
632C2×#41—61no—
633C2×#41—61no—
634C22×D4—33no—
635C22×D4—63no—
636#137—33no—
637#137—31no—
638#137—33no—
639#137—33no—
640#137—33no—
641#137—33no—
642AGL(1,ℤ/8)—33no—
643AGL(1,ℤ/8)—33no—
644AGL(1,ℤ/8)—33no—
645AGL(1,ℤ/8)—33no—
646AGL(1,ℤ/8)—33no—
647AGL(1,ℤ/8)—36no—
648AGL(1,ℤ/8)—33no—
649AGL(1,ℤ/8)—36no—
650AGL(1,ℤ/8)—36no—
651AGL(1,ℤ/8)—33no—
652AGL(1,ℤ/8)—33no—
653AGL(1,ℤ/8)C2×C3×D313yescomplemented
654AGL(1,ℤ/8)C2×C3×D313yescomplemented
655#135—33no—
656#135—33no—
657#135—36no—
658#135—36no—
659#135—33no—
660#135C2×C3×D313yescomplemented
661C2×SD16—33no—
662C2×SD16—36no—
663C2×SD16—33no—
664C2×D8—33no—
665C2×D8—36no—
666C2×D8C2×C3×D313yescomplemented
667#131—31no—
668#131—33no—
669#131—33no—
670#131C2×C3×D311yescharacteristic, complemented
671C2×M16—33no—
672C2×M16—33no—
673C23×C3—23no—
674C23×C3—23no—
675C23×C3—23no—
676C23×C3—23no—
677C23×C3—33no—
678C23×C3—43no—
679C23×C3—43no—
680C23×C3—63no—
681C23×C3—63no—
682C23×C3—66no—
683C23×C3—63no—
684C23×C3—246no—
685C22×D3—23no—
686C22×D3—23no—
687C22×D3—23no—
688C22×D3—26no—
689C22×D3—86no—
690C22×D3C2×C3×D413yes—
691C3×Q8—21no—
692C3×Q8—21no—
693C3×Q8—21no—
694C3×Q8—33no—
695C3×Q8—33no—
696C3×Q8—31no—
697C3×Q8—63no—
698C3×Q8—61no—
699C3×Q8—63no—
700C3×Q8D3×D411yescharacteristic
701C3×Q8C2×C3×D411yescharacteristic
702C3×Q8C23×D311yescharacteristic
703C3×Q8C23×D311yescharacteristic
704C3×Q8C24×C311yescharacteristic
705C3×Q8C24×C311yescharacteristic
706C3×D4—23no—
707C3×D4—23no—
708C3×D4—23no—
709C3×D4—23no—
710C3×D4—23no—
711C3×D4—23no—
712C3×D4—23no—
713C3×D4—23no—
714C3×D4—23no—
715C3×D4—23no—
716C3×D4—23no—
717C3×D4—36no—
718C3×D4—33no—
719C3×D4—31no—
720C3×D4—33no—
721C3×D4—43no—
722C3×D4—43no—
723C3×D4—43no—
724C3×D4—43no—
725C3×D4—63no—
726C3×D4—61no—
727C3×D4—63no—
728C3×D4—66no—
729C3×D4—63no—
730C3×D4—63no—
731C3×D4—63no—
732C3×D4—66no—
733C3×D4—63no—
734C3×D4—63no—
735C3×D4—63no—
736C3×D4D3×D413yes—
737C3×D4C2×C3×D413yes—
738C3×D4C23×D313yes—
739C3×D4C23×D313yes—
740C3×D4C24×C313yes—
741C3×D4C24×C313yes—
742C2×C3×C4—23no—
743C2×C3×C4—23no—
744C2×C3×C4—23no—
745C2×C3×C4—23no—
746C2×C3×C4—23no—
747C2×C3×C4—33no—
748C2×C3×C4—33no—
749C2×C3×C4—33no—
750C2×C3×C4—33no—
751C2×C3×C4—31no—
752C2×C3×C4—43no—
753C2×C3×C4—43no—
754C2×C3×C4—61no—
755C2×C3×C4—63no—
756C2×C3×C4—61no—
757C2×C3×C4—63no—
758C2×C3×C4—63no—
759C2×C3×C4—63no—
760C2×C3×C4—66no—
761C2×C3×C4—63no—
762C2×C3×C4—63no—
763C2×C3×C4—63no—
764C2×C3×C4C23×D313yes—
765C2×C3×C4C24×C313yes—
766#67—23no—
767#67—23no—
768#67—23no—
769#67—23no—
770#67—26no—
771#67—26no—
772#67—23no—
773#67—23no—
774#67C2×C3×D416yes—
775C2×Dic3—23no—
776C2×Dic3—26no—
777C2×Dic3—23no—
778C2×Dic3—23no—
779C2×Dic3C2×C3×D413yes—
780D12—23no—
781D12—21no—
782D12—23no—
783D12C2×C3×D413yes—
784D12C24×C313yes—
785D12C24×C311yescharacteristic
786C4×D3—21no—
787C4×D3—23no—
788C4×D3—23no—
789C4×D3—23no—
790C4×D3—21no—
791C4×D3—23no—
792C4×D3C2×C3×D413yes—
793C4×D3C2×C3×D413yes—
794C4×D3C24×C313yes—
795C4×D3C24×C311yescharacteristic
796Dic6—23no—
797Dic6—23no—
798Dic6—21no—
799Dic6C2×C3×D413yes—
800Dic6C24×C313yes—
801Dic6C24×C311yescharacteristic
802C3×C8—21no—
803C3×C8—23no—
804C3×C8—33no—
805C3×C8—31no—
806C3×C8C23×D313yes—
807C3×C8C23×D311yescharacteristic
808C3×C8C24×C313yes—
809C3×C8C24×C311yescharacteristic
810C3⋊C8C24×C313yes—
811C3⋊C8C24×C311yescharacteristic
812C2×C32—23no—
813C2×C32—43no—
814C2×C32—43no—
815C2×C32C23×D411yescharacteristic
816C3×D3—21no—
817C3×D3—23no—
818C3×D3—43no—
819C3×D3—41no—
820C24—63no—
821#41—21no—
822#41—21no—
823#41—31no—
824#41—33no—
825#41—33no—
826#41—33no—
827#41—31no—
828#41—36no—
829#41—33no—
830#41—33no—
831#41—33no—
832#41—33no—
833#41—63no—
834#41—63no—
835#41—63no—
836#41—63no—
837#41—63no—
838#41—63no—
839#41—63no—
840#41—63no—
841#41—66no—
842#41—63no—
843#41—63no—
844#41—61no—
845#41—63no—
846#41C22×C3×D313yes—
847#41C22×C3×D311yescharacteristic
848#41C22×C3×D313yescomplemented
849C2×Q8—31no—
850C2×Q8—33no—
851C2×Q8—31no—
852C2×Q8—33no—
853C2×Q8—63no—
854C2×Q8—61no—
855C2×D4—23no—
856C2×D4—23no—
857C2×D4—33no—
858C2×D4—33no—
859C2×D4—36no—
860C2×D4—33no—
861C2×D4—33no—
862C2×D4—63no—
863C2×D4—63no—
864C2×D4—63no—
865C2×D4—63no—
866C2×D4—66no—
867C2×D4—63no—
868C2×D4—63no—
869C2×D4—63no—
870C2×D4—63no—
871C2×D4—66no—
872C2×D4—66no—
873C2×D4—63no—
874C2×D4—63no—
875C2×D4C22×C3×D313yes—
876C2×D4C22×C3×D313yescomplemented
877C22×C4—33no—
878C22×C4—63no—
879C22×C4—63no—
880C22×C4—63no—
881Q16—33no—
882Q16—31no—
883Q16—33no—
884Q16C22×C3×D311yescharacteristic, complemented
885SD16—33no—
886SD16—31no—
887SD16—33no—
888SD16—36no—
889SD16—33no—
890SD16—36no—
891SD16—33no—
892SD16—31no—
893SD16C22×C3×D313yescomplemented
894SD16C22×C3×D313yescomplemented
895D8—33no—
896D8—33no—
897D8—36no—
898D8—33no—
899D8C22×C3×D316yescomplemented
900D8C22×C3×D313yescomplemented
901M16—33no—
902M16—33no—
903M16—31no—
904M16—33no—
905M16—33no—
906M16C22×C3×D313yescomplemented
907C2×C8—33no—
908C2×C8—36no—
909C2×C8C22×C3×D313yescomplemented
910C22×C3—23no—
911C22×C3—23no—
912C22×C3—23no—
913C22×C3—23no—
914C22×C3—23no—
915C22×C3—31no—
916C22×C3—33no—
917C22×C3—43no—
918C22×C3—43no—
919C22×C3—61no—
920C22×C3—63no—
921C22×C3—83no—
922C22×C3—83no—
923C22×C3—83no—
924C22×C3—83no—
925C22×C3—123no—
926C22×C3—126no—
927C22×C3—163no—
928C22×C3—163no—
929C22×C3—243no—
930C22×C3—246no—
931C22×C3—243no—
932C22×C3C2×D3×D413yes—
933C22×C3C22×C3×D413yes—
934C2×D3—21no—
935C2×D3—23no—
936C2×D3—43no—
937C2×D3—46no—
938C2×D3—86no—
939C2×D3—83no—
940C2×D3—83no—
941C2×D3C22×C3×D411yescharacteristic
942C2×D3C22×C3×D413yes—
943C3×C4—21no—
944C3×C4—21no—
945C3×C4—21no—
946C3×C4—21no—
947C3×C4—23no—
948C3×C4—21no—
949C3×C4—31no—
950C3×C4—33no—
951C3×C4—41no—
952C3×C4—41no—
953C3×C4—61no—
954C3×C4—63no—
955C3×C4C2×D3×D413yes—
956C3×C4C22×C3×D413yes—
957C3×C4C24×D311yescharacteristic
958C3×C4C25×C311yescharacteristic
959Dic3—23no—
960Dic3—21no—
961Dic3C22×C3×D413yes—
962Dic3C22×C3×D411yescharacteristic
963C32#358511yescharacteristic, complemented, Sylow
964C23—23no—
965C23—23no—
966C23—33no—
967C23—63no—
968C23—63no—
969C23—66no—
970C23—63no—
971C23—246no—
972Q8—33no—
973Q8—33no—
974Q8—31no—
975Q8—63no—
976Q8—61no—
977Q8—63no—
978Q8C3×D3×D411yescharacteristic
979Q8C23×C3×D311yescharacteristic
980Q8C23×C3×D311yescharacteristic
981D4—23no—
982D4—23no—
983D4—23no—
984D4—23no—
985D4—36no—
986D4—33no—
987D4—31no—
988D4—33no—
989D4—63no—
990D4—61no—
991D4—63no—
992D4—66no—
993D4—63no—
994D4—63no—
995D4—63no—
996D4—66no—
997D4—63no—
998D4—63no—
999D4—63no—
1000D4C3×D3×D413yes—
1001D4C23×C3×D313yes—
1002D4C23×C3×D313yes—
1003C2×C4—23no—
1004C2×C4—23no—
1005C2×C4—33no—
1006C2×C4—33no—
1007C2×C4—33no—
1008C2×C4—33no—
1009C2×C4—31no—
1010C2×C4—61no—
1011C2×C4—63no—
1012C2×C4—61no—
1013C2×C4—63no—
1014C2×C4—63no—
1015C2×C4—63no—
1016C2×C4—66no—
1017C2×C4—63no—
1018C2×C4—63no—
1019C2×C4—63no—
1020C2×C4C23×C3×D313yes—
1021C8—31no—
1022C8—33no—
1023C8C23×C3×D313yes—
1024C8C23×C3×D311yescharacteristic
1025C2×C3—23no—
1026C2×C3—23no—
1027C2×C3—21no—
1028C2×C3—43no—
1029C2×C3—43no—
1030C2×C3—43no—
1031C2×C3—43no—
1032C2×C3—43no—
1033C2×C3—61no—
1034C2×C3—63no—
1035C2×C3—83no—
1036C2×C3—83no—
1037C2×C3—123no—
1038C2×C3—121no—
1039C2×C3C22×D3×D411yescharacteristic
1040C2×C3C23×C3×D411yescharacteristic
1041D3—21no—
1042D3—23no—
1043D3—43no—
1044D3—41no—
1045C22—23no—
1046C22—23no—
1047C22—31no—
1048C22—33no—
1049C22—61no—
1050C22—63no—
1051C22—83no—
1052C22—83no—
1053C22—123no—
1054C22—126no—
1055C22—243no—
1056C22—246no—
1057C22—243no—
1058C22C2×C3×D3×D413yes—
1059C4—21no—
1060C4—21no—
1061C4—31no—
1062C4—33no—
1063C4—61no—
1064C4—63no—
1065C4C2×C3×D3×D413yes—
1066C4C24×C3×D311yescharacteristic
1067C3—21no—
1068C3#8720411yescharacteristic, direct product factor
1069C3C3×#358511yescharacteristic, complemented
1070C2—23no—
1071C2—43no—
1072C2—43no—
1073C2—61no—
1074C2—63no—
1075C2—123no—
1076C2—121no—
1077C2C22×C3×D3×D411yescharacteristic
subgroupG/H
centerC2×C3C22×D3×D4
commutator, cosocleC3×C4C25×C3
FrattiniC4C24×C3×D3
FittingC32×#576C2
socleC2×C32C23×D4
hypercenterC3×#576D3
hypocenterC3C3×#3585
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C3×#41 ◁ C3×#576

Complements

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

NH ≅ G/Ntype
1. C3×#5966C2semidirect
2. C3×D3×H(5,𝔽2)C2semidirect
3. C32×#576C2semidirect
4. C3×#5836C2semidirect
5. C3×#5835C2semidirect
6. C3×#5775C2semidirect
7. C3×#5774C2semidirect
8. C3×#5773C2semidirect
9. C3×D3×AGL(1,ℤ/8)C2semidirect
10. C3×#5770C2semidirect
11. C3×#5768C2semidirect
12. C3×#5757C2semidirect
13. C2×C3×#911C2semidirect
14. C3×#5751C2semidirect
15. C3×#5750C2semidirect
17. #87204C3direct (N × H)
18. C32×H(5,𝔽2)C22semidirect
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
33. C3×#1004C22semidirect
34. C3×#1004C22semidirect
36. C2×C3×#237C22semidirect
38. C2×C3×D3×D4C22semidirect
39. C32×AGL(1,ℤ/8)C22semidirect
40. C32×AGL(1,ℤ/8)C22semidirect
41. C32×#135C22semidirect
42. C2×C32×D8C22semidirect
43. C32×#131C22semidirect
44. C3×#951C22semidirect
45. C3×#950C22semidirect
46. C3×#950C22semidirect
47. C3×#949C22semidirect
48. C3×#948C22semidirect
49. C2×C3×#214C22semidirect
50. C3×#932C22semidirect
51. C3×#932C22semidirect
52. C2×C3×#213C22semidirect
53. C3×#918C22semidirect
54. C3×#918C22semidirect
55. C3×#916C22semidirect
56. C3×#915C22semidirect
57. C3×#915C22semidirect
58. C3×#914C22semidirect
59. C3×#914C22semidirect
60. C3×D3×SD16C22semidirect
61. C3×#912C22semidirect
62. C3×#911C22semidirect
63. C3×#911C22semidirect
64. C3×#911C22semidirect
65. C3×#911C22semidirect
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×ΓL(1,𝔽25)C22semidirect
78. #5966C2×C3semidirect
79. D3×H(5,𝔽2)C2×C3semidirect
88. C3×#576D3semidirect
89. C3×#576C2×C3semidirect
95. #5836C2×C3semidirect
96. #5835C2×C3semidirect
97. #5775C2×C3semidirect
98. #5774C2×C3semidirect
99. #5773C2×C3semidirect
100. D3×AGL(1,ℤ/8)C2×C3semidirect
101. #5770C2×C3semidirect
102. #5768C2×C3semidirect
103. #5757C2×C3semidirect
104. C2×#911C2×C3semidirect
105. #5751C2×C3semidirect
106. #5750C2×C3semidirect
112. C32×#41C23semidirect
116. C2×C32×D4C23semidirect
129. C3×D3×Q8C23semidirect
141. C3×#237C23semidirect
153. C3×D3×D4C23semidirect
160. C3×#235C23semidirect
167. C2×C3×Dic6C23semidirect
168. C32×Q16C23semidirect
169. C32×SD16C23semidirect
170. C32×SD16C23semidirect
171. C32×D8C23semidirect
172. C32×D8C23semidirect
173. C32×M16C23semidirect
174. C2×C32×C8C23semidirect
175. C3×#216C23semidirect
176. C3×#216C23semidirect
177. C3×#215C23semidirect
178. C3×#215C23semidirect
179. C3×#214C23semidirect
180. C3×#214C23semidirect
181. C3×#214C23semidirect
182. C3×#213C23semidirect
183. C3×#213C23semidirect
184. C3×#213C23semidirect
185. C3×#208C23semidirect
186. C2×C3×C3⋊C8C23semidirect
187. C3×Dic12C23semidirect
188. C3×D24C23semidirect
189. C3×#204C23semidirect
190. C3×#204C23semidirect
191. C3×#204C23semidirect
194. C3×ΓL(1,𝔽25)C23semidirect
195. C3×ΓL(1,𝔽25)C23semidirect
196. C3×D3×C8C23semidirect
210. C3×H(5,𝔽2)C2×D3semidirect
211. C3×H(5,𝔽2)C2×D3semidirect
212. C3×H(5,𝔽2)C22×C3semidirect
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
236. #1004C22×C3semidirect
237. #1004C22×C3semidirect
239. C2×#237C22×C3semidirect
241. C2×D3×D4C22×C3semidirect
261. C3×AGL(1,ℤ/8)C2×D3semidirect
262. C3×AGL(1,ℤ/8)C2×D3semidirect
263. C3×AGL(1,ℤ/8)C22×C3semidirect
264. C3×AGL(1,ℤ/8)C22×C3semidirect
271. C3×#135C2×D3semidirect
272. C3×#135C22×C3semidirect
279. C2×C3×D8C2×D3semidirect
280. C2×C3×D8C22×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×#214C22×C3semidirect
295. #932C22×C3semidirect
296. #932C22×C3semidirect
297. C2×#213C22×C3semidirect
298. #918C22×C3semidirect
299. #918C22×C3semidirect
300. #916C22×C3semidirect
301. #915C22×C3semidirect
302. #915C22×C3semidirect
303. #914C22×C3semidirect
304. #914C22×C3semidirect
305. D3×SD16C22×C3semidirect
306. #912C22×C3semidirect
307. #911C22×C3semidirect
308. #911C22×C3semidirect
309. #911C22×C3semidirect
310. #911C22×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×ΓL(1,𝔽25)C22×C3semidirect
391. #576C3×D3semidirect
433. C3×#41C22×D3semidirect
436. C3×#41C23×C3semidirect
470. C2×C3×D4C22×D3semidirect
472. C2×C3×D4C23×C3semidirect
489. D3×Q8C23×C3semidirect
501. #237C23×C3semidirect
513. D3×D4C23×C3semidirect
520. #235C23×C3semidirect
527. C2×Dic6C23×C3semidirect
532. C3×Q16C22×D3semidirect
533. C3×Q16C23×C3semidirect
544. C3×SD16C22×D3semidirect
545. C3×SD16C22×D3semidirect
546. C3×SD16C23×C3semidirect
547. C3×SD16C23×C3semidirect
554. C3×D8C22×D3semidirect
555. C3×D8C22×D3semidirect
556. C3×D8C23×C3semidirect
557. C3×D8C23×C3semidirect
564. C3×M16C22×D3semidirect
565. C3×M16C23×C3semidirect
569. C2×C3×C8C22×D3semidirect
570. C2×C3×C8C23×C3semidirect
571. #216C23×C3semidirect
572. #216C23×C3semidirect
573. #215C23×C3semidirect
574. #215C23×C3semidirect
575. #214C23×C3semidirect
576. #214C23×C3semidirect
577. #214C23×C3semidirect
578. #213C23×C3semidirect
579. #213C23×C3semidirect
580. #213C23×C3semidirect
581. #208C23×C3semidirect
582. C2×C3⋊C8C23×C3semidirect
583. Dic12C23×C3semidirect
584. D24C23×C3semidirect
585. #204C23×C3semidirect
586. #204C23×C3semidirect
587. #204C23×C3semidirect
590. ΓL(1,𝔽25)C23×C3semidirect
591. ΓL(1,𝔽25)C23×C3semidirect
592. D3×C8C23×C3semidirect
625. H(5,𝔽2)C2×C3×D3semidirect
626. H(5,𝔽2)C2×C3×D3semidirect
653. AGL(1,ℤ/8)C2×C3×D3semidirect
654. AGL(1,ℤ/8)C2×C3×D3semidirect
660. #135C2×C3×D3semidirect
666. C2×D8C2×C3×D3semidirect
670. #131C2×C3×D3semidirect
848. #41C22×C3×D3semidirect
876. C2×D4C22×C3×D3semidirect
884. Q16C22×C3×D3semidirect
893. SD16C22×C3×D3semidirect
894. SD16C22×C3×D3semidirect
899. D8C22×C3×D3semidirect
900. D8C22×C3×D3semidirect
906. M16C22×C3×D3semidirect
909. C2×C8C22×C3×D3semidirect
963. C32#3585semidirect
1068. C3#87204direct (N × H)
1069. C3C3×#3585semidirect

Maximal subgroups

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

subgroupindex
C3×#59662
C3×D3×H(5,𝔽2)2
C32×#5762
C3×#58362
C3×#58352
C3×#57752
C3×#57742
C3×#57732
C3×D3×AGL(1,ℤ/8)2
C3×#57702
C3×#57682
C3×#57572
C2×C3×#9112
C3×#57512
C3×#57502
C3×#35853
#872043