Finite Group Databasebeta

← C2×C3×#10591510 #72269506

Subgroups — C2×C3×#10591510 #72269506

Order 3456.

5194 conjugacy classes of subgroups.

The subgroup lattice has 1452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#1004C211yesmaximal, characteristic, complemented
2C2×C3×#64149C211yesmaximal, characteristic, complemented
3C2×C3×#63825C212yesmaximal, complemented
4C2×C32×#833C211yesmaximal, characteristic, complemented
5C3×#10591510C218yesmaximal, direct product factor
6C2×C3×#63568C212yesmaximal, complemented
7C2×#10591510C311yesmaximal, characteristic, direct product factor
8C2×C3×#4747—31nomaximal
9C2×C3×#5241—31nomaximal
10C22×C33×D4C2211yescharacteristic
11C22×C3×#638—22no—
12C22×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
13C22×C32×#67—22no—
14C32×#1004—22no—
15C32×#1004—24no—
16C32×#1004C2214yescomplemented
17C2×C32×#237—22no—
18C2×C32×D3×D4—22no—
19C2×C32×#235C2212yes—
20C3×#64149—22no—
21C3×#64149C2214yescomplemented
22C2×C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
23C2×C32×#208C2212yescomplemented
24C2×C3×#3717—22no—
25C3×#63825—24no—
26C3×#63825C2218yescomplemented
27C2×C3×#3714—22no—
28C32×#833C2214yescomplemented
29C3×#63568C2218yescomplemented
30C2×C32×H(5,𝔽2)—31no—
31C2×C3×#1004—21no—
32C2×C3×#1004D311yescharacteristic, complemented
33C2×C3×#1004C2×C311yescharacteristic, complemented
34C2×#64149C2×C311yescharacteristic, complemented
35C2×C3×#949—32no—
36C2×C3×#940—31no—
37C2×C3×#940—31no—
38C2×C3×#940—61no—
39C2×C3×#908—32no—
40C2×#63825C2×C312yescomplemented
41C2×C32×#100—31no—
42C3×#5241—38no—
43C2×C3×#837—32no—
44C2×C3×#833—21no—
45C2×C3×#833D311yescharacteristic, complemented
46C2×C3×#833C2×C311yescharacteristic, complemented
47C2×C3×#825—32no—
48C3×#4747—38no—
49#10591510C2×C318yesdirect product factor
50C2×#63568C2×C312yescomplemented
51C24×C33D412yes—
52C23×C3×C3⋊D3—21no—
53C23×C32×D3—22no—
54C2×C33×D4—22no—
55C2×C33×D4—22no—
56C2×C33×D4D412yes—
57C2×C33×D4C2312yes—
58C22×C33×C4C2311yescharacteristic
59C2×C3×#638—28no—
60C2×C3×#638—48no—
61C22×C3×C3⋊Dic3—21no—
62C2×C3×C4⋊(C3⋊D3)—22no—
63C2×C3×C4⋊(C3⋊D3)—22no—
64C2×C3×C4⋊(C3⋊D3)—21no—
65C2×C3×C4⋊(C3⋊D3)C2312yescomplemented
66C2×C32×#67—24no—
67C2×C32×#67—28no—
68C2×C32×#67—22no—
69C2×C32×#67—28no—
70C22×C32×Dic3—22no—
71C32×#237—28no—
72C32×#237—28no—
73C32×D3×D4—28no—
74C32×D3×D4—28no—
75C32×#235—22no—
76C32×#235—22no—
77C32×#235D414yescomplemented
78C32×#235C2314yes—
79C2×C32×D12D412yescomplemented
80C2×C32×C4×D3—22no—
81C2×C32×Dic6D412yescomplemented
82C3×C4×C3⋊Dic3—21no—
83C3×C4×C3⋊Dic3C2312yescomplemented
84C32×#208—22no—
85C32×#208C2314yescomplemented
86C2×C32×C3⋊C8—22no—
87C3×#3717—28no—
88C3×#3714—28no—
89C2×C3×#453—91no—
90C2×#5241—31no—
91C2×#4747—31no—
92C32×H(5,𝔽2)—34no—
93C32×H(5,𝔽2)—64no—
94C32×H(5,𝔽2)—62no—
95C2×C32×#41—32no—
96C2×C32×#41—62no—
97C22×C32×D4—21no—
98C22×C32×D4—21no—
99C22×C32×D4—21no—
100C22×C32×D4—41no—
101C22×C32×D4—62no—
102C22×C32×D4—62no—
103C22×C32×D4C2×D311yescharacteristic
104C22×C32×D4C2×D311yescharacteristic
105C22×C32×D4C22×C311yescharacteristic
106C22×#638—22no—
107C22×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
108C22×C3×#67—24no—
109C22×C3×#67—22no—
110C22×C3×#67—22no—
111C22×C3×#67—64no—
112C22×C3×#67—62no—
113C22×C3×#67—62no—
114C3×#1004—24no—
115C3×#1004—28no—
116C3×#1004—22no—
117C3×#1004—22no—
118C3×#1004—24no—
119C3×#1004—24no—
120C3×#1004—24no—
121C3×#1004C2×D314yescomplemented
122C3×#1004C22×C314yescomplemented
123C2×C3×#237—24no—
124C2×C3×#237—22no—
125C2×C3×#237—22no—
126C2×C3×D3×D4—24no—
127C2×C3×D3×D4—22no—
128C2×C3×D3×D4—22no—
129C2×C3×#235—22no—
130C2×C3×#235C2×D312yes—
131C2×C3×#235C22×C312yes—
132C22×C3×D12—31no—
133C22×C3×D12—31no—
134C22×C3×D12—61no—
135C2×C32×M16—32no—
136#64149—22no—
137#64149C22×C314yescomplemented
138C2×C4×C3⋊Dic3C22×C311yescharacteristic, complemented
139C3×#949—38no—
140C3×#949—64no—
141C2×C3×#215—62no—
142C3×#940—34no—
143C3×#940—34no—
144C3×#940—64no—
145C3×#940—64no—
146C3×#940—62no—
147C3×#940—62no—
148C2×C3×#213—62no—
149C2×C3×C4×Dic3—31no—
150C2×C3×C4×Dic3—31no—
151C2×C3×C4×Dic3—61no—
152C2×C3×#208—22no—
153C2×C3×#208C2×D312yescomplemented
154C2×C3×#208C22×C312yescomplemented
155C3×#908—38no—
156C3×#908—64no—
157C2×C3×D24—62no—
158C2×C3×#204—62no—
159C2×#3717—22no—
160#63825—24no—
161#63825C22×C318yescomplemented
162C2×#3714—22no—
163C32×#100—34no—
164C3×#837—38no—
165C3×#833—24no—
166C3×#833C2×D314yescomplemented
167C3×#833C22×C314yescomplemented
168C3×#825—38no—
169#63568C22×C318yescomplemented
170C23×C33—22no—
171C23×C33—22no—
172C23×C33—44no—
173C23×C33C2×D411yescharacteristic
174C23×C33C2×D414yes—
175C22×C3×C3⋊D3—22no—
176C22×C3×C3⋊D3—44no—
177C22×C3×C3⋊D3—41no—
178C22×C3×C3⋊D3—41no—
179C22×C32×D3—22no—
180C22×C32×D3—28no—
181C22×C32×D3—84no—
182C33×D4—24no—
183C33×D4—24no—
184C2×C33×C4C2×D411yescharacteristic
185C2×C33×C4C2×D412yes—
186C2×C33×C4C2×D412yes—
187C2×C33×C4C2411yescharacteristic
188C3×#638—416no—
189C2×C3×C3⋊Dic3—24no—
190C2×C3×C3⋊Dic3—22no—
191C3×C4⋊(C3⋊D3)—24no—
192C3×C4⋊(C3⋊D3)—42no—
193C32×#67—216no—
194C32×#67—24no—
195C32×#67—24no—
196C2×C32×Dic3—28no—
197C2×C32×Dic3—22no—
198C32×D12—22no—
199C32×D12C2×D414yescomplemented
200C32×C4×D3—24no—
201C32×C4×D3—24no—
202C32×Dic6—22no—
203C32×Dic6C2×D414yescomplemented
204C32×C3⋊C8—24no—
205C2×C3×H(5,𝔽2)—31no—
206C2×C3×H(5,𝔽2)—31no—
207C2×C3×H(5,𝔽2)—61no—
208C2×#1004C3×D311yescharacteristic, complemented
209C2×C3×AGL(1,ℤ/8)—92no—
210C2×C3×#127—91no—
211C2×#949—32no—
212C2×#940—31no—
213C2×#940—31no—
214C2×#940—61no—
215C2×#908—32no—
216C3×#453—98no—
217C2×C3×#104—92no—
218C2×C3×#100—31no—
219C2×C3×#100—31no—
220C2×C3×#100—61no—
221#5241—38no—
222C2×#837—32no—
223C2×#833C3×D311yescharacteristic, complemented
224C2×#825—32no—
225#4747—38no—
226C24×C32—22no—
227C24×C32—22no—
228C24×C32—22no—
229C24×C32—42no—
230C24×C32—62no—
231C24×C32D1212yes—
232C24×C32#6712yes—
233C24×C32C3×D412yes—
234C23×C3⋊D3—21no—
235C23×C3×D3—24no—
236C23×C3×D3—22no—
237C23×C3×D3—22no—
238C23×C3×D3—62no—
239C23×C3×D3—61no—
240C23×C3×D3—61no—
241C32×#41—34no—
242C32×#41—34no—
243C32×#41—68no—
244C32×#41—68no—
245C32×#41—62no—
246C32×#41—62no—
247C2×C32×Q8—32no—
248C2×C32×D4—24no—
249C2×C32×D4—24no—
250C2×C32×D4—22no—
251C2×C32×D4—22no—
252C2×C32×D4—22no—
253C2×C32×D4—22no—
254C2×C32×D4—22no—
255C2×C32×D4—22no—
256C2×C32×D4—22no—
257C2×C32×D4—22no—
258C2×C32×D4—22no—
259C2×C32×D4—22no—
260C2×C32×D4—22no—
261C2×C32×D4—22no—
262C2×C32×D4—32no—
263C2×C32×D4—42no—
264C2×C32×D4—42no—
265C2×C32×D4—42no—
266C2×C32×D4—42no—
267C2×C32×D4—42no—
268C2×C32×D4—42no—
269C2×C32×D4—44no—
270C2×C32×D4—44no—
271C2×C32×D4—68no—
272C2×C32×D4—68no—
273C2×C32×D4—64no—
274C2×C32×D4—68no—
275C2×C32×D4—62no—
276C2×C32×D4—68no—
277C2×C32×D4D1212yes—
278C2×C32×D4#6712yes—
279C2×C32×D4C3×D412yes—
280C2×C32×D4C22×D312yes—
281C2×C32×D4C22×D312yes—
282C2×C32×D4C23×C312yes—
283C22×C32×C4—21no—
284C22×C32×C4—21no—
285C22×C32×C4—21no—
286C22×C32×C4—41no—
287C22×C32×C4—62no—
288C22×C32×C4—62no—
289C22×C32×C4C22×D311yescharacteristic
290C22×C32×C4C22×D311yescharacteristic
291C22×C32×C4C23×C311yescharacteristic
292C2×#638—28no—
293C2×#638—48no—
294C22×C3⋊Dic3—21no—
295C2×C4⋊(C3⋊D3)—22no—
296C2×C4⋊(C3⋊D3)—22no—
297C2×C4⋊(C3⋊D3)—21no—
298C2×C4⋊(C3⋊D3)C23×C312yescomplemented
299C2×C3×#67—24no—
300C2×C3×#67—28no—
301C2×C3×#67—24no—
302C2×C3×#67—24no—
303C2×C3×#67—216no—
304C2×C3×#67—216no—
305C2×C3×#67—28no—
306C2×C3×#67—28no—
307C2×C3×#67—22no—
308C2×C3×#67—28no—
309C2×C3×#67—22no—
310C2×C3×#67—28no—
311C2×C3×#67—616no—
312C2×C3×#67—68no—
313C2×C3×#67—68no—
314C2×C3×#67—128no—
315C2×C3×#67—128no—
316C2×C3×#67—1216no—
317C22×C3×Dic3—24no—
318C22×C3×Dic3—22no—
319C22×C3×Dic3—22no—
320C22×C3×Dic3—62no—
321C22×C3×Dic3—61no—
322C22×C3×Dic3—61no—
323C3×#237—216no—
324C3×#237—28no—
325C3×#237—28no—
326C3×#237—216no—
327C3×#237—28no—
328C3×#237—28no—
329C3×D3×D4—216no—
330C3×D3×D4—216no—
331C3×D3×D4—28no—
332C3×D3×D4—28no—
333C3×D3×D4—28no—
334C3×D3×D4—28no—
335C3×#235—24no—
336C3×#235—24no—
337C3×#235—24no—
338C3×#235—24no—
339C3×#235—22no—
340C3×#235—22no—
341C3×#235—22no—
342C3×#235—22no—
343C3×#235#6714yescomplemented
344C3×#235C3×D414yescomplemented
345C3×#235C22×D314yes—
346C3×#235C23×C314yes—
347C2×C3×D12—22no—
348C2×C3×D12—32no—
349C2×C3×D12—32no—
350C2×C3×D12—62no—
351C2×C3×D12—62no—
352C2×C3×D12—62no—
353C2×C3×D12—62no—
354C2×C3×D12—62no—
355C2×C3×D12—62no—
356C2×C3×D12—61no—
357C2×C3×D12—61no—
358C2×C3×D12—122no—
359C2×C3×D12—122no—
360C2×C3×D12#6712yescomplemented
361C2×C3×D12C3×D412yescomplemented
362C2×C3×C4×D3—24no—
363C2×C3×C4×D3—22no—
364C2×C3×C4×D3—22no—
365C2×C3×Dic6—22no—
366C2×C3×Dic6#6712yescomplemented
367C2×C3×Dic6C3×D412yescomplemented
368C32×M16—34no—
369C32×M16—62no—
370C2×C32×C8—62no—
371C4×C3⋊Dic3—21no—
372C4×C3⋊Dic3C23×C312yescomplemented
373C3×#215—68no—
374C3×#213—68no—
375C3×C4×Dic3—32no—
376C3×C4×Dic3—32no—
377C3×C4×Dic3—62no—
378C3×C4×Dic3—62no—
379C3×C4×Dic3—61no—
380C3×C4×Dic3—61no—
381C3×#208—22no—
382C3×#208—22no—
383C3×#208—24no—
384C3×#208—42no—
385C3×#208C22×D314yescomplemented
386C3×#208C23×C314yescomplemented
387C2×C3×C3⋊C8—22no—
388C2×C3×C3⋊C8—22no—
389C2×C3×C3⋊C8—42no—
390C3×D24—68no—
391C3×#204—68no—
392#3717—28no—
393#3714—28no—
394C2×#453—91noSylow
395C22×C33—22no—
396C22×C33—24no—
397C22×C33—44no—
398C22×C33—44no—
399C22×C33—82no—
400C22×C33#12011yescharacteristic
401C22×C33#12011yescharacteristic
402C22×C33C22×D411yescharacteristic
403C2×C3×C3⋊D3—44no—
404C2×C3×C3⋊D3—42no—
405C2×C3×C3⋊D3—82no—
406C2×C3×C3⋊D3—82no—
407C2×C32×D3—24no—
408C2×C32×D3—44no—
409C2×C32×D3—88no—
410C33×C4#12012yes—
411C33×C4C22×D412yes—
412C3×C3⋊Dic3—24no—
413C32×Dic3—24no—
414C3×H(5,𝔽2)—34no—
415C3×H(5,𝔽2)—34no—
416C3×H(5,𝔽2)—64no—
417C3×H(5,𝔽2)—64no—
418C3×H(5,𝔽2)—64no—
419C3×H(5,𝔽2)—68no—
420C3×H(5,𝔽2)—64no—
421C3×H(5,𝔽2)—62no—
422C3×H(5,𝔽2)—62no—
423C2×C3×#41—32no—
424C2×C3×#41—32no—
425C2×C3×#41—62no—
426C2×C3×#41—62no—
427C2×C3×#41—62no—
428C2×C3×#41—64no—
429C22×C3×D4—21no—
430C22×C3×D4—21no—
431C22×C3×D4—21no—
432C22×C3×D4—41no—
433C22×C3×D4—62no—
434C22×C3×D4—62no—
435C22×C3×D4—64no—
436C22×C3×D4—64no—
437C22×C3×D4—62no—
438C22×C3×D4—62no—
439C22×C3×D4—91no—
440C22×C3×D4—182no—
441C22×C3×D4D3211yescharacteristic
442C22×C3×D4C2×C3×D311yescharacteristic
443C22×C3×D4C2×C3×D311yescharacteristic
444C22×#67—22no—
445C22×#67—64no—
446C22×#67—62no—
447C22×#67—62no—
448#1004—22no—
449#1004—24no—
450#1004C2×C3×D314yescomplemented
451C2×#237—22no—
452C2×D3×D4—22no—
453C2×#235C2×C3×D312yes—
454C22×D12—31no—
455C22×D12—31no—
456C22×D12—61no—
457C3×AGL(1,ℤ/8)—98no—
458C3×AGL(1,ℤ/8)—184no—
459C2×C3×SD16—182no—
460C2×C3×D8—182no—
461C2×C3×M16—32no—
462C2×C3×M16—32no—
463C2×C3×M16—62no—
464C3×#127—94no—
465C3×#127—182no—
466C2×C3×C42—91no—
467#949—38no—
468#949—64no—
469C2×#215—62no—
470#940—34no—
471#940—34no—
472#940—64no—
473#940—64no—
474#940—62no—
475#940—62no—
476C2×#213—62no—
477C2×C4×Dic3—31no—
478C2×C4×Dic3—31no—
479C2×C4×Dic3—61no—
480C2×#208C2×C3×D312yescomplemented
481#908—38no—
482#908—64no—
483C2×D24—62no—
484C2×#204—62no—
485C3×#104—98no—
486C3×#100—34no—
487C3×#100—34no—
488C3×#100—64no—
489#837—38no—
490#833C2×C3×D314yescomplemented
491#825—38no—
492C23×C32—22no—
493C23×C32—22no—
494C23×C32—24no—
495C23×C32—24no—
496C23×C32—22no—
497C23×C32—22no—
498C23×C32—22no—
499C23×C32—22no—
500C23×C32—21no—
501C23×C32—24no—
502C23×C32—21no—
503C23×C32—24no—
504C23×C32—21no—
505C23×C32—24no—
506C23×C32—41no—
507C23×C32—44no—
508C23×C32—42no—
509C23×C32—42no—
510C23×C32—42no—
511C23×C32—42no—
512C23×C32—44no—
513C23×C32—44no—
514C23×C32—44no—
515C23×C32—44no—
516C23×C32—44no—
517C23×C32—48no—
518C23×C32—68no—
519C23×C32—62no—
520C23×C32—84no—
521C23×C32—84no—
522C23×C32—88no—
523C23×C32—244no—
524C23×C32C2×D1211yescharacteristic
525C23×C32C2×D1214yes—
526C23×C32C2×#6711yescharacteristic
527C23×C32C2×#6714yes—
528C23×C32C2×C3×D411yescharacteristic
529C23×C32C2×C3×D414yes—
530C22×C3⋊D3—22no—
531C22×C3⋊D3—44no—
532C22×C3⋊D3—41no—
533C22×C3⋊D3—41no—
534C22×C3×D3—24no—
535C22×C3×D3—22no—
536C22×C3×D3—22no—
537C22×C3×D3—216no—
538C22×C3×D3—28no—
539C22×C3×D3—28no—
540C22×C3×D3—64no—
541C22×C3×D3—62no—
542C22×C3×D3—62no—
543C22×C3×D3—88no—
544C22×C3×D3—84no—
545C22×C3×D3—84no—
546C22×C3×D3—122no—
547C22×C3×D3—122no—
548C22×C3×D3—128no—
549C22×C3×D3—124no—
550C22×C3×D3—124no—
551C22×C3×D3—121no—
552C22×C3×D3—121no—
553C22×C3×D3—121no—
554C22×C3×D3—121no—
555C32×Q8—34no—
556C32×Q8—62no—
557C32×D4—24no—
558C32×D4—24no—
559C32×D4—28no—
560C32×D4—28no—
561C32×D4—24no—
562C32×D4—24no—
563C32×D4—24no—
564C32×D4—24no—
565C32×D4—34no—
566C32×D4—44no—
567C32×D4—44no—
568C32×D4—44no—
569C32×D4—44no—
570C32×D4—48no—
571C32×D4—48no—
572C32×D4—616no—
573C32×D4—64no—
574C32×D4—64no—
575C32×D4—62no—
576C2×C32×C4—21no—
577C2×C32×C4—21no—
578C2×C32×C4—21no—
579C2×C32×C4—21no—
580C2×C32×C4—22no—
581C2×C32×C4—22no—
582C2×C32×C4—21no—
583C2×C32×C4—22no—
584C2×C32×C4—22no—
585C2×C32×C4—22no—
586C2×C32×C4—21no—
587C2×C32×C4—22no—
588C2×C32×C4—41no—
589C2×C32×C4—42no—
590C2×C32×C4—42no—
591C2×C32×C4—41no—
592C2×C32×C4—68no—
593C2×C32×C4—62no—
594C2×C32×C4—64no—
595C2×C32×C4—64no—
596C2×C32×C4C2×D1211yescharacteristic
597C2×C32×C4D3×D412yes—
598C2×C32×C4D3×D412yes—
599C2×C32×C4C2×#6711yescharacteristic
600C2×C32×C4C2×#6712yes—
601C2×C32×C4C2×#6712yes—
602C2×C32×C4C2×C3×D411yescharacteristic
603C2×C32×C4C2×C3×D412yes—
604C2×C32×C4C2×C3×D412yes—
605C2×C32×C4C23×D311yescharacteristic
606C2×C32×C4C23×D311yescharacteristic
607C2×C32×C4C24×C311yescharacteristic
608#638—416no—
609C2×C3⋊Dic3—24no—
610C2×C3⋊Dic3—22no—
611C4⋊(C3⋊D3)—24no—
612C4⋊(C3⋊D3)—42no—
613C3×#67—28no—
614C3×#67—28no—
615C3×#67—232no—
616C3×#67—216no—
617C3×#67—216no—
618C3×#67—24no—
619C3×#67—24no—
620C3×#67—24no—
621C3×#67—24no—
622C3×#67—1216no—
623C3×#67—1216no—
624C3×#67—1232no—
625C2×C3×Dic3—24no—
626C2×C3×Dic3—216no—
627C2×C3×Dic3—28no—
628C2×C3×Dic3—28no—
629C2×C3×Dic3—22no—
630C2×C3×Dic3—22no—
631C2×C3×Dic3—64no—
632C2×C3×Dic3—68no—
633C2×C3×Dic3—64no—
634C2×C3×Dic3—64no—
635C2×C3×Dic3—62no—
636C2×C3×Dic3—62no—
637C3×D12—24no—
638C3×D12—22no—
639C3×D12—22no—
640C3×D12—24no—
641C3×D12—64no—
642C3×D12—64no—
643C3×D12—124no—
644C3×D12—124no—
645C3×D12—122no—
646C3×D12—122no—
647C3×D12C2×#6714yescomplemented
648C3×D12C2×C3×D414yescomplemented
649C3×C4×D3—28no—
650C3×C4×D3—28no—
651C3×C4×D3—24no—
652C3×C4×D3—24no—
653C3×C4×D3—24no—
654C3×C4×D3—24no—
655C3×Dic6—24no—
656C3×Dic6—22no—
657C3×Dic6—22no—
658C3×Dic6—24no—
659C3×Dic6C2×#6714yescomplemented
660C3×Dic6C2×C3×D414yescomplemented
661C32×C8—64no—
662C3×C3⋊C8—24no—
663C3×C3⋊C8—24no—
664C3×C3⋊C8—44no—
665C2×H(5,𝔽2)—31no—
666C2×AGL(1,ℤ/8)—92no—
667C2×#127—91no—
668#453—98no—
669C2×#104—92no—
670C2×#100—31no—
671C2×C33—21no—
672C2×C33—21no—
673C2×C33—44no—
674C2×C33#45312yescomplemented
675C2×C33C2×#12011yescharacteristic
676C3×C3⋊D3—82no—
677C32×D3—44no—
678C24×C3—22no—
679C24×C3—22no—
680C24×C3—22no—
681C24×C3—42no—
682C24×C3—64no—
683C24×C3—62no—
684C24×C3—62no—
685C24×C3—181no—
686C24×C3#62612yes—
687C24×C3C3×D1212yes—
688C24×C3C3×#6712yes—
689C23×D3—22no—
690C23×D3—62no—
691C23×D3—61no—
692C23×D3—61no—
693C3×#41—34no—
694C3×#41—34no—
695C3×#41—34no—
696C3×#41—34no—
697C3×#41—64no—
698C3×#41—64no—
699C3×#41—64no—
700C3×#41—64no—
701C3×#41—68no—
702C3×#41—68no—
703C3×#41—616no—
704C3×#41—616no—
705C3×#41—68no—
706C3×#41—68no—
707C3×#41—62no—
708C3×#41—62no—
709C3×#41—62no—
710C3×#41—62no—
711C2×C3×Q8—32no—
712C2×C3×Q8—32no—
713C2×C3×Q8—62no—
714C2×C3×D4—24no—
715C2×C3×D4—24no—
716C2×C3×D4—22no—
717C2×C3×D4—22no—
718C2×C3×D4—22no—
719C2×C3×D4—22no—
720C2×C3×D4—22no—
721C2×C3×D4—22no—
722C2×C3×D4—22no—
723C2×C3×D4—22no—
724C2×C3×D4—22no—
725C2×C3×D4—22no—
726C2×C3×D4—22no—
727C2×C3×D4—22no—
728C2×C3×D4—32no—
729C2×C3×D4—32no—
730C2×C3×D4—42no—
731C2×C3×D4—42no—
732C2×C3×D4—42no—
733C2×C3×D4—42no—
734C2×C3×D4—44no—
735C2×C3×D4—44no—
736C2×C3×D4—42no—
737C2×C3×D4—42no—
738C2×C3×D4—62no—
739C2×C3×D4—68no—
740C2×C3×D4—68no—
741C2×C3×D4—616no—
742C2×C3×D4—616no—
743C2×C3×D4—68no—
744C2×C3×D4—68no—
745C2×C3×D4—68no—
746C2×C3×D4—64no—
747C2×C3×D4—64no—
748C2×C3×D4—64no—
749C2×C3×D4—616no—
750C2×C3×D4—68no—
751C2×C3×D4—68no—
752C2×C3×D4—616no—
753C2×C3×D4—62no—
754C2×C3×D4—68no—
755C2×C3×D4—62no—
756C2×C3×D4—68no—
757C2×C3×D4—92no—
758C2×C3×D4—188no—
759C2×C3×D4—181no—
760C2×C3×D4—182no—
761C2×C3×D4—182no—
762C2×C3×D4—368no—
763C2×C3×D4#62612yes—
764C2×C3×D4C3×D1212yes—
765C2×C3×D4C3×#6712yes—
766C2×C3×D4C2×D3212yes—
767C2×C3×D4C22×C3×D312yes—
768C2×C3×D4C22×C3×D312yes—
769C22×C3×C4—21no—
770C22×C3×C4—21no—
771C22×C3×C4—21no—
772C22×C3×C4—41no—
773C22×C3×C4—64no—
774C22×C3×C4—64no—
775C22×C3×C4—62no—
776C22×C3×C4—62no—
777C22×C3×C4—62no—
778C22×C3×C4—62no—
779C22×C3×C4—181no—
780C22×C3×C4C2×D3211yescharacteristic
781C22×C3×C4C22×C3×D311yescharacteristic
782C22×C3×C4C22×C3×D311yescharacteristic
783C2×#67—24no—
784C2×#67—28no—
785C2×#67—22no—
786C2×#67—28no—
787C2×#67—616no—
788C2×#67—68no—
789C2×#67—68no—
790C2×#67—128no—
791C2×#67—128no—
792C2×#67—1216no—
793C22×Dic3—22no—
794C22×Dic3—62no—
795C22×Dic3—61no—
796C22×Dic3—61no—
797#237—28no—
798#237—28no—
799D3×D4—28no—
800D3×D4—28no—
801#235—22no—
802#235—22no—
803#235C3×#6714yescomplemented
804#235C22×C3×D314yes—
805C2×D12—32no—
806C2×D12—32no—
807C2×D12—62no—
808C2×D12—62no—
809C2×D12—62no—
810C2×D12—62no—
811C2×D12—62no—
812C2×D12—62no—
813C2×D12—61no—
814C2×D12—61no—
815C2×D12—122no—
816C2×D12—122no—
817C2×D12C3×#6712yescomplemented
818C2×C4×D3—22no—
819C2×Dic6C3×#6712yescomplemented
820C3×SD16—188no—
821C3×D8—188no—
822C3×M16—34no—
823C3×M16—34no—
824C3×M16—64no—
825C3×M16—62no—
826C3×M16—62no—
827C3×M16—122no—
828C2×C3×C8—62no—
829C2×C3×C8—62no—
830C2×C3×C8—122no—
831C3×C42—92no—
832C3×C42—181no—
833#215—68no—
834#213—68no—
835C4×Dic3—32no—
836C4×Dic3—32no—
837C4×Dic3—62no—
838C4×Dic3—62no—
839C4×Dic3—61no—
840C4×Dic3—61no—
841#208—22no—
842#208C22×C3×D314yescomplemented
843C2×C3⋊C8—22no—
844D24—68no—
845#204—68no—
846C22×C32—22no—
847C22×C32—24no—
848C22×C32—24no—
849C22×C32—22no—
850C22×C32—22no—
851C22×C32—28no—
852C22×C32—24no—
853C22×C32—24no—
854C22×C32—21no—
855C22×C32—21no—
856C22×C32—21no—
857C22×C32—21no—
858C22×C32—21no—
859C22×C32—21no—
860C22×C32—21no—
861C22×C32—21no—
862C22×C32—21no—
863C22×C32—41no—
864C22×C32—41no—
865C22×C32—41no—
866C22×C32—42no—
867C22×C32—42no—
868C22×C32—44no—
869C22×C32—44no—
870C22×C32—44no—
871C22×C32—48no—
872C22×C32—44no—
873C22×C32—44no—
874C22×C32—44no—
875C22×C32—44no—
876C22×C32—48no—
877C22×C32—48no—
878C22×C32—44no—
879C22×C32—44no—
880C22×C32—64no—
881C22×C32—84no—
882C22×C32—84no—
883C22×C32—84no—
884C22×C32—84no—
885C22×C32—88no—
886C22×C32—88no—
887C22×C32—82no—
888C22×C32—82no—
889C22×C32—82no—
890C22×C32—84no—
891C22×C32—84no—
892C22×C32—84no—
893C22×C32—88no—
894C22×C32—124no—
895C22×C32—248no—
896C22×C32#88211yescharacteristic
897C22×C32#88211yescharacteristic
898C22×C32#95311yescharacteristic
899C22×C32#95311yescharacteristic
900C22×C32C3×#12011yescharacteristic
901C22×C32C3×#12011yescharacteristic
902C22×C32C22×D1211yescharacteristic
903C22×C32C22×#6711yescharacteristic
904C22×C32C22×C3×D411yescharacteristic
905C2×C3⋊D3—44no—
906C2×C3⋊D3—42no—
907C2×C3⋊D3—82no—
908C2×C3⋊D3—82no—
909C2×C3×D3—28no—
910C2×C3×D3—24no—
911C2×C3×D3—24no—
912C2×C3×D3—48no—
913C2×C3×D3—44no—
914C2×C3×D3—44no—
915C2×C3×D3—816no—
916C2×C3×D3—88no—
917C2×C3×D3—88no—
918C2×C3×D3—124no—
919C2×C3×D3—128no—
920C2×C3×D3—124no—
921C2×C3×D3—124no—
922C2×C3×D3—122no—
923C2×C3×D3—122no—
924C2×C3×D3—244no—
925C2×C3×D3—242no—
926C2×C3×D3—242no—
927C2×C3×D3—244no—
928C2×C3×D3—242no—
929C2×C3×D3—242no—
930C32×C4—22no—
931C32×C4—22no—
932C32×C4—22no—
933C32×C4—22no—
934C32×C4—22no—
935C32×C4—22no—
936C32×C4—42no—
937C32×C4—42no—
938C32×C4—64no—
939C32×C4#88212yes—
940C32×C4#95312yes—
941C32×C4C3×#12012yes—
942C32×C4C2×D3×D412yes—
943C32×C4C22×#6712yes—
944C32×C4C22×C3×D412yes—
945C3⋊Dic3—24no—
946C3×Dic3—28no—
947C3×Dic3—24no—
948C3×Dic3—24no—
949C3×Dic3—68no—
950C3×Dic3—64no—
951C3×Dic3—64no—
952H(5,𝔽2)—34no—
953H(5,𝔽2)—64no—
954H(5,𝔽2)—62no—
955C2×#41—32no—
956C2×#41—62no—
957C22×D4—62no—
958C22×D4—62no—
959C22×D4—91no—
960C22×D4—182no—
961C22×D4C3×D3211yescharacteristic
962AGL(1,ℤ/8)—98no—
963AGL(1,ℤ/8)—184no—
964C2×SD16—182no—
965C2×D8—182no—
966C2×M16—32no—
967#127—94no—
968#127—182no—
969C2×C42—91no—
970#104—98no—
971#100—34no—
972C33C2×#45311yescharacteristic, complemented, Sylow
973C23×C3—24no—
974C23×C3—24no—
975C23×C3—22no—
976C23×C3—22no—
977C23×C3—22no—
978C23×C3—22no—
979C23×C3—22no—
980C23×C3—22no—
981C23×C3—21no—
982C23×C3—21no—
983C23×C3—21no—
984C23×C3—24no—
985C23×C3—24no—
986C23×C3—24no—
987C23×C3—42no—
988C23×C3—42no—
989C23×C3—42no—
990C23×C3—42no—
991C23×C3—44no—
992C23×C3—44no—
993C23×C3—44no—
994C23×C3—44no—
995C23×C3—44no—
996C23×C3—48no—
997C23×C3—41no—
998C23×C3—44no—
999C23×C3—64no—
1000C23×C3—616no—
1001C23×C3—68no—
1002C23×C3—68no—
1003C23×C3—62no—
1004C23×C3—62no—
1005C23×C3—84no—
1006C23×C3—84no—
1007C23×C3—88no—
1008C23×C3—182no—
1009C23×C3—248no—
1010C23×C3—244no—
1011C23×C3—244no—
1012C23×C3—364no—
1013C23×C3—361no—
1014C23×C3—361no—
1015C23×C3C2×#62611yescharacteristic
1016C23×C3C2×#62614yes—
1017C23×C3C2×C3×D1211yescharacteristic
1018C23×C3C2×C3×D1214yes—
1019C23×C3C2×C3×#6711yescharacteristic
1020C23×C3C2×C3×#6714yes—
1021C22×D3—22no—
1022C22×D3—28no—
1023C22×D3—64no—
1024C22×D3—62no—
1025C22×D3—62no—
1026C22×D3—84no—
1027C22×D3—122no—
1028C22×D3—122no—
1029C22×D3—128no—
1030C22×D3—124no—
1031C22×D3—124no—
1032C22×D3—121no—
1033C22×D3—121no—
1034C22×D3—121no—
1035C22×D3—121no—
1036C3×Q8—34no—
1037C3×Q8—34no—
1038C3×Q8—64no—
1039C3×Q8—64no—
1040C3×Q8—62no—
1041C3×Q8—62no—
1042C3×D4—28no—
1043C3×D4—28no—
1044C3×D4—24no—
1045C3×D4—24no—
1046C3×D4—24no—
1047C3×D4—24no—
1048C3×D4—24no—
1049C3×D4—24no—
1050C3×D4—34no—
1051C3×D4—34no—
1052C3×D4—44no—
1053C3×D4—44no—
1054C3×D4—44no—
1055C3×D4—44no—
1056C3×D4—48no—
1057C3×D4—48no—
1058C3×D4—64no—
1059C3×D4—64no—
1060C3×D4—632no—
1061C3×D4—616no—
1062C3×D4—616no—
1063C3×D4—68no—
1064C3×D4—68no—
1065C3×D4—64no—
1066C3×D4—64no—
1067C3×D4—64no—
1068C3×D4—64no—
1069C3×D4—62no—
1070C3×D4—62no—
1071C3×D4—184no—
1072C3×D4—3616no—
1073C3×D4—362no—
1074C2×C3×C4—21no—
1075C2×C3×C4—21no—
1076C2×C3×C4—21no—
1077C2×C3×C4—21no—
1078C2×C3×C4—21no—
1079C2×C3×C4—21no—
1080C2×C3×C4—22no—
1081C2×C3×C4—22no—
1082C2×C3×C4—22no—
1083C2×C3×C4—22no—
1084C2×C3×C4—22no—
1085C2×C3×C4—22no—
1086C2×C3×C4—41no—
1087C2×C3×C4—41no—
1088C2×C3×C4—42no—
1089C2×C3×C4—42no—
1090C2×C3×C4—68no—
1091C2×C3×C4—68no—
1092C2×C3×C4—64no—
1093C2×C3×C4—616no—
1094C2×C3×C4—68no—
1095C2×C3×C4—68no—
1096C2×C3×C4—62no—
1097C2×C3×C4—62no—
1098C2×C3×C4—64no—
1099C2×C3×C4—64no—
1100C2×C3×C4—64no—
1101C2×C3×C4—64no—
1102C2×C3×C4—184no—
1103C2×C3×C4—182no—
1104C2×C3×C4C2×#62611yescharacteristic
1105C2×C3×C4D3×#6712yes—
1106C2×C3×C4D3×#6712yes—
1107C2×C3×C4C2×C3×D1211yescharacteristic
1108C2×C3×C4C3×D3×D412yes—
1109C2×C3×C4C3×D3×D412yes—
1110C2×C3×C4C2×C3×#6711yescharacteristic
1111C2×C3×C4C2×C3×#6712yes—
1112C2×C3×C4C2×C3×#6712yes—
1113C2×C3×C4C22×D3211yescharacteristic
1114C2×C3×C4C23×C3×D311yescharacteristic
1115C2×C3×C4C23×C3×D311yescharacteristic
1116#67—216no—
1117#67—24no—
1118#67—24no—
1119#67—1216no—
1120#67—1216no—
1121#67—1232no—
1122C2×Dic3—28no—
1123C2×Dic3—22no—
1124C2×Dic3—64no—
1125C2×Dic3—68no—
1126C2×Dic3—64no—
1127C2×Dic3—64no—
1128C2×Dic3—62no—
1129C2×Dic3—62no—
1130D12—22no—
1131D12—64no—
1132D12—64no—
1133D12—124no—
1134D12—124no—
1135D12—122no—
1136D12—122no—
1137D12C2×C3×#6714yescomplemented
1138C4×D3—24no—
1139C4×D3—24no—
1140Dic6—22no—
1141Dic6C2×C3×#6714yescomplemented
1142C3×C8—64no—
1143C3×C8—64no—
1144C3×C8—124no—
1145C3⋊C8—24no—
1146C2×C32—21no—
1147C2×C32—21no—
1148C2×C32—22no—
1149C2×C32—22no—
1150C2×C32—21no—
1151C2×C32—21no—
1152C2×C32—21no—
1153C2×C32—21no—
1154C2×C32—21no—
1155C2×C32—22no—
1156C2×C32—22no—
1157C2×C32—21no—
1158C2×C32—22no—
1159C2×C32—21no—
1160C2×C32—41no—
1161C2×C32—42no—
1162C2×C32—41no—
1163C2×C32—41no—
1164C2×C32—41no—
1165C2×C32—41no—
1166C2×C32—42no—
1167C2×C32—42no—
1168C2×C32—44no—
1169C2×C32—48no—
1170C2×C32—44no—
1171C2×C32—44no—
1172C2×C32—84no—
1173C2×C32—84no—
1174C2×C32—88no—
1175C2×C32—124no—
1176C2×C32#474712yescomplemented
1177C2×C32#524112yescomplemented
1178C2×C32C3×#45312yescomplemented
1179C2×C32C2×#88211yescharacteristic
1180C2×C32C2×#95311yescharacteristic
1181C2×C32C2×C3×#12011yescharacteristic
1182C3⋊D3—82no—
1183C3×D3—48no—
1184C3×D3—44no—
1185C3×D3—44no—
1186C3×D3—244no—
1187C3×D3—242no—
1188C3×D3—242no—
1189C24—62no—
1190C24—181no—
1191C24C3×#62612yes—
1192#41—34no—
1193#41—34no—
1194#41—68no—
1195#41—68no—
1196#41—62no—
1197#41—62no—
1198C2×Q8—32no—
1199C2×D4—22no—
1200C2×D4—22no—
1201C2×D4—32no—
1202C2×D4—68no—
1203C2×D4—68no—
1204C2×D4—64no—
1205C2×D4—68no—
1206C2×D4—62no—
1207C2×D4—68no—
1208C2×D4—92no—
1209C2×D4—188no—
1210C2×D4—181no—
1211C2×D4—182no—
1212C2×D4—182no—
1213C2×D4—368no—
1214C2×D4C3×#62612yes—
1215C2×D4C2×C3×D3212yes—
1216C22×C4—62no—
1217C22×C4—62no—
1218C22×C4—181no—
1219C22×C4C2×C3×D3211yescharacteristic
1220SD16—188no—
1221D8—188no—
1222M16—34no—
1223M16—62no—
1224C2×C8—62no—
1225C42—92no—
1226C42—181no—
1227C22×C3—24no—
1228C22×C3—22no—
1229C22×C3—22no—
1230C22×C3—22no—
1231C22×C3—28no—
1232C22×C3—24no—
1233C22×C3—24no—
1234C22×C3—24no—
1235C22×C3—21no—
1236C22×C3—21no—
1237C22×C3—21no—
1238C22×C3—21no—
1239C22×C3—21no—
1240C22×C3—21no—
1241C22×C3—21no—
1242C22×C3—21no—
1243C22×C3—21no—
1244C22×C3—42no—
1245C22×C3—42no—
1246C22×C3—44no—
1247C22×C3—44no—
1248C22×C3—44no—
1249C22×C3—48no—
1250C22×C3—44no—
1251C22×C3—44no—
1252C22×C3—44no—
1253C22×C3—48no—
1254C22×C3—48no—
1255C22×C3—44no—
1256C22×C3—44no—
1257C22×C3—44no—
1258C22×C3—41no—
1259C22×C3—41no—
1260C22×C3—41no—
1261C22×C3—68no—
1262C22×C3—64no—
1263C22×C3—64no—
1264C22×C3—84no—
1265C22×C3—84no—
1266C22×C3—84no—
1267C22×C3—84no—
1268C22×C3—88no—
1269C22×C3—88no—
1270C22×C3—82no—
1271C22×C3—82no—
1272C22×C3—82no—
1273C22×C3—84no—
1274C22×C3—84no—
1275C22×C3—84no—
1276C22×C3—88no—
1277C22×C3—128no—
1278C22×C3—124no—
1279C22×C3—124no—
1280C22×C3—2416no—
1281C22×C3—248no—
1282C22×C3—248no—
1283C22×C3—364no—
1284C22×C3—362no—
1285C22×C3—722no—
1286C22×C3—722no—
1287C22×C3#6397711yescharacteristic
1288C22×C3#6397711yescharacteristic
1289C22×C3C3×#88211yescharacteristic
1290C22×C3C3×#88211yescharacteristic
1291C22×C3C3×#95311yescharacteristic
1292C22×C3C3×#95311yescharacteristic
1293C22×C3C22×#62611yescharacteristic
1294C22×C3C22×C3×D1211yescharacteristic
1295C22×C3C22×C3×#6711yescharacteristic
1296C2×D3—24no—
1297C2×D3—44no—
1298C2×D3—88no—
1299C2×D3—124no—
1300C2×D3—128no—
1301C2×D3—124no—
1302C2×D3—124no—
1303C2×D3—122no—
1304C2×D3—122no—
1305C2×D3—244no—
1306C2×D3—242no—
1307C2×D3—242no—
1308C2×D3—244no—
1309C2×D3—242no—
1310C2×D3—242no—
1311C3×C4—22no—
1312C3×C4—22no—
1313C3×C4—22no—
1314C3×C4—22no—
1315C3×C4—22no—
1316C3×C4—22no—
1317C3×C4—42no—
1318C3×C4—42no—
1319C3×C4—68no—
1320C3×C4—64no—
1321C3×C4—64no—
1322C3×C4—184no—
1323C3×C4#6397712yes—
1324C3×C4C3×#88212yes—
1325C3×C4C3×#95312yes—
1326C3×C4C2×D3×#6712yes—
1327C3×C4C2×C3×D3×D412yes—
1328C3×C4C22×C3×#6712yes—
1329Dic3—24no—
1330Dic3—68no—
1331Dic3—64no—
1332Dic3—64no—
1333C32—21no—
1334C32—21no—
1335C32—21no—
1336C32—41no—
1337C32C2×#474711yescharacteristic, complemented
1338C32C2×#524111yescharacteristic, complemented
1339C32C2×C3×#45311yescharacteristic, complemented
1340C23—22no—
1341C23—22no—
1342C23—44no—
1343C23—68no—
1344C23—62no—
1345C23—182no—
1346C23—244no—
1347C23—364no—
1348C23—361no—
1349C23—361no—
1350C23C2×C3×#62611yescharacteristic
1351C23C2×C3×#62614yes—
1352Q8—34no—
1353Q8—62no—
1354D4—24no—
1355D4—24no—
1356D4—34no—
1357D4—616no—
1358D4—64no—
1359D4—64no—
1360D4—62no—
1361D4—184no—
1362D4—3616no—
1363D4—362no—
1364C2×C4—68no—
1365C2×C4—62no—
1366C2×C4—64no—
1367C2×C4—64no—
1368C2×C4—184no—
1369C2×C4—182no—
1370C2×C4C2×C3×#62611yescharacteristic
1371C2×C4C3×D3×#6712yes—
1372C2×C4C3×D3×#6712yes—
1373C2×C4C22×C3×D3211yescharacteristic
1374C8—64no—
1375C2×C3—22no—
1376C2×C3—22no—
1377C2×C3—21no—
1378C2×C3—21no—
1379C2×C3—21no—
1380C2×C3—21no—
1381C2×C3—21no—
1382C2×C3—21no—
1383C2×C3—21no—
1384C2×C3—21no—
1385C2×C3—21no—
1386C2×C3—22no—
1387C2×C3—22no—
1388C2×C3—22no—
1389C2×C3—41no—
1390C2×C3—41no—
1391C2×C3—41no—
1392C2×C3—41no—
1393C2×C3—42no—
1394C2×C3—42no—
1395C2×C3—48no—
1396C2×C3—44no—
1397C2×C3—44no—
1398C2×C3—44no—
1399C2×C3—41no—
1400C2×C3—42no—
1401C2×C3—84no—
1402C2×C3—84no—
1403C2×C3—88no—
1404C2×C3—128no—
1405C2×C3—124no—
1406C2×C3—124no—
1407C2×C3—722no—
1408C2×C3#1059151012yesdirect product factor
1409C2×C3C3×#474712yescomplemented
1410C2×C3C3×#524112yescomplemented
1411C2×C3C2×#6397711yescharacteristic
1412C2×C3C2×C3×#88211yescharacteristic
1413C2×C3C2×C3×#95311yescharacteristic
1414D3—44no—
1415D3—244no—
1416D3—242no—
1417D3—242no—
1418C22—22no—
1419C22—24no—
1420C22—44no—
1421C22—44no—
1422C22—64no—
1423C22—82no—
1424C22—124no—
1425C22—248no—
1426C22—364no—
1427C22—362no—
1428C22—722no—
1429C22—722no—
1430C22C3×#6397711yescharacteristic
1431C22C3×#6397711yescharacteristic
1432C22C22×C3×#62611yescharacteristic
1433C4—64no—
1434C4—184no—
1435C4C3×#6397712yes—
1436C4C2×C3×D3×#6712yes—
1437C3—21no—
1438C3—21no—
1439C3—21no—
1440C3—41no—
1441C3C2×C3×#524111yescharacteristic, complemented
1442C3C2×C3×#474711yescharacteristic, complemented
1443C3C2×#1059151011yescharacteristic, direct product factor
1444C2—21no—
1445C2—21no—
1446C2—44no—
1447C2—124no—
1448C2—722no—
1449C2C3×#1059151012yesdirect product factor
1450C2C2×C3×#6397711yescharacteristic
subgroupG/H
centerC22×C3#63977
commutator, cosocleC2×C32×C4C24×C3
FrattiniC2×C4C22×C3×D32
FittingC22×C33×D4C22
socleC22×C33#120
hypercenterC22×C3×D4D32
hypocenterC32C2×C3×#453
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×#1004C2semidirect
2. C2×C3×#64149C2semidirect
3. C2×C3×#63825C2semidirect
4. C2×C32×#833C2semidirect
5. C3×#10591510C2direct (N × H)
6. C2×C3×#63568C2semidirect
7. C2×#10591510C3direct (N × H)
12. C22×C3×C4⋊(C3⋊D3)C22semidirect
16. C32×#1004C22semidirect
21. C3×#64149C22semidirect
22. C2×C3×C4×C3⋊Dic3C22semidirect
23. C2×C32×#208C22semidirect
26. C3×#63825C22semidirect
28. C32×#833C22semidirect
29. C3×#63568C22semidirect
32. C2×C3×#1004D3semidirect
33. C2×C3×#1004C2×C3semidirect
34. C2×#64149C2×C3semidirect
40. C2×#63825C2×C3semidirect
45. C2×C3×#833D3semidirect
46. C2×C3×#833C2×C3semidirect
49. #10591510C2×C3direct (N × H)
50. C2×#63568C2×C3semidirect
65. C2×C3×C4⋊(C3⋊D3)C23semidirect
77. C32×#235D4semidirect
79. C2×C32×D12D4semidirect
81. C2×C32×Dic6D4semidirect
83. C3×C4×C3⋊Dic3C23semidirect
85. C32×#208C23semidirect
107. C22×C4⋊(C3⋊D3)C22×C3semidirect
121. C3×#1004C2×D3semidirect
122. C3×#1004C22×C3semidirect
137. #64149C22×C3semidirect
138. C2×C4×C3⋊Dic3C22×C3semidirect
153. C2×C3×#208C2×D3semidirect
154. C2×C3×#208C22×C3semidirect
161. #63825C22×C3semidirect
166. C3×#833C2×D3semidirect
167. C3×#833C22×C3semidirect
169. #63568C22×C3semidirect
199. C32×D12C2×D4semidirect
203. C32×Dic6C2×D4semidirect
208. C2×#1004C3×D3semidirect
223. C2×#833C3×D3semidirect
298. C2×C4⋊(C3⋊D3)C23×C3semidirect
343. C3×#235#67semidirect
344. C3×#235C3×D4semidirect
360. C2×C3×D12#67semidirect
361. C2×C3×D12C3×D4semidirect
366. C2×C3×Dic6#67semidirect
367. C2×C3×Dic6C3×D4semidirect
372. C4×C3⋊Dic3C23×C3semidirect
385. C3×#208C22×D3semidirect
386. C3×#208C23×C3semidirect
450. #1004C2×C3×D3semidirect
480. C2×#208C2×C3×D3semidirect
490. #833C2×C3×D3semidirect
647. C3×D12C2×#67semidirect
648. C3×D12C2×C3×D4semidirect
659. C3×Dic6C2×#67semidirect
660. C3×Dic6C2×C3×D4semidirect
674. C2×C33#453semidirect
803. #235C3×#67semidirect
817. C2×D12C3×#67semidirect
819. C2×Dic6C3×#67semidirect
842. #208C22×C3×D3semidirect
972. C33C2×#453semidirect
1137. D12C2×C3×#67semidirect
1141. Dic6C2×C3×#67semidirect
1176. C2×C32#4747semidirect
1177. C2×C32#5241semidirect
1178. C2×C32C3×#453semidirect
1337. C32C2×#4747semidirect
1338. C32C2×#5241semidirect
1339. C32C2×C3×#453semidirect
1408. C2×C3#10591510direct (N × H)
1409. C2×C3C3×#4747semidirect
1410. C2×C3C3×#5241semidirect
1441. C3C2×C3×#5241semidirect
1442. C3C2×C3×#4747semidirect
1443. C3C2×#10591510direct (N × H)
1449. C2C3×#10591510direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#10042
C2×C3×#641492
C2×C3×#638252
C2×C32×#8332
C3×#105915102
C2×C3×#635682
C2×#105915103
C2×C3×#47473
C2×C3×#52413