Finite Group Databasebeta

← C2×#11724408 #13181312

Subgroups — C2×#11724408 #13181312

Order 1728.

4178 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6294C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
3C2×#89028C212yesmaximal, complemented
4C2×C3×#3811C211yesmaximal, characteristic, complemented
5C2×C3×#3805C212yesmaximal, complemented
6C2×#88962C212yesmaximal, complemented
7C2×#88961C212yesmaximal, complemented
8C2×#88957C211yesmaximal, characteristic, complemented
9C2×#88952C211yesmaximal, characteristic, complemented
10C2×D3×#624C211yesmaximal, characteristic, complemented
11#11724408C2116yesmaximal, direct product factor
12C2×D32×Dic3C211yesmaximal, characteristic, complemented
13C2×#64312—31nomaximal
14C2×D3×#237—32nomaximal
15C23×C3×C3⋊D3C2211yescharacteristic
16C22×D3×C3⋊D3C2211yescharacteristic
17C22×C3×D32C2211yescharacteristic
18C2×#6312C2211yescharacteristic, complemented
19C22×C3×C3⋊Dic3C2212yescomplemented
20C2×C32×#67C2211yescharacteristic, complemented
21C2×C32×#67C2212yescomplemented
22C2×#6294C2211yescharacteristic
23C2×#6294C2211yescharacteristic
24C2×#6294C2218yescomplemented
25C2×#6294C2212yescomplemented
26C3⋊D3×#67C2218yescomplemented
27C2×#6293C2212yescomplemented
28C2×#6292C2211yescharacteristic, complemented
29C2×#6291C2212yescomplemented
30C2×#6290C2211yescharacteristic, complemented
31C2×#6289C2212yescomplemented
32C2×Dic3×C3⋊D3C2211yescharacteristic
33#89028C22116yescomplemented
34C2×D3×C3⋊Dic3C2212yescomplemented
35C3×#3811C2218yescomplemented
36C2×C3×#627C2212yescomplemented
37C2×C3×#626C2212yescomplemented
38C2×C3×#625C2212yescomplemented
39C2×C3×#624C2211yescharacteristic
40C3×#3805C22116yescomplemented
41C2×C3×D3×Dic3C2212yescomplemented
42C2×C3×D3×Dic3C2212yescomplemented
43#88962C22116yescomplemented
44#88961C22116yescomplemented
45#88957C2218yescomplemented
46#88952C2218yescomplemented
47D3×#624C2218yescomplemented
48D32×Dic3C2218yescomplemented
49C2×#3830—32no—
50C2×D4×C3⋊D3—31no—
51C2×C3×#237—32no—
52C2×C3×#237—32no—
53C2×C3×D3×D4—32no—
54C2×#3811—31no—
55C2×#3811D311yescharacteristic, complemented
56C2×D3×#67—32no—
57C2×D3×#67—32no—
58C2×D3×#67—61no—
59C22×#624—31no—
60C22×#624—31no—
61C2×#3805—32no—
62C2×#3805D312yescomplemented
63C2×#3804—32no—
64C2×#3804—32no—
65C2×#3804—32no—
66C2×#3804—32no—
67C2×#3804—62no—
68C22×D3×Dic3—32no—
69C22×D3×Dic3—32no—
70#64312—316no—
71D3×#237—332no—
72C2×C4×D32—32no—
73C2×C4×D32—31no—
74C2×#3799—32no—
75C2×#3797—31no—
76C2×#3796—32no—
77C2×#3795—32no—
78C2×D3×Dic6—32no—
79C23×C33C2311yescharacteristic
80C22×C3⋊(C3⋊D3)C2311yescharacteristic
81C22×C3×C3⋊D3—24no—
82C22×C3×C3⋊D3C2311yescharacteristic
83C22×C3×C3⋊D3C2314yes—
84C22×C3×C3⋊D3C2311yescharacteristic
85C22×C32×D3C2312yes—
86C22×C32×D3C2311yescharacteristic
87C2×D3×C3⋊D3—24no—
88C2×D3×C3⋊D3C2314yes—
89C2×C3×D32—24no—
90C2×C3×D32C2314yes—
91#6312C2314yescomplemented
92C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
93C2×C3×C3⋊Dic3C2312yes—
94C2×C3×C3⋊Dic3C2312yes—
95C2×C3×C3⋊Dic3C2318yescomplemented
96C32×#67C2314yescomplemented
97C32×#67C2318yescomplemented
98C2×C32×Dic3C2311yescharacteristic
99C2×C32×Dic3C2312yes—
100#6294C2314yes—
101#6294C2314yes—
102#6294C2318yescomplemented
103#6293C2318yescomplemented
104#6292C2314yescomplemented
105#6291C2318yescomplemented
106#6290C2314yescomplemented
107#6289C2318yescomplemented
108Dic3×C3⋊D3C2314yes—
109D3×C3⋊Dic3C2318yescomplemented
110C3×#627C2318yescomplemented
111C3×#626C2318yescomplemented
112C3×#625C2318yescomplemented
113C3×#624C2314yes—
114C3×D3×Dic3C2318yescomplemented
115C3×D3×Dic3C2318yescomplemented
116C2×D3×#41—92no—
117C22×#237—91no—
118C23×C3⋊D3—31no—
119C23×C3⋊D3C2×D311yescharacteristic
120C23×C3×D3—32no—
121C23×C3×D3—32no—
122C23×C3×D3—61no—
123C22×D32—32no—
124C22×D32—61no—
125C22×D32C2×D311yescharacteristic
126C2×C32×D4—32no—
127C2×C32×D4—31no—
128C2×#638—31no—
129C2×#638—32no—
130C2×#638—31no—
131C2×#638—32no—
132C2×#638—62no—
133C2×#638—61no—
134C2×#638—121no—
135C22×C3⋊Dic3—32no—
136C22×C3⋊Dic3C2×D312yescomplemented
137#3830—316no—
138D4×C3⋊D3—38no—
139C2×C4⋊(C3⋊D3)—31no—
140C2×C4×C3⋊D3—31no—
141C2×C4×C3⋊D3—32no—
142C2×#634—32no—
143C2×C3×#67—22no—
144C2×C3×#67—21no—
145C2×C3×#67—32no—
146C2×C3×#67—32no—
147C2×C3×#67—32no—
148C2×C3×#67C2×D312yescomplemented
149C2×C3×#67C2×D312yescomplemented
150C2×C3×#67C2×D312yescomplemented
151C22×C3×Dic3—32no—
152C22×C3×Dic3—32no—
153C22×C3×Dic3—32no—
154C22×C3×Dic3—32no—
155C22×C3×Dic3—62no—
156C3×#237—316no—
157C3×#237—316no—
158C3×D3×D4—316no—
159C2×C3×D12—32no—
160C2×C3×C4×D3—32no—
161C2×C3×C4×D3—32no—
162C2×C3×C4×D3—32no—
163C2×C3×Dic6—32no—
164C2×C3×Dic6—32no—
165#3811—38no—
166#3811C2×D318yescomplemented
167D3×#67—316no—
168D3×#67—316no—
169D3×#67—68no—
170C2×#627—32no—
171C2×#627—32no—
172C2×#627—62no—
173C2×#627C2×D312yescomplemented
174C2×#626—32no—
175C2×#626—32no—
176C2×#626—32no—
177C2×#626—61no—
178C2×#626—62no—
179C2×#626C2×D312yescomplemented
180C2×#625—32no—
181C2×#625—61no—
182C2×#625C2×D312yescomplemented
183C2×#624—31no—
184C2×#624—32no—
185C2×#624—31no—
186C2×#624—38no—
187C2×#624—32no—
188C2×#624—32no—
189C2×#624—38no—
190C2×#624—62no—
191C2×#624C2×D311yescharacteristic
192#3805—316no—
193#3805C2×D3116yescomplemented
194#3804—316no—
195#3804—316no—
196#3804—316no—
197#3804—316no—
198#3804—616no—
199C2×D3×Dic3—32no—
200C2×D3×Dic3—32no—
201C2×D3×Dic3—32no—
202C2×D3×Dic3—32no—
203C2×D3×Dic3—32no—
204C2×D3×Dic3—32no—
205C2×D3×Dic3—316no—
206C2×D3×Dic3—32no—
207C2×D3×Dic3—316no—
208C2×D3×Dic3—61no—
209C2×D3×Dic3—62no—
210C2×D3×Dic3C2×D312yescomplemented
211C2×D3×Dic3C2×D312yescomplemented
212C4×D32—38no—
213C4×D32—316no—
214#3799—316no—
215#3797—38no—
216#3796—316no—
217#3795—316no—
218D3×Dic6—316no—
219C22×C33—22no—
220C22×C33C2412yes—
221C22×C33C2411yescharacteristic
222C2×C3⋊(C3⋊D3)—22no—
223C2×C3⋊(C3⋊D3)C2412yes—
224C2×C3×C3⋊D3—22no—
225C2×C3×C3⋊D3—28no—
226C2×C3×C3⋊D3#4114yescomplemented
227C2×C3×C3⋊D3C2412yes—
228C2×C3×C3⋊D3C2412yes—
229C2×C32×D3—24no—
230C2×C32×D3—22no—
231C2×C32×D3C2412yes—
232C2×C32×D3C2414yes—
233D3×C3⋊D3—28no—
234C3×D32—28no—
235C3⋊(C3⋊Dic3)C2412yes—
236C3×C3⋊Dic3C2414yes—
237C3×C3⋊Dic3C2414yes—
238C32×Dic3C2412yes—
239C32×Dic3C2414yes—
240C2×C3×#41—92no—
241C22×C3×D4—91no—
242C22×#67—91no—
243C22×#67—91no—
244C23×Dic3—91no—
245C23×Dic3—91no—
246D3×#41—932no—
247C2×#239—92no—
248C2×D3×Q8—92no—
249C2×#237—32no—
250C2×#237—32no—
251C2×#237—92no—
252C2×#237—92no—
253C2×#237—916no—
254C2×#237—92no—
255C2×#237—92no—
256C2×#237—92no—
257C2×#237—182no—
258C2×D3×D4—32no—
259C2×D3×D4—92no—
260C2×D3×D4—92no—
261C2×D3×D4—181no—
262C2×#235—92no—
263C2×#235—92no—
264C2×#235—92no—
265C22×C4×D3—91no—
266C22×C4×D3—92no—
267C22×C4×D3—92no—
268C22×C4×D3—92no—
269C22×Dic6—91no—
270C23×C32—21no—
271C23×C32—22no—
272C23×C32—32no—
273C23×C32—31no—
274C23×C32—41no—
275C23×C32C22×D312yes—
276C23×C32C22×D311yescharacteristic
277C22×C3⋊D3—24no—
278C22×C3⋊D3—32no—
279C22×C3⋊D3—31no—
280C22×C3⋊D3—34no—
281C22×C3⋊D3—61no—
282C22×C3⋊D3—62no—
283C22×C3⋊D3—64no—
284C22×C3⋊D3—121no—
285C22×C3⋊D3C22×D311yescharacteristic
286C22×C3⋊D3C22×D314yes—
287C22×C3⋊D3C22×D311yescharacteristic
288C22×C3×D3—21no—
289C22×C3×D3—22no—
290C22×C3×D3—32no—
291C22×C3×D3—32no—
292C22×C3×D3—38no—
293C22×C3×D3—38no—
294C22×C3×D3—61no—
295C22×C3×D3—61no—
296C22×C3×D3—64no—
297C22×C3×D3—68no—
298C22×C3×D3—68no—
299C22×C3×D3—124no—
300C22×C3×D3C22×D312yes—
301C22×C3×D3C22×D312yes—
302C22×C3×D3C22×D312yes—
303C2×D32—24no—
304C2×D32—38no—
305C2×D32—64no—
306C2×D32—68no—
307C2×D32—124no—
308C2×D32C22×D314yes—
309C32×D4—38no—
310C32×D4—34no—
311C2×C32×C4—31no—
312C2×C32×C4—32no—
313#638—34no—
314#638—38no—
315#638—34no—
316#638—38no—
317#638—68no—
318#638—64no—
319#638—124no—
320C2×C3⋊Dic3—32no—
321C2×C3⋊Dic3—31no—
322C2×C3⋊Dic3—38no—
323C2×C3⋊Dic3—61no—
324C2×C3⋊Dic3—62no—
325C2×C3⋊Dic3—121no—
326C2×C3⋊Dic3C22×D312yes—
327C2×C3⋊Dic3C22×D312yes—
328C2×C3⋊Dic3C22×D318yescomplemented
329C4⋊(C3⋊D3)—34no—
330C4×C3⋊D3—34no—
331C4×C3⋊D3—38no—
332#634—38no—
333C3×#67—28no—
334C3×#67—24no—
335C3×#67—38no—
336C3×#67—38no—
337C3×#67—38no—
338C3×#67C22×D318yescomplemented
339C3×#67C22×D318yescomplemented
340C3×#67C22×D318yescomplemented
341C2×C3×Dic3—21no—
342C2×C3×Dic3—22no—
343C2×C3×Dic3—32no—
344C2×C3×Dic3—32no—
345C2×C3×Dic3—32no—
346C2×C3×Dic3—32no—
347C2×C3×Dic3—38no—
348C2×C3×Dic3—38no—
349C2×C3×Dic3—38no—
350C2×C3×Dic3—38no—
351C2×C3×Dic3—62no—
352C2×C3×Dic3—62no—
353C2×C3×Dic3—68no—
354C2×C3×Dic3C22×D312yes—
355C2×C3×Dic3C22×D312yes—
356C2×C3×Dic3C22×D312yes—
357C3×D12—38no—
358C3×C4×D3—38no—
359C3×C4×D3—38no—
360C3×C4×D3—38no—
361C3×Dic6—38no—
362C3×Dic6—38no—
363#627—38no—
364#627—38no—
365#627—68no—
366#627C22×D318yescomplemented
367#626—38no—
368#626—38no—
369#626—38no—
370#626—68no—
371#626—64no—
372#626C22×D318yescomplemented
373#625—38no—
374#625—64no—
375#625C22×D318yescomplemented
376#624—34no—
377#624—34no—
378#624—38no—
379#624—38no—
380#624—38no—
381#624—68no—
382#624C22×D314yes—
383D3×Dic3—38no—
384D3×Dic3—38no—
385D3×Dic3—38no—
386D3×Dic3—38no—
387D3×Dic3—38no—
388D3×Dic3—38no—
389D3×Dic3—38no—
390D3×Dic3—68no—
391D3×Dic3—64no—
392D3×Dic3C22×D318yescomplemented
393D3×Dic3C22×D318yescomplemented
394C22×#41—271noSylow
395C2×C33—22no—
396C2×C33C2×#4112yescomplemented
397C2×C33C2511yescharacteristic
398C3⋊(C3⋊D3)—22no—
399C3×C3⋊D3—22no—
400C3×C3⋊D3C2×#4114yescomplemented
401C32×D3—24no—
402C32×D3—22no—
403C24×C3—91no—
404C24×C3—91no—
405C23×D3—32no—
406C23×D3—32no—
407C23×D3—61no—
408C23×D3—92no—
409C23×D3—91no—
410C23×D3—181no—
411C3×#41—916no—
412C2×C3×Q8—92no—
413C2×C3×D4—32no—
414C2×C3×D4—32no—
415C2×C3×D4—32no—
416C2×C3×D4—61no—
417C2×C3×D4—62no—
418C2×C3×D4—92no—
419C2×C3×D4—98no—
420C2×C3×D4—92no—
421C22×C3×C4—91no—
422C22×C3×C4—92no—
423C22×C3×C4—92no—
424C22×C3×C4—92no—
425C2×#67—32no—
426C2×#67—32no—
427C2×#67—32no—
428C2×#67—92no—
429C2×#67—92no—
430C2×#67—98no—
431C2×#67—92no—
432C2×#67—92no—
433C2×#67—91no—
434C2×#67—91no—
435C2×#67—98no—
436C2×#67—91no—
437C2×#67—182no—
438C2×#67—181no—
439C2×#67—181no—
440C2×#67—182no—
441C2×#67—361no—
442C2×#67D3212yescomplemented
443C2×#67D3211yescharacteristic, complemented
444C22×Dic3—32no—
445C22×Dic3—32no—
446C22×Dic3—32no—
447C22×Dic3—32no—
448C22×Dic3—62no—
449C22×Dic3—91no—
450C22×Dic3—91no—
451C22×Dic3—92no—
452C22×Dic3—98no—
453C22×Dic3—98no—
454C22×Dic3—92no—
455C22×Dic3—92no—
456C22×Dic3—91no—
457C22×Dic3—182no—
458#239—916no—
459D3×Q8—916no—
460#237—316no—
461#237—316no—
462#237—916no—
463#237—916no—
464#237—916no—
465#237—916no—
466#237—916no—
467#237—1816no—
468D3×D4—316no—
469D3×D4—916no—
470D3×D4—916no—
471D3×D4—188no—
472#235—916no—
473#235—916no—
474#235—916no—
475C2×D12—32no—
476C2×D12—92no—
477C2×D12—92no—
478C2×D12—181no—
479C2×C4×D3—32no—
480C2×C4×D3—32no—
481C2×C4×D3—32no—
482C2×C4×D3—98no—
483C2×C4×D3—916no—
484C2×C4×D3—916no—
485C2×C4×D3—92no—
486C2×C4×D3—92no—
487C2×C4×D3—92no—
488C2×C4×D3—92no—
489C2×C4×D3—92no—
490C2×C4×D3—92no—
491C2×C4×D3—916no—
492C2×C4×D3—92no—
493C2×C4×D3—92no—
494C2×C4×D3—92no—
495C2×C4×D3—182no—
496C2×C4×D3—181no—
497C2×Dic6—32no—
498C2×Dic6—32no—
499C2×Dic6—98no—
500C2×Dic6—92no—
501C2×Dic6—92no—
502C2×Dic6—92no—
503C2×Dic6—182no—
504C22×C32—22no—
505C22×C32—24no—
506C22×C32—22no—
507C22×C32—21no—
508C22×C32—24no—
509C22×C32—22no—
510C22×C32—32no—
511C22×C32—34no—
512C22×C32—41no—
513C22×C32—42no—
514C22×C32—42no—
515C22×C32—44no—
516C22×C32—62no—
517C22×C32—64no—
518C22×C32—82no—
519C22×C32C23×D312yes—
520C22×C32C23×D314yes—
521C22×C32C23×D311yescharacteristic
522C22×C32C23×D312yes—
523C2×C3⋊D3—22no—
524C2×C3⋊D3—28no—
525C2×C3⋊D3—32no—
526C2×C3⋊D3—34no—
527C2×C3⋊D3—64no—
528C2×C3⋊D3—62no—
529C2×C3⋊D3—62no—
530C2×C3⋊D3—64no—
531C2×C3⋊D3—68no—
532C2×C3⋊D3—122no—
533C2×C3⋊D3—122no—
534C2×C3⋊D3—124no—
535C2×C3⋊D3—242no—
536C2×C3⋊D3#23714yescomplemented
537C2×C3⋊D3C23×D312yes—
538C2×C3⋊D3C23×D312yes—
539C2×C3×D3—24no—
540C2×C3×D3—24no—
541C2×C3×D3—24no—
542C2×C3×D3—24no—
543C2×C3×D3—22no—
544C2×C3×D3—38no—
545C2×C3×D3—34no—
546C2×C3×D3—34no—
547C2×C3×D3—42no—
548C2×C3×D3—44no—
549C2×C3×D3—64no—
550C2×C3×D3—62no—
551C2×C3×D3—62no—
552C2×C3×D3—616no—
553C2×C3×D3—616no—
554C2×C3×D3—64no—
555C2×C3×D3—128no—
556C2×C3×D3—122no—
557C2×C3×D3C23×D314yes—
558C2×C3×D3C23×D314yes—
559C2×C3×D3C23×D314yes—
560D32—28no—
561D32—616no—
562D32—128no—
563C32×C4—32no—
564C32×C4—34no—
565C3⋊Dic3—34no—
566C3⋊Dic3—32no—
567C3⋊Dic3—62no—
568C3⋊Dic3—64no—
569C3⋊Dic3—122no—
570C3⋊Dic3C23×D314yes—
571C3⋊Dic3C23×D314yes—
572C3×Dic3—22no—
573C3×Dic3—24no—
574C3×Dic3—34no—
575C3×Dic3—34no—
576C3×Dic3—34no—
577C3×Dic3—34no—
578C3×Dic3—64no—
579C3×Dic3—64no—
580C3×Dic3C23×D314yes—
581C3×Dic3C23×D314yes—
582C3×Dic3C23×D314yes—
583C2×#41—92no—
584C2×#41—272no—
585C2×#41—272no—
586C2×#41—272no—
587C2×#41—2716no—
588C22×Q8—271no—
589C22×D4—91no—
590C22×D4—271no—
591C22×D4—271no—
592C23×C4—271no—
593C23×C4—271no—
594C23×C4—271no—
595C33C22×#4111yescharacteristic, complemented, Sylow
596C23×C3—22no—
597C23×C3—21no—
598C23×C3—32no—
599C23×C3—32no—
600C23×C3—32no—
601C23×C3—41no—
602C23×C3—62no—
603C23×C3—61no—
604C23×C3—94no—
605C23×C3—91no—
606C23×C3—94no—
607C23×C3—91no—
608C23×C3—184no—
609C23×C3—184no—
610C23×C3C2×D3211yescharacteristic
611C23×C3C2×D3212yes—
612C22×D3—32no—
613C22×D3—32no—
614C22×D3—38no—
615C22×D3—38no—
616C22×D3—61no—
617C22×D3—61no—
618C22×D3—64no—
619C22×D3—68no—
620C22×D3—68no—
621C22×D3—98no—
622C22×D3—92no—
623C22×D3—91no—
624C22×D3—94no—
625C22×D3—124no—
626C22×D3—184no—
627C22×D3—182no—
628C22×D3—181no—
629C22×D3—184no—
630C22×D3—188no—
631C22×D3—361no—
632C22×D3—364no—
633C22×D3C2×D3211yescharacteristic
634C22×D3C2×D3212yes—
635C3×Q8—98no—
636C3×D4—38no—
637C3×D4—38no—
638C3×D4—38no—
639C3×D4—64no—
640C3×D4—68no—
641C3×D4—98no—
642C3×D4—98no—
643C2×C3×C4—32no—
644C2×C3×C4—32no—
645C2×C3×C4—32no—
646C2×C3×C4—62no—
647C2×C3×C4—61no—
648C2×C3×C4—94no—
649C2×C3×C4—98no—
650C2×C3×C4—98no—
651C2×C3×C4—92no—
652C2×C3×C4—92no—
653C2×C3×C4—98no—
654#67—38no—
655#67—38no—
656#67—38no—
657#67—98no—
658#67—98no—
659#67—98no—
660#67—98no—
661#67—94no—
662#67—94no—
663#67—94no—
664#67—188no—
665#67—184no—
666#67—184no—
667#67—188no—
668#67—364no—
669#67C2×D3218yescomplemented
670#67C2×D3214yescomplemented
671C2×Dic3—32no—
672C2×Dic3—32no—
673C2×Dic3—32no—
674C2×Dic3—32no—
675C2×Dic3—38no—
676C2×Dic3—38no—
677C2×Dic3—38no—
678C2×Dic3—38no—
679C2×Dic3—62no—
680C2×Dic3—62no—
681C2×Dic3—68no—
682C2×Dic3—94no—
683C2×Dic3—94no—
684C2×Dic3—98no—
685C2×Dic3—98no—
686C2×Dic3—98no—
687C2×Dic3—92no—
688C2×Dic3—91no—
689C2×Dic3—94no—
690C2×Dic3—188no—
691C2×Dic3—182no—
692C2×Dic3—181no—
693C2×Dic3—361no—
694C2×Dic3C2×D3211yescharacteristic
695C2×Dic3C2×D3212yes—
696D12—38no—
697D12—98no—
698D12—98no—
699D12—184no—
700C4×D3—38no—
701C4×D3—38no—
702C4×D3—38no—
703C4×D3—98no—
704C4×D3—98no—
705C4×D3—98no—
706C4×D3—98no—
707C4×D3—98no—
708C4×D3—98no—
709C4×D3—98no—
710C4×D3—98no—
711C4×D3—98no—
712C4×D3—188no—
713C4×D3—184no—
714Dic6—38no—
715Dic6—38no—
716Dic6—98no—
717Dic6—98no—
718Dic6—98no—
719Dic6—188no—
720C2×C32—22no—
721C2×C32—24no—
722C2×C32—24no—
723C2×C32—22no—
724C2×C32—22no—
725C2×C32—21no—
726C2×C32—42no—
727C2×C32—41no—
728C2×C32—42no—
729C2×C32—44no—
730C2×C32—62no—
731C2×C32—64no—
732C2×C32—82no—
733C2×C32C2×#23712yescomplemented
734C2×C32D3×#4114yescomplemented
735C2×C32C24×D311yescharacteristic
736C2×C32C24×D312yes—
737C3⋊D3—22no—
738C3⋊D3—62no—
739C3⋊D3—64no—
740C3⋊D3—122no—
741C3⋊D3—124no—
742C3⋊D3—242no—
743C3⋊D3C2×#23714yescomplemented
744C3×D3—24no—
745C3×D3—24no—
746C3×D3—24no—
747C3×D3—38no—
748C3×D3—42no—
749C3×D3—44no—
750C3×D3—64no—
751C3×D3—64no—
752C3×D3—122no—
753C24—91no—
754C24—91no—
755C24—271no—
756#41—916no—
757#41—2716no—
758#41—2716no—
759#41—2716no—
760C2×Q8—92no—
761C2×Q8—272no—
762C2×Q8—278no—
763C2×D4—32no—
764C2×D4—31no—
765C2×D4—92no—
766C2×D4—98no—
767C2×D4—92no—
768C2×D4—271no—
769C2×D4—272no—
770C2×D4—278no—
771C2×D4—278no—
772C2×D4—271no—
773C2×D4—271no—
774C22×C4—91no—
775C22×C4—92no—
776C22×C4—92no—
777C22×C4—92no—
778C22×C4—272no—
779C22×C4—271no—
780C22×C4—278no—
781C22×C4—271no—
782C22×C4—271no—
783C22×C4—278no—
784C22×C4—278no—
785C22×C4—272no—
786C22×C4—272no—
787C22×C3—24no—
788C22×C3—22no—
789C22×C3—24no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—21no—
793C22×C3—34no—
794C22×C3—34no—
795C22×C3—34no—
796C22×C3—42no—
797C22×C3—44no—
798C22×C3—42no—
799C22×C3—41no—
800C22×C3—64no—
801C22×C3—62no—
802C22×C3—64no—
803C22×C3—64no—
804C22×C3—64no—
805C22×C3—82no—
806C22×C3—94no—
807C22×C3—92no—
808C22×C3—92no—
809C22×C3—122no—
810C22×C3—124no—
811C22×C3—188no—
812C22×C3—188no—
813C22×C3—182no—
814C22×C3C22×D3212yes—
815C22×C3C22×D3214yes—
816C22×C3C22×D3212yes—
817C22×C3C22×D3211yescharacteristic
818C2×D3—24no—
819C2×D3—22no—
820C2×D3—38no—
821C2×D3—34no—
822C2×D3—34no—
823C2×D3—62no—
824C2×D3—64no—
825C2×D3—62no—
826C2×D3—616no—
827C2×D3—616no—
828C2×D3—64no—
829C2×D3—94no—
830C2×D3—92no—
831C2×D3—128no—
832C2×D3—122no—
833C2×D3—184no—
834C2×D3—182no—
835C2×D3—188no—
836C2×D3—1816no—
837C2×D3—184no—
838C2×D3—182no—
839C2×D3—362no—
840C2×D3—368no—
841C2×D3—362no—
842C2×D3—364no—
843C2×D3—722no—
844C2×D3C22×D3212yes—
845C2×D3C22×D3214yes—
846C3×C4—34no—
847C3×C4—34no—
848C3×C4—34no—
849C3×C4—64no—
850C3×C4—62no—
851C3×C4—94no—
852C3×C4—94no—
853Dic3—34no—
854Dic3—34no—
855Dic3—34no—
856Dic3—34no—
857Dic3—64no—
858Dic3—64no—
859Dic3—94no—
860Dic3—92no—
861Dic3—184no—
862Dic3—182no—
863Dic3—362no—
864Dic3C22×D3212yes—
865Dic3C22×D3214yes—
866C32—22no—
867C32—21no—
868C32—41no—
869C32C22×#23711yescharacteristic, complemented
870C32C2×D3×#4112yescomplemented
871C23—31no—
872C23—32no—
873C23—94no—
874C23—91no—
875C23—94no—
876C23—91no—
877C23—184no—
878C23—184no—
879C23—274no—
880C23—271no—
881C23—544no—
882C23D3311yescharacteristic
883Q8—98no—
884Q8—278no—
885D4—38no—
886D4—34no—
887D4—98no—
888D4—98no—
889D4—274no—
890D4—278no—
891D4—274no—
892D4—274no—
893C2×C4—32no—
894C2×C4—31no—
895C2×C4—94no—
896C2×C4—98no—
897C2×C4—98no—
898C2×C4—98no—
899C2×C4—92no—
900C2×C4—92no—
901C2×C4—278no—
902C2×C4—274no—
903C2×C4—274no—
904C2×C4—274no—
905C2×C4—278no—
906C2×C4—278no—
907C2×C4—271no—
908C2×C3—24no—
909C2×C3—22no—
910C2×C3—22no—
911C2×C3—24no—
912C2×C3—22no—
913C2×C3—21no—
914C2×C3—42no—
915C2×C3—44no—
916C2×C3—42no—
917C2×C3—41no—
918C2×C3—64no—
919C2×C3—64no—
920C2×C3—64no—
921C2×C3—82no—
922C2×C3—94no—
923C2×C3—122no—
924C2×C3—124no—
925C2×C3—182no—
926C2×C3D3×#23714yescomplemented
927C2×C3#6431212yescomplemented
928C2×C3C23×D3212yes—
929C2×C3C23×D3211yescharacteristic
930D3—24no—
931D3—22no—
932D3—38no—
933D3—64no—
934D3—64no—
935D3—122no—
936D3—184no—
937D3—182no—
938D3—362no—
939D3—364no—
940D3—722no—
941C22—22no—
942C22—32no—
943C22—34no—
944C22—64no—
945C22—62no—
946C22—94no—
947C22—92no—
948C22—92no—
949C22—188no—
950C22—188no—
951C22—182no—
952C22—272no—
953C22—548no—
954C22—542no—
955C22C2×D3312yes—
956C22C2×D3311yescharacteristic
957C4—34no—
958C4—32no—
959C4—94no—
960C4—94no—
961C4—272no—
962C3—21no—
963C3—22no—
964C3—41no—
965C3C2×D3×#23712yescomplemented
966C3C2×#6431211yescharacteristic, complemented
967C2—22no—
968C2—64no—
969C2—62no—
970C2—94no—
971C2—182no—
972C2—542no—
973C2#1172440812yesdirect product factor
974C2C22×D3311yescharacteristic
subgroupG/H
centerC22C2×D33
commutator, cosocleC2×C33C25
FrattiniC2C22×D33
FittingC23×C33C23
socleC22×C33C24
hypercenterC23D33
hypocenterC33C22×#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×#6294C2semidirect
2. C2×C3⋊D3×#67C2semidirect
3. C2×#89028C2semidirect
4. C2×C3×#3811C2semidirect
5. C2×C3×#3805C2semidirect
6. C2×#88962C2semidirect
7. C2×#88961C2semidirect
8. C2×#88957C2semidirect
9. C2×#88952C2semidirect
10. C2×D3×#624C2semidirect
11. #11724408C2direct (N × H)
12. C2×D32×Dic3C2semidirect
18. C2×#6312C22semidirect
19. C22×C3×C3⋊Dic3C22semidirect
20. C2×C32×#67C22semidirect
21. C2×C32×#67C22semidirect
24. C2×#6294C22semidirect
25. C2×#6294C22semidirect
26. C3⋊D3×#67C22semidirect
27. C2×#6293C22semidirect
28. C2×#6292C22semidirect
29. C2×#6291C22semidirect
30. C2×#6290C22semidirect
31. C2×#6289C22semidirect
33. #89028C22semidirect
34. C2×D3×C3⋊Dic3C22semidirect
35. C3×#3811C22semidirect
36. C2×C3×#627C22semidirect
37. C2×C3×#626C22semidirect
38. C2×C3×#625C22semidirect
40. C3×#3805C22semidirect
41. C2×C3×D3×Dic3C22semidirect
42. C2×C3×D3×Dic3C22semidirect
43. #88962C22semidirect
44. #88961C22semidirect
45. #88957C22semidirect
46. #88952C22semidirect
47. D3×#624C22semidirect
48. D32×Dic3C22semidirect
55. C2×#3811D3semidirect
62. C2×#3805D3semidirect
91. #6312C23semidirect
95. C2×C3×C3⋊Dic3C23semidirect
96. C32×#67C23semidirect
97. C32×#67C23semidirect
102. #6294C23semidirect
103. #6293C23semidirect
104. #6292C23semidirect
105. #6291C23semidirect
106. #6290C23semidirect
107. #6289C23semidirect
109. D3×C3⋊Dic3C23semidirect
110. C3×#627C23semidirect
111. C3×#626C23semidirect
112. C3×#625C23semidirect
114. C3×D3×Dic3C23semidirect
115. C3×D3×Dic3C23semidirect
136. C22×C3⋊Dic3C2×D3semidirect
148. C2×C3×#67C2×D3semidirect
149. C2×C3×#67C2×D3semidirect
150. C2×C3×#67C2×D3semidirect
166. #3811C2×D3semidirect
173. C2×#627C2×D3semidirect
179. C2×#626C2×D3semidirect
182. C2×#625C2×D3semidirect
193. #3805C2×D3semidirect
210. C2×D3×Dic3C2×D3semidirect
211. C2×D3×Dic3C2×D3semidirect
226. C2×C3×C3⋊D3#41semidirect
328. C2×C3⋊Dic3C22×D3semidirect
338. C3×#67C22×D3semidirect
339. C3×#67C22×D3semidirect
340. C3×#67C22×D3semidirect
366. #627C22×D3semidirect
372. #626C22×D3semidirect
375. #625C22×D3semidirect
392. D3×Dic3C22×D3semidirect
393. D3×Dic3C22×D3semidirect
396. C2×C33C2×#41semidirect
400. C3×C3⋊D3C2×#41semidirect
442. C2×#67D32semidirect
443. C2×#67D32semidirect
536. C2×C3⋊D3#237semidirect
595. C33C22×#41semidirect
669. #67C2×D32semidirect
670. #67C2×D32semidirect
733. C2×C32C2×#237semidirect
734. C2×C32D3×#41semidirect
743. C3⋊D3C2×#237semidirect
869. C32C22×#237semidirect
870. C32C2×D3×#41semidirect
926. C2×C3D3×#237semidirect
927. C2×C3#64312semidirect
965. C3C2×D3×#237semidirect
966. C3C2×#64312semidirect
973. C2#11724408direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#62942
C2×C3⋊D3×#672
C2×#890282
C2×C3×#38112
C2×C3×#38052
C2×#889622
C2×#889612
C2×#889572
C2×#889522
C2×D3×#6242
#117244082
C2×D32×Dic32
C2×#643123
C2×D3×#2373