Finite Group Databasebeta

← C2×#11724410 #13181317

Subgroups — C2×#11724410 #13181317

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
1C2×#89049C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
3C2×#89031C212yesmaximal, complemented
4C22×C3×#624C211yesmaximal, characteristic, complemented
5C2×C3×#3804C212yesmaximal, complemented
6C2×#88965C212yesmaximal, complemented
7C2×#88960C212yesmaximal, complemented
8C2×#88957C211yesmaximal, characteristic, complemented
9C2×#88955C211yesmaximal, characteristic, complemented
10C2×#88949C211yesmaximal, characteristic, complemented
11#11724410C2116yesmaximal, direct product factor
12C2×D3×#624C211yesmaximal, characteristic, complemented
13C2×#64312—31nomaximal
14C2×D3×#235—32nomaximal
15C23×C3×C3⋊D3C2211yescharacteristic
16C22×#1113C2211yescharacteristic
17C22×D3×C3⋊D3C2211yescharacteristic
18C2×#6312C2211yescharacteristic, complemented
19C2×C3×#638C2212yescomplemented
20C2×C32×#67C2211yescharacteristic, complemented
21C22×C32×Dic3C2212yescomplemented
22#89049C2218yescomplemented
23C2×#6295C2212yescomplemented
24C2×#6294C2211yescharacteristic
25C3⋊D3×#67C2218yescomplemented
26C2×#6293C2212yescomplemented
27C2×#6292C2212yescomplemented
28C2×#6292C2211yescharacteristic, complemented
29C2×#6290C2211yescharacteristic, complemented
30C2×#6289C2212yescomplemented
31#89031C22116yescomplemented
32C2×Dic3×C3⋊D3C2211yescharacteristic
33C2×Dic3×C3⋊D3C2212yescomplemented
34C2×C3×#627C2212yescomplemented
35C2×C3×#626C2212yescomplemented
36C2×C3×#624C2211yescharacteristic
37C2×C3×#624C2211yescharacteristic
38C2×C3×#624C2218yescomplemented
39C2×C3×#624C2212yescomplemented
40C2×C3×#624C2212yescomplemented
41C3×#3804C22116yescomplemented
42C2×C3×D3×Dic3C2212yescomplemented
43#88965C22116yescomplemented
44#88960C22116yescomplemented
45#88957C2218yescomplemented
46#88955C2218yescomplemented
47#88949C2218yescomplemented
48D3×#624C2218yescomplemented
49C2×D4×C3⋊D3—31no—
50C2×#3828—32no—
51C2×C3×#237—32no—
52C2×C3×#235—32no—
53C22×C3×C4×D3—32no—
54C2×#3811—31no—
55C2×#3811—31no—
56C2×D3×#67—32no—
57C2×D3×#67—32no—
58C2×D3×#67—61no—
59C22×#624—31no—
60C22×#624D311yescharacteristic, complemented
61C2×#3804—32no—
62C2×#3804—32no—
63C2×#3804—32no—
64C2×#3804—62no—
65C2×#3804D312yescomplemented
66#64312—316no—
67D3×#235—332no—
68C2×D3×D12—32no—
69C2×C4×D32—31no—
70C2×C4×D32—32no—
71C2×C4×D32—32no—
72C2×#3799—32no—
73C2×#3799—32no—
74C2×#3798—32no—
75C2×#3798—32no—
76C2×#3797—31no—
77C2×#3795—32no—
78C2×D3×Dic6—32no—
79C23×C33C2311yescharacteristic
80C22×C3⋊(C3⋊D3)C2311yescharacteristic
81C22×C3×C3⋊D3—24no—
82C22×C3×C3⋊D3C2312yes—
83C22×C3×C3⋊D3C2311yescharacteristic
84C22×C3×C3⋊D3C2314yes—
85C22×C3×C3⋊D3C2311yescharacteristic
86C22×C32×D3C2311yescharacteristic
87C2×#1113—24no—
88C2×#1113C2314yes—
89C2×D3×C3⋊D3—24no—
90C2×D3×C3⋊D3C2314yes—
91#6312C2314yescomplemented
92C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
93C3×#638C2318yescomplemented
94C2×C3×C3⋊Dic3C2312yes—
95C32×#67C2314yescomplemented
96C2×C32×Dic3C2312yes—
97C2×C32×Dic3C2312yes—
98C2×C32×Dic3C2311yescharacteristic
99C2×C32×Dic3C2318yescomplemented
100#6295C2318yescomplemented
101#6294C2314yes—
102#6293C2318yescomplemented
103#6292C2318yescomplemented
104#6292C2314yescomplemented
105#6290C2314yescomplemented
106#6289C2318yescomplemented
107Dic3×C3⋊D3C2314yes—
108Dic3×C3⋊D3C2318yescomplemented
109C3×#627C2318yescomplemented
110C3×#626C2318yescomplemented
111C3×#624C2314yes—
112C3×#624C2314yes—
113C3×#624C2318yescomplemented
114C3×#624C2318yescomplemented
115C3×D3×Dic3C2318yescomplemented
116C2×D3×#41—92no—
117C22×#235—91no—
118C23×C3⋊D3—31no—
119C23×C3⋊D3C2×D311yescharacteristic
120C23×C3×D3—32no—
121C23×C3×D3—61no—
122C22×D32—32no—
123C22×D32—31no—
124C22×D32—32no—
125C22×D32—61no—
126C2×C32×D4—31no—
127C22×C32×C4—32no—
128C2×#638—31no—
129C2×#638—32no—
130C2×#638—31no—
131C2×#638—62no—
132C2×#638—61no—
133C2×#638—121no—
134C2×#638C2×D312yescomplemented
135D4×C3⋊D3—38no—
136#3828—316no—
137C2×C4⋊(C3⋊D3)—31no—
138C2×C4⋊(C3⋊D3)—32no—
139C2×C4×C3⋊D3—31no—
140C2×C4×C3⋊D3—32no—
141C2×C4×C3⋊D3—32no—
142C2×#634—32no—
143C2×C3×#67—21no—
144C2×C3×#67—32no—
145C2×C3×#67—32no—
146C2×C3×#67—32no—
147C2×C3×#67—62no—
148C2×C3×#67C2×D312yescomplemented
149C22×C3×Dic3—22no—
150C22×C3×Dic3—32no—
151C22×C3×Dic3C2×D312yescomplemented
152C22×C3×Dic3C2×D312yescomplemented
153C3×#237—316no—
154C3×#235—316no—
155C2×C3×D12—32no—
156C2×C3×C4×D3—32no—
157C2×C3×C4×D3—32no—
158C2×C3×C4×D3—32no—
159C2×C3×C4×D3—32no—
160C2×C3×C4×D3—32no—
161C2×C3×C4×D3—32no—
162C2×C3×C4×D3—32no—
163C2×C3×C4×D3—316no—
164C2×C3×Dic6—32no—
165C2×C3×Dic6—32no—
166#3811—38no—
167#3811—38no—
168D3×#67—316no—
169D3×#67—316no—
170D3×#67—68no—
171C2×#627—32no—
172C2×#627—32no—
173C2×#627—62no—
174C2×#627C2×D312yescomplemented
175C2×#626—32no—
176C2×#626—32no—
177C2×#626—32no—
178C2×#626—32no—
179C2×#626—32no—
180C2×#626—62no—
181C2×#626—61no—
182C2×#626C2×D312yescomplemented
183C2×#625—32no—
184C2×#625—32no—
185C2×#625—61no—
186C2×#624—31no—
187C2×#624—32no—
188C2×#624—32no—
189C2×#624—38no—
190C2×#624—62no—
191C2×#624C2×D311yescharacteristic
192C2×#624C2×D311yescharacteristic
193C2×#624C2×D318yescomplemented
194C2×#624C2×D312yescomplemented
195C2×#624C2×D312yescomplemented
196#3804—316no—
197#3804—316no—
198#3804—316no—
199#3804—616no—
200#3804C2×D3116yescomplemented
201C2×D3×Dic3—32no—
202C2×D3×Dic3—32no—
203C2×D3×Dic3—32no—
204C2×D3×Dic3—32no—
205C2×D3×Dic3—62no—
206C2×D3×Dic3—61no—
207C2×D3×Dic3C2×D312yescomplemented
208D3×D12—316no—
209C4×D32—38no—
210C4×D32—316no—
211C4×D32—316no—
212#3799—316no—
213#3799—316no—
214#3798—316no—
215#3798—316no—
216#3797—38no—
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—24no—
225C2×C3×C3⋊D3—22no—
226C2×C3×C3⋊D3—28no—
227C2×C3×C3⋊D3#4114yescomplemented
228C2×C3×C3⋊D3C2412yes—
229C2×C3×C3⋊D3C2414yes—
230C2×C3×C3⋊D3C2412yes—
231C2×C32×D3—22no—
232C2×C32×D3C2412yes—
233#1113—28no—
234D3×C3⋊D3—28no—
235C3⋊(C3⋊Dic3)C2412yes—
236C3×C3⋊Dic3C2414yes—
237C32×Dic3C2414yes—
238C32×Dic3C2414yes—
239C32×Dic3C2412yes—
240C2×C3×#41—92no—
241C23×C3×C4—91no—
242C22×#67—91no—
243C22×#67—91no—
244D3×#41—932no—
245C2×#239—92no—
246C2×D3×Q8—92no—
247C2×#237—32no—
248C2×#237—92no—
249C2×#237—92no—
250C2×D3×D4—92no—
251C2×D3×D4—92no—
252C2×D3×D4—92no—
253C2×D3×D4—181no—
254C2×#235—32no—
255C2×#235—92no—
256C2×#235—92no—
257C2×#235—92no—
258C2×#235—92no—
259C2×#235—916no—
260C2×#235—92no—
261C2×#235—92no—
262C2×#235—182no—
263C22×D12—91no—
264C22×C4×D3—32no—
265C22×C4×D3—91no—
266C22×C4×D3—91no—
267C22×C4×D3—92no—
268C22×C4×D3—92no—
269C22×Dic6—91no—
270C23×C32—21no—
271C23×C32—22no—
272C23×C32—31no—
273C23×C32—41no—
274C23×C32C22×D312yes—
275C23×C32C22×D311yescharacteristic
276C22×C3⋊D3—24no—
277C22×C3⋊D3—32no—
278C22×C3⋊D3—31no—
279C22×C3⋊D3—34no—
280C22×C3⋊D3—61no—
281C22×C3⋊D3—62no—
282C22×C3⋊D3—64no—
283C22×C3⋊D3—121no—
284C22×C3⋊D3C22×D312yes—
285C22×C3⋊D3C22×D311yescharacteristic
286C22×C3⋊D3C22×D314yes—
287C22×C3⋊D3C22×D311yescharacteristic
288C22×C3×D3—21no—
289C22×C3×D3—32no—
290C22×C3×D3—32no—
291C22×C3×D3—32no—
292C22×C3×D3—32no—
293C22×C3×D3—38no—
294C22×C3×D3—61no—
295C22×C3×D3—61no—
296C22×C3×D3—64no—
297C22×C3×D3—62no—
298C22×C3×D3—68no—
299C22×C3×D3—124no—
300C22×C3×D3C22×D312yes—
301C2×D32—38no—
302C2×D32—34no—
303C2×D32—38no—
304C2×D32—64no—
305C2×D32—68no—
306C2×D32—68no—
307C2×D32—64no—
308C2×D32—124no—
309C32×D4—34no—
310C2×C32×C4—31no—
311C2×C32×C4—32no—
312C2×C32×C4—32no—
313C2×C32×C4—38no—
314#638—34no—
315#638—38no—
316#638—34no—
317#638—68no—
318#638—64no—
319#638—124no—
320#638C22×D318yescomplemented
321C2×C3⋊Dic3—32no—
322C2×C3⋊Dic3—31no—
323C2×C3⋊Dic3—61no—
324C2×C3⋊Dic3—62no—
325C2×C3⋊Dic3—121no—
326C2×C3⋊Dic3C22×D312yes—
327C4⋊(C3⋊D3)—34no—
328C4⋊(C3⋊D3)—38no—
329C4×C3⋊D3—34no—
330C4×C3⋊D3—38no—
331C4×C3⋊D3—38no—
332#634—38no—
333C3×#67—24no—
334C3×#67—38no—
335C3×#67—38no—
336C3×#67—38no—
337C3×#67—68no—
338C3×#67C22×D318yescomplemented
339C2×C3×Dic3—22no—
340C2×C3×Dic3—21no—
341C2×C3×Dic3—22no—
342C2×C3×Dic3—28no—
343C2×C3×Dic3—32no—
344C2×C3×Dic3—32no—
345C2×C3×Dic3—38no—
346C2×C3×Dic3—62no—
347C2×C3×Dic3C22×D312yes—
348C2×C3×Dic3C22×D312yes—
349C2×C3×Dic3C22×D312yes—
350C2×C3×Dic3C22×D312yes—
351C2×C3×Dic3C22×D312yes—
352C2×C3×Dic3C22×D318yescomplemented
353C2×C3×Dic3C22×D318yescomplemented
354C3×D12—38no—
355C3×C4×D3—38no—
356C3×C4×D3—38no—
357C3×C4×D3—38no—
358C3×C4×D3—38no—
359C3×C4×D3—38no—
360C3×C4×D3—38no—
361C3×C4×D3—38no—
362C3×Dic6—38no—
363C3×Dic6—38no—
364#627—38no—
365#627—38no—
366#627—68no—
367#627C22×D318yescomplemented
368#626—38no—
369#626—38no—
370#626—38no—
371#626—38no—
372#626—38no—
373#626—68no—
374#626—64no—
375#626C22×D318yescomplemented
376#625—38no—
377#625—38no—
378#625—64no—
379#624—34no—
380#624—38no—
381#624—38no—
382#624—68no—
383#624C22×D314yes—
384#624C22×D314yes—
385#624C22×D318yescomplemented
386#624C22×D318yescomplemented
387D3×Dic3—38no—
388D3×Dic3—38no—
389D3×Dic3—38no—
390D3×Dic3—38no—
391D3×Dic3—64no—
392D3×Dic3—68no—
393D3×Dic3C22×D318yescomplemented
394C22×#41—271noSylow
395C2×C33—22no—
396C2×C33C2×#4112yescomplemented
397C2×C33C2511yescharacteristic
398C3⋊(C3⋊D3)—22no—
399C3×C3⋊D3—24no—
400C3×C3⋊D3—22no—
401C3×C3⋊D3C2×#4114yescomplemented
402C32×D3—22no—
403C24×C3—91no—
404C23×D3—32no—
405C23×D3—61no—
406C23×D3—91no—
407C23×D3—92no—
408C23×D3—92no—
409C23×D3—91no—
410C23×D3—181no—
411C3×#41—916no—
412C2×C3×Q8—92no—
413C2×C3×D4—32no—
414C2×C3×D4—61no—
415C2×C3×D4—92no—
416C2×C3×D4—92no—
417C22×C3×C4—32no—
418C22×C3×C4—32no—
419C22×C3×C4—62no—
420C22×C3×C4—91no—
421C22×C3×C4—91no—
422C22×C3×C4—92no—
423C22×C3×C4—92no—
424C22×C3×C4—98no—
425C22×C3×C4—92no—
426C2×#67—32no—
427C2×#67—32no—
428C2×#67—32no—
429C2×#67—62no—
430C2×#67—92no—
431C2×#67—92no—
432C2×#67—98no—
433C2×#67—92no—
434C2×#67—91no—
435C2×#67—92no—
436C2×#67—91no—
437C2×#67—98no—
438C2×#67—91no—
439C2×#67—92no—
440C2×#67—181no—
441C2×#67—182no—
442C2×#67—181no—
443C2×#67—361no—
444C2×#67D3211yescharacteristic, complemented
445C22×Dic3—32no—
446C22×Dic3—91no—
447C22×Dic3—91no—
448C22×Dic3—92no—
449C22×Dic3D3212yescomplemented
450#239—916no—
451D3×Q8—916no—
452#237—316no—
453#237—916no—
454#237—916no—
455D3×D4—916no—
456D3×D4—916no—
457D3×D4—916no—
458D3×D4—188no—
459#235—316no—
460#235—916no—
461#235—916no—
462#235—916no—
463#235—916no—
464#235—916no—
465#235—916no—
466#235—1816no—
467C2×D12—32no—
468C2×D12—98no—
469C2×D12—92no—
470C2×D12—92no—
471C2×D12—92no—
472C2×D12—92no—
473C2×D12—182no—
474C2×D12—181no—
475C2×C4×D3—32no—
476C2×C4×D3—32no—
477C2×C4×D3—32no—
478C2×C4×D3—32no—
479C2×C4×D3—32no—
480C2×C4×D3—32no—
481C2×C4×D3—32no—
482C2×C4×D3—316no—
483C2×C4×D3—98no—
484C2×C4×D3—98no—
485C2×C4×D3—916no—
486C2×C4×D3—916no—
487C2×C4×D3—92no—
488C2×C4×D3—92no—
489C2×C4×D3—92no—
490C2×C4×D3—92no—
491C2×C4×D3—92no—
492C2×C4×D3—92no—
493C2×C4×D3—92no—
494C2×C4×D3—182no—
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—41no—
512C22×C32—42no—
513C22×C32—42no—
514C22×C32—44no—
515C22×C32—62no—
516C22×C32—82no—
517C22×C32C23×D312yes—
518C22×C32C23×D314yes—
519C22×C32C23×D311yescharacteristic
520C22×C32C23×D312yes—
521C2×C3⋊D3—22no—
522C2×C3⋊D3—24no—
523C2×C3⋊D3—28no—
524C2×C3⋊D3—32no—
525C2×C3⋊D3—34no—
526C2×C3⋊D3—64no—
527C2×C3⋊D3—62no—
528C2×C3⋊D3—62no—
529C2×C3⋊D3—64no—
530C2×C3⋊D3—68no—
531C2×C3⋊D3—122no—
532C2×C3⋊D3—122no—
533C2×C3⋊D3—124no—
534C2×C3⋊D3—242no—
535C2×C3⋊D3#23514yescomplemented
536C2×C3⋊D3C23×D312yes—
537C2×C3⋊D3C23×D314yes—
538C2×C3⋊D3C23×D312yes—
539C2×C3×D3—24no—
540C2×C3×D3—22no—
541C2×C3×D3—38no—
542C2×C3×D3—34no—
543C2×C3×D3—34no—
544C2×C3×D3—34no—
545C2×C3×D3—34no—
546C2×C3×D3—42no—
547C2×C3×D3—64no—
548C2×C3×D3—62no—
549C2×C3×D3—64no—
550C2×C3×D3—62no—
551C2×C3×D3—616no—
552C2×C3×D3—64no—
553C2×C3×D3—64no—
554C2×C3×D3—64no—
555C2×C3×D3—128no—
556C2×C3×D3—124no—
557C2×C3×D3—122no—
558C2×C3×D3C23×D314yes—
559D32—616no—
560D32—616no—
561D32—68no—
562D32—128no—
563C32×C4—32no—
564C32×C4—34no—
565C32×C4—34no—
566C3⋊Dic3—34no—
567C3⋊Dic3—32no—
568C3⋊Dic3—62no—
569C3⋊Dic3—64no—
570C3⋊Dic3—122no—
571C3⋊Dic3C23×D314yes—
572C3×Dic3—24no—
573C3×Dic3—22no—
574C3×Dic3—24no—
575C3×Dic3—34no—
576C3×Dic3—34no—
577C3×Dic3—64no—
578C3×Dic3C23×D314yes—
579C3×Dic3C23×D314yes—
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—271no—
590C22×D4—271no—
591C22×D4—271no—
592C23×C4—91no—
593C23×C4—271no—
594C23×C4—271no—
595C33C22×#4111yescharacteristic, complemented, Sylow
596C23×C3—22no—
597C23×C3—21no—
598C23×C3—32no—
599C23×C3—41no—
600C23×C3—61no—
601C23×C3—91no—
602C23×C3—92no—
603C23×C3—94no—
604C23×C3—91no—
605C23×C3—184no—
606C23×C3C2×D3212yes—
607C23×C3C2×D3211yescharacteristic
608C22×D3—32no—
609C22×D3—32no—
610C22×D3—38no—
611C22×D3—32no—
612C22×D3—32no—
613C22×D3—61no—
614C22×D3—62no—
615C22×D3—61no—
616C22×D3—64no—
617C22×D3—68no—
618C22×D3—94no—
619C22×D3—98no—
620C22×D3—98no—
621C22×D3—92no—
622C22×D3—91no—
623C22×D3—94no—
624C22×D3—124no—
625C22×D3—184no—
626C22×D3—182no—
627C22×D3—181no—
628C22×D3—184no—
629C22×D3—188no—
630C22×D3—188no—
631C22×D3—184no—
632C22×D3—361no—
633C22×D3—364no—
634C22×D3C2×D3211yescharacteristic
635C3×Q8—98no—
636C3×D4—38no—
637C3×D4—64no—
638C3×D4—98no—
639C3×D4—98no—
640C2×C3×C4—32no—
641C2×C3×C4—32no—
642C2×C3×C4—32no—
643C2×C3×C4—32no—
644C2×C3×C4—32no—
645C2×C3×C4—38no—
646C2×C3×C4—38no—
647C2×C3×C4—62no—
648C2×C3×C4—62no—
649C2×C3×C4—61no—
650C2×C3×C4—68no—
651C2×C3×C4—94no—
652C2×C3×C4—94no—
653C2×C3×C4—98no—
654C2×C3×C4—98no—
655C2×C3×C4—98no—
656C2×C3×C4—92no—
657#67—38no—
658#67—38no—
659#67—38no—
660#67—68no—
661#67—98no—
662#67—98no—
663#67—98no—
664#67—94no—
665#67—98no—
666#67—94no—
667#67—94no—
668#67—98no—
669#67—184no—
670#67—188no—
671#67—184no—
672#67—364no—
673#67C2×D3214yescomplemented
674C2×Dic3—32no—
675C2×Dic3—32no—
676C2×Dic3—38no—
677C2×Dic3—62no—
678C2×Dic3—94no—
679C2×Dic3—92no—
680C2×Dic3—91no—
681C2×Dic3—94no—
682C2×Dic3—98no—
683C2×Dic3—182no—
684C2×Dic3—181no—
685C2×Dic3—361no—
686C2×Dic3C2×D3211yescharacteristic
687C2×Dic3C2×D3212yes—
688C2×Dic3C2×D3212yes—
689C2×Dic3C2×D3218yescomplemented
690D12—38no—
691D12—98no—
692D12—98no—
693D12—98no—
694D12—98no—
695D12—188no—
696D12—184no—
697C4×D3—38no—
698C4×D3—38no—
699C4×D3—38no—
700C4×D3—38no—
701C4×D3—38no—
702C4×D3—38no—
703C4×D3—38no—
704C4×D3—98no—
705C4×D3—98no—
706C4×D3—98no—
707C4×D3—98no—
708C4×D3—98no—
709C4×D3—98no—
710C4×D3—98no—
711C4×D3—188no—
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—82no—
732C2×C32C2×#23512yescomplemented
733C2×C32D3×#4114yescomplemented
734C2×C32C24×D311yescharacteristic
735C2×C32C24×D312yes—
736C3⋊D3—22no—
737C3⋊D3—24no—
738C3⋊D3—62no—
739C3⋊D3—64no—
740C3⋊D3—122no—
741C3⋊D3—124no—
742C3⋊D3—242no—
743C3⋊D3C2×#23514yescomplemented
744C3×D3—24no—
745C3×D3—38no—
746C3×D3—42no—
747C3×D3—64no—
748C3×D3—64no—
749C3×D3—64no—
750C3×D3—64no—
751C3×D3—124no—
752C3×D3—122no—
753C24—91no—
754C24—271no—
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—31no—
764C2×D4—92no—
765C2×D4—92no—
766C2×D4—272no—
767C2×D4—271no—
768C2×D4—278no—
769C2×D4—272no—
770C2×D4—278no—
771C2×D4—278no—
772C2×D4—271no—
773C2×D4—271no—
774C22×C4—32no—
775C22×C4—91no—
776C22×C4—91no—
777C22×C4—98no—
778C22×C4—92no—
779C22×C4—92no—
780C22×C4—92no—
781C22×C4—272no—
782C22×C4—271no—
783C22×C4—272no—
784C22×C4—278no—
785C22×C4—278no—
786C22×C4—271no—
787C22×C3—24no—
788C22×C3—22no—
789C22×C3—24no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—21no—
793C22×C3—34no—
794C22×C3—42no—
795C22×C3—44no—
796C22×C3—42no—
797C22×C3—41no—
798C22×C3—62no—
799C22×C3—64no—
800C22×C3—82no—
801C22×C3—94no—
802C22×C3—92no—
803C22×C3—94no—
804C22×C3—92no—
805C22×C3—122no—
806C22×C3—188no—
807C22×C3—184no—
808C22×C3—182no—
809C22×C3C22×D3214yes—
810C22×C3C22×D3212yes—
811C22×C3C22×D3212yes—
812C22×C3C22×D3211yescharacteristic
813C2×D3—22no—
814C2×D3—38no—
815C2×D3—34no—
816C2×D3—34no—
817C2×D3—34no—
818C2×D3—34no—
819C2×D3—62no—
820C2×D3—64no—
821C2×D3—64no—
822C2×D3—62no—
823C2×D3—616no—
824C2×D3—64no—
825C2×D3—64no—
826C2×D3—64no—
827C2×D3—94no—
828C2×D3—92no—
829C2×D3—128no—
830C2×D3—122no—
831C2×D3—124no—
832C2×D3—184no—
833C2×D3—182no—
834C2×D3—188no—
835C2×D3—1816no—
836C2×D3—1816no—
837C2×D3—188no—
838C2×D3—184no—
839C2×D3—182no—
840C2×D3—362no—
841C2×D3—368no—
842C2×D3—362no—
843C2×D3—364no—
844C2×D3—722no—
845C2×D3C22×D3212yes—
846C3×C4—34no—
847C3×C4—34no—
848C3×C4—34no—
849C3×C4—34no—
850C3×C4—34no—
851C3×C4—64no—
852C3×C4—64no—
853C3×C4—62no—
854C3×C4—94no—
855Dic3—34no—
856Dic3—34no—
857Dic3—64no—
858Dic3—94no—
859Dic3—92no—
860Dic3—184no—
861Dic3—182no—
862Dic3—362no—
863Dic3C22×D3212yes—
864Dic3C22×D3214yes—
865Dic3C22×D3214yes—
866C32—22no—
867C32—21no—
868C32—41no—
869C32C22×#23511yescharacteristic, complemented
870C32C2×D3×#4112yescomplemented
871C23—31no—
872C23—91no—
873C23—94no—
874C23—91no—
875C23—92no—
876C23—184no—
877C23—274no—
878C23—274no—
879C23—271no—
880C23—544no—
881C23—544no—
882C23D3311yescharacteristic
883Q8—98no—
884Q8—278no—
885D4—34no—
886D4—98no—
887D4—98no—
888D4—278no—
889D4—274no—
890D4—278no—
891D4—274no—
892D4—274no—
893C2×C4—38no—
894C2×C4—32no—
895C2×C4—32no—
896C2×C4—31no—
897C2×C4—94no—
898C2×C4—94no—
899C2×C4—98no—
900C2×C4—98no—
901C2×C4—98no—
902C2×C4—92no—
903C2×C4—278no—
904C2×C4—274no—
905C2×C4—278no—
906C2×C4—274no—
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—82no—
920C2×C3—94no—
921C2×C3—122no—
922C2×C3—184no—
923C2×C3—182no—
924C2×C3D3×#23514yescomplemented
925C2×C3#6431212yescomplemented
926C2×C3C23×D3212yes—
927C2×C3C23×D3211yescharacteristic
928D3—22no—
929D3—38no—
930D3—64no—
931D3—64no—
932D3—64no—
933D3—64no—
934D3—122no—
935D3—124no—
936D3—184no—
937D3—182no—
938D3—362no—
939D3—364no—
940D3—722no—
941C22—22no—
942C22—32no—
943C22—62no—
944C22—94no—
945C22—92no—
946C22—92no—
947C22—94no—
948C22—188no—
949C22—182no—
950C22—184no—
951C22—272no—
952C22—548no—
953C22—548no—
954C22—542no—
955C22C2×D3312yes—
956C22C2×D3311yescharacteristic
957C4—34no—
958C4—34no—
959C4—32no—
960C4—94no—
961C4—272no—
962C3—21no—
963C3—22no—
964C3—41no—
965C3C2×D3×#23512yescomplemented
966C3C2×#6431211yescharacteristic, complemented
967C2—22no—
968C2—62no—
969C2—94no—
970C2—182no—
971C2—184no—
972C2—542no—
973C2#1172441012yesdirect 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. C2×#89049C2semidirect
2. C2×C3⋊D3×#67C2semidirect
3. C2×#89031C2semidirect
4. C22×C3×#624C2semidirect
5. C2×C3×#3804C2semidirect
6. C2×#88965C2semidirect
7. C2×#88960C2semidirect
8. C2×#88957C2semidirect
9. C2×#88955C2semidirect
10. C2×#88949C2semidirect
11. #11724410C2direct (N × H)
12. C2×D3×#624C2semidirect
18. C2×#6312C22semidirect
19. C2×C3×#638C22semidirect
20. C2×C32×#67C22semidirect
21. C22×C32×Dic3C22semidirect
22. #89049C22semidirect
23. C2×#6295C22semidirect
25. C3⋊D3×#67C22semidirect
26. C2×#6293C22semidirect
27. C2×#6292C22semidirect
28. C2×#6292C22semidirect
29. C2×#6290C22semidirect
30. C2×#6289C22semidirect
31. #89031C22semidirect
33. C2×Dic3×C3⋊D3C22semidirect
34. C2×C3×#627C22semidirect
35. C2×C3×#626C22semidirect
38. C2×C3×#624C22semidirect
39. C2×C3×#624C22semidirect
40. C2×C3×#624C22semidirect
41. C3×#3804C22semidirect
42. C2×C3×D3×Dic3C22semidirect
43. #88965C22semidirect
44. #88960C22semidirect
45. #88957C22semidirect
46. #88955C22semidirect
47. #88949C22semidirect
48. D3×#624C22semidirect
60. C22×#624D3semidirect
65. C2×#3804D3semidirect
91. #6312C23semidirect
93. C3×#638C23semidirect
95. C32×#67C23semidirect
99. C2×C32×Dic3C23semidirect
100. #6295C23semidirect
102. #6293C23semidirect
103. #6292C23semidirect
104. #6292C23semidirect
105. #6290C23semidirect
106. #6289C23semidirect
108. Dic3×C3⋊D3C23semidirect
109. C3×#627C23semidirect
110. C3×#626C23semidirect
113. C3×#624C23semidirect
114. C3×#624C23semidirect
115. C3×D3×Dic3C23semidirect
134. C2×#638C2×D3semidirect
148. C2×C3×#67C2×D3semidirect
151. C22×C3×Dic3C2×D3semidirect
152. C22×C3×Dic3C2×D3semidirect
174. C2×#627C2×D3semidirect
182. C2×#626C2×D3semidirect
193. C2×#624C2×D3semidirect
194. C2×#624C2×D3semidirect
195. C2×#624C2×D3semidirect
200. #3804C2×D3semidirect
207. C2×D3×Dic3C2×D3semidirect
227. C2×C3×C3⋊D3#41semidirect
320. #638C22×D3semidirect
338. C3×#67C22×D3semidirect
352. C2×C3×Dic3C22×D3semidirect
353. C2×C3×Dic3C22×D3semidirect
367. #627C22×D3semidirect
375. #626C22×D3semidirect
385. #624C22×D3semidirect
386. #624C22×D3semidirect
393. D3×Dic3C22×D3semidirect
396. C2×C33C2×#41semidirect
401. C3×C3⋊D3C2×#41semidirect
444. C2×#67D32semidirect
449. C22×Dic3D32semidirect
535. C2×C3⋊D3#235semidirect
595. C33C22×#41semidirect
673. #67C2×D32semidirect
689. C2×Dic3C2×D32semidirect
732. C2×C32C2×#235semidirect
733. C2×C32D3×#41semidirect
743. C3⋊D3C2×#235semidirect
869. C32C22×#235semidirect
870. C32C2×D3×#41semidirect
924. C2×C3D3×#235semidirect
925. C2×C3#64312semidirect
965. C3C2×D3×#235semidirect
966. C3C2×#64312semidirect
973. C2#11724410direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#890492
C2×C3⋊D3×#672
C2×#890312
C22×C3×#6242
C2×C3×#38042
C2×#889652
C2×#889602
C2×#889572
C2×#889552
C2×#889492
#117244102
C2×D3×#6242
C2×#643123
C2×D3×#2353