Finite Group Databasebeta

← C2×#11724416 #13181323

Subgroups — C2×#11724416 #13181323

Order 1728.

4282 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6295C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×#67C212yesmaximal, complemented
3C2×#89028C211yesmaximal, characteristic, complemented
4C2×C3×#3811C212yesmaximal, complemented
5C2×C3×#3805C211yesmaximal, characteristic, complemented
6C2×#88965C211yesmaximal, characteristic, complemented
7C2×#88964C211yesmaximal, characteristic, complemented
8C2×#88960C212yesmaximal, complemented
9C2×#88954C211yesmaximal, characteristic, complemented
10C2×D3×#626C212yesmaximal, complemented
11#11724416C2116yesmaximal, direct product factor
12C2×D3×#625C211yesmaximal, characteristic, complemented
13C2×#64314—32nomaximal
14C2×#64313—31nomaximal
15C23×C3×C3⋊D3C2212yescomplemented
16C22×D3×C3⋊D3C2212yescomplemented
17C22×C3×D32C2212yescomplemented
18C2×#6312C2211yescharacteristic, complemented
19C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
20C2×C32×#67C2212yescomplemented
21C2×C32×#67C2211yescharacteristic, complemented
22C2×#6295C2211yescharacteristic, complemented
23C2×#6295C2212yescomplemented
24C2×#6295C2211yescharacteristic, complemented
25C2×#6295C2218yescomplemented
26C3⋊D3×#67C22116yescomplemented
27C2×#6293C2211yescharacteristic, complemented
28C2×#6292C2212yescomplemented
29C2×#6291C2211yescharacteristic, complemented
30C2×#6290C2212yescomplemented
31C2×#6289C2211yescharacteristic, complemented
32C2×Dic3×C3⋊D3C2212yescomplemented
33#89028C2218yescomplemented
34C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
35C3×#3811C22116yescomplemented
36C2×C3×#627C2211yescharacteristic, complemented
37C2×C3×#626C2212yescomplemented
38C2×C3×#626C2212yescomplemented
39C2×C3×#625C2211yescharacteristic, complemented
40C2×C3×#624C2212yescomplemented
41C3×#3805C2218yescomplemented
42C2×C3×D3×Dic3C2212yescomplemented
43#88965C2218yescomplemented
44#88964C2218yescomplemented
45#88960C22116yescomplemented
46#88954C2218yescomplemented
47D3×#626C22116yescomplemented
48D3×#625C2218yescomplemented
49C2×#3830—31no—
50C2×D4×C3⋊D3—32no—
51C2×C3×#237—32no—
52C2×C3×D3×D4—32no—
53C2×C3×D3×D4—32no—
54C2×#3811—32no—
55C2×#3811D312yescomplemented
56C2×D3×#67—32no—
57C2×D3×#67—32no—
58C2×D3×#67—32no—
59C2×D3×#67—32no—
60C2×D3×#67—62no—
61C22×#626—32no—
62C22×#626—32no—
63C22×#625—31no—
64C22×#625—31no—
65C2×#3805—31no—
66C2×#3805D311yescharacteristic, complemented
67C2×#3804—32no—
68C2×#3804—32no—
69C2×#3804—61no—
70#64314—332no—
71#64313—316no—
72C2×#3802—31no—
73C2×D3×D12—32no—
74C2×#3799—32no—
75C2×#3798—31no—
76C2×#3798—32no—
77C2×#3796—32no—
78C2×#3795—32no—
79C23×C33C2311yescharacteristic
80C22×C3⋊(C3⋊D3)C2311yescharacteristic
81C22×C3×C3⋊D3—44no—
82C22×C3×C3⋊D3C2312yes—
83C22×C3×C3⋊D3C2312yes—
84C22×C3×C3⋊D3C2318yescomplemented
85C22×C32×D3C2311yescharacteristic
86C22×C32×D3C2312yes—
87C2×D3×C3⋊D3—44no—
88C2×D3×C3⋊D3C2318yescomplemented
89C2×C3×D32—44no—
90C2×C3×D32C2318yescomplemented
91#6312C2314yescomplemented
92C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
93C2×C3×C3⋊Dic3C2311yescharacteristic
94C2×C3×C3⋊Dic3C2311yescharacteristic
95C2×C3×C3⋊Dic3C2314yescomplemented
96C32×#67C2318yescomplemented
97C32×#67C2314yescomplemented
98C2×C32×Dic3C2312yes—
99C2×C32×Dic3C2311yescharacteristic
100#6295C2314yescomplemented
101#6295C2318yescomplemented
102#6295C2314yescomplemented
103#6293C2314yescomplemented
104#6292C2318yescomplemented
105#6291C2314yescomplemented
106#6290C2318yescomplemented
107#6289C2314yescomplemented
108Dic3×C3⋊D3C2318yescomplemented
109D3×C3⋊Dic3C2314yescomplemented
110C3×#627C2314yescomplemented
111C3×#626C2318yescomplemented
112C3×#626C2318yescomplemented
113C3×#625C2314yescomplemented
114C3×#624C2318yescomplemented
115C3×D3×Dic3C2318yescomplemented
116C2×#1009—91no—
117C2×#1004—92no—
118C23×C3⋊D3—32no—
119C23×C3⋊D3C2×D312yescomplemented
120C23×C3×D3—32no—
121C23×C3×D3—32no—
122C23×C3×D3—32no—
123C23×C3×D3—32no—
124C23×C3×D3—62no—
125C22×D32—32no—
126C22×D32—32no—
127C22×D32—62no—
128C22×D32C2×D312yescomplemented
129C2×C32×D4—31no—
130C2×C32×D4—32no—
131C2×#638—32no—
132C2×#638—31no—
133C2×#638—32no—
134C2×#638—31no—
135C2×#638—61no—
136C2×#638—62no—
137C2×#638—121no—
138C22×C3⋊Dic3—31no—
139C22×C3⋊Dic3C2×D311yescharacteristic, complemented
140#3830—38no—
141D4×C3⋊D3—316no—
142C2×C4⋊(C3⋊D3)—32no—
143C2×C4×C3⋊D3—32no—
144C2×C4×C3⋊D3—31no—
145C2×#634—31no—
146C2×C3×#67—21no—
147C2×C3×#67—22no—
148C2×C3×#67—32no—
149C2×C3×#67—32no—
150C2×C3×#67—32no—
151C2×C3×#67C2×D312yescomplemented
152C2×C3×#67C2×D312yescomplemented
153C2×C3×#67C2×D312yescomplemented
154C22×C3×Dic3—32no—
155C22×C3×Dic3—32no—
156C22×C3×Dic3—61no—
157C3×#237—316no—
158C3×D3×D4—316no—
159C3×D3×D4—316no—
160C2×C3×D12—32no—
161C2×C3×D12—32no—
162C2×C3×C4×D3—32no—
163C2×C3×C4×D3—32no—
164C2×C3×C4×D3—32no—
165C2×C3×Dic6—32no—
166#3811—316no—
167#3811C2×D3116yescomplemented
168D3×#67—316no—
169D3×#67—316no—
170D3×#67—316no—
171D3×#67—316no—
172D3×#67—616no—
173C2×#627—32no—
174C2×#627—61no—
175C2×#627C2×D311yescharacteristic, complemented
176C2×#626—32no—
177C2×#626—32no—
178C2×#626—32no—
179C2×#626—32no—
180C2×#626—316no—
181C2×#626—32no—
182C2×#626—32no—
183C2×#626—32no—
184C2×#626—316no—
185C2×#626—62no—
186C2×#626—61no—
187C2×#626C2×D312yescomplemented
188C2×#626C2×D312yescomplemented
189C2×#625—32no—
190C2×#625—32no—
191C2×#625—32no—
192C2×#625—31no—
193C2×#625—31no—
194C2×#625—38no—
195C2×#625—38no—
196C2×#625—62no—
197C2×#625C2×D311yescharacteristic, complemented
198C2×#624—32no—
199C2×#624—61no—
200C2×#624C2×D312yescomplemented
201#3805—38no—
202#3805C2×D318yescomplemented
203#3804—316no—
204#3804—316no—
205#3804—68no—
206C2×D3×Dic3—32no—
207C2×D3×Dic3—32no—
208C2×D3×Dic3—32no—
209C2×D3×Dic3—62no—
210C2×D3×Dic3—61no—
211C2×D3×Dic3C2×D312yescomplemented
212#3802—38no—
213D3×D12—316no—
214#3799—316no—
215#3798—38no—
216#3798—316no—
217#3796—316no—
218#3795—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—24no—
226C2×C3×C3⋊D3—48no—
227C2×C3×C3⋊D3C2414yes—
228C2×C3×C3⋊D3C2414yes—
229C2×C32×D3—22no—
230C2×C32×D3—24no—
231C2×C32×D3C2414yes—
232C2×C32×D3C2412yes—
233D3×C3⋊D3—48no—
234C3×D32—48no—
235C3⋊(C3⋊Dic3)C2412yes—
236C3×C3⋊Dic3C2412yes—
237C3×C3⋊Dic3C2412yes—
238C32×Dic3C2414yes—
239C32×Dic3C2412yes—
240C2×C3×#41—91no—
241C22×C3×D4—92no—
242C22×#67—92no—
243C22×#67—92no—
244C22×#67—92no—
245C22×#67—92no—
246#1009—916no—
247C2×#239—91no—
248C2×#239—91no—
249#1004—932no—
250C2×#237—32no—
251C2×#237—92no—
252C2×#237—92no—
253C2×#237—92no—
254C2×#237—181no—
255C2×D3×D4—32no—
256C2×D3×D4—32no—
257C2×D3×D4—92no—
258C2×D3×D4—92no—
259C2×D3×D4—91no—
260C2×D3×D4—92no—
261C2×D3×D4—92no—
262C2×D3×D4—91no—
263C2×D3×D4—182no—
264C2×#235—92no—
265C2×#235—92no—
266C2×#235—92no—
267C2×#235—91no—
268C22×D12—92no—
269C22×D12—91no—
270C23×C32—22no—
271C23×C32—21no—
272C23×C32—31no—
273C23×C32—32no—
274C23×C32—41no—
275C23×C32C22×D311yescharacteristic
276C23×C32C22×D312yes—
277C22×C3⋊D3—31no—
278C22×C3⋊D3—32no—
279C22×C3⋊D3—38no—
280C22×C3⋊D3—44no—
281C22×C3⋊D3—62no—
282C22×C3⋊D3—61no—
283C22×C3⋊D3—121no—
284C22×C3⋊D3—124no—
285C22×C3⋊D3C22×D312yes—
286C22×C3⋊D3C22×D312yes—
287C22×C3⋊D3C22×D318yescomplemented
288C22×C3×D3—22no—
289C22×C3×D3—21no—
290C22×C3×D3—32no—
291C22×C3×D3—32no—
292C22×C3×D3—32no—
293C22×C3×D3—32no—
294C22×C3×D3—38no—
295C22×C3×D3—38no—
296C22×C3×D3—38no—
297C22×C3×D3—38no—
298C22×C3×D3—62no—
299C22×C3×D3—62no—
300C22×C3×D3—68no—
301C22×C3×D3—124no—
302C22×C3×D3—124no—
303C22×C3×D3—124no—
304C22×C3×D3—124no—
305C22×C3×D3—128no—
306C22×C3×D3C22×D312yes—
307C22×C3×D3C22×D312yes—
308C22×C3×D3C22×D312yes—
309C2×D32—38no—
310C2×D32—38no—
311C2×D32—44no—
312C2×D32—68no—
313C2×D32—124no—
314C2×D32—124no—
315C2×D32—128no—
316C2×D32C22×D318yescomplemented
317C32×D4—34no—
318C32×D4—38no—
319C2×C32×C4—32no—
320C2×C32×C4—31no—
321#638—38no—
322#638—34no—
323#638—38no—
324#638—34no—
325#638—64no—
326#638—68no—
327#638—124no—
328C2×C3⋊Dic3—31no—
329C2×C3⋊Dic3—32no—
330C2×C3⋊Dic3—34no—
331C2×C3⋊Dic3—62no—
332C2×C3⋊Dic3—61no—
333C2×C3⋊Dic3—121no—
334C2×C3⋊Dic3C22×D311yescharacteristic
335C2×C3⋊Dic3C22×D311yescharacteristic
336C2×C3⋊Dic3C22×D314yescomplemented
337C4⋊(C3⋊D3)—38no—
338C4×C3⋊D3—38no—
339C4×C3⋊D3—34no—
340#634—34no—
341C3×#67—24no—
342C3×#67—28no—
343C3×#67—38no—
344C3×#67—38no—
345C3×#67—38no—
346C3×#67C22×D318yescomplemented
347C3×#67C22×D318yescomplemented
348C3×#67C22×D318yescomplemented
349C2×C3×Dic3—22no—
350C2×C3×Dic3—21no—
351C2×C3×Dic3—32no—
352C2×C3×Dic3—32no—
353C2×C3×Dic3—38no—
354C2×C3×Dic3—38no—
355C2×C3×Dic3—61no—
356C2×C3×Dic3—61no—
357C2×C3×Dic3—64no—
358C2×C3×Dic3C22×D312yes—
359C2×C3×Dic3C22×D312yes—
360C2×C3×Dic3C22×D312yes—
361C3×D12—38no—
362C3×D12—38no—
363C3×C4×D3—38no—
364C3×C4×D3—38no—
365C3×C4×D3—38no—
366C3×Dic6—38no—
367#627—38no—
368#627—64no—
369#627C22×D314yescomplemented
370#626—38no—
371#626—38no—
372#626—38no—
373#626—38no—
374#626—38no—
375#626—38no—
376#626—38no—
377#626—64no—
378#626—68no—
379#626C22×D318yescomplemented
380#626C22×D318yescomplemented
381#625—38no—
382#625—38no—
383#625—38no—
384#625—34no—
385#625—34no—
386#625—68no—
387#625C22×D314yescomplemented
388#624—38no—
389#624—64no—
390#624C22×D318yescomplemented
391D3×Dic3—38no—
392D3×Dic3—38no—
393D3×Dic3—38no—
394D3×Dic3—64no—
395D3×Dic3—68no—
396D3×Dic3C22×D318yescomplemented
397C2×H(5,𝔽2)—271noSylow
398C2×C33—22no—
399C2×C33H(5,𝔽2)12yescomplemented
400C2×C33C2511yescharacteristic
401C3⋊(C3⋊D3)—22no—
402C3×C3⋊D3—24no—
403C3×C3⋊D3—24no—
404C32×D3—22no—
405C32×D3—24no—
406C24×C3—92no—
407C24×C3—92no—
408C23×D3—32no—
409C23×D3—32no—
410C23×D3—32no—
411C23×D3—32no—
412C23×D3—62no—
413C23×D3—92no—
414C23×D3—92no—
415C23×D3—92no—
416C23×D3—182no—
417C3×#41—98no—
418C2×C3×Q8—91no—
419C2×C3×D4—32no—
420C2×C3×D4—32no—
421C2×C3×D4—32no—
422C2×C3×D4—62no—
423C2×C3×D4—61no—
424C2×C3×D4—92no—
425C2×C3×D4—92no—
426C2×C3×D4—916no—
427C2×C3×D4—91no—
428C22×C3×C4—92no—
429C22×C3×C4—92no—
430C22×C3×C4—91no—
431C2×#67—32no—
432C2×#67—32no—
433C2×#67—32no—
434C2×#67—916no—
435C2×#67—92no—
436C2×#67—92no—
437C2×#67—92no—
438C2×#67—92no—
439C2×#67—916no—
440C2×#67—92no—
441C2×#67—916no—
442C2×#67—92no—
443C2×#67—92no—
444C2×#67—91no—
445C2×#67—92no—
446C2×#67—92no—
447C2×#67—916no—
448C2×#67—92no—
449C2×#67—181no—
450C2×#67—182no—
451C2×#67—182no—
452C2×#67—181no—
453C2×#67—361no—
454C2×#67D3211yescharacteristic, complemented
455C2×#67D3212yescomplemented
456C22×Dic3—32no—
457C22×Dic3—32no—
458C22×Dic3—61no—
459C22×Dic3—92no—
460C22×Dic3—92no—
461C22×Dic3—181no—
462#239—98no—
463#239—98no—
464#237—316no—
465#237—916no—
466#237—916no—
467#237—916no—
468#237—188no—
469D3×D4—316no—
470D3×D4—316no—
471D3×D4—916no—
472D3×D4—916no—
473D3×D4—98no—
474D3×D4—916no—
475D3×D4—916no—
476D3×D4—98no—
477D3×D4—1816no—
478#235—916no—
479#235—916no—
480#235—916no—
481#235—98no—
482C2×D12—32no—
483C2×D12—32no—
484C2×D12—916no—
485C2×D12—92no—
486C2×D12—92no—
487C2×D12—92no—
488C2×D12—91no—
489C2×D12—91no—
490C2×D12—98no—
491C2×D12—91no—
492C2×D12—182no—
493C2×C4×D3—32no—
494C2×C4×D3—32no—
495C2×C4×D3—32no—
496C2×C4×D3—92no—
497C2×C4×D3—92no—
498C2×C4×D3—92no—
499C2×C4×D3—91no—
500C2×C4×D3—91no—
501C2×C4×D3—181no—
502C2×C4×D3—182no—
503C2×Dic6—32no—
504C2×Dic6—92no—
505C2×Dic6—91no—
506C2×Dic6—181no—
507C22×C32—24no—
508C22×C32—22no—
509C22×C32—21no—
510C22×C32—22no—
511C22×C32—22no—
512C22×C32—24no—
513C22×C32—34no—
514C22×C32—32no—
515C22×C32—41no—
516C22×C32—42no—
517C22×C32—44no—
518C22×C32—42no—
519C22×C32—64no—
520C22×C32—62no—
521C22×C32—82no—
522C22×C32C23×D314yes—
523C22×C32C23×D312yes—
524C22×C32C23×D312yes—
525C22×C32C23×D311yescharacteristic
526C2×C3⋊D3—24no—
527C2×C3⋊D3—24no—
528C2×C3⋊D3—34no—
529C2×C3⋊D3—32no—
530C2×C3⋊D3—48no—
531C2×C3⋊D3—62no—
532C2×C3⋊D3—64no—
533C2×C3⋊D3—64no—
534C2×C3⋊D3—62no—
535C2×C3⋊D3—122no—
536C2×C3⋊D3—124no—
537C2×C3⋊D3—122no—
538C2×C3⋊D3—128no—
539C2×C3⋊D3—242no—
540C2×C3⋊D3C23×D314yes—
541C2×C3⋊D3C23×D314yes—
542C2×C3×D3—24no—
543C2×C3×D3—24no—
544C2×C3×D3—24no—
545C2×C3×D3—22no—
546C2×C3×D3—24no—
547C2×C3×D3—34no—
548C2×C3×D3—34no—
549C2×C3×D3—34no—
550C2×C3×D3—34no—
551C2×C3×D3—44no—
552C2×C3×D3—42no—
553C2×C3×D3—64no—
554C2×C3×D3—64no—
555C2×C3×D3—68no—
556C2×C3×D3—64no—
557C2×C3×D3—64no—
558C2×C3×D3—64no—
559C2×C3×D3—64no—
560C2×C3×D3—124no—
561C2×C3×D3—128no—
562C2×C3×D3—128no—
563C2×C3×D3—128no—
564C2×C3×D3—128no—
565C2×C3×D3—1216no—
566C2×C3×D3C23×D314yes—
567C2×C3×D3C23×D314yes—
568C2×C3×D3C23×D314yes—
569D32—48no—
570D32—128no—
571D32—128no—
572D32—1216no—
573C32×C4—34no—
574C32×C4—32no—
575C3⋊Dic3—32no—
576C3⋊Dic3—34no—
577C3⋊Dic3—64no—
578C3⋊Dic3—62no—
579C3⋊Dic3—122no—
580C3⋊Dic3C23×D312yes—
581C3⋊Dic3C23×D312yes—
582C3×Dic3—24no—
583C3×Dic3—22no—
584C3×Dic3—34no—
585C3×Dic3—34no—
586C3×Dic3—62no—
587C3×Dic3—62no—
588C3×Dic3C23×D314yes—
589C3×Dic3C23×D314yes—
590C3×Dic3C23×D314yes—
591H(5,𝔽2)—2716no—
592C2×#41—91no—
593C2×#41—272no—
594C2×#41—271no—
595C2×#41—271no—
596C2×#41—271no—
597C22×D4—92no—
598C22×D4—272no—
599C22×D4—271no—
600C22×D4—272no—
601C22×D4—271no—
602C22×D4—271no—
603C33C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
604C23×C3—21no—
605C23×C3—22no—
606C23×C3—32no—
607C23×C3—32no—
608C23×C3—32no—
609C23×C3—41no—
610C23×C3—61no—
611C23×C3—62no—
612C23×C3—98no—
613C23×C3—92no—
614C23×C3—92no—
615C23×C3—98no—
616C23×C3—364no—
617C23×C3—364no—
618C23×C3C2×D3212yes—
619C23×C3C2×D3211yescharacteristic
620C22×D3—32no—
621C22×D3—32no—
622C22×D3—32no—
623C22×D3—32no—
624C22×D3—38no—
625C22×D3—38no—
626C22×D3—38no—
627C22×D3—38no—
628C22×D3—62no—
629C22×D3—62no—
630C22×D3—68no—
631C22×D3—98no—
632C22×D3—98no—
633C22×D3—91no—
634C22×D3—92no—
635C22×D3—98no—
636C22×D3—124no—
637C22×D3—124no—
638C22×D3—124no—
639C22×D3—124no—
640C22×D3—128no—
641C22×D3—188no—
642C22×D3—181no—
643C22×D3—182no—
644C22×D3—361no—
645C22×D3—364no—
646C22×D3—364no—
647C22×D3—364no—
648C22×D3—368no—
649C22×D3C2×D3212yes—
650C22×D3C2×D3211yescharacteristic
651C3×Q8—94no—
652C3×D4—38no—
653C3×D4—38no—
654C3×D4—38no—
655C3×D4—68no—
656C3×D4—64no—
657C3×D4—98no—
658C3×D4—98no—
659C3×D4—94no—
660C2×C3×C4—32no—
661C2×C3×C4—32no—
662C2×C3×C4—32no—
663C2×C3×C4—61no—
664C2×C3×C4—62no—
665C2×C3×C4—98no—
666C2×C3×C4—98no—
667C2×C3×C4—91no—
668C2×C3×C4—91no—
669C2×C3×C4—94no—
670#67—38no—
671#67—38no—
672#67—38no—
673#67—98no—
674#67—98no—
675#67—98no—
676#67—98no—
677#67—98no—
678#67—98no—
679#67—98no—
680#67—94no—
681#67—98no—
682#67—98no—
683#67—98no—
684#67—184no—
685#67—188no—
686#67—188no—
687#67—184no—
688#67—364no—
689#67C2×D3214yescomplemented
690#67C2×D3218yescomplemented
691C2×Dic3—32no—
692C2×Dic3—32no—
693C2×Dic3—38no—
694C2×Dic3—38no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—64no—
698C2×Dic3—98no—
699C2×Dic3—91no—
700C2×Dic3—92no—
701C2×Dic3—98no—
702C2×Dic3—184no—
703C2×Dic3—181no—
704C2×Dic3—182no—
705C2×Dic3—361no—
706C2×Dic3C2×D3212yes—
707C2×Dic3C2×D3211yescharacteristic
708D12—38no—
709D12—38no—
710D12—98no—
711D12—98no—
712D12—98no—
713D12—94no—
714D12—94no—
715D12—94no—
716D12—188no—
717C4×D3—38no—
718C4×D3—38no—
719C4×D3—38no—
720C4×D3—98no—
721C4×D3—98no—
722C4×D3—98no—
723C4×D3—94no—
724C4×D3—94no—
725C4×D3—184no—
726C4×D3—188no—
727Dic6—38no—
728Dic6—98no—
729Dic6—94no—
730Dic6—184no—
731C2×C32—24no—
732C2×C32—22no—
733C2×C32—22no—
734C2×C32—24no—
735C2×C32—21no—
736C2×C32—22no—
737C2×C32—42no—
738C2×C32—41no—
739C2×C32—44no—
740C2×C32—42no—
741C2×C32—64no—
742C2×C32—62no—
743C2×C32—82no—
744C2×C32#100414yescomplemented
745C2×C32#100912yescomplemented
746C2×C32C24×D312yes—
747C2×C32C24×D311yescharacteristic
748C3⋊D3—24no—
749C3⋊D3—24no—
750C3⋊D3—64no—
751C3⋊D3—62no—
752C3⋊D3—124no—
753C3⋊D3—122no—
754C3⋊D3—242no—
755C3×D3—24no—
756C3×D3—24no—
757C3×D3—24no—
758C3×D3—44no—
759C3×D3—42no—
760C3×D3—68no—
761C3×D3—64no—
762C3×D3—64no—
763C3×D3—64no—
764C3×D3—64no—
765C3×D3—124no—
766C24—92no—
767C24—92no—
768C24—272no—
769#41—98no—
770#41—2716no—
771#41—278no—
772#41—278no—
773#41—278no—
774C2×Q8—91no—
775C2×Q8—271no—
776C2×D4—31no—
777C2×D4—32no—
778C2×D4—92no—
779C2×D4—92no—
780C2×D4—916no—
781C2×D4—91no—
782C2×D4—272no—
783C2×D4—2716no—
784C2×D4—271no—
785C2×D4—272no—
786C2×D4—271no—
787C2×D4—271no—
788C2×D4—278no—
789C2×D4—2716no—
790C2×D4—278no—
791C2×D4—278no—
792C2×D4—272no—
793C2×D4—271no—
794C22×C4—92no—
795C22×C4—92no—
796C22×C4—91no—
797C22×C4—271no—
798C22×C4—272no—
799C22×C4—271no—
800C22×C3—22no—
801C22×C3—24no—
802C22×C3—22no—
803C22×C3—24no—
804C22×C3—21no—
805C22×C3—22no—
806C22×C3—34no—
807C22×C3—34no—
808C22×C3—34no—
809C22×C3—44no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—41no—
813C22×C3—62no—
814C22×C3—64no—
815C22×C3—64no—
816C22×C3—64no—
817C22×C3—64no—
818C22×C3—82no—
819C22×C3—94no—
820C22×C3—94no—
821C22×C3—124no—
822C22×C3—122no—
823C22×C3—184no—
824C22×C3—184no—
825C22×C3—368no—
826C22×C3—368no—
827C22×C3C22×D3214yes—
828C22×C3C22×D3212yes—
829C22×C3C22×D3211yescharacteristic
830C22×C3C22×D3212yes—
831C2×D3—22no—
832C2×D3—24no—
833C2×D3—34no—
834C2×D3—34no—
835C2×D3—34no—
836C2×D3—34no—
837C2×D3—64no—
838C2×D3—64no—
839C2×D3—68no—
840C2×D3—64no—
841C2×D3—64no—
842C2×D3—64no—
843C2×D3—64no—
844C2×D3—92no—
845C2×D3—94no—
846C2×D3—124no—
847C2×D3—128no—
848C2×D3—128no—
849C2×D3—128no—
850C2×D3—128no—
851C2×D3—1216no—
852C2×D3—182no—
853C2×D3—184no—
854C2×D3—182no—
855C2×D3—184no—
856C2×D3—362no—
857C2×D3—364no—
858C2×D3—362no—
859C2×D3—368no—
860C2×D3—368no—
861C2×D3—368no—
862C2×D3—3616no—
863C2×D3—722no—
864C2×D3C22×D3214yes—
865C2×D3C22×D3212yes—
866C3×C4—34no—
867C3×C4—34no—
868C3×C4—34no—
869C3×C4—62no—
870C3×C4—64no—
871C3×C4—92no—
872C3×C4—92no—
873Dic3—34no—
874Dic3—34no—
875Dic3—62no—
876Dic3—62no—
877Dic3—92no—
878Dic3—94no—
879Dic3—182no—
880Dic3—184no—
881Dic3—362no—
882Dic3C22×D3214yes—
883Dic3C22×D3212yes—
884C32—21no—
885C32—22no—
886C32—41no—
887C32C2×#100412yescomplemented
888C32C2×#100911yescharacteristic, complemented
889C23—32no—
890C23—31no—
891C23—98no—
892C23—92no—
893C23—92no—
894C23—98no—
895C23—278no—
896C23—271no—
897C23—364no—
898C23—364no—
899C23—1084no—
900C23D3311yescharacteristic
901Q8—94no—
902Q8—274no—
903D4—34no—
904D4—38no—
905D4—98no—
906D4—98no—
907D4—94no—
908D4—278no—
909D4—274no—
910D4—278no—
911D4—274no—
912D4—274no—
913D4—278no—
914D4—274no—
915C2×C4—31no—
916C2×C4—32no—
917C2×C4—98no—
918C2×C4—98no—
919C2×C4—94no—
920C2×C4—91no—
921C2×C4—91no—
922C2×C4—274no—
923C2×C4—278no—
924C2×C4—274no—
925C2×C4—271no—
926C2×C3—22no—
927C2×C3—24no—
928C2×C3—24no—
929C2×C3—22no—
930C2×C3—21no—
931C2×C3—22no—
932C2×C3—44no—
933C2×C3—42no—
934C2×C3—42no—
935C2×C3—41no—
936C2×C3—64no—
937C2×C3—64no—
938C2×C3—64no—
939C2×C3—82no—
940C2×C3—124no—
941C2×C3—122no—
942C2×C3—184no—
943C2×C3—184no—
944C2×C3#6431312yescomplemented
945C2×C3#6431414yescomplemented
946C2×C3C23×D3211yescharacteristic
947C2×C3C23×D3212yes—
948D3—22no—
949D3—24no—
950D3—68no—
951D3—64no—
952D3—64no—
953D3—64no—
954D3—64no—
955D3—124no—
956D3—182no—
957D3—184no—
958D3—364no—
959D3—362no—
960D3—722no—
961C22—22no—
962C22—34no—
963C22—32no—
964C22—62no—
965C22—64no—
966C22—94no—
967C22—94no—
968C22—184no—
969C22—184no—
970C22—272no—
971C22—368no—
972C22—368no—
973C22—542no—
974C22—1088no—
975C22C2×D3312yes—
976C22C2×D3311yescharacteristic
977C4—32no—
978C4—34no—
979C4—92no—
980C4—92no—
981C4—272no—
982C3—22no—
983C3—21no—
984C3—41no—
985C3C2×#6431311yescharacteristic, complemented
986C3C2×#6431412yescomplemented
987C2—22no—
988C2—62no—
989C2—64no—
990C2—184no—
991C2—184no—
992C2—542no—
993C2#1172441612yesdirect product factor
994C2C22×D3311yescharacteristic
subgroupG/H
centerC22C2×D33
commutator, cosocleC2×C33C25
FrattiniC2C22×D33
FittingC23×C33C23
socleC22×C33C24
hypercenterC23D33
hypocenterC33C2×H(5,𝔽2)
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×#6295C2semidirect
2. C2×C3⋊D3×#67C2semidirect
3. C2×#89028C2semidirect
4. C2×C3×#3811C2semidirect
5. C2×C3×#3805C2semidirect
6. C2×#88965C2semidirect
7. C2×#88964C2semidirect
8. C2×#88960C2semidirect
9. C2×#88954C2semidirect
10. C2×D3×#626C2semidirect
11. #11724416C2direct (N × H)
12. C2×D3×#625C2semidirect
15. C23×C3×C3⋊D3C22semidirect
16. C22×D3×C3⋊D3C22semidirect
17. C22×C3×D32C22semidirect
18. C2×#6312C22semidirect
19. C22×C3×C3⋊Dic3C22semidirect
20. C2×C32×#67C22semidirect
21. C2×C32×#67C22semidirect
22. C2×#6295C22semidirect
23. C2×#6295C22semidirect
24. C2×#6295C22semidirect
25. C2×#6295C22semidirect
26. C3⋊D3×#67C22semidirect
27. C2×#6293C22semidirect
28. C2×#6292C22semidirect
29. C2×#6291C22semidirect
30. C2×#6290C22semidirect
31. C2×#6289C22semidirect
32. C2×Dic3×C3⋊D3C22semidirect
33. #89028C22semidirect
34. C2×D3×C3⋊Dic3C22semidirect
35. C3×#3811C22semidirect
36. C2×C3×#627C22semidirect
37. C2×C3×#626C22semidirect
38. C2×C3×#626C22semidirect
39. C2×C3×#625C22semidirect
40. C2×C3×#624C22semidirect
41. C3×#3805C22semidirect
42. C2×C3×D3×Dic3C22semidirect
43. #88965C22semidirect
44. #88964C22semidirect
45. #88960C22semidirect
46. #88954C22semidirect
47. D3×#626C22semidirect
48. D3×#625C22semidirect
55. C2×#3811D3semidirect
66. C2×#3805D3semidirect
84. C22×C3×C3⋊D3C23semidirect
88. C2×D3×C3⋊D3C23semidirect
90. C2×C3×D32C23semidirect
91. #6312C23semidirect
95. C2×C3×C3⋊Dic3C23semidirect
96. C32×#67C23semidirect
97. C32×#67C23semidirect
100. #6295C23semidirect
101. #6295C23semidirect
102. #6295C23semidirect
103. #6293C23semidirect
104. #6292C23semidirect
105. #6291C23semidirect
106. #6290C23semidirect
107. #6289C23semidirect
108. Dic3×C3⋊D3C23semidirect
109. D3×C3⋊Dic3C23semidirect
110. C3×#627C23semidirect
111. C3×#626C23semidirect
112. C3×#626C23semidirect
113. C3×#625C23semidirect
114. C3×#624C23semidirect
115. C3×D3×Dic3C23semidirect
119. C23×C3⋊D3C2×D3semidirect
128. C22×D32C2×D3semidirect
139. C22×C3⋊Dic3C2×D3semidirect
151. C2×C3×#67C2×D3semidirect
152. C2×C3×#67C2×D3semidirect
153. C2×C3×#67C2×D3semidirect
167. #3811C2×D3semidirect
175. C2×#627C2×D3semidirect
187. C2×#626C2×D3semidirect
188. C2×#626C2×D3semidirect
197. C2×#625C2×D3semidirect
200. C2×#624C2×D3semidirect
202. #3805C2×D3semidirect
211. C2×D3×Dic3C2×D3semidirect
287. C22×C3⋊D3C22×D3semidirect
316. C2×D32C22×D3semidirect
336. C2×C3⋊Dic3C22×D3semidirect
346. C3×#67C22×D3semidirect
347. C3×#67C22×D3semidirect
348. C3×#67C22×D3semidirect
369. #627C22×D3semidirect
379. #626C22×D3semidirect
380. #626C22×D3semidirect
387. #625C22×D3semidirect
390. #624C22×D3semidirect
396. D3×Dic3C22×D3semidirect
399. C2×C33H(5,𝔽2)semidirect
454. C2×#67D32semidirect
455. C2×#67D32semidirect
603. C33C2×H(5,𝔽2)semidirect
689. #67C2×D32semidirect
690. #67C2×D32semidirect
744. C2×C32#1004semidirect
745. C2×C32#1009semidirect
887. C32C2×#1004semidirect
888. C32C2×#1009semidirect
944. C2×C3#64313semidirect
945. C2×C3#64314semidirect
985. C3C2×#64313semidirect
986. C3C2×#64314semidirect
993. C2#11724416direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#62952
C2×C3⋊D3×#672
C2×#890282
C2×C3×#38112
C2×C3×#38052
C2×#889652
C2×#889642
C2×#889602
C2×#889542
C2×D3×#6262
#117244162
C2×D3×#6252
C2×#643143
C2×#643133