Finite Group Databasebeta

← C2×#11724419 #13181326

Subgroups — C2×#11724419 #13181326

Order 1728.

4434 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89046C211yesmaximal, characteristic, complemented
2C2×#89039C212yesmaximal, complemented
3C22×#6291C211yesmaximal, characteristic, complemented
4C2×C3×D3×#67C212yesmaximal, complemented
5C2×C3×#3805C211yesmaximal, characteristic, complemented
6C2×#88962C212yesmaximal, complemented
7C2×#88959C212yesmaximal, complemented
8C2×#88952C212yesmaximal, complemented
9#11724419C2116yesmaximal, direct product factor
10C2×D3×#626C212yesmaximal, complemented
11C2×#64330—31nomaximal
12C2×#64314—32nomaximal
13C23×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
14C23×C32×D3C2211yescharacteristic, complemented
15C22×D3×C3⋊D3C2212yescomplemented
16C22×C3×D32C2212yescomplemented
17C2×C3×#638C2212yescomplemented
18C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
19C2×C32×#67C2212yescomplemented
20C2×#6296C2211yescharacteristic, complemented
21C2×#6295C2211yescharacteristic, complemented
22#89046C2218yescomplemented
23C2×#6294C2212yescomplemented
24#89039C22116yescomplemented
25C2×#6292C2212yescomplemented
26C2×#6291C2212yescomplemented
27C2×#6291C2212yescomplemented
28C2×#6291C2212yescomplemented
29C2×#6291C2218yescomplemented
30C2×#6289C2212yescomplemented
31C3×D3×#67C22116yescomplemented
32C2×C3×#627C2211yescharacteristic, complemented
33C2×C3×#626C2212yescomplemented
34C2×C3×#625C2211yescharacteristic, complemented
35C2×C3×#625C2212yescomplemented
36C3×#3805C2218yescomplemented
37C2×C3×D3×Dic3C2212yescomplemented
38C2×C3×D3×Dic3C2212yescomplemented
39#88962C22116yescomplemented
40#88959C22116yescomplemented
41#88952C22116yescomplemented
42D3×#626C22116yescomplemented
43C22×#638—31no—
44C2×D4×C3⋊D3—32no—
45C22×C3×#67—32no—
46C2×C3×#237—32no—
47C2×C3×D3×D4—32no—
48#64330—316no—
49C2×#3811—32no—
50C2×#3811—32no—
51C2×#3811—32no—
52C2×#3811—62no—
53C2×D3×#67—32no—
54C2×D3×#67—32no—
55C2×D3×#67—32no—
56C2×D3×#67D312yescomplemented
57C22×#626—32no—
58C22×#626—32no—
59C22×#626—61no—
60C2×#3805—31no—
61C2×#3805D311yescharacteristic, complemented
62C2×#3804—32no—
63C2×#3804—32no—
64C2×#3804—32no—
65C2×#3804—32no—
66#64314—332no—
67C2×D3×D12—32no—
68C2×#3799—32no—
69C2×#3798—32no—
70C2×#3796—32no—
71C23×C33C2311yescharacteristic
72C22×C3⋊(C3⋊D3)—42no—
73C22×C3⋊(C3⋊D3)C2312yes—
74C22×C3⋊(C3⋊D3)C2314yescomplemented
75C22×C3×C3⋊D3C2312yes—
76C22×C32×D3—42no—
77C22×C32×D3C2312yes—
78C22×C32×D3C2312yes—
79C22×C32×D3C2314yescomplemented
80C2×D3×C3⋊D3—44no—
81C2×D3×C3⋊D3C2318yescomplemented
82C2×C3×D32—44no—
83C2×C3×D32C2318yescomplemented
84C3×#638C2318yescomplemented
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C2×C3×C3⋊Dic3C2312yes—
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C2×C3×C3⋊Dic3C2314yescomplemented
89C32×#67C2318yescomplemented
90C2×C32×Dic3C2312yes—
91#6296C2314yescomplemented
92#6295C2314yescomplemented
93#6294C2318yescomplemented
94#6292C2318yescomplemented
95#6291C2318yescomplemented
96#6291C2318yescomplemented
97#6291C2318yescomplemented
98#6289C2318yescomplemented
99C3×#627C2314yescomplemented
100C3×#626C2318yescomplemented
101C3×#625C2314yescomplemented
102C3×#625C2318yescomplemented
103C3×D3×Dic3C2318yescomplemented
104C3×D3×Dic3C2318yescomplemented
105C2×#1009—91no—
106C2×#1004—92no—
107C24×C32—31no—
108C23×C3⋊D3—32no—
109C23×C3⋊D3—31no—
110C23×C3⋊D3—32no—
111C23×C3⋊D3—61no—
112C23×C3⋊D3—62no—
113C23×C3⋊D3—121no—
114C23×C3×D3—21no—
115C23×C3×D3—32no—
116C23×C3×D3—32no—
117C23×C3×D3C2×D312yescomplemented
118C22×D32—32no—
119C22×D32—32no—
120C22×D32—62no—
121C22×D32C2×D312yescomplemented
122C2×C32×D4—32no—
123C2×#638—32no—
124C2×#638—32no—
125C2×#638—32no—
126C2×#638—38no—
127C2×#638C2×D312yescomplemented
128C22×C3⋊Dic3C2×D311yescharacteristic, complemented
129D4×C3⋊D3—316no—
130C2×C4⋊(C3⋊D3)—32no—
131C2×C4×C3⋊D3—32no—
132C2×C3×#67—22no—
133C2×C3×#67—32no—
134C2×C3×#67—32no—
135C2×C3×#67—32no—
136C2×C3×#67—32no—
137C2×C3×#67—32no—
138C2×C3×#67—316no—
139C2×C3×#67—32no—
140C2×C3×#67—62no—
141C2×C3×#67C2×D312yescomplemented
142C2×C3×#67C2×D312yescomplemented
143C22×C3×Dic3—32no—
144C22×C3×Dic3—32no—
145C22×C3×Dic3—32no—
146C22×C3×Dic3—61no—
147C3×#237—316no—
148C3×D3×D4—316no—
149C2×C3×D12—32no—
150C2×C3×C4×D3—32no—
151C2×C3×C4×D3—32no—
152C2×C3×Dic6—32no—
153#3811—316no—
154#3811—316no—
155#3811—316no—
156#3811—616no—
157D3×#67—316no—
158D3×#67—316no—
159D3×#67—316no—
160D3×#67C2×D3116yescomplemented
161C2×#627—32no—
162C2×#627—31no—
163C2×#627C2×D311yescharacteristic, complemented
164C2×#626—32no—
165C2×#626—32no—
166C2×#626—32no—
167C2×#626—32no—
168C2×#626—32no—
169C2×#626—32no—
170C2×#626—32no—
171C2×#626—316no—
172C2×#626—32no—
173C2×#626—32no—
174C2×#626—316no—
175C2×#626—62no—
176C2×#626—62no—
177C2×#626—62no—
178C2×#626—68no—
179C2×#626—62no—
180C2×#626C2×D312yescomplemented
181C2×#625—31no—
182C2×#625C2×D312yescomplemented
183C2×#625C2×D311yescharacteristic, complemented
184C2×#624—32no—
185C2×#624—32no—
186C2×#624—32no—
187C2×#624—62no—
188#3805—38no—
189#3805C2×D318yescomplemented
190#3804—316no—
191#3804—316no—
192#3804—316no—
193#3804—316no—
194C2×D3×Dic3—32no—
195C2×D3×Dic3—32no—
196C2×D3×Dic3C2×D312yescomplemented
197C2×D3×Dic3C2×D312yescomplemented
198D3×D12—316no—
199#3799—316no—
200#3798—316no—
201#3796—316no—
202C22×C33—22no—
203C22×C33C2412yes—
204C22×C33C2411yescharacteristic
205C2×C3⋊(C3⋊D3)—24no—
206C2×C3⋊(C3⋊D3)—44no—
207C2×C3⋊(C3⋊D3)C2414yes—
208C2×C3×C3⋊D3—24no—
209C2×C3×C3⋊D3C2414yes—
210C2×C32×D3—24no—
211C2×C32×D3—24no—
212C2×C32×D3—44no—
213C2×C32×D3C2414yes—
214C2×C32×D3C2414yes—
215D3×C3⋊D3—48no—
216C3×D32—48no—
217C3×C3⋊Dic3C2412yes—
218C3×C3⋊Dic3C2414yes—
219C3×C3⋊Dic3C2412yes—
220C32×Dic3C2414yes—
221C2×C3×#41—91no—
222C22×C3×D4—92no—
223C22×#67—32no—
224C22×#67—92no—
225C22×#67—92no—
226C22×#67—92no—
227C22×#67—181no—
228#1009—916no—
229C2×#239—92no—
230#1004—932no—
231C2×#237—32no—
232C2×#237—92no—
233C2×#237—92no—
234C2×#237—92no—
235C2×D3×D4—32no—
236C2×D3×D4—92no—
237C2×D3×D4—92no—
238C2×D3×D4—92no—
239C2×D3×D4—92no—
240C2×D3×D4—92no—
241C2×D3×D4—92no—
242C2×D3×D4—182no—
243C2×#235—92no—
244C2×#235—92no—
245C2×#235—92no—
246C2×#235—91no—
247C22×D12—92no—
248C22×D12—91no—
249C23×C32—21no—
250C23×C32—22no—
251C23×C32—32no—
252C23×C32—32no—
253C23×C32—34no—
254C23×C32—41no—
255C23×C32—122no—
256C23×C32C22×D312yes—
257C23×C32C22×D311yescharacteristic
258C22×C3⋊D3—32no—
259C22×C3⋊D3—32no—
260C22×C3⋊D3—32no—
261C22×C3⋊D3—38no—
262C22×C3⋊D3—34no—
263C22×C3⋊D3—38no—
264C22×C3⋊D3—62no—
265C22×C3⋊D3—62no—
266C22×C3⋊D3—62no—
267C22×C3⋊D3—64no—
268C22×C3⋊D3—68no—
269C22×C3⋊D3—122no—
270C22×C3⋊D3—124no—
271C22×C3⋊D3—124no—
272C22×C3⋊D3—124no—
273C22×C3⋊D3—122no—
274C22×C3⋊D3—128no—
275C22×C3⋊D3—124no—
276C22×C3⋊D3—128no—
277C22×C3⋊D3C22×D312yes—
278C22×C3×D3—22no—
279C22×C3×D3—22no—
280C22×C3×D3—24no—
281C22×C3×D3—32no—
282C22×C3×D3—32no—
283C22×C3×D3—38no—
284C22×C3×D3—38no—
285C22×C3×D3—44no—
286C22×C3×D3—44no—
287C22×C3×D3—62no—
288C22×C3×D3—124no—
289C22×C3×D3—124no—
290C22×C3×D3C22×D312yes—
291C22×C3×D3C22×D312yes—
292C22×C3×D3C22×D312yes—
293C22×C3×D3C22×D312yes—
294C22×C3×D3C22×D318yescomplemented
295C2×D32—38no—
296C2×D32—38no—
297C2×D32—44no—
298C2×D32—68no—
299C2×D32—124no—
300C2×D32—124no—
301C2×D32—128no—
302C2×D32C22×D318yescomplemented
303C32×D4—38no—
304C2×C32×C4—32no—
305#638—38no—
306#638—38no—
307#638—38no—
308#638C22×D318yescomplemented
309C2×C3⋊Dic3C22×D311yescharacteristic
310C2×C3⋊Dic3C22×D312yes—
311C2×C3⋊Dic3C22×D311yescharacteristic
312C2×C3⋊Dic3C22×D314yescomplemented
313C4⋊(C3⋊D3)—38no—
314C4×C3⋊D3—38no—
315C3×#67—28no—
316C3×#67—38no—
317C3×#67—38no—
318C3×#67—38no—
319C3×#67—38no—
320C3×#67—38no—
321C3×#67—38no—
322C3×#67—68no—
323C3×#67C22×D318yescomplemented
324C3×#67C22×D318yescomplemented
325C2×C3×Dic3—22no—
326C2×C3×Dic3—32no—
327C2×C3×Dic3—32no—
328C2×C3×Dic3—32no—
329C2×C3×Dic3—32no—
330C2×C3×Dic3—38no—
331C2×C3×Dic3—38no—
332C2×C3×Dic3—38no—
333C2×C3×Dic3—62no—
334C2×C3×Dic3—61no—
335C2×C3×Dic3—61no—
336C2×C3×Dic3—64no—
337C2×C3×Dic3C22×D312yes—
338C2×C3×Dic3C22×D312yes—
339C3×D12—38no—
340C3×C4×D3—38no—
341C3×C4×D3—38no—
342C3×Dic6—38no—
343#627—38no—
344#627—34no—
345#627C22×D314yescomplemented
346#626—38no—
347#626—38no—
348#626—38no—
349#626—38no—
350#626—38no—
351#626—38no—
352#626—38no—
353#626—38no—
354#626—38no—
355#626—68no—
356#626—68no—
357#626—68no—
358#626—68no—
359#626C22×D318yescomplemented
360#625—34no—
361#625C22×D318yescomplemented
362#625C22×D314yescomplemented
363#624—38no—
364#624—38no—
365#624—38no—
366#624—68no—
367D3×Dic3—38no—
368D3×Dic3—38no—
369D3×Dic3C22×D318yescomplemented
370D3×Dic3C22×D318yescomplemented
371C2×H(5,𝔽2)—271noSylow
372C2×C33—22no—
373C2×C33H(5,𝔽2)12yescomplemented
374C2×C33C2511yescharacteristic
375C3⋊(C3⋊D3)—24no—
376C3×C3⋊D3—24no—
377C32×D3—24no—
378C32×D3—24no—
379C24×C3—32no—
380C24×C3—61no—
381C24×C3—92no—
382C23×D3—32no—
383C23×D3—32no—
384C23×D3—92no—
385C23×D3—92no—
386C23×D3—91no—
387C23×D3—92no—
388C23×D3—92no—
389C23×D3—182no—
390C23×D3—182no—
391C23×D3—181no—
392C23×D3—361no—
393C23×D3D3211yescharacteristic, complemented
394C3×#41—98no—
395C2×C3×Q8—91no—
396C2×C3×D4—32no—
397C2×C3×D4—32no—
398C2×C3×D4—62no—
399C2×C3×D4—92no—
400C2×C3×D4—916no—
401C2×C3×D4—91no—
402C2×C3×D4—92no—
403C2×C3×D4—92no—
404C22×C3×C4—92no—
405C22×C3×C4—92no—
406C22×C3×C4—91no—
407C2×#67—32no—
408C2×#67—32no—
409C2×#67—32no—
410C2×#67—32no—
411C2×#67—32no—
412C2×#67—316no—
413C2×#67—32no—
414C2×#67—62no—
415C2×#67—916no—
416C2×#67—92no—
417C2×#67—92no—
418C2×#67—92no—
419C2×#67—92no—
420C2×#67—92no—
421C2×#67—92no—
422C2×#67—92no—
423C2×#67—916no—
424C2×#67—916no—
425C2×#67—92no—
426C2×#67—182no—
427C2×#67—182no—
428C2×#67—182no—
429C2×#67—188no—
430C2×#67D3212yescomplemented
431C22×Dic3—32no—
432C22×Dic3—32no—
433C22×Dic3—32no—
434C22×Dic3—61no—
435C22×Dic3—92no—
436#239—916no—
437#237—316no—
438#237—916no—
439#237—916no—
440#237—916no—
441D3×D4—316no—
442D3×D4—916no—
443D3×D4—916no—
444D3×D4—916no—
445D3×D4—916no—
446D3×D4—916no—
447D3×D4—916no—
448D3×D4—1816no—
449#235—916no—
450#235—916no—
451#235—916no—
452#235—98no—
453C2×D12—32no—
454C2×D12—916no—
455C2×D12—92no—
456C2×D12—92no—
457C2×D12—91no—
458C2×D12—92no—
459C2×D12—92no—
460C2×D12—92no—
461C2×D12—98no—
462C2×D12—182no—
463C2×C4×D3—32no—
464C2×C4×D3—32no—
465C2×C4×D3—92no—
466C2×C4×D3—92no—
467C2×C4×D3—92no—
468C2×C4×D3—92no—
469C2×C4×D3—92no—
470C2×C4×D3—182no—
471C2×Dic6—32no—
472C2×Dic6—91no—
473C2×Dic6—92no—
474C22×C32—22no—
475C22×C32—24no—
476C22×C32—24no—
477C22×C32—22no—
478C22×C32—22no—
479C22×C32—21no—
480C22×C32—24no—
481C22×C32—34no—
482C22×C32—34no—
483C22×C32—42no—
484C22×C32—41no—
485C22×C32—44no—
486C22×C32—44no—
487C22×C32—64no—
488C22×C32—64no—
489C22×C32—124no—
490C22×C32C23×D314yes—
491C22×C32C23×D312yes—
492C22×C32C23×D312yes—
493C22×C32C23×D311yescharacteristic
494C2×C3⋊D3—24no—
495C2×C3⋊D3—34no—
496C2×C3⋊D3—34no—
497C2×C3⋊D3—34no—
498C2×C3⋊D3—64no—
499C2×C3⋊D3—64no—
500C2×C3⋊D3—64no—
501C2×C3⋊D3—64no—
502C2×C3⋊D3—68no—
503C2×C3⋊D3—64no—
504C2×C3⋊D3—64no—
505C2×C3⋊D3—124no—
506C2×C3⋊D3—124no—
507C2×C3⋊D3—124no—
508C2×C3⋊D3—128no—
509C2×C3⋊D3—128no—
510C2×C3⋊D3—128no—
511C2×C3⋊D3—124no—
512C2×C3⋊D3—1216no—
513C2×C3⋊D3—128no—
514C2×C3⋊D3—1216no—
515C2×C3⋊D3C23×D314yes—
516C2×C3×D3—24no—
517C2×C3×D3—24no—
518C2×C3×D3—24no—
519C2×C3×D3—24no—
520C2×C3×D3—24no—
521C2×C3×D3—24no—
522C2×C3×D3—34no—
523C2×C3×D3—34no—
524C2×C3×D3—44no—
525C2×C3×D3—44no—
526C2×C3×D3—48no—
527C2×C3×D3—48no—
528C2×C3×D3—64no—
529C2×C3×D3—64no—
530C2×C3×D3—64no—
531C2×C3×D3—124no—
532C2×C3×D3—128no—
533C2×C3×D3—128no—
534C2×C3×D3C23×D314yes—
535C2×C3×D3C23×D314yes—
536C2×C3×D3C23×D314yes—
537C2×C3×D3C23×D314yes—
538D32—48no—
539D32—128no—
540D32—128no—
541D32—1216no—
542C32×C4—34no—
543C3⋊Dic3C23×D312yes—
544C3⋊Dic3C23×D314yes—
545C3⋊Dic3C23×D312yes—
546C3×Dic3—24no—
547C3×Dic3—34no—
548C3×Dic3—34no—
549C3×Dic3—34no—
550C3×Dic3—34no—
551C3×Dic3—64no—
552C3×Dic3—62no—
553C3×Dic3—62no—
554C3×Dic3C23×D314yes—
555C3×Dic3C23×D314yes—
556H(5,𝔽2)—2716no—
557C2×#41—91no—
558C2×#41—272no—
559C2×#41—271no—
560C2×#41—272no—
561C22×D4—92no—
562C22×D4—272no—
563C22×D4—271no—
564C22×D4—272no—
565C22×D4—272no—
566C33C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
567C23×C3—21no—
568C23×C3—22no—
569C23×C3—32no—
570C23×C3—32no—
571C23×C3—32no—
572C23×C3—32no—
573C23×C3—38no—
574C23×C3—41no—
575C23×C3—62no—
576C23×C3—64no—
577C23×C3—62no—
578C23×C3—98no—
579C23×C3—92no—
580C23×C3—124no—
581C23×C3—124no—
582C23×C3—364no—
583C23×C3C2×D3212yes—
584C23×C3C2×D3211yescharacteristic
585C22×D3—32no—
586C22×D3—32no—
587C22×D3—38no—
588C22×D3—38no—
589C22×D3—42no—
590C22×D3—62no—
591C22×D3—98no—
592C22×D3—98no—
593C22×D3—92no—
594C22×D3—92no—
595C22×D3—92no—
596C22×D3—94no—
597C22×D3—98no—
598C22×D3—98no—
599C22×D3—124no—
600C22×D3—124no—
601C22×D3—188no—
602C22×D3—182no—
603C22×D3—182no—
604C22×D3—188no—
605C22×D3—182no—
606C22×D3—184no—
607C22×D3—362no—
608C22×D3—364no—
609C22×D3—364no—
610C22×D3—364no—
611C22×D3—364no—
612C22×D3—368no—
613C22×D3—364no—
614C22×D3—362no—
615C22×D3—368no—
616C22×D3—364no—
617C22×D3—368no—
618C22×D3C2×D3212yes—
619C22×D3C2×D3212yes—
620C22×D3C2×D3214yescomplemented
621C3×Q8—94no—
622C3×D4—38no—
623C3×D4—38no—
624C3×D4—68no—
625C3×D4—98no—
626C3×D4—94no—
627C3×D4—98no—
628C3×D4—98no—
629C2×C3×C4—32no—
630C2×C3×C4—32no—
631C2×C3×C4—62no—
632C2×C3×C4—98no—
633C2×C3×C4—98no—
634C2×C3×C4—92no—
635C2×C3×C4—91no—
636C2×C3×C4—91no—
637C2×C3×C4—94no—
638#67—38no—
639#67—38no—
640#67—38no—
641#67—38no—
642#67—38no—
643#67—38no—
644#67—68no—
645#67—98no—
646#67—98no—
647#67—98no—
648#67—98no—
649#67—98no—
650#67—98no—
651#67—98no—
652#67—98no—
653#67—188no—
654#67—188no—
655#67—188no—
656#67C2×D3218yescomplemented
657C2×Dic3—32no—
658C2×Dic3—32no—
659C2×Dic3—32no—
660C2×Dic3—32no—
661C2×Dic3—38no—
662C2×Dic3—38no—
663C2×Dic3—38no—
664C2×Dic3—62no—
665C2×Dic3—61no—
666C2×Dic3—61no—
667C2×Dic3—64no—
668C2×Dic3—98no—
669C2×Dic3C2×D3212yes—
670D12—38no—
671D12—98no—
672D12—98no—
673D12—94no—
674D12—98no—
675D12—98no—
676D12—98no—
677D12—188no—
678C4×D3—38no—
679C4×D3—38no—
680C4×D3—98no—
681C4×D3—98no—
682C4×D3—98no—
683C4×D3—98no—
684C4×D3—98no—
685C4×D3—188no—
686Dic6—38no—
687Dic6—94no—
688Dic6—98no—
689C2×C32—22no—
690C2×C32—24no—
691C2×C32—24no—
692C2×C32—24no—
693C2×C32—22no—
694C2×C32—22no—
695C2×C32—21no—
696C2×C32—42no—
697C2×C32—41no—
698C2×C32—44no—
699C2×C32—44no—
700C2×C32—64no—
701C2×C32—64no—
702C2×C32#100414yescomplemented
703C2×C32#100912yescomplemented
704C2×C32C24×D312yes—
705C2×C32C24×D311yescharacteristic
706C3⋊D3—24no—
707C3⋊D3—64no—
708C3⋊D3—68no—
709C3⋊D3—64no—
710C3⋊D3—64no—
711C3⋊D3—124no—
712C3⋊D3—124no—
713C3⋊D3—128no—
714C3×D3—24no—
715C3×D3—24no—
716C3×D3—24no—
717C3×D3—24no—
718C3×D3—44no—
719C3×D3—44no—
720C3×D3—64no—
721C3×D3—64no—
722C3×D3—124no—
723C24—31no—
724C24—92no—
725C24—272no—
726C24—271no—
727#41—98no—
728#41—2716no—
729#41—278no—
730#41—2716no—
731C2×Q8—91no—
732C2×Q8—271no—
733C2×D4—32no—
734C2×D4—92no—
735C2×D4—916no—
736C2×D4—92no—
737C2×D4—91no—
738C2×D4—92no—
739C2×D4—272no—
740C2×D4—2716no—
741C2×D4—272no—
742C2×D4—272no—
743C2×D4—272no—
744C2×D4—278no—
745C2×D4—271no—
746C2×D4—2716no—
747C2×D4—2716no—
748C22×C4—92no—
749C22×C4—92no—
750C22×C4—91no—
751C22×C4—272no—
752C22×C4—272no—
753C22×C3—24no—
754C22×C3—24no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—24no—
758C22×C3—21no—
759C22×C3—22no—
760C22×C3—34no—
761C22×C3—34no—
762C22×C3—34no—
763C22×C3—34no—
764C22×C3—44no—
765C22×C3—44no—
766C22×C3—42no—
767C22×C3—41no—
768C22×C3—64no—
769C22×C3—64no—
770C22×C3—64no—
771C22×C3—64no—
772C22×C3—64no—
773C22×C3—64no—
774C22×C3—94no—
775C22×C3—124no—
776C22×C3—124no—
777C22×C3—128no—
778C22×C3—128no—
779C22×C3—184no—
780C22×C3—368no—
781C22×C3C22×D3214yes—
782C22×C3C22×D3212yes—
783C22×C3C22×D3212yes—
784C22×C3C22×D3211yescharacteristic
785C2×D3—24no—
786C2×D3—24no—
787C2×D3—34no—
788C2×D3—34no—
789C2×D3—44no—
790C2×D3—64no—
791C2×D3—64no—
792C2×D3—64no—
793C2×D3—94no—
794C2×D3—94no—
795C2×D3—94no—
796C2×D3—124no—
797C2×D3—128no—
798C2×D3—128no—
799C2×D3—184no—
800C2×D3—184no—
801C2×D3—184no—
802C2×D3—188no—
803C2×D3—184no—
804C2×D3—184no—
805C2×D3—184no—
806C2×D3—364no—
807C2×D3—364no—
808C2×D3—364no—
809C2×D3—368no—
810C2×D3—368no—
811C2×D3—368no—
812C2×D3—368no—
813C2×D3—3616no—
814C2×D3—368no—
815C2×D3—364no—
816C2×D3—3616no—
817C2×D3—368no—
818C2×D3—3616no—
819C2×D3C22×D3214yes—
820C2×D3C22×D3214yes—
821C3×C4—34no—
822C3×C4—34no—
823C3×C4—64no—
824C3×C4—94no—
825C3×C4—92no—
826C3×C4—92no—
827Dic3—34no—
828Dic3—34no—
829Dic3—34no—
830Dic3—34no—
831Dic3—64no—
832Dic3—62no—
833Dic3—62no—
834Dic3C22×D3214yes—
835C32—22no—
836C32—21no—
837C32—41no—
838C32C2×#100412yescomplemented
839C32C2×#100911yescharacteristic, complemented
840C23—32no—
841C23—32no—
842C23—34no—
843C23—98no—
844C23—92no—
845C23—122no—
846C23—278no—
847C23—272no—
848C23—274no—
849C23—364no—
850C23—1082no—
851C23—1084no—
852C23D3311yescharacteristic
853Q8—94no—
854Q8—274no—
855D4—38no—
856D4—98no—
857D4—98no—
858D4—94no—
859D4—98no—
860D4—278no—
861D4—278no—
862D4—278no—
863D4—278no—
864D4—274no—
865C2×C4—32no—
866C2×C4—98no—
867C2×C4—98no—
868C2×C4—94no—
869C2×C4—91no—
870C2×C4—92no—
871C2×C4—91no—
872C2×C4—278no—
873C2×C4—278no—
874C2×C3—24no—
875C2×C3—24no—
876C2×C3—22no—
877C2×C3—24no—
878C2×C3—22no—
879C2×C3—21no—
880C2×C3—22no—
881C2×C3—44no—
882C2×C3—44no—
883C2×C3—42no—
884C2×C3—41no—
885C2×C3—64no—
886C2×C3—64no—
887C2×C3—64no—
888C2×C3—64no—
889C2×C3—124no—
890C2×C3—124no—
891C2×C3—184no—
892C2×C3#6431414yescomplemented
893C2×C3#6433012yescomplemented
894C2×C3C23×D3212yes—
895C2×C3C23×D3211yescharacteristic
896D3—24no—
897D3—24no—
898D3—64no—
899D3—64no—
900D3—124no—
901D3—188no—
902D3—184no—
903D3—184no—
904D3—184no—
905D3—364no—
906D3—364no—
907D3—368no—
908C22—22no—
909C22—34no—
910C22—34no—
911C22—64no—
912C22—64no—
913C22—94no—
914C22—124no—
915C22—184no—
916C22—274no—
917C22—368no—
918C22—544no—
919C22—1084no—
920C22—1088no—
921C22C2×D3312yes—
922C22C2×D3311yescharacteristic
923C4—34no—
924C4—92no—
925C4—94no—
926C4—92no—
927C3—22no—
928C3—21no—
929C3—41no—
930C3C2×#6431412yescomplemented
931C3C2×#6433011yescharacteristic, complemented
932C2—22no—
933C2—64no—
934C2—64no—
935C2—184no—
936C2—544no—
937C2#1172441912yesdirect product factor
938C2C22×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. C2×#89046C2semidirect
2. C2×#89039C2semidirect
3. C22×#6291C2semidirect
4. C2×C3×D3×#67C2semidirect
5. C2×C3×#3805C2semidirect
6. C2×#88962C2semidirect
7. C2×#88959C2semidirect
8. C2×#88952C2semidirect
9. #11724419C2direct (N × H)
10. C2×D3×#626C2semidirect
13. C23×C3⋊(C3⋊D3)C22semidirect
14. C23×C32×D3C22semidirect
15. C22×D3×C3⋊D3C22semidirect
16. C22×C3×D32C22semidirect
17. C2×C3×#638C22semidirect
18. C22×C3×C3⋊Dic3C22semidirect
19. C2×C32×#67C22semidirect
20. C2×#6296C22semidirect
21. C2×#6295C22semidirect
22. #89046C22semidirect
23. C2×#6294C22semidirect
24. #89039C22semidirect
25. C2×#6292C22semidirect
26. C2×#6291C22semidirect
27. C2×#6291C22semidirect
28. C2×#6291C22semidirect
29. C2×#6291C22semidirect
30. C2×#6289C22semidirect
31. C3×D3×#67C22semidirect
32. C2×C3×#627C22semidirect
33. C2×C3×#626C22semidirect
34. C2×C3×#625C22semidirect
35. C2×C3×#625C22semidirect
36. C3×#3805C22semidirect
37. C2×C3×D3×Dic3C22semidirect
38. C2×C3×D3×Dic3C22semidirect
39. #88962C22semidirect
40. #88959C22semidirect
41. #88952C22semidirect
42. D3×#626C22semidirect
56. C2×D3×#67D3semidirect
61. C2×#3805D3semidirect
74. C22×C3⋊(C3⋊D3)C23semidirect
79. C22×C32×D3C23semidirect
81. C2×D3×C3⋊D3C23semidirect
83. C2×C3×D32C23semidirect
84. C3×#638C23semidirect
88. C2×C3×C3⋊Dic3C23semidirect
89. C32×#67C23semidirect
91. #6296C23semidirect
92. #6295C23semidirect
93. #6294C23semidirect
94. #6292C23semidirect
95. #6291C23semidirect
96. #6291C23semidirect
97. #6291C23semidirect
98. #6289C23semidirect
99. C3×#627C23semidirect
100. C3×#626C23semidirect
101. C3×#625C23semidirect
102. C3×#625C23semidirect
103. C3×D3×Dic3C23semidirect
104. C3×D3×Dic3C23semidirect
117. C23×C3×D3C2×D3semidirect
121. C22×D32C2×D3semidirect
127. C2×#638C2×D3semidirect
128. C22×C3⋊Dic3C2×D3semidirect
141. C2×C3×#67C2×D3semidirect
142. C2×C3×#67C2×D3semidirect
160. D3×#67C2×D3semidirect
163. C2×#627C2×D3semidirect
180. C2×#626C2×D3semidirect
182. C2×#625C2×D3semidirect
183. C2×#625C2×D3semidirect
189. #3805C2×D3semidirect
196. C2×D3×Dic3C2×D3semidirect
197. C2×D3×Dic3C2×D3semidirect
294. C22×C3×D3C22×D3semidirect
302. C2×D32C22×D3semidirect
308. #638C22×D3semidirect
312. C2×C3⋊Dic3C22×D3semidirect
323. C3×#67C22×D3semidirect
324. C3×#67C22×D3semidirect
345. #627C22×D3semidirect
359. #626C22×D3semidirect
361. #625C22×D3semidirect
362. #625C22×D3semidirect
369. D3×Dic3C22×D3semidirect
370. D3×Dic3C22×D3semidirect
373. C2×C33H(5,𝔽2)semidirect
393. C23×D3D32semidirect
430. C2×#67D32semidirect
566. C33C2×H(5,𝔽2)semidirect
620. C22×D3C2×D32semidirect
656. #67C2×D32semidirect
702. C2×C32#1004semidirect
703. C2×C32#1009semidirect
838. C32C2×#1004semidirect
839. C32C2×#1009semidirect
892. C2×C3#64314semidirect
893. C2×C3#64330semidirect
930. C3C2×#64314semidirect
931. C3C2×#64330semidirect
937. C2#11724419direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#890462
C2×#890392
C22×#62912
C2×C3×D3×#672
C2×C3×#38052
C2×#889622
C2×#889592
C2×#889522
#117244192
C2×D3×#6262
C2×#643303
C2×#643143