Finite Group Databasebeta

← C2×#11724420 #13181327

Subgroups — C2×#11724420 #13181327

Order 1728.

4434 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89049C211yesmaximal, characteristic, complemented
2C2×#89039C212yesmaximal, complemented
3C22×#6292C211yesmaximal, characteristic, complemented
4C2×C3×#3811C211yesmaximal, characteristic, complemented
5C2×C3×#3804C212yesmaximal, complemented
6C2×#88965C212yesmaximal, complemented
7C2×#88962C212yesmaximal, complemented
8C2×#88955C212yesmaximal, complemented
9#11724420C2116yesmaximal, direct product factor
10C2×D3×#626C212yesmaximal, complemented
11C2×#64314—32nomaximal
12C2×#64308—31nomaximal
13C23×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
14C23×C3×C3⋊D3C2211yescharacteristic, complemented
15C22×#1113C2211yescharacteristic, complemented
16C22×D3×C3⋊D3C2212yescomplemented
17C22×C3×D32C2211yescharacteristic, complemented
18C2×C3×#638C2212yescomplemented
19C2×C32×#67C2212yescomplemented
20C22×C32×Dic3C2211yescharacteristic, complemented
21#89049C2218yescomplemented
22C2×#6295C2212yescomplemented
23C2×#6294C2211yescharacteristic, complemented
24#89039C22116yescomplemented
25C2×#6292C2212yescomplemented
26C2×#6292C2212yescomplemented
27C2×#6292C2212yescomplemented
28C2×#6292C2218yescomplemented
29C2×#6291C2212yescomplemented
30C2×#6289C2212yescomplemented
31C3×#3811C2218yescomplemented
32C2×C3×#627C2212yescomplemented
33C2×C3×#626C2212yescomplemented
34C2×C3×#626C2212yescomplemented
35C2×C3×#624C2212yescomplemented
36C2×C3×#624C2211yescharacteristic, complemented
37C3×#3804C22116yescomplemented
38C2×C3×D3×Dic3C2212yescomplemented
39#88965C22116yescomplemented
40#88962C22116yescomplemented
41#88955C22116yescomplemented
42D3×#626C22116yescomplemented
43C2×D4×C3⋊D3—32no—
44C22×C4⋊(C3⋊D3)—31no—
45C2×C3×#237—32no—
46C2×C3×D3×D4—32no—
47C2×C3×#235—32no—
48C2×#3811—32no—
49C2×#3811—32no—
50C2×#3811—32no—
51C2×#3811—31no—
52C2×#3811—62no—
53C2×#3811D311yescharacteristic, complemented
54C2×D3×#67—32no—
55C2×D3×#67—32no—
56C22×#626—32no—
57C22×#626—32no—
58C22×#626—61no—
59C2×#3804—32no—
60C2×#3804D312yescomplemented
61#64314—332no—
62#64308—316no—
63C2×D3×D12—32no—
64C2×D3×D12—32no—
65C2×D3×D12—32no—
66C2×#3799—32no—
67C2×#3799—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⋊D3—42no—
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C3×C3⋊D3C2312yes—
78C22×C3×C3⋊D3C2311yescharacteristic
79C22×C3×C3⋊D3C2314yescomplemented
80C22×C32×D3C2312yes—
81C2×#1113—42no—
82C2×#1113C2314yescomplemented
83C2×D3×C3⋊D3—44no—
84C2×D3×C3⋊D3C2318yescomplemented
85C2×C3×D32—42no—
86C2×C3×D32C2314yescomplemented
87C3×#638C2318yescomplemented
88C2×C3×C3⋊Dic3C2312yes—
89C32×#67C2318yescomplemented
90C2×C32×Dic3C2312yes—
91C2×C32×Dic3C2312yes—
92C2×C32×Dic3C2314yescomplemented
93#6295C2318yescomplemented
94#6294C2314yescomplemented
95#6292C2318yescomplemented
96#6292C2318yescomplemented
97#6292C2318yescomplemented
98#6291C2318yescomplemented
99#6289C2318yescomplemented
100C3×#627C2318yescomplemented
101C3×#626C2318yescomplemented
102C3×#626C2318yescomplemented
103C3×#624C2318yescomplemented
104C3×#624C2314yescomplemented
105C3×D3×Dic3C2318yescomplemented
106C2×#1009—92no—
107C2×#1004—91no—
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⋊D3C2×D311yescharacteristic, complemented
115C23×C3×D3—32no—
116C23×C3×D3—32no—
117C23×C3×D3—61no—
118C22×D32—31no—
119C22×D32—32no—
120C22×D32—32no—
121C22×D32—32no—
122C22×D32—62no—
123C22×D32C2×D311yescharacteristic, complemented
124C2×C32×D4—32no—
125C22×C32×C4—31no—
126C2×#638—32no—
127C2×#638C2×D312yescomplemented
128D4×C3⋊D3—316no—
129C2×C4⋊(C3⋊D3)—32no—
130C2×C4⋊(C3⋊D3)—32no—
131C2×C4⋊(C3⋊D3)—32no—
132C2×C4⋊(C3⋊D3)—38no—
133C2×C4×C3⋊D3—32no—
134C2×C3×#67—22no—
135C2×C3×#67—32no—
136C2×C3×#67—32no—
137C2×C3×#67—32no—
138C2×C3×#67—32no—
139C2×C3×#67—62no—
140C2×C3×#67C2×D312yescomplemented
141C2×C3×#67C2×D312yescomplemented
142C22×C3×Dic3—21no—
143C22×C3×Dic3—32no—
144C22×C3×Dic3C2×D312yescomplemented
145C3×#237—316no—
146C3×D3×D4—316no—
147C3×#235—316no—
148C2×C3×D12—32no—
149C2×C3×D12—32no—
150C2×C3×C4×D3—32no—
151C2×C3×C4×D3—32no—
152C2×C3×C4×D3—32no—
153C2×C3×C4×D3—32no—
154C2×C3×Dic6—32no—
155C2×C3×Dic6—32no—
156#3811—38no—
157#3811—316no—
158#3811—316no—
159#3811—316no—
160#3811—616no—
161#3811C2×D318yescomplemented
162D3×#67—316no—
163D3×#67—316no—
164C2×#627C2×D312yescomplemented
165C2×#626—32no—
166C2×#626—32no—
167C2×#626—32no—
168C2×#626—32no—
169C2×#626—32no—
170C2×#626—32no—
171C2×#626—32no—
172C2×#626—32no—
173C2×#626—32no—
174C2×#626—32no—
175C2×#626—316no—
176C2×#626—316no—
177C2×#626—62no—
178C2×#626—62no—
179C2×#626—68no—
180C2×#626—62no—
181C2×#626—62no—
182C2×#626C2×D312yescomplemented
183C2×#626C2×D312yescomplemented
184C2×#625—32no—
185C2×#624—31no—
186C2×#624—32no—
187C2×#624—32no—
188C2×#624—62no—
189C2×#624C2×D311yescharacteristic, complemented
190C2×#624C2×D312yescomplemented
191#3804—316no—
192#3804C2×D3116yescomplemented
193C2×D3×Dic3—32no—
194C2×D3×Dic3C2×D312yescomplemented
195D3×D12—316no—
196D3×D12—316no—
197D3×D12—316no—
198#3799—316no—
199#3799—316no—
200#3799—316no—
201#3798—316no—
202#3796—316no—
203C22×C33—22no—
204C22×C33C2412yes—
205C22×C33C2411yescharacteristic
206C2×C3⋊(C3⋊D3)—24no—
207C2×C3⋊(C3⋊D3)—44no—
208C2×C3⋊(C3⋊D3)C2414yes—
209C2×C3×C3⋊D3—22no—
210C2×C3×C3⋊D3—24no—
211C2×C3×C3⋊D3—22no—
212C2×C3×C3⋊D3—44no—
213C2×C3×C3⋊D3C2414yes—
214C2×C3×C3⋊D3C2412yes—
215C2×C3×C3⋊D3C2412yes—
216C2×C32×D3—24no—
217C2×C32×D3C2414yes—
218#1113—44no—
219D3×C3⋊D3—48no—
220C3×D32—44no—
221C3×C3⋊Dic3C2414yes—
222C32×Dic3C2414yes—
223C32×Dic3C2414yes—
224C2×C3×#41—92no—
225C22×C3×D4—91no—
226C22×#67—92no—
227C22×#67—91no—
228C22×#67—91no—
229#1009—932no—
230C2×#239—92no—
231C2×#239—92no—
232#1004—916no—
233C2×#237—32no—
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—92no—
243C2×D3×D4—182no—
244C2×#235—32no—
245C2×#235—92no—
246C2×#235—92no—
247C2×#235—92no—
248C22×D12—92no—
249C22×D12—92no—
250C22×D12—92no—
251C22×D12—181no—
252C23×C32—21no—
253C23×C32—22no—
254C23×C32—32no—
255C23×C32—41no—
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—42no—
265C22×C3⋊D3—62no—
266C22×C3⋊D3—62no—
267C22×C3⋊D3—62no—
268C22×C3⋊D3—64no—
269C22×C3⋊D3—68no—
270C22×C3⋊D3—122no—
271C22×C3⋊D3—124no—
272C22×C3⋊D3—124no—
273C22×C3⋊D3—124no—
274C22×C3⋊D3—122no—
275C22×C3⋊D3—128no—
276C22×C3⋊D3—124no—
277C22×C3⋊D3—128no—
278C22×C3⋊D3C22×D312yes—
279C22×C3⋊D3C22×D311yescharacteristic
280C22×C3⋊D3C22×D311yescharacteristic
281C22×C3⋊D3C22×D314yescomplemented
282C22×C3×D3—22no—
283C22×C3×D3—32no—
284C22×C3×D3—32no—
285C22×C3×D3—32no—
286C22×C3×D3—32no—
287C22×C3×D3—38no—
288C22×C3×D3—38no—
289C22×C3×D3—62no—
290C22×C3×D3—61no—
291C22×C3×D3—61no—
292C22×C3×D3—64no—
293C22×C3×D3—124no—
294C22×C3×D3—124no—
295C22×C3×D3—124no—
296C22×C3×D3C22×D312yes—
297C22×C3×D3C22×D312yes—
298C2×D32—34no—
299C2×D32—38no—
300C2×D32—38no—
301C2×D32—38no—
302C2×D32—42no—
303C2×D32—68no—
304C2×D32—124no—
305C2×D32—124no—
306C2×D32—128no—
307C2×D32—122no—
308C2×D32—124no—
309C2×D32C22×D314yescomplemented
310C32×D4—38no—
311C2×C32×C4—32no—
312C2×C32×C4—32no—
313C2×C32×C4—34no—
314#638—38no—
315#638C22×D318yescomplemented
316C2×C3⋊Dic3C22×D312yes—
317C4⋊(C3⋊D3)—38no—
318C4⋊(C3⋊D3)—38no—
319C4⋊(C3⋊D3)—38no—
320C4×C3⋊D3—38no—
321C3×#67—28no—
322C3×#67—38no—
323C3×#67—38no—
324C3×#67—38no—
325C3×#67—38no—
326C3×#67—68no—
327C3×#67C22×D318yescomplemented
328C3×#67C22×D318yescomplemented
329C2×C3×Dic3—22no—
330C2×C3×Dic3—22no—
331C2×C3×Dic3—24no—
332C2×C3×Dic3—32no—
333C2×C3×Dic3—32no—
334C2×C3×Dic3—38no—
335C2×C3×Dic3—62no—
336C2×C3×Dic3C22×D312yes—
337C2×C3×Dic3C22×D312yes—
338C2×C3×Dic3C22×D312yes—
339C2×C3×Dic3C22×D312yes—
340C2×C3×Dic3C22×D318yescomplemented
341C3×D12—38no—
342C3×D12—38no—
343C3×C4×D3—38no—
344C3×C4×D3—38no—
345C3×C4×D3—38no—
346C3×C4×D3—38no—
347C3×Dic6—38no—
348C3×Dic6—38no—
349#627C22×D318yescomplemented
350#626—38no—
351#626—38no—
352#626—38no—
353#626—38no—
354#626—38no—
355#626—38no—
356#626—38no—
357#626—38no—
358#626—38no—
359#626—38no—
360#626—68no—
361#626—68no—
362#626—68no—
363#626—68no—
364#626C22×D318yescomplemented
365#626C22×D318yescomplemented
366#625—38no—
367#624—34no—
368#624—38no—
369#624—38no—
370#624—68no—
371#624C22×D314yescomplemented
372#624C22×D318yescomplemented
373D3×Dic3—38no—
374D3×Dic3C22×D318yescomplemented
375C2×H(5,𝔽2)—271noSylow
376C2×C33—22no—
377C2×C33H(5,𝔽2)12yescomplemented
378C2×C33C2511yescharacteristic
379C3⋊(C3⋊D3)—24no—
380C3×C3⋊D3—22no—
381C3×C3⋊D3—24no—
382C3×C3⋊D3—22no—
383C32×D3—24no—
384C24×C3—91no—
385C24×C3—91no—
386C23×D3—32no—
387C23×D3—32no—
388C23×D3—61no—
389C23×D3—92no—
390C23×D3—91no—
391C23×D3—92no—
392C23×D3—92no—
393C23×D3—92no—
394C23×D3—91no—
395C23×D3—92no—
396C23×D3—182no—
397C23×D3—181no—
398C23×D3—182no—
399C23×D3—361no—
400C3×#41—916no—
401C2×C3×Q8—92no—
402C2×C3×D4—32no—
403C2×C3×D4—32no—
404C2×C3×D4—62no—
405C2×C3×D4—92no—
406C2×C3×D4—92no—
407C2×C3×D4—98no—
408C2×C3×D4—92no—
409C22×C3×C4—32no—
410C22×C3×C4—61no—
411C22×C3×C4—92no—
412C22×C3×C4—91no—
413C22×C3×C4—92no—
414C2×#67—32no—
415C2×#67—32no—
416C2×#67—32no—
417C2×#67—32no—
418C2×#67—62no—
419C2×#67—916no—
420C2×#67—92no—
421C2×#67—92no—
422C2×#67—92no—
423C2×#67—92no—
424C2×#67—98no—
425C2×#67—92no—
426C2×#67—92no—
427C2×#67—92no—
428C2×#67—98no—
429C2×#67—182no—
430C2×#67D3212yescomplemented
431C22×Dic3—32no—
432C22×Dic3—91no—
433C22×Dic3D3211yescharacteristic, complemented
434#239—916no—
435#239—916no—
436#237—316no—
437#237—916no—
438D3×D4—316no—
439D3×D4—916no—
440D3×D4—916no—
441D3×D4—916no—
442D3×D4—916no—
443D3×D4—916no—
444D3×D4—916no—
445D3×D4—916no—
446D3×D4—1816no—
447#235—316no—
448#235—916no—
449#235—916no—
450#235—916no—
451C2×D12—32no—
452C2×D12—32no—
453C2×D12—916no—
454C2×D12—916no—
455C2×D12—92no—
456C2×D12—92no—
457C2×D12—92no—
458C2×D12—92no—
459C2×D12—92no—
460C2×D12—916no—
461C2×D12—92no—
462C2×D12—92no—
463C2×D12—92no—
464C2×D12—182no—
465C2×D12—182no—
466C2×D12—188no—
467C2×D12—182no—
468C2×C4×D3—32no—
469C2×C4×D3—32no—
470C2×C4×D3—32no—
471C2×C4×D3—32no—
472C2×C4×D3—92no—
473C2×C4×D3—92no—
474C2×C4×D3—92no—
475C2×C4×D3—92no—
476C2×C4×D3—182no—
477C2×Dic6—32no—
478C2×Dic6—32no—
479C22×C32—22no—
480C22×C32—24no—
481C22×C32—24no—
482C22×C32—22no—
483C22×C32—21no—
484C22×C32—22no—
485C22×C32—24no—
486C22×C32—34no—
487C22×C32—42no—
488C22×C32—41no—
489C22×C32—44no—
490C22×C32—44no—
491C22×C32—64no—
492C22×C32C23×D314yes—
493C22×C32C23×D312yes—
494C22×C32C23×D311yescharacteristic
495C22×C32C23×D312yes—
496C2×C3⋊D3—22no—
497C2×C3⋊D3—22no—
498C2×C3⋊D3—24no—
499C2×C3⋊D3—34no—
500C2×C3⋊D3—34no—
501C2×C3⋊D3—34no—
502C2×C3⋊D3—44no—
503C2×C3⋊D3—64no—
504C2×C3⋊D3—64no—
505C2×C3⋊D3—64no—
506C2×C3⋊D3—64no—
507C2×C3⋊D3—68no—
508C2×C3⋊D3—64no—
509C2×C3⋊D3—64no—
510C2×C3⋊D3—124no—
511C2×C3⋊D3—124no—
512C2×C3⋊D3—124no—
513C2×C3⋊D3—128no—
514C2×C3⋊D3—128no—
515C2×C3⋊D3—128no—
516C2×C3⋊D3—124no—
517C2×C3⋊D3—1216no—
518C2×C3⋊D3—128no—
519C2×C3⋊D3—1216no—
520C2×C3⋊D3C23×D312yes—
521C2×C3⋊D3C23×D312yes—
522C2×C3⋊D3C23×D314yes—
523C2×C3×D3—24no—
524C2×C3×D3—24no—
525C2×C3×D3—24no—
526C2×C3×D3—34no—
527C2×C3×D3—34no—
528C2×C3×D3—34no—
529C2×C3×D3—34no—
530C2×C3×D3—44no—
531C2×C3×D3—62no—
532C2×C3×D3—62no—
533C2×C3×D3—64no—
534C2×C3×D3—64no—
535C2×C3×D3—64no—
536C2×C3×D3—64no—
537C2×C3×D3—64no—
538C2×C3×D3—124no—
539C2×C3×D3—122no—
540C2×C3×D3—122no—
541C2×C3×D3—128no—
542C2×C3×D3—128no—
543C2×C3×D3—128no—
544C2×C3×D3C23×D314yes—
545C2×C3×D3C23×D314yes—
546D32—44no—
547D32—128no—
548D32—128no—
549D32—1216no—
550D32—124no—
551D32—128no—
552C32×C4—34no—
553C32×C4—34no—
554C3⋊Dic3C23×D314yes—
555C3×Dic3—24no—
556C3×Dic3—24no—
557C3×Dic3—34no—
558C3×Dic3—34no—
559C3×Dic3—64no—
560C3×Dic3C23×D314yes—
561C3×Dic3C23×D314yes—
562C3×Dic3C23×D314yes—
563C3×Dic3C23×D314yes—
564H(5,𝔽2)—2716no—
565C2×#41—92no—
566C2×#41—272no—
567C2×#41—272no—
568C22×D4—91no—
569C22×D4—271no—
570C22×D4—272no—
571C22×D4—272no—
572C22×D4—272no—
573C22×D4—271no—
574C33C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
575C23×C3—21no—
576C23×C3—22no—
577C23×C3—32no—
578C23×C3—32no—
579C23×C3—41no—
580C23×C3—62no—
581C23×C3—94no—
582C23×C3—91no—
583C23×C3—91no—
584C23×C3—92no—
585C23×C3—94no—
586C23×C3—362no—
587C23×C3—362no—
588C23×C3C2×D3211yescharacteristic
589C23×C3C2×D3212yes—
590C22×D3—32no—
591C22×D3—32no—
592C22×D3—32no—
593C22×D3—32no—
594C22×D3—38no—
595C22×D3—38no—
596C22×D3—61no—
597C22×D3—61no—
598C22×D3—62no—
599C22×D3—64no—
600C22×D3—98no—
601C22×D3—94no—
602C22×D3—98no—
603C22×D3—98no—
604C22×D3—92no—
605C22×D3—92no—
606C22×D3—92no—
607C22×D3—98no—
608C22×D3—94no—
609C22×D3—98no—
610C22×D3—124no—
611C22×D3—124no—
612C22×D3—124no—
613C22×D3—188no—
614C22×D3—182no—
615C22×D3—182no—
616C22×D3—184no—
617C22×D3—182no—
618C22×D3—188no—
619C22×D3—362no—
620C22×D3—364no—
621C22×D3—364no—
622C22×D3—362no—
623C22×D3—364no—
624C22×D3—364no—
625C22×D3—364no—
626C22×D3—368no—
627C22×D3—362no—
628C22×D3—364no—
629C22×D3—368no—
630C22×D3—364no—
631C22×D3—368no—
632C22×D3C2×D3212yes—
633C3×Q8—98no—
634C3×D4—38no—
635C3×D4—38no—
636C3×D4—68no—
637C3×D4—98no—
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—38no—
645C2×C3×C4—62no—
646C2×C3×C4—64no—
647C2×C3×C4—62no—
648C2×C3×C4—98no—
649C2×C3×C4—94no—
650C2×C3×C4—98no—
651C2×C3×C4—92no—
652#67—38no—
653#67—38no—
654#67—38no—
655#67—38no—
656#67—68no—
657#67—98no—
658#67—98no—
659#67—98no—
660#67—98no—
661#67—98no—
662#67—98no—
663#67—98no—
664#67—188no—
665#67C2×D3218yescomplemented
666C2×Dic3—32no—
667C2×Dic3—32no—
668C2×Dic3—38no—
669C2×Dic3—62no—
670C2×Dic3—94no—
671C2×Dic3C2×D3212yes—
672C2×Dic3C2×D3212yes—
673C2×Dic3C2×D3214yescomplemented
674D12—38no—
675D12—38no—
676D12—98no—
677D12—98no—
678D12—98no—
679D12—98no—
680D12—98no—
681D12—98no—
682D12—98no—
683D12—98no—
684D12—188no—
685D12—188no—
686D12—188no—
687C4×D3—38no—
688C4×D3—38no—
689C4×D3—38no—
690C4×D3—38no—
691C4×D3—98no—
692C4×D3—98no—
693C4×D3—98no—
694C4×D3—98no—
695C4×D3—188no—
696Dic6—38no—
697Dic6—38no—
698C2×C32—22no—
699C2×C32—24no—
700C2×C32—24no—
701C2×C32—22no—
702C2×C32—24no—
703C2×C32—21no—
704C2×C32—22no—
705C2×C32—42no—
706C2×C32—41no—
707C2×C32—44no—
708C2×C32—44no—
709C2×C32—64no—
710C2×C32#100412yescomplemented
711C2×C32#100914yescomplemented
712C2×C32C24×D311yescharacteristic
713C2×C32C24×D312yes—
714C3⋊D3—22no—
715C3⋊D3—22no—
716C3⋊D3—24no—
717C3⋊D3—64no—
718C3⋊D3—68no—
719C3⋊D3—64no—
720C3⋊D3—64no—
721C3⋊D3—124no—
722C3⋊D3—124no—
723C3⋊D3—128no—
724C3×D3—24no—
725C3×D3—24no—
726C3×D3—44no—
727C3×D3—64no—
728C3×D3—64no—
729C3×D3—64no—
730C3×D3—64no—
731C3×D3—124no—
732C3×D3—122no—
733C3×D3—122no—
734C24—91no—
735C24—91no—
736C24—272no—
737C24—271no—
738C24—271no—
739#41—916no—
740#41—2716no—
741#41—2716no—
742C2×Q8—92no—
743C2×D4—32no—
744C2×D4—92no—
745C2×D4—92no—
746C2×D4—98no—
747C2×D4—92no—
748C2×D4—272no—
749C2×D4—272no—
750C2×D4—272no—
751C2×D4—278no—
752C2×D4—2716no—
753C2×D4—2716no—
754C2×D4—272no—
755C2×D4—272no—
756C2×D4—2716no—
757C2×D4—278no—
758C22×C4—31no—
759C22×C4—91no—
760C22×C4—92no—
761C22×C4—92no—
762C22×C4—272no—
763C22×C4—271no—
764C22×C3—24no—
765C22×C3—22no—
766C22×C3—24no—
767C22×C3—22no—
768C22×C3—24no—
769C22×C3—22no—
770C22×C3—21no—
771C22×C3—34no—
772C22×C3—34no—
773C22×C3—44no—
774C22×C3—44no—
775C22×C3—42no—
776C22×C3—41no—
777C22×C3—64no—
778C22×C3—64no—
779C22×C3—64no—
780C22×C3—92no—
781C22×C3—92no—
782C22×C3—94no—
783C22×C3—124no—
784C22×C3—182no—
785C22×C3—182no—
786C22×C3—184no—
787C22×C3—364no—
788C22×C3—364no—
789C22×C3C22×D3212yes—
790C22×C3C22×D3214yes—
791C22×C3C22×D3211yescharacteristic
792C22×C3C22×D3212yes—
793C2×D3—24no—
794C2×D3—34no—
795C2×D3—34no—
796C2×D3—34no—
797C2×D3—34no—
798C2×D3—62no—
799C2×D3—62no—
800C2×D3—64no—
801C2×D3—64no—
802C2×D3—64no—
803C2×D3—64no—
804C2×D3—64no—
805C2×D3—94no—
806C2×D3—94no—
807C2×D3—94no—
808C2×D3—122no—
809C2×D3—122no—
810C2×D3—124no—
811C2×D3—128no—
812C2×D3—128no—
813C2×D3—128no—
814C2×D3—184no—
815C2×D3—184no—
816C2×D3—184no—
817C2×D3—188no—
818C2×D3—184no—
819C2×D3—184no—
820C2×D3—184no—
821C2×D3—364no—
822C2×D3—364no—
823C2×D3—364no—
824C2×D3—368no—
825C2×D3—368no—
826C2×D3—364no—
827C2×D3—368no—
828C2×D3—368no—
829C2×D3—368no—
830C2×D3—3616no—
831C2×D3—364no—
832C2×D3—368no—
833C2×D3—3616no—
834C2×D3—368no—
835C2×D3—3616no—
836C2×D3C22×D3214yes—
837C3×C4—34no—
838C3×C4—34no—
839C3×C4—34no—
840C3×C4—34no—
841C3×C4—64no—
842C3×C4—64no—
843C3×C4—94no—
844Dic3—34no—
845Dic3—34no—
846Dic3—64no—
847Dic3C22×D3214yes—
848Dic3C22×D3214yes—
849C32—21no—
850C32—22no—
851C32—41no—
852C32C2×#100411yescharacteristic, complemented
853C32C2×#100912yescomplemented
854C23—32no—
855C23—94no—
856C23—92no—
857C23—91no—
858C23—91no—
859C23—94no—
860C23—278no—
861C23—274no—
862C23—272no—
863C23—274no—
864C23—362no—
865C23—362no—
866C23—1082no—
867C23—1084no—
868C23—1082no—
869C23D3311yescharacteristic
870Q8—98no—
871D4—38no—
872D4—98no—
873D4—98no—
874D4—98no—
875D4—278no—
876D4—278no—
877D4—278no—
878D4—278no—
879D4—278no—
880C2×C4—34no—
881C2×C4—32no—
882C2×C4—32no—
883C2×C4—94no—
884C2×C4—98no—
885C2×C4—98no—
886C2×C4—92no—
887C2×C4—278no—
888C2×C4—274no—
889C2×C3—24no—
890C2×C3—22no—
891C2×C3—24no—
892C2×C3—22no—
893C2×C3—24no—
894C2×C3—22no—
895C2×C3—21no—
896C2×C3—44no—
897C2×C3—44no—
898C2×C3—42no—
899C2×C3—41no—
900C2×C3—64no—
901C2×C3—64no—
902C2×C3—124no—
903C2×C3—182no—
904C2×C3—182no—
905C2×C3—184no—
906C2×C3#6430812yescomplemented
907C2×C3#6431414yescomplemented
908C2×C3C23×D3211yescharacteristic
909C2×C3C23×D3212yes—
910D3—24no—
911D3—64no—
912D3—64no—
913D3—64no—
914D3—64no—
915D3—122no—
916D3—122no—
917D3—124no—
918D3—188no—
919D3—184no—
920D3—184no—
921D3—184no—
922D3—364no—
923D3—364no—
924D3—368no—
925C22—22no—
926C22—34no—
927C22—64no—
928C22—94no—
929C22—92no—
930C22—92no—
931C22—182no—
932C22—182no—
933C22—184no—
934C22—274no—
935C22—364no—
936C22—364no—
937C22—544no—
938C22—1084no—
939C22—1088no—
940C22—1084no—
941C22C2×D3312yes—
942C22C2×D3311yescharacteristic
943C4—34no—
944C4—34no—
945C4—94no—
946C3—21no—
947C3—22no—
948C3—41no—
949C3C2×#6430811yescharacteristic, complemented
950C3C2×#6431412yescomplemented
951C2—22no—
952C2—64no—
953C2—182no—
954C2—182no—
955C2—184no—
956C2—544no—
957C2#1172442012yesdirect product factor
958C2C22×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×#89049C2semidirect
2. C2×#89039C2semidirect
3. C22×#6292C2semidirect
4. C2×C3×#3811C2semidirect
5. C2×C3×#3804C2semidirect
6. C2×#88965C2semidirect
7. C2×#88962C2semidirect
8. C2×#88955C2semidirect
9. #11724420C2direct (N × H)
10. C2×D3×#626C2semidirect
13. C23×C3⋊(C3⋊D3)C22semidirect
14. C23×C3×C3⋊D3C22semidirect
15. C22×#1113C22semidirect
16. C22×D3×C3⋊D3C22semidirect
17. C22×C3×D32C22semidirect
18. C2×C3×#638C22semidirect
19. C2×C32×#67C22semidirect
20. C22×C32×Dic3C22semidirect
21. #89049C22semidirect
22. C2×#6295C22semidirect
23. C2×#6294C22semidirect
24. #89039C22semidirect
25. C2×#6292C22semidirect
26. C2×#6292C22semidirect
27. C2×#6292C22semidirect
28. C2×#6292C22semidirect
29. C2×#6291C22semidirect
30. C2×#6289C22semidirect
31. C3×#3811C22semidirect
32. C2×C3×#627C22semidirect
33. C2×C3×#626C22semidirect
34. C2×C3×#626C22semidirect
35. C2×C3×#624C22semidirect
36. C2×C3×#624C22semidirect
37. C3×#3804C22semidirect
38. C2×C3×D3×Dic3C22semidirect
39. #88965C22semidirect
40. #88962C22semidirect
41. #88955C22semidirect
42. D3×#626C22semidirect
53. C2×#3811D3semidirect
60. C2×#3804D3semidirect
74. C22×C3⋊(C3⋊D3)C23semidirect
79. C22×C3×C3⋊D3C23semidirect
82. C2×#1113C23semidirect
84. C2×D3×C3⋊D3C23semidirect
86. C2×C3×D32C23semidirect
87. C3×#638C23semidirect
89. C32×#67C23semidirect
92. C2×C32×Dic3C23semidirect
93. #6295C23semidirect
94. #6294C23semidirect
95. #6292C23semidirect
96. #6292C23semidirect
97. #6292C23semidirect
98. #6291C23semidirect
99. #6289C23semidirect
100. C3×#627C23semidirect
101. C3×#626C23semidirect
102. C3×#626C23semidirect
103. C3×#624C23semidirect
104. C3×#624C23semidirect
105. C3×D3×Dic3C23semidirect
114. C23×C3⋊D3C2×D3semidirect
123. C22×D32C2×D3semidirect
127. C2×#638C2×D3semidirect
140. C2×C3×#67C2×D3semidirect
141. C2×C3×#67C2×D3semidirect
144. C22×C3×Dic3C2×D3semidirect
161. #3811C2×D3semidirect
164. C2×#627C2×D3semidirect
182. C2×#626C2×D3semidirect
183. C2×#626C2×D3semidirect
189. C2×#624C2×D3semidirect
190. C2×#624C2×D3semidirect
192. #3804C2×D3semidirect
194. C2×D3×Dic3C2×D3semidirect
281. C22×C3⋊D3C22×D3semidirect
309. C2×D32C22×D3semidirect
315. #638C22×D3semidirect
327. C3×#67C22×D3semidirect
328. C3×#67C22×D3semidirect
340. C2×C3×Dic3C22×D3semidirect
349. #627C22×D3semidirect
364. #626C22×D3semidirect
365. #626C22×D3semidirect
371. #624C22×D3semidirect
372. #624C22×D3semidirect
374. D3×Dic3C22×D3semidirect
377. C2×C33H(5,𝔽2)semidirect
430. C2×#67D32semidirect
433. C22×Dic3D32semidirect
574. C33C2×H(5,𝔽2)semidirect
665. #67C2×D32semidirect
673. C2×Dic3C2×D32semidirect
710. C2×C32#1004semidirect
711. C2×C32#1009semidirect
852. C32C2×#1004semidirect
853. C32C2×#1009semidirect
906. C2×C3#64308semidirect
907. C2×C3#64314semidirect
949. C3C2×#64308semidirect
950. C3C2×#64314semidirect
957. C2#11724420direct (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×#890392
C22×#62922
C2×C3×#38112
C2×C3×#38042
C2×#889652
C2×#889622
C2×#889552
#117244202
C2×D3×#6262
C2×#643143
C2×#643083