Finite Group Databasebeta

← #13178632

Subgroups — #13178632

Order 1728.

1796 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#89041C211yesmaximal, characteristic, complemented
3C3×#64147C211yesmaximal, characteristic, complemented
4C3×#64145C211yesmaximal, characteristic, complemented
5#11723727C212yesmaximal, complemented
6#11723725C212yesmaximal, complemented
7#11723724C212yesmaximal, complemented
8#11723723C212yesmaximal, complemented
9C4×#6295C211yesmaximal, characteristic, complemented
10#11723691C211yesmaximal, characteristic, complemented
11#11723674C211yesmaximal, characteristic, complemented
12#10595243—31nomaximal
13#10595229—31nomaximal
14#10595228—31nomaximal
15C23×C3×C3⋊D3C2212yes—
16C2×C33×D4C2211yescharacteristic
17C2×C3×#638C2212yes—
18C2×C3×#638C2212yescomplemented
19C3×D4×C3⋊D3—24no—
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
23C2×C3×#634C2211yescharacteristic, complemented
24C2×#6295C2211yescharacteristic
25C2×#6295C2212yescomplemented
26C2×#6294C2212yescomplemented
27C2×#6294C2212yescomplemented
28#89041—24no—
29C3×#3757C2212yescomplemented
30C3×#3757C2212yescomplemented
31C3×#3757C2212yescomplemented
32C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
33C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
34#88815C2212yescomplemented
35#88815C2211yescharacteristic, complemented
36#88814C2212yes—
37#88814C2211yescharacteristic
38#88814C2212yescomplemented
39#88814C2211yescharacteristic, complemented
40C2×D4×C3⋊D3D311yescharacteristic, complemented
41C2×C3×D3×D4—31no—
42C2×C3×D3×D4—31no—
43C2×C3×D3×D4—61no—
44C2×#3799—31no—
45C2×#3796—31no—
46C2×#3795—31no—
47#64147D311yescharacteristic, complemented
48#64145D311yescharacteristic, complemented
49C3×#938—31no—
50C3×#938—31no—
51C3×#938—61no—
52C3×#936—31no—
53C3×#936—31no—
54C3×#936—61no—
55#63981—32no—
56#63977—32no—
57#63976—32no—
58#63975—32no—
59#63974—32no—
60#63971—32no—
61#63970—32no—
62#63969—32no—
63#63969—32no—
64D3×#217—32no—
65D3×#217—32no—
66#63958—32no—
67C4×#626—31no—
68C4×#626—31no—
69C4×#625—31no—
70#63898—31no—
71#63894—31no—
72Dic3×D12—31no—
73#63871—31no—
74#63857—31no—
75#63856—31no—
76C23×C33C2312yes—
77C22×C3×C3⋊D3—24no—
78C22×C3×C3⋊D3—24no—
79C22×C3×C3⋊D3—42no—
80C22×C3×C3⋊D3C2311yescharacteristic
81C22×C3×C3⋊D3C2312yes—
82C22×C3×C3⋊D3C2311yescharacteristic
83C33×D4—22no—
84C2×C33×C4C2311yescharacteristic
85C3×#638—24no—
86C3×#638—42no—
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C2×C3×C3⋊Dic3C2311yescharacteristic
89C2×C3×C3⋊Dic3C2312yes—
90C2×C3×C3⋊Dic3C2311yescharacteristic
91C2×C3×C3⋊Dic3C2312yes—
92C2×C3×C3⋊Dic3C2311yescharacteristic
93C3×C4⋊(C3⋊D3)D414yescomplemented
94C3×C4×C3⋊D3—22no—
95C3×C4×C3⋊D3—22no—
96C3×#634—22no—
97#6295—24no—
98#6295—22no—
99#6294—24no—
100#6294—42no—
101#5806—91no—
102#5676—91no—
103#5612—91no—
104C23×C3⋊D3C2×D312yes—
105C23×C3×D3—32no—
106C23×C3×D3—32no—
107C23×C3×D3—62no—
108C2×C32×D4—21no—
109C2×C32×D4—21no—
110C2×C32×D4—21no—
111C2×C32×D4—41no—
112C2×C32×D4C2×D311yescharacteristic
113C2×C32×D4C2×D311yescharacteristic
114C2×C32×D4C2×D311yescharacteristic
115C2×#638C2×D312yes—
116C2×#638C2×D312yescomplemented
117D4×C3⋊D3—24no—
118C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
119C2×C4×C3⋊D3C2×D311yescharacteristic
120C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
121C2×#634C2×D311yescharacteristic, complemented
122C2×C3×#67—32no—
123C2×C3×#67—32no—
124C2×C3×#67—32no—
125C2×C3×#67—32no—
126C2×C3×#67—62no—
127C2×C3×#67—62no—
128C3×D3×D4—64no—
129C3×D3×D4—64no—
130C3×D3×D4—68no—
131C2×C3×D12—31no—
132C2×C3×D12—31no—
133C2×C3×D12—61no—
134C2×C3×C4×D3—31no—
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—61no—
139C2×C3×C4×D3—61no—
140C2×C3×Dic6—31no—
141C2×C3×Dic6—31no—
142C2×C3×Dic6—61no—
143C2×#626—32no—
144C2×#626—32no—
145C2×#626—31no—
146C2×#626—31no—
147C2×#625—32no—
148C2×#625—31no—
149C2×#624—32no—
150C2×#624—32no—
151C2×D3×Dic3—32no—
152C2×D3×Dic3—32no—
153C2×D3×Dic3—32no—
154C2×D3×Dic3—32no—
155#3799—64no—
156#3796—64no—
157#3795—64no—
158#3757C2×D312yescomplemented
159#3757C2×D312yescomplemented
160#3757C2×D312yescomplemented
161C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
162C4×C3⋊Dic3C2×D311yescharacteristic, complemented
163C3×#217—32no—
164C3×#217—32no—
165C3×#217—32no—
166C3×#217—32no—
167C3×#217—32no—
168C3×#217—32no—
169C3×#217—62no—
170C3×#217—62no—
171C3×#217—62no—
172C3×C4⋊Dic3—31no—
173C3×C4⋊Dic3—31no—
174C3×C4⋊Dic3—61no—
175C3×C4×Dic3—31no—
176C3×C4×Dic3—31no—
177C3×C4×Dic3—61no—
178#3724—32no—
179#3724—31no—
180Dic3⋊Dic3—32no—
181Dic3⋊Dic3—32no—
182Dic3⋊Dic3—31no—
183Dic3⋊Dic3—31no—
184#3722—32no—
185#3722—32no—
186#3722—31no—
187#3722—31no—
188(C2×D3)⋊Dic3—32no—
189(C2×D3)⋊Dic3—32no—
190(C2×D3)⋊Dic3—32no—
191(C2×D3)⋊Dic3—32no—
192(C2×D3)⋊Dic3—31no—
193(C2×D3)⋊Dic3—31no—
194(C2×D3)⋊Dic3—31no—
195(C2×D3)⋊Dic3—31no—
196C22×C33—22no—
197C22×C33—22no—
198C22×C33—22no—
199C22×C33C2411yescharacteristic
200C2×C3×C3⋊D3—21no—
201C2×C3×C3⋊D3—22no—
202C2×C3×C3⋊D3—21no—
203C2×C3×C3⋊D3—22no—
204C2×C3×C3⋊D3—21no—
205C2×C3×C3⋊D3—21no—
206C2×C3×C3⋊D3—21no—
207C2×C3×C3⋊D3—48no—
208C2×C3×C3⋊D3C2×D414yes—
209C2×C3×C3⋊D3#4112yescomplemented
210C33×C4C2×D412yes—
211C3×C3⋊Dic3—21no—
212C3×C3⋊Dic3—21no—
213C3×C3⋊Dic3—22no—
214C3×C3⋊Dic3—21no—
215C3×C3⋊Dic3—21no—
216C3×C3⋊Dic3—22no—
217C22×C3×D4—91no—
218C2×#239—91no—
219C2×#237—91no—
220C2×D3×D4—31no—
221C2×D3×D4—31no—
222C2×D3×D4—61no—
223C2×#235—91no—
224C3×#124—91no—
225C3×#121—91no—
226#953—92no—
227C2×#217—92no—
228#946—91no—
229#939—92no—
230#938—31no—
231#938—31no—
232#938—61no—
233#938—92no—
234#937—92no—
235#936—31no—
236#936—31no—
237#936—61no—
238#935—92no—
239D4×Dic3—91no—
240C4×#67—91no—
241C4×#67—91no—
242#924—91no—
243#897—91no—
244#893—91no—
245#884—92no—
246#883—92no—
247#883—92no—
248#882—92no—
249D3×C22⋊C4—92no—
250D3×C22⋊C4—92no—
251C4×D12—91no—
252C4×D12—91no—
253C23×C32—22no—
254C23×C32—22no—
255C23×C32—22no—
256C23×C32—42no—
257C23×C32C22×D312yes—
258C23×C32C22×D312yes—
259C23×C32C22×D312yes—
260C22×C3⋊D3—24no—
261C22×C3⋊D3—24no—
262C22×C3⋊D3—42no—
263C22×C3⋊D3C22×D311yescharacteristic
264C22×C3⋊D3C22×D311yescharacteristic
265C22×C3⋊D3C22×D312yes—
266C22×C3×D3—31no—
267C22×C3×D3—31no—
268C22×C3×D3—32no—
269C22×C3×D3—32no—
270C22×C3×D3—31no—
271C22×C3×D3—31no—
272C22×C3×D3—61no—
273C22×C3×D3—62no—
274C22×C3×D3—61no—
275C22×C3×D3—64no—
276C22×C3×D3—64no—
277C22×C3×D3—64no—
278C22×C3×D3—64no—
279C22×C3×D3—68no—
280C22×C3×D3—124no—
281C22×C3×D3—122no—
282C22×C3×D3—122no—
283C22×C3×D3—124no—
284C32×D4—22no—
285C32×D4—24no—
286C32×D4—22no—
287C32×D4—22no—
288C32×D4—42no—
289C32×D4—42no—
290C32×D4—44no—
291C2×C32×C4—21no—
292C2×C32×C4—21no—
293C2×C32×C4—21no—
294C2×C32×C4—41no—
295C2×C32×C4C22×D311yescharacteristic
296C2×C32×C4C22×D311yescharacteristic
297C2×C32×C4C22×D311yescharacteristic
298#638—24no—
299#638—42no—
300C2×C3⋊Dic3C22×D311yescharacteristic
301C2×C3⋊Dic3C22×D312yes—
302C2×C3⋊Dic3C22×D311yescharacteristic
303C2×C3⋊Dic3C22×D311yescharacteristic
304C2×C3⋊Dic3C22×D311yescharacteristic
305C2×C3⋊Dic3C22×D312yes—
306C4⋊(C3⋊D3)#6714yescomplemented
307C4×C3⋊D3—22no—
308C4×C3⋊D3—22no—
309#634—22no—
310C3×#67—64no—
311C3×#67—64no—
312C3×#67—68no—
313C3×#67—122no—
314C3×#67—122no—
315C3×#67—124no—
316C2×C3×Dic3—31no—
317C2×C3×Dic3—32no—
318C2×C3×Dic3—31no—
319C2×C3×Dic3—31no—
320C2×C3×Dic3—31no—
321C2×C3×Dic3—31no—
322C2×C3×Dic3—32no—
323C2×C3×Dic3—31no—
324C2×C3×Dic3—32no—
325C2×C3×Dic3—31no—
326C2×C3×Dic3—31no—
327C2×C3×Dic3—32no—
328C2×C3×Dic3—61no—
329C2×C3×Dic3—61no—
330C2×C3×Dic3—61no—
331C2×C3×Dic3—62no—
332C2×C3×Dic3—62no—
333C2×C3×Dic3—61no—
334C3×D12—34no—
335C3×D12—34no—
336C3×D12—64no—
337C3×C4×D3—64no—
338C3×C4×D3—62no—
339C3×C4×D3—62no—
340C3×C4×D3—62no—
341C3×C4×D3—62no—
342C3×C4×D3—122no—
343C3×Dic6—62no—
344C3×Dic6—62no—
345C3×Dic6—122no—
346#626—64no—
347#626—62no—
348#626—62no—
349#626—64no—
350#625—64no—
351#625—62no—
352#624—64no—
353#624—122no—
354D3×Dic3—64no—
355D3×Dic3—64no—
356D3×Dic3—122no—
357D3×Dic3—122no—
358#546—271noSylow
359C2×C33—42no—
360C2×C33C22×D411yescharacteristic
361C2×C33C2×#4111yescharacteristic
362C2×C33H(5,𝔽2)11yescharacteristic
363C3×C3⋊D3—22no—
364C3×C3⋊D3—24no—
365C3×C3⋊D3—41no—
366C24×C3—92no—
367C23×D3—32no—
368C23×D3—32no—
369C23×D3—62no—
370C2×C3×Q8—91no—
371C2×C3×D4—21no—
372C2×C3×D4—21no—
373C2×C3×D4—21no—
374C2×C3×D4—41no—
375C2×C3×D4—92no—
376C2×C3×D4—92no—
377C2×C3×D4—91no—
378C2×C3×D4—184no—
379C2×C3×D4D3211yescharacteristic
380C2×C3×D4D3211yescharacteristic
381C2×C3×D4D3211yescharacteristic
382C22×C3×C4—91no—
383C22×C3×C4—91no—
384C2×#67—32no—
385C2×#67—32no—
386C2×#67—32no—
387C2×#67—32no—
388C2×#67—62no—
389C2×#67—62no—
390C2×#67—91no—
391C2×#67—91no—
392C2×#67—92no—
393C2×#67—92no—
394C22×Dic3—92no—
395C22×Dic3—92no—
396#239—184no—
397#237—184no—
398D3×D4—64no—
399D3×D4—64no—
400D3×D4—68no—
401#235—184no—
402C2×D12—31no—
403C2×D12—31no—
404C2×D12—61no—
405C2×D12—91no—
406C2×D12—92no—
407C2×C4×D3—31no—
408C2×C4×D3—31no—
409C2×C4×D3—31no—
410C2×C4×D3—31no—
411C2×C4×D3—61no—
412C2×C4×D3—61no—
413C2×C4×D3—92no—
414C2×C4×D3—92no—
415C2×C4×D3—92no—
416C2×C4×D3—92no—
417C2×Dic6—31no—
418C2×Dic6—31no—
419C2×Dic6—61no—
420C3×C4⋊C4—91no—
421C3×C22⋊C4—92no—
422C3×C22⋊C4—92no—
423C3×C22⋊C4—92no—
424C3×C42—91no—
425#217—32no—
426#217—32no—
427#217—32no—
428#217—32no—
429#217—32no—
430#217—32no—
431#217—62no—
432#217—62no—
433#217—62no—
434#217—92no—
435#217—91no—
436#217—91no—
437#217—92no—
438(C2×D3)⋊C4—91no—
439(C2×D3)⋊C4—92no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4—92no—
443(C2×D3)⋊C4—92no—
444(C2×D3)⋊C4—92no—
445(C2×D3)⋊C4—91no—
446C4⋊Dic3—31no—
447C4⋊Dic3—31no—
448C4⋊Dic3—61no—
449C4⋊Dic3—91no—
450C4⋊Dic3—92no—
451Dic3⋊C4—91no—
452Dic3⋊C4—92no—
453Dic3⋊C4—92no—
454Dic3⋊C4—91no—
455C4×Dic3—31no—
456C4×Dic3—31no—
457C4×Dic3—61no—
458C22×C32—22no—
459C22×C32—24no—
460C22×C32—22no—
461C22×C32—22no—
462C22×C32—22no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—21no—
469C22×C32—21no—
470C22×C32—21no—
471C22×C32—41no—
472C22×C32—42no—
473C22×C32—42no—
474C22×C32—44no—
475C22×C32—42no—
476C22×C32—42no—
477C22×C32—42no—
478C22×C32—42no—
479C22×C32—42no—
480C22×C32—42no—
481C22×C32—82no—
482C22×C32—82no—
483C22×C32C23×D311yescharacteristic
484C22×C32C23×D311yescharacteristic
485C22×C32C23×D311yescharacteristic
486C2×C3⋊D3—21no—
487C2×C3⋊D3—21no—
488C2×C3⋊D3—21no—
489C2×C3⋊D3—22no—
490C2×C3⋊D3—22no—
491C2×C3⋊D3—21no—
492C2×C3⋊D3—21no—
493C2×C3⋊D3—48no—
494C2×C3⋊D3#23712yescomplemented
495C2×C3⋊D3C2×#6714yes—
496C2×C3×D3—34no—
497C2×C3×D3—34no—
498C2×C3×D3—32no—
499C2×C3×D3—32no—
500C2×C3×D3—62no—
501C2×C3×D3—64no—
502C2×C3×D3—62no—
503C2×C3×D3—62no—
504C2×C3×D3—61no—
505C2×C3×D3—61no—
506C2×C3×D3—62no—
507C2×C3×D3—61no—
508C2×C3×D3—62no—
509C2×C3×D3—62no—
510C2×C3×D3—62no—
511C2×C3×D3—61no—
512C2×C3×D3—62no—
513C2×C3×D3—61no—
514C2×C3×D3—61no—
515C2×C3×D3—61no—
516C2×C3×D3—61no—
517C2×C3×D3—61no—
518C2×C3×D3—61no—
519C2×C3×D3—121no—
520C2×C3×D3—121no—
521C2×C3×D3—122no—
522C2×C3×D3—122no—
523C2×C3×D3—128no—
524C2×C3×D3—128no—
525C2×C3×D3—1216no—
526C32×C4—22no—
527C32×C4—22no—
528C32×C4—22no—
529C32×C4—42no—
530C32×C4D3×D412yes—
531C32×C4D3×D412yes—
532C32×C4C2×#6712yes—
533C3⋊Dic3—21no—
534C3⋊Dic3—21no—
535C3⋊Dic3—22no—
536C3⋊Dic3—22no—
537C3⋊Dic3—21no—
538C3⋊Dic3—21no—
539C3×Dic3—62no—
540C3×Dic3—61no—
541C3×Dic3—62no—
542C3×Dic3—61no—
543C3×Dic3—61no—
544C3×Dic3—61no—
545C3×Dic3—61no—
546C3×Dic3—61no—
547C3×Dic3—62no—
548C3×Dic3—61no—
549C3×Dic3—62no—
550C3×Dic3—61no—
551C3×Dic3—62no—
552C3×Dic3—122no—
553C3×Dic3—121no—
554C3×Dic3—121no—
555C3×Dic3—121no—
556C3×Dic3—122no—
557C2×#41—271no—
558C22×D4—91no—
559#124—91no—
560#123—272no—
561C22⋊Q8—271no—
562#121—91no—
563#121—272no—
564#120—272no—
565C4×D4—271no—
566C4×D4—271no—
567C2×C22⋊C4—272no—
568C33#54611yescharacteristic, complemented, Sylow
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—22no—
572C23×C3—42no—
573C23×C3—91no—
574C23×C3—92no—
575C23×C3—91no—
576C23×C3—184no—
577C23×C3—184no—
578C23×C3—362no—
579C23×C3C2×D3212yes—
580C23×C3C2×D3212yes—
581C23×C3C2×D3212yes—
582C22×D3—31no—
583C22×D3—31no—
584C22×D3—32no—
585C22×D3—32no—
586C22×D3—31no—
587C22×D3—31no—
588C22×D3—61no—
589C22×D3—61no—
590C22×D3—62no—
591C22×D3—64no—
592C22×D3—64no—
593C22×D3—64no—
594C22×D3—64no—
595C22×D3—68no—
596C22×D3—124no—
597C22×D3—122no—
598C22×D3—122no—
599C22×D3—124no—
600C3×Q8—182no—
601C3×D4—24no—
602C3×D4—22no—
603C3×D4—22no—
604C3×D4—22no—
605C3×D4—42no—
606C3×D4—42no—
607C3×D4—44no—
608C3×D4—94no—
609C3×D4—184no—
610C3×D4—362no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—41no—
615C2×C3×C4—91no—
616C2×C3×C4—91no—
617C2×C3×C4—92no—
618C2×C3×C4—91no—
619C2×C3×C4—92no—
620C2×C3×C4—91no—
621C2×C3×C4—182no—
622C2×C3×C4—182no—
623C2×C3×C4C2×D3211yescharacteristic
624C2×C3×C4C2×D3211yescharacteristic
625C2×C3×C4C2×D3211yescharacteristic
626#67—64no—
627#67—64no—
628#67—68no—
629#67—122no—
630#67—122no—
631#67—124no—
632#67—184no—
633#67—182no—
634#67—184no—
635#67—182no—
636C2×Dic3—31no—
637C2×Dic3—31no—
638C2×Dic3—31no—
639C2×Dic3—31no—
640C2×Dic3—31no—
641C2×Dic3—32no—
642C2×Dic3—32no—
643C2×Dic3—31no—
644C2×Dic3—32no—
645C2×Dic3—31no—
646C2×Dic3—32no—
647C2×Dic3—31no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—62no—
652C2×Dic3—62no—
653C2×Dic3—61no—
654C2×Dic3—184no—
655C2×Dic3—362no—
656D12—34no—
657D12—34no—
658D12—64no—
659D12—182no—
660D12—184no—
661C4×D3—64no—
662C4×D3—62no—
663C4×D3—62no—
664C4×D3—62no—
665C4×D3—62no—
666C4×D3—122no—
667C4×D3—184no—
668C4×D3—184no—
669C4×D3—362no—
670C4×D3—362no—
671Dic6—62no—
672Dic6—62no—
673Dic6—122no—
674C2×C32—21no—
675C2×C32—21no—
676C2×C32—21no—
677C2×C32—21no—
678C2×C32—21no—
679C2×C32—21no—
680C2×C32—21no—
681C2×C32—21no—
682C2×C32—21no—
683C2×C32—41no—
684C2×C32—41no—
685C2×C32—41no—
686C2×C32—42no—
687C2×C32—44no—
688C2×C32—42no—
689C2×C32—42no—
690C2×C32—82no—
691C2×C32—82no—
692C2×C32—84no—
693C2×C32C2×D3×D411yescharacteristic
694C2×C32C2×D3×D411yescharacteristic
695C2×C32C2×#23711yescharacteristic
696C2×C32#100411yescharacteristic
697C2×C32#100411yescharacteristic
698C2×C32D3×#4111yescharacteristic
699C2×C32D3×#4111yescharacteristic
700C2×C32#100911yescharacteristic
701C2×C32C22×#6711yescharacteristic
702C3⋊D3—22no—
703C3⋊D3—24no—
704C3⋊D3—41no—
705C3×D3—64no—
706C3×D3—64no—
707C3×D3—62no—
708C3×D3—64no—
709C3×D3—62no—
710C3×D3—124no—
711C3×D3—122no—
712C3×D3—121no—
713C3×D3—121no—
714C24—92no—
715#41—544no—
716C2×Q8—91no—
717C2×D4—92no—
718C2×D4—92no—
719C2×D4—91no—
720C2×D4—184no—
721C2×D4—271no—
722C2×D4—272no—
723C2×D4#111311yescharacteristic
724C22×C4—91no—
725C22×C4—91no—
726C22×C4—272no—
727C22×C4—272no—
728C4⋊C4—91no—
729C4⋊C4—271no—
730C4⋊C4—272no—
731C22⋊C4—92no—
732C22⋊C4—92no—
733C22⋊C4—92no—
734C22⋊C4—271no—
735C22⋊C4—272no—
736C22⋊C4—272no—
737C22⋊C4—271no—
738C42—91no—
739C22×C3—24no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—42no—
753C22×C3—42no—
754C22×C3—42no—
755C22×C3—42no—
756C22×C3—42no—
757C22×C3—42no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—44no—
761C22×C3—41no—
762C22×C3—82no—
763C22×C3—82no—
764C22×C3—92no—
765C22×C3—94no—
766C22×C3—182no—
767C22×C3—182no—
768C22×C3—181no—
769C22×C3—181no—
770C22×C3—181no—
771C22×C3—181no—
772C22×C3—181no—
773C22×C3—368no—
774C22×C3C22×D3211yescharacteristic
775C22×C3C22×D3211yescharacteristic
776C22×C3C22×D3211yescharacteristic
777C2×D3—32no—
778C2×D3—32no—
779C2×D3—34no—
780C2×D3—34no—
781C2×D3—62no—
782C2×D3—64no—
783C2×D3—62no—
784C2×D3—62no—
785C2×D3—62no—
786C2×D3—62no—
787C2×D3—62no—
788C2×D3—61no—
789C2×D3—62no—
790C2×D3—61no—
791C2×D3—61no—
792C2×D3—61no—
793C2×D3—62no—
794C2×D3—61no—
795C2×D3—61no—
796C2×D3—61no—
797C2×D3—61no—
798C2×D3—61no—
799C2×D3—61no—
800C2×D3—121no—
801C2×D3—122no—
802C2×D3—122no—
803C2×D3—121no—
804C2×D3—128no—
805C2×D3—128no—
806C2×D3—1216no—
807C3×C4—22no—
808C3×C4—22no—
809C3×C4—22no—
810C3×C4—42no—
811C3×C4—181no—
812C3×C4—181no—
813C3×C4—182no—
814C3×C4—181no—
815C3×C4—182no—
816C3×C4—181no—
817C3×C4D3×#6712yes—
818C3×C4D3×#6712yes—
819C3×C4#381112yes—
820Dic3—62no—
821Dic3—61no—
822Dic3—61no—
823Dic3—62no—
824Dic3—61no—
825Dic3—61no—
826Dic3—62no—
827Dic3—62no—
828Dic3—61no—
829Dic3—61no—
830Dic3—61no—
831Dic3—62no—
832Dic3—61no—
833Dic3—122no—
834Dic3—121no—
835Dic3—122no—
836Dic3—121no—
837Dic3—121no—
838C32—21no—
839C32—21no—
840C32—21no—
841C32—41no—
842C32#561211yescharacteristic, complemented
843C32#567611yescharacteristic, complemented
844C32#580611yescharacteristic, complemented
845C23—91no—
846C23—92no—
847C23—91no—
848C23—184no—
849C23—184no—
850C23—362no—
851C23C2×#111312yes—
852Q8—182no—
853D4—22no—
854D4—94no—
855D4—184no—
856D4—362no—
857D4—544no—
858D4—542no—
859C2×C4—91no—
860C2×C4—91no—
861C2×C4—91no—
862C2×C4—92no—
863C2×C4—92no—
864C2×C4—91no—
865C2×C4—182no—
866C2×C4—182no—
867C2×C4—544no—
868C2×C4—1082no—
869C2×C4C2×#111311yescharacteristic
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—44no—
880C2×C3—42no—
881C2×C3—42no—
882C2×C3—42no—
883C2×C3—41no—
884C2×C3—41no—
885C2×C3—41no—
886C2×C3—82no—
887C2×C3—82no—
888C2×C3—84no—
889C2×C3—182no—
890C2×C3—184no—
891C2×C3—361no—
892C2×C3D3×#23711yescharacteristic
893C2×C3D3×#23711yescharacteristic
894C2×C3#6431211yescharacteristic
895C2×C3#6431311yescharacteristic
896C2×C3#6431411yescharacteristic
897C2×C3#6431411yescharacteristic
898C2×C3C2×D3×#6711yescharacteristic
899C2×C3C2×D3×#6711yescharacteristic
900C2×C3C2×#381111yescharacteristic
901D3—64no—
902D3—62no—
903D3—64no—
904D3—62no—
905D3—64no—
906D3—124no—
907D3—122no—
908D3—121no—
909D3—121no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—92no—
914C22—94no—
915C22—182no—
916C22—182no—
917C22—181no—
918C22—181no—
919C22—181no—
920C22—181no—
921C22—181no—
922C22—368no—
923C22C22×#111311yescharacteristic
924C4—181no—
925C4—181no—
926C4—182no—
927C4—181no—
928C4—181no—
929C4—182no—
930C4#8904912yes—
931C3—21no—
932C3—21no—
933C3—21no—
934C3—41no—
935C3#1059522811yescharacteristic, complemented
936C3#1059522911yescharacteristic, complemented
937C3#1059524311yescharacteristic, complemented
938C2—42no—
939C2—182no—
940C2—184no—
941C2—361no—
942C2#1172462211yescharacteristic
943C2#1172462311yescharacteristic
944C2C2×#8904911yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×C3⋊D3C2semidirect
2. C2×#89041C2semidirect
3. C3×#64147C2semidirect
4. C3×#64145C2semidirect
5. #11723727C2semidirect
6. #11723725C2semidirect
7. #11723724C2semidirect
8. #11723723C2semidirect
9. C4×#6295C2semidirect
10. #11723691C2semidirect
11. #11723674C2semidirect
18. C2×C3×#638C22semidirect
22. C2×C3×C4×C3⋊D3C22semidirect
23. C2×C3×#634C22semidirect
25. C2×#6295C22semidirect
26. C2×#6294C22semidirect
27. C2×#6294C22semidirect
29. C3×#3757C22semidirect
30. C3×#3757C22semidirect
31. C3×#3757C22semidirect
32. C3×C4⋊(C3⋊Dic3)C22semidirect
33. C3×C4×C3⋊Dic3C22semidirect
34. #88815C22semidirect
35. #88815C22semidirect
38. #88814C22semidirect
39. #88814C22semidirect
40. C2×D4×C3⋊D3D3semidirect
47. #64147D3semidirect
48. #64145D3semidirect
93. C3×C4⋊(C3⋊D3)D4semidirect
116. C2×#638C2×D3semidirect
120. C2×C4×C3⋊D3C2×D3semidirect
121. C2×#634C2×D3semidirect
158. #3757C2×D3semidirect
159. #3757C2×D3semidirect
160. #3757C2×D3semidirect
161. C4⋊(C3⋊Dic3)C2×D3semidirect
162. C4×C3⋊Dic3C2×D3semidirect
209. C2×C3×C3⋊D3#41semidirect
306. C4⋊(C3⋊D3)#67semidirect
494. C2×C3⋊D3#237semidirect
568. C33#546semidirect
842. C32#5612semidirect
843. C32#5676semidirect
844. C32#5806semidirect
935. C3#10595228semidirect
936. C3#10595229semidirect
937. C3#10595243semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×C3⋊D32
C2×#890412
C3×#641472
C3×#641452
#117237272
#117237252
#117237242
#117237232
C4×#62952
#117236912
#117236742
#105952433
#105952293
#105952283