Finite Group Databasebeta

← #13177380

Subgroups — #13177380

Order 1728.

2524 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89039C211yesmaximal, characteristic, complemented
2C2×#89028C211yesmaximal, characteristic, complemented
3#11723978C211yesmaximal, characteristic, complemented
4C3×#64148C211yesmaximal, characteristic, complemented
5C32×#940C211yesmaximal, characteristic, complemented
6#11723643C211yesmaximal, characteristic, complemented
7#11723638C211yesmaximal, characteristic, complemented
8#11723635C211yesmaximal, characteristic, complemented
9#11723633C211yesmaximal, characteristic, complemented
10#11723615C211yesmaximal, characteristic, complemented
11#11723600C211yesmaximal, characteristic, complemented
12#11723540C211yesmaximal, characteristic, complemented
13#11723475C211yesmaximal, characteristic, complemented
14#11723468C211yesmaximal, characteristic, complemented
15#11723416C211yesmaximal, characteristic, complemented
16#10596186—31nomaximal
17#10595299—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic
22C2×#6312C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic
24C2×C3×#638C2211yescharacteristic, complemented
25C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
26C2×C32×#67C2211yescharacteristic
27C2×C32×#67C2211yescharacteristic, complemented
28C2×C32×#67C2211yescharacteristic, complemented
29C2×C32×#67C2211yescharacteristic, complemented
30C2×C32×D12C2211yescharacteristic, complemented
31#89039—24no—
32C2×#6293C2211yescharacteristic, complemented
33C2×#6292C2211yescharacteristic
34C2×#6291C2211yescharacteristic
35C2×#6291C2211yescharacteristic
36C2×#6291C2211yescharacteristic, complemented
37C2×#6290C2211yescharacteristic, complemented
38C2×#6289C2211yescharacteristic
39#89028—24no—
40C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
41#88864C2211yescharacteristic, complemented
42#88859C2211yescharacteristic
43#88859C2211yescharacteristic, complemented
44C3×#3757C2211yescharacteristic, complemented
45C3×#3752C2211yescharacteristic, complemented
46C3×#3750C2211yescharacteristic, complemented
47C32×C4×Dic3C2211yescharacteristic, complemented
48#88807C2211yescharacteristic, complemented
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic, complemented
51#88803C2211yescharacteristic, complemented
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C2×#3830—31no—
56C2×D4×C3⋊D3—31no—
57C2×#3811—34no—
58C2×#3804—34no—
59C32×#127—31no—
60#64149—31no—
61#64148—31no—
62#64148—31no—
63#64148—31no—
64#64148D311yescharacteristic, complemented
65#64146—31no—
66#64146—31no—
67#64146—31no—
68#64146—34no—
69#64146—31no—
70#64146—64no—
71#64145—31no—
72#64084—31no—
73#64081—31no—
74C3×#940D314yescomplemented
75C3×#939—34no—
76#63983—34no—
77#63981—34no—
78#63979—34no—
79#63978—34no—
80#63970—34no—
81#63959—34no—
82#63922—34no—
83#63886—34no—
84#63852—34no—
85#63836—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3⋊(C3⋊D3)—22no—
89C22×C3⋊(C3⋊D3)—41no—
90C22×C3⋊(C3⋊D3)—41no—
91C22×C3⋊(C3⋊D3)C2311yescharacteristic
92C22×C3⋊(C3⋊D3)C2311yescharacteristic
93C22×C3×C3⋊D3C2311yescharacteristic
94C22×C32×D3C2311yescharacteristic
95C22×C32×D3C2311yescharacteristic
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3—41no—
98C2×D3×C3⋊D3—41no—
99C33×D4—41no—
100C2×C33×C4C2311yescharacteristic
101#6312—22no—
102#6312—41no—
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C3×#638—22no—
106C3×#638—41no—
107C2×C3×C3⋊Dic3—22no—
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C32×#67—22no—
112C32×#67—22no—
113C32×#67—41no—
114C32×#67—41no—
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C32×D12—41no—
118#6293—22no—
119#6292—22no—
120#6291—22no—
121#6291—22no—
122#6291—41no—
123#6290—41no—
124#6289D414yescomplemented
125D3×C3⋊Dic3—22no—
126#5715—94no—
127#5607—91no—
128C23×C3⋊D3—31no—
129C23×C3⋊D3—34no—
130C23×C3⋊D3—31no—
131C23×C3⋊D3—64no—
132C22×D32—34no—
133C2×C32×D4—24no—
134C2×C32×D4—31no—
135C2×C32×D4—31no—
136C2×C32×D4—31no—
137C2×C32×D4—31no—
138C2×C32×D4—31no—
139C2×C32×D4C2×D314yescomplemented
140C2×C32×D4C2×D311yescharacteristic, complemented
141C2×#638—31no—
142C2×#638—34no—
143C2×#638—31no—
144C2×#638—34no—
145C2×#638—31no—
146C2×#638—31no—
147C2×#638—31no—
148C2×#638—31no—
149C2×#638—64no—
150C2×#638—64no—
151C2×#638C2×D311yescharacteristic
152C2×#638C2×D311yescharacteristic, complemented
153C22×C3⋊Dic3—31no—
154C22×C3⋊Dic3C2×D311yescharacteristic, complemented
155#3830—64no—
156D4×C3⋊D3—64no—
157C2×C4⋊(C3⋊D3)—31no—
158C2×C4×C3⋊D3—31no—
159C2×#634—31no—
160C2×C3×#67—34no—
161C2×C3×#67—34no—
162C2×C3×#67C2×D314yes—
163C2×C3×#67C2×D314yescomplemented
164C2×C3×#67C2×D314yescomplemented
165C2×C3×#67C2×D314yescomplemented
166C22×C3×Dic3—34no—
167C2×C3×D12C2×D314yescomplemented
168#3811—616no—
169C2×#627—34no—
170C2×#626—34no—
171C2×#626—34no—
172C2×#626—34no—
173C2×#626—34no—
174C2×#625—34no—
175C2×#624—34no—
176#3804—616no—
177C2×D3×Dic3—34no—
178C32×C42—31no—
179#3757—31no—
180#3757—34no—
181#3757—31no—
182#3757—31no—
183#3757—64no—
184#3757C2×D311yescharacteristic, complemented
185#3752—31no—
186#3752—31no—
187#3752—31no—
188#3752—34no—
189#3752—34no—
190#3752—31no—
191#3752—31no—
192#3752—64no—
193#3752—64no—
194#3752C2×D311yescharacteristic, complemented
195#3750—31no—
196#3750C2×D311yescharacteristic, complemented
197C4×C3⋊Dic3—31no—
198C3×#217—34no—
199C3×(C2×D3)⋊C4—34no—
200C3×Dic3⋊C4—34no—
201C3×C4×Dic3C2×D314yescomplemented
202Dic3⋊Dic3—34no—
203#3722—34no—
204#3722—34no—
205(C2×D3)⋊Dic3—34no—
206(C2×D3)⋊Dic3—34no—
207(C2×D3)⋊Dic3—34no—
208Dic32—34no—
209C22×C33—21no—
210C22×C33—21no—
211C22×C33—21no—
212C22×C33—21no—
213C22×C33—21no—
214C22×C33—21no—
215C22×C33C2411yescharacteristic
216C2×C3⋊(C3⋊D3)—21no—
217C2×C3⋊(C3⋊D3)—21no—
218C2×C3⋊(C3⋊D3)—21no—
219C2×C3⋊(C3⋊D3)—21no—
220C2×C3⋊(C3⋊D3)—21no—
221C2×C3⋊(C3⋊D3)—44no—
222C2×C3⋊(C3⋊D3)C2×D412yes—
223C2×C3×C3⋊D3—21no—
224C2×C3×C3⋊D3—21no—
225C2×C3×C3⋊D3—21no—
226C2×C32×D3—21no—
227C2×C32×D3—21no—
228C2×C32×D3—21no—
229C2×C32×D3—21no—
230C2×C32×D3—21no—
231C2×C32×D3—21no—
232D3×C3⋊D3—44no—
233C33×C4—21no—
234C3⋊(C3⋊Dic3)—21no—
235C3⋊(C3⋊Dic3)—21no—
236C3×C3⋊Dic3—21no—
237C3×C3⋊Dic3—21no—
238C3×C3⋊Dic3C2×D412yes—
239C32×Dic3—21no—
240C32×Dic3C2×D412yes—
241C2×#237—94no—
242C2×D3×D4—94no—
243C2×D3×D4—91no—
244C2×#235—91no—
245C3×#127—34no—
246C3×#121—91no—
247#940—94no—
248#940—91no—
249#940C3⋊D311yescharacteristic, complemented
250#939—34no—
251#939—94no—
252#939—94no—
253#939—94no—
254#938—91no—
255#937—94no—
256#937—94no—
257#937—94no—
258#937—94no—
259#937—91no—
260#937—91no—
261#937—184no—
262#936—94no—
263#930—91no—
264#895—91no—
265#892—91no—
266#885—91no—
267#885—91no—
268#882—91no—
269#882—91no—
270#875—94no—
271#872—94no—
272C23×C32—24no—
273C23×C32—24no—
274C23×C32—31no—
275C23×C32—31no—
276C23×C32C22×D314yes—
277C23×C32C22×D314yes—
278C23×C32C22×D311yescharacteristic
279C23×C32C22×D311yescharacteristic
280C22×C3⋊D3—31no—
281C22×C3⋊D3—31no—
282C22×C3⋊D3—34no—
283C22×C3⋊D3—34no—
284C22×C3⋊D3—64no—
285C22×C3⋊D3—64no—
286C22×C3⋊D3—62no—
287C22×C3⋊D3—62no—
288C22×C3⋊D3—68no—
289C22×C3⋊D3—128no—
290C22×C3⋊D3—121no—
291C22×C3⋊D3—121no—
292C22×C3⋊D3—121no—
293C22×C3⋊D3—121no—
294C22×C3⋊D3—124no—
295C22×C3⋊D3—124no—
296C22×C3⋊D3—128no—
297C22×C3⋊D3—128no—
298C22×C3⋊D3C22×D311yescharacteristic
299C22×C3×D3—34no—
300C22×C3×D3C22×D314yes—
301C22×C3×D3C22×D314yes—
302C2×D32—68no—
303C2×D32—124no—
304C2×D32—124no—
305C32×D4—41no—
306C32×D4—44no—
307C32×D4—48no—
308C32×D4—62no—
309C32×D4—62no—
310C32×D4—121no—
311C32×D4—121no—
312C32×D4—121no—
313C2×C32×C4—24no—
314C2×C32×C4—31no—
315C2×C32×C4—31no—
316C2×C32×C4C22×D314yes—
317C2×C32×C4C22×D311yescharacteristic
318#638—22no—
319#638—41no—
320#638—62no—
321#638—62no—
322#638—62no—
323#638—68no—
324#638—128no—
325#638—121no—
326#638—121no—
327#638—121no—
328#638—124no—
329#638—128no—
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3—31no—
332C2×C3⋊Dic3—31no—
333C2×C3⋊Dic3—34no—
334C2×C3⋊Dic3—34no—
335C2×C3⋊Dic3—64no—
336C2×C3⋊Dic3—64no—
337C2×C3⋊Dic3—62no—
338C2×C3⋊Dic3C22×D311yescharacteristic
339C2×C3⋊Dic3C22×D311yescharacteristic
340C2×C3⋊Dic3C22×D311yescharacteristic
341C4⋊(C3⋊D3)—62no—
342C4×C3⋊D3—34no—
343#634—62no—
344C3×#67—28no—
345C3×#67—28no—
346C3×#67—44no—
347C3×#67—44no—
348C3×#67—68no—
349C3×#67—124no—
350C2×C3×Dic3—34no—
351C2×C3×Dic3—34no—
352C2×C3×Dic3—34no—
353C2×C3×Dic3—68no—
354C2×C3×Dic3C22×D314yes—
355C2×C3×Dic3C22×D314yes—
356C3×D12—44no—
357#627—68no—
358#626—68no—
359#626—68no—
360#626—68no—
361#626—124no—
362#625—124no—
363#624—316no—
364D3×Dic3—68no—
365#535—271noSylow
366C2×C33—41no—
367C2×C33—41no—
368C2×C33C22×D411yescharacteristic
369C2×C33H(5,𝔽2)11yescharacteristic
370C2×C33H(5,𝔽2)11yescharacteristic
371C3⋊(C3⋊D3)—22no—
372C3⋊(C3⋊D3)—41no—
373C3×C3⋊D3—41no—
374C32×D3—41no—
375C32×D3—41no—
376C23×D3—94no—
377C23×D3—94no—
378C23×D3—91no—
379C23×D3—91no—
380C23×D3—184no—
381C2×C3×D4—24no—
382C2×C3×D4—34no—
383C2×C3×D4—34no—
384C2×C3×D4—34no—
385C2×C3×D4—34no—
386C2×C3×D4—34no—
387C2×C3×D4—91no—
388C2×C3×D4—91no—
389C2×C3×D4D3214yescomplemented
390C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
391C22×C3×C4—91no—
392C2×#67—34no—
393C2×#67—34no—
394C2×#67—94no—
395C2×#67—94no—
396C2×#67—94no—
397C2×#67—94no—
398C2×#67—91no—
399C2×#67—94no—
400C2×#67—94no—
401C2×#67—91no—
402C2×#67—91no—
403C2×#67—91no—
404C2×#67—184no—
405C2×#67—184no—
406C2×#67C2×C3⋊D311yescharacteristic
407C2×#67C2×C3⋊D311yescharacteristic, complemented
408C2×#67C2×C3⋊D311yescharacteristic, complemented
409C2×#67C2×C3⋊D311yescharacteristic, complemented
410C22×Dic3—34no—
411C22×Dic3—94no—
412#237—1816no—
413D3×D4—184no—
414D3×D4—1816no—
415#235—184no—
416C2×D12—94no—
417C2×D12—91no—
418C2×D12—91no—
419C2×D12—91no—
420C2×D12C2×C3⋊D311yescharacteristic, complemented
421C2×C4×D3—94no—
422C2×C4×D3—91no—
423C2×C4×D3—91no—
424C2×Dic6—94no—
425C2×Dic6—91no—
426C3×C4⋊C4—91no—
427C3×C22⋊C4—91no—
428C3×C22⋊C4—91no—
429C3×C42—34no—
430#217—34no—
431#217—94no—
432#217—94no—
433#217—94no—
434#217—91no—
435#217—91no—
436#217—184no—
437(C2×D3)⋊C4—34no—
438(C2×D3)⋊C4—94no—
439(C2×D3)⋊C4—94no—
440(C2×D3)⋊C4—94no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4—91no—
443(C2×D3)⋊C4—94no—
444(C2×D3)⋊C4—94no—
445(C2×D3)⋊C4—91no—
446(C2×D3)⋊C4—91no—
447(C2×D3)⋊C4—91no—
448(C2×D3)⋊C4—91no—
449(C2×D3)⋊C4—184no—
450(C2×D3)⋊C4—184no—
451C4⋊Dic3—91no—
452Dic3⋊C4—34no—
453Dic3⋊C4—94no—
454C4×Dic3—94no—
455C4×Dic3—91no—
456C4×Dic3C2×C3⋊D311yescharacteristic, complemented
457C22×C32—28no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—24no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—24no—
466C22×C32—24no—
467C22×C32—24no—
468C22×C32—24no—
469C22×C32—24no—
470C22×C32—24no—
471C22×C32—44no—
472C22×C32—44no—
473C22×C32—44no—
474C22×C32—44no—
475C22×C32—44no—
476C22×C32—61no—
477C22×C32—61no—
478C22×C32—61no—
479C22×C32—61no—
480C22×C32—61no—
481C22×C32—61no—
482C22×C32C23×D314yes—
483C22×C32C23×D311yescharacteristic
484C2×C3⋊D3—21no—
485C2×C3⋊D3—21no—
486C2×C3⋊D3—21no—
487C2×C3⋊D3—32no—
488C2×C3⋊D3—38no—
489C2×C3⋊D3—68no—
490C2×C3⋊D3—61no—
491C2×C3⋊D3—61no—
492C2×C3⋊D3—68no—
493C2×C3⋊D3—61no—
494C2×C3⋊D3—64no—
495C2×C3⋊D3—61no—
496C2×C3⋊D3—61no—
497C2×C3⋊D3—64no—
498C2×C3⋊D3—64no—
499C2×C3⋊D3—64no—
500C2×C3⋊D3—64no—
501C2×C3⋊D3—124no—
502C2×C3⋊D3—124no—
503C2×C3⋊D3—124no—
504C2×C3⋊D3—124no—
505C2×C3⋊D3—124no—
506C2×C3⋊D3—124no—
507C2×C3⋊D3—1216no—
508C2×C3⋊D3—1232no—
509C2×C3×D3—24no—
510C2×C3×D3—24no—
511C2×C3×D3—24no—
512C2×C3×D3—24no—
513C2×C3×D3—24no—
514C2×C3×D3—24no—
515C2×C3×D3—64no—
516C2×C3×D3—64no—
517C2×C3×D3—64no—
518D32—1216no—
519C32×C4—21no—
520C32×C4—24no—
521C32×C4—32no—
522C32×C4—44no—
523C32×C4—61no—
524C3⋊Dic3—21no—
525C3⋊Dic3—21no—
526C3⋊Dic3—61no—
527C3⋊Dic3—61no—
528C3⋊Dic3—64no—
529C3⋊Dic3—64no—
530C3⋊Dic3—124no—
531C3⋊Dic3—124no—
532C3⋊Dic3D3×D412yes—
533C3×Dic3—24no—
534C3×Dic3—38no—
535C3×Dic3—64no—
536C3×Dic3—64no—
537C3×Dic3D3×D418yes—
538C2×#41—271no—
539C22×D4—271no—
540#127—31no—
541#127—271no—
542#124—271no—
543#124—271no—
544#121—91no—
545#121—271no—
546#121—271no—
547#121—271no—
548#120—271no—
549#120—271no—
550#120—271no—
551#120—271no—
552#117—271no—
553C33#53511yescharacteristic, complemented, Sylow
554C23×C3—24no—
555C23×C3—24no—
556C23×C3—34no—
557C23×C3—34no—
558C23×C3—91no—
559C23×C3C2×D3214yes—
560C23×C3C2×D3214yes—
561C23×C3C22×C3⋊D311yescharacteristic
562C23×C3C22×C3⋊D311yescharacteristic
563C22×D3—34no—
564C22×D3—94no—
565C22×D3—91no—
566C22×D3—94no—
567C22×D3—91no—
568C22×D3—184no—
569C22×D3—184no—
570C22×D3—182no—
571C22×D3—188no—
572C22×D3—182no—
573C22×D3—188no—
574C22×D3—368no—
575C22×D3—361no—
576C22×D3—361no—
577C22×D3—364no—
578C22×D3—364no—
579C22×D3—364no—
580C22×D3—364no—
581C22×D3—361no—
582C22×D3—361no—
583C22×D3—368no—
584C22×D3—368no—
585C22×D3C22×C3⋊D311yescharacteristic
586C22×D3C22×C3⋊D311yescharacteristic
587C3×D4—44no—
588C3×D4—41no—
589C3×D4—48no—
590C3×D4—68no—
591C3×D4—68no—
592C3×D4—124no—
593C3×D4—124no—
594C3×D4—124no—
595C3×D4—182no—
596C3×D4—361no—
597C2×C3×C4—24no—
598C2×C3×C4—34no—
599C2×C3×C4—34no—
600C2×C3×C4—91no—
601C2×C3×C4—91no—
602C2×C3×C4—91no—
603C2×C3×C4—182no—
604C2×C3×C4C2×D3214yes—
605C2×C3×C4C22×C3⋊D311yescharacteristic
606#67—22no—
607#67—22no—
608#67—41no—
609#67—41no—
610#67—68no—
611#67—124no—
612#67—188no—
613#67—188no—
614#67—182no—
615#67—188no—
616#67—182no—
617#67—368no—
618#67—364no—
619#67—361no—
620#67—364no—
621#67—364no—
622#67—361no—
623#67—368no—
624C2×Dic3—34no—
625C2×Dic3—34no—
626C2×Dic3—34no—
627C2×Dic3—68no—
628C2×Dic3—94no—
629C2×Dic3—94no—
630C2×Dic3—91no—
631C2×Dic3—91no—
632C2×Dic3—184no—
633C2×Dic3—184no—
634C2×Dic3—188no—
635C2×Dic3C22×C3⋊D311yescharacteristic
636C2×Dic3C22×C3⋊D311yescharacteristic
637D12—41no—
638D12—188no—
639D12—182no—
640D12—182no—
641D12—361no—
642C4×D3—916no—
643C4×D3—94no—
644C4×D3—182no—
645Dic6—188no—
646Dic6—182no—
647C2×C32—24no—
648C2×C32—24no—
649C2×C32—24no—
650C2×C32—48no—
651C2×C32—44no—
652C2×C32—41no—
653C2×C32—41no—
654C2×C32—44no—
655C2×C32—84no—
656C2×C32—121no—
657C2×C32—121no—
658C2×C32C2×D3×D414yes—
659C2×C32C2×D3×D411yescharacteristic
660C2×C32#100414yes—
661C2×C32#100414yes—
662C2×C32#100411yescharacteristic
663C2×C32#100911yescharacteristic
664C3⋊D3—41no—
665C3⋊D3—62no—
666C3⋊D3—68no—
667C3⋊D3—128no—
668C3⋊D3—128no—
669C3⋊D3—124no—
670C3⋊D3—121no—
671C3×D3—44no—
672C3×D3—44no—
673C3×D3—124no—
674C24—271no—
675C24—271no—
676#41—544no—
677C2×Q8—271no—
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—31no—
681C2×D4—31no—
682C2×D4—31no—
683C2×D4—91no—
684C2×D4—91no—
685C2×D4—271no—
686C2×D4—271no—
687C2×D4—271no—
688C2×D4—271no—
689C2×D4—271no—
690C2×D4—271no—
691C2×D4—271no—
692C2×D4—544no—
693C2×D4D3×C3⋊D311yescharacteristic, complemented
694C22×C4—91no—
695C22×C4—271no—
696C22×C4—271no—
697C4⋊C4—91no—
698C4⋊C4—271no—
699C22⋊C4—91no—
700C22⋊C4—91no—
701C22⋊C4—271no—
702C22⋊C4—271no—
703C22⋊C4—271no—
704C22⋊C4—271no—
705C22⋊C4—271no—
706C22⋊C4—271no—
707C22⋊C4—271no—
708C22⋊C4—271no—
709C42—31no—
710C42—271no—
711C22×C3—28no—
712C22×C3—24no—
713C22×C3—24no—
714C22×C3—24no—
715C22×C3—24no—
716C22×C3—24no—
717C22×C3—24no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—24no—
725C22×C3—44no—
726C22×C3—44no—
727C22×C3—44no—
728C22×C3—44no—
729C22×C3—44no—
730C22×C3—64no—
731C22×C3—64no—
732C22×C3—64no—
733C22×C3—64no—
734C22×C3—64no—
735C22×C3—64no—
736C22×C3—181no—
737C22×C3—181no—
738C22×C3—181no—
739C22×C3C22×D3214yes—
740C22×C3C23×C3⋊D311yescharacteristic
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—21no—
747C2×D3—64no—
748C2×D3—64no—
749C2×D3—64no—
750C2×D3—98no—
751C2×D3—92no—
752C2×D3—188no—
753C2×D3—184no—
754C2×D3—184no—
755C2×D3—181no—
756C2×D3—181no—
757C2×D3—188no—
758C2×D3—184no—
759C2×D3—184no—
760C2×D3—184no—
761C2×D3—181no—
762C2×D3—181no—
763C2×D3—181no—
764C2×D3—364no—
765C2×D3—364no—
766C2×D3—364no—
767C2×D3—364no—
768C2×D3—364no—
769C2×D3—3616no—
770C2×D3—364no—
771C2×D3—3616no—
772C2×D3—3632no—
773C3×C4—24no—
774C3×C4—21no—
775C3×C4—38no—
776C3×C4—44no—
777C3×C4—64no—
778C3×C4—92no—
779C3×C4—181no—
780C3×C4—181no—
781Dic3—21no—
782Dic3—38no—
783Dic3—64no—
784Dic3—64no—
785Dic3—184no—
786Dic3—184no—
787Dic3—181no—
788Dic3—181no—
789Dic3—364no—
790Dic3—364no—
791Dic3D4×C3⋊D312yes—
792C32—24no—
793C32#560711yescharacteristic, complemented
794C32#571514yescomplemented
795C23—31no—
796C23—31no—
797C23—91no—
798C23—271no—
799C23—271no—
800C23—542no—
801C23—542no—
802C23—1081no—
803C23—1081no—
804C23—1081no—
805C23—1081no—
806C23C2×D3×C3⋊D311yescharacteristic
807C23C2×D3×C3⋊D311yescharacteristic
808Q8—542no—
809D4—41no—
810D4—62no—
811D4—62no—
812D4—121no—
813D4—121no—
814D4—121no—
815D4—182no—
816D4—361no—
817D4—542no—
818D4—542no—
819D4—542no—
820D4—542no—
821D4—1081no—
822D4—1081no—
823D4—1081no—
824C2×C4—31no—
825C2×C4—31no—
826C2×C4—91no—
827C2×C4—91no—
828C2×C4—91no—
829C2×C4—182no—
830C2×C4—274no—
831C2×C4—271no—
832C2×C4—271no—
833C2×C4—542no—
834C2×C4C2×D3×C3⋊D311yescharacteristic
835C2×C3—24no—
836C2×C3—24no—
837C2×C3—24no—
838C2×C3—48no—
839C2×C3—41no—
840C2×C3—41no—
841C2×C3—44no—
842C2×C3—44no—
843C2×C3—84no—
844C2×C3—124no—
845C2×C3—124no—
846C2×C3—361no—
847C2×C3D32×D414yes—
848C2×C3#6431414yes—
849C2×C3#6433014yes—
850C2×C3C2×D4×C3⋊D311yescharacteristic
851C2×C3#6436111yescharacteristic
852C2×C3#6436111yescharacteristic
853D3—41no—
854D3—41no—
855D3—124no—
856D3—182no—
857D3—188no—
858D3—368no—
859D3—368no—
860D3—361no—
861D3—364no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—61no—
869C22—61no—
870C22—61no—
871C22—61no—
872C22—61no—
873C22—61no—
874C22—181no—
875C22—181no—
876C22—181no—
877C22—272no—
878C22—541no—
879C22—541no—
880C22—541no—
881C22—541no—
882C22—541no—
883C22—1084no—
884C22—1084no—
885C22C22×D3×C3⋊D311yescharacteristic
886C4—21no—
887C4—32no—
888C4—61no—
889C4—92no—
890C4—181no—
891C4—181no—
892C4—541no—
893C4—541no—
894C3—24no—
895C3#1059529914yescomplemented
896C3#1059618611yescharacteristic, complemented
897C2—41no—
898C2—41no—
899C2—121no—
900C2—121no—
901C2—361no—
902C2—542no—
903C2—1081no—
904C2D3×D4×C3⋊D311yescharacteristic
905C2#1172458811yescharacteristic
906C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#535
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#89039C2semidirect
2. C2×#89028C2semidirect
3. #11723978C2semidirect
4. C3×#64148C2semidirect
5. C32×#940C2semidirect
6. #11723643C2semidirect
7. #11723638C2semidirect
8. #11723635C2semidirect
9. #11723633C2semidirect
10. #11723615C2semidirect
11. #11723600C2semidirect
12. #11723540C2semidirect
13. #11723475C2semidirect
14. #11723468C2semidirect
15. #11723416C2semidirect
20. C2×C33×D4C22semidirect
22. C2×#6312C22semidirect
24. C2×C3×#638C22semidirect
25. C22×C3×C3⋊Dic3C22semidirect
27. C2×C32×#67C22semidirect
28. C2×C32×#67C22semidirect
29. C2×C32×#67C22semidirect
30. C2×C32×D12C22semidirect
32. C2×#6293C22semidirect
36. C2×#6291C22semidirect
37. C2×#6290C22semidirect
40. C2×D3×C3⋊Dic3C22semidirect
41. #88864C22semidirect
43. #88859C22semidirect
44. C3×#3757C22semidirect
45. C3×#3752C22semidirect
46. C3×#3750C22semidirect
47. C32×C4×Dic3C22semidirect
48. #88807C22semidirect
50. #88804C22semidirect
51. #88803C22semidirect
52. (C2×D3)⋊(C3⋊Dic3)C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
64. #64148D3semidirect
74. C3×#940D3semidirect
124. #6289D4semidirect
139. C2×C32×D4C2×D3semidirect
140. C2×C32×D4C2×D3semidirect
152. C2×#638C2×D3semidirect
154. C22×C3⋊Dic3C2×D3semidirect
163. C2×C3×#67C2×D3semidirect
164. C2×C3×#67C2×D3semidirect
165. C2×C3×#67C2×D3semidirect
167. C2×C3×D12C2×D3semidirect
184. #3757C2×D3semidirect
194. #3752C2×D3semidirect
196. #3750C2×D3semidirect
201. C3×C4×Dic3C2×D3semidirect
249. #940C3⋊D3semidirect
389. C2×C3×D4D32semidirect
390. C2×C3×D4C2×C3⋊D3semidirect
407. C2×#67C2×C3⋊D3semidirect
408. C2×#67C2×C3⋊D3semidirect
409. C2×#67C2×C3⋊D3semidirect
420. C2×D12C2×C3⋊D3semidirect
456. C4×Dic3C2×C3⋊D3semidirect
553. C33#535semidirect
693. C2×D4D3×C3⋊D3semidirect
793. C32#5607semidirect
794. C32#5715semidirect
895. C3#10595299semidirect
896. C3#10596186semidirect

Maximal subgroups

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

subgroupindex
C2×#890392
C2×#890282
#117239782
C3×#641482
C32×#9402
#117236432
#117236382
#117236352
#117236332
#117236152
#117236002
#117235402
#117234752
#117234682
#117234162
#105961863
#105952993