Finite Group Databasebeta

← #13177372

Subgroups — #13177372

Order 1728.

2380 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#638C211yesmaximal, characteristic, complemented
2C2×#89029C211yesmaximal, characteristic, complemented
3#11723980C211yesmaximal, characteristic, complemented
4C3×#64149C211yesmaximal, characteristic, complemented
5C32×#937C211yesmaximal, characteristic, complemented
6#11723643C211yesmaximal, characteristic, complemented
7#11723637C211yesmaximal, characteristic, complemented
8#11723633C211yesmaximal, characteristic, complemented
9#11723629C211yesmaximal, characteristic, complemented
10#11723624C211yesmaximal, characteristic, complemented
11#11723591C211yesmaximal, characteristic, complemented
12#11723541C211yesmaximal, characteristic, complemented
13#11723519C211yesmaximal, characteristic, complemented
14#11723459C211yesmaximal, characteristic, complemented
15#11723419C211yesmaximal, characteristic, complemented
16#10596063—31nomaximal
17#10595286—34nomaximal
18C23×C32×D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic
22C2×#6312C2211yescharacteristic, complemented
23C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
24C2×C3×#638C2211yescharacteristic
25C2×C3×#638C2211yescharacteristic, complemented
26C2×C3×#638C2211yescharacteristic, complemented
27C2×C3×#638C2211yescharacteristic, complemented
28C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
29C2×C32×#67C2211yescharacteristic
30C2×C32×#67C2211yescharacteristic, complemented
31D3×#638—24no—
32C2×#6293C2211yescharacteristic, complemented
33C2×#6292C2211yescharacteristic, complemented
34C2×#6291C2211yescharacteristic
35C2×#6290C2211yescharacteristic
36C2×#6290C2211yescharacteristic
37C2×#6290C2211yescharacteristic, complemented
38C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
39#89029—24no—
40C2×D3×C3⋊Dic3C2211yescharacteristic
41#88864C2211yescharacteristic, complemented
42#88859C2211yescharacteristic, complemented
43#88857C2211yescharacteristic, complemented
44C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
45C32×#217C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic
47C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
48#88806C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50#88803C2211yescharacteristic, complemented
51#88803C2211yescharacteristic, complemented
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C22×#638—31no—
56C2×#3830—31no—
57C2×D3×#67—34no—
58C2×#3805—34no—
59C32×#120—31no—
60#64162—31no—
61#64149—31no—
62#64149D311yescharacteristic, complemented
63#64148—31no—
64#64148—31no—
65#64148—34no—
66#64148—64no—
67#64146—31no—
68#64094—31no—
69#64094—31no—
70#64093—31no—
71#64093—31no—
72#64091—31no—
73#64086—31no—
74C3×#940—34no—
75C3×#937D314yescomplemented
76#63983—34no—
77#63980—34no—
78#63979—34no—
79#63976—34no—
80#63971—34no—
81#63959—34no—
82#63922—34no—
83#63885—34no—
84#63877—34no—
85#63852—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C3×C3⋊D3C2311yescharacteristic
90C22×C3×C3⋊D3C2311yescharacteristic
91C22×C32×D3—22no—
92C22×C32×D3—41no—
93C22×C32×D3—41no—
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)—22no—
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C3×#638—22no—
108C3×#638—22no—
109C3×#638—41no—
110C3×#638—41no—
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C3×C4⋊(C3⋊D3)—41no—
114C32×#67—22no—
115C32×#67—41no—
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6293—22no—
119#6292—41no—
120#6291—22no—
121#6290—22no—
122#6290—22no—
123#6290—41no—
124Dic3×C3⋊D3—22no—
125D3×C3⋊Dic3D414yescomplemented
126#5715—91no—
127#5592—94no—
128C24×C32—31no—
129C23×C3⋊D3—31no—
130C23×C3×D3C2×D314yes—
131C22×D32—34no—
132C2×C32×D4—24no—
133C2×C32×D4—31no—
134C2×C32×D4—31no—
135C2×C32×D4C2×D314yescomplemented
136C2×C32×D4C2×D311yescharacteristic, complemented
137C2×#638—31no—
138C2×#638—34no—
139C2×#638—31no—
140C2×#638—31no—
141C2×#638—31no—
142C2×#638—34no—
143C2×#638—31no—
144C2×#638—31no—
145C2×#638—64no—
146C2×#638—64no—
147C2×#638—64no—
148C2×#638C2×D311yescharacteristic
149C2×#638C2×D311yescharacteristic, complemented
150C2×#638C2×D311yescharacteristic, complemented
151C2×#638C2×D311yescharacteristic, complemented
152C22×C3⋊Dic3—31no—
153C22×C3⋊Dic3—31no—
154C22×C3⋊Dic3—34no—
155C22×C3⋊Dic3—64no—
156#3830—64no—
157C2×C4⋊(C3⋊D3)—31no—
158C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
159C2×C4×C3⋊D3—31no—
160C2×#634—31no—
161C2×C3×#67—34no—
162C2×C3×#67—34no—
163C2×C3×#67—34no—
164C2×C3×#67—34no—
165C2×C3×#67C2×D314yes—
166C2×C3×#67C2×D314yescomplemented
167C2×C3×D12—34no—
168D3×#67—616no—
169C2×#627—34no—
170C2×#626—34no—
171C2×#626—34no—
172C2×#625—34no—
173C2×#625—34no—
174C2×#625—34no—
175#3805—616no—
176C2×D3×Dic3—34no—
177C2×D3×Dic3—34no—
178C32×C22⋊C4—31no—
179C32×C22⋊C4—31no—
180C32×C22⋊C4—31no—
181#3757—31no—
182#3757—34no—
183#3757—31no—
184#3757—31no—
185#3757—64no—
186#3752—31no—
187#3752—31no—
188#3752—31no—
189#3752—34no—
190#3752—31no—
191#3752—64no—
192#3750—31no—
193#3750—34no—
194#3750—31no—
195#3750—64no—
196C4×C3⋊Dic3—31no—
197C4×C3⋊Dic3C2×D311yescharacteristic, complemented
198C3×#217C2×D314yescomplemented
199C3×(C2×D3)⋊C4C2×D314yes—
200C3×(C2×D3)⋊C4C2×D314yescomplemented
201C3×C4×Dic3—34no—
202#3724—34no—
203#3722—34no—
204(C2×D3)⋊Dic3—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—21no—
222C2×C3×C3⋊D3—21no—
223C2×C3×C3⋊D3—21no—
224C2×C3×C3⋊D3—21no—
225C2×C32×D3—21no—
226C2×C32×D3—21no—
227C2×C32×D3—21no—
228C2×C32×D3—21no—
229C2×C32×D3—21no—
230C2×C32×D3—44no—
231C2×C32×D3C2×D412yes—
232D3×C3⋊D3—44no—
233C33×C4—21no—
234C3⋊(C3⋊Dic3)—21no—
235C3⋊(C3⋊Dic3)—21no—
236C3⋊(C3⋊Dic3)C2×D412yes—
237C3×C3⋊Dic3—21no—
238C3×C3⋊Dic3C2×D412yes—
239C32×Dic3—21no—
240C32×Dic3—21no—
241C22×#67—94no—
242C2×#237—94no—
243C2×#237—91no—
244C2×D3×D4—91no—
245C3×#127—91no—
246C3×#120—34no—
247#953—94no—
248#940—34no—
249#940—94no—
250#940—91no—
251#939—94no—
252#939—94no—
253#939—91no—
254#939—91no—
255#939—91no—
256#939—91no—
257#939—184no—
258#937—94no—
259#937—91no—
260#937—91no—
261#937—91no—
262#937C3⋊D311yescharacteristic, complemented
263#936—91no—
264#885—94no—
265#885—94no—
266#884—94no—
267#884—94no—
268#882—94no—
269#877—94no—
270#875—91no—
271#872—91no—
272C23×C32—24no—
273C23×C32—24no—
274C23×C32—31no—
275C23×C32—31no—
276C23×C32—62no—
277C23×C32—121no—
278C23×C32—121no—
279C23×C32C22×D314yes—
280C23×C32C22×D314yes—
281C23×C32C22×D311yescharacteristic
282C23×C32C22×D311yescharacteristic
283C22×C3⋊D3—31no—
284C22×C3⋊D3—34no—
285C22×C3⋊D3—64no—
286C22×C3⋊D3—62no—
287C22×C3⋊D3—121no—
288C22×C3⋊D3—121no—
289C22×C3⋊D3C22×D311yescharacteristic
290C22×C3⋊D3C22×D311yescharacteristic
291C22×C3×D3—28no—
292C22×C3×D3—34no—
293C22×C3×D3—34no—
294C22×C3×D3—44no—
295C22×C3×D3—44no—
296C22×C3×D3C22×D314yes—
297C22×C3×D3C22×D314yes—
298C2×D32—68no—
299C2×D32—124no—
300C2×D32—124no—
301C32×D4—41no—
302C32×D4—44no—
303C32×D4—48no—
304C32×D4—62no—
305C32×D4—121no—
306C2×C32×C4—24no—
307C2×C32×C4—31no—
308C2×C32×C4—31no—
309C2×C32×C4C22×D314yes—
310C2×C32×C4C22×D311yescharacteristic
311#638—22no—
312#638—22no—
313#638—41no—
314#638—41no—
315#638—62no—
316#638—62no—
317#638—62no—
318#638—62no—
319#638—68no—
320#638—128no—
321#638—121no—
322#638—121no—
323#638—124no—
324#638—128no—
325C2×C3⋊Dic3—31no—
326C2×C3⋊Dic3—34no—
327C2×C3⋊Dic3—31no—
328C2×C3⋊Dic3—31no—
329C2×C3⋊Dic3—34no—
330C2×C3⋊Dic3—34no—
331C2×C3⋊Dic3—34no—
332C2×C3⋊Dic3—64no—
333C2×C3⋊Dic3—64no—
334C2×C3⋊Dic3—64no—
335C2×C3⋊Dic3—62no—
336C2×C3⋊Dic3—68no—
337C2×C3⋊Dic3—128no—
338C2×C3⋊Dic3C22×D311yescharacteristic
339C2×C3⋊Dic3C22×D311yescharacteristic
340C4⋊(C3⋊D3)—41no—
341C4⋊(C3⋊D3)—121no—
342C4×C3⋊D3—62no—
343#634—62no—
344C3×#67—28no—
345C3×#67—44no—
346C3×#67—68no—
347C3×#67—68no—
348C3×#67—124no—
349C3×#67—124no—
350C2×C3×Dic3—34no—
351C2×C3×Dic3—34no—
352C2×C3×Dic3C22×D314yes—
353C2×C3×Dic3C22×D314yes—
354C3×D12—124no—
355#627—68no—
356#626—68no—
357#626—124no—
358#625—68no—
359#625—68no—
360#625—124no—
361D3×Dic3—316no—
362D3×Dic3—68no—
363#535—271noSylow
364C2×C33—41no—
365C2×C33—41no—
366C2×C33C22×D411yescharacteristic
367C2×C33H(5,𝔽2)11yescharacteristic
368C2×C33H(5,𝔽2)11yescharacteristic
369C3⋊(C3⋊D3)—41no—
370C3×C3⋊D3—41no—
371C3×C3⋊D3—41no—
372C32×D3—22no—
373C32×D3—41no—
374C24×C3—34no—
375C23×D3—94no—
376C23×D3—91no—
377C23×D3C2×C3⋊D311yescharacteristic
378C2×C3×D4—24no—
379C2×C3×D4—34no—
380C2×C3×D4—34no—
381C2×C3×D4—91no—
382C2×C3×D4—91no—
383C2×C3×D4—91no—
384C2×C3×D4—91no—
385C2×C3×D4—91no—
386C2×C3×D4D3214yescomplemented
387C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
388C2×#67—34no—
389C2×#67—34no—
390C2×#67—34no—
391C2×#67—34no—
392C2×#67—94no—
393C2×#67—94no—
394C2×#67—94no—
395C2×#67—94no—
396C2×#67—91no—
397C2×#67—91no—
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×#67—1816no—
407C2×#67C2×C3⋊D311yescharacteristic
408C2×#67C2×C3⋊D311yescharacteristic, complemented
409C22×Dic3—94no—
410C22×Dic3—94no—
411C22×Dic3—91no—
412C22×Dic3—91no—
413C22×Dic3—184no—
414#237—184no—
415#237—1816no—
416D3×D4—184no—
417C2×D12—34no—
418C2×D12—91no—
419C2×D12—94no—
420C2×C4×D3—91no—
421C2×C4×D3—94no—
422C2×Dic6—94no—
423C2×Dic6—91no—
424C3×C22⋊C4—34no—
425C3×C22⋊C4—34no—
426C3×C22⋊C4—34no—
427C3×C42—91no—
428#217—94no—
429#217—94no—
430#217—94no—
431#217—91no—
432#217—91no—
433#217—91no—
434#217—184no—
435#217C2×C3⋊D311yescharacteristic, complemented
436(C2×D3)⋊C4—94no—
437(C2×D3)⋊C4—94no—
438(C2×D3)⋊C4—94no—
439(C2×D3)⋊C4—91no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—94no—
442(C2×D3)⋊C4—91no—
443(C2×D3)⋊C4—91no—
444(C2×D3)⋊C4—184no—
445(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
446(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
447Dic3⋊C4—94no—
448Dic3⋊C4—94no—
449Dic3⋊C4—91no—
450Dic3⋊C4—91no—
451Dic3⋊C4—184no—
452C4×Dic3—34no—
453C4×Dic3—94no—
454C4×Dic3—91no—
455C22×C32—28no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—24no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32—24no—
464C22×C32—24no—
465C22×C32—24no—
466C22×C32—24no—
467C22×C32—24no—
468C22×C32—24no—
469C22×C32—32no—
470C22×C32—44no—
471C22×C32—44no—
472C22×C32—44no—
473C22×C32—44no—
474C22×C32—44no—
475C22×C32—61no—
476C22×C32—61no—
477C22×C32—61no—
478C22×C32—61no—
479C22×C32—61no—
480C22×C32—124no—
481C22×C32C23×D314yes—
482C22×C32C23×D311yescharacteristic
483C2×C3⋊D3—21no—
484C2×C3⋊D3—21no—
485C2×C3⋊D3—21no—
486C2×C3⋊D3—21no—
487C2×C3⋊D3—21no—
488C2×C3⋊D3—21no—
489C2×C3⋊D3—61no—
490C2×C3⋊D3—61no—
491C2×C3⋊D3—61no—
492C2×C3⋊D3—64no—
493C2×C3⋊D3—64no—
494C2×C3⋊D3—64no—
495C2×C3⋊D3—124no—
496C2×C3⋊D3—124no—
497C2×C3⋊D3—124no—
498C2×C3⋊D3—124no—
499C2×C3×D3—24no—
500C2×C3×D3—24no—
501C2×C3×D3—24no—
502C2×C3×D3—24no—
503C2×C3×D3—24no—
504C2×C3×D3—416no—
505C2×C3×D3—64no—
506C2×C3×D3—64no—
507C2×C3×D3—64no—
508C2×C3×D3—64no—
509C2×C3×D3—64no—
510C2×C3×D3—64no—
511C2×C3×D3D3×D418yes—
512D32—1216no—
513C32×C4—21no—
514C32×C4—24no—
515C32×C4—44no—
516C32×C4—61no—
517C32×C4—61no—
518C3⋊Dic3—21no—
519C3⋊Dic3—32no—
520C3⋊Dic3—38no—
521C3⋊Dic3—68no—
522C3⋊Dic3—61no—
523C3⋊Dic3—61no—
524C3⋊Dic3—64no—
525C3⋊Dic3—64no—
526C3⋊Dic3—124no—
527C3⋊Dic3—124no—
528C3⋊Dic3D3×D412yes—
529C3×Dic3—24no—
530C3×Dic3—24no—
531C3×Dic3—38no—
532C3×Dic3—64no—
533C2×#41—271no—
534C22×D4—271no—
535#127—91no—
536#127—271no—
537#124—271no—
538#124—271no—
539#121—271no—
540#121—271no—
541#121—271no—
542#121—271no—
543#120—31no—
544#120—271no—
545#120—271no—
546#120—271no—
547#117—271no—
548C33#53511yescharacteristic, complemented, Sylow
549C23×C3—24no—
550C23×C3—24no—
551C23×C3—34no—
552C23×C3—34no—
553C23×C3—68no—
554C23×C3—91no—
555C23×C3—91no—
556C23×C3—124no—
557C23×C3—124no—
558C23×C3C2×D3214yes—
559C23×C3C2×D3214yes—
560C23×C3C22×C3⋊D311yescharacteristic
561C23×C3C22×C3⋊D311yescharacteristic
562C22×D3—22no—
563C22×D3—34no—
564C22×D3—34no—
565C22×D3—41no—
566C22×D3—41no—
567C22×D3—94no—
568C22×D3—91no—
569C22×D3—184no—
570C22×D3—188no—
571C22×D3—182no—
572C22×D3—361no—
573C22×D3—361no—
574C22×D3—364no—
575C22×D3—364no—
576C22×D3C22×C3⋊D311yescharacteristic
577C22×D3C22×C3⋊D311yescharacteristic
578C3×D4—44no—
579C3×D4—41no—
580C3×D4—48no—
581C3×D4—68no—
582C3×D4—124no—
583C3×D4—182no—
584C3×D4—182no—
585C3×D4—361no—
586C3×D4—361no—
587C3×D4—361no—
588C2×C3×C4—24no—
589C2×C3×C4—34no—
590C2×C3×C4—34no—
591C2×C3×C4—91no—
592C2×C3×C4—91no—
593C2×C3×C4C2×D3214yes—
594C2×C3×C4C22×C3⋊D311yescharacteristic
595#67—22no—
596#67—41no—
597#67—68no—
598#67—68no—
599#67—124no—
600#67—124no—
601#67—188no—
602#67—182no—
603#67—188no—
604#67—182no—
605#67—188no—
606#67—188no—
607#67—182no—
608#67—368no—
609#67—361no—
610#67—361no—
611#67—364no—
612#67—364no—
613#67—361no—
614#67—368no—
615C2×Dic3—34no—
616C2×Dic3—34no—
617C2×Dic3—916no—
618C2×Dic3—94no—
619C2×Dic3—91no—
620C2×Dic3—94no—
621C2×Dic3—94no—
622C2×Dic3—91no—
623C2×Dic3—91no—
624C2×Dic3—184no—
625C2×Dic3—184no—
626C2×Dic3—184no—
627C2×Dic3—182no—
628C2×Dic3—182no—
629C2×Dic3—188no—
630C2×Dic3—368no—
631C2×Dic3C22×C3⋊D311yescharacteristic
632C2×Dic3C22×C3⋊D311yescharacteristic
633D12—124no—
634D12—182no—
635D12—364no—
636C4×D3—94no—
637C4×D3—188no—
638Dic6—182no—
639Dic6—188no—
640C2×C32—24no—
641C2×C32—24no—
642C2×C32—24no—
643C2×C32—48no—
644C2×C32—41no—
645C2×C32—41no—
646C2×C32—44no—
647C2×C32—44no—
648C2×C32—62no—
649C2×C32—84no—
650C2×C32—121no—
651C2×C32C2×D3×D414yes—
652C2×C32C2×D3×D411yescharacteristic
653C2×C32#100414yes—
654C2×C32#100414yes—
655C2×C32#100411yescharacteristic
656C2×C32#100411yescharacteristic
657C3⋊D3—41no—
658C3⋊D3—41no—
659C3⋊D3—121no—
660C3⋊D3—124no—
661C3⋊D3—244no—
662C3×D3—28no—
663C3×D3—44no—
664C3×D3—124no—
665C3×D3—124no—
666C24—31no—
667C24—271no—
668#41—544no—
669C2×Q8—271no—
670C2×D4—31no—
671C2×D4—31no—
672C2×D4—91no—
673C2×D4—91no—
674C2×D4—91no—
675C2×D4—91no—
676C2×D4—91no—
677C2×D4—271no—
678C2×D4—271no—
679C2×D4—271no—
680C2×D4—271no—
681C2×D4—271no—
682C2×D4—271no—
683C2×D4—271no—
684C2×D4—544no—
685C2×D4D3×C3⋊D311yescharacteristic, complemented
686C22×C4—271no—
687C22×C4—271no—
688C22×C4—271no—
689C4⋊C4—271no—
690C4⋊C4—271no—
691C22⋊C4—31no—
692C22⋊C4—31no—
693C22⋊C4—31no—
694C22⋊C4—271no—
695C22⋊C4—271no—
696C22⋊C4—271no—
697C22⋊C4—271no—
698C22⋊C4—271no—
699C22⋊C4—271no—
700C22⋊C4—271no—
701C42—91no—
702C42—271no—
703C22×C3—28no—
704C22×C3—24no—
705C22×C3—24no—
706C22×C3—24no—
707C22×C3—24no—
708C22×C3—24no—
709C22×C3—24no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—24no—
717C22×C3—38no—
718C22×C3—44no—
719C22×C3—44no—
720C22×C3—44no—
721C22×C3—44no—
722C22×C3—44no—
723C22×C3—64no—
724C22×C3—64no—
725C22×C3—64no—
726C22×C3—64no—
727C22×C3—64no—
728C22×C3—1216no—
729C22×C3—181no—
730C22×C3—181no—
731C22×C3—181no—
732C22×C3—181no—
733C22×C3—181no—
734C22×C3—181no—
735C22×C3C22×D3214yes—
736C22×C3C23×C3⋊D311yescharacteristic
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—44no—
743C2×D3—64no—
744C2×D3—64no—
745C2×D3—64no—
746C2×D3—64no—
747C2×D3—64no—
748C2×D3—64no—
749C2×D3—184no—
750C2×D3—184no—
751C2×D3—184no—
752C2×D3—181no—
753C2×D3—181no—
754C2×D3—181no—
755C2×D3—364no—
756C2×D3—364no—
757C2×D3—364no—
758C2×D3—364no—
759C2×D3—3616no—
760C2×D3D4×C3⋊D312yes—
761C3×C4—24no—
762C3×C4—21no—
763C3×C4—44no—
764C3×C4—64no—
765C3×C4—64no—
766C3×C4—92no—
767C3×C4—181no—
768Dic3—21no—
769Dic3—21no—
770Dic3—38no—
771Dic3—64no—
772Dic3—98no—
773Dic3—92no—
774Dic3—188no—
775Dic3—184no—
776Dic3—184no—
777Dic3—181no—
778Dic3—181no—
779Dic3—364no—
780Dic3—364no—
781C32—24no—
782C32#559214yescomplemented
783C32#571511yescharacteristic, complemented
784C23—31no—
785C23—31no—
786C23—62no—
787C23—91no—
788C23—91no—
789C23—121no—
790C23—121no—
791C23—271no—
792C23—542no—
793C23—1081no—
794C23—1081no—
795C23C2×D3×C3⋊D311yescharacteristic
796C23C2×D3×C3⋊D311yescharacteristic
797Q8—542no—
798D4—41no—
799D4—62no—
800D4—121no—
801D4—182no—
802D4—182no—
803D4—361no—
804D4—361no—
805D4—361no—
806D4—542no—
807D4—542no—
808D4—542no—
809D4—542no—
810D4—1081no—
811D4—1081no—
812D4—1081no—
813C2×C4—31no—
814C2×C4—31no—
815C2×C4—91no—
816C2×C4—91no—
817C2×C4—274no—
818C2×C4—271no—
819C2×C4—271no—
820C2×C4—271no—
821C2×C4—542no—
822C2×C4—542no—
823C2×C4C2×D3×C3⋊D311yescharacteristic
824C2×C3—24no—
825C2×C3—24no—
826C2×C3—24no—
827C2×C3—48no—
828C2×C3—44no—
829C2×C3—44no—
830C2×C3—41no—
831C2×C3—41no—
832C2×C3—68no—
833C2×C3—84no—
834C2×C3—124no—
835C2×C3—361no—
836C2×C3—361no—
837C2×C3D32×D414yes—
838C2×C3#6431314yes—
839C2×C3#6433014yes—
840C2×C3C2×D4×C3⋊D311yescharacteristic
841C2×C3#6436111yescharacteristic
842C2×C3#6436111yescharacteristic
843D3—22no—
844D3—41no—
845D3—124no—
846D3—124no—
847D3—364no—
848D3—361no—
849D3—724no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—32no—
857C22—61no—
858C22—61no—
859C22—61no—
860C22—61no—
861C22—61no—
862C22—124no—
863C22—181no—
864C22—181no—
865C22—181no—
866C22—181no—
867C22—181no—
868C22—181no—
869C22—541no—
870C22—541no—
871C22—541no—
872C22—1084no—
873C22C22×D3×C3⋊D311yescharacteristic
874C4—21no—
875C4—61no—
876C4—61no—
877C4—92no—
878C4—181no—
879C4—272no—
880C4—541no—
881C4—541no—
882C3—24no—
883C3#1059528614yescomplemented
884C3#1059606311yescharacteristic, complemented
885C2—41no—
886C2—41no—
887C2—62no—
888C2—121no—
889C2—361no—
890C2—361no—
891C2—1081no—
892C2D3×D4×C3⋊D311yescharacteristic
893C2#1172458711yescharacteristic
894C2#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×D3×#638C2semidirect
2. C2×#89029C2semidirect
3. #11723980C2semidirect
4. C3×#64149C2semidirect
5. C32×#937C2semidirect
6. #11723643C2semidirect
7. #11723637C2semidirect
8. #11723633C2semidirect
9. #11723629C2semidirect
10. #11723624C2semidirect
11. #11723591C2semidirect
12. #11723541C2semidirect
13. #11723519C2semidirect
14. #11723459C2semidirect
15. #11723419C2semidirect
20. C2×C33×D4C22semidirect
22. C2×#6312C22semidirect
23. C22×C3⋊(C3⋊Dic3)C22semidirect
25. C2×C3×#638C22semidirect
26. C2×C3×#638C22semidirect
27. C2×C3×#638C22semidirect
28. C2×C3×C4⋊(C3⋊D3)C22semidirect
30. C2×C32×#67C22semidirect
32. C2×#6293C22semidirect
33. C2×#6292C22semidirect
37. C2×#6290C22semidirect
38. C2×Dic3×C3⋊D3C22semidirect
41. #88864C22semidirect
42. #88859C22semidirect
43. #88857C22semidirect
44. C3×C4×C3⋊Dic3C22semidirect
45. C32×#217C22semidirect
47. C32×(C2×D3)⋊C4C22semidirect
48. #88806C22semidirect
49. #88804C22semidirect
50. #88803C22semidirect
51. #88803C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
62. #64149D3semidirect
75. C3×#937D3semidirect
125. D3×C3⋊Dic3D4semidirect
135. C2×C32×D4C2×D3semidirect
136. C2×C32×D4C2×D3semidirect
149. C2×#638C2×D3semidirect
150. C2×#638C2×D3semidirect
151. C2×#638C2×D3semidirect
158. C2×C4⋊(C3⋊D3)C2×D3semidirect
166. C2×C3×#67C2×D3semidirect
197. C4×C3⋊Dic3C2×D3semidirect
198. C3×#217C2×D3semidirect
200. C3×(C2×D3)⋊C4C2×D3semidirect
262. #937C3⋊D3semidirect
386. C2×C3×D4D32semidirect
387. C2×C3×D4C2×C3⋊D3semidirect
408. C2×#67C2×C3⋊D3semidirect
435. #217C2×C3⋊D3semidirect
446. (C2×D3)⋊C4C2×C3⋊D3semidirect
548. C33#535semidirect
685. C2×D4D3×C3⋊D3semidirect
782. C32#5592semidirect
783. C32#5715semidirect
883. C3#10595286semidirect
884. C3#10596063semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6382
C2×#890292
#117239802
C3×#641492
C32×#9372
#117236432
#117236372
#117236332
#117236292
#117236242
#117235912
#117235412
#117235192
#117234592
#117234192
#105960633
#105952863