Finite Group Databasebeta

← #13177369

Subgroups — #13177369

Order 1728.

2436 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#638C211yesmaximal, characteristic, complemented
2C2×#89028C211yesmaximal, characteristic, complemented
3#11723981C211yesmaximal, characteristic, complemented
4C3×#64148C211yesmaximal, characteristic, complemented
5C32×#937C211yesmaximal, characteristic, complemented
6#11723643C211yesmaximal, characteristic, complemented
7#11723635C211yesmaximal, characteristic, complemented
8#11723633C211yesmaximal, characteristic, complemented
9#11723630C211yesmaximal, characteristic, complemented
10#11723623C211yesmaximal, characteristic, complemented
11#11723592C211yesmaximal, characteristic, complemented
12#11723542C211yesmaximal, characteristic, complemented
13#11723530C211yesmaximal, characteristic, complemented
14#11723525C211yesmaximal, characteristic, complemented
15#11723460C211yesmaximal, characteristic, complemented
16#10596063—31nomaximal
17#10595285—34nomaximal
18C23×C32×D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic
22C2×#6312C2211yescharacteristic, complemented
23C2×#6312C2211yescharacteristic, complemented
24C2×#6312C2211yescharacteristic, complemented
25C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
26C2×C3×#638C2211yescharacteristic
27C2×C3×#638C2211yescharacteristic, complemented
28C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
29C2×C32×#67C2211yescharacteristic
30C2×C32×#67C2211yescharacteristic, complemented
31D3×#638—24no—
32C2×#6293C2211yescharacteristic, complemented
33C2×#6292C2211yescharacteristic, complemented
34C2×#6291C2211yescharacteristic
35C2×#6291C2211yescharacteristic
36C2×#6291C2211yescharacteristic, complemented
37C2×#6290C2211yescharacteristic
38C2×#6289C2211yescharacteristic, complemented
39#89028—24no—
40C2×D3×C3⋊Dic3C2211yescharacteristic
41C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
42C3×#3757C2211yescharacteristic, complemented
43C3×#3752C2211yescharacteristic, complemented
44C3×#3750C2211yescharacteristic, complemented
45C32×#217C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic
47C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
48#88807C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50#88804C2211yescharacteristic, 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×#3804—34no—
59C32×#120—31no—
60#64162—31no—
61#64149—31no—
62#64149—31no—
63#64149—34no—
64#64149—64no—
65#64148—31no—
66#64148D311yescharacteristic, complemented
67#64146—31no—
68#64094—31no—
69#64094—31no—
70#64093—31no—
71#64093—31no—
72#64091—31no—
73#64086—31no—
74C3×#939—34no—
75C3×#937D314yescomplemented
76#63983—34no—
77#63979—34no—
78#63978—34no—
79#63977—34no—
80#63958—34no—
81#63953—34no—
82#63923—34no—
83#63915—34no—
84#63910—34no—
85#63878—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C3⋊(C3⋊D3)C2311yescharacteristic
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—22no—
103#6312—41no—
104#6312—41no—
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊(C3⋊D3))—41no—
108C3×#638—22no—
109C3×#638—41no—
110C2×C3×C3⋊Dic3—22no—
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C32×#67—22no—
115C32×#67—41no—
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6293—22no—
119#6292—41no—
120#6291—22no—
121#6291—22no—
122#6291—41no—
123#6290—22no—
124#6289—22no—
125D3×C3⋊Dic3D414yescomplemented
126#5607—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—31no—
139C2×#638—34no—
140C2×#638—34no—
141C2×#638—31no—
142C2×#638—31no—
143C2×#638—31no—
144C2×#638—34no—
145C2×#638—34no—
146C2×#638—31no—
147C2×#638—31no—
148C2×#638—31no—
149C2×#638—64no—
150C2×#638—64no—
151C2×#638—64no—
152C2×#638—64no—
153C2×#638—64no—
154C2×#638C2×D311yescharacteristic
155C2×#638C2×D311yescharacteristic, complemented
156C22×C3⋊Dic3—31no—
157C22×C3⋊Dic3C2×D311yescharacteristic, complemented
158#3830—64no—
159C2×C4⋊(C3⋊D3)—31no—
160C2×C4⋊(C3⋊D3)—31no—
161C2×C4⋊(C3⋊D3)—34no—
162C2×C4⋊(C3⋊D3)—64no—
163C2×C4×C3⋊D3—31no—
164C2×#634—31no—
165C2×C3×#67—34no—
166C2×C3×#67—34no—
167C2×C3×#67C2×D314yes—
168C2×C3×#67C2×D314yescomplemented
169C22×C3×Dic3—34no—
170D3×#67—616no—
171C2×#627—34no—
172C2×#626—34no—
173C2×#626—34no—
174C2×#626—34no—
175C2×#626—34no—
176C2×#625—34no—
177C2×#624—34no—
178#3804—616no—
179C2×D3×Dic3—34no—
180C32×C22⋊C4—31no—
181C32×C22⋊C4—31no—
182C32×C22⋊C4—31no—
183#3757—31no—
184#3757—31no—
185#3757C2×D311yescharacteristic, complemented
186#3752—31no—
187#3752—31no—
188#3752—31no—
189#3752C2×D311yescharacteristic, complemented
190#3750—31no—
191#3750C2×D311yescharacteristic, complemented
192C4×C3⋊Dic3—31no—
193C4×C3⋊Dic3—34no—
194C4×C3⋊Dic3—31no—
195C4×C3⋊Dic3—64no—
196C3×#217—34no—
197C3×#217C2×D314yescomplemented
198C3×(C2×D3)⋊C4—34no—
199C3×(C2×D3)⋊C4C2×D314yes—
200C3×(C2×D3)⋊C4C2×D314yescomplemented
201C3×Dic3⋊C4—34no—
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)—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)C2×D412yes—
236C3×C3⋊Dic3—21no—
237C3×C3⋊Dic3—21no—
238C3×C3⋊Dic3C2×D412yes—
239C32×Dic3—21no—
240C32×Dic3—21no—
241C22×#67—94no—
242C2×#237—94no—
243C2×D3×D4—91no—
244C2×#235—91no—
245C3×#121—91no—
246C3×#120—34no—
247#953—94no—
248#940—94no—
249#940—94no—
250#940—91no—
251#940—91no—
252#940—184no—
253#939—34no—
254#939—94no—
255#938—91no—
256#937—94no—
257#937—91no—
258#937C3⋊D311yescharacteristic, complemented
259#930—91no—
260#895—91no—
261#892—91no—
262#885—94no—
263#885—94no—
264#885—91no—
265#885—91no—
266#884—94no—
267#884—94no—
268#882—94no—
269#882—91no—
270#882—91no—
271#877—94no—
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—31no—
285C22×C3⋊D3—34no—
286C22×C3⋊D3—34no—
287C22×C3⋊D3—64no—
288C22×C3⋊D3—64no—
289C22×C3⋊D3—62no—
290C22×C3⋊D3—121no—
291C22×C3⋊D3—121no—
292C22×C3⋊D3C22×D311yescharacteristic
293C22×C3×D3—28no—
294C22×C3×D3—34no—
295C22×C3×D3—44no—
296C22×C3×D3—44no—
297C22×C3×D3C22×D314yes—
298C22×C3×D3C22×D314yes—
299C2×D32—68no—
300C2×D32—124no—
301C2×D32—124no—
302C32×D4—41no—
303C32×D4—44no—
304C32×D4—48no—
305C32×D4—62no—
306C32×D4—121no—
307C2×C32×C4—24no—
308C2×C32×C4—31no—
309C2×C32×C4—31no—
310C2×C32×C4C22×D314yes—
311C2×C32×C4C22×D311yescharacteristic
312#638—22no—
313#638—41no—
314#638—62no—
315#638—62no—
316#638—62no—
317#638—62no—
318#638—62no—
319#638—68no—
320#638—68no—
321#638—128no—
322#638—128no—
323#638—121no—
324#638—121no—
325#638—121no—
326#638—124no—
327#638—124no—
328#638—128no—
329#638—128no—
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3—31no—
332C2×C3⋊Dic3—34no—
333C2×C3⋊Dic3—31no—
334C2×C3⋊Dic3—34no—
335C2×C3⋊Dic3—34no—
336C2×C3⋊Dic3—64no—
337C2×C3⋊Dic3—64no—
338C2×C3⋊Dic3C22×D311yescharacteristic
339C2×C3⋊Dic3C22×D311yescharacteristic
340C2×C3⋊Dic3C22×D311yescharacteristic
341C4⋊(C3⋊D3)—121no—
342C4⋊(C3⋊D3)—124no—
343C4⋊(C3⋊D3)—128no—
344C4⋊(C3⋊D3)—121no—
345C4×C3⋊D3—62no—
346#634—62no—
347C3×#67—28no—
348C3×#67—44no—
349C3×#67—68no—
350C3×#67—124no—
351C2×C3×Dic3—34no—
352C2×C3×Dic3—34no—
353C2×C3×Dic3—34no—
354C2×C3×Dic3—68no—
355C2×C3×Dic3C22×D314yes—
356C2×C3×Dic3C22×D314yes—
357#627—68no—
358#626—68no—
359#626—68no—
360#626—124no—
361#626—124no—
362#625—68no—
363#624—68no—
364D3×Dic3—316no—
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)—41no—
372C3⋊(C3⋊D3)—41no—
373C3×C3⋊D3—41no—
374C32×D3—22no—
375C32×D3—41no—
376C24×C3—34no—
377C23×D3—94no—
378C23×D3—91no—
379C23×D3C2×C3⋊D311yescharacteristic
380C2×C3×D4—24no—
381C2×C3×D4—34no—
382C2×C3×D4—34no—
383C2×C3×D4—91no—
384C2×C3×D4—91no—
385C2×C3×D4D3214yescomplemented
386C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
387C22×C3×C4—91no—
388C2×#67—34no—
389C2×#67—34no—
390C2×#67—94no—
391C2×#67—94no—
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—184no—
407C2×#67—184no—
408C2×#67—1816no—
409C2×#67C2×C3⋊D311yescharacteristic
410C2×#67C2×C3⋊D311yescharacteristic, complemented
411C22×Dic3—34no—
412C22×Dic3—94no—
413#237—1816no—
414D3×D4—184no—
415#235—184no—
416C2×D12—91no—
417C2×D12—91no—
418C2×D12—94no—
419C2×D12—91no—
420C2×D12—94no—
421C2×D12—91no—
422C2×D12—184no—
423C2×C4×D3—91no—
424C2×C4×D3—94no—
425C2×C4×D3—91no—
426C2×Dic6—94no—
427C2×Dic6—91no—
428C3×C4⋊C4—91no—
429C3×C22⋊C4—34no—
430C3×C22⋊C4—34no—
431C3×C22⋊C4—34no—
432C3×C22⋊C4—91no—
433C3×C22⋊C4—91no—
434#217—34no—
435#217—94no—
436#217—94no—
437#217—91no—
438#217C2×C3⋊D311yescharacteristic, complemented
439(C2×D3)⋊C4—34no—
440(C2×D3)⋊C4—94no—
441(C2×D3)⋊C4—94no—
442(C2×D3)⋊C4—94no—
443(C2×D3)⋊C4—91no—
444(C2×D3)⋊C4—91no—
445(C2×D3)⋊C4—91no—
446(C2×D3)⋊C4—91no—
447(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
448(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
449C4⋊Dic3—91no—
450Dic3⋊C4—34no—
451Dic3⋊C4—94no—
452C4×Dic3—94no—
453C4×Dic3—94no—
454C4×Dic3—91no—
455C4×Dic3—91no—
456C4×Dic3—184no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
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—24no—
470C22×C32—32no—
471C22×C32—44no—
472C22×C32—44no—
473C22×C32—44no—
474C22×C32—44no—
475C22×C32—44no—
476C22×C32—44no—
477C22×C32—61no—
478C22×C32—61no—
479C22×C32—61no—
480C22×C32—61no—
481C22×C32—61no—
482C22×C32—124no—
483C22×C32C23×D314yes—
484C22×C32C23×D311yescharacteristic
485C2×C3⋊D3—21no—
486C2×C3⋊D3—21no—
487C2×C3⋊D3—21no—
488C2×C3⋊D3—61no—
489C2×C3⋊D3—61no—
490C2×C3⋊D3—61no—
491C2×C3⋊D3—61no—
492C2×C3⋊D3—61no—
493C2×C3⋊D3—61no—
494C2×C3⋊D3—64no—
495C2×C3⋊D3—64no—
496C2×C3⋊D3—64no—
497C2×C3⋊D3—64no—
498C2×C3⋊D3—64no—
499C2×C3⋊D3—64no—
500C2×C3⋊D3—124no—
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—24no—
508C2×C3×D3—24no—
509C2×C3×D3—24no—
510C2×C3×D3—24no—
511C2×C3×D3—24no—
512C2×C3×D3—416no—
513C2×C3×D3—64no—
514C2×C3×D3—64no—
515C2×C3×D3—64no—
516C2×C3×D3D3×D418yes—
517D32—1216no—
518C32×C4—28no—
519C32×C4—24no—
520C32×C4—21no—
521C32×C4—61no—
522C32×C4—61no—
523C3⋊Dic3—21no—
524C3⋊Dic3—21no—
525C3⋊Dic3—32no—
526C3⋊Dic3—38no—
527C3⋊Dic3—68no—
528C3⋊Dic3—68no—
529C3⋊Dic3—64no—
530C3⋊Dic3—61no—
531C3⋊Dic3D3×D412yes—
532C3×Dic3—24no—
533C3×Dic3—24no—
534C3×Dic3—38no—
535C3×Dic3—64no—
536C3×Dic3—64no—
537C2×#41—271no—
538C22×D4—271no—
539#127—271no—
540#127—271no—
541#124—271no—
542#124—271no—
543#121—91no—
544#121—271no—
545#121—271no—
546#121—271no—
547#120—31no—
548#120—271no—
549#120—271no—
550#120—271no—
551#117—271no—
552C33#53511yescharacteristic, complemented, Sylow
553C23×C3—24no—
554C23×C3—24no—
555C23×C3—34no—
556C23×C3—34no—
557C23×C3—68no—
558C23×C3—91no—
559C23×C3—124no—
560C23×C3—124no—
561C23×C3C2×D3214yes—
562C23×C3C2×D3214yes—
563C23×C3C22×C3⋊D311yescharacteristic
564C23×C3C22×C3⋊D311yescharacteristic
565C22×D3—22no—
566C22×D3—34no—
567C22×D3—41no—
568C22×D3—41no—
569C22×D3—94no—
570C22×D3—94no—
571C22×D3—91no—
572C22×D3—91no—
573C22×D3—184no—
574C22×D3—184no—
575C22×D3—188no—
576C22×D3—182no—
577C22×D3—361no—
578C22×D3—361no—
579C22×D3—364no—
580C22×D3—364no—
581C22×D3C22×C3⋊D311yescharacteristic
582C22×D3C22×C3⋊D311yescharacteristic
583C3×D4—44no—
584C3×D4—41no—
585C3×D4—48no—
586C3×D4—68no—
587C3×D4—124no—
588C3×D4—182no—
589C3×D4—361no—
590C2×C3×C4—24no—
591C2×C3×C4—34no—
592C2×C3×C4—34no—
593C2×C3×C4—91no—
594C2×C3×C4—91no—
595C2×C3×C4—91no—
596C2×C3×C4—182no—
597C2×C3×C4C2×D3214yes—
598C2×C3×C4C22×C3⋊D311yescharacteristic
599#67—22no—
600#67—41no—
601#67—68no—
602#67—124no—
603#67—188no—
604#67—188no—
605#67—182no—
606#67—188no—
607#67—182no—
608#67—182no—
609#67—188no—
610#67—188no—
611#67—368no—
612#67—368no—
613#67—361no—
614#67—364no—
615#67—364no—
616#67—364no—
617#67—361no—
618#67—361no—
619#67—368no—
620#67—368no—
621C2×Dic3—34no—
622C2×Dic3—34no—
623C2×Dic3—34no—
624C2×Dic3—68no—
625C2×Dic3—916no—
626C2×Dic3—94no—
627C2×Dic3—91no—
628C2×Dic3—94no—
629C2×Dic3—91no—
630C2×Dic3—184no—
631C2×Dic3—184no—
632C2×Dic3C22×C3⋊D311yescharacteristic
633C2×Dic3C22×C3⋊D311yescharacteristic
634D12—182no—
635D12—182no—
636D12—364no—
637D12—361no—
638D12—368no—
639D12—364no—
640D12—361no—
641C4×D3—94no—
642C4×D3—182no—
643C4×D3—188no—
644Dic6—182no—
645Dic6—188no—
646C2×C32—24no—
647C2×C32—24no—
648C2×C32—24no—
649C2×C32—41no—
650C2×C32—41no—
651C2×C32—44no—
652C2×C32—44no—
653C2×C32—62no—
654C2×C32—84no—
655C2×C32—84no—
656C2×C32—121no—
657C2×C32C2×D3×D414yes—
658C2×C32C2×D3×D411yescharacteristic
659C2×C32#100414yes—
660C2×C32#100414yes—
661C2×C32#100411yescharacteristic
662C2×C32#100911yescharacteristic
663C3⋊D3—41no—
664C3⋊D3—121no—
665C3⋊D3—121no—
666C3⋊D3—124no—
667C3⋊D3—124no—
668C3⋊D3—244no—
669C3⋊D3—244no—
670C3×D3—28no—
671C3×D3—44no—
672C3×D3—124no—
673C24—31no—
674C24—271no—
675#41—544no—
676C2×Q8—271no—
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—91no—
680C2×D4—91no—
681C2×D4—271no—
682C2×D4—271no—
683C2×D4—271no—
684C2×D4—271no—
685C2×D4—271no—
686C2×D4—271no—
687C2×D4—271no—
688C2×D4—271no—
689C2×D4—271no—
690C2×D4—271no—
691C2×D4—544no—
692C2×D4D3×C3⋊D311yescharacteristic, complemented
693C22×C4—91no—
694C22×C4—271no—
695C22×C4—271no—
696C4⋊C4—91no—
697C4⋊C4—271no—
698C22⋊C4—31no—
699C22⋊C4—31no—
700C22⋊C4—31no—
701C22⋊C4—91no—
702C22⋊C4—91no—
703C22⋊C4—271no—
704C22⋊C4—271no—
705C22⋊C4—271no—
706C22⋊C4—271no—
707C22⋊C4—271no—
708C42—271no—
709C42—271no—
710C22×C3—24no—
711C22×C3—24no—
712C22×C3—24no—
713C22×C3—24no—
714C22×C3—24no—
715C22×C3—24no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—24no—
723C22×C3—38no—
724C22×C3—44no—
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—1216no—
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—44no—
747C2×D3—64no—
748C2×D3—64no—
749C2×D3—64no—
750C2×D3—184no—
751C2×D3—184no—
752C2×D3—184no—
753C2×D3—184no—
754C2×D3—184no—
755C2×D3—184no—
756C2×D3—181no—
757C2×D3—181no—
758C2×D3—181no—
759C2×D3—181no—
760C2×D3—181no—
761C2×D3—181no—
762C2×D3—364no—
763C2×D3—364no—
764C2×D3—364no—
765C2×D3—364no—
766C2×D3—364no—
767C2×D3—364no—
768C2×D3—364no—
769C2×D3—3616no—
770C2×D3D4×C3⋊D312yes—
771C3×C4—28no—
772C3×C4—24no—
773C3×C4—21no—
774C3×C4—64no—
775C3×C4—64no—
776C3×C4—92no—
777C3×C4—181no—
778C3×C4—181no—
779Dic3—21no—
780Dic3—21no—
781Dic3—38no—
782Dic3—64no—
783Dic3—64no—
784Dic3—98no—
785Dic3—92no—
786Dic3—188no—
787Dic3—188no—
788Dic3—184no—
789Dic3—181no—
790C32—24no—
791C32#559214yescomplemented
792C32#560711yescharacteristic, complemented
793C23—31no—
794C23—31no—
795C23—62no—
796C23—91no—
797C23—121no—
798C23—121no—
799C23—271no—
800C23—271no—
801C23—542no—
802C23—1081no—
803C23—1081no—
804C23C2×D3×C3⋊D311yescharacteristic
805C23C2×D3×C3⋊D311yescharacteristic
806Q8—542no—
807D4—41no—
808D4—62no—
809D4—121no—
810D4—182no—
811D4—361no—
812D4—542no—
813D4—542no—
814D4—542no—
815D4—542no—
816D4—542no—
817D4—1081no—
818D4—1081no—
819D4—1081no—
820D4—1081no—
821D4—1081no—
822C2×C4—31no—
823C2×C4—31no—
824C2×C4—91no—
825C2×C4—91no—
826C2×C4—91no—
827C2×C4—182no—
828C2×C4—274no—
829C2×C4—271no—
830C2×C4—271no—
831C2×C4—542no—
832C2×C4C2×D3×C3⋊D311yescharacteristic
833C2×C3—24no—
834C2×C3—24no—
835C2×C3—24no—
836C2×C3—44no—
837C2×C3—44no—
838C2×C3—41no—
839C2×C3—41no—
840C2×C3—68no—
841C2×C3—84no—
842C2×C3—84no—
843C2×C3—124no—
844C2×C3—361no—
845C2×C3D32×D414yes—
846C2×C3#6431414yes—
847C2×C3#6433014yes—
848C2×C3C2×D4×C3⋊D311yescharacteristic
849C2×C3#6436111yescharacteristic
850C2×C3#6436111yescharacteristic
851D3—22no—
852D3—41no—
853D3—124no—
854D3—364no—
855D3—364no—
856D3—361no—
857D3—361no—
858D3—724no—
859D3—724no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—32no—
867C22—61no—
868C22—61no—
869C22—61no—
870C22—61no—
871C22—61no—
872C22—124no—
873C22—181no—
874C22—181no—
875C22—181no—
876C22—541no—
877C22—541no—
878C22—541no—
879C22—541no—
880C22—541no—
881C22—541no—
882C22—1084no—
883C22C22×D3×C3⋊D311yescharacteristic
884C4—21no—
885C4—61no—
886C4—61no—
887C4—92no—
888C4—181no—
889C4—181no—
890C4—272no—
891C4—541no—
892C3—24no—
893C3#1059528514yescomplemented
894C3#1059606311yescharacteristic, complemented
895C2—41no—
896C2—41no—
897C2—62no—
898C2—121no—
899C2—361no—
900C2—1081no—
901C2—1081no—
902C2D3×D4×C3⋊D311yescharacteristic
903C2#1172458811yescharacteristic
904C2#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×#89028C2semidirect
3. #11723981C2semidirect
4. C3×#64148C2semidirect
5. C32×#937C2semidirect
6. #11723643C2semidirect
7. #11723635C2semidirect
8. #11723633C2semidirect
9. #11723630C2semidirect
10. #11723623C2semidirect
11. #11723592C2semidirect
12. #11723542C2semidirect
13. #11723530C2semidirect
14. #11723525C2semidirect
15. #11723460C2semidirect
20. C2×C33×D4C22semidirect
22. C2×#6312C22semidirect
23. C2×#6312C22semidirect
24. C2×#6312C22semidirect
25. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
27. C2×C3×#638C22semidirect
28. C22×C3×C3⋊Dic3C22semidirect
30. C2×C32×#67C22semidirect
32. C2×#6293C22semidirect
33. C2×#6292C22semidirect
36. C2×#6291C22semidirect
38. C2×#6289C22semidirect
41. C4×C3⋊(C3⋊Dic3)C22semidirect
42. C3×#3757C22semidirect
43. C3×#3752C22semidirect
44. C3×#3750C22semidirect
45. C32×#217C22semidirect
47. C32×(C2×D3)⋊C4C22semidirect
48. #88807C22semidirect
49. #88804C22semidirect
50. #88804C22semidirect
51. #88803C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
66. #64148D3semidirect
75. C3×#937D3semidirect
125. D3×C3⋊Dic3D4semidirect
135. C2×C32×D4C2×D3semidirect
136. C2×C32×D4C2×D3semidirect
155. C2×#638C2×D3semidirect
157. C22×C3⋊Dic3C2×D3semidirect
168. C2×C3×#67C2×D3semidirect
185. #3757C2×D3semidirect
189. #3752C2×D3semidirect
191. #3750C2×D3semidirect
197. C3×#217C2×D3semidirect
200. C3×(C2×D3)⋊C4C2×D3semidirect
258. #937C3⋊D3semidirect
385. C2×C3×D4D32semidirect
386. C2×C3×D4C2×C3⋊D3semidirect
410. C2×#67C2×C3⋊D3semidirect
438. #217C2×C3⋊D3semidirect
448. (C2×D3)⋊C4C2×C3⋊D3semidirect
552. C33#535semidirect
692. C2×D4D3×C3⋊D3semidirect
791. C32#5592semidirect
792. C32#5607semidirect
893. C3#10595285semidirect
894. 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×#890282
#117239812
C3×#641482
C32×#9372
#117236432
#117236352
#117236332
#117236302
#117236232
#117235922
#117235422
#117235302
#117235252
#117234602
#105960633
#105952853