Finite Group Databasebeta

← C3×#10595498 #13175087

Subgroups — C3×#10595498 #13175087

Order 1728.

1950 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C32×Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#3804C211yesmaximal, characteristic, complemented
3C3×#64162C211yesmaximal, characteristic, complemented
4C32×#953C211yesmaximal, characteristic, complemented
5C3×#63978C212yesmaximal, complemented
6C3×Dic3×#67C212yesmaximal, complemented
7C3×#63966C211yesmaximal, characteristic, complemented
8C3×#63964C212yesmaximal, complemented
9C3×#63961C211yesmaximal, characteristic, complemented
10C3×#63955C211yesmaximal, characteristic, complemented
11C3×#63952C212yesmaximal, complemented
12C3×#5791—31nomaximal
13C3×#5586—31nomaximal
14#10595498C311yesmaximal, characteristic, direct product factor
15C24×C33C2211yescharacteristic
16C2×C3×#638C2211yescharacteristic
17C2×C3×#638C2212yes—
18C2×C32×#67C2211yescharacteristic
19C2×C32×#67C2212yes—
20C22×C32×Dic3—24no—
21C22×C32×Dic3C2212yes—
22C22×C32×Dic3C2211yescharacteristic
23C22×C32×Dic3C2212yes—
24C22×C32×Dic3C2211yescharacteristic
25C2×C3×#627C2211yescharacteristic, complemented
26C2×C3×#626C2211yescharacteristic, complemented
27C2×C3×#624C2211yescharacteristic, complemented
28C3×#3804—24no—
29C2×C3×D3×Dic3C2211yescharacteristic, complemented
30C3×#3757C2211yescharacteristic
31C3×#3757C2212yes—
32C32×#217C2212yes—
33C32×#217C2211yescharacteristic
34C3×#3724C2212yescomplemented
35C3×Dic3⋊Dic3C2212yescomplemented
36C3×Dic3⋊Dic3C2212yescomplemented
37C3×#3722C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C3×Dic32C2212yescomplemented
40C23×C32×C4—31no—
41C23×C3×Dic3—21no—
42C23×C3×Dic3D311yescharacteristic, complemented
43C23×C3×Dic3C2×C311yescharacteristic, complemented
44C2×C3×#237—31no—
45C2×C3×#235—31no—
46C2×#3804C2×C311yescharacteristic, complemented
47C32×#120—31no—
48#64162C2×C311yescharacteristic, complemented
49C3×#953—21no—
50C3×#953—31no—
51C3×#953—31no—
52C3×#953—61no—
53C3×#953D311yescharacteristic, complemented
54C3×#953C2×C311yescharacteristic, complemented
55C3×#939—32no—
56C3×#935—31no—
57C3×D4×Dic3—32no—
58C3×#930—32no—
59C3×#929—31no—
60C3×#929—31no—
61C3×C4×#67—32no—
62C3×C4×#67—32no—
63C3×#926—31no—
64C3×#924—32no—
65C3×#886—31no—
66C3×#67⋊C4—32no—
67C3×#878—32no—
68C3×#877—31no—
69#63978C2×C312yescomplemented
70Dic3×#67C2×C312yescomplemented
71#63966C2×C311yescharacteristic, complemented
72#63964C2×C312yescomplemented
73#63961C2×C311yescharacteristic, complemented
74#63955C2×C311yescharacteristic, complemented
75#63952C2×C312yescomplemented
76C23×C33—22no—
77C23×C33—24no—
78C23×C33C2311yescharacteristic
79C23×C33C2312yes—
80C22×C3×C3⋊D3C2311yescharacteristic
81C22×C32×D3C2311yescharacteristic
82C3×#638—22no—
83C3×#638—24no—
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2312yes—
86C32×#67—22no—
87C32×#67—24no—
88C2×C32×Dic3—22no—
89C2×C32×Dic3—24no—
90C2×C32×Dic3—24no—
91C2×C32×Dic3D414yescomplemented
92C2×C32×Dic3C2311yescharacteristic
93C2×C32×Dic3C2312yes—
94C2×C32×Dic3C2312yes—
95C2×C32×Dic3C2311yescharacteristic
96C2×C32×Dic3C2311yescharacteristic
97C3×#627—22no—
98C3×#626—22no—
99C3×#624—22no—
100C3×D3×Dic3—22no—
101C3×#525—91no—
102#5791—31no—
103#5586—31no—
104C24×C32—21no—
105C24×C32—21no—
106C24×C32—21no—
107C24×C32—41no—
108C24×C32C2×D311yescharacteristic
109C24×C32C2×D311yescharacteristic
110C24×C32C22×C311yescharacteristic
111C2×C32×D4—32no—
112C2×C32×D4—31no—
113C22×C32×C4—31no—
114C22×C32×C4—32no—
115C22×C32×C4—32no—
116C22×C32×C4—31no—
117C22×C32×C4—64no—
118C2×#638C22×C311yescharacteristic
119C2×#638C22×C312yes—
120C2×C3×#67—22no—
121C2×C3×#67—21no—
122C2×C3×#67—32no—
123C2×C3×#67—31no—
124C2×C3×#67—32no—
125C2×C3×#67—31no—
126C2×C3×#67—31no—
127C2×C3×#67—62no—
128C2×C3×#67—61no—
129C2×C3×#67C2×D312yes—
130C2×C3×#67C2×D311yescharacteristic
131C2×C3×#67C22×C311yescharacteristic
132C2×C3×#67C22×C312yes—
133C22×C3×Dic3—28no—
134C22×C3×Dic3—22no—
135C22×C3×Dic3—22no—
136C22×C3×Dic3—21no—
137C22×C3×Dic3—21no—
138C22×C3×Dic3—24no—
139C22×C3×Dic3—24no—
140C22×C3×Dic3—31no—
141C22×C3×Dic3C2×D312yes—
142C22×C3×Dic3C2×D312yes—
143C22×C3×Dic3C2×D311yescharacteristic
144C22×C3×Dic3C2×D311yescharacteristic
145C22×C3×Dic3C22×C312yes—
146C22×C3×Dic3C22×C311yescharacteristic
147C22×C3×Dic3C22×C312yes—
148C22×C3×Dic3C22×C311yescharacteristic
149C3×#237—64no—
150C3×#235—64no—
151C2×C3×D12—31no—
152C2×C3×C4×D3—31no—
153C2×C3×C4×D3—31no—
154C2×C3×C4×D3—31no—
155C2×C3×Dic6—31no—
156C2×C3×Dic6—31no—
157C2×#627C22×C311yescharacteristic, complemented
158C2×#626C22×C311yescharacteristic, complemented
159C2×#624C22×C311yescharacteristic, complemented
160#3804—24no—
161C2×D3×Dic3C22×C311yescharacteristic, complemented
162C32×C22⋊C4—31no—
163C32×C22⋊C4—32no—
164#3757C22×C311yescharacteristic
165#3757C22×C312yes—
166C3×#217—22no—
167C3×#217—21no—
168C3×#217—31no—
169C3×#217—32no—
170C3×#217—32no—
171C3×#217—31no—
172C3×#217—32no—
173C3×#217—61no—
174C3×#217—62no—
175C3×#217C2×D312yes—
176C3×#217C2×D311yescharacteristic
177C3×#217C22×C312yes—
178C3×#217C22×C311yescharacteristic
179C3×(C2×D3)⋊C4—32no—
180C3×(C2×D3)⋊C4—32no—
181C3×(C2×D3)⋊C4—32no—
182C3×C4⋊Dic3—32no—
183C3×C4⋊Dic3—32no—
184C3×Dic3⋊C4—32no—
185C3×Dic3⋊C4—32no—
186C3×Dic3⋊C4—32no—
187C3×Dic3⋊C4—32no—
188C3×C4×Dic3—32no—
189C3×C4×Dic3—32no—
190#3724C22×C312yescomplemented
191Dic3⋊Dic3C22×C312yescomplemented
192Dic3⋊Dic3C22×C312yescomplemented
193#3722C22×C312yescomplemented
194(C2×D3)⋊Dic3C22×C312yescomplemented
195Dic32C22×C312yescomplemented
196C22×C33—28no—
197C22×C33—22no—
198C22×C33—22no—
199C22×C33—22no—
200C22×C33C2×D412yes—
201C22×C33#4114yescomplemented
202C22×C33C2411yescharacteristic
203C2×C3×C3⋊D3—21no—
204C2×C3×C3⋊D3—22no—
205C2×C32×D3—21no—
206C2×C32×D3—22no—
207C3×C3⋊Dic3—21no—
208C3×C3⋊Dic3—22no—
209C32×Dic3—22no—
210C32×Dic3—21no—
211C32×Dic3—22no—
212C32×Dic3C2×D412yes—
213C32×Dic3C2×D412yes—
214C2×C3×#41—91no—
215C23×C3×C4—31no—
216C23×C3×C4—31no—
217C23×C3×C4—61no—
218C23×Dic3C3×D311yescharacteristic, complemented
219C2×#237—31no—
220C2×#235—31no—
221C3×#123—91no—
222C3×#123—91no—
223C3×C22⋊Q8—92no—
224C3×#121—92no—
225C3×#120—31no—
226C3×#120—31no—
227C3×#120—61no—
228C3×#120—91no—
229C3×C4×D4—92no—
230C3×C4×D4—92no—
231C3×#117—91no—
232#953—31no—
233#953—31no—
234#953—61no—
235#953C3×D311yescharacteristic, complemented
236#939—32no—
237#935—31no—
238D4×Dic3—32no—
239#930—32no—
240#929—31no—
241#929—31no—
242C4×#67—32no—
243C4×#67—32no—
244#926—31no—
245#924—32no—
246#886—31no—
247#67⋊C4—32no—
248#878—32no—
249#877—31no—
250C23×C32—22no—
251C23×C32—24no—
252C23×C32—28no—
253C23×C32—24no—
254C23×C32—24no—
255C23×C32—22no—
256C23×C32—22no—
257C23×C32—24no—
258C23×C32—22no—
259C23×C32—21no—
260C23×C32—22no—
261C23×C32—21no—
262C23×C32—21no—
263C23×C32—22no—
264C23×C32—31no—
265C23×C32—41no—
266C23×C32—42no—
267C23×C32—44no—
268C23×C32—42no—
269C23×C32—42no—
270C23×C32—44no—
271C23×C32—44no—
272C23×C32—48no—
273C23×C32C22×D312yes—
274C23×C32C22×D311yescharacteristic
275C23×C32C22×D312yes—
276C23×C32C22×D311yescharacteristic
277C23×C32C23×C311yescharacteristic
278C23×C32C23×C312yes—
279C22×C3⋊D3C23×C311yescharacteristic
280C22×C3×D3—21no—
281C22×C3×D3—31no—
282C22×C3×D3—31no—
283C22×C3×D3—61no—
284C22×C3×D3C22×D311yescharacteristic
285C22×C3×D3C23×C311yescharacteristic
286C32×D4—64no—
287C32×D4—62no—
288C2×C32×C4—34no—
289C2×C32×C4—31no—
290C2×C32×C4—31no—
291C2×C32×C4—32no—
292C2×C32×C4—32no—
293C2×C32×C4—31no—
294C2×C32×C4—64no—
295C2×C32×C4—64no—
296C2×C32×C4—62no—
297#638—22no—
298#638—24no—
299C2×C3⋊Dic3C23×C312yes—
300C2×C3⋊Dic3C23×C311yescharacteristic
301C3×#67—22no—
302C3×#67—24no—
303C3×#67—22no—
304C3×#67—24no—
305C3×#67—42no—
306C3×#67—44no—
307C3×#67—64no—
308C3×#67—62no—
309C3×#67—64no—
310C3×#67—62no—
311C3×#67—62no—
312C3×#67—124no—
313C3×#67—122no—
314C2×C3×Dic3—24no—
315C2×C3×Dic3—28no—
316C2×C3×Dic3—28no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—24no—
320C2×C3×Dic3—24no—
321C2×C3×Dic3—24no—
322C2×C3×Dic3—24no—
323C2×C3×Dic3—24no—
324C2×C3×Dic3—22no—
325C2×C3×Dic3—21no—
326C2×C3×Dic3—21no—
327C2×C3×Dic3—22no—
328C2×C3×Dic3—21no—
329C2×C3×Dic3—32no—
330C2×C3×Dic3—32no—
331C2×C3×Dic3—31no—
332C2×C3×Dic3—31no—
333C2×C3×Dic3—62no—
334C2×C3×Dic3—61no—
335C2×C3×Dic3—62no—
336C2×C3×Dic3#6714yescomplemented
337C2×C3×Dic3C3×D414yescomplemented
338C2×C3×Dic3C22×D312yes—
339C2×C3×Dic3C22×D311yescharacteristic
340C2×C3×Dic3C22×D312yes—
341C2×C3×Dic3C22×D311yescharacteristic
342C2×C3×Dic3C22×D311yescharacteristic
343C2×C3×Dic3C23×C312yes—
344C2×C3×Dic3C23×C312yes—
345C2×C3×Dic3C23×C311yescharacteristic
346C2×C3×Dic3C23×C311yescharacteristic
347C2×C3×Dic3C23×C311yescharacteristic
348C3×D12—62no—
349C3×C4×D3—62no—
350C3×C4×D3—62no—
351C3×C4×D3—62no—
352C3×Dic6—62no—
353C3×Dic6—62no—
354#627—22no—
355#626—22no—
356#624—22no—
357D3×Dic3—22no—
358#525—91noSylow
359C2×C33—22no—
360C2×C33—24no—
361C2×C33C22×D411yescharacteristic
362C2×C33C2×#4112yes—
363C3×C3⋊D3—41no—
364C32×D3—41no—
365C24×C3—21no—
366C24×C3—21no—
367C24×C3—21no—
368C24×C3—41no—
369C24×C3D3211yescharacteristic
370C24×C3C2×C3×D311yescharacteristic
371C24×C3C2×C3×D311yescharacteristic
372C3×#41—184no—
373C2×C3×Q8—91no—
374C2×C3×D4—32no—
375C2×C3×D4—31no—
376C2×C3×D4—32no—
377C2×C3×D4—31no—
378C2×C3×D4—62no—
379C2×C3×D4—61no—
380C2×C3×D4—91no—
381C2×C3×D4—92no—
382C2×C3×D4—91no—
383C22×C3×C4—31no—
384C22×C3×C4—31no—
385C22×C3×C4—32no—
386C22×C3×C4—32no—
387C22×C3×C4—31no—
388C22×C3×C4—32no—
389C22×C3×C4—32no—
390C22×C3×C4—31no—
391C22×C3×C4—61no—
392C22×C3×C4—62no—
393C22×C3×C4—62no—
394C22×C3×C4—61no—
395C22×C3×C4—64no—
396C22×C3×C4—64no—
397C22×C3×C4—68no—
398C22×C3×C4—91no—
399C22×C3×C4—91no—
400C2×#67—32no—
401C2×#67—31no—
402C2×#67—32no—
403C2×#67—31no—
404C2×#67—31no—
405C2×#67—62no—
406C2×#67—61no—
407C2×#67C2×C3×D312yes—
408C2×#67C2×C3×D311yescharacteristic
409C22×Dic3—24no—
410C22×Dic3—31no—
411C22×Dic3C2×C3×D312yes—
412C22×Dic3C2×C3×D312yes—
413C22×Dic3C2×C3×D311yescharacteristic
414C22×Dic3C2×C3×D311yescharacteristic
415#237—64no—
416#235—64no—
417C2×D12—31no—
418C2×C4×D3—31no—
419C2×C4×D3—31no—
420C2×C4×D3—31no—
421C2×Dic6—31no—
422C2×Dic6—31no—
423C3×C4⋊C4—92no—
424C3×C4⋊C4—92no—
425C3×C4⋊C4—92no—
426C3×C22⋊C4—31no—
427C3×C22⋊C4—32no—
428C3×C22⋊C4—31no—
429C3×C22⋊C4—32no—
430C3×C22⋊C4—61no—
431C3×C22⋊C4—62no—
432C3×C22⋊C4—92no—
433C3×C22⋊C4—92no—
434C3×C22⋊C4—91no—
435C3×C22⋊C4—92no—
436C3×C42—92no—
437#217—31no—
438#217—32no—
439#217—32no—
440#217—31no—
441#217—32no—
442#217—61no—
443#217—62no—
444#217C2×C3×D312yes—
445#217C2×C3×D311yescharacteristic
446(C2×D3)⋊C4—32no—
447(C2×D3)⋊C4—32no—
448(C2×D3)⋊C4—32no—
449C4⋊Dic3—32no—
450C4⋊Dic3—32no—
451Dic3⋊C4—32no—
452Dic3⋊C4—32no—
453Dic3⋊C4—32no—
454Dic3⋊C4—32no—
455C4×Dic3—32no—
456C4×Dic3—32no—
457C22×C32—28no—
458C22×C32—22no—
459C22×C32—22no—
460C22×C32—22no—
461C22×C32—24no—
462C22×C32—216no—
463C22×C32—28no—
464C22×C32—28no—
465C22×C32—24no—
466C22×C32—24no—
467C22×C32—22no—
468C22×C32—22no—
469C22×C32—22no—
470C22×C32—22no—
471C22×C32—22no—
472C22×C32—22no—
473C22×C32—21no—
474C22×C32—21no—
475C22×C32—21no—
476C22×C32—24no—
477C22×C32—22no—
478C22×C32—24no—
479C22×C32—22no—
480C22×C32—24no—
481C22×C32—22no—
482C22×C32—42no—
483C22×C32—44no—
484C22×C32—41no—
485C22×C32—42no—
486C22×C32—42no—
487C22×C32—42no—
488C22×C32—42no—
489C22×C32—42no—
490C22×C32—42no—
491C22×C32—44no—
492C22×C32—44no—
493C22×C32—44no—
494C22×C32—48no—
495C22×C32—48no—
496C22×C32—416no—
497C22×C32—62no—
498C22×C32—61no—
499C22×C32#23514yescomplemented
500C22×C32D3×D412yes—
501C22×C32#23714yescomplemented
502C22×C32C2×#6712yes—
503C22×C32C2×C3×D412yes—
504C22×C32C3×#4114yescomplemented
505C22×C32C23×D311yescharacteristic
506C22×C32C23×D311yescharacteristic
507C22×C32C24×C311yescharacteristic
508C2×C3⋊D3—21no—
509C2×C3⋊D3—22no—
510C2×C3×D3—21no—
511C2×C3×D3—22no—
512C2×C3×D3—21no—
513C2×C3×D3—22no—
514C2×C3×D3—41no—
515C2×C3×D3—42no—
516C2×C3×D3—62no—
517C2×C3×D3—61no—
518C2×C3×D3—62no—
519C2×C3×D3—61no—
520C2×C3×D3—122no—
521C2×C3×D3—121no—
522C32×C4—32no—
523C32×C4—32no—
524C32×C4—62no—
525C32×C4—62no—
526C32×C4—61no—
527C3⋊Dic3—21no—
528C3⋊Dic3—22no—
529C3×Dic3—24no—
530C3×Dic3—21no—
531C3×Dic3—22no—
532C3×Dic3—22no—
533C3×Dic3—21no—
534C3×Dic3—22no—
535C3×Dic3—22no—
536C3×Dic3—22no—
537C3×Dic3—22no—
538C3×Dic3—41no—
539C3×Dic3—42no—
540C3×Dic3—62no—
541C3×Dic3—61no—
542C3×Dic3—62no—
543C3×Dic3—61no—
544C3×Dic3—122no—
545C3×Dic3—121no—
546C3×Dic3C2×#6712yes—
547C3×Dic3C2×#6712yes—
548C3×Dic3C2×C3×D412yes—
549C3×Dic3C2×C3×D412yes—
550C2×#41—91no—
551C23×C4—31no—
552#123—91no—
553#123—91no—
554C22⋊Q8—92no—
555#121—92no—
556#120—31no—
557#120—91no—
558C4×D4—92no—
559C4×D4—92no—
560#117—91no—
561C33#52511yescharacteristic, complemented, Sylow
562C23×C3—24no—
563C23×C3—28no—
564C23×C3—24no—
565C23×C3—22no—
566C23×C3—24no—
567C23×C3—22no—
568C23×C3—24no—
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—21no—
572C23×C3—22no—
573C23×C3—21no—
574C23×C3—22no—
575C23×C3—21no—
576C23×C3—31no—
577C23×C3—31no—
578C23×C3—44no—
579C23×C3—44no—
580C23×C3—42no—
581C23×C3—42no—
582C23×C3—48no—
583C23×C3—44no—
584C23×C3—42no—
585C23×C3—41no—
586C23×C3—61no—
587C23×C3—91no—
588C23×C3C2×D3212yes—
589C23×C3C2×D3211yescharacteristic
590C23×C3C22×C3×D312yes—
591C23×C3C22×C3×D311yescharacteristic
592C23×C3C22×C3×D312yes—
593C23×C3C22×C3×D311yescharacteristic
594C22×D3—31no—
595C22×D3—31no—
596C22×D3—61no—
597C22×D3C22×C3×D311yescharacteristic
598C3×Q8—182no—
599C3×D4—64no—
600C3×D4—62no—
601C3×D4—64no—
602C3×D4—62no—
603C3×D4—124no—
604C3×D4—122no—
605C3×D4—182no—
606C3×D4—184no—
607C3×D4—182no—
608C2×C3×C4—31no—
609C2×C3×C4—31no—
610C2×C3×C4—31no—
611C2×C3×C4—31no—
612C2×C3×C4—34no—
613C2×C3×C4—34no—
614C2×C3×C4—32no—
615C2×C3×C4—31no—
616C2×C3×C4—32no—
617C2×C3×C4—32no—
618C2×C3×C4—32no—
619C2×C3×C4—31no—
620C2×C3×C4—61no—
621C2×C3×C4—61no—
622C2×C3×C4—64no—
623C2×C3×C4—62no—
624C2×C3×C4—62no—
625C2×C3×C4—61no—
626C2×C3×C4—64no—
627C2×C3×C4—64no—
628C2×C3×C4—64no—
629C2×C3×C4—64no—
630C2×C3×C4—68no—
631C2×C3×C4—68no—
632C2×C3×C4—64no—
633C2×C3×C4—62no—
634C2×C3×C4—62no—
635C2×C3×C4—92no—
636C2×C3×C4—91no—
637C2×C3×C4—182no—
638C2×C3×C4—182no—
639#67—22no—
640#67—24no—
641#67—64no—
642#67—62no—
643#67—64no—
644#67—62no—
645#67—62no—
646#67—124no—
647#67—122no—
648C2×Dic3—22no—
649C2×Dic3—24no—
650C2×Dic3—24no—
651C2×Dic3—32no—
652C2×Dic3—32no—
653C2×Dic3—31no—
654C2×Dic3—31no—
655C2×Dic3—62no—
656C2×Dic3—61no—
657C2×Dic3—62no—
658C2×Dic3C3×#6714yescomplemented
659C2×Dic3C22×C3×D312yes—
660C2×Dic3C22×C3×D311yescharacteristic
661C2×Dic3C22×C3×D312yes—
662C2×Dic3C22×C3×D311yescharacteristic
663C2×Dic3C22×C3×D311yescharacteristic
664D12—62no—
665C4×D3—62no—
666C4×D3—62no—
667C4×D3—62no—
668Dic6—62no—
669Dic6—62no—
670C2×C32—22no—
671C2×C32—24no—
672C2×C32—28no—
673C2×C32—24no—
674C2×C32—24no—
675C2×C32—22no—
676C2×C32—22no—
677C2×C32—24no—
678C2×C32—22no—
679C2×C32—21no—
680C2×C32—22no—
681C2×C32—21no—
682C2×C32—22no—
683C2×C32—21no—
684C2×C32—41no—
685C2×C32—42no—
686C2×C32—42no—
687C2×C32—44no—
688C2×C32—44no—
689C2×C32—42no—
690C2×C32—44no—
691C2×C32—48no—
692C2×C32—121no—
693C2×C32C2×#23512yes—
694C2×C32C2×D3×D411yescharacteristic
695C2×C32C2×#23712yes—
696C2×C32C22×#6711yescharacteristic
697C2×C32C22×C3×D411yescharacteristic
698C2×C32C2×C3×#4112yes—
699C3⋊D3—41no—
700C3×D3—41no—
701C3×D3—41no—
702C3×D3—81no—
703C3×D3—121no—
704C3×D3—121no—
705C3×D3—241no—
706C24C3×D3211yescharacteristic
707#41—184no—
708C2×Q8—91no—
709C2×D4—32no—
710C2×D4—31no—
711C2×D4—91no—
712C2×D4—92no—
713C2×D4—91no—
714C22×C4—31no—
715C22×C4—32no—
716C22×C4—32no—
717C22×C4—31no—
718C22×C4—64no—
719C22×C4—91no—
720C22×C4—91no—
721C4⋊C4—92no—
722C4⋊C4—92no—
723C4⋊C4—92no—
724C22⋊C4—31no—
725C22⋊C4—32no—
726C22⋊C4—92no—
727C22⋊C4—92no—
728C22⋊C4—91no—
729C22⋊C4—92no—
730C42—92no—
731C22×C3—24no—
732C22×C3—28no—
733C22×C3—216no—
734C22×C3—28no—
735C22×C3—28no—
736C22×C3—24no—
737C22×C3—24no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—24no—
751C22×C3—24no—
752C22×C3—24no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—42no—
757C22×C3—42no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—42no—
762C22×C3—48no—
763C22×C3—48no—
764C22×C3—416no—
765C22×C3—44no—
766C22×C3—44no—
767C22×C3—44no—
768C22×C3—41no—
769C22×C3—44no—
770C22×C3—42no—
771C22×C3—62no—
772C22×C3—61no—
773C22×C3—62no—
774C22×C3—61no—
775C22×C3—122no—
776C22×C3—121no—
777C22×C3—182no—
778C22×C3—181no—
779C22×C3#380414yescomplemented
780C22×C3D3×#6712yes—
781C22×C3C3×#23514yescomplemented
782C22×C3C3×D3×D412yes—
783C22×C3C3×#23714yescomplemented
784C22×C3C2×C3×#6712yes—
785C22×C3C22×D3211yescharacteristic
786C22×C3C23×C3×D311yescharacteristic
787C22×C3C23×C3×D311yescharacteristic
788C2×D3—21no—
789C2×D3—22no—
790C2×D3—62no—
791C2×D3—61no—
792C2×D3—62no—
793C2×D3—61no—
794C2×D3—122no—
795C2×D3—121no—
796C3×C4—32no—
797C3×C4—32no—
798C3×C4—32no—
799C3×C4—32no—
800C3×C4—62no—
801C3×C4—62no—
802C3×C4—64no—
803C3×C4—62no—
804C3×C4—62no—
805C3×C4—61no—
806C3×C4—62no—
807C3×C4—62no—
808C3×C4—61no—
809C3×C4—122no—
810C3×C4—121no—
811C3×C4—182no—
812C3×C4—181no—
813Dic3—21no—
814Dic3—22no—
815Dic3—22no—
816Dic3—62no—
817Dic3—61no—
818Dic3—62no—
819Dic3—61no—
820Dic3—122no—
821Dic3—121no—
822Dic3C2×C3×#6712yes—
823Dic3C2×C3×#6712yes—
824C32—21no—
825C32—21no—
826C32—21no—
827C32—41no—
828C32#558611yescharacteristic, complemented
829C32#579111yescharacteristic, complemented
830C32C3×#52511yescharacteristic, complemented
831C23—24no—
832C23—22no—
833C23—31no—
834C23—91no—
835C23C2×C3×D3212yes—
836C23C2×C3×D3211yescharacteristic
837Q8—182no—
838D4—64no—
839D4—62no—
840D4—182no—
841D4—184no—
842D4—182no—
843C2×C4—31no—
844C2×C4—31no—
845C2×C4—34no—
846C2×C4—32no—
847C2×C4—31no—
848C2×C4—32no—
849C2×C4—64no—
850C2×C4—64no—
851C2×C4—62no—
852C2×C4—92no—
853C2×C4—91no—
854C2×C4—182no—
855C2×C4—182no—
856C2×C3—28no—
857C2×C3—24no—
858C2×C3—24no—
859C2×C3—22no—
860C2×C3—22no—
861C2×C3—24no—
862C2×C3—24no—
863C2×C3—22no—
864C2×C3—22no—
865C2×C3—22no—
866C2×C3—22no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—44no—
871C2×C3—44no—
872C2×C3—42no—
873C2×C3—42no—
874C2×C3—48no—
875C2×C3—44no—
876C2×C3—42no—
877C2×C3—41no—
878C2×C3—121no—
879C2×C3—121no—
880C2×C3—241no—
881C2×C3—361no—
882C2×C3C2×#380412yes—
883C2×C3C2×D3×#6711yescharacteristic
884C2×C3C2×C3×#23512yes—
885C2×C3C2×C3×D3×D411yescharacteristic
886C2×C3C2×C3×#23712yes—
887C2×C3C22×C3×#6711yescharacteristic
888D3—41no—
889D3—121no—
890D3—121no—
891D3—241no—
892C22—28no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—62no—
897C22—61no—
898C22—182no—
899C22—181no—
900C22C3×#380414yescomplemented
901C22C3×D3×#6712yes—
902C22C22×C3×D3211yescharacteristic
903C4—32no—
904C4—32no—
905C4—62no—
906C4—62no—
907C4—61no—
908C4—182no—
909C4—181no—
910C3—21no—
911C3—21no—
912C3—21no—
913C3—41no—
914C3#1059549811yescharacteristic, direct product factor
915C3C3×#558611yescharacteristic, complemented
916C3C3×#579111yescharacteristic, complemented
917C2—24no—
918C2—22no—
919C2—121no—
920C2—361no—
921C2C2×C3×#380412yes—
922C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC24×C33C22
socleC22×C33C24
hypercenterC24×C3D32
hypocenterC32C3×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C24×C3

Complements

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

NH ≅ G/Ntype
1. C23×C32×Dic3C2semidirect
2. C2×C3×#3804C2semidirect
3. C3×#64162C2semidirect
4. C32×#953C2semidirect
5. C3×#63978C2semidirect
6. C3×Dic3×#67C2semidirect
7. C3×#63966C2semidirect
8. C3×#63964C2semidirect
9. C3×#63961C2semidirect
10. C3×#63955C2semidirect
11. C3×#63952C2semidirect
14. #10595498C3direct (N × H)
25. C2×C3×#627C22semidirect
26. C2×C3×#626C22semidirect
27. C2×C3×#624C22semidirect
29. C2×C3×D3×Dic3C22semidirect
34. C3×#3724C22semidirect
35. C3×Dic3⋊Dic3C22semidirect
36. C3×Dic3⋊Dic3C22semidirect
37. C3×#3722C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
39. C3×Dic32C22semidirect
42. C23×C3×Dic3D3semidirect
43. C23×C3×Dic3C2×C3semidirect
46. C2×#3804C2×C3semidirect
48. #64162C2×C3semidirect
53. C3×#953D3semidirect
54. C3×#953C2×C3semidirect
69. #63978C2×C3semidirect
70. Dic3×#67C2×C3semidirect
71. #63966C2×C3semidirect
72. #63964C2×C3semidirect
73. #63961C2×C3semidirect
74. #63955C2×C3semidirect
75. #63952C2×C3semidirect
91. C2×C32×Dic3D4semidirect
157. C2×#627C22×C3semidirect
158. C2×#626C22×C3semidirect
159. C2×#624C22×C3semidirect
161. C2×D3×Dic3C22×C3semidirect
190. #3724C22×C3semidirect
191. Dic3⋊Dic3C22×C3semidirect
192. Dic3⋊Dic3C22×C3semidirect
193. #3722C22×C3semidirect
194. (C2×D3)⋊Dic3C22×C3semidirect
195. Dic32C22×C3semidirect
201. C22×C33#41semidirect
218. C23×Dic3C3×D3semidirect
235. #953C3×D3semidirect
336. C2×C3×Dic3#67semidirect
337. C2×C3×Dic3C3×D4semidirect
499. C22×C32#235semidirect
501. C22×C32#237semidirect
504. C22×C32C3×#41semidirect
561. C33#525semidirect
658. C2×Dic3C3×#67semidirect
779. C22×C3#3804semidirect
781. C22×C3C3×#235semidirect
783. C22×C3C3×#237semidirect
828. C32#5586semidirect
829. C32#5791semidirect
830. C32C3×#525semidirect
900. C22C3×#3804semidirect
914. C3#10595498direct (N × H)
915. C3C3×#5586semidirect
916. C3C3×#5791semidirect

Maximal subgroups

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

subgroupindex
C23×C32×Dic32
C2×C3×#38042
C3×#641622
C32×#9532
C3×#639782
C3×Dic3×#672
C3×#639662
C3×#639642
C3×#639612
C3×#639552
C3×#639522
C3×#57913
C3×#55863
#105954983