Finite Group Databasebeta

← C3×#10595524 #13175121

Subgroups — C3×#10595524 #13175121

Order 1728.

2014 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×#67C211yesmaximal, characteristic, complemented
2C2×C3×D3×#67C211yesmaximal, characteristic, complemented
3C3×#64162C211yesmaximal, characteristic, complemented
4C32×#953C211yesmaximal, characteristic, complemented
5C3×#63983C212yesmaximal, complemented
6C3×#63971C212yesmaximal, complemented
7C3×#63970C212yesmaximal, complemented
8C3×#63969C212yesmaximal, complemented
9C3×D3×#217C211yesmaximal, characteristic, complemented
10C3×#63966C211yesmaximal, characteristic, complemented
11C3×#63961C211yesmaximal, characteristic, complemented
12C3×#5804—31nomaximal
13C3×#5589—31nomaximal
14#10595524C311yesmaximal, characteristic, direct product factor
15C24×C33C2211yescharacteristic, complemented
16C23×C32×D3C2211yescharacteristic
17C22×C3×D32C2211yescharacteristic, complemented
18C2×C3×#638C2211yescharacteristic
19C2×C3×#638C2212yescomplemented
20C2×C32×#67—24no—
21C2×C32×#67C2211yescharacteristic
22C2×C32×#67C2212yes—
23C2×C32×#67C2212yescomplemented
24C2×C32×#67C2212yescomplemented
25C22×C32×Dic3C2211yescharacteristic, complemented
26C3×D3×#67—24no—
27C2×C3×#626C2211yescharacteristic, complemented
28C2×C3×#625C2211yescharacteristic, complemented
29C2×C3×D3×Dic3C2211yescharacteristic, complemented
30C2×C3×D3×Dic3C2212yescomplemented
31C3×#3757C2211yescharacteristic, complemented
32C3×#3757C2212yescomplemented
33C32×#217C2211yescharacteristic, complemented
34C32×#217C2212yescomplemented
35C3×#3724C2212yescomplemented
36C3×Dic3⋊Dic3C2212yescomplemented
37C3×#3722C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C22×C32×D4—31no—
41C22×C3×#67—21no—
42C22×C3×#67—31no—
43C22×C3×#67D311yescharacteristic, complemented
44C22×C3×#67C2×C311yescharacteristic, complemented
45C2×C3×D3×D4—31no—
46C2×D3×#67C2×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
55C2×C3×#217—31no—
56C3×#939—32no—
57C3×#939—32no—
58C3×#938—32no—
59C3×#937—32no—
60C3×#937—32no—
61C3×#935—31no—
62C3×#935—32no—
63C3×#929—31no—
64C3×#929—31no—
65C3×#886—31no—
66C3×#884—32no—
67C3×#883—32no—
68C3×D3×C22⋊C4—31no—
69#63983C2×C312yescomplemented
70#63971C2×C312yescomplemented
71#63970C2×C312yescomplemented
72#63969C2×C312yescomplemented
73D3×#217C2×C311yescharacteristic, complemented
74#63966C2×C311yescharacteristic, complemented
75#63961C2×C311yescharacteristic, complemented
76C23×C33—22no—
77C23×C33—42no—
78C23×C33C2312yes—
79C23×C33C2311yescharacteristic
80C22×C3×C3⋊D3C2311yescharacteristic
81C22×C32×D3—42no—
82C22×C32×D3D414yescomplemented
83C22×C32×D3C2311yescharacteristic
84C22×C32×D3C2311yescharacteristic
85C22×C32×D3C2311yescharacteristic
86C2×C3×D32—22no—
87C2×C3×D32—42no—
88C3×#638—22no—
89C3×#638—42no—
90C2×C3×C3⋊Dic3C2311yescharacteristic
91C2×C3×C3⋊Dic3C2312yes—
92C32×#67—22no—
93C32×#67—24no—
94C32×#67—24no—
95C32×#67—42no—
96C2×C32×Dic3—22no—
97C2×C32×Dic3C2311yescharacteristic
98C2×C32×Dic3C2312yes—
99C2×C32×Dic3C2312yes—
100C3×#626—22no—
101C3×#625—22no—
102C3×D3×Dic3—22no—
103C3×D3×Dic3—42no—
104C3×#534—91no—
105#5804—31no—
106#5589—31no—
107C24×C32—21no—
108C24×C32—21no—
109C24×C32—21no—
110C24×C32—31no—
111C24×C32—41no—
112C24×C32C2×D311yescharacteristic, complemented
113C24×C32C2×D311yescharacteristic, complemented
114C24×C32C22×C311yescharacteristic, complemented
115C23×C3×D3—21no—
116C23×C3×D3—31no—
117C23×C3×D3—31no—
118C23×C3×D3C2×D311yescharacteristic
119C23×C3×D3C22×C311yescharacteristic
120C22×D32C22×C311yescharacteristic, complemented
121C2×C32×D4—32no—
122C2×C32×D4—31no—
123C2×C32×D4—32no—
124C2×C32×D4—32no—
125C2×C32×D4—64no—
126C22×C32×C4—31no—
127C2×#638C22×C311yescharacteristic
128C2×#638C22×C312yescomplemented
129C2×C3×#67—28no—
130C2×C3×#67—22no—
131C2×C3×#67—22no—
132C2×C3×#67—24no—
133C2×C3×#67—24no—
134C2×C3×#67—21no—
135C2×C3×#67—22no—
136C2×C3×#67—31no—
137C2×C3×#67—31no—
138C2×C3×#67—31no—
139C2×C3×#67—31no—
140C2×C3×#67—32no—
141C2×C3×#67—32no—
142C2×C3×#67—31no—
143C2×C3×#67—64no—
144C2×C3×#67—61no—
145C2×C3×#67—62no—
146C2×C3×#67C2×D312yes—
147C2×C3×#67C2×D311yescharacteristic
148C2×C3×#67C2×D312yescomplemented
149C2×C3×#67C2×D312yescomplemented
150C2×C3×#67C22×C311yescharacteristic
151C2×C3×#67C22×C312yes—
152C2×C3×#67C22×C312yescomplemented
153C2×C3×#67C22×C312yescomplemented
154C22×C3×Dic3—21no—
155C22×C3×Dic3—31no—
156C22×C3×Dic3—32no—
157C22×C3×Dic3C2×D311yescharacteristic, complemented
158C22×C3×Dic3C22×C311yescharacteristic, complemented
159C3×D3×D4—64no—
160C2×C3×D12—31no—
161C2×C3×C4×D3—31no—
162C2×C3×C4×D3—32no—
163D3×#67—24no—
164C2×#626C22×C311yescharacteristic, complemented
165C2×#625C22×C311yescharacteristic, complemented
166C2×D3×Dic3C22×C311yescharacteristic, complemented
167C2×D3×Dic3C22×C312yescomplemented
168C32×C22⋊C4—31no—
169C32×C22⋊C4—32no—
170#3757C22×C311yescharacteristic, complemented
171#3757C22×C312yescomplemented
172C3×#217—21no—
173C3×#217—22no—
174C3×#217—31no—
175C3×#217—32no—
176C3×#217—31no—
177C3×#217—32no—
178C3×#217—32no—
179C3×#217—32no—
180C3×#217—61no—
181C3×#217—62no—
182C3×#217C2×D311yescharacteristic, complemented
183C3×#217C2×D312yescomplemented
184C3×#217C22×C311yescharacteristic, complemented
185C3×#217C22×C312yescomplemented
186C3×(C2×D3)⋊C4—32no—
187C3×(C2×D3)⋊C4—32no—
188C3×(C2×D3)⋊C4—32no—
189C3×(C2×D3)⋊C4—32no—
190C3×C4⋊Dic3—32no—
191C3×Dic3⋊C4—32no—
192C3×Dic3⋊C4—32no—
193C3×Dic3⋊C4—32no—
194#3724C22×C312yescomplemented
195Dic3⋊Dic3C22×C312yescomplemented
196#3722C22×C312yescomplemented
197(C2×D3)⋊Dic3C22×C312yescomplemented
198(C2×D3)⋊Dic3C22×C312yescomplemented
199C22×C33—22no—
200C22×C33—22no—
201C22×C33—22no—
202C22×C33—22no—
203C22×C33—44no—
204C22×C33C2×D412yes—
205C22×C33C2411yescharacteristic
206C2×C3×C3⋊D3—21no—
207C2×C3×C3⋊D3—22no—
208C2×C32×D3—22no—
209C2×C32×D3—22no—
210C2×C32×D3—21no—
211C2×C32×D3—22no—
212C2×C32×D3—44no—
213C2×C32×D3C2×D412yes—
214C2×C32×D3C2×D412yes—
215C3×D32—44no—
216C3×C3⋊Dic3—21no—
217C3×C3⋊Dic3—22no—
218C32×Dic3—22no—
219C32×Dic3—21no—
220C32×Dic3—22no—
221C22×C3×D4—31no—
222C22×C3×D4—31no—
223C22×C3×D4—61no—
224C22×C3×D4—91no—
225C22×#67—31no—
226C22×#67C3×D311yescharacteristic, complemented
227C2×D3×D4—31no—
228C3×#123—91no—
229C3×#123—92no—
230C3×#123—91no—
231C3×#121—92no—
232C3×#121—92no—
233C3×#120—31no—
234C3×#120—31no—
235C3×#120—61no—
236C3×#120—92no—
237C3×#120—91no—
238C2×C3×C22⋊C4—91no—
239#953—31no—
240#953—31no—
241#953—61no—
242#953C3×D311yescharacteristic, complemented
243C2×#217—31no—
244#939—32no—
245#939—32no—
246#938—32no—
247#937—32no—
248#937—32no—
249#935—31no—
250#935—32no—
251#929—31no—
252#929—31no—
253#886—31no—
254#884—32no—
255#883—32no—
256D3×C22⋊C4—31no—
257C23×C32—22no—
258C23×C32—24no—
259C23×C32—22no—
260C23×C32—22no—
261C23×C32—22no—
262C23×C32—21no—
263C23×C32—21no—
264C23×C32—22no—
265C23×C32—21no—
266C23×C32—22no—
267C23×C32—31no—
268C23×C32—31no—
269C23×C32—34no—
270C23×C32—31no—
271C23×C32—41no—
272C23×C32—42no—
273C23×C32—42no—
274C23×C32—42no—
275C23×C32—44no—
276C23×C32—42no—
277C23×C32—42no—
278C23×C32—42no—
279C23×C32—44no—
280C23×C32—44no—
281C23×C32—44no—
282C23×C32—48no—
283C23×C32—122no—
284C23×C32C22×D312yes—
285C23×C32C22×D312yes—
286C23×C32C22×D311yescharacteristic
287C23×C32C22×D311yescharacteristic
288C23×C32C23×C312yes—
289C23×C32C23×C311yescharacteristic
290C22×C3⋊D3C23×C311yescharacteristic
291C22×C3×D3—24no—
292C22×C3×D3—21no—
293C22×C3×D3—21no—
294C22×C3×D3—21no—
295C22×C3×D3—31no—
296C22×C3×D3—31no—
297C22×C3×D3—42no—
298C22×C3×D3—42no—
299C22×C3×D3—44no—
300C22×C3×D3—61no—
301C22×C3×D3—62no—
302C22×C3×D3—62no—
303C22×C3×D3—122no—
304C22×C3×D3—122no—
305C22×C3×D3#6714yescomplemented
306C22×C3×D3C3×D414yescomplemented
307C22×C3×D3C22×D311yescharacteristic
308C22×C3×D3C22×D311yescharacteristic
309C22×C3×D3C22×D311yescharacteristic
310C22×C3×D3C23×C311yescharacteristic
311C22×C3×D3C23×C311yescharacteristic
312C22×C3×D3C23×C311yescharacteristic
313C2×D32—22no—
314C2×D32—42no—
315C32×D4—64no—
316C32×D4—64no—
317C32×D4—62no—
318C32×D4—122no—
319C2×C32×C4—32no—
320C2×C32×C4—31no—
321C2×C32×C4—32no—
322C2×C32×C4—62no—
323#638—22no—
324#638—42no—
325C2×C3⋊Dic3C23×C312yes—
326C2×C3⋊Dic3C23×C311yescharacteristic
327C3×#67—28no—
328C3×#67—28no—
329C3×#67—22no—
330C3×#67—22no—
331C3×#67—24no—
332C3×#67—24no—
333C3×#67—24no—
334C3×#67—24no—
335C3×#67—42no—
336C3×#67—42no—
337C3×#67—42no—
338C3×#67—44no—
339C3×#67—62no—
340C3×#67—62no—
341C3×#67—62no—
342C3×#67—62no—
343C3×#67—62no—
344C3×#67—122no—
345C3×#67—122no—
346C3×#67—122no—
347C3×#67—124no—
348C2×C3×Dic3—24no—
349C2×C3×Dic3—22no—
350C2×C3×Dic3—22no—
351C2×C3×Dic3—22no—
352C2×C3×Dic3—21no—
353C2×C3×Dic3—22no—
354C2×C3×Dic3—31no—
355C2×C3×Dic3—32no—
356C2×C3×Dic3—32no—
357C2×C3×Dic3—31no—
358C2×C3×Dic3—62no—
359C2×C3×Dic3—61no—
360C2×C3×Dic3—62no—
361C2×C3×Dic3—122no—
362C2×C3×Dic3C22×D311yescharacteristic
363C2×C3×Dic3C22×D312yes—
364C2×C3×Dic3C22×D312yes—
365C2×C3×Dic3C23×C312yes—
366C2×C3×Dic3C23×C312yes—
367C2×C3×Dic3C23×C311yescharacteristic
368C3×D12—62no—
369C3×C4×D3—62no—
370C3×C4×D3—122no—
371#626—22no—
372#625—22no—
373D3×Dic3—22no—
374D3×Dic3—42no—
375#534—91noSylow
376C2×C33—22no—
377C2×C33—42no—
378C2×C33C22×D411yescharacteristic
379C2×C33H(5,𝔽2)12yes—
380C3×C3⋊D3—41no—
381C32×D3—22no—
382C32×D3—22no—
383C32×D3—41no—
384C24×C3—21no—
385C24×C3—21no—
386C24×C3—21no—
387C24×C3—31no—
388C24×C3—31no—
389C24×C3—41no—
390C24×C3—61no—
391C24×C3—91no—
392C24×C3D3211yescharacteristic, complemented
393C24×C3C2×C3×D311yescharacteristic, complemented
394C24×C3C2×C3×D311yescharacteristic, complemented
395C23×D3—31no—
396C23×D3—31no—
397C23×D3C2×C3×D311yescharacteristic
398C2×C3×D4—31no—
399C2×C3×D4—32no—
400C2×C3×D4—32no—
401C2×C3×D4—32no—
402C2×C3×D4—31no—
403C2×C3×D4—32no—
404C2×C3×D4—32no—
405C2×C3×D4—32no—
406C2×C3×D4—62no—
407C2×C3×D4—62no—
408C2×C3×D4—61no—
409C2×C3×D4—62no—
410C2×C3×D4—64no—
411C2×C3×D4—64no—
412C2×C3×D4—68no—
413C2×C3×D4—91no—
414C2×C3×D4—91no—
415C2×C3×D4—91no—
416C2×C3×D4—92no—
417C2×C3×D4—184no—
418C22×C3×C4—31no—
419C22×C3×C4—31no—
420C22×C3×C4—61no—
421C22×C3×C4—91no—
422C22×C3×C4—92no—
423C2×#67—24no—
424C2×#67—31no—
425C2×#67—31no—
426C2×#67—31no—
427C2×#67—31no—
428C2×#67—32no—
429C2×#67—32no—
430C2×#67—31no—
431C2×#67—61no—
432C2×#67—62no—
433C2×#67—64no—
434C2×#67C2×C3×D312yes—
435C2×#67C2×C3×D311yescharacteristic
436C2×#67C2×C3×D312yescomplemented
437C2×#67C2×C3×D312yescomplemented
438C22×Dic3—31no—
439C22×Dic3—32no—
440C22×Dic3C2×C3×D311yescharacteristic, complemented
441D3×D4—64no—
442C2×D12—31no—
443C2×C4×D3—31no—
444C2×C4×D3—32no—
445C3×C4⋊C4—92no—
446C3×C4⋊C4—92no—
447C3×C22⋊C4—31no—
448C3×C22⋊C4—32no—
449C3×C22⋊C4—31no—
450C3×C22⋊C4—32no—
451C3×C22⋊C4—61no—
452C3×C22⋊C4—62no—
453C3×C22⋊C4—92no—
454C3×C22⋊C4—92no—
455C3×C22⋊C4—92no—
456C3×C22⋊C4—91no—
457C3×C22⋊C4—92no—
458#217—31no—
459#217—32no—
460#217—31no—
461#217—32no—
462#217—32no—
463#217—32no—
464#217—61no—
465#217—62no—
466#217C2×C3×D311yescharacteristic, complemented
467#217C2×C3×D312yescomplemented
468(C2×D3)⋊C4—32no—
469(C2×D3)⋊C4—32no—
470(C2×D3)⋊C4—32no—
471(C2×D3)⋊C4—32no—
472C4⋊Dic3—32no—
473Dic3⋊C4—32no—
474Dic3⋊C4—32no—
475Dic3⋊C4—32no—
476C22×C32—22no—
477C22×C32—22no—
478C22×C32—22no—
479C22×C32—22no—
480C22×C32—24no—
481C22×C32—22no—
482C22×C32—22no—
483C22×C32—24no—
484C22×C32—24no—
485C22×C32—24no—
486C22×C32—22no—
487C22×C32—22no—
488C22×C32—22no—
489C22×C32—22no—
490C22×C32—22no—
491C22×C32—22no—
492C22×C32—21no—
493C22×C32—21no—
494C22×C32—21no—
495C22×C32—22no—
496C22×C32—22no—
497C22×C32—22no—
498C22×C32—32no—
499C22×C32—32no—
500C22×C32—42no—
501C22×C32—41no—
502C22×C32—42no—
503C22×C32—42no—
504C22×C32—42no—
505C22×C32—42no—
506C22×C32—42no—
507C22×C32—42no—
508C22×C32—42no—
509C22×C32—42no—
510C22×C32—44no—
511C22×C32—44no—
512C22×C32—44no—
513C22×C32—44no—
514C22×C32—44no—
515C22×C32—48no—
516C22×C32—44no—
517C22×C32—44no—
518C22×C32—48no—
519C22×C32—48no—
520C22×C32—416no—
521C22×C32—62no—
522C22×C32—62no—
523C22×C32—62no—
524C22×C32—61no—
525C22×C32—124no—
526C22×C32D3×D412yes—
527C22×C32C2×#6712yes—
528C22×C32C2×C3×D412yes—
529C22×C32C23×D311yescharacteristic
530C22×C32C23×D311yescharacteristic
531C22×C32C24×C311yescharacteristic
532C2×C3⋊D3—21no—
533C2×C3⋊D3—22no—
534C2×C3×D3—22no—
535C2×C3×D3—22no—
536C2×C3×D3—22no—
537C2×C3×D3—22no—
538C2×C3×D3—21no—
539C2×C3×D3—22no—
540C2×C3×D3—21no—
541C2×C3×D3—22no—
542C2×C3×D3—22no—
543C2×C3×D3—22no—
544C2×C3×D3—42no—
545C2×C3×D3—42no—
546C2×C3×D3—41no—
547C2×C3×D3—42no—
548C2×C3×D3—44no—
549C2×C3×D3—44no—
550C2×C3×D3—48no—
551C2×C3×D3—61no—
552C2×C3×D3—62no—
553C2×C3×D3—62no—
554C2×C3×D3—61no—
555C2×C3×D3—121no—
556C2×C3×D3—122no—
557C2×C3×D3—124no—
558C2×C3×D3—124no—
559C2×C3×D3C2×#6712yes—
560C2×C3×D3C2×#6712yes—
561C2×C3×D3C2×C3×D412yes—
562C2×C3×D3C2×C3×D412yes—
563D32—44no—
564C32×C4—62no—
565C32×C4—62no—
566C32×C4—61no—
567C3⋊Dic3—21no—
568C3⋊Dic3—22no—
569C3×Dic3—24no—
570C3×Dic3—21no—
571C3×Dic3—22no—
572C3×Dic3—22no—
573C3×Dic3—21no—
574C3×Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—41no—
577C3×Dic3—42no—
578C3×Dic3—61no—
579C3×Dic3—62no—
580C3×Dic3—62no—
581C3×Dic3—61no—
582C3×Dic3—121no—
583C3×Dic3—122no—
584C22×D4—31no—
585C22×D4—91no—
586#123—91no—
587#123—92no—
588#123—91no—
589#121—92no—
590#121—92no—
591#120—31no—
592#120—92no—
593#120—91no—
594C2×C22⋊C4—91no—
595C33#53411yescharacteristic, complemented, Sylow
596C23×C3—24no—
597C23×C3—22no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—21no—
601C23×C3—22no—
602C23×C3—21no—
603C23×C3—22no—
604C23×C3—22no—
605C23×C3—21no—
606C23×C3—31no—
607C23×C3—31no—
608C23×C3—31no—
609C23×C3—31no—
610C23×C3—34no—
611C23×C3—34no—
612C23×C3—31no—
613C23×C3—31no—
614C23×C3—42no—
615C23×C3—42no—
616C23×C3—44no—
617C23×C3—42no—
618C23×C3—42no—
619C23×C3—42no—
620C23×C3—44no—
621C23×C3—44no—
622C23×C3—44no—
623C23×C3—48no—
624C23×C3—42no—
625C23×C3—41no—
626C23×C3—61no—
627C23×C3—61no—
628C23×C3—64no—
629C23×C3—61no—
630C23×C3—91no—
631C23×C3—122no—
632C23×C3—122no—
633C23×C3—124no—
634C23×C3—182no—
635C23×C3—362no—
636C23×C3C2×D3212yes—
637C23×C3C2×D3211yescharacteristic
638C23×C3C22×C3×D312yes—
639C23×C3C22×C3×D312yes—
640C23×C3C22×C3×D311yescharacteristic
641C23×C3C22×C3×D311yescharacteristic
642C22×D3—31no—
643C22×D3—31no—
644C22×D3—42no—
645C22×D3—61no—
646C22×D3—62no—
647C22×D3—62no—
648C22×D3—122no—
649C22×D3—122no—
650C22×D3C3×#6714yescomplemented
651C22×D3C22×C3×D311yescharacteristic
652C22×D3C22×C3×D311yescharacteristic
653C22×D3C22×C3×D311yescharacteristic
654C3×D4—64no—
655C3×D4—64no—
656C3×D4—64no—
657C3×D4—64no—
658C3×D4—68no—
659C3×D4—68no—
660C3×D4—62no—
661C3×D4—62no—
662C3×D4—122no—
663C3×D4—122no—
664C3×D4—122no—
665C3×D4—124no—
666C3×D4—182no—
667C3×D4—182no—
668C3×D4—182no—
669C3×D4—362no—
670C2×C3×C4—32no—
671C2×C3×C4—31no—
672C2×C3×C4—32no—
673C2×C3×C4—32no—
674C2×C3×C4—31no—
675C2×C3×C4—32no—
676C2×C3×C4—62no—
677C2×C3×C4—62no—
678C2×C3×C4—61no—
679C2×C3×C4—64no—
680C2×C3×C4—62no—
681C2×C3×C4—62no—
682C2×C3×C4—92no—
683C2×C3×C4—91no—
684C2×C3×C4—182no—
685C2×C3×C4—362no—
686#67—22no—
687#67—24no—
688#67—24no—
689#67—42no—
690#67—62no—
691#67—62no—
692#67—62no—
693#67—62no—
694#67—62no—
695#67—122no—
696#67—122no—
697#67—122no—
698#67—124no—
699C2×Dic3—22no—
700C2×Dic3—31no—
701C2×Dic3—32no—
702C2×Dic3—32no—
703C2×Dic3—31no—
704C2×Dic3—62no—
705C2×Dic3—61no—
706C2×Dic3—62no—
707C2×Dic3—122no—
708C2×Dic3C22×C3×D311yescharacteristic
709C2×Dic3C22×C3×D312yes—
710C2×Dic3C22×C3×D312yes—
711D12—62no—
712C4×D3—62no—
713C4×D3—122no—
714C2×C32—22no—
715C2×C32—24no—
716C2×C32—22no—
717C2×C32—22no—
718C2×C32—21no—
719C2×C32—22no—
720C2×C32—21no—
721C2×C32—22no—
722C2×C32—22no—
723C2×C32—21no—
724C2×C32—41no—
725C2×C32—42no—
726C2×C32—42no—
727C2×C32—42no—
728C2×C32—44no—
729C2×C32—44no—
730C2×C32—44no—
731C2×C32—44no—
732C2×C32—48no—
733C2×C32—42no—
734C2×C32—42no—
735C2×C32—42no—
736C2×C32—62no—
737C2×C32—62no—
738C2×C32—121no—
739C2×C32C2×D3×D411yescharacteristic
740C2×C32#100412yes—
741C2×C32#100412yes—
742C2×C32C22×#6711yescharacteristic
743C2×C32C22×C3×D411yescharacteristic
744C2×C32C3×H(5,𝔽2)12yes—
745C3⋊D3—41no—
746C3×D3—22no—
747C3×D3—22no—
748C3×D3—22no—
749C3×D3—22no—
750C3×D3—42no—
751C3×D3—42no—
752C3×D3—41no—
753C3×D3—41no—
754C3×D3—81no—
755C3×D3—121no—
756C3×D3—121no—
757C3×D3—241no—
758C24—31no—
759C24—91no—
760C24C3×D3211yescharacteristic, complemented
761C2×D4—31no—
762C2×D4—32no—
763C2×D4—32no—
764C2×D4—32no—
765C2×D4—64no—
766C2×D4—91no—
767C2×D4—91no—
768C2×D4—91no—
769C2×D4—92no—
770C2×D4—184no—
771C22×C4—31no—
772C22×C4—91no—
773C22×C4—92no—
774C4⋊C4—92no—
775C4⋊C4—92no—
776C22⋊C4—31no—
777C22⋊C4—32no—
778C22⋊C4—92no—
779C22⋊C4—92no—
780C22⋊C4—92no—
781C22⋊C4—91no—
782C22⋊C4—92no—
783C22×C3—24no—
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—24no—
788C22×C3—24no—
789C22×C3—24no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—22no—
794C22×C3—22no—
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—32no—
806C22×C3—32no—
807C22×C3—32no—
808C22×C3—32no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—42no—
814C22×C3—42no—
815C22×C3—42no—
816C22×C3—42no—
817C22×C3—44no—
818C22×C3—44no—
819C22×C3—44no—
820C22×C3—44no—
821C22×C3—48no—
822C22×C3—44no—
823C22×C3—44no—
824C22×C3—44no—
825C22×C3—48no—
826C22×C3—48no—
827C22×C3—416no—
828C22×C3—41no—
829C22×C3—42no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—62no—
835C22×C3—62no—
836C22×C3—61no—
837C22×C3—62no—
838C22×C3—62no—
839C22×C3—61no—
840C22×C3—122no—
841C22×C3—122no—
842C22×C3—121no—
843C22×C3—122no—
844C22×C3—124no—
845C22×C3—124no—
846C22×C3—128no—
847C22×C3—181no—
848C22×C3—182no—
849C22×C3—364no—
850C22×C3D3×#6712yes—
851C22×C3C3×D3×D412yes—
852C22×C3C2×C3×#6712yes—
853C22×C3C22×D3211yescharacteristic
854C22×C3C23×C3×D311yescharacteristic
855C22×C3C23×C3×D311yescharacteristic
856C2×D3—22no—
857C2×D3—22no—
858C2×D3—21no—
859C2×D3—22no—
860C2×D3—44no—
861C2×D3—61no—
862C2×D3—62no—
863C2×D3—62no—
864C2×D3—61no—
865C2×D3—121no—
866C2×D3—122no—
867C2×D3—124no—
868C2×D3—124no—
869C2×D3C2×C3×#6712yes—
870C2×D3C2×C3×#6712yes—
871C3×C4—64no—
872C3×C4—62no—
873C3×C4—61no—
874C3×C4—62no—
875C3×C4—62no—
876C3×C4—62no—
877C3×C4—61no—
878C3×C4—121no—
879C3×C4—122no—
880C3×C4—181no—
881C3×C4—182no—
882Dic3—21no—
883Dic3—22no—
884Dic3—22no—
885Dic3—61no—
886Dic3—62no—
887Dic3—62no—
888Dic3—61no—
889Dic3—121no—
890Dic3—122no—
891C32—21no—
892C32—21no—
893C32—21no—
894C32—41no—
895C32#558911yescharacteristic, complemented
896C32#580411yescharacteristic, complemented
897C32C3×#53411yescharacteristic, complemented
898C23—22no—
899C23—31no—
900C23—31no—
901C23—34no—
902C23—31no—
903C23—42no—
904C23—91no—
905C23—122no—
906C23—182no—
907C23—362no—
908C23C2×C3×D3212yes—
909C23C2×C3×D3211yescharacteristic
910D4—64no—
911D4—64no—
912D4—62no—
913D4—122no—
914D4—182no—
915D4—182no—
916D4—182no—
917D4—362no—
918C2×C4—32no—
919C2×C4—31no—
920C2×C4—32no—
921C2×C4—62no—
922C2×C4—92no—
923C2×C4—91no—
924C2×C4—182no—
925C2×C4—362no—
926C2×C3—24no—
927C2×C3—22no—
928C2×C3—22no—
929C2×C3—22no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—22no—
934C2×C3—22no—
935C2×C3—22no—
936C2×C3—42no—
937C2×C3—42no—
938C2×C3—44no—
939C2×C3—44no—
940C2×C3—44no—
941C2×C3—44no—
942C2×C3—48no—
943C2×C3—42no—
944C2×C3—42no—
945C2×C3—42no—
946C2×C3—41no—
947C2×C3—42no—
948C2×C3—62no—
949C2×C3—62no—
950C2×C3—62no—
951C2×C3—62no—
952C2×C3—122no—
953C2×C3—122no—
954C2×C3—121no—
955C2×C3—121no—
956C2×C3—241no—
957C2×C3—361no—
958C2×C3C2×D3×#6711yescharacteristic
959C2×C3#6433012yes—
960C2×C3C2×C3×D3×D411yescharacteristic
961C2×C3C3×#100412yes—
962C2×C3C3×#100412yes—
963C2×C3C22×C3×#6711yescharacteristic
964D3—22no—
965D3—22no—
966D3—41no—
967D3—121no—
968D3—121no—
969D3—241no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—22no—
974C22—32no—
975C22—32no—
976C22—44no—
977C22—62no—
978C22—62no—
979C22—61no—
980C22—62no—
981C22—124no—
982C22—181no—
983C22—182no—
984C22—364no—
985C22C3×D3×#6712yes—
986C22C22×C3×D3211yescharacteristic
987C4—62no—
988C4—61no—
989C4—62no—
990C4—181no—
991C4—182no—
992C3—21no—
993C3—21no—
994C3—21no—
995C3—41no—
996C3#1059552411yescharacteristic, direct product factor
997C3C3×#558911yescharacteristic, complemented
998C3C3×#580411yescharacteristic, complemented
999C2—22no—
1000C2—42no—
1001C2—62no—
1002C2—62no—
1003C2—121no—
1004C2—361no—
1005C2C2×C3×D3×#6711yescharacteristic
1006C2C3×#6433012yes—
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC24×C33C22
socleC22×C33C24
hypercenterC24×C3D32
hypocenterC32C3×#534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C24×C3

Complements

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

NH ≅ G/Ntype
1. C22×C32×#67C2semidirect
2. C2×C3×D3×#67C2semidirect
3. C3×#64162C2semidirect
4. C32×#953C2semidirect
5. C3×#63983C2semidirect
6. C3×#63971C2semidirect
7. C3×#63970C2semidirect
8. C3×#63969C2semidirect
9. C3×D3×#217C2semidirect
10. C3×#63966C2semidirect
11. C3×#63961C2semidirect
14. #10595524C3direct (N × H)
15. C24×C33C22semidirect
17. C22×C3×D32C22semidirect
19. C2×C3×#638C22semidirect
23. C2×C32×#67C22semidirect
24. C2×C32×#67C22semidirect
25. C22×C32×Dic3C22semidirect
27. C2×C3×#626C22semidirect
28. C2×C3×#625C22semidirect
29. C2×C3×D3×Dic3C22semidirect
30. C2×C3×D3×Dic3C22semidirect
31. C3×#3757C22semidirect
32. C3×#3757C22semidirect
33. C32×#217C22semidirect
34. C32×#217C22semidirect
35. C3×#3724C22semidirect
36. C3×Dic3⋊Dic3C22semidirect
37. C3×#3722C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
43. C22×C3×#67D3semidirect
44. C22×C3×#67C2×C3semidirect
46. C2×D3×#67C2×C3semidirect
48. #64162C2×C3semidirect
53. C3×#953D3semidirect
54. C3×#953C2×C3semidirect
69. #63983C2×C3semidirect
70. #63971C2×C3semidirect
71. #63970C2×C3semidirect
72. #63969C2×C3semidirect
73. D3×#217C2×C3semidirect
74. #63966C2×C3semidirect
75. #63961C2×C3semidirect
82. C22×C32×D3D4semidirect
112. C24×C32C2×D3semidirect
113. C24×C32C2×D3semidirect
114. C24×C32C22×C3semidirect
120. C22×D32C22×C3semidirect
128. C2×#638C22×C3semidirect
148. C2×C3×#67C2×D3semidirect
149. C2×C3×#67C2×D3semidirect
152. C2×C3×#67C22×C3semidirect
153. C2×C3×#67C22×C3semidirect
157. C22×C3×Dic3C2×D3semidirect
158. C22×C3×Dic3C22×C3semidirect
164. C2×#626C22×C3semidirect
165. C2×#625C22×C3semidirect
166. C2×D3×Dic3C22×C3semidirect
167. C2×D3×Dic3C22×C3semidirect
170. #3757C22×C3semidirect
171. #3757C22×C3semidirect
182. C3×#217C2×D3semidirect
183. C3×#217C2×D3semidirect
184. C3×#217C22×C3semidirect
185. C3×#217C22×C3semidirect
194. #3724C22×C3semidirect
195. Dic3⋊Dic3C22×C3semidirect
196. #3722C22×C3semidirect
197. (C2×D3)⋊Dic3C22×C3semidirect
198. (C2×D3)⋊Dic3C22×C3semidirect
226. C22×#67C3×D3semidirect
242. #953C3×D3semidirect
305. C22×C3×D3#67semidirect
306. C22×C3×D3C3×D4semidirect
392. C24×C3D32semidirect
393. C24×C3C2×C3×D3semidirect
394. C24×C3C2×C3×D3semidirect
436. C2×#67C2×C3×D3semidirect
437. C2×#67C2×C3×D3semidirect
440. C22×Dic3C2×C3×D3semidirect
466. #217C2×C3×D3semidirect
467. #217C2×C3×D3semidirect
595. C33#534semidirect
650. C22×D3C3×#67semidirect
760. C24C3×D32semidirect
895. C32#5589semidirect
896. C32#5804semidirect
897. C32C3×#534semidirect
996. C3#10595524direct (N × H)
997. C3C3×#5589semidirect
998. C3C3×#5804semidirect

Maximal subgroups

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

subgroupindex
C22×C32×#672
C2×C3×D3×#672
C3×#641622
C32×#9532
C3×#639832
C3×#639712
C3×#639702
C3×#639692
C3×D3×#2172
C3×#639662
C3×#639612
C3×#58043
C3×#55893
#105955243