Finite Group Databasebeta

← C3×#10595513 #13175088

Subgroups — C3×#10595513 #13175088

Order 1728.

1966 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×#67C211yesmaximal, characteristic, complemented
2C2×C3×#3804C211yesmaximal, characteristic, complemented
3C3×#64162C211yesmaximal, characteristic, complemented
4C32×#953C211yesmaximal, characteristic, complemented
5C3×#63979C212yesmaximal, complemented
6C3×#63977C211yesmaximal, characteristic, complemented
7C3×#63976C211yesmaximal, characteristic, complemented
8C3×#63970C212yesmaximal, complemented
9C3×#63959C212yesmaximal, complemented
10C3×#63958C212yesmaximal, complemented
11C3×#63955C211yesmaximal, characteristic, complemented
12C3×#5805—31nomaximal
13C3×#5592—31nomaximal
14#10595513C311yesmaximal, characteristic, direct product factor
15C24×C33C2211yescharacteristic
16C23×C32×D3C2211yescharacteristic
17C2×C3×#638C2211yescharacteristic
18C2×C3×#638C2212yescomplemented
19C2×C32×#67—24no—
20C2×C32×#67C2211yescharacteristic
21C2×C32×#67C2212yes—
22C2×C32×#67C2212yes—
23C2×C32×#67C2212yescomplemented
24C22×C32×Dic3C2211yescharacteristic
25C2×C3×#627C2211yescharacteristic, complemented
26C2×C3×#626C2211yescharacteristic, complemented
27C2×C3×#626C2212yescomplemented
28C2×C3×#625C2212yescomplemented
29C2×C3×#624C2211yescharacteristic, complemented
30C3×#3804—24no—
31C2×C3×D3×Dic3C2211yescharacteristic, complemented
32C3×#3757C2211yescharacteristic
33C3×#3757C2212yescomplemented
34C32×#217C2211yescharacteristic
35C32×#217C2212yescomplemented
36C3×Dic3⋊Dic3C2212yescomplemented
37C3×(C2×D3)⋊Dic3C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C3×Dic32C2212yescomplemented
40C22×C32×D4—31no—
41C22×C3×#67—21no—
42C22×C3×#67D311yescharacteristic, complemented
43C22×C3×#67C2×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—31no—
53C3×#953—31no—
54C3×#953—61no—
55C3×#953D311yescharacteristic, complemented
56C3×#953C2×C311yescharacteristic, complemented
57C3×#940—32no—
58C3×#940—32no—
59C3×#939—32no—
60C3×#938—32no—
61C3×#938—32no—
62C3×#937—31no—
63C3×#936—32no—
64C3×#926—31no—
65C3×#885—32no—
66C3×#884—32no—
67C3×#882—31no—
68C3×#877—31no—
69#63979C2×C312yescomplemented
70#63977C2×C311yescharacteristic, complemented
71#63976C2×C311yescharacteristic, complemented
72#63970C2×C312yescomplemented
73#63959C2×C312yescomplemented
74#63958C2×C312yescomplemented
75#63955C2×C311yescharacteristic, complemented
76C23×C33—22no—
77C23×C33—42no—
78C23×C33C2312yes—
79C23×C33C2311yescharacteristic
80C22×C3×C3⋊D3C2311yescharacteristic
81C22×C32×D3—22no—
82C22×C32×D3—42no—
83C22×C32×D3C2312yes—
84C22×C32×D3C2311yescharacteristic
85C3×#638—22no—
86C3×#638—42no—
87C2×C3×C3⋊Dic3C2312yes—
88C2×C3×C3⋊Dic3C2311yescharacteristic
89C32×#67—22no—
90C32×#67—24no—
91C32×#67—24no—
92C32×#67—42no—
93C2×C32×Dic3D414yescomplemented
94C2×C32×Dic3C2312yes—
95C2×C32×Dic3C2311yescharacteristic
96C2×C32×Dic3C2311yescharacteristic
97C2×C32×Dic3C2311yescharacteristic
98C3×#627—22no—
99C3×#626—22no—
100C3×#626—42no—
101C3×#625—42no—
102C3×#624—22no—
103C3×D3×Dic3—22no—
104C3×#535—91no—
105#5805—31no—
106#5592—31no—
107C24×C32—21no—
108C24×C32—21no—
109C24×C32—21no—
110C24×C32—31no—
111C24×C32—41no—
112C24×C32C2×D311yescharacteristic
113C24×C32C2×D311yescharacteristic
114C24×C32C22×C311yescharacteristic
115C23×C3×D3—21no—
116C23×C3×D3C2×D311yescharacteristic
117C23×C3×D3C22×C311yescharacteristic
118C2×C32×D4—32no—
119C2×C32×D4—31no—
120C2×C32×D4—32no—
121C2×C32×D4—32no—
122C2×C32×D4—64no—
123C22×C32×C4—31no—
124C2×#638C22×C311yescharacteristic
125C2×#638C22×C312yescomplemented
126C2×C3×#67—28no—
127C2×C3×#67—22no—
128C2×C3×#67—22no—
129C2×C3×#67—21no—
130C2×C3×#67—22no—
131C2×C3×#67—24no—
132C2×C3×#67—24no—
133C2×C3×#67—31no—
134C2×C3×#67—31no—
135C2×C3×#67—32no—
136C2×C3×#67—32no—
137C2×C3×#67—32no—
138C2×C3×#67—32no—
139C2×C3×#67—31no—
140C2×C3×#67—32no—
141C2×C3×#67—61no—
142C2×C3×#67—62no—
143C2×C3×#67C2×D312yes—
144C2×C3×#67C2×D312yes—
145C2×C3×#67C2×D311yescharacteristic
146C2×C3×#67C2×D312yescomplemented
147C2×C3×#67C22×C311yescharacteristic
148C2×C3×#67C22×C312yes—
149C2×C3×#67C22×C312yes—
150C2×C3×#67C22×C312yescomplemented
151C22×C3×Dic3—21no—
152C22×C3×Dic3—31no—
153C22×C3×Dic3C2×D311yescharacteristic
154C22×C3×Dic3C22×C311yescharacteristic
155C3×#237—64no—
156C3×#235—64no—
157C2×C3×D12—31no—
158C2×C3×D12—32no—
159C2×C3×C4×D3—31no—
160C2×C3×C4×D3—31no—
161C2×C3×C4×D3—31no—
162C2×C3×Dic6—31no—
163C2×C3×Dic6—31no—
164C2×#627C22×C311yescharacteristic, complemented
165C2×#626C22×C311yescharacteristic, complemented
166C2×#626C22×C312yescomplemented
167C2×#625C22×C312yescomplemented
168C2×#624C22×C311yescharacteristic, complemented
169#3804—24no—
170C2×D3×Dic3C22×C311yescharacteristic, complemented
171C32×C22⋊C4—31no—
172C32×C22⋊C4—32no—
173#3757C22×C311yescharacteristic
174#3757C22×C312yescomplemented
175C3×#217—21no—
176C3×#217—22no—
177C3×#217—31no—
178C3×#217—32no—
179C3×#217—31no—
180C3×#217—32no—
181C3×#217—32no—
182C3×#217—32no—
183C3×#217—61no—
184C3×#217—62no—
185C3×#217C2×D311yescharacteristic
186C3×#217C2×D312yescomplemented
187C3×#217C22×C311yescharacteristic
188C3×#217C22×C312yescomplemented
189C3×(C2×D3)⋊C4—32no—
190C3×(C2×D3)⋊C4—32no—
191C3×C4⋊Dic3—32no—
192C3×Dic3⋊C4—32no—
193C3×C4×Dic3—32no—
194C3×C4×Dic3—32no—
195Dic3⋊Dic3C22×C312yescomplemented
196(C2×D3)⋊Dic3C22×C312yescomplemented
197(C2×D3)⋊Dic3C22×C312yescomplemented
198Dic32C22×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—21no—
210C2×C32×D3—22no—
211C2×C32×D3—22no—
212C2×C32×D3—22no—
213C2×C32×D3—44no—
214C3×C3⋊Dic3—21no—
215C3×C3⋊Dic3—22no—
216C32×Dic3—21no—
217C32×Dic3—22no—
218C32×Dic3C2×D412yes—
219C32×Dic3C2×D412yes—
220C2×C3×#41—91no—
221C22×C3×D4—31no—
222C22×C3×D4—31no—
223C22×C3×D4—61no—
224C22×#67C3×D311yescharacteristic, complemented
225C2×#237—31no—
226C2×#235—31no—
227C3×#127—92no—
228C3×#124—92no—
229C3×#121—92no—
230C3×#121—92no—
231C3×#120—31no—
232C3×#120—31no—
233C3×#120—61no—
234C3×#120—91no—
235C3×#120—91no—
236C3×#120—91no—
237C3×#117—91no—
238#953—31no—
239#953—31no—
240#953—31no—
241#953—31no—
242#953—61no—
243#953C3×D311yescharacteristic, complemented
244#940—32no—
245#940—32no—
246#939—32no—
247#938—32no—
248#938—32no—
249#937—31no—
250#936—32no—
251#926—31no—
252#885—32no—
253#884—32no—
254#882—31no—
255#877—31no—
256C23×C32—22no—
257C23×C32—24no—
258C23×C32—22no—
259C23×C32—22no—
260C23×C32—22no—
261C23×C32—21no—
262C23×C32—21no—
263C23×C32—22no—
264C23×C32—21no—
265C23×C32—22no—
266C23×C32—32no—
267C23×C32—31no—
268C23×C32—41no—
269C23×C32—42no—
270C23×C32—42no—
271C23×C32—42no—
272C23×C32—44no—
273C23×C32—42no—
274C23×C32—42no—
275C23×C32—42no—
276C23×C32—44no—
277C23×C32—44no—
278C23×C32—44no—
279C23×C32—48no—
280C23×C32—62no—
281C23×C32—122no—
282C23×C32C22×D312yes—
283C23×C32C22×D312yes—
284C23×C32C22×D311yescharacteristic
285C23×C32C22×D311yescharacteristic
286C23×C32C23×C312yes—
287C23×C32C23×C311yescharacteristic
288C22×C3⋊D3C23×C311yescharacteristic
289C22×C3×D3—24no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3—21no—
294C22×C3×D3—31no—
295C22×C3×D3—31no—
296C22×C3×D3—42no—
297C22×C3×D3—42no—
298C22×C3×D3—44no—
299C22×C3×D3—61no—
300C22×C3×D3C22×D312yes—
301C22×C3×D3C22×D311yescharacteristic
302C22×C3×D3C23×C312yes—
303C22×C3×D3C23×C311yescharacteristic
304C32×D4—64no—
305C32×D4—64no—
306C32×D4—62no—
307C32×D4—122no—
308C2×C32×C4—34no—
309C2×C32×C4—31no—
310C2×C32×C4—31no—
311C2×C32×C4—32no—
312C2×C32×C4—31no—
313#638—22no—
314#638—42no—
315C2×C3⋊Dic3C23×C312yes—
316C2×C3⋊Dic3C23×C311yescharacteristic
317C3×#67—28no—
318C3×#67—28no—
319C3×#67—22no—
320C3×#67—22no—
321C3×#67—24no—
322C3×#67—24no—
323C3×#67—24no—
324C3×#67—24no—
325C3×#67—42no—
326C3×#67—42no—
327C3×#67—42no—
328C3×#67—44no—
329C3×#67—62no—
330C3×#67—62no—
331C3×#67—62no—
332C3×#67—122no—
333C3×#67—122no—
334C3×#67—122no—
335C3×#67—122no—
336C3×#67—122no—
337C3×#67—122no—
338C3×#67—124no—
339C2×C3×Dic3—24no—
340C2×C3×Dic3—21no—
341C2×C3×Dic3—21no—
342C2×C3×Dic3—22no—
343C2×C3×Dic3—21no—
344C2×C3×Dic3—32no—
345C2×C3×Dic3—32no—
346C2×C3×Dic3—31no—
347C2×C3×Dic3—31no—
348C2×C3×Dic3—62no—
349C2×C3×Dic3—61no—
350C2×C3×Dic3—62no—
351C2×C3×Dic3#6714yescomplemented
352C2×C3×Dic3C3×D414yescomplemented
353C2×C3×Dic3C22×D312yes—
354C2×C3×Dic3C22×D311yescharacteristic
355C2×C3×Dic3C22×D311yescharacteristic
356C2×C3×Dic3C22×D311yescharacteristic
357C2×C3×Dic3C23×C312yes—
358C2×C3×Dic3C23×C311yescharacteristic
359C2×C3×Dic3C23×C311yescharacteristic
360C2×C3×Dic3C23×C311yescharacteristic
361C3×D12—62no—
362C3×D12—122no—
363C3×C4×D3—62no—
364C3×C4×D3—62no—
365C3×C4×D3—62no—
366C3×Dic6—62no—
367C3×Dic6—62no—
368#627—22no—
369#626—22no—
370#626—42no—
371#625—42no—
372#624—22no—
373D3×Dic3—22no—
374#535—91noSylow
375C2×C33—22no—
376C2×C33—42no—
377C2×C33C22×D411yescharacteristic
378C2×C33H(5,𝔽2)12yes—
379C3×C3⋊D3—41no—
380C32×D3—42no—
381C32×D3—41no—
382C24×C3—21no—
383C24×C3—21no—
384C24×C3—21no—
385C24×C3—31no—
386C24×C3—31no—
387C24×C3—41no—
388C24×C3—61no—
389C24×C3D3211yescharacteristic
390C24×C3C2×C3×D311yescharacteristic
391C24×C3C2×C3×D311yescharacteristic
392C23×D3C2×C3×D311yescharacteristic
393C3×#41—184no—
394C2×C3×Q8—91no—
395C2×C3×D4—31no—
396C2×C3×D4—32no—
397C2×C3×D4—32no—
398C2×C3×D4—32no—
399C2×C3×D4—31no—
400C2×C3×D4—32no—
401C2×C3×D4—32no—
402C2×C3×D4—32no—
403C2×C3×D4—62no—
404C2×C3×D4—62no—
405C2×C3×D4—61no—
406C2×C3×D4—62no—
407C2×C3×D4—64no—
408C2×C3×D4—64no—
409C2×C3×D4—68no—
410C2×C3×D4—91no—
411C2×C3×D4—92no—
412C2×C3×D4—91no—
413C2×C3×D4—92no—
414C2×C3×D4—92no—
415C22×C3×C4—31no—
416C22×C3×C4—31no—
417C22×C3×C4—61no—
418C22×C3×C4—91no—
419C22×C3×C4—91no—
420C2×#67—24no—
421C2×#67—31no—
422C2×#67—31no—
423C2×#67—32no—
424C2×#67—32no—
425C2×#67—32no—
426C2×#67—32no—
427C2×#67—31no—
428C2×#67—32no—
429C2×#67—61no—
430C2×#67—62no—
431C2×#67C2×C3×D312yes—
432C2×#67C2×C3×D312yes—
433C2×#67C2×C3×D311yescharacteristic
434C2×#67C2×C3×D312yescomplemented
435C22×Dic3—31no—
436C22×Dic3C2×C3×D311yescharacteristic
437#237—64no—
438#235—64no—
439C2×D12—31no—
440C2×D12—32no—
441C2×C4×D3—31no—
442C2×C4×D3—31no—
443C2×C4×D3—31no—
444C2×Dic6—31no—
445C2×Dic6—31no—
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—91no—
456C3×C22⋊C4—92no—
457C3×C42—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
467#217C2×C3×D312yescomplemented
468(C2×D3)⋊C4—32no—
469(C2×D3)⋊C4—32no—
470C4⋊Dic3—32no—
471Dic3⋊C4—32no—
472C4×Dic3—32no—
473C4×Dic3—32no—
474C22×C32—22no—
475C22×C32—22no—
476C22×C32—22no—
477C22×C32—22no—
478C22×C32—24no—
479C22×C32—22no—
480C22×C32—22no—
481C22×C32—24no—
482C22×C32—24no—
483C22×C32—24no—
484C22×C32—22no—
485C22×C32—22no—
486C22×C32—22no—
487C22×C32—22no—
488C22×C32—22no—
489C22×C32—22no—
490C22×C32—21no—
491C22×C32—21no—
492C22×C32—21no—
493C22×C32—22no—
494C22×C32—22no—
495C22×C32—22no—
496C22×C32—42no—
497C22×C32—41no—
498C22×C32—42no—
499C22×C32—42no—
500C22×C32—42no—
501C22×C32—42no—
502C22×C32—42no—
503C22×C32—42no—
504C22×C32—42no—
505C22×C32—42no—
506C22×C32—44no—
507C22×C32—44no—
508C22×C32—44no—
509C22×C32—44no—
510C22×C32—44no—
511C22×C32—48no—
512C22×C32—44no—
513C22×C32—44no—
514C22×C32—48no—
515C22×C32—48no—
516C22×C32—416no—
517C22×C32—62no—
518C22×C32—62no—
519C22×C32—62no—
520C22×C32—62no—
521C22×C32—61no—
522C22×C32—124no—
523C22×C32D3×D412yes—
524C22×C32C2×#6712yes—
525C22×C32C2×C3×D412yes—
526C22×C32C23×D311yescharacteristic
527C22×C32C23×D311yescharacteristic
528C22×C32C24×C311yescharacteristic
529C2×C3⋊D3—21no—
530C2×C3⋊D3—22no—
531C2×C3×D3—24no—
532C2×C3×D3—21no—
533C2×C3×D3—22no—
534C2×C3×D3—22no—
535C2×C3×D3—22no—
536C2×C3×D3—22no—
537C2×C3×D3—21no—
538C2×C3×D3—22no—
539C2×C3×D3—22no—
540C2×C3×D3—22no—
541C2×C3×D3—22no—
542C2×C3×D3—42no—
543C2×C3×D3—42no—
544C2×C3×D3—41no—
545C2×C3×D3—42no—
546C2×C3×D3—48no—
547C2×C3×D3—44no—
548C2×C3×D3—44no—
549C2×C3×D3—61no—
550C2×C3×D3—62no—
551C2×C3×D3—62no—
552C2×C3×D3—61no—
553C2×C3×D3—121no—
554C2×C3×D3—122no—
555C32×C4—32no—
556C32×C4—32no—
557C32×C4—62no—
558C32×C4—61no—
559C3⋊Dic3—21no—
560C3⋊Dic3—22no—
561C3×Dic3—21no—
562C3×Dic3—22no—
563C3×Dic3—21no—
564C3×Dic3—22no—
565C3×Dic3—22no—
566C3×Dic3—22no—
567C3×Dic3—41no—
568C3×Dic3—42no—
569C3×Dic3—61no—
570C3×Dic3—62no—
571C3×Dic3—62no—
572C3×Dic3—61no—
573C3×Dic3—121no—
574C3×Dic3—122no—
575C3×Dic3C2×#6712yes—
576C3×Dic3C2×#6712yes—
577C3×Dic3C2×C3×D412yes—
578C3×Dic3C2×C3×D412yes—
579C2×#41—91no—
580C22×D4—31no—
581#127—92no—
582#124—92no—
583#121—92no—
584#121—92no—
585#120—31no—
586#120—91no—
587#120—91no—
588#120—91no—
589#117—91no—
590C33#53511yescharacteristic, complemented, Sylow
591C23×C3—24no—
592C23×C3—22no—
593C23×C3—22no—
594C23×C3—22no—
595C23×C3—21no—
596C23×C3—22no—
597C23×C3—21no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—21no—
601C23×C3—32no—
602C23×C3—31no—
603C23×C3—32no—
604C23×C3—31no—
605C23×C3—42no—
606C23×C3—42no—
607C23×C3—44no—
608C23×C3—42no—
609C23×C3—42no—
610C23×C3—42no—
611C23×C3—44no—
612C23×C3—44no—
613C23×C3—44no—
614C23×C3—48no—
615C23×C3—42no—
616C23×C3—41no—
617C23×C3—62no—
618C23×C3—61no—
619C23×C3—64no—
620C23×C3—62no—
621C23×C3—62no—
622C23×C3—91no—
623C23×C3—122no—
624C23×C3—122no—
625C23×C3—124no—
626C23×C3C2×D3212yes—
627C23×C3C2×D3211yescharacteristic
628C23×C3C22×C3×D312yes—
629C23×C3C22×C3×D312yes—
630C23×C3C22×C3×D311yescharacteristic
631C23×C3C22×C3×D311yescharacteristic
632C22×D3—22no—
633C22×D3—31no—
634C22×D3—31no—
635C22×D3—42no—
636C22×D3—61no—
637C22×D3C22×C3×D312yes—
638C22×D3C22×C3×D311yescharacteristic
639C3×Q8—182no—
640C3×D4—64no—
641C3×D4—64no—
642C3×D4—64no—
643C3×D4—64no—
644C3×D4—68no—
645C3×D4—68no—
646C3×D4—62no—
647C3×D4—62no—
648C3×D4—122no—
649C3×D4—122no—
650C3×D4—122no—
651C3×D4—124no—
652C3×D4—182no—
653C3×D4—182no—
654C3×D4—362no—
655C3×D4—362no—
656C3×D4—362no—
657C2×C3×C4—31no—
658C2×C3×C4—31no—
659C2×C3×C4—31no—
660C2×C3×C4—31no—
661C2×C3×C4—34no—
662C2×C3×C4—34no—
663C2×C3×C4—32no—
664C2×C3×C4—31no—
665C2×C3×C4—32no—
666C2×C3×C4—31no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—64no—
670C2×C3×C4—62no—
671C2×C3×C4—61no—
672C2×C3×C4—92no—
673C2×C3×C4—91no—
674C2×C3×C4—182no—
675C2×C3×C4—182no—
676#67—22no—
677#67—24no—
678#67—24no—
679#67—42no—
680#67—62no—
681#67—62no—
682#67—62no—
683#67—122no—
684#67—122no—
685#67—122no—
686#67—122no—
687#67—122no—
688#67—122no—
689#67—124no—
690C2×Dic3—32no—
691C2×Dic3—32no—
692C2×Dic3—31no—
693C2×Dic3—31no—
694C2×Dic3—62no—
695C2×Dic3—61no—
696C2×Dic3—62no—
697C2×Dic3C3×#6714yescomplemented
698C2×Dic3C22×C3×D312yes—
699C2×Dic3C22×C3×D311yescharacteristic
700C2×Dic3C22×C3×D311yescharacteristic
701C2×Dic3C22×C3×D311yescharacteristic
702D12—62no—
703D12—122no—
704C4×D3—62no—
705C4×D3—62no—
706C4×D3—62no—
707Dic6—62no—
708Dic6—62no—
709C2×C32—22no—
710C2×C32—24no—
711C2×C32—22no—
712C2×C32—22no—
713C2×C32—21no—
714C2×C32—22no—
715C2×C32—21no—
716C2×C32—22no—
717C2×C32—22no—
718C2×C32—21no—
719C2×C32—41no—
720C2×C32—42no—
721C2×C32—42no—
722C2×C32—42no—
723C2×C32—44no—
724C2×C32—44no—
725C2×C32—44no—
726C2×C32—44no—
727C2×C32—48no—
728C2×C32—42no—
729C2×C32—42no—
730C2×C32—42no—
731C2×C32—122no—
732C2×C32—121no—
733C2×C32C2×D3×D411yescharacteristic
734C2×C32#100412yes—
735C2×C32#100412yes—
736C2×C32C22×#6711yescharacteristic
737C2×C32C22×C3×D411yescharacteristic
738C2×C32C3×H(5,𝔽2)12yes—
739C3⋊D3—41no—
740C3×D3—44no—
741C3×D3—42no—
742C3×D3—41no—
743C3×D3—41no—
744C3×D3—42no—
745C3×D3—81no—
746C3×D3—121no—
747C3×D3—121no—
748C3×D3—241no—
749C24—31no—
750C24C3×D3211yescharacteristic
751#41—184no—
752C2×Q8—91no—
753C2×D4—31no—
754C2×D4—32no—
755C2×D4—32no—
756C2×D4—32no—
757C2×D4—64no—
758C2×D4—91no—
759C2×D4—92no—
760C2×D4—91no—
761C2×D4—92no—
762C2×D4—92no—
763C22×C4—31no—
764C22×C4—91no—
765C22×C4—91no—
766C4⋊C4—92no—
767C22⋊C4—31no—
768C22⋊C4—32no—
769C22⋊C4—92no—
770C22⋊C4—92no—
771C22⋊C4—91no—
772C22⋊C4—92no—
773C42—92no—
774C22×C3—24no—
775C22×C3—22no—
776C22×C3—22no—
777C22×C3—22no—
778C22×C3—24no—
779C22×C3—24no—
780C22×C3—24no—
781C22×C3—22no—
782C22×C3—22no—
783C22×C3—22no—
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—22no—
790C22×C3—21no—
791C22×C3—21no—
792C22×C3—21no—
793C22×C3—22no—
794C22×C3—22no—
795C22×C3—22no—
796C22×C3—42no—
797C22×C3—42no—
798C22×C3—42no—
799C22×C3—42no—
800C22×C3—42no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3—42no—
804C22×C3—44no—
805C22×C3—44no—
806C22×C3—44no—
807C22×C3—44no—
808C22×C3—48no—
809C22×C3—44no—
810C22×C3—44no—
811C22×C3—44no—
812C22×C3—48no—
813C22×C3—48no—
814C22×C3—416no—
815C22×C3—41no—
816C22×C3—42no—
817C22×C3—64no—
818C22×C3—61no—
819C22×C3—62no—
820C22×C3—62no—
821C22×C3—62no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3—62no—
827C22×C3—61no—
828C22×C3—122no—
829C22×C3—122no—
830C22×C3—121no—
831C22×C3—122no—
832C22×C3—128no—
833C22×C3—124no—
834C22×C3—124no—
835C22×C3—181no—
836C22×C3—182no—
837C22×C3D3×#6712yes—
838C22×C3C3×D3×D412yes—
839C22×C3C2×C3×#6712yes—
840C22×C3C22×D3211yescharacteristic
841C22×C3C23×C3×D311yescharacteristic
842C22×C3C23×C3×D311yescharacteristic
843C2×D3—21no—
844C2×D3—22no—
845C2×D3—22no—
846C2×D3—22no—
847C2×D3—22no—
848C2×D3—44no—
849C2×D3—61no—
850C2×D3—62no—
851C2×D3—62no—
852C2×D3—61no—
853C2×D3—121no—
854C2×D3—122no—
855C3×C4—32no—
856C3×C4—32no—
857C3×C4—32no—
858C3×C4—32no—
859C3×C4—62no—
860C3×C4—62no—
861C3×C4—61no—
862C3×C4—62no—
863C3×C4—62no—
864C3×C4—61no—
865C3×C4—121no—
866C3×C4—122no—
867C3×C4—181no—
868C3×C4—182no—
869Dic3—21no—
870Dic3—22no—
871Dic3—61no—
872Dic3—62no—
873Dic3—62no—
874Dic3—61no—
875Dic3—121no—
876Dic3—122no—
877Dic3C2×C3×#6712yes—
878Dic3C2×C3×#6712yes—
879C32—21no—
880C32—21no—
881C32—21no—
882C32—41no—
883C32#559211yescharacteristic, complemented
884C32#580511yescharacteristic, complemented
885C32C3×#53511yescharacteristic, complemented
886C23—22no—
887C23—32no—
888C23—31no—
889C23—42no—
890C23—62no—
891C23—91no—
892C23—122no—
893C23C2×C3×D3212yes—
894C23C2×C3×D3211yescharacteristic
895Q8—182no—
896D4—64no—
897D4—64no—
898D4—62no—
899D4—122no—
900D4—182no—
901D4—182no—
902D4—362no—
903D4—362no—
904D4—362no—
905C2×C4—31no—
906C2×C4—31no—
907C2×C4—34no—
908C2×C4—32no—
909C2×C4—31no—
910C2×C4—92no—
911C2×C4—91no—
912C2×C4—182no—
913C2×C4—182no—
914C2×C3—24no—
915C2×C3—22no—
916C2×C3—22no—
917C2×C3—22no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—22no—
922C2×C3—22no—
923C2×C3—22no—
924C2×C3—42no—
925C2×C3—42no—
926C2×C3—44no—
927C2×C3—44no—
928C2×C3—44no—
929C2×C3—44no—
930C2×C3—48no—
931C2×C3—42no—
932C2×C3—42no—
933C2×C3—42no—
934C2×C3—41no—
935C2×C3—42no—
936C2×C3—124no—
937C2×C3—121no—
938C2×C3—122no—
939C2×C3—122no—
940C2×C3—121no—
941C2×C3—241no—
942C2×C3—361no—
943C2×C3C2×D3×#6711yescharacteristic
944C2×C3#6433012yes—
945C2×C3C2×C3×D3×D411yescharacteristic
946C2×C3C3×#100412yes—
947C2×C3C3×#100412yes—
948C2×C3C22×C3×#6711yescharacteristic
949D3—42no—
950D3—41no—
951D3—121no—
952D3—121no—
953D3—241no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—44no—
959C22—61no—
960C22—62no—
961C22—62no—
962C22—62no—
963C22—62no—
964C22—124no—
965C22—181no—
966C22—182no—
967C22C3×D3×#6712yes—
968C22C22×C3×D3211yescharacteristic
969C4—32no—
970C4—32no—
971C4—61no—
972C4—62no—
973C4—181no—
974C4—182no—
975C3—21no—
976C3—21no—
977C3—21no—
978C3—41no—
979C3#1059551311yescharacteristic, direct product factor
980C3C3×#559211yescharacteristic, complemented
981C3C3×#580511yescharacteristic, complemented
982C2—22no—
983C2—42no—
984C2—122no—
985C2—121no—
986C2—361no—
987C2C2×C3×D3×#6711yescharacteristic
988C2C3×#6433012yes—
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC24×C33C22
socleC22×C33C24
hypercenterC24×C3D32
hypocenterC32C3×#535
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×#3804C2semidirect
3. C3×#64162C2semidirect
4. C32×#953C2semidirect
5. C3×#63979C2semidirect
6. C3×#63977C2semidirect
7. C3×#63976C2semidirect
8. C3×#63970C2semidirect
9. C3×#63959C2semidirect
10. C3×#63958C2semidirect
11. C3×#63955C2semidirect
14. #10595513C3direct (N × H)
18. C2×C3×#638C22semidirect
23. C2×C32×#67C22semidirect
25. C2×C3×#627C22semidirect
26. C2×C3×#626C22semidirect
27. C2×C3×#626C22semidirect
28. C2×C3×#625C22semidirect
29. C2×C3×#624C22semidirect
31. C2×C3×D3×Dic3C22semidirect
33. C3×#3757C22semidirect
35. C32×#217C22semidirect
36. C3×Dic3⋊Dic3C22semidirect
37. C3×(C2×D3)⋊Dic3C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
39. C3×Dic32C22semidirect
42. C22×C3×#67D3semidirect
43. C22×C3×#67C2×C3semidirect
46. C2×#3804C2×C3semidirect
48. #64162C2×C3semidirect
55. C3×#953D3semidirect
56. C3×#953C2×C3semidirect
69. #63979C2×C3semidirect
70. #63977C2×C3semidirect
71. #63976C2×C3semidirect
72. #63970C2×C3semidirect
73. #63959C2×C3semidirect
74. #63958C2×C3semidirect
75. #63955C2×C3semidirect
93. C2×C32×Dic3D4semidirect
125. C2×#638C22×C3semidirect
146. C2×C3×#67C2×D3semidirect
150. C2×C3×#67C22×C3semidirect
164. C2×#627C22×C3semidirect
165. C2×#626C22×C3semidirect
166. C2×#626C22×C3semidirect
167. C2×#625C22×C3semidirect
168. C2×#624C22×C3semidirect
170. C2×D3×Dic3C22×C3semidirect
174. #3757C22×C3semidirect
186. C3×#217C2×D3semidirect
188. C3×#217C22×C3semidirect
195. Dic3⋊Dic3C22×C3semidirect
196. (C2×D3)⋊Dic3C22×C3semidirect
197. (C2×D3)⋊Dic3C22×C3semidirect
198. Dic32C22×C3semidirect
224. C22×#67C3×D3semidirect
243. #953C3×D3semidirect
351. C2×C3×Dic3#67semidirect
352. C2×C3×Dic3C3×D4semidirect
434. C2×#67C2×C3×D3semidirect
467. #217C2×C3×D3semidirect
590. C33#535semidirect
697. C2×Dic3C3×#67semidirect
883. C32#5592semidirect
884. C32#5805semidirect
885. C32C3×#535semidirect
979. C3#10595513direct (N × H)
980. C3C3×#5592semidirect
981. C3C3×#5805semidirect

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×#38042
C3×#641622
C32×#9532
C3×#639792
C3×#639772
C3×#639762
C3×#639702
C3×#639592
C3×#639582
C3×#639552
C3×#58053
C3×#55923
#105955133