Finite Group Databasebeta

← C3×#10595507 #13175098

Subgroups — C3×#10595507 #13175098

Order 1728.

1526 conjugacy classes of subgroups.

The subgroup lattice has 1254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64162C211yesmaximal, characteristic, complemented
2C32×#953C211yesmaximal, characteristic, complemented
3C2×C32×#217C211yesmaximal, characteristic, complemented
4C3×#63978C211yesmaximal, characteristic, complemented
5C3×#63975C211yesmaximal, characteristic, complemented
6C3×Dic3×#67C211yesmaximal, characteristic, complemented
7C3×#63971C211yesmaximal, characteristic, complemented
8C3×#63969C211yesmaximal, characteristic, complemented
9C3×#63964C211yesmaximal, characteristic, complemented
10C3×#63959C211yesmaximal, characteristic, complemented
11C3×#63958C211yesmaximal, characteristic, complemented
12C3×#63956C211yesmaximal, characteristic, complemented
13C3×#63956C211yesmaximal, characteristic, complemented
14C3×#63953C211yesmaximal, characteristic, complemented
15C3×#63952C211yesmaximal, characteristic, complemented
16C3×#5593—31nomaximal
17C3×#5494—31nomaximal
18#10595507C311yesmaximal, characteristic, direct product factor
19C24×C33C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C22×C32×Dic3C2211yescharacteristic
27C22×C32×Dic3C2211yescharacteristic
28C2×C3×#627C2211yescharacteristic, complemented
29C2×C3×#626C2211yescharacteristic, complemented
30C2×C3×#624C2211yescharacteristic, complemented
31C2×C3×D3×Dic3C2211yescharacteristic, complemented
32C3×#3757C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C3×#3757C2211yescharacteristic
35C32×#217C2211yescharacteristic
36C32×#217C2211yescharacteristic
37C32×#217C2211yescharacteristic
38C32×#217C2211yescharacteristic
39C32×#217C2211yescharacteristic
40C32×#217C2211yescharacteristic
41C32×#217C2211yescharacteristic
42C3×#3724C2211yescharacteristic, complemented
43C3×#3724C2211yescharacteristic, complemented
44C3×Dic3⋊Dic3C2211yescharacteristic, complemented
45C3×Dic3⋊Dic3C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×#3722C2211yescharacteristic, complemented
49C3×#3722C2211yescharacteristic, complemented
50C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
51C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52C3×Dic32C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54C32×#120—31no—
55C2×C32×C22⋊C4—31no—
56#64162C2×C311yescharacteristic, complemented
57C3×#953—21no—
58C3×#953—31no—
59C3×#953—31no—
60C3×#953—61no—
61C3×#953D311yescharacteristic, complemented
62C3×#953C2×C311yescharacteristic, complemented
63C2×C3×#217—21no—
64C2×C3×#217D311yescharacteristic, complemented
65C2×C3×#217C2×C311yescharacteristic, complemented
66C3×#939—31no—
67C3×#939—31no—
68C3×#938—31no—
69C3×#936—31no—
70C3×#935—31no—
71C3×D4×Dic3—31no—
72C3×#930—31no—
73C3×C4×#67—31no—
74C3×C4×#67—31no—
75C3×#924—31no—
76C3×#885—31no—
77C3×#885—31no—
78C3×#885—31no—
79C3×#884—31no—
80C3×#884—31no—
81C3×#883—31no—
82C3×#883—31no—
83C3×#883—31no—
84C3×#67⋊C4—31no—
85C3×#879—31no—
86C3×#879—31no—
87C3×#879—31no—
88C3×#879—31no—
89C3×#878—31no—
90#63978C2×C311yescharacteristic, complemented
91#63975C2×C311yescharacteristic, complemented
92Dic3×#67C2×C311yescharacteristic, complemented
93#63971C2×C311yescharacteristic, complemented
94#63969C2×C311yescharacteristic, complemented
95#63964C2×C311yescharacteristic, complemented
96#63959C2×C311yescharacteristic, complemented
97#63958C2×C311yescharacteristic, complemented
98#63956C2×C311yescharacteristic, complemented
99#63956C2×C311yescharacteristic, complemented
100#63953C2×C311yescharacteristic, complemented
101#63952C2×C311yescharacteristic, complemented
102C23×C33—22no—
103C23×C33—41no—
104C23×C33—41no—
105C23×C33C2311yescharacteristic
106C23×C33C2311yescharacteristic
107C23×C33C2311yescharacteristic
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C32×D3C2311yescharacteristic
110C3×#638—22no—
111C3×#638—41no—
112C3×#638—41no—
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C32×#67—22no—
117C32×#67—41no—
118C32×#67—41no—
119C2×C32×Dic3—41no—
120C2×C32×Dic3—41no—
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128C3×#627—41no—
129C3×#626—41no—
130C3×#624—41no—
131C3×D3×Dic3—41no—
132C3×#538—91no—
133#5593—31no—
134#5494—31no—
135C24×C32—21no—
136C24×C32—21no—
137C24×C32—21no—
138C24×C32—41no—
139C24×C32C2×D311yescharacteristic
140C24×C32C2×D311yescharacteristic
141C24×C32C22×C311yescharacteristic
142C2×C32×D4—31no—
143C2×C32×D4—31no—
144C2×C32×D4—31no—
145C22×C32×C4—31no—
146C22×C32×C4—31no—
147C2×#638C22×C311yescharacteristic
148C2×#638C22×C311yescharacteristic
149C2×#638C22×C311yescharacteristic
150C2×C3×#67—21no—
151C2×C3×#67—21no—
152C2×C3×#67—21no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C2×C3×#67—31no—
159C2×C3×#67—31no—
160C2×C3×#67—61no—
161C2×C3×#67—61no—
162C2×C3×#67—61no—
163C2×C3×#67C2×D311yescharacteristic
164C2×C3×#67C2×D311yescharacteristic
165C2×C3×#67C2×D311yescharacteristic
166C2×C3×#67C22×C311yescharacteristic
167C2×C3×#67C22×C311yescharacteristic
168C2×C3×#67C22×C311yescharacteristic
169C22×C3×Dic3—21no—
170C22×C3×Dic3—21no—
171C22×C3×Dic3—31no—
172C22×C3×Dic3C2×D311yescharacteristic
173C22×C3×Dic3C2×D311yescharacteristic
174C22×C3×Dic3C22×C311yescharacteristic
175C22×C3×Dic3C22×C311yescharacteristic
176C2×C3×D12—31no—
177C2×C3×C4×D3—31no—
178C2×C3×C4×D3—31no—
179C2×C3×C4×D3—31no—
180C2×C3×Dic6—31no—
181C2×C3×Dic6—31no—
182C2×#627C22×C311yescharacteristic, complemented
183C2×#626C22×C311yescharacteristic, complemented
184C2×#624C22×C311yescharacteristic, complemented
185C2×D3×Dic3C22×C311yescharacteristic, complemented
186C32×C22⋊C4—31no—
187C32×C22⋊C4—31no—
188C32×C22⋊C4—31no—
189C32×C22⋊C4—31no—
190C32×C22⋊C4—31no—
191C32×C22⋊C4—31no—
192C32×C22⋊C4—31no—
193#3757C22×C311yescharacteristic
194#3757C22×C311yescharacteristic
195#3757C22×C311yescharacteristic
196C3×#217—21no—
197C3×#217—21no—
198C3×#217—21no—
199C3×#217—21no—
200C3×#217—21no—
201C3×#217—21no—
202C3×#217—21no—
203C3×#217—31no—
204C3×#217—31no—
205C3×#217—31no—
206C3×#217—31no—
207C3×#217—31no—
208C3×#217—31no—
209C3×#217—31no—
210C3×#217—31no—
211C3×#217—61no—
212C3×#217—61no—
213C3×#217—61no—
214C3×#217C2×D311yescharacteristic
215C3×#217C2×D311yescharacteristic
216C3×#217C2×D311yescharacteristic
217C3×#217C2×D311yescharacteristic
218C3×#217C2×D311yescharacteristic
219C3×#217C2×D311yescharacteristic
220C3×#217C2×D311yescharacteristic
221C3×#217C22×C311yescharacteristic
222C3×#217C22×C311yescharacteristic
223C3×#217C22×C311yescharacteristic
224C3×#217C22×C311yescharacteristic
225C3×#217C22×C311yescharacteristic
226C3×#217C22×C311yescharacteristic
227C3×#217C22×C311yescharacteristic
228C3×(C2×D3)⋊C4—31no—
229C3×(C2×D3)⋊C4—31no—
230C3×(C2×D3)⋊C4—31no—
231C3×(C2×D3)⋊C4—31no—
232C3×(C2×D3)⋊C4—31no—
233C3×(C2×D3)⋊C4—31no—
234C3×C4⋊Dic3—31no—
235C3×C4⋊Dic3—31no—
236C3×C4⋊Dic3—31no—
237C3×C4⋊Dic3—31no—
238C3×Dic3⋊C4—31no—
239C3×Dic3⋊C4—31no—
240C3×Dic3⋊C4—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4—31no—
244C3×Dic3⋊C4—31no—
245C3×Dic3⋊C4—31no—
246C3×C4×Dic3—31no—
247C3×C4×Dic3—31no—
248C3×C4×Dic3—31no—
249C3×C4×Dic3—31no—
250#3724C22×C311yescharacteristic, complemented
251#3724C22×C311yescharacteristic, complemented
252Dic3⋊Dic3C22×C311yescharacteristic, complemented
253Dic3⋊Dic3C22×C311yescharacteristic, complemented
254Dic3⋊Dic3C22×C311yescharacteristic, complemented
255Dic3⋊Dic3C22×C311yescharacteristic, complemented
256#3722C22×C311yescharacteristic, complemented
257#3722C22×C311yescharacteristic, complemented
258(C2×D3)⋊Dic3C22×C311yescharacteristic, complemented
259(C2×D3)⋊Dic3C22×C311yescharacteristic, complemented
260Dic32C22×C311yescharacteristic, complemented
261Dic32C22×C311yescharacteristic, complemented
262C22×C33—21no—
263C22×C33—21no—
264C22×C33—21no—
265C22×C33—21no—
266C22×C33—21no—
267C22×C33—21no—
268C22×C33—21no—
269C22×C33—21no—
270C22×C33—44no—
271C22×C33#4112yes—
272C22×C33C2411yescharacteristic
273C2×C3×C3⋊D3—21no—
274C2×C3×C3⋊D3—21no—
275C2×C3×C3⋊D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3—21no—
278C2×C32×D3—21no—
279C3×C3⋊Dic3—21no—
280C3×C3⋊Dic3—21no—
281C3×C3⋊Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C32×Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#126—91no—
290C3×#126—91no—
291C3×#124—91no—
292C3×#124—91no—
293C3×#123—91no—
294C3×#123—91no—
295C3×C22⋊Q8—91no—
296C3×#121—91no—
297C3×#121—91no—
298C3×#121—91no—
299C3×#120—31no—
300C3×#120—31no—
301C3×#120—61no—
302C3×#120—91no—
303C3×C4×D4—91no—
304C3×C4×D4—91no—
305C2×C3×C22⋊C4—31no—
306C2×C3×C22⋊C4—31no—
307C2×C3×C22⋊C4—61no—
308#953—31no—
309#953—31no—
310#953—61no—
311#953C3×D311yescharacteristic, complemented
312C2×#217C3×D311yescharacteristic, complemented
313#939—31no—
314#939—31no—
315#938—31no—
316#936—31no—
317#935—31no—
318D4×Dic3—31no—
319#930—31no—
320C4×#67—31no—
321C4×#67—31no—
322#924—31no—
323#885—31no—
324#885—31no—
325#885—31no—
326#884—31no—
327#884—31no—
328#883—31no—
329#883—31no—
330#883—31no—
331#67⋊C4—31no—
332#879—31no—
333#879—31no—
334#879—31no—
335#879—31no—
336#878—31no—
337C23×C32—22no—
338C23×C32—24no—
339C23×C32—22no—
340C23×C32—22no—
341C23×C32—21no—
342C23×C32—21no—
343C23×C32—21no—
344C23×C32—21no—
345C23×C32—21no—
346C23×C32—21no—
347C23×C32—21no—
348C23×C32—21no—
349C23×C32—21no—
350C23×C32—31no—
351C23×C32—41no—
352C23×C32—41no—
353C23×C32—41no—
354C23×C32—42no—
355C23×C32—42no—
356C23×C32—44no—
357C23×C32—41no—
358C23×C32—41no—
359C23×C32—41no—
360C23×C32—41no—
361C23×C32—41no—
362C23×C32—41no—
363C23×C32—42no—
364C23×C32—42no—
365C23×C32—42no—
366C23×C32—42no—
367C23×C32—42no—
368C23×C32—42no—
369C23×C32—44no—
370C23×C32—44no—
371C23×C32C22×D311yescharacteristic
372C23×C32C22×D311yescharacteristic
373C23×C32C22×D311yescharacteristic
374C23×C32C22×D311yescharacteristic
375C23×C32C22×D311yescharacteristic
376C23×C32C22×D311yescharacteristic
377C23×C32C23×C311yescharacteristic
378C23×C32C23×C311yescharacteristic
379C23×C32C23×C311yescharacteristic
380C22×C3⋊D3C23×C311yescharacteristic
381C22×C3×D3—21no—
382C22×C3×D3—31no—
383C22×C3×D3—31no—
384C22×C3×D3—61no—
385C22×C3×D3C22×D311yescharacteristic
386C22×C3×D3C23×C311yescharacteristic
387C32×D4—62no—
388C32×D4—121no—
389C32×D4—121no—
390C2×C32×C4—31no—
391C2×C32×C4—31no—
392C2×C32×C4—31no—
393C2×C32×C4—31no—
394C2×C32×C4—31no—
395C2×C32×C4—31no—
396C2×C32×C4—31no—
397C2×C32×C4—121no—
398C2×C32×C4—121no—
399#638—22no—
400#638—41no—
401#638—41no—
402C2×C3⋊Dic3C23×C311yescharacteristic
403C2×C3⋊Dic3C23×C311yescharacteristic
404C2×C3⋊Dic3C23×C311yescharacteristic
405C3×#67—22no—
406C3×#67—22no—
407C3×#67—42no—
408C3×#67—41no—
409C3×#67—41no—
410C3×#67—41no—
411C3×#67—41no—
412C3×#67—42no—
413C3×#67—42no—
414C3×#67—62no—
415C3×#67—62no—
416C3×#67—122no—
417C3×#67—121no—
418C3×#67—121no—
419C3×#67—121no—
420C3×#67—121no—
421C3×#67—121no—
422C3×#67—122no—
423C3×#67—122no—
424C2×C3×Dic3—21no—
425C2×C3×Dic3—21no—
426C2×C3×Dic3—21no—
427C2×C3×Dic3—21no—
428C2×C3×Dic3—21no—
429C2×C3×Dic3—21no—
430C2×C3×Dic3—21no—
431C2×C3×Dic3—31no—
432C2×C3×Dic3—31no—
433C2×C3×Dic3—31no—
434C2×C3×Dic3—31no—
435C2×C3×Dic3—31no—
436C2×C3×Dic3—31no—
437C2×C3×Dic3—41no—
438C2×C3×Dic3—41no—
439C2×C3×Dic3—41no—
440C2×C3×Dic3—41no—
441C2×C3×Dic3—42no—
442C2×C3×Dic3—42no—
443C2×C3×Dic3—61no—
444C2×C3×Dic3—61no—
445C2×C3×Dic3—61no—
446C2×C3×Dic3—121no—
447C2×C3×Dic3C22×D311yescharacteristic
448C2×C3×Dic3C22×D311yescharacteristic
449C2×C3×Dic3C22×D311yescharacteristic
450C2×C3×Dic3C22×D311yescharacteristic
451C2×C3×Dic3C22×D311yescharacteristic
452C2×C3×Dic3C22×D311yescharacteristic
453C2×C3×Dic3C22×D311yescharacteristic
454C2×C3×Dic3C23×C311yescharacteristic
455C2×C3×Dic3C23×C311yescharacteristic
456C2×C3×Dic3C23×C311yescharacteristic
457C2×C3×Dic3C23×C311yescharacteristic
458C2×C3×Dic3C23×C311yescharacteristic
459C2×C3×Dic3C23×C311yescharacteristic
460C2×C3×Dic3C23×C311yescharacteristic
461C3×D12—121no—
462C3×C4×D3—121no—
463C3×C4×D3—121no—
464C3×C4×D3—121no—
465C3×Dic6—121no—
466C3×Dic6—121no—
467#627—41no—
468#626—41no—
469#624—41no—
470D3×Dic3—41no—
471#538—91noSylow
472C2×C33—22no—
473C2×C33—41no—
474C2×C33—41no—
475C2×C33C2×#4111yescharacteristic
476C2×C33H(5,𝔽2)11yescharacteristic
477C2×C33H(5,𝔽2)11yescharacteristic
478C3×C3⋊D3—41no—
479C32×D3—41no—
480C24×C3—21no—
481C24×C3—21no—
482C24×C3—21no—
483C24×C3—41no—
484C24×C3D3211yescharacteristic
485C24×C3C2×C3×D311yescharacteristic
486C24×C3C2×C3×D311yescharacteristic
487C2×C3×Q8—91no—
488C2×C3×D4—31no—
489C2×C3×D4—31no—
490C2×C3×D4—31no—
491C2×C3×D4—31no—
492C2×C3×D4—31no—
493C2×C3×D4—31no—
494C2×C3×D4—61no—
495C2×C3×D4—61no—
496C2×C3×D4—61no—
497C2×C3×D4—91no—
498C2×C3×D4—91no—
499C2×C3×D4—91no—
500C2×C3×D4—91no—
501C22×C3×C4—31no—
502C22×C3×C4—31no—
503C22×C3×C4—31no—
504C22×C3×C4—31no—
505C22×C3×C4—61no—
506C22×C3×C4—61no—
507C22×C3×C4—91no—
508C22×C3×C4—91no—
509C2×#67—31no—
510C2×#67—31no—
511C2×#67—31no—
512C2×#67—31no—
513C2×#67—31no—
514C2×#67—31no—
515C2×#67—31no—
516C2×#67—61no—
517C2×#67—61no—
518C2×#67—61no—
519C2×#67C2×C3×D311yescharacteristic
520C2×#67C2×C3×D311yescharacteristic
521C2×#67C2×C3×D311yescharacteristic
522C22×Dic3—31no—
523C22×Dic3C2×C3×D311yescharacteristic
524C22×Dic3C2×C3×D311yescharacteristic
525C2×D12—31no—
526C2×C4×D3—31no—
527C2×C4×D3—31no—
528C2×C4×D3—31no—
529C2×Dic6—31no—
530C2×Dic6—31no—
531C3×C4⋊C4—91no—
532C3×C4⋊C4—91no—
533C3×C4⋊C4—91no—
534C3×C4⋊C4—91no—
535C3×C4⋊C4—91no—
536C3×C4⋊C4—91no—
537C3×C22⋊C4—31no—
538C3×C22⋊C4—31no—
539C3×C22⋊C4—31no—
540C3×C22⋊C4—31no—
541C3×C22⋊C4—31no—
542C3×C22⋊C4—31no—
543C3×C22⋊C4—31no—
544C3×C22⋊C4—31no—
545C3×C22⋊C4—31no—
546C3×C22⋊C4—31no—
547C3×C22⋊C4—31no—
548C3×C22⋊C4—31no—
549C3×C22⋊C4—31no—
550C3×C22⋊C4—31no—
551C3×C22⋊C4—61no—
552C3×C22⋊C4—61no—
553C3×C22⋊C4—61no—
554C3×C22⋊C4—61no—
555C3×C22⋊C4—61no—
556C3×C22⋊C4—61no—
557C3×C22⋊C4—61no—
558C3×C22⋊C4—91no—
559C3×C22⋊C4—91no—
560C3×C22⋊C4—91no—
561C3×C22⋊C4—91no—
562C3×C22⋊C4—91no—
563C3×C22⋊C4—91no—
564C3×C22⋊C4—91no—
565C3×C42—91no—
566C3×C42—91no—
567#217—31no—
568#217—31no—
569#217—31no—
570#217—31no—
571#217—31no—
572#217—31no—
573#217—31no—
574#217—31no—
575#217—61no—
576#217—61no—
577#217—61no—
578#217C2×C3×D311yescharacteristic
579#217C2×C3×D311yescharacteristic
580#217C2×C3×D311yescharacteristic
581#217C2×C3×D311yescharacteristic
582#217C2×C3×D311yescharacteristic
583#217C2×C3×D311yescharacteristic
584#217C2×C3×D311yescharacteristic
585(C2×D3)⋊C4—31no—
586(C2×D3)⋊C4—31no—
587(C2×D3)⋊C4—31no—
588(C2×D3)⋊C4—31no—
589(C2×D3)⋊C4—31no—
590(C2×D3)⋊C4—31no—
591C4⋊Dic3—31no—
592C4⋊Dic3—31no—
593C4⋊Dic3—31no—
594C4⋊Dic3—31no—
595Dic3⋊C4—31no—
596Dic3⋊C4—31no—
597Dic3⋊C4—31no—
598Dic3⋊C4—31no—
599Dic3⋊C4—31no—
600Dic3⋊C4—31no—
601Dic3⋊C4—31no—
602Dic3⋊C4—31no—
603C4×Dic3—31no—
604C4×Dic3—31no—
605C4×Dic3—31no—
606C4×Dic3—31no—
607C22×C32—21no—
608C22×C32—21no—
609C22×C32—21no—
610C22×C32—21no—
611C22×C32—21no—
612C22×C32—21no—
613C22×C32—21no—
614C22×C32—21no—
615C22×C32—22no—
616C22×C32—22no—
617C22×C32—21no—
618C22×C32—21no—
619C22×C32—21no—
620C22×C32—21no—
621C22×C32—22no—
622C22×C32—22no—
623C22×C32—22no—
624C22×C32—22no—
625C22×C32—22no—
626C22×C32—22no—
627C22×C32—21no—
628C22×C32—21no—
629C22×C32—21no—
630C22×C32—21no—
631C22×C32—21no—
632C22×C32—21no—
633C22×C32—21no—
634C22×C32—21no—
635C22×C32—21no—
636C22×C32—21no—
637C22×C32—21no—
638C22×C32—21no—
639C22×C32—21no—
640C22×C32—21no—
641C22×C32—21no—
642C22×C32—22no—
643C22×C32—22no—
644C22×C32—22no—
645C22×C32—42no—
646C22×C32—41no—
647C22×C32—41no—
648C22×C32—41no—
649C22×C32—41no—
650C22×C32—41no—
651C22×C32—41no—
652C22×C32—41no—
653C22×C32—41no—
654C22×C32—41no—
655C22×C32—41no—
656C22×C32—41no—
657C22×C32—41no—
658C22×C32—41no—
659C22×C32—41no—
660C22×C32—41no—
661C22×C32—41no—
662C22×C32—41no—
663C22×C32—42no—
664C22×C32—42no—
665C22×C32—42no—
666C22×C32—42no—
667C22×C32—42no—
668C22×C32—42no—
669C22×C32—42no—
670C22×C32—42no—
671C22×C32—44no—
672C22×C32—48no—
673C22×C32—44no—
674C22×C32—44no—
675C22×C32—48no—
676C22×C32—48no—
677C22×C32—416no—
678C22×C32—61no—
679C22×C32—61no—
680C22×C32—61no—
681C22×C32#23512yes—
682C22×C32#23712yes—
683C22×C32C3×#4112yes—
684C22×C32C23×D311yescharacteristic
685C22×C32C23×D311yescharacteristic
686C22×C32C24×C311yescharacteristic
687C2×C3⋊D3—21no—
688C2×C3⋊D3—21no—
689C2×C3⋊D3—21no—
690C2×C3×D3—21no—
691C2×C3×D3—21no—
692C2×C3×D3—21no—
693C2×C3×D3—21no—
694C2×C3×D3—21no—
695C2×C3×D3—21no—
696C2×C3×D3—41no—
697C2×C3×D3—41no—
698C2×C3×D3—41no—
699C2×C3×D3—61no—
700C2×C3×D3—61no—
701C2×C3×D3—61no—
702C2×C3×D3—61no—
703C2×C3×D3—61no—
704C2×C3×D3—61no—
705C2×C3×D3—121no—
706C2×C3×D3—121no—
707C2×C3×D3—121no—
708C32×C4—61no—
709C32×C4—61no—
710C32×C4—61no—
711C32×C4—61no—
712C32×C4—61no—
713C32×C4—61no—
714C32×C4—61no—
715C3⋊Dic3—21no—
716C3⋊Dic3—21no—
717C3⋊Dic3—21no—
718C3×Dic3—21no—
719C3×Dic3—21no—
720C3×Dic3—21no—
721C3×Dic3—21no—
722C3×Dic3—21no—
723C3×Dic3—21no—
724C3×Dic3—21no—
725C3×Dic3—21no—
726C3×Dic3—21no—
727C3×Dic3—21no—
728C3×Dic3—21no—
729C3×Dic3—21no—
730C3×Dic3—21no—
731C3×Dic3—21no—
732C3×Dic3—41no—
733C3×Dic3—41no—
734C3×Dic3—41no—
735C3×Dic3—41no—
736C3×Dic3—41no—
737C3×Dic3—41no—
738C3×Dic3—41no—
739C3×Dic3—61no—
740C3×Dic3—61no—
741C3×Dic3—61no—
742C3×Dic3—61no—
743C3×Dic3—61no—
744C3×Dic3—61no—
745C3×Dic3—121no—
746C3×Dic3—121no—
747C3×Dic3—121no—
748#126—91no—
749#126—91no—
750#124—91no—
751#124—91no—
752#123—91no—
753#123—91no—
754C22⋊Q8—91no—
755#121—91no—
756#121—91no—
757#121—91no—
758#120—31no—
759#120—91no—
760C4×D4—91no—
761C4×D4—91no—
762C2×C22⋊C4—31no—
763C33#53811yescharacteristic, complemented, Sylow
764C23×C3—24no—
765C23×C3—22no—
766C23×C3—22no—
767C23×C3—22no—
768C23×C3—21no—
769C23×C3—21no—
770C23×C3—21no—
771C23×C3—21no—
772C23×C3—21no—
773C23×C3—21no—
774C23×C3—21no—
775C23×C3—21no—
776C23×C3—21no—
777C23×C3—31no—
778C23×C3—31no—
779C23×C3—42no—
780C23×C3—42no—
781C23×C3—44no—
782C23×C3—41no—
783C23×C3—41no—
784C23×C3—41no—
785C23×C3—41no—
786C23×C3—41no—
787C23×C3—41no—
788C23×C3—42no—
789C23×C3—42no—
790C23×C3—42no—
791C23×C3—42no—
792C23×C3—42no—
793C23×C3—42no—
794C23×C3—44no—
795C23×C3—44no—
796C23×C3—41no—
797C23×C3—41no—
798C23×C3—41no—
799C23×C3—61no—
800C23×C3—91no—
801C23×C3C2×D3211yescharacteristic
802C23×C3C2×D3211yescharacteristic
803C23×C3C2×D3211yescharacteristic
804C23×C3C22×C3×D311yescharacteristic
805C23×C3C22×C3×D311yescharacteristic
806C23×C3C22×C3×D311yescharacteristic
807C23×C3C22×C3×D311yescharacteristic
808C23×C3C22×C3×D311yescharacteristic
809C23×C3C22×C3×D311yescharacteristic
810C22×D3—31no—
811C22×D3—31no—
812C22×D3—61no—
813C22×D3C22×C3×D311yescharacteristic
814C3×Q8—361no—
815C3×D4—62no—
816C3×D4—62no—
817C3×D4—122no—
818C3×D4—121no—
819C3×D4—121no—
820C3×D4—121no—
821C3×D4—121no—
822C3×D4—122no—
823C3×D4—122no—
824C3×D4—182no—
825C3×D4—361no—
826C3×D4—361no—
827C3×D4—361no—
828C2×C3×C4—31no—
829C2×C3×C4—31no—
830C2×C3×C4—31no—
831C2×C3×C4—31no—
832C2×C3×C4—31no—
833C2×C3×C4—31no—
834C2×C3×C4—31no—
835C2×C3×C4—31no—
836C2×C3×C4—31no—
837C2×C3×C4—31no—
838C2×C3×C4—31no—
839C2×C3×C4—31no—
840C2×C3×C4—31no—
841C2×C3×C4—31no—
842C2×C3×C4—61no—
843C2×C3×C4—61no—
844C2×C3×C4—61no—
845C2×C3×C4—61no—
846C2×C3×C4—61no—
847C2×C3×C4—61no—
848C2×C3×C4—61no—
849C2×C3×C4—91no—
850C2×C3×C4—91no—
851C2×C3×C4—91no—
852C2×C3×C4—121no—
853C2×C3×C4—121no—
854C2×C3×C4—121no—
855C2×C3×C4—121no—
856C2×C3×C4—122no—
857C2×C3×C4—122no—
858C2×C3×C4—361no—
859C2×C3×C4—361no—
860#67—22no—
861#67—41no—
862#67—41no—
863#67—62no—
864#67—62no—
865#67—122no—
866#67—121no—
867#67—121no—
868#67—121no—
869#67—121no—
870#67—121no—
871#67—122no—
872#67—122no—
873C2×Dic3—31no—
874C2×Dic3—31no—
875C2×Dic3—31no—
876C2×Dic3—31no—
877C2×Dic3—31no—
878C2×Dic3—31no—
879C2×Dic3—41no—
880C2×Dic3—41no—
881C2×Dic3—61no—
882C2×Dic3—61no—
883C2×Dic3—61no—
884C2×Dic3—121no—
885C2×Dic3C22×C3×D311yescharacteristic
886C2×Dic3C22×C3×D311yescharacteristic
887C2×Dic3C22×C3×D311yescharacteristic
888C2×Dic3C22×C3×D311yescharacteristic
889C2×Dic3C22×C3×D311yescharacteristic
890C2×Dic3C22×C3×D311yescharacteristic
891C2×Dic3C22×C3×D311yescharacteristic
892D12—121no—
893C4×D3—121no—
894C4×D3—121no—
895C4×D3—121no—
896Dic6—121no—
897Dic6—121no—
898C2×C32—22no—
899C2×C32—24no—
900C2×C32—22no—
901C2×C32—22no—
902C2×C32—21no—
903C2×C32—21no—
904C2×C32—21no—
905C2×C32—21no—
906C2×C32—21no—
907C2×C32—21no—
908C2×C32—21no—
909C2×C32—21no—
910C2×C32—21no—
911C2×C32—41no—
912C2×C32—41no—
913C2×C32—41no—
914C2×C32—42no—
915C2×C32—42no—
916C2×C32—44no—
917C2×C32—42no—
918C2×C32—42no—
919C2×C32—42no—
920C2×C32—42no—
921C2×C32—42no—
922C2×C32—42no—
923C2×C32—44no—
924C2×C32—44no—
925C2×C32—41no—
926C2×C32—41no—
927C2×C32—41no—
928C2×C32—41no—
929C2×C32—41no—
930C2×C32—41no—
931C2×C32—121no—
932C2×C32C2×#23511yescharacteristic
933C2×C32C2×#23711yescharacteristic
934C2×C32#100411yescharacteristic
935C2×C32#100411yescharacteristic
936C2×C32#100411yescharacteristic
937C2×C32#100411yescharacteristic
938C2×C32C2×C3×#4111yescharacteristic
939C2×C32C3×H(5,𝔽2)11yescharacteristic
940C2×C32C3×H(5,𝔽2)11yescharacteristic
941C3⋊D3—41no—
942C3×D3—41no—
943C3×D3—41no—
944C3×D3—81no—
945C3×D3—121no—
946C3×D3—121no—
947C3×D3—241no—
948C24C3×D3211yescharacteristic
949C2×Q8—91no—
950C2×D4—31no—
951C2×D4—31no—
952C2×D4—31no—
953C2×D4—91no—
954C2×D4—91no—
955C2×D4—91no—
956C2×D4—91no—
957C22×C4—31no—
958C22×C4—31no—
959C22×C4—91no—
960C22×C4—91no—
961C4⋊C4—91no—
962C4⋊C4—91no—
963C4⋊C4—91no—
964C4⋊C4—91no—
965C4⋊C4—91no—
966C4⋊C4—91no—
967C22⋊C4—31no—
968C22⋊C4—31no—
969C22⋊C4—31no—
970C22⋊C4—31no—
971C22⋊C4—31no—
972C22⋊C4—31no—
973C22⋊C4—31no—
974C22⋊C4—91no—
975C22⋊C4—91no—
976C22⋊C4—91no—
977C22⋊C4—91no—
978C22⋊C4—91no—
979C22⋊C4—91no—
980C22⋊C4—91no—
981C42—91no—
982C42—91no—
983C22×C3—22no—
984C22×C3—22no—
985C22×C3—21no—
986C22×C3—21no—
987C22×C3—21no—
988C22×C3—21no—
989C22×C3—21no—
990C22×C3—21no—
991C22×C3—22no—
992C22×C3—22no—
993C22×C3—22no—
994C22×C3—22no—
995C22×C3—22no—
996C22×C3—22no—
997C22×C3—21no—
998C22×C3—21no—
999C22×C3—21no—
1000C22×C3—21no—
1001C22×C3—21no—
1002C22×C3—21no—
1003C22×C3—21no—
1004C22×C3—21no—
1005C22×C3—21no—
1006C22×C3—21no—
1007C22×C3—21no—
1008C22×C3—21no—
1009C22×C3—21no—
1010C22×C3—21no—
1011C22×C3—21no—
1012C22×C3—21no—
1013C22×C3—21no—
1014C22×C3—21no—
1015C22×C3—21no—
1016C22×C3—21no—
1017C22×C3—21no—
1018C22×C3—22no—
1019C22×C3—22no—
1020C22×C3—22no—
1021C22×C3—41no—
1022C22×C3—41no—
1023C22×C3—41no—
1024C22×C3—41no—
1025C22×C3—41no—
1026C22×C3—41no—
1027C22×C3—41no—
1028C22×C3—41no—
1029C22×C3—41no—
1030C22×C3—41no—
1031C22×C3—41no—
1032C22×C3—41no—
1033C22×C3—41no—
1034C22×C3—41no—
1035C22×C3—41no—
1036C22×C3—41no—
1037C22×C3—42no—
1038C22×C3—42no—
1039C22×C3—42no—
1040C22×C3—42no—
1041C22×C3—42no—
1042C22×C3—42no—
1043C22×C3—42no—
1044C22×C3—42no—
1045C22×C3—48no—
1046C22×C3—44no—
1047C22×C3—44no—
1048C22×C3—44no—
1049C22×C3—48no—
1050C22×C3—48no—
1051C22×C3—416no—
1052C22×C3—41no—
1053C22×C3—42no—
1054C22×C3—61no—
1055C22×C3—61no—
1056C22×C3—61no—
1057C22×C3—61no—
1058C22×C3—61no—
1059C22×C3—61no—
1060C22×C3—121no—
1061C22×C3—121no—
1062C22×C3—121no—
1063C22×C3—181no—
1064C22×C3—181no—
1065C22×C3—181no—
1066C22×C3#380412yes—
1067C22×C3C3×#23512yes—
1068C22×C3C3×#23712yes—
1069C22×C3C22×D3211yescharacteristic
1070C22×C3C23×C3×D311yescharacteristic
1071C22×C3C23×C3×D311yescharacteristic
1072C2×D3—21no—
1073C2×D3—21no—
1074C2×D3—21no—
1075C2×D3—61no—
1076C2×D3—61no—
1077C2×D3—61no—
1078C2×D3—61no—
1079C2×D3—61no—
1080C2×D3—61no—
1081C2×D3—121no—
1082C2×D3—121no—
1083C2×D3—121no—
1084C3×C4—61no—
1085C3×C4—61no—
1086C3×C4—61no—
1087C3×C4—61no—
1088C3×C4—61no—
1089C3×C4—61no—
1090C3×C4—61no—
1091C3×C4—61no—
1092C3×C4—61no—
1093C3×C4—61no—
1094C3×C4—61no—
1095C3×C4—61no—
1096C3×C4—61no—
1097C3×C4—61no—
1098C3×C4—121no—
1099C3×C4—121no—
1100C3×C4—121no—
1101C3×C4—121no—
1102C3×C4—121no—
1103C3×C4—121no—
1104C3×C4—121no—
1105C3×C4—181no—
1106C3×C4—181no—
1107C3×C4—181no—
1108Dic3—21no—
1109Dic3—21no—
1110Dic3—21no—
1111Dic3—21no—
1112Dic3—21no—
1113Dic3—21no—
1114Dic3—21no—
1115Dic3—61no—
1116Dic3—61no—
1117Dic3—61no—
1118Dic3—61no—
1119Dic3—61no—
1120Dic3—61no—
1121Dic3—121no—
1122Dic3—121no—
1123Dic3—121no—
1124C32—21no—
1125C32—21no—
1126C32—21no—
1127C32—41no—
1128C32#549411yescharacteristic, complemented
1129C32#559311yescharacteristic, complemented
1130C32C3×#53811yescharacteristic, complemented
1131C23—22no—
1132C23—31no—
1133C23—41no—
1134C23—41no—
1135C23—91no—
1136C23C2×C3×D3211yescharacteristic
1137C23C2×C3×D3211yescharacteristic
1138C23C2×C3×D3211yescharacteristic
1139Q8—361no—
1140D4—62no—
1141D4—121no—
1142D4—121no—
1143D4—182no—
1144D4—361no—
1145D4—361no—
1146D4—361no—
1147C2×C4—31no—
1148C2×C4—31no—
1149C2×C4—31no—
1150C2×C4—31no—
1151C2×C4—31no—
1152C2×C4—31no—
1153C2×C4—31no—
1154C2×C4—91no—
1155C2×C4—91no—
1156C2×C4—91no—
1157C2×C4—121no—
1158C2×C4—121no—
1159C2×C4—361no—
1160C2×C4—361no—
1161C2×C3—24no—
1162C2×C3—22no—
1163C2×C3—22no—
1164C2×C3—22no—
1165C2×C3—21no—
1166C2×C3—21no—
1167C2×C3—21no—
1168C2×C3—21no—
1169C2×C3—21no—
1170C2×C3—21no—
1171C2×C3—21no—
1172C2×C3—21no—
1173C2×C3—21no—
1174C2×C3—42no—
1175C2×C3—42no—
1176C2×C3—44no—
1177C2×C3—42no—
1178C2×C3—42no—
1179C2×C3—42no—
1180C2×C3—42no—
1181C2×C3—42no—
1182C2×C3—42no—
1183C2×C3—44no—
1184C2×C3—44no—
1185C2×C3—41no—
1186C2×C3—41no—
1187C2×C3—41no—
1188C2×C3—41no—
1189C2×C3—41no—
1190C2×C3—41no—
1191C2×C3—41no—
1192C2×C3—41no—
1193C2×C3—41no—
1194C2×C3—121no—
1195C2×C3—121no—
1196C2×C3—241no—
1197C2×C3—361no—
1198C2×C3C2×#380411yescharacteristic
1199C2×C3#6433011yescharacteristic
1200C2×C3#6433011yescharacteristic
1201C2×C3C2×C3×#23511yescharacteristic
1202C2×C3C2×C3×#23711yescharacteristic
1203C2×C3C3×#100411yescharacteristic
1204C2×C3C3×#100411yescharacteristic
1205C2×C3C3×#100411yescharacteristic
1206C2×C3C3×#100411yescharacteristic
1207D3—41no—
1208D3—121no—
1209D3—121no—
1210D3—241no—
1211C22—21no—
1212C22—21no—
1213C22—21no—
1214C22—21no—
1215C22—21no—
1216C22—21no—
1217C22—21no—
1218C22—21no—
1219C22—44no—
1220C22—61no—
1221C22—61no—
1222C22—61no—
1223C22—181no—
1224C22—181no—
1225C22—181no—
1226C22C3×#380412yes—
1227C22C22×C3×D3211yescharacteristic
1228C4—61no—
1229C4—61no—
1230C4—61no—
1231C4—61no—
1232C4—61no—
1233C4—61no—
1234C4—61no—
1235C4—181no—
1236C4—181no—
1237C4—181no—
1238C3—21no—
1239C3—21no—
1240C3—21no—
1241C3—41no—
1242C3#1059550711yescharacteristic, direct product factor
1243C3C3×#549411yescharacteristic, complemented
1244C3C3×#559311yescharacteristic, complemented
1245C2—22no—
1246C2—41no—
1247C2—41no—
1248C2—121no—
1249C2—361no—
1250C2C2×C3×#380411yescharacteristic
1251C2C3×#6433011yescharacteristic
1252C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC24×C33C22
socleC22×C33C24
hypercenterC24×C3D32
hypocenterC32C3×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C24×C3

Complements

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

NH ≅ G/Ntype
1. C3×#64162C2semidirect
2. C32×#953C2semidirect
3. C2×C32×#217C2semidirect
4. C3×#63978C2semidirect
5. C3×#63975C2semidirect
6. C3×Dic3×#67C2semidirect
7. C3×#63971C2semidirect
8. C3×#63969C2semidirect
9. C3×#63964C2semidirect
10. C3×#63959C2semidirect
11. C3×#63958C2semidirect
12. C3×#63956C2semidirect
13. C3×#63956C2semidirect
14. C3×#63953C2semidirect
15. C3×#63952C2semidirect
18. #10595507C3direct (N × H)
28. C2×C3×#627C22semidirect
29. C2×C3×#626C22semidirect
30. C2×C3×#624C22semidirect
31. C2×C3×D3×Dic3C22semidirect
42. C3×#3724C22semidirect
43. C3×#3724C22semidirect
44. C3×Dic3⋊Dic3C22semidirect
45. C3×Dic3⋊Dic3C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
48. C3×#3722C22semidirect
49. C3×#3722C22semidirect
50. C3×(C2×D3)⋊Dic3C22semidirect
51. C3×(C2×D3)⋊Dic3C22semidirect
52. C3×Dic32C22semidirect
53. C3×Dic32C22semidirect
56. #64162C2×C3semidirect
61. C3×#953D3semidirect
62. C3×#953C2×C3semidirect
64. C2×C3×#217D3semidirect
65. C2×C3×#217C2×C3semidirect
90. #63978C2×C3semidirect
91. #63975C2×C3semidirect
92. Dic3×#67C2×C3semidirect
93. #63971C2×C3semidirect
94. #63969C2×C3semidirect
95. #63964C2×C3semidirect
96. #63959C2×C3semidirect
97. #63958C2×C3semidirect
98. #63956C2×C3semidirect
99. #63956C2×C3semidirect
100. #63953C2×C3semidirect
101. #63952C2×C3semidirect
182. C2×#627C22×C3semidirect
183. C2×#626C22×C3semidirect
184. C2×#624C22×C3semidirect
185. C2×D3×Dic3C22×C3semidirect
250. #3724C22×C3semidirect
251. #3724C22×C3semidirect
252. Dic3⋊Dic3C22×C3semidirect
253. Dic3⋊Dic3C22×C3semidirect
254. Dic3⋊Dic3C22×C3semidirect
255. Dic3⋊Dic3C22×C3semidirect
256. #3722C22×C3semidirect
257. #3722C22×C3semidirect
258. (C2×D3)⋊Dic3C22×C3semidirect
259. (C2×D3)⋊Dic3C22×C3semidirect
260. Dic32C22×C3semidirect
261. Dic32C22×C3semidirect
311. #953C3×D3semidirect
312. C2×#217C3×D3semidirect
763. C33#538semidirect
1128. C32#5494semidirect
1129. C32#5593semidirect
1130. C32C3×#538semidirect
1242. C3#10595507direct (N × H)
1243. C3C3×#5494semidirect
1244. C3C3×#5593semidirect

Maximal subgroups

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

subgroupindex
C3×#641622
C32×#9532
C2×C32×#2172
C3×#639782
C3×#639752
C3×Dic3×#672
C3×#639712
C3×#639692
C3×#639642
C3×#639592
C3×#639582
C3×#639562
C3×#639532
C3×#639522
C3×#55933
C3×#54943
#105955073