Finite Group Databasebeta

← C3×#10595204 #13174754

Subgroups — C3×#10595204 #13174754

Order 1728.

1288 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64148C211yesmaximal, characteristic, complemented
2C32×#939C211yesmaximal, characteristic, complemented
3C32×D4×Dic3C211yesmaximal, characteristic, complemented
4C3×#63978C211yesmaximal, characteristic, complemented
5C3×#67⋊Dic3C211yesmaximal, characteristic, complemented
6C3×#63971C211yesmaximal, characteristic, complemented
7C2×C3×#3724C211yesmaximal, characteristic, complemented
8C3×#63961C211yesmaximal, characteristic, complemented
9C3×#63956C211yesmaximal, characteristic, complemented
10C3×#63952C211yesmaximal, characteristic, complemented
11C3×#63952C211yesmaximal, characteristic, complemented
12C3×#63877C211yesmaximal, characteristic, complemented
13C3×#63868C211yesmaximal, characteristic, complemented
14C3×#63854C211yesmaximal, characteristic, complemented
15C3×#63847C211yesmaximal, characteristic, complemented
16C3×#5601—31nomaximal
17C3×#5540—31nomaximal
18#10595204C311yesmaximal, characteristic, direct product factor
19C2×C33×D4C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C22×C32×Dic3C2211yescharacteristic
26C22×C32×Dic3C2211yescharacteristic
27C22×C32×Dic3C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#624C2211yescharacteristic
30C2×C3×D3×Dic3C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32C3×#3752C2211yescharacteristic
33C3×#3750C2211yescharacteristic
34C32×#217C2211yescharacteristic
35C32×#217C2211yescharacteristic
36C32×#217C2211yescharacteristic
37C32×(C2×D3)⋊C4C2211yescharacteristic
38C32×C4⋊Dic3C2211yescharacteristic
39C32×Dic3⋊C4C2211yescharacteristic
40C32×C4×Dic3C2211yescharacteristic
41C3×#3724C2211yescharacteristic
42C3×#3724C2211yescharacteristic
43C3×#3724C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C32×#121—31no—
55C32×C4×D4—31no—
56#64148C2×C311yescharacteristic, complemented
57C3×#939—21no—
58C3×#939—31no—
59C3×#939—31no—
60C3×#939—31no—
61C3×#939—31no—
62C3×#939—61no—
63C3×#939D311yescharacteristic, complemented
64C3×#939C2×C311yescharacteristic, complemented
65C3×#935—31no—
66C3×D4×Dic3—21no—
67C3×D4×Dic3—31no—
68C3×D4×Dic3D311yescharacteristic, complemented
69C3×D4×Dic3C2×C311yescharacteristic, complemented
70C3×#930—31no—
71C3×#929—31no—
72C3×C4×#67—31no—
73C3×C4×#67—31no—
74C2×C3×Dic3⋊C4—31no—
75C2×C3×Dic3⋊C4—31no—
76C3×#898—31no—
77C3×#894—31no—
78C3×#889—31no—
79C3×#889—31no—
80C3×#884—31no—
81C3×#883—31no—
82C3×#67⋊C4—31no—
83C3×#67⋊C4—31no—
84C3×#67⋊C4—31no—
85C3×#879—31no—
86C3×#879—31no—
87C3×#877—31no—
88C3×#876—31no—
89C3×#872—31no—
90#63978C2×C311yescharacteristic, complemented
91#67⋊Dic3C2×C311yescharacteristic, complemented
92#63971C2×C311yescharacteristic, complemented
93C2×#3724C2×C311yescharacteristic, complemented
94#63961C2×C311yescharacteristic, complemented
95#63956C2×C311yescharacteristic, complemented
96#63952C2×C311yescharacteristic, complemented
97#63952C2×C311yescharacteristic, complemented
98#63877C2×C311yescharacteristic, complemented
99#63868C2×C311yescharacteristic, complemented
100#63854C2×C311yescharacteristic, complemented
101#63847C2×C311yescharacteristic, complemented
102C23×C33C2311yescharacteristic
103C23×C33C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C33×D4—22no—
107C2×C33×C4C2311yescharacteristic
108C3×#638—22no—
109C3×#638—22no—
110C2×C3×C3⋊Dic3—22no—
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C32×#67—22no—
115C32×#67—41no—
116C2×C32×Dic3—41no—
117C2×C32×Dic3—41no—
118C2×C32×Dic3—41no—
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C3×#626—41no—
127C3×#624—41no—
128C3×D3×Dic3—22no—
129C3×#553—91no—
130#5601—31no—
131#5540—31no—
132C2×C32×D4—21no—
133C2×C32×D4—21no—
134C2×C32×D4—21no—
135C2×C32×D4—31no—
136C2×C32×D4—31no—
137C2×C32×D4—41no—
138C2×C32×D4C2×D311yescharacteristic
139C2×C32×D4C2×D311yescharacteristic
140C2×C32×D4C22×C311yescharacteristic
141C22×C32×C4—31no—
142C22×C32×C4—31no—
143C22×C32×C4—31no—
144C2×#638C22×C311yescharacteristic
145C2×#638C22×C311yescharacteristic
146C22×C3⋊Dic3C22×C311yescharacteristic
147C2×C3×#67—21no—
148C2×C3×#67—21no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—31no—
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C2×C3×#67—61no—
155C2×C3×#67—61no—
156C2×C3×#67C2×D311yescharacteristic
157C2×C3×#67C2×D311yescharacteristic
158C2×C3×#67C22×C311yescharacteristic
159C2×C3×#67C22×C311yescharacteristic
160C22×C3×Dic3—21no—
161C22×C3×Dic3—21no—
162C22×C3×Dic3—21no—
163C22×C3×Dic3—31no—
164C22×C3×Dic3—31no—
165C22×C3×Dic3—31no—
166C22×C3×Dic3—61no—
167C22×C3×Dic3C2×D311yescharacteristic
168C22×C3×Dic3C2×D311yescharacteristic
169C22×C3×Dic3C2×D311yescharacteristic
170C22×C3×Dic3C22×C311yescharacteristic
171C22×C3×Dic3C22×C311yescharacteristic
172C22×C3×Dic3C22×C311yescharacteristic
173C2×C3×D12—31no—
174C2×C3×C4×D3—31no—
175C2×C3×C4×D3—31no—
176C2×C3×C4×D3—31no—
177C2×#626C22×C311yescharacteristic
178C2×#624C22×C311yescharacteristic
179C2×D3×Dic3C22×C311yescharacteristic
180C32×C4⋊C4—31no—
181C32×C4⋊C4—31no—
182C32×C22⋊C4—31no—
183C32×C22⋊C4—31no—
184C32×C22⋊C4—31no—
185C32×C22⋊C4—31no—
186C32×C42—31no—
187#3757C22×C311yescharacteristic
188#3752C22×C311yescharacteristic
189#3750C22×C311yescharacteristic
190C3×#217—21no—
191C3×#217—21no—
192C3×#217—21no—
193C3×#217—31no—
194C3×#217—31no—
195C3×#217—31no—
196C3×#217—31no—
197C3×#217—61no—
198C3×#217C2×D311yescharacteristic
199C3×#217C2×D311yescharacteristic
200C3×#217C2×D311yescharacteristic
201C3×#217C22×C311yescharacteristic
202C3×#217C22×C311yescharacteristic
203C3×#217C22×C311yescharacteristic
204C3×(C2×D3)⋊C4—21no—
205C3×(C2×D3)⋊C4—31no—
206C3×(C2×D3)⋊C4—31no—
207C3×(C2×D3)⋊C4—31no—
208C3×(C2×D3)⋊C4—31no—
209C3×(C2×D3)⋊C4—31no—
210C3×(C2×D3)⋊C4—31no—
211C3×(C2×D3)⋊C4—31no—
212C3×(C2×D3)⋊C4—31no—
213C3×(C2×D3)⋊C4—61no—
214C3×(C2×D3)⋊C4C2×D311yescharacteristic
215C3×(C2×D3)⋊C4C22×C311yescharacteristic
216C3×C4⋊Dic3—21no—
217C3×C4⋊Dic3—31no—
218C3×C4⋊Dic3—31no—
219C3×C4⋊Dic3C2×D311yescharacteristic
220C3×C4⋊Dic3C22×C311yescharacteristic
221C3×Dic3⋊C4—21no—
222C3×Dic3⋊C4—31no—
223C3×Dic3⋊C4—31no—
224C3×Dic3⋊C4—31no—
225C3×Dic3⋊C4—31no—
226C3×Dic3⋊C4—31no—
227C3×Dic3⋊C4—31no—
228C3×Dic3⋊C4—31no—
229C3×Dic3⋊C4—31no—
230C3×Dic3⋊C4—31no—
231C3×Dic3⋊C4—31no—
232C3×Dic3⋊C4—31no—
233C3×Dic3⋊C4—31no—
234C3×Dic3⋊C4—31no—
235C3×Dic3⋊C4—31no—
236C3×Dic3⋊C4—61no—
237C3×Dic3⋊C4C2×D311yescharacteristic
238C3×Dic3⋊C4C22×C311yescharacteristic
239C3×C4×Dic3—21no—
240C3×C4×Dic3—31no—
241C3×C4×Dic3—31no—
242C3×C4×Dic3—31no—
243C3×C4×Dic3—31no—
244C3×C4×Dic3C2×D311yescharacteristic
245C3×C4×Dic3C22×C311yescharacteristic
246#3724C22×C311yescharacteristic
247#3724C22×C311yescharacteristic
248#3724C22×C311yescharacteristic
249#3724C22×C311yescharacteristic
250#3724C22×C311yescharacteristic
251Dic3⋊Dic3C22×C311yescharacteristic
252Dic3⋊Dic3C22×C311yescharacteristic
253#3722C22×C311yescharacteristic
254#3722C22×C311yescharacteristic
255(C2×D3)⋊Dic3C22×C311yescharacteristic
256(C2×D3)⋊Dic3C22×C311yescharacteristic
257Dic32C22×C311yescharacteristic
258Dic32C22×C311yescharacteristic
259C22×C33—21no—
260C22×C33—21no—
261C22×C33—21no—
262C22×C33—21no—
263C22×C33—21no—
264C22×C33#4112yes—
265C22×C33C2411yescharacteristic
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3—21no—
269C2×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3—21no—
272C33×C4—21no—
273C3×C3⋊Dic3—21no—
274C3×C3⋊Dic3—21no—
275C3×C3⋊Dic3#4112yes—
276C32×Dic3—21no—
277C32×Dic3—21no—
278C32×Dic3—21no—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C3×#126—91no—
284C3×#126—91no—
285C3×#125—91no—
286C3×#123—91no—
287C3×#123—91no—
288C3×#121—31no—
289C3×#121—31no—
290C3×#121—61no—
291C3×#121—91no—
292C3×#121—91no—
293C3×#121—91no—
294C3×C4×D4—31no—
295C3×C4×D4—31no—
296C3×C4×D4—61no—
297C3×C4×D4—91no—
298C3×C4×D4—91no—
299C3×C4×D4—91no—
300C3×#117—91no—
301C2×C3×C4⋊C4—91no—
302#939—31no—
303#939—31no—
304#939—31no—
305#939—31no—
306#939—61no—
307#939C3×D311yescharacteristic, complemented
308#935—31no—
309D4×Dic3—31no—
310D4×Dic3C3×D311yescharacteristic, complemented
311#930—31no—
312#929—31no—
313C4×#67—31no—
314C4×#67—31no—
315C2×Dic3⋊C4—31no—
316C2×Dic3⋊C4—31no—
317#898—31no—
318#894—31no—
319#889—31no—
320#889—31no—
321#884—31no—
322#883—31no—
323#67⋊C4—31no—
324#67⋊C4—31no—
325#67⋊C4—31no—
326#879—31no—
327#879—31no—
328#877—31no—
329#876—31no—
330#872—31no—
331C23×C32—21no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—21no—
335C23×C32—21no—
336C23×C32—21no—
337C23×C32—31no—
338C23×C32—41no—
339C23×C32—41no—
340C23×C32C22×D311yescharacteristic
341C23×C32C22×D311yescharacteristic
342C23×C32C22×D311yescharacteristic
343C23×C32C22×D311yescharacteristic
344C23×C32C23×C311yescharacteristic
345C23×C32C23×C311yescharacteristic
346C22×C3⋊D3C23×C311yescharacteristic
347C22×C3×D3—21no—
348C22×C3×D3—31no—
349C22×C3×D3—31no—
350C22×C3×D3—61no—
351C22×C3×D3C22×D311yescharacteristic
352C22×C3×D3C23×C311yescharacteristic
353C32×D4—22no—
354C32×D4—24no—
355C32×D4—22no—
356C32×D4—22no—
357C32×D4—42no—
358C32×D4—42no—
359C32×D4—44no—
360C32×D4—62no—
361C32×D4—121no—
362C2×C32×C4—21no—
363C2×C32×C4—21no—
364C2×C32×C4—21no—
365C2×C32×C4—31no—
366C2×C32×C4—31no—
367C2×C32×C4—31no—
368C2×C32×C4—31no—
369C2×C32×C4—31no—
370C2×C32×C4—31no—
371C2×C32×C4—31no—
372C2×C32×C4—41no—
373C2×C32×C4—121no—
374C2×C32×C4—121no—
375C2×C32×C4—121no—
376C2×C32×C4C22×D311yescharacteristic
377C2×C32×C4C22×D311yescharacteristic
378C2×C32×C4C23×C311yescharacteristic
379#638—22no—
380#638—22no—
381C2×C3⋊Dic3—22no—
382C2×C3⋊Dic3C23×C311yescharacteristic
383C2×C3⋊Dic3C23×C311yescharacteristic
384C2×C3⋊Dic3C23×C311yescharacteristic
385C3×#67—22no—
386C3×#67—22no—
387C3×#67—42no—
388C3×#67—41no—
389C3×#67—41no—
390C3×#67—42no—
391C3×#67—62no—
392C3×#67—62no—
393C3×#67—62no—
394C3×#67—62no—
395C3×#67—122no—
396C3×#67—122no—
397C3×#67—121no—
398C2×C3×Dic3—21no—
399C2×C3×Dic3—21no—
400C2×C3×Dic3—21no—
401C2×C3×Dic3—21no—
402C2×C3×Dic3—21no—
403C2×C3×Dic3—21no—
404C2×C3×Dic3—21no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—31no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—41no—
412C2×C3×Dic3—41no—
413C2×C3×Dic3—41no—
414C2×C3×Dic3—41no—
415C2×C3×Dic3—41no—
416C2×C3×Dic3—41no—
417C2×C3×Dic3—42no—
418C2×C3×Dic3—42no—
419C2×C3×Dic3—42no—
420C2×C3×Dic3—61no—
421C2×C3×Dic3—61no—
422C2×C3×Dic3—61no—
423C2×C3×Dic3—62no—
424C2×C3×Dic3—62no—
425C2×C3×Dic3—62no—
426C2×C3×Dic3—122no—
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C22×D311yescharacteristic
433C2×C3×Dic3C22×D311yescharacteristic
434C2×C3×Dic3C23×C311yescharacteristic
435C2×C3×Dic3C23×C311yescharacteristic
436C2×C3×Dic3C23×C311yescharacteristic
437C2×C3×Dic3C23×C311yescharacteristic
438C2×C3×Dic3C23×C311yescharacteristic
439C2×C3×Dic3C23×C311yescharacteristic
440C2×C3×Dic3C23×C311yescharacteristic
441C3×D12—121no—
442C3×C4×D3—62no—
443C3×C4×D3—121no—
444C3×C4×D3—121no—
445#626—41no—
446#624—41no—
447D3×Dic3—22no—
448#553—91noSylow
449C2×C33—22no—
450C2×C33—41no—
451C2×C33C2×#4111yescharacteristic
452C2×C33C2×#4111yescharacteristic
453C2×C33H(5,𝔽2)11yescharacteristic
454C3×C3⋊D3—41no—
455C32×D3—41no—
456C2×C3×D4—21no—
457C2×C3×D4—21no—
458C2×C3×D4—21no—
459C2×C3×D4—31no—
460C2×C3×D4—31no—
461C2×C3×D4—31no—
462C2×C3×D4—31no—
463C2×C3×D4—41no—
464C2×C3×D4—61no—
465C2×C3×D4—61no—
466C2×C3×D4—91no—
467C2×C3×D4—91no—
468C2×C3×D4—91no—
469C2×C3×D4D3211yescharacteristic
470C2×C3×D4C2×C3×D311yescharacteristic
471C2×C3×D4C2×C3×D311yescharacteristic
472C22×C3×C4—31no—
473C22×C3×C4—31no—
474C22×C3×C4—31no—
475C22×C3×C4—31no—
476C22×C3×C4—31no—
477C22×C3×C4—31no—
478C22×C3×C4—61no—
479C22×C3×C4—61no—
480C22×C3×C4—61no—
481C22×C3×C4—91no—
482C22×C3×C4—91no—
483C22×C3×C4—91no—
484C2×#67—31no—
485C2×#67—31no—
486C2×#67—31no—
487C2×#67—31no—
488C2×#67—31no—
489C2×#67—61no—
490C2×#67—61no—
491C2×#67C2×C3×D311yescharacteristic
492C2×#67C2×C3×D311yescharacteristic
493C22×Dic3—31no—
494C22×Dic3—31no—
495C22×Dic3—31no—
496C22×Dic3—61no—
497C22×Dic3C2×C3×D311yescharacteristic
498C22×Dic3C2×C3×D311yescharacteristic
499C22×Dic3C2×C3×D311yescharacteristic
500C2×D12—31no—
501C2×C4×D3—31no—
502C2×C4×D3—31no—
503C2×C4×D3—31no—
504C3×C4⋊C4—31no—
505C3×C4⋊C4—31no—
506C3×C4⋊C4—31no—
507C3×C4⋊C4—31no—
508C3×C4⋊C4—61no—
509C3×C4⋊C4—61no—
510C3×C4⋊C4—91no—
511C3×C4⋊C4—91no—
512C3×C4⋊C4—91no—
513C3×C4⋊C4—91no—
514C3×C4⋊C4—91no—
515C3×C4⋊C4—91no—
516C3×C4⋊C4—91no—
517C3×C4⋊C4—91no—
518C3×C22⋊C4—31no—
519C3×C22⋊C4—31no—
520C3×C22⋊C4—31no—
521C3×C22⋊C4—31no—
522C3×C22⋊C4—31no—
523C3×C22⋊C4—31no—
524C3×C22⋊C4—31no—
525C3×C22⋊C4—31no—
526C3×C22⋊C4—61no—
527C3×C22⋊C4—61no—
528C3×C22⋊C4—61no—
529C3×C22⋊C4—61no—
530C3×C22⋊C4—91no—
531C3×C22⋊C4—91no—
532C3×C22⋊C4—91no—
533C3×C22⋊C4—91no—
534C3×C22⋊C4—91no—
535C3×C22⋊C4—91no—
536C3×C42—31no—
537C3×C42—31no—
538C3×C42—61no—
539C3×C42—91no—
540C3×C42—91no—
541#217—31no—
542#217—31no—
543#217—31no—
544#217—31no—
545#217—61no—
546#217C2×C3×D311yescharacteristic
547#217C2×C3×D311yescharacteristic
548#217C2×C3×D311yescharacteristic
549(C2×D3)⋊C4—31no—
550(C2×D3)⋊C4—31no—
551(C2×D3)⋊C4—31no—
552(C2×D3)⋊C4—31no—
553(C2×D3)⋊C4—31no—
554(C2×D3)⋊C4—31no—
555(C2×D3)⋊C4—31no—
556(C2×D3)⋊C4—31no—
557(C2×D3)⋊C4—61no—
558(C2×D3)⋊C4C2×C3×D311yescharacteristic
559C4⋊Dic3—31no—
560C4⋊Dic3—31no—
561C4⋊Dic3C2×C3×D311yescharacteristic
562Dic3⋊C4—31no—
563Dic3⋊C4—31no—
564Dic3⋊C4—31no—
565Dic3⋊C4—31no—
566Dic3⋊C4—31no—
567Dic3⋊C4—31no—
568Dic3⋊C4—31no—
569Dic3⋊C4—31no—
570Dic3⋊C4—31no—
571Dic3⋊C4—31no—
572Dic3⋊C4—31no—
573Dic3⋊C4—31no—
574Dic3⋊C4—31no—
575Dic3⋊C4—31no—
576Dic3⋊C4—61no—
577Dic3⋊C4C2×C3×D311yescharacteristic
578C4×Dic3—31no—
579C4×Dic3—31no—
580C4×Dic3—31no—
581C4×Dic3—31no—
582C4×Dic3C2×C3×D311yescharacteristic
583C22×C32—21no—
584C22×C32—21no—
585C22×C32—21no—
586C22×C32—21no—
587C22×C32—21no—
588C22×C32—21no—
589C22×C32—21no—
590C22×C32—22no—
591C22×C32—21no—
592C22×C32—21no—
593C22×C32—21no—
594C22×C32—21no—
595C22×C32—21no—
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—21no—
599C22×C32—21no—
600C22×C32—21no—
601C22×C32—21no—
602C22×C32—22no—
603C22×C32—22no—
604C22×C32—22no—
605C22×C32—41no—
606C22×C32—42no—
607C22×C32—41no—
608C22×C32—41no—
609C22×C32—42no—
610C22×C32—41no—
611C22×C32—41no—
612C22×C32—41no—
613C22×C32—41no—
614C22×C32—41no—
615C22×C32—41no—
616C22×C32—41no—
617C22×C32—41no—
618C22×C32—41no—
619C22×C32—41no—
620C22×C32—41no—
621C22×C32—41no—
622C22×C32—61no—
623C22×C32—61no—
624C22×C32—61no—
625C22×C32—81no—
626C22×C32—81no—
627C22×C32—81no—
628C22×C32—81no—
629C22×C32#23512yes—
630C22×C32#23712yes—
631C22×C32C3×#4112yes—
632C22×C32C23×D311yescharacteristic
633C22×C32C23×D311yescharacteristic
634C22×C32C24×C311yescharacteristic
635C2×C3⋊D3—21no—
636C2×C3⋊D3—21no—
637C2×C3⋊D3—21no—
638C2×C3×D3—21no—
639C2×C3×D3—21no—
640C2×C3×D3—21no—
641C2×C3×D3—21no—
642C2×C3×D3—21no—
643C2×C3×D3—21no—
644C2×C3×D3—41no—
645C2×C3×D3—41no—
646C2×C3×D3—41no—
647C2×C3×D3—61no—
648C2×C3×D3—61no—
649C2×C3×D3—61no—
650C2×C3×D3—61no—
651C2×C3×D3—61no—
652C2×C3×D3—61no—
653C2×C3×D3—121no—
654C2×C3×D3—121no—
655C2×C3×D3—121no—
656C32×C4—21no—
657C32×C4—22no—
658C32×C4—21no—
659C32×C4—21no—
660C32×C4—41no—
661C32×C4—41no—
662C32×C4—42no—
663C32×C4—61no—
664C32×C4—61no—
665C32×C4—61no—
666C32×C4—61no—
667C32×C4—61no—
668C32×C4—61no—
669C32×C4—61no—
670C3⋊Dic3—21no—
671C3⋊Dic3—21no—
672C3⋊Dic3C3×#4112yes—
673C3×Dic3—22no—
674C3×Dic3—22no—
675C3×Dic3—21no—
676C3×Dic3—21no—
677C3×Dic3—21no—
678C3×Dic3—21no—
679C3×Dic3—21no—
680C3×Dic3—21no—
681C3×Dic3—21no—
682C3×Dic3—21no—
683C3×Dic3—21no—
684C3×Dic3—21no—
685C3×Dic3—21no—
686C3×Dic3—21no—
687C3×Dic3—21no—
688C3×Dic3—21no—
689C3×Dic3—32no—
690C3×Dic3—32no—
691C3×Dic3—41no—
692C3×Dic3—41no—
693C3×Dic3—41no—
694C3×Dic3—41no—
695C3×Dic3—41no—
696C3×Dic3—62no—
697C3×Dic3—61no—
698C3×Dic3—61no—
699C3×Dic3—61no—
700C3×Dic3—61no—
701C3×Dic3—121no—
702C3×Dic3—121no—
703#126—91no—
704#126—91no—
705#125—91no—
706#123—91no—
707#123—91no—
708#121—31no—
709#121—91no—
710#121—91no—
711#121—91no—
712C4×D4—31no—
713C4×D4—91no—
714C4×D4—91no—
715C4×D4—91no—
716#117—91no—
717C2×C4⋊C4—91no—
718C33#55311yescharacteristic, complemented, Sylow
719C23×C3—21no—
720C23×C3—21no—
721C23×C3—21no—
722C23×C3—21no—
723C23×C3—21no—
724C23×C3—21no—
725C23×C3—31no—
726C23×C3—31no—
727C23×C3—41no—
728C23×C3—41no—
729C23×C3—61no—
730C23×C3—91no—
731C23×C3C2×D3211yescharacteristic
732C23×C3C2×D3211yescharacteristic
733C23×C3C22×C3×D311yescharacteristic
734C23×C3C22×C3×D311yescharacteristic
735C23×C3C22×C3×D311yescharacteristic
736C23×C3C22×C3×D311yescharacteristic
737C22×D3—31no—
738C22×D3—31no—
739C22×D3—61no—
740C22×D3C22×C3×D311yescharacteristic
741C3×D4—24no—
742C3×D4—22no—
743C3×D4—22no—
744C3×D4—22no—
745C3×D4—42no—
746C3×D4—42no—
747C3×D4—44no—
748C3×D4—62no—
749C3×D4—62no—
750C3×D4—122no—
751C3×D4—121no—
752C3×D4—121no—
753C3×D4—122no—
754C3×D4—182no—
755C3×D4—182no—
756C3×D4—361no—
757C2×C3×C4—21no—
758C2×C3×C4—21no—
759C2×C3×C4—21no—
760C2×C3×C4—31no—
761C2×C3×C4—31no—
762C2×C3×C4—31no—
763C2×C3×C4—31no—
764C2×C3×C4—31no—
765C2×C3×C4—31no—
766C2×C3×C4—31no—
767C2×C3×C4—31no—
768C2×C3×C4—31no—
769C2×C3×C4—31no—
770C2×C3×C4—31no—
771C2×C3×C4—31no—
772C2×C3×C4—31no—
773C2×C3×C4—31no—
774C2×C3×C4—41no—
775C2×C3×C4—61no—
776C2×C3×C4—61no—
777C2×C3×C4—61no—
778C2×C3×C4—61no—
779C2×C3×C4—61no—
780C2×C3×C4—61no—
781C2×C3×C4—61no—
782C2×C3×C4—91no—
783C2×C3×C4—91no—
784C2×C3×C4—91no—
785C2×C3×C4—121no—
786C2×C3×C4—121no—
787C2×C3×C4—121no—
788C2×C3×C4—121no—
789C2×C3×C4—121no—
790C2×C3×C4—121no—
791C2×C3×C4—122no—
792C2×C3×C4—122no—
793C2×C3×C4—122no—
794C2×C3×C4—182no—
795C2×C3×C4—182no—
796C2×C3×C4—361no—
797C2×C3×C4C2×D3211yescharacteristic
798C2×C3×C4C22×C3×D311yescharacteristic
799C2×C3×C4C22×C3×D311yescharacteristic
800#67—22no—
801#67—41no—
802#67—62no—
803#67—62no—
804#67—62no—
805#67—62no—
806#67—122no—
807#67—122no—
808#67—121no—
809C2×Dic3—31no—
810C2×Dic3—31no—
811C2×Dic3—31no—
812C2×Dic3—31no—
813C2×Dic3—31no—
814C2×Dic3—31no—
815C2×Dic3—41no—
816C2×Dic3—41no—
817C2×Dic3—41no—
818C2×Dic3—61no—
819C2×Dic3—61no—
820C2×Dic3—61no—
821C2×Dic3—62no—
822C2×Dic3—62no—
823C2×Dic3—62no—
824C2×Dic3—122no—
825C2×Dic3C22×C3×D311yescharacteristic
826C2×Dic3C22×C3×D311yescharacteristic
827C2×Dic3C22×C3×D311yescharacteristic
828C2×Dic3C22×C3×D311yescharacteristic
829C2×Dic3C22×C3×D311yescharacteristic
830C2×Dic3C22×C3×D311yescharacteristic
831C2×Dic3C22×C3×D311yescharacteristic
832D12—121no—
833C4×D3—62no—
834C4×D3—121no—
835C4×D3—121no—
836C2×C32—22no—
837C2×C32—22no—
838C2×C32—22no—
839C2×C32—21no—
840C2×C32—21no—
841C2×C32—21no—
842C2×C32—21no—
843C2×C32—21no—
844C2×C32—21no—
845C2×C32—21no—
846C2×C32—21no—
847C2×C32—21no—
848C2×C32—41no—
849C2×C32—41no—
850C2×C32—41no—
851C2×C32—42no—
852C2×C32—42no—
853C2×C32—42no—
854C2×C32—41no—
855C2×C32—42no—
856C2×C32—41no—
857C2×C32—41no—
858C2×C32—82no—
859C2×C32—81no—
860C2×C32—81no—
861C2×C32—82no—
862C2×C32—121no—
863C2×C32C2×#23511yescharacteristic
864C2×C32C2×#23711yescharacteristic
865C2×C32#100411yescharacteristic
866C2×C32#100411yescharacteristic
867C2×C32D3×#4111yescharacteristic
868C2×C32D3×#4111yescharacteristic
869C2×C32C2×C3×#4111yescharacteristic
870C2×C32C2×C3×#4111yescharacteristic
871C2×C32C3×H(5,𝔽2)11yescharacteristic
872C3⋊D3—41no—
873C3×D3—41no—
874C3×D3—41no—
875C3×D3—81no—
876C3×D3—121no—
877C3×D3—121no—
878C3×D3—241no—
879C2×D4—31no—
880C2×D4—31no—
881C2×D4—91no—
882C2×D4—91no—
883C2×D4—91no—
884C2×D4C3×D3211yescharacteristic
885C22×C4—31no—
886C22×C4—31no—
887C22×C4—31no—
888C22×C4—91no—
889C22×C4—91no—
890C22×C4—91no—
891C4⋊C4—31no—
892C4⋊C4—31no—
893C4⋊C4—91no—
894C4⋊C4—91no—
895C4⋊C4—91no—
896C4⋊C4—91no—
897C4⋊C4—91no—
898C4⋊C4—91no—
899C4⋊C4—91no—
900C4⋊C4—91no—
901C22⋊C4—31no—
902C22⋊C4—31no—
903C22⋊C4—31no—
904C22⋊C4—31no—
905C22⋊C4—91no—
906C22⋊C4—91no—
907C22⋊C4—91no—
908C22⋊C4—91no—
909C22⋊C4—91no—
910C22⋊C4—91no—
911C42—31no—
912C42—91no—
913C42—91no—
914C22×C3—21no—
915C22×C3—21no—
916C22×C3—21no—
917C22×C3—21no—
918C22×C3—21no—
919C22×C3—21no—
920C22×C3—22no—
921C22×C3—21no—
922C22×C3—21no—
923C22×C3—21no—
924C22×C3—21no—
925C22×C3—21no—
926C22×C3—21no—
927C22×C3—21no—
928C22×C3—21no—
929C22×C3—21no—
930C22×C3—21no—
931C22×C3—21no—
932C22×C3—21no—
933C22×C3—22no—
934C22×C3—22no—
935C22×C3—22no—
936C22×C3—41no—
937C22×C3—41no—
938C22×C3—41no—
939C22×C3—41no—
940C22×C3—41no—
941C22×C3—41no—
942C22×C3—41no—
943C22×C3—41no—
944C22×C3—41no—
945C22×C3—41no—
946C22×C3—41no—
947C22×C3—41no—
948C22×C3—41no—
949C22×C3—41no—
950C22×C3—42no—
951C22×C3—41no—
952C22×C3—42no—
953C22×C3—61no—
954C22×C3—61no—
955C22×C3—61no—
956C22×C3—61no—
957C22×C3—61no—
958C22×C3—61no—
959C22×C3—81no—
960C22×C3—81no—
961C22×C3—81no—
962C22×C3—81no—
963C22×C3—121no—
964C22×C3—121no—
965C22×C3—121no—
966C22×C3—181no—
967C22×C3—181no—
968C22×C3—181no—
969C22×C3#380412yes—
970C22×C3C3×#23512yes—
971C22×C3C3×#23712yes—
972C22×C3C22×D3211yescharacteristic
973C22×C3C23×C3×D311yescharacteristic
974C22×C3C23×C3×D311yescharacteristic
975C2×D3—21no—
976C2×D3—21no—
977C2×D3—21no—
978C2×D3—61no—
979C2×D3—61no—
980C2×D3—61no—
981C2×D3—61no—
982C2×D3—61no—
983C2×D3—61no—
984C2×D3—121no—
985C2×D3—121no—
986C2×D3—121no—
987C3×C4—22no—
988C3×C4—21no—
989C3×C4—21no—
990C3×C4—21no—
991C3×C4—41no—
992C3×C4—41no—
993C3×C4—42no—
994C3×C4—62no—
995C3×C4—62no—
996C3×C4—61no—
997C3×C4—61no—
998C3×C4—61no—
999C3×C4—61no—
1000C3×C4—61no—
1001C3×C4—61no—
1002C3×C4—61no—
1003C3×C4—61no—
1004C3×C4—61no—
1005C3×C4—61no—
1006C3×C4—61no—
1007C3×C4—61no—
1008C3×C4—61no—
1009C3×C4—61no—
1010C3×C4—92no—
1011C3×C4—121no—
1012C3×C4—121no—
1013C3×C4—121no—
1014C3×C4—121no—
1015C3×C4—121no—
1016C3×C4—181no—
1017C3×C4—181no—
1018Dic3—21no—
1019Dic3—21no—
1020Dic3—21no—
1021Dic3—21no—
1022Dic3—21no—
1023Dic3—21no—
1024Dic3—21no—
1025Dic3—32no—
1026Dic3—32no—
1027Dic3—62no—
1028Dic3—61no—
1029Dic3—61no—
1030Dic3—61no—
1031Dic3—61no—
1032Dic3—121no—
1033Dic3—121no—
1034C32—21no—
1035C32—21no—
1036C32—21no—
1037C32—41no—
1038C32#554011yescharacteristic, complemented
1039C32#560111yescharacteristic, complemented
1040C32C3×#55311yescharacteristic, complemented
1041C23—31no—
1042C23—91no—
1043C23C2×C3×D3211yescharacteristic
1044C23C2×C3×D3211yescharacteristic
1045D4—22no—
1046D4—62no—
1047D4—121no—
1048D4—182no—
1049D4—182no—
1050D4—361no—
1051C2×C4—31no—
1052C2×C4—31no—
1053C2×C4—31no—
1054C2×C4—31no—
1055C2×C4—31no—
1056C2×C4—31no—
1057C2×C4—31no—
1058C2×C4—91no—
1059C2×C4—91no—
1060C2×C4—91no—
1061C2×C4—121no—
1062C2×C4—121no—
1063C2×C4—121no—
1064C2×C4—182no—
1065C2×C4—182no—
1066C2×C4—361no—
1067C2×C4C2×C3×D3211yescharacteristic
1068C2×C3—22no—
1069C2×C3—22no—
1070C2×C3—22no—
1071C2×C3—21no—
1072C2×C3—21no—
1073C2×C3—21no—
1074C2×C3—21no—
1075C2×C3—21no—
1076C2×C3—21no—
1077C2×C3—21no—
1078C2×C3—21no—
1079C2×C3—21no—
1080C2×C3—42no—
1081C2×C3—42no—
1082C2×C3—42no—
1083C2×C3—42no—
1084C2×C3—41no—
1085C2×C3—41no—
1086C2×C3—41no—
1087C2×C3—41no—
1088C2×C3—41no—
1089C2×C3—41no—
1090C2×C3—82no—
1091C2×C3—81no—
1092C2×C3—81no—
1093C2×C3—82no—
1094C2×C3—121no—
1095C2×C3—121no—
1096C2×C3—241no—
1097C2×C3—361no—
1098C2×C3#6431211yescharacteristic
1099C2×C3#6431311yescharacteristic
1100C2×C3C2×#380411yescharacteristic
1101C2×C3C2×C3×#23511yescharacteristic
1102C2×C3C2×C3×#23711yescharacteristic
1103C2×C3C3×#100411yescharacteristic
1104C2×C3C3×#100411yescharacteristic
1105C2×C3C3×D3×#4111yescharacteristic
1106C2×C3C3×D3×#4111yescharacteristic
1107D3—41no—
1108D3—121no—
1109D3—121no—
1110D3—241no—
1111C22—21no—
1112C22—21no—
1113C22—21no—
1114C22—21no—
1115C22—21no—
1116C22—61no—
1117C22—61no—
1118C22—61no—
1119C22—181no—
1120C22—181no—
1121C22—181no—
1122C22C3×#380412yes—
1123C22C22×C3×D3211yescharacteristic
1124C4—21no—
1125C4—61no—
1126C4—61no—
1127C4—61no—
1128C4—61no—
1129C4—61no—
1130C4—61no—
1131C4—61no—
1132C4—92no—
1133C4—181no—
1134C4—181no—
1135C3—21no—
1136C3—21no—
1137C3—21no—
1138C3—41no—
1139C3#1059520411yescharacteristic, direct product factor
1140C3C3×#554011yescharacteristic, complemented
1141C3C3×#560111yescharacteristic, complemented
1142C2—22no—
1143C2—41no—
1144C2—121no—
1145C2—361no—
1146C2C3×#6431211yescharacteristic
1147C2C3×#6431311yescharacteristic
1148C2C2×C3×#380411yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#553
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C3×#64148C2semidirect
2. C32×#939C2semidirect
3. C32×D4×Dic3C2semidirect
4. C3×#63978C2semidirect
5. C3×#67⋊Dic3C2semidirect
6. C3×#63971C2semidirect
7. C2×C3×#3724C2semidirect
8. C3×#63961C2semidirect
9. C3×#63956C2semidirect
10. C3×#63952C2semidirect
11. C3×#63952C2semidirect
12. C3×#63877C2semidirect
13. C3×#63868C2semidirect
14. C3×#63854C2semidirect
15. C3×#63847C2semidirect
18. #10595204C3direct (N × H)
56. #64148C2×C3semidirect
63. C3×#939D3semidirect
64. C3×#939C2×C3semidirect
68. C3×D4×Dic3D3semidirect
69. C3×D4×Dic3C2×C3semidirect
90. #63978C2×C3semidirect
91. #67⋊Dic3C2×C3semidirect
92. #63971C2×C3semidirect
93. C2×#3724C2×C3semidirect
94. #63961C2×C3semidirect
95. #63956C2×C3semidirect
96. #63952C2×C3semidirect
97. #63952C2×C3semidirect
98. #63877C2×C3semidirect
99. #63868C2×C3semidirect
100. #63854C2×C3semidirect
101. #63847C2×C3semidirect
307. #939C3×D3semidirect
310. D4×Dic3C3×D3semidirect
718. C33#553semidirect
1038. C32#5540semidirect
1039. C32#5601semidirect
1040. C32C3×#553semidirect
1139. C3#10595204direct (N × H)
1140. C3C3×#5540semidirect
1141. C3C3×#5601semidirect

Maximal subgroups

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

subgroupindex
C3×#641482
C32×#9392
C32×D4×Dic32
C3×#639782
C3×#67⋊Dic32
C3×#639712
C2×C3×#37242
C3×#639612
C3×#639562
C3×#639522
C3×#638772
C3×#638682
C3×#638542
C3×#638472
C3×#56013
C3×#55403
#105952043