Finite Group Databasebeta

← C3×#10594057 #13173636

Subgroups — C3×#10594057 #13173636

Order 1728.

1342 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3805C211yesmaximal, characteristic
2C2×C3×D3×Dic6C211yesmaximal, characteristic, complemented
3C3×#64087C211yesmaximal, characteristic, complemented
4C32×#885C211yesmaximal, characteristic, complemented
5C32×#883C211yesmaximal, characteristic, complemented
6C3×#63982C211yesmaximal, characteristic, complemented
7C3×#63969C211yesmaximal, characteristic, complemented
8C3×#63959C211yesmaximal, characteristic, complemented
9C3×#63918C211yesmaximal, characteristic, complemented
10C3×#63905C211yesmaximal, characteristic, complemented
11C3×#63899C211yesmaximal, characteristic, complemented
12C3×#63896C211yesmaximal, characteristic, complemented
13C3×#63891C211yesmaximal, characteristic, complemented
14C3×#63877C211yesmaximal, characteristic, complemented
15C3×#63839C211yesmaximal, characteristic, complemented
16C3×#5675—31nomaximal
17C3×#5648—31nomaximal
18#10594057C311yesmaximal, characteristic, direct product factor
19C22×C3×C3⋊Dic3C2211yescharacteristic
20C2×C3×#634C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×C4×D3C2211yescharacteristic
24C2×C32×Dic6C2211yescharacteristic
25C2×C3×#627C2211yescharacteristic
26C2×C3×#627C2211yescharacteristic
27C2×C3×#627C2211yescharacteristic
28C2×C3×#625C2211yescharacteristic
29C3×#3805—24no—
30C2×C3×D3×Dic3C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic
32C2×C3×D3×Dic3C2211yescharacteristic
33C3×D3×Dic6—24no—
34C33×C22⋊C4C2211yescharacteristic
35C3×#3757C2211yescharacteristic
36C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
37C3×#3750C2211yescharacteristic
38C3×#3750C2211yescharacteristic
39C32×#217C2211yescharacteristic
40C32×#217C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×C4⋊Dic3C2211yescharacteristic
45C32×Dic3⋊C4C2211yescharacteristic
46C32×C4×Dic3C2211yescharacteristic
47C3×#3724C2211yescharacteristic
48C3×#3724C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×Dic3⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×Dic32C2211yescharacteristic
56C2×C3×D3×Q8—31no—
57C2×C3×#237—31no—
58C2×C3×#237—31no—
59C22×C3×Dic6—31no—
60C2×#3805C2×C311yescharacteristic
61C2×D3×Dic6C2×C311yescharacteristic, complemented
62C32×#124—31no—
63C32×#123—31no—
64#64087C2×C311yescharacteristic, complemented
65C3×#944—31no—
66C3×#936—31no—
67C3×#935—31no—
68C3×#929—31no—
69C3×#896—31no—
70C3×#896—31no—
71C3×#888—31no—
72C3×#888—31no—
73C3×#886—31no—
74C3×#885—21no—
75C3×#885—31no—
76C3×#885D311yescharacteristic, complemented
77C3×#885C2×C311yescharacteristic, complemented
78C3×#883—21no—
79C3×#883—31no—
80C3×#883—31no—
81C3×#883—31no—
82C3×#883D311yescharacteristic, complemented
83C3×#883C2×C311yescharacteristic, complemented
84C3×#878—31no—
85C3×#878—31no—
86C3×#878—31no—
87C3×#878—31no—
88C3×#878—31no—
89C3×#878—31no—
90C3×#878—61no—
91C3×#877—31no—
92C3×#872—31no—
93C3×#869—31no—
94#63982C2×C311yescharacteristic, complemented
95#63969C2×C311yescharacteristic, complemented
96#63959C2×C311yescharacteristic, complemented
97#63918C2×C311yescharacteristic, complemented
98#63905C2×C311yescharacteristic, complemented
99#63899C2×C311yescharacteristic, complemented
100#63896C2×C311yescharacteristic, complemented
101#63891C2×C311yescharacteristic, complemented
102#63877C2×C311yescharacteristic, complemented
103#63839C2×C311yescharacteristic, complemented
104C23×C33C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×C33×C4C2311yescharacteristic
108C2×C33×C4C2311yescharacteristic
109C2×C3×C3⋊Dic3—22no—
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C3×#634—22no—
115C32×#67—22no—
116C32×#67—22no—
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C32×C4×D3—22no—
124C32×Dic6—22no—
125C3×#627—22no—
126C3×#627—22no—
127C3×#627—22no—
128C3×#625—22no—
129C3×D3×Dic3—22no—
130C3×D3×Dic3—22no—
131C3×D3×Dic3D414yes—
132C3×#536—91no—
133#5675—31no—
134#5648—31no—
135C2×C32×Q8—31no—
136C2×C32×D4—31no—
137C2×C32×D4—31no—
138C22×C32×C4—31no—
139C22×C3⋊Dic3C22×C311yescharacteristic
140C2×#634C22×C311yescharacteristic
141C2×C3×#67—21no—
142C2×C3×#67—21no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67C2×D311yescharacteristic
146C2×C3×#67C2×D311yescharacteristic
147C2×C3×#67C22×C311yescharacteristic
148C2×C3×#67C22×C311yescharacteristic
149C22×C3×Dic3—31no—
150C22×C3×Dic3—31no—
151C22×C3×Dic3—31no—
152C22×C3×Dic3—31no—
153C22×C3×Dic3—31no—
154C22×C3×Dic3—61no—
155C3×D3×Q8—64no—
156C3×#237—64no—
157C3×#237—64no—
158C2×C3×C4×D3—21no—
159C2×C3×C4×D3—31no—
160C2×C3×C4×D3—31no—
161C2×C3×C4×D3—31no—
162C2×C3×C4×D3C2×D311yescharacteristic
163C2×C3×C4×D3C22×C311yescharacteristic
164C2×C3×Dic6—21no—
165C2×C3×Dic6—31no—
166C2×C3×Dic6—31no—
167C2×C3×Dic6—31no—
168C2×C3×Dic6—31no—
169C2×C3×Dic6—31no—
170C2×C3×Dic6—31no—
171C2×C3×Dic6—31no—
172C2×C3×Dic6—31no—
173C2×C3×Dic6—64no—
174C2×C3×Dic6—61no—
175C2×C3×Dic6C2×D311yescharacteristic
176C2×C3×Dic6C22×C311yescharacteristic
177C2×#627C22×C311yescharacteristic
178C2×#627C22×C311yescharacteristic
179C2×#627C22×C311yescharacteristic
180C2×#625C22×C311yescharacteristic
181#3805—24no—
182C2×D3×Dic3C22×C311yescharacteristic
183C2×D3×Dic3C22×C311yescharacteristic
184C2×D3×Dic3C22×C311yescharacteristic
185D3×Dic6—24no—
186C32×C4⋊C4—31no—
187C32×C4⋊C4—31no—
188C32×C22⋊C4—21no—
189C32×C22⋊C4—21no—
190C32×C22⋊C4—21no—
191C32×C22⋊C4—31no—
192C32×C22⋊C4—31no—
193C32×C22⋊C4—31no—
194C32×C22⋊C4—31no—
195C32×C22⋊C4—31no—
196C32×C22⋊C4—41no—
197C32×C22⋊C4C2×D311yescharacteristic
198C32×C22⋊C4C2×D311yescharacteristic
199C32×C22⋊C4C22×C311yescharacteristic
200C32×C42—31no—
201#3757C22×C311yescharacteristic
202C4⋊(C3⋊Dic3)C22×C311yescharacteristic
203#3750C22×C311yescharacteristic
204#3750C22×C311yescharacteristic
205C3×#217—21no—
206C3×#217—21no—
207C3×#217—31no—
208C3×#217—31no—
209C3×#217—31no—
210C3×#217—31no—
211C3×#217—31no—
212C3×#217—61no—
213C3×#217C2×D311yescharacteristic
214C3×#217C2×D311yescharacteristic
215C3×#217C22×C311yescharacteristic
216C3×#217C22×C311yescharacteristic
217C3×(C2×D3)⋊C4—21no—
218C3×(C2×D3)⋊C4—21no—
219C3×(C2×D3)⋊C4—21no—
220C3×(C2×D3)⋊C4—31no—
221C3×(C2×D3)⋊C4—31no—
222C3×(C2×D3)⋊C4—31no—
223C3×(C2×D3)⋊C4C2×D311yescharacteristic
224C3×(C2×D3)⋊C4C2×D311yescharacteristic
225C3×(C2×D3)⋊C4C2×D311yescharacteristic
226C3×(C2×D3)⋊C4C22×C311yescharacteristic
227C3×(C2×D3)⋊C4C22×C311yescharacteristic
228C3×(C2×D3)⋊C4C22×C311yescharacteristic
229C3×C4⋊Dic3—21no—
230C3×C4⋊Dic3—31no—
231C3×C4⋊Dic3—31no—
232C3×C4⋊Dic3—31no—
233C3×C4⋊Dic3—31no—
234C3×C4⋊Dic3—31no—
235C3×C4⋊Dic3—61no—
236C3×C4⋊Dic3C2×D311yescharacteristic
237C3×C4⋊Dic3C22×C311yescharacteristic
238C3×Dic3⋊C4—21no—
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×Dic3⋊C4—31no—
247C3×Dic3⋊C4—31no—
248C3×Dic3⋊C4—31no—
249C3×Dic3⋊C4—31no—
250C3×Dic3⋊C4—61no—
251C3×Dic3⋊C4—61no—
252C3×Dic3⋊C4C2×D311yescharacteristic
253C3×Dic3⋊C4C22×C311yescharacteristic
254C3×C4×Dic3—21no—
255C3×C4×Dic3—31no—
256C3×C4×Dic3—31no—
257C3×C4×Dic3C2×D311yescharacteristic
258C3×C4×Dic3C22×C311yescharacteristic
259#3724C22×C311yescharacteristic
260#3724C22×C311yescharacteristic
261Dic3⋊Dic3C22×C311yescharacteristic
262Dic3⋊Dic3C22×C311yescharacteristic
263Dic3⋊Dic3C22×C311yescharacteristic
264(C2×D3)⋊Dic3C22×C311yescharacteristic
265(C2×D3)⋊Dic3C22×C311yescharacteristic
266(C2×D3)⋊Dic3C22×C311yescharacteristic
267Dic32C22×C311yescharacteristic
268C22×C33—21no—
269C22×C33—21no—
270C22×C33—21no—
271C22×C33C2411yescharacteristic
272C2×C32×D3—21no—
273C2×C32×D3—21no—
274C2×C32×D3—21no—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3C2×D412yes—
278C33×C4—21no—
279C33×C4—21no—
280C3×C3⋊Dic3—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3C2×D412yes—
284C32×Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C32×Dic3C2×D412yes—
290C2×C3×#41—91no—
291C22×C3×Q8—91no—
292C2×D3×Q8—31no—
293C2×#237—31no—
294C2×#237—31no—
295C22×Dic6—31no—
296C3×C4⋊Q8—91no—
297C3×C4⋊Q8—91no—
298C3×#124—31no—
299C3×#124—31no—
300C3×#124—61no—
301C3×#124—91no—
302C3×#123—31no—
303C3×#123—31no—
304C3×#123—61no—
305C3×#123—91no—
306C3×#123—91no—
307C3×#123—91no—
308C3×C22⋊Q8—91no—
309C3×C22⋊Q8—91no—
310C3×C22⋊Q8—91no—
311C3×C22⋊Q8—91no—
312C3×#117—91no—
313#944—31no—
314#936—31no—
315#935—31no—
316#929—31no—
317#896—31no—
318#896—31no—
319#888—31no—
320#888—31no—
321#886—31no—
322#885—31no—
323#885C3×D311yescharacteristic, complemented
324#883—31no—
325#883—31no—
326#883—31no—
327#883C3×D311yescharacteristic, complemented
328#878—31no—
329#878—31no—
330#878—31no—
331#878—31no—
332#878—31no—
333#878—31no—
334#878—61no—
335#877—31no—
336#872—31no—
337#869—31no—
338C23×C32—21no—
339C23×C32—21no—
340C23×C32—21no—
341C23×C32—31no—
342C23×C32—31no—
343C23×C32—41no—
344C23×C32C22×D311yescharacteristic
345C23×C32C22×D311yescharacteristic
346C23×C32C23×C311yescharacteristic
347C22×C3×D3—21no—
348C22×C3×D3—21no—
349C22×C3×D3C22×D311yescharacteristic
350C22×C3×D3C22×D311yescharacteristic
351C22×C3×D3C23×C311yescharacteristic
352C22×C3×D3C23×C311yescharacteristic
353C32×Q8—62no—
354C32×D4—62no—
355C32×D4—62no—
356C2×C32×C4—21no—
357C2×C32×C4—21no—
358C2×C32×C4—21no—
359C2×C32×C4—21no—
360C2×C32×C4—21no—
361C2×C32×C4—21no—
362C2×C32×C4—31no—
363C2×C32×C4—31no—
364C2×C32×C4—31no—
365C2×C32×C4—31no—
366C2×C32×C4—31no—
367C2×C32×C4—31no—
368C2×C32×C4—41no—
369C2×C32×C4—41no—
370C2×C32×C4—62no—
371C2×C32×C4C22×D311yescharacteristic
372C2×C32×C4C22×D311yescharacteristic
373C2×C32×C4C22×D311yescharacteristic
374C2×C32×C4C22×D311yescharacteristic
375C2×C32×C4C23×C311yescharacteristic
376C2×C32×C4C23×C311yescharacteristic
377C2×C3⋊Dic3—22no—
378C2×C3⋊Dic3C23×C311yescharacteristic
379C2×C3⋊Dic3C23×C311yescharacteristic
380C2×C3⋊Dic3C23×C311yescharacteristic
381C2×C3⋊Dic3C23×C311yescharacteristic
382#634—22no—
383C3×#67—22no—
384C3×#67—22no—
385C3×#67—22no—
386C3×#67—22no—
387C3×#67—42no—
388C3×#67—42no—
389C3×#67—62no—
390C3×#67—62no—
391C2×C3×Dic3—21no—
392C2×C3×Dic3—21no—
393C2×C3×Dic3—21no—
394C2×C3×Dic3—21no—
395C2×C3×Dic3—21no—
396C2×C3×Dic3—21no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—31no—
399C2×C3×Dic3—34no—
400C2×C3×Dic3—31no—
401C2×C3×Dic3—31no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—61no—
407C2×C3×Dic3—61no—
408C2×C3×Dic3—61no—
409C2×C3×Dic3—61no—
410C2×C3×Dic3—62no—
411C2×C3×Dic3—62no—
412C2×C3×Dic3—62no—
413C2×C3×Dic3—62no—
414C2×C3×Dic3—122no—
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C2×C3×Dic3C22×D311yescharacteristic
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C23×C311yescharacteristic
422C2×C3×Dic3C23×C311yescharacteristic
423C2×C3×Dic3C23×C311yescharacteristic
424C2×C3×Dic3C23×C311yescharacteristic
425C2×C3×Dic3C23×C311yescharacteristic
426C2×C3×Dic3C23×C311yescharacteristic
427C3×C4×D3—22no—
428C3×C4×D3—22no—
429C3×C4×D3—34no—
430C3×C4×D3—42no—
431C3×C4×D3—62no—
432C3×C4×D3—62no—
433C3×Dic6—22no—
434C3×Dic6—22no—
435C3×Dic6—42no—
436C3×Dic6—62no—
437C3×Dic6—62no—
438C3×Dic6—62no—
439C3×Dic6—62no—
440C3×Dic6—62no—
441C3×Dic6—62no—
442C3×Dic6—62no—
443C3×Dic6—62no—
444C3×Dic6—122no—
445#627—22no—
446#627—22no—
447#627—22no—
448#625—22no—
449D3×Dic3—22no—
450D3×Dic3—22no—
451D3×Dic3C3×D414yes—
452#536—91noSylow
453C2×C33—41no—
454C2×C33C22×D411yescharacteristic
455C2×C332−1+411yescharacteristic
456C2×C332−1+411yescharacteristic
457C32×D3—22no—
458C32×D3—41no—
459C3×#41—184no—
460C2×C3×Q8—31no—
461C2×C3×Q8—31no—
462C2×C3×Q8—61no—
463C2×C3×Q8—91no—
464C2×C3×Q8—91no—
465C2×C3×Q8—91no—
466C2×C3×Q8—91no—
467C2×C3×Q8—184no—
468C2×C3×D4—31no—
469C2×C3×D4—31no—
470C2×C3×D4—31no—
471C2×C3×D4—31no—
472C2×C3×D4—61no—
473C2×C3×D4—61no—
474C2×C3×D4—91no—
475C22×C3×C4—31no—
476C22×C3×C4—31no—
477C22×C3×C4—61no—
478C22×C3×C4—91no—
479C22×C3×C4—91no—
480C22×C3×C4—91no—
481C22×C3×C4—91no—
482C2×#67—31no—
483C2×#67—31no—
484C2×#67C2×C3×D311yescharacteristic
485C2×#67C2×C3×D311yescharacteristic
486C22×Dic3—31no—
487C22×Dic3—31no—
488C22×Dic3—31no—
489C22×Dic3—31no—
490C22×Dic3—31no—
491C22×Dic3—61no—
492D3×Q8—64no—
493#237—64no—
494#237—64no—
495C2×C4×D3—31no—
496C2×C4×D3—31no—
497C2×C4×D3—31no—
498C2×C4×D3C2×C3×D311yescharacteristic
499C2×Dic6—31no—
500C2×Dic6—31no—
501C2×Dic6—31no—
502C2×Dic6—31no—
503C2×Dic6—31no—
504C2×Dic6—31no—
505C2×Dic6—31no—
506C2×Dic6—31no—
507C2×Dic6—61no—
508C2×Dic6—64no—
509C2×Dic6C2×C3×D311yescharacteristic
510C3×C4⋊C4—31no—
511C3×C4⋊C4—31no—
512C3×C4⋊C4—31no—
513C3×C4⋊C4—31no—
514C3×C4⋊C4—61no—
515C3×C4⋊C4—61no—
516C3×C4⋊C4—91no—
517C3×C4⋊C4—91no—
518C3×C4⋊C4—91no—
519C3×C4⋊C4—91no—
520C3×C4⋊C4—91no—
521C3×C4⋊C4—91no—
522C3×C4⋊C4—91no—
523C3×C4⋊C4—91no—
524C3×C22⋊C4—21no—
525C3×C22⋊C4—21no—
526C3×C22⋊C4—21no—
527C3×C22⋊C4—31no—
528C3×C22⋊C4—31no—
529C3×C22⋊C4—31no—
530C3×C22⋊C4—31no—
531C3×C22⋊C4—31no—
532C3×C22⋊C4—31no—
533C3×C22⋊C4—31no—
534C3×C22⋊C4—31no—
535C3×C22⋊C4—31no—
536C3×C22⋊C4—31no—
537C3×C22⋊C4—41no—
538C3×C22⋊C4—61no—
539C3×C22⋊C4—61no—
540C3×C22⋊C4—61no—
541C3×C22⋊C4—61no—
542C3×C22⋊C4—61no—
543C3×C22⋊C4—91no—
544C3×C22⋊C4—91no—
545C3×C22⋊C4—91no—
546C3×C22⋊C4—91no—
547C3×C22⋊C4D3211yescharacteristic
548C3×C22⋊C4C2×C3×D311yescharacteristic
549C3×C22⋊C4C2×C3×D311yescharacteristic
550C3×C42—31no—
551C3×C42—31no—
552C3×C42—61no—
553C3×C42—91no—
554#217—31no—
555#217—31no—
556#217—31no—
557#217—31no—
558#217—31no—
559#217—61no—
560#217C2×C3×D311yescharacteristic
561#217C2×C3×D311yescharacteristic
562(C2×D3)⋊C4—31no—
563(C2×D3)⋊C4—31no—
564(C2×D3)⋊C4—31no—
565(C2×D3)⋊C4C2×C3×D311yescharacteristic
566(C2×D3)⋊C4C2×C3×D311yescharacteristic
567(C2×D3)⋊C4C2×C3×D311yescharacteristic
568C4⋊Dic3—31no—
569C4⋊Dic3—31no—
570C4⋊Dic3—31no—
571C4⋊Dic3—31no—
572C4⋊Dic3—31no—
573C4⋊Dic3—61no—
574C4⋊Dic3C2×C3×D311yescharacteristic
575Dic3⋊C4—31no—
576Dic3⋊C4—31no—
577Dic3⋊C4—31no—
578Dic3⋊C4—31no—
579Dic3⋊C4—31no—
580Dic3⋊C4—31no—
581Dic3⋊C4—31no—
582Dic3⋊C4—31no—
583Dic3⋊C4—31no—
584Dic3⋊C4—31no—
585Dic3⋊C4—31no—
586Dic3⋊C4—61no—
587Dic3⋊C4—61no—
588Dic3⋊C4C2×C3×D311yescharacteristic
589C4×Dic3—31no—
590C4×Dic3—31no—
591C4×Dic3C2×C3×D311yescharacteristic
592C22×C32—21no—
593C22×C32—22no—
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—21no—
603C22×C32—21no—
604C22×C32—21no—
605C22×C32—32no—
606C22×C32—41no—
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—61no—
617C22×C32—61no—
618C22×C32—61no—
619C22×C32—61no—
620C22×C32—61no—
621C22×C32—81no—
622C22×C32—81no—
623C22×C32C23×D311yescharacteristic
624C22×C32C23×D311yescharacteristic
625C22×C32C24×C311yescharacteristic
626C2×C3×D3—21no—
627C2×C3×D3—21no—
628C2×C3×D3—21no—
629C2×C3×D3—21no—
630C2×C3×D3—21no—
631C2×C3×D3—21no—
632C2×C3×D3—21no—
633C2×C3×D3—21no—
634C2×C3×D3—21no—
635C2×C3×D3—21no—
636C2×C3×D3—22no—
637C2×C3×D3—41no—
638C2×C3×D3—41no—
639C2×C3×D3—41no—
640C2×C3×D3—41no—
641C2×C3×D3—41no—
642C2×C3×D3D3×D412yes—
643C2×C3×D3C2×C3×D412yes—
644C32×C4—21no—
645C32×C4—21no—
646C32×C4—21no—
647C32×C4—21no—
648C32×C4—21no—
649C32×C4—21no—
650C32×C4—32no—
651C32×C4—41no—
652C32×C4—41no—
653C32×C4—41no—
654C32×C4—41no—
655C32×C4—41no—
656C32×C4—41no—
657C32×C4—61no—
658C32×C4—61no—
659C32×C4—61no—
660C32×C4—61no—
661C32×C4—61no—
662C32×C4—81no—
663C32×C4—81no—
664C3⋊Dic3—21no—
665C3⋊Dic3—21no—
666C3⋊Dic3—21no—
667C3⋊Dic3C2×C3×D412yes—
668C3×Dic3—21no—
669C3×Dic3—21no—
670C3×Dic3—21no—
671C3×Dic3—21no—
672C3×Dic3—21no—
673C3×Dic3—21no—
674C3×Dic3—21no—
675C3×Dic3—21no—
676C3×Dic3—21no—
677C3×Dic3—21no—
678C3×Dic3—22no—
679C3×Dic3—32no—
680C3×Dic3—32no—
681C3×Dic3—41no—
682C3×Dic3—41no—
683C3×Dic3—41no—
684C3×Dic3—41no—
685C3×Dic3—41no—
686C3×Dic3—62no—
687C3×Dic3—61no—
688C3×Dic3—61no—
689C3×Dic3—61no—
690C3×Dic3—61no—
691C3×Dic3—61no—
692C3×Dic3—61no—
693C3×Dic3—121no—
694C3×Dic3—121no—
695C3×Dic3—121no—
696C3×Dic3D3×D412yes—
697C3×Dic3C2×C3×D412yes—
698C2×#41—91no—
699C22×Q8—91no—
700C4⋊Q8—91no—
701C4⋊Q8—91no—
702#124—31no—
703#124—91no—
704#123—31no—
705#123—91no—
706#123—91no—
707#123—91no—
708C22⋊Q8—91no—
709C22⋊Q8—91no—
710C22⋊Q8—91no—
711C22⋊Q8—91no—
712#117—91no—
713C33#53611yescharacteristic, complemented, Sylow
714C23×C3—21no—
715C23×C3—21no—
716C23×C3—21no—
717C23×C3—31no—
718C23×C3—31no—
719C23×C3—31no—
720C23×C3—31no—
721C23×C3—41no—
722C23×C3—61no—
723C23×C3—61no—
724C23×C3C2×D3211yescharacteristic
725C23×C3C22×C3×D311yescharacteristic
726C23×C3C22×C3×D311yescharacteristic
727C22×D3C22×C3×D311yescharacteristic
728C22×D3C22×C3×D311yescharacteristic
729C3×Q8—62no—
730C3×Q8—62no—
731C3×Q8—122no—
732C3×Q8—182no—
733C3×Q8—182no—
734C3×Q8—182no—
735C3×Q8—182no—
736C3×D4—62no—
737C3×D4—62no—
738C3×D4—62no—
739C3×D4—62no—
740C3×D4—122no—
741C3×D4—122no—
742C3×D4—182no—
743C2×C3×C4—21no—
744C2×C3×C4—21no—
745C2×C3×C4—21no—
746C2×C3×C4—21no—
747C2×C3×C4—21no—
748C2×C3×C4—21no—
749C2×C3×C4—31no—
750C2×C3×C4—31no—
751C2×C3×C4—31no—
752C2×C3×C4—31no—
753C2×C3×C4—31no—
754C2×C3×C4—31no—
755C2×C3×C4—31no—
756C2×C3×C4—31no—
757C2×C3×C4—31no—
758C2×C3×C4—31no—
759C2×C3×C4—31no—
760C2×C3×C4—31no—
761C2×C3×C4—41no—
762C2×C3×C4—41no—
763C2×C3×C4—61no—
764C2×C3×C4—61no—
765C2×C3×C4—61no—
766C2×C3×C4—61no—
767C2×C3×C4—61no—
768C2×C3×C4—61no—
769C2×C3×C4—62no—
770C2×C3×C4—62no—
771C2×C3×C4—94no—
772C2×C3×C4—91no—
773C2×C3×C4—91no—
774C2×C3×C4—91no—
775C2×C3×C4—91no—
776C2×C3×C4—122no—
777C2×C3×C4—182no—
778C2×C3×C4—182no—
779C2×C3×C4—182no—
780C2×C3×C4C2×D3211yescharacteristic
781C2×C3×C4C2×D3211yescharacteristic
782C2×C3×C4C22×C3×D311yescharacteristic
783C2×C3×C4C22×C3×D311yescharacteristic
784C2×C3×C4C22×C3×D311yescharacteristic
785C2×C3×C4C22×C3×D311yescharacteristic
786#67—22no—
787#67—22no—
788#67—62no—
789#67—62no—
790C2×Dic3—31no—
791C2×Dic3—31no—
792C2×Dic3—34no—
793C2×Dic3—31no—
794C2×Dic3—31no—
795C2×Dic3—31no—
796C2×Dic3—31no—
797C2×Dic3—31no—
798C2×Dic3—31no—
799C2×Dic3—61no—
800C2×Dic3—61no—
801C2×Dic3—61no—
802C2×Dic3—61no—
803C2×Dic3—62no—
804C2×Dic3—62no—
805C2×Dic3—62no—
806C2×Dic3—62no—
807C2×Dic3—122no—
808C2×Dic3C22×C3×D311yescharacteristic
809C2×Dic3C22×C3×D311yescharacteristic
810C2×Dic3C22×C3×D311yescharacteristic
811C2×Dic3C22×C3×D311yescharacteristic
812C2×Dic3C22×C3×D311yescharacteristic
813C2×Dic3C22×C3×D311yescharacteristic
814C4×D3—22no—
815C4×D3—34no—
816C4×D3—62no—
817C4×D3—62no—
818Dic6—22no—
819Dic6—62no—
820Dic6—62no—
821Dic6—62no—
822Dic6—62no—
823Dic6—62no—
824Dic6—62no—
825Dic6—62no—
826Dic6—62no—
827Dic6—122no—
828C2×C32—21no—
829C2×C32—21no—
830C2×C32—21no—
831C2×C32—21no—
832C2×C32—21no—
833C2×C32—21no—
834C2×C32—21no—
835C2×C32—21no—
836C2×C32—21no—
837C2×C32—41no—
838C2×C32—41no—
839C2×C32—41no—
840C2×C32—41no—
841C2×C32—42no—
842C2×C32—41no—
843C2×C32—41no—
844C2×C32—62no—
845C2×C32—81no—
846C2×C32—81no—
847C2×C32—82no—
848C2×C32—121no—
849C2×C32C2×D3×D411yescharacteristic
850C2×C32C2×D3×D411yescharacteristic
851C2×C32#101011yescharacteristic
852C2×C32#101011yescharacteristic
853C2×C32#101011yescharacteristic
854C2×C32#101011yescharacteristic
855C2×C32C22×C3×D411yescharacteristic
856C2×C32C3×2−1+411yescharacteristic
857C2×C32C3×2−1+411yescharacteristic
858C3×D3—22no—
859C3×D3—22no—
860C3×D3—42no—
861C3×D3—41no—
862C3×D3—41no—
863C3×D3—81no—
864#41—184no—
865C2×Q8—31no—
866C2×Q8—91no—
867C2×Q8—91no—
868C2×Q8—91no—
869C2×Q8—91no—
870C2×Q8—184no—
871C2×D4—31no—
872C2×D4—31no—
873C2×D4—91no—
874C22×C4—31no—
875C22×C4—91no—
876C22×C4—91no—
877C22×C4—91no—
878C22×C4—91no—
879C4⋊C4—31no—
880C4⋊C4—31no—
881C4⋊C4—91no—
882C4⋊C4—91no—
883C4⋊C4—91no—
884C4⋊C4—91no—
885C4⋊C4—91no—
886C4⋊C4—91no—
887C4⋊C4—91no—
888C4⋊C4—91no—
889C22⋊C4—31no—
890C22⋊C4—31no—
891C22⋊C4—31no—
892C22⋊C4—31no—
893C22⋊C4—31no—
894C22⋊C4—91no—
895C22⋊C4—91no—
896C22⋊C4—91no—
897C22⋊C4—91no—
898C22⋊C4C3×D3211yescharacteristic
899C42—31no—
900C42—91no—
901C22×C3—22no—
902C22×C3—21no—
903C22×C3—21no—
904C22×C3—21no—
905C22×C3—21no—
906C22×C3—21no—
907C22×C3—21no—
908C22×C3—21no—
909C22×C3—21no—
910C22×C3—21no—
911C22×C3—21no—
912C22×C3—21no—
913C22×C3—21no—
914C22×C3—32no—
915C22×C3—32no—
916C22×C3—41no—
917C22×C3—41no—
918C22×C3—41no—
919C22×C3—41no—
920C22×C3—41no—
921C22×C3—41no—
922C22×C3—41no—
923C22×C3—41no—
924C22×C3—42no—
925C22×C3—41no—
926C22×C3—62no—
927C22×C3—61no—
928C22×C3—61no—
929C22×C3—61no—
930C22×C3—61no—
931C22×C3—61no—
932C22×C3—61no—
933C22×C3—61no—
934C22×C3—61no—
935C22×C3—61no—
936C22×C3—61no—
937C22×C3—81no—
938C22×C3—81no—
939C22×C3—121no—
940C22×C3—121no—
941C22×C3—121no—
942C22×C3—121no—
943C22×C3—121no—
944C22×C3C22×D3211yescharacteristic
945C22×C3C23×C3×D311yescharacteristic
946C22×C3C23×C3×D311yescharacteristic
947C2×D3—21no—
948C2×D3—21no—
949C2×D3—21no—
950C2×D3—21no—
951C2×D3—21no—
952C2×D3C3×D3×D412yes—
953C3×C4—21no—
954C3×C4—21no—
955C3×C4—21no—
956C3×C4—21no—
957C3×C4—21no—
958C3×C4—21no—
959C3×C4—32no—
960C3×C4—32no—
961C3×C4—41no—
962C3×C4—41no—
963C3×C4—41no—
964C3×C4—41no—
965C3×C4—41no—
966C3×C4—41no—
967C3×C4—62no—
968C3×C4—61no—
969C3×C4—61no—
970C3×C4—61no—
971C3×C4—61no—
972C3×C4—61no—
973C3×C4—61no—
974C3×C4—61no—
975C3×C4—61no—
976C3×C4—61no—
977C3×C4—61no—
978C3×C4—81no—
979C3×C4—81no—
980C3×C4—92no—
981C3×C4—121no—
982C3×C4—121no—
983C3×C4—121no—
984C3×C4—121no—
985C3×C4—121no—
986C3×C4—181no—
987C3×C4—181no—
988C3×C4—181no—
989Dic3—21no—
990Dic3—21no—
991Dic3—21no—
992Dic3—21no—
993Dic3—21no—
994Dic3—32no—
995Dic3—32no—
996Dic3—62no—
997Dic3—61no—
998Dic3—61no—
999Dic3—61no—
1000Dic3—61no—
1001Dic3—61no—
1002Dic3—61no—
1003Dic3—121no—
1004Dic3—121no—
1005Dic3—121no—
1006Dic3C3×D3×D412yes—
1007C32—21no—
1008C32—21no—
1009C32—21no—
1010C32—41no—
1011C32#564811yescharacteristic, complemented
1012C32#567511yescharacteristic, complemented
1013C32C3×#53611yescharacteristic, complemented
1014C23—31no—
1015C23—31no—
1016C23C2×C3×D3211yescharacteristic
1017Q8—62no—
1018Q8—182no—
1019Q8—182no—
1020Q8—182no—
1021Q8—182no—
1022D4—62no—
1023D4—62no—
1024D4—182no—
1025C2×C4—31no—
1026C2×C4—31no—
1027C2×C4—31no—
1028C2×C4—31no—
1029C2×C4—31no—
1030C2×C4—31no—
1031C2×C4—62no—
1032C2×C4—94no—
1033C2×C4—91no—
1034C2×C4—91no—
1035C2×C4—91no—
1036C2×C4—91no—
1037C2×C4—182no—
1038C2×C4—182no—
1039C2×C4—182no—
1040C2×C4C2×C3×D3211yescharacteristic
1041C2×C4C2×C3×D3211yescharacteristic
1042C2×C3—21no—
1043C2×C3—21no—
1044C2×C3—21no—
1045C2×C3—21no—
1046C2×C3—21no—
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—21no—
1051C2×C3—42no—
1052C2×C3—41no—
1053C2×C3—41no—
1054C2×C3—41no—
1055C2×C3—41no—
1056C2×C3—41no—
1057C2×C3—41no—
1058C2×C3—62no—
1059C2×C3—62no—
1060C2×C3—81no—
1061C2×C3—81no—
1062C2×C3—82no—
1063C2×C3—122no—
1064C2×C3—121no—
1065C2×C3—121no—
1066C2×C3—241no—
1067C2×C3#6429811yescharacteristic
1068C2×C3#6430911yescharacteristic
1069C2×C3D32×D411yescharacteristic
1070C2×C3C2×C3×D3×D411yescharacteristic
1071C2×C3C2×C3×D3×D411yescharacteristic
1072C2×C3C3×#101011yescharacteristic
1073C2×C3C3×#101011yescharacteristic
1074C2×C3C3×#101011yescharacteristic
1075C2×C3C3×#101011yescharacteristic
1076D3—22no—
1077D3—41no—
1078C22—21no—
1079C22—21no—
1080C22—21no—
1081C22—32no—
1082C22—61no—
1083C22—61no—
1084C22—61no—
1085C22—61no—
1086C22—61no—
1087C22C22×C3×D3211yescharacteristic
1088C4—21no—
1089C4—21no—
1090C4—32no—
1091C4—61no—
1092C4—61no—
1093C4—61no—
1094C4—61no—
1095C4—61no—
1096C4—92no—
1097C4—181no—
1098C4—181no—
1099C4—181no—
1100C3—21no—
1101C3—21no—
1102C3—21no—
1103C3—41no—
1104C3#1059405711yescharacteristic, direct product factor
1105C3C3×#564811yescharacteristic, complemented
1106C3C3×#567511yescharacteristic, complemented
1107C2—41no—
1108C2—62no—
1109C2—121no—
1110C2C3×#6429811yescharacteristic
1111C2C3×#6430911yescharacteristic
1112C2C3×D32×D411yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C22⋊C4C22
socleC22×C33C24
prime radicalC2×C3×#3805C2
hypercenterC3×C22⋊C4D32
hypocenterC32C3×#536
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×Dic6C2semidirect
3. C3×#64087C2semidirect
4. C32×#885C2semidirect
5. C32×#883C2semidirect
6. C3×#63982C2semidirect
7. C3×#63969C2semidirect
8. C3×#63959C2semidirect
9. C3×#63918C2semidirect
10. C3×#63905C2semidirect
11. C3×#63899C2semidirect
12. C3×#63896C2semidirect
13. C3×#63891C2semidirect
14. C3×#63877C2semidirect
15. C3×#63839C2semidirect
18. #10594057C3direct (N × H)
61. C2×D3×Dic6C2×C3semidirect
64. #64087C2×C3semidirect
76. C3×#885D3semidirect
77. C3×#885C2×C3semidirect
82. C3×#883D3semidirect
83. C3×#883C2×C3semidirect
94. #63982C2×C3semidirect
95. #63969C2×C3semidirect
96. #63959C2×C3semidirect
97. #63918C2×C3semidirect
98. #63905C2×C3semidirect
99. #63899C2×C3semidirect
100. #63896C2×C3semidirect
101. #63891C2×C3semidirect
102. #63877C2×C3semidirect
103. #63839C2×C3semidirect
323. #885C3×D3semidirect
327. #883C3×D3semidirect
713. C33#536semidirect
1011. C32#5648semidirect
1012. C32#5675semidirect
1013. C32C3×#536semidirect
1104. C3#10594057direct (N × H)
1105. C3C3×#5648semidirect
1106. C3C3×#5675semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38052
C2×C3×D3×Dic62
C3×#640872
C32×#8852
C32×#8832
C3×#639822
C3×#639692
C3×#639592
C3×#639182
C3×#639052
C3×#638992
C3×#638962
C3×#638912
C3×#638772
C3×#638392
C3×#56753
C3×#56483
#105940573