Finite Group Databasebeta

← C3×#10595509 #13175100

Subgroups — C3×#10595509 #13175100

Order 1728.

1520 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3757C211yesmaximal, characteristic, complemented
2C32×#953C211yesmaximal, characteristic
3C2×C32×#217C211yesmaximal, characteristic, complemented
4C3×#63982C211yesmaximal, characteristic, complemented
5C3×#67⋊Dic3C211yesmaximal, characteristic, complemented
6C3×Dic3×#67C211yesmaximal, characteristic, complemented
7C3×#63969C211yesmaximal, characteristic, complemented
8C3×#63964C211yesmaximal, characteristic, complemented
9C3×#63962C211yesmaximal, characteristic, complemented
10C3×#63961C211yesmaximal, characteristic, complemented
11C3×#63959C211yesmaximal, characteristic, complemented
12C3×#63957C211yesmaximal, characteristic, complemented
13C3×#63956C211yesmaximal, characteristic, complemented
14C3×#63956C211yesmaximal, characteristic, complemented
15C3×#63955C211yesmaximal, characteristic, complemented
16C3×#5587—31nomaximal
17C3×#5495—31nomaximal
18#10595509C311yesmaximal, characteristic, direct product factor
19C24×C33C2211yescharacteristic
20C22×C3×C3⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C22×C32×Dic3C2211yescharacteristic
26C22×C32×Dic3C2211yescharacteristic
27C2×C3×#627C2211yescharacteristic, complemented
28C2×C3×D3×Dic3C2211yescharacteristic, complemented
29C3×#3757C2211yescharacteristic
30C3×#3757C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32C3×#3757C2211yescharacteristic
33C32×#217C2211yescharacteristic
34C32×#217C2211yescharacteristic
35C32×#217C2211yescharacteristic
36C32×#217C2211yescharacteristic
37C32×#217C2211yescharacteristic
38C32×#217C2211yescharacteristic
39C32×#217C2211yescharacteristic
40C3×#3724C2211yescharacteristic, complemented
41C3×#3724C2211yescharacteristic, complemented
42C3×#3724C2211yescharacteristic, complemented
43C3×Dic3⋊Dic3C2211yescharacteristic, complemented
44C3×Dic3⋊Dic3C2211yescharacteristic, complemented
45C3×Dic3⋊Dic3C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
49C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
50C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
51C3×Dic32C2211yescharacteristic, complemented
52C3×Dic32C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54C32×#120—31no—
55C2×C32×C22⋊C4—31no—
56C2×#3757C2×C311yescharacteristic, complemented
57C3×#953—21no—
58C3×#953D311yescharacteristic
59C3×#953C2×C311yescharacteristic
60C2×C3×#217—21no—
61C2×C3×#217—31no—
62C2×C3×#217—31no—
63C2×C3×#217—61no—
64C2×C3×#217D311yescharacteristic, complemented
65C2×C3×#217C2×C311yescharacteristic, complemented
66C3×#936—31no—
67C3×#935—31no—
68C3×#935—31no—
69C3×#935—31no—
70C3×D4×Dic3—31no—
71C3×D4×Dic3—31no—
72C3×#929—31no—
73C3×C4×#67—31no—
74C3×#926—31no—
75C3×#924—31no—
76C3×#886—31no—
77C3×#885—31no—
78C3×#883—31no—
79C3×#67⋊C4—31no—
80C3×#879—31no—
81C3×#879—31no—
82C3×#879—31no—
83C3×#879—31no—
84C3×#878—31no—
85C3×#878—31no—
86C3×#878—31no—
87C3×#877—31no—
88C3×#877—31no—
89C3×#877—31no—
90#63982C2×C311yescharacteristic, complemented
91#67⋊Dic3C2×C311yescharacteristic, complemented
92Dic3×#67C2×C311yescharacteristic, complemented
93#63969C2×C311yescharacteristic, complemented
94#63964C2×C311yescharacteristic, complemented
95#63962C2×C311yescharacteristic, complemented
96#63961C2×C311yescharacteristic, complemented
97#63959C2×C311yescharacteristic, complemented
98#63957C2×C311yescharacteristic, complemented
99#63956C2×C311yescharacteristic, complemented
100#63956C2×C311yescharacteristic, complemented
101#63955C2×C311yescharacteristic, complemented
102C23×C33—22no—
103C23×C33—22no—
104C23×C33—41no—
105C23×C33C2311yescharacteristic
106C23×C33C2311yescharacteristic
107C23×C33C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×C3×C3⋊Dic3—22no—
110C2×C3×C3⋊Dic3—41no—
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C32×#67—22no—
116C32×#67—22no—
117C32×#67—41no—
118C2×C32×Dic3—22no—
119C2×C32×Dic3—41no—
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127C3×#627—41no—
128C3×D3×Dic3—41no—
129C3×#551—91no—
130#5587—31no—
131#5495—31no—
132C24×C32—21no—
133C24×C32—21no—
134C24×C32—21no—
135C24×C32—41no—
136C24×C32C2×D311yescharacteristic
137C24×C32C2×D311yescharacteristic
138C24×C32C22×C311yescharacteristic
139C2×C32×D4—31no—
140C2×C32×D4—31no—
141C2×C32×D4—31no—
142C22×C32×C4—31no—
143C22×C32×C4—31no—
144C22×C3⋊Dic3C22×C311yescharacteristic
145C22×C3⋊Dic3C22×C311yescharacteristic
146C2×C3×#67—21no—
147C2×C3×#67—21no—
148C2×C3×#67—21no—
149C2×C3×#67C2×D311yescharacteristic
150C2×C3×#67C2×D311yescharacteristic
151C2×C3×#67C2×D311yescharacteristic
152C2×C3×#67C22×C311yescharacteristic
153C2×C3×#67C22×C311yescharacteristic
154C2×C3×#67C22×C311yescharacteristic
155C22×C3×Dic3—21no—
156C22×C3×Dic3—21no—
157C22×C3×Dic3—31no—
158C22×C3×Dic3—31no—
159C22×C3×Dic3—31no—
160C22×C3×Dic3—31no—
161C22×C3×Dic3—31no—
162C22×C3×Dic3—61no—
163C22×C3×Dic3—61no—
164C22×C3×Dic3C2×D311yescharacteristic
165C22×C3×Dic3C2×D311yescharacteristic
166C22×C3×Dic3C22×C311yescharacteristic
167C22×C3×Dic3C22×C311yescharacteristic
168C2×C3×C4×D3—31no—
169C2×C3×Dic6—31no—
170C2×C3×Dic6—31no—
171C2×#627C22×C311yescharacteristic, complemented
172C2×D3×Dic3C22×C311yescharacteristic, complemented
173C32×C22⋊C4—31no—
174C32×C22⋊C4—31no—
175C32×C22⋊C4—31no—
176C32×C22⋊C4—31no—
177C32×C22⋊C4—31no—
178C32×C22⋊C4—31no—
179C32×C22⋊C4—31no—
180#3757C22×C311yescharacteristic
181#3757C22×C311yescharacteristic
182#3757C22×C311yescharacteristic
183#3757C22×C311yescharacteristic
184C3×#217—21no—
185C3×#217—21no—
186C3×#217—21no—
187C3×#217—21no—
188C3×#217—21no—
189C3×#217—21no—
190C3×#217—21no—
191C3×#217—31no—
192C3×#217—31no—
193C3×#217—31no—
194C3×#217—31no—
195C3×#217—31no—
196C3×#217—31no—
197C3×#217—31no—
198C3×#217—31no—
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—31no—
202C3×#217—61no—
203C3×#217—61no—
204C3×#217—61no—
205C3×#217—61no—
206C3×#217C2×D311yescharacteristic
207C3×#217C2×D311yescharacteristic
208C3×#217C2×D311yescharacteristic
209C3×#217C2×D311yescharacteristic
210C3×#217C2×D311yescharacteristic
211C3×#217C2×D311yescharacteristic
212C3×#217C2×D311yescharacteristic
213C3×#217C22×C311yescharacteristic
214C3×#217C22×C311yescharacteristic
215C3×#217C22×C311yescharacteristic
216C3×#217C22×C311yescharacteristic
217C3×#217C22×C311yescharacteristic
218C3×#217C22×C311yescharacteristic
219C3×#217C22×C311yescharacteristic
220C3×(C2×D3)⋊C4—31no—
221C3×(C2×D3)⋊C4—31no—
222C3×(C2×D3)⋊C4—31no—
223C3×C4⋊Dic3—31no—
224C3×C4⋊Dic3—31no—
225C3×C4⋊Dic3—31no—
226C3×C4⋊Dic3—31no—
227C3×C4⋊Dic3—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—31no—
237C3×Dic3⋊C4—31no—
238C3×Dic3⋊C4—31no—
239C3×C4×Dic3—31no—
240C3×C4×Dic3—31no—
241C3×C4×Dic3—31no—
242C3×C4×Dic3—31no—
243C3×C4×Dic3—31no—
244C3×C4×Dic3—31no—
245#3724C22×C311yescharacteristic, complemented
246#3724C22×C311yescharacteristic, complemented
247#3724C22×C311yescharacteristic, complemented
248Dic3⋊Dic3C22×C311yescharacteristic, complemented
249Dic3⋊Dic3C22×C311yescharacteristic, complemented
250Dic3⋊Dic3C22×C311yescharacteristic, complemented
251Dic3⋊Dic3C22×C311yescharacteristic, complemented
252Dic3⋊Dic3C22×C311yescharacteristic, complemented
253(C2×D3)⋊Dic3C22×C311yescharacteristic, complemented
254(C2×D3)⋊Dic3C22×C311yescharacteristic, complemented
255(C2×D3)⋊Dic3C22×C311yescharacteristic, complemented
256Dic32C22×C311yescharacteristic, complemented
257Dic32C22×C311yescharacteristic, complemented
258Dic32C22×C311yescharacteristic, complemented
259C22×C33—21no—
260C22×C33—21no—
261C22×C33—21no—
262C22×C33—21no—
263C22×C33—21no—
264C22×C33—21no—
265C22×C33—21no—
266C22×C33—44no—
267C22×C33#4112yes—
268C22×C33#4112yes—
269C22×C33C2411yescharacteristic
270C2×C32×D3—21no—
271C2×C32×D3—21no—
272C2×C32×D3—21no—
273C3×C3⋊Dic3—21no—
274C3×C3⋊Dic3—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C32×Dic3—21no—
278C32×Dic3—21no—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C3×#126—91no—
285C3×#126—91no—
286C3×#124—91no—
287C3×#123—91no—
288C3×#123—91no—
289C3×#123—91no—
290C3×C22⋊Q8—91no—
291C3×C22⋊Q8—91no—
292C3×#120—31no—
293C3×#120—31no—
294C3×#120—61no—
295C3×C4×D4—91no—
296C3×C4×D4—91no—
297C3×#117—91no—
298C3×#117—91no—
299C2×C3×C22⋊C4—31no—
300C2×C3×C22⋊C4—31no—
301C2×C3×C22⋊C4—61no—
302C2×C3×C22⋊C4—91no—
303#953C3×D311yescharacteristic
304C2×#217—31no—
305C2×#217—31no—
306C2×#217—61no—
307C2×#217C3×D311yescharacteristic, complemented
308#936—31no—
309#935—31no—
310#935—31no—
311#935—31no—
312D4×Dic3—31no—
313D4×Dic3—31no—
314#929—31no—
315C4×#67—31no—
316#926—31no—
317#924—31no—
318#886—31no—
319#885—31no—
320#883—31no—
321#67⋊C4—31no—
322#879—31no—
323#879—31no—
324#879—31no—
325#879—31no—
326#878—31no—
327#878—31no—
328#878—31no—
329#877—31no—
330#877—31no—
331#877—31no—
332C23×C32—22no—
333C23×C32—22no—
334C23×C32—24no—
335C23×C32—24no—
336C23×C32—22no—
337C23×C32—22no—
338C23×C32—22no—
339C23×C32—22no—
340C23×C32—21no—
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—31no—
350C23×C32—41no—
351C23×C32—41no—
352C23×C32—41no—
353C23×C32—42no—
354C23×C32—42no—
355C23×C32—42no—
356C23×C32—42no—
357C23×C32—44no—
358C23×C32—44no—
359C23×C32—41no—
360C23×C32—41no—
361C23×C32—41no—
362C23×C32—42no—
363C23×C32—42no—
364C23×C32—42no—
365C23×C32—44no—
366C23×C32C22×D311yescharacteristic
367C23×C32C22×D311yescharacteristic
368C23×C32C22×D311yescharacteristic
369C23×C32C22×D311yescharacteristic
370C23×C32C22×D311yescharacteristic
371C23×C32C22×D311yescharacteristic
372C23×C32C23×C311yescharacteristic
373C23×C32C23×C311yescharacteristic
374C23×C32C23×C311yescharacteristic
375C22×C3×D3—21no—
376C22×C3×D3C22×D311yescharacteristic
377C22×C3×D3C23×C311yescharacteristic
378C32×D4—62no—
379C32×D4—62no—
380C32×D4—121no—
381C2×C32×C4—31no—
382C2×C32×C4—31no—
383C2×C32×C4—31no—
384C2×C32×C4—31no—
385C2×C32×C4—31no—
386C2×C32×C4—31no—
387C2×C32×C4—31no—
388C2×C32×C4—62no—
389C2×C32×C4—121no—
390C2×C3⋊Dic3—22no—
391C2×C3⋊Dic3—41no—
392C2×C3⋊Dic3C23×C311yescharacteristic
393C2×C3⋊Dic3C23×C311yescharacteristic
394C2×C3⋊Dic3C23×C311yescharacteristic
395C2×C3⋊Dic3C23×C311yescharacteristic
396C3×#67—22no—
397C3×#67—22no—
398C3×#67—22no—
399C3×#67—22no—
400C3×#67—42no—
401C3×#67—42no—
402C3×#67—41no—
403C3×#67—41no—
404C3×#67—42no—
405C2×C3×Dic3—22no—
406C2×C3×Dic3—22no—
407C2×C3×Dic3—21no—
408C2×C3×Dic3—21no—
409C2×C3×Dic3—21no—
410C2×C3×Dic3—21no—
411C2×C3×Dic3—21no—
412C2×C3×Dic3—21no—
413C2×C3×Dic3—21no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—31no—
417C2×C3×Dic3—31no—
418C2×C3×Dic3—31no—
419C2×C3×Dic3—31no—
420C2×C3×Dic3—31no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—42no—
423C2×C3×Dic3—41no—
424C2×C3×Dic3—41no—
425C2×C3×Dic3—42no—
426C2×C3×Dic3—61no—
427C2×C3×Dic3—61no—
428C2×C3×Dic3—61no—
429C2×C3×Dic3—61no—
430C2×C3×Dic3—62no—
431C2×C3×Dic3—62no—
432C2×C3×Dic3—122no—
433C2×C3×Dic3—121no—
434C2×C3×Dic3—121no—
435C2×C3×Dic3—121no—
436C2×C3×Dic3—122no—
437C2×C3×Dic3C22×D311yescharacteristic
438C2×C3×Dic3C22×D311yescharacteristic
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C2×C3×Dic3C22×D311yescharacteristic
443C2×C3×Dic3C22×D311yescharacteristic
444C2×C3×Dic3C23×C311yescharacteristic
445C2×C3×Dic3C23×C311yescharacteristic
446C2×C3×Dic3C23×C311yescharacteristic
447C2×C3×Dic3C23×C311yescharacteristic
448C2×C3×Dic3C23×C311yescharacteristic
449C2×C3×Dic3C23×C311yescharacteristic
450C2×C3×Dic3C23×C311yescharacteristic
451C3×C4×D3—121no—
452C3×Dic6—121no—
453C3×Dic6—121no—
454#627—41no—
455D3×Dic3—41no—
456#551—91noSylow
457C2×C33—22no—
458C2×C33—22no—
459C2×C33—41no—
460C2×C33C2×#4111yescharacteristic
461C2×C33C2×#4111yescharacteristic
462C2×C33H(5,𝔽2)11yescharacteristic
463C32×D3—41no—
464C24×C3—21no—
465C24×C3—21no—
466C24×C3—21no—
467C24×C3—41no—
468C24×C3D3211yescharacteristic
469C24×C3C2×C3×D311yescharacteristic
470C24×C3C2×C3×D311yescharacteristic
471C2×C3×Q8—91no—
472C2×C3×D4—31no—
473C2×C3×D4—31no—
474C2×C3×D4—31no—
475C2×C3×D4—31no—
476C2×C3×D4—31no—
477C2×C3×D4—31no—
478C2×C3×D4—61no—
479C2×C3×D4—61no—
480C2×C3×D4—61no—
481C22×C3×C4—31no—
482C22×C3×C4—31no—
483C22×C3×C4—31no—
484C22×C3×C4—31no—
485C22×C3×C4—61no—
486C22×C3×C4—61no—
487C22×C3×C4—91no—
488C22×C3×C4—91no—
489C22×C3×C4—91no—
490C2×#67C2×C3×D311yescharacteristic
491C2×#67C2×C3×D311yescharacteristic
492C2×#67C2×C3×D311yescharacteristic
493C22×Dic3—31no—
494C22×Dic3—31no—
495C22×Dic3—31no—
496C22×Dic3—31no—
497C22×Dic3—31no—
498C22×Dic3—61no—
499C22×Dic3—61no—
500C22×Dic3C2×C3×D311yescharacteristic
501C22×Dic3C2×C3×D311yescharacteristic
502C2×C4×D3—31no—
503C2×Dic6—31no—
504C2×Dic6—31no—
505C3×C4⋊C4—91no—
506C3×C4⋊C4—91no—
507C3×C4⋊C4—91no—
508C3×C4⋊C4—91no—
509C3×C4⋊C4—91no—
510C3×C4⋊C4—91no—
511C3×C4⋊C4—91no—
512C3×C4⋊C4—91no—
513C3×C22⋊C4—31no—
514C3×C22⋊C4—31no—
515C3×C22⋊C4—31no—
516C3×C22⋊C4—31no—
517C3×C22⋊C4—31no—
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—31no—
527C3×C22⋊C4—61no—
528C3×C22⋊C4—61no—
529C3×C22⋊C4—61no—
530C3×C22⋊C4—61no—
531C3×C22⋊C4—61no—
532C3×C22⋊C4—61no—
533C3×C22⋊C4—61no—
534C3×C22⋊C4—91no—
535C3×C22⋊C4—91no—
536C3×C22⋊C4—91no—
537C3×C22⋊C4—91no—
538C3×C22⋊C4—91no—
539C3×C22⋊C4—91no—
540C3×C22⋊C4—91no—
541C3×C42—91no—
542C3×C42—91no—
543C3×C42—91no—
544#217—31no—
545#217—31no—
546#217—31no—
547#217—31no—
548#217—31no—
549#217—31no—
550#217—31no—
551#217—31no—
552#217—31no—
553#217—31no—
554#217—31no—
555#217—61no—
556#217—61no—
557#217—61no—
558#217—61no—
559#217C2×C3×D311yescharacteristic
560#217C2×C3×D311yescharacteristic
561#217C2×C3×D311yescharacteristic
562#217C2×C3×D311yescharacteristic
563#217C2×C3×D311yescharacteristic
564#217C2×C3×D311yescharacteristic
565#217C2×C3×D311yescharacteristic
566(C2×D3)⋊C4—31no—
567(C2×D3)⋊C4—31no—
568(C2×D3)⋊C4—31no—
569C4⋊Dic3—31no—
570C4⋊Dic3—31no—
571C4⋊Dic3—31no—
572C4⋊Dic3—31no—
573C4⋊Dic3—31no—
574Dic3⋊C4—31no—
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—
585C4×Dic3—31no—
586C4×Dic3—31no—
587C4×Dic3—31no—
588C4×Dic3—31no—
589C4×Dic3—31no—
590C4×Dic3—31no—
591C22×C32—21no—
592C22×C32—21no—
593C22×C32—21no—
594C22×C32—21no—
595C22×C32—21no—
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—22no—
599C22×C32—22no—
600C22×C32—22no—
601C22×C32—22no—
602C22×C32—21no—
603C22×C32—21no—
604C22×C32—21no—
605C22×C32—21no—
606C22×C32—21no—
607C22×C32—21no—
608C22×C32—21no—
609C22×C32—21no—
610C22×C32—22no—
611C22×C32—22no—
612C22×C32—22no—
613C22×C32—21no—
614C22×C32—21no—
615C22×C32—21no—
616C22×C32—21no—
617C22×C32—21no—
618C22×C32—21no—
619C22×C32—21no—
620C22×C32—21no—
621C22×C32—21no—
622C22×C32—22no—
623C22×C32—22no—
624C22×C32—22no—
625C22×C32—22no—
626C22×C32—22no—
627C22×C32—22no—
628C22×C32—42no—
629C22×C32—42no—
630C22×C32—41no—
631C22×C32—41no—
632C22×C32—41no—
633C22×C32—41no—
634C22×C32—41no—
635C22×C32—41no—
636C22×C32—41no—
637C22×C32—41no—
638C22×C32—41no—
639C22×C32—41no—
640C22×C32—41no—
641C22×C32—41no—
642C22×C32—41no—
643C22×C32—41no—
644C22×C32—41no—
645C22×C32—42no—
646C22×C32—42no—
647C22×C32—42no—
648C22×C32—42no—
649C22×C32—42no—
650C22×C32—42no—
651C22×C32—42no—
652C22×C32—44no—
653C22×C32—44no—
654C22×C32—44no—
655C22×C32—48no—
656C22×C32—48no—
657C22×C32—48no—
658C22×C32—416no—
659C22×C32—61no—
660C22×C32—61no—
661C22×C32—61no—
662C22×C32#23512yes—
663C22×C32#23712yes—
664C22×C32#23712yes—
665C22×C32#23712yes—
666C22×C32C3×#4112yes—
667C22×C32C3×#4112yes—
668C22×C32C23×D311yescharacteristic
669C22×C32C23×D311yescharacteristic
670C22×C32C24×C311yescharacteristic
671C2×C3×D3—21no—
672C2×C3×D3—21no—
673C2×C3×D3—21no—
674C2×C3×D3—21no—
675C2×C3×D3—21no—
676C2×C3×D3—21no—
677C2×C3×D3—41no—
678C2×C3×D3—41no—
679C2×C3×D3—41no—
680C32×C4—61no—
681C32×C4—61no—
682C32×C4—61no—
683C32×C4—61no—
684C32×C4—61no—
685C32×C4—61no—
686C32×C4—61no—
687C3⋊Dic3—21no—
688C3⋊Dic3—21no—
689C3⋊Dic3—21no—
690C3⋊Dic3—21no—
691C3×Dic3—21no—
692C3×Dic3—21no—
693C3×Dic3—21no—
694C3×Dic3—21no—
695C3×Dic3—21no—
696C3×Dic3—21no—
697C3×Dic3—21no—
698C3×Dic3—21no—
699C3×Dic3—21no—
700C3×Dic3—21no—
701C3×Dic3—21no—
702C3×Dic3—21no—
703C3×Dic3—21no—
704C3×Dic3—21no—
705C3×Dic3—41no—
706C3×Dic3—41no—
707C3×Dic3—41no—
708C3×Dic3—41no—
709C3×Dic3—41no—
710C3×Dic3—41no—
711C3×Dic3—41no—
712C3×Dic3—61no—
713C3×Dic3—61no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—61no—
717C3×Dic3—61no—
718C3×Dic3—61no—
719C3×Dic3—61no—
720C3×Dic3—121no—
721C3×Dic3—121no—
722C3×Dic3—121no—
723C3×Dic3—121no—
724#126—91no—
725#126—91no—
726#124—91no—
727#123—91no—
728#123—91no—
729#123—91no—
730C22⋊Q8—91no—
731C22⋊Q8—91no—
732#120—31no—
733C4×D4—91no—
734C4×D4—91no—
735#117—91no—
736#117—91no—
737C2×C22⋊C4—31no—
738C2×C22⋊C4—91no—
739C33#55111yescharacteristic, complemented, Sylow
740C23×C3—24no—
741C23×C3—24no—
742C23×C3—22no—
743C23×C3—22no—
744C23×C3—22no—
745C23×C3—22no—
746C23×C3—22no—
747C23×C3—22no—
748C23×C3—21no—
749C23×C3—21no—
750C23×C3—21no—
751C23×C3—21no—
752C23×C3—21no—
753C23×C3—21no—
754C23×C3—21no—
755C23×C3—21no—
756C23×C3—21no—
757C23×C3—31no—
758C23×C3—31no—
759C23×C3—42no—
760C23×C3—42no—
761C23×C3—42no—
762C23×C3—42no—
763C23×C3—44no—
764C23×C3—44no—
765C23×C3—41no—
766C23×C3—41no—
767C23×C3—41no—
768C23×C3—42no—
769C23×C3—42no—
770C23×C3—42no—
771C23×C3—44no—
772C23×C3—41no—
773C23×C3—41no—
774C23×C3—41no—
775C23×C3—61no—
776C23×C3C2×D3211yescharacteristic
777C23×C3C2×D3211yescharacteristic
778C23×C3C2×D3211yescharacteristic
779C23×C3C22×C3×D311yescharacteristic
780C23×C3C22×C3×D311yescharacteristic
781C23×C3C22×C3×D311yescharacteristic
782C23×C3C22×C3×D311yescharacteristic
783C23×C3C22×C3×D311yescharacteristic
784C23×C3C22×C3×D311yescharacteristic
785C22×D3C22×C3×D311yescharacteristic
786C3×Q8—361no—
787C3×D4—62no—
788C3×D4—62no—
789C3×D4—62no—
790C3×D4—62no—
791C3×D4—122no—
792C3×D4—122no—
793C3×D4—121no—
794C3×D4—121no—
795C3×D4—122no—
796C2×C3×C4—31no—
797C2×C3×C4—31no—
798C2×C3×C4—31no—
799C2×C3×C4—31no—
800C2×C3×C4—31no—
801C2×C3×C4—31no—
802C2×C3×C4—31no—
803C2×C3×C4—31no—
804C2×C3×C4—31no—
805C2×C3×C4—31no—
806C2×C3×C4—31no—
807C2×C3×C4—31no—
808C2×C3×C4—31no—
809C2×C3×C4—31no—
810C2×C3×C4—61no—
811C2×C3×C4—61no—
812C2×C3×C4—61no—
813C2×C3×C4—61no—
814C2×C3×C4—61no—
815C2×C3×C4—61no—
816C2×C3×C4—61no—
817C2×C3×C4—62no—
818C2×C3×C4—62no—
819C2×C3×C4—91no—
820C2×C3×C4—91no—
821C2×C3×C4—91no—
822C2×C3×C4—91no—
823C2×C3×C4—122no—
824C2×C3×C4—121no—
825C2×C3×C4—121no—
826C2×C3×C4—122no—
827C2×C3×C4—182no—
828C2×C3×C4—361no—
829C2×C3×C4—361no—
830#67—22no—
831#67—22no—
832#67—41no—
833C2×Dic3—22no—
834C2×Dic3—31no—
835C2×Dic3—31no—
836C2×Dic3—31no—
837C2×Dic3—31no—
838C2×Dic3—31no—
839C2×Dic3—31no—
840C2×Dic3—31no—
841C2×Dic3—31no—
842C2×Dic3—41no—
843C2×Dic3—61no—
844C2×Dic3—61no—
845C2×Dic3—61no—
846C2×Dic3—61no—
847C2×Dic3—62no—
848C2×Dic3—62no—
849C2×Dic3—122no—
850C2×Dic3—121no—
851C2×Dic3—121no—
852C2×Dic3—121no—
853C2×Dic3—122no—
854C2×Dic3C22×C3×D311yescharacteristic
855C2×Dic3C22×C3×D311yescharacteristic
856C2×Dic3C22×C3×D311yescharacteristic
857C2×Dic3C22×C3×D311yescharacteristic
858C2×Dic3C22×C3×D311yescharacteristic
859C2×Dic3C22×C3×D311yescharacteristic
860C2×Dic3C22×C3×D311yescharacteristic
861C4×D3—121no—
862Dic6—121no—
863Dic6—121no—
864C2×C32—22no—
865C2×C32—22no—
866C2×C32—24no—
867C2×C32—24no—
868C2×C32—22no—
869C2×C32—22no—
870C2×C32—22no—
871C2×C32—22no—
872C2×C32—21no—
873C2×C32—21no—
874C2×C32—21no—
875C2×C32—21no—
876C2×C32—21no—
877C2×C32—21no—
878C2×C32—21no—
879C2×C32—21no—
880C2×C32—21no—
881C2×C32—41no—
882C2×C32—41no—
883C2×C32—41no—
884C2×C32—42no—
885C2×C32—42no—
886C2×C32—42no—
887C2×C32—42no—
888C2×C32—44no—
889C2×C32—44no—
890C2×C32—42no—
891C2×C32—42no—
892C2×C32—42no—
893C2×C32—44no—
894C2×C32—41no—
895C2×C32—41no—
896C2×C32—41no—
897C2×C32—121no—
898C2×C32C2×#23511yescharacteristic
899C2×C32C2×#23711yescharacteristic
900C2×C32C2×#23711yescharacteristic
901C2×C32C2×#23711yescharacteristic
902C2×C32#100411yescharacteristic
903C2×C32#100411yescharacteristic
904C2×C32C2×C3×#4111yescharacteristic
905C2×C32C2×C3×#4111yescharacteristic
906C2×C32C3×H(5,𝔽2)11yescharacteristic
907C3×D3—41no—
908C3×D3—41no—
909C3×D3—81no—
910C24C3×D3211yescharacteristic
911C2×Q8—91no—
912C2×D4—31no—
913C2×D4—31no—
914C2×D4—31no—
915C22×C4—31no—
916C22×C4—31no—
917C22×C4—91no—
918C22×C4—91no—
919C22×C4—91no—
920C4⋊C4—91no—
921C4⋊C4—91no—
922C4⋊C4—91no—
923C4⋊C4—91no—
924C4⋊C4—91no—
925C4⋊C4—91no—
926C4⋊C4—91no—
927C4⋊C4—91no—
928C22⋊C4—31no—
929C22⋊C4—31no—
930C22⋊C4—31no—
931C22⋊C4—31no—
932C22⋊C4—31no—
933C22⋊C4—31no—
934C22⋊C4—31no—
935C22⋊C4—91no—
936C22⋊C4—91no—
937C22⋊C4—91no—
938C22⋊C4—91no—
939C22⋊C4—91no—
940C22⋊C4—91no—
941C22⋊C4—91no—
942C42—91no—
943C42—91no—
944C42—91no—
945C22×C3—22no—
946C22×C3—22no—
947C22×C3—22no—
948C22×C3—22no—
949C22×C3—21no—
950C22×C3—21no—
951C22×C3—21no—
952C22×C3—21no—
953C22×C3—21no—
954C22×C3—21no—
955C22×C3—21no—
956C22×C3—21no—
957C22×C3—21no—
958C22×C3—21no—
959C22×C3—21no—
960C22×C3—21no—
961C22×C3—22no—
962C22×C3—22no—
963C22×C3—22no—
964C22×C3—21no—
965C22×C3—21no—
966C22×C3—21no—
967C22×C3—21no—
968C22×C3—21no—
969C22×C3—21no—
970C22×C3—21no—
971C22×C3—21no—
972C22×C3—21no—
973C22×C3—21no—
974C22×C3—21no—
975C22×C3—21no—
976C22×C3—22no—
977C22×C3—22no—
978C22×C3—22no—
979C22×C3—22no—
980C22×C3—22no—
981C22×C3—22no—
982C22×C3—41no—
983C22×C3—41no—
984C22×C3—41no—
985C22×C3—41no—
986C22×C3—41no—
987C22×C3—41no—
988C22×C3—41no—
989C22×C3—41no—
990C22×C3—41no—
991C22×C3—41no—
992C22×C3—41no—
993C22×C3—41no—
994C22×C3—41no—
995C22×C3—41no—
996C22×C3—42no—
997C22×C3—42no—
998C22×C3—42no—
999C22×C3—42no—
1000C22×C3—42no—
1001C22×C3—42no—
1002C22×C3—42no—
1003C22×C3—44no—
1004C22×C3—44no—
1005C22×C3—44no—
1006C22×C3—48no—
1007C22×C3—48no—
1008C22×C3—48no—
1009C22×C3—416no—
1010C22×C3—41no—
1011C22×C3—42no—
1012C22×C3—42no—
1013C22×C3—61no—
1014C22×C3—61no—
1015C22×C3—61no—
1016C22×C3—61no—
1017C22×C3—61no—
1018C22×C3—61no—
1019C22×C3—121no—
1020C22×C3—121no—
1021C22×C3—121no—
1022C22×C3#380412yes—
1023C22×C3#380512yes—
1024C22×C3C3×#23512yes—
1025C22×C3C3×#23712yes—
1026C22×C3C3×#23712yes—
1027C22×C3C3×#23712yes—
1028C22×C3C22×D3211yescharacteristic
1029C22×C3C23×C3×D311yescharacteristic
1030C22×C3C23×C3×D311yescharacteristic
1031C2×D3—21no—
1032C2×D3—21no—
1033C2×D3—21no—
1034C3×C4—61no—
1035C3×C4—61no—
1036C3×C4—61no—
1037C3×C4—61no—
1038C3×C4—61no—
1039C3×C4—61no—
1040C3×C4—61no—
1041C3×C4—61no—
1042C3×C4—61no—
1043C3×C4—61no—
1044C3×C4—61no—
1045C3×C4—61no—
1046C3×C4—61no—
1047C3×C4—61no—
1048C3×C4—121no—
1049C3×C4—121no—
1050C3×C4—121no—
1051C3×C4—121no—
1052C3×C4—121no—
1053C3×C4—121no—
1054C3×C4—121no—
1055C3×C4—181no—
1056C3×C4—181no—
1057C3×C4—181no—
1058C3×C4—181no—
1059Dic3—21no—
1060Dic3—21no—
1061Dic3—21no—
1062Dic3—21no—
1063Dic3—21no—
1064Dic3—21no—
1065Dic3—21no—
1066Dic3—61no—
1067Dic3—61no—
1068Dic3—61no—
1069Dic3—61no—
1070Dic3—61no—
1071Dic3—61no—
1072Dic3—61no—
1073Dic3—61no—
1074Dic3—121no—
1075Dic3—121no—
1076Dic3—121no—
1077Dic3—121no—
1078C32—21no—
1079C32—21no—
1080C32—21no—
1081C32—41no—
1082C32#549511yescharacteristic, complemented
1083C32#558711yescharacteristic, complemented
1084C32C3×#55111yescharacteristic, complemented
1085C23—22no—
1086C23—22no—
1087C23—31no—
1088C23—41no—
1089C23C2×C3×D3211yescharacteristic
1090C23C2×C3×D3211yescharacteristic
1091C23C2×C3×D3211yescharacteristic
1092Q8—361no—
1093D4—62no—
1094D4—62no—
1095D4—121no—
1096C2×C4—31no—
1097C2×C4—31no—
1098C2×C4—31no—
1099C2×C4—31no—
1100C2×C4—31no—
1101C2×C4—31no—
1102C2×C4—31no—
1103C2×C4—62no—
1104C2×C4—91no—
1105C2×C4—91no—
1106C2×C4—91no—
1107C2×C4—91no—
1108C2×C4—121no—
1109C2×C4—182no—
1110C2×C4—361no—
1111C2×C4—361no—
1112C2×C3—24no—
1113C2×C3—24no—
1114C2×C3—22no—
1115C2×C3—22no—
1116C2×C3—22no—
1117C2×C3—22no—
1118C2×C3—22no—
1119C2×C3—22no—
1120C2×C3—21no—
1121C2×C3—21no—
1122C2×C3—21no—
1123C2×C3—21no—
1124C2×C3—21no—
1125C2×C3—21no—
1126C2×C3—21no—
1127C2×C3—21no—
1128C2×C3—21no—
1129C2×C3—42no—
1130C2×C3—42no—
1131C2×C3—42no—
1132C2×C3—42no—
1133C2×C3—44no—
1134C2×C3—44no—
1135C2×C3—42no—
1136C2×C3—42no—
1137C2×C3—42no—
1138C2×C3—44no—
1139C2×C3—41no—
1140C2×C3—41no—
1141C2×C3—41no—
1142C2×C3—41no—
1143C2×C3—41no—
1144C2×C3—41no—
1145C2×C3—121no—
1146C2×C3—121no—
1147C2×C3—241no—
1148C2×C3C2×#380411yescharacteristic
1149C2×C3C2×#380511yescharacteristic
1150C2×C3#6433011yescharacteristic
1151C2×C3C2×C3×#23511yescharacteristic
1152C2×C3C2×C3×#23711yescharacteristic
1153C2×C3C2×C3×#23711yescharacteristic
1154C2×C3C2×C3×#23711yescharacteristic
1155C2×C3C3×#100411yescharacteristic
1156C2×C3C3×#100411yescharacteristic
1157D3—41no—
1158C22—21no—
1159C22—21no—
1160C22—21no—
1161C22—21no—
1162C22—21no—
1163C22—21no—
1164C22—21no—
1165C22—44no—
1166C22—61no—
1167C22—61no—
1168C22—61no—
1169C22C3×#380412yes—
1170C22C3×#380512yes—
1171C22C22×C3×D3211yescharacteristic
1172C4—61no—
1173C4—61no—
1174C4—61no—
1175C4—61no—
1176C4—61no—
1177C4—61no—
1178C4—61no—
1179C4—181no—
1180C4—181no—
1181C4—181no—
1182C4—181no—
1183C3—21no—
1184C3—21no—
1185C3—21no—
1186C3—41no—
1187C3#1059550911yescharacteristic, direct product factor
1188C3C3×#549511yescharacteristic, complemented
1189C3C3×#558711yescharacteristic, complemented
1190C2—22no—
1191C2—22no—
1192C2—41no—
1193C2—121no—
1194C2C2×C3×#380411yescharacteristic
1195C2C2×C3×#380511yescharacteristic
1196C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC24×C33C22
socleC22×C33C24
prime radicalC32×#953C2
hypercenterC24×C3D32
hypocenterC32C3×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C24×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3757C2semidirect
3. C2×C32×#217C2semidirect
4. C3×#63982C2semidirect
5. C3×#67⋊Dic3C2semidirect
6. C3×Dic3×#67C2semidirect
7. C3×#63969C2semidirect
8. C3×#63964C2semidirect
9. C3×#63962C2semidirect
10. C3×#63961C2semidirect
11. C3×#63959C2semidirect
12. C3×#63957C2semidirect
13. C3×#63956C2semidirect
14. C3×#63956C2semidirect
15. C3×#63955C2semidirect
18. #10595509C3direct (N × H)
27. C2×C3×#627C22semidirect
28. C2×C3×D3×Dic3C22semidirect
40. C3×#3724C22semidirect
41. C3×#3724C22semidirect
42. C3×#3724C22semidirect
43. C3×Dic3⋊Dic3C22semidirect
44. C3×Dic3⋊Dic3C22semidirect
45. C3×Dic3⋊Dic3C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
48. C3×(C2×D3)⋊Dic3C22semidirect
49. C3×(C2×D3)⋊Dic3C22semidirect
50. C3×(C2×D3)⋊Dic3C22semidirect
51. C3×Dic32C22semidirect
52. C3×Dic32C22semidirect
53. C3×Dic32C22semidirect
56. C2×#3757C2×C3semidirect
64. C2×C3×#217D3semidirect
65. C2×C3×#217C2×C3semidirect
90. #63982C2×C3semidirect
91. #67⋊Dic3C2×C3semidirect
92. Dic3×#67C2×C3semidirect
93. #63969C2×C3semidirect
94. #63964C2×C3semidirect
95. #63962C2×C3semidirect
96. #63961C2×C3semidirect
97. #63959C2×C3semidirect
98. #63957C2×C3semidirect
99. #63956C2×C3semidirect
100. #63956C2×C3semidirect
101. #63955C2×C3semidirect
171. C2×#627C22×C3semidirect
172. C2×D3×Dic3C22×C3semidirect
245. #3724C22×C3semidirect
246. #3724C22×C3semidirect
247. #3724C22×C3semidirect
248. Dic3⋊Dic3C22×C3semidirect
249. Dic3⋊Dic3C22×C3semidirect
250. Dic3⋊Dic3C22×C3semidirect
251. Dic3⋊Dic3C22×C3semidirect
252. Dic3⋊Dic3C22×C3semidirect
253. (C2×D3)⋊Dic3C22×C3semidirect
254. (C2×D3)⋊Dic3C22×C3semidirect
255. (C2×D3)⋊Dic3C22×C3semidirect
256. Dic32C22×C3semidirect
257. Dic32C22×C3semidirect
258. Dic32C22×C3semidirect
307. C2×#217C3×D3semidirect
739. C33#551semidirect
1082. C32#5495semidirect
1083. C32#5587semidirect
1084. C32C3×#551semidirect
1187. C3#10595509direct (N × H)
1188. C3C3×#5495semidirect
1189. C3C3×#5587semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37572
C32×#9532
C2×C32×#2172
C3×#639822
C3×#67⋊Dic32
C3×Dic3×#672
C3×#639692
C3×#639642
C3×#639622
C3×#639612
C3×#639592
C3×#639572
C3×#639562
C3×#639552
C3×#55873
C3×#54953
#105955093