Finite Group Databasebeta

← C3×#10595118 #13174756

Subgroups — C3×#10595118 #13174756

Order 1728.

1348 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64146C211yesmaximal, characteristic
2C32×#935C211yesmaximal, characteristic, complemented
3C32×D4×Dic3C211yesmaximal, characteristic, complemented
4C3×#63975C211yesmaximal, characteristic, complemented
5C3×#63974C211yesmaximal, characteristic, complemented
6C3×#63966C211yesmaximal, characteristic, complemented
7C3×#63964C211yesmaximal, characteristic, complemented
8C2×C3×#3722C211yesmaximal, characteristic, complemented
9C3×#63955C211yesmaximal, characteristic, complemented
10C3×#63953C211yesmaximal, characteristic, complemented
11C3×#63952C211yesmaximal, characteristic, complemented
12C3×#63895C211yesmaximal, characteristic, complemented
13C3×#63868C211yesmaximal, characteristic, complemented
14C3×#63848C211yesmaximal, characteristic, complemented
15C3×#63836C211yesmaximal, characteristic, complemented
16C3×#5658—31nomaximal
17C3×#5556—31nomaximal
18#10595118C311yesmaximal, characteristic, direct product factor
19C23×C3×C3⋊D3C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic
25C22×C32×Dic3C2211yescharacteristic, complemented
26C2×C3×#627C2211yescharacteristic, complemented
27C2×C3×#624C2211yescharacteristic
28C2×C3×#624C2211yescharacteristic
29C3×#3757C2211yescharacteristic
30C3×#3752C2211yescharacteristic
31C3×#3752C2211yescharacteristic
32C32×#217C2211yescharacteristic
33C32×#217C2211yescharacteristic
34C32×#217C2211yescharacteristic, complemented
35C32×#217C2211yescharacteristic, complemented
36C32×#217C2211yescharacteristic, complemented
37C32×C4⋊Dic3C2211yescharacteristic, complemented
38C32×Dic3⋊C4C2211yescharacteristic, complemented
39C32×Dic3⋊C4C2211yescharacteristic, complemented
40C32×C4×Dic3C2211yescharacteristic, complemented
41C3×#3724C2211yescharacteristic, complemented
42C3×Dic3⋊Dic3C2211yescharacteristic, complemented
43C3×Dic3⋊Dic3C2211yescharacteristic, complemented
44C3×Dic3⋊Dic3C2211yescharacteristic, complemented
45C3×Dic3⋊Dic3C2211yescharacteristic, complemented
46C3×#3722C2211yescharacteristic
47C3×#3722C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×Dic32C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54C32×#123—31no—
55C32×C4×D4—31no—
56#64146C2×C311yescharacteristic
57C3×#937—31no—
58C3×#937—31no—
59C3×#937—61no—
60C3×#935—21no—
61C3×#935D311yescharacteristic, complemented
62C3×#935C2×C311yescharacteristic, complemented
63C3×D4×Dic3—21no—
64C3×D4×Dic3D311yescharacteristic, complemented
65C3×D4×Dic3C2×C311yescharacteristic, complemented
66C3×#929—31no—
67C3×C4×#67—31no—
68C2×C3×(C2×D3)⋊C4—31no—
69C2×C3×(C2×D3)⋊C4—31no—
70C3×#926—31no—
71C3×#924—31no—
72C3×#898—31no—
73C3×#898—31no—
74C3×#898—31no—
75C3×#897—31no—
76C3×#896—31no—
77C3×#892—31no—
78C3×#886—31no—
79C3×#885—31no—
80C3×#885—31no—
81C3×#883—31no—
82C3×#883—31no—
83C3×#67⋊C4—31no—
84C3×D3×C22⋊C4—31no—
85C3×D3×C22⋊C4—31no—
86C3×#878—31no—
87C3×#877—31no—
88C3×#876—31no—
89C3×#872—31no—
90#63975C2×C311yescharacteristic, complemented
91#63974C2×C311yescharacteristic, complemented
92#63966C2×C311yescharacteristic, complemented
93#63964C2×C311yescharacteristic, complemented
94C2×#3722C2×C311yescharacteristic, complemented
95#63955C2×C311yescharacteristic, complemented
96#63953C2×C311yescharacteristic, complemented
97#63952C2×C311yescharacteristic, complemented
98#63895C2×C311yescharacteristic, complemented
99#63868C2×C311yescharacteristic, complemented
100#63848C2×C311yescharacteristic, complemented
101#63836C2×C311yescharacteristic, complemented
102C23×C33C2311yescharacteristic
103C23×C33C2311yescharacteristic
104C22×C3×C3⋊D3—22no—
105C22×C3×C3⋊D3—22no—
106C22×C3×C3⋊D3—41no—
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C3×C3⋊D3C2311yescharacteristic
109C33×D4—22no—
110C2×C33×C4C2311yescharacteristic
111C3×#638—22no—
112C3×#638—41no—
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C32×Dic3—22no—
116C2×C32×Dic3—41no—
117C2×C32×Dic3—41no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C3×#627—41no—
127C3×#624—22no—
128C3×#624—41no—
129C3×#551—91no—
130#5658—31no—
131#5556—31no—
132C23×C3⋊D3C22×C311yescharacteristic
133C23×C3×D3—31no—
134C23×C3×D3—31no—
135C23×C3×D3—61no—
136C2×C32×D4—21no—
137C2×C32×D4—21no—
138C2×C32×D4—21no—
139C2×C32×D4—41no—
140C2×C32×D4C2×D311yescharacteristic
141C2×C32×D4C2×D311yescharacteristic
142C2×C32×D4C22×C311yescharacteristic
143C22×C32×C4—31no—
144C22×C32×C4—31no—
145C22×C32×C4—31no—
146C2×#638C22×C311yescharacteristic
147C2×#638C22×C311yescharacteristic
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—31no—
152C2×C3×#67—61no—
153C2×C3×#67—61no—
154C22×C3×Dic3—21no—
155C22×C3×Dic3—21no—
156C22×C3×Dic3—21no—
157C22×C3×Dic3C2×D311yescharacteristic
158C22×C3×Dic3C2×D311yescharacteristic
159C22×C3×Dic3C2×D311yescharacteristic, complemented
160C22×C3×Dic3C22×C311yescharacteristic
161C22×C3×Dic3C22×C311yescharacteristic
162C22×C3×Dic3C22×C311yescharacteristic, complemented
163C2×C3×C4×D3—31no—
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—31no—
166C2×C3×C4×D3—31no—
167C2×C3×Dic6—31no—
168C2×C3×Dic6—31no—
169C2×#627C22×C311yescharacteristic, complemented
170C2×#624C22×C311yescharacteristic
171C2×#624C22×C311yescharacteristic
172C32×C4⋊C4—31no—
173C32×C4⋊C4—31no—
174C32×C4⋊C4—31no—
175C32×C22⋊C4—31no—
176C32×C22⋊C4—31no—
177C32×C22⋊C4—31no—
178C32×C22⋊C4—31no—
179C32×C22⋊C4—31no—
180C32×C42—31no—
181#3757C22×C311yescharacteristic
182#3752C22×C311yescharacteristic
183#3752C22×C311yescharacteristic
184C3×#217—21no—
185C3×#217—21no—
186C3×#217—21no—
187C3×#217—21no—
188C3×#217—21no—
189C3×#217—31no—
190C3×#217—31no—
191C3×#217—61no—
192C3×#217C2×D311yescharacteristic
193C3×#217C2×D311yescharacteristic
194C3×#217C2×D311yescharacteristic, complemented
195C3×#217C2×D311yescharacteristic, complemented
196C3×#217C2×D311yescharacteristic, complemented
197C3×#217C22×C311yescharacteristic
198C3×#217C22×C311yescharacteristic
199C3×#217C22×C311yescharacteristic, complemented
200C3×#217C22×C311yescharacteristic, complemented
201C3×#217C22×C311yescharacteristic, complemented
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—31no—
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—31no—
214C3×(C2×D3)⋊C4—31no—
215C3×(C2×D3)⋊C4—31no—
216C3×(C2×D3)⋊C4—31no—
217C3×(C2×D3)⋊C4—31no—
218C3×(C2×D3)⋊C4—61no—
219C3×(C2×D3)⋊C4—61no—
220C3×C4⋊Dic3—21no—
221C3×C4⋊Dic3—31no—
222C3×C4⋊Dic3—31no—
223C3×C4⋊Dic3—31no—
224C3×C4⋊Dic3—31no—
225C3×C4⋊Dic3C2×D311yescharacteristic, complemented
226C3×C4⋊Dic3C22×C311yescharacteristic, complemented
227C3×Dic3⋊C4—21no—
228C3×Dic3⋊C4—21no—
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⋊C4C2×D311yescharacteristic, complemented
236C3×Dic3⋊C4C2×D311yescharacteristic, complemented
237C3×Dic3⋊C4C22×C311yescharacteristic, complemented
238C3×Dic3⋊C4C22×C311yescharacteristic, complemented
239C3×C4×Dic3—21no—
240C3×C4×Dic3—31no—
241C3×C4×Dic3—31no—
242C3×C4×Dic3—31no—
243C3×C4×Dic3—31no—
244C3×C4×Dic3C2×D311yescharacteristic, complemented
245C3×C4×Dic3C22×C311yescharacteristic, complemented
246#3724C22×C311yescharacteristic, complemented
247Dic3⋊Dic3C22×C311yescharacteristic, complemented
248Dic3⋊Dic3C22×C311yescharacteristic, complemented
249Dic3⋊Dic3C22×C311yescharacteristic, complemented
250Dic3⋊Dic3C22×C311yescharacteristic, complemented
251#3722C22×C311yescharacteristic
252#3722C22×C311yescharacteristic
253#3722C22×C311yescharacteristic
254#3722C22×C311yescharacteristic
255#3722C22×C311yescharacteristic
256#3722C22×C311yescharacteristic
257Dic32C22×C311yescharacteristic, complemented
258Dic32C22×C311yescharacteristic, complemented
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×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3—44no—
272C2×C3×C3⋊D3#4112yes—
273C33×C4—21no—
274C3×C3⋊Dic3—21no—
275C3×C3⋊Dic3—21no—
276C32×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—31no—
288C3×#123—31no—
289C3×#123—61no—
290C3×#123—91no—
291C3×#123—91no—
292C3×C22⋊Q8—91no—
293C3×C22⋊Q8—91no—
294C3×#120—91no—
295C3×C4×D4—31no—
296C3×C4×D4—31no—
297C3×C4×D4—61no—
298C3×C4×D4—91no—
299C3×#117—91no—
300C3×#117—91no—
301C2×C3×C22⋊C4—91no—
302C2×C3×C22⋊C4—91no—
303#937—31no—
304#937—31no—
305#937—61no—
306#935C3×D311yescharacteristic, complemented
307D4×Dic3C3×D311yescharacteristic, complemented
308#929—31no—
309C4×#67—31no—
310C2×(C2×D3)⋊C4—31no—
311C2×(C2×D3)⋊C4—31no—
312#926—31no—
313#924—31no—
314#898—31no—
315#898—31no—
316#898—31no—
317#897—31no—
318#896—31no—
319#892—31no—
320#886—31no—
321#885—31no—
322#885—31no—
323#883—31no—
324#883—31no—
325#67⋊C4—31no—
326D3×C22⋊C4—31no—
327D3×C22⋊C4—31no—
328#878—31no—
329#877—31no—
330#876—31no—
331#872—31no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—21no—
335C23×C32—21no—
336C23×C32—21no—
337C23×C32—21no—
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⋊D3—22no—
347C22×C3⋊D3—22no—
348C22×C3⋊D3—41no—
349C22×C3⋊D3C23×C311yescharacteristic
350C22×C3⋊D3C23×C311yescharacteristic
351C22×C3×D3—31no—
352C22×C3×D3—31no—
353C22×C3×D3—31no—
354C22×C3×D3—31no—
355C22×C3×D3—61no—
356C22×C3×D3—61no—
357C22×C3×D3—62no—
358C22×C3×D3—62no—
359C22×C3×D3—62no—
360C22×C3×D3—62no—
361C22×C3×D3—122no—
362C22×C3×D3—122no—
363C22×C3×D3—121no—
364C22×C3×D3—121no—
365C22×C3×D3—122no—
366C32×D4—22no—
367C32×D4—24no—
368C32×D4—22no—
369C32×D4—22no—
370C32×D4—42no—
371C32×D4—42no—
372C32×D4—44no—
373C2×C32×C4—21no—
374C2×C32×C4—21no—
375C2×C32×C4—21no—
376C2×C32×C4—31no—
377C2×C32×C4—31no—
378C2×C32×C4—31no—
379C2×C32×C4—31no—
380C2×C32×C4—31no—
381C2×C32×C4—31no—
382C2×C32×C4—31no—
383C2×C32×C4—31no—
384C2×C32×C4—41no—
385C2×C32×C4—62no—
386C2×C32×C4—121no—
387C2×C32×C4—121no—
388C2×C32×C4C22×D311yescharacteristic
389C2×C32×C4C22×D311yescharacteristic
390C2×C32×C4C23×C311yescharacteristic
391#638—22no—
392#638—41no—
393C2×C3⋊Dic3C23×C311yescharacteristic
394C2×C3⋊Dic3C23×C311yescharacteristic
395C3×#67—62no—
396C3×#67—62no—
397C3×#67—122no—
398C3×#67—121no—
399C3×#67—121no—
400C3×#67—122no—
401C2×C3×Dic3—22no—
402C2×C3×Dic3—22no—
403C2×C3×Dic3—21no—
404C2×C3×Dic3—21no—
405C2×C3×Dic3—21no—
406C2×C3×Dic3—21no—
407C2×C3×Dic3—21no—
408C2×C3×Dic3—21no—
409C2×C3×Dic3—21no—
410C2×C3×Dic3—21no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—42no—
416C2×C3×Dic3—41no—
417C2×C3×Dic3—41no—
418C2×C3×Dic3—41no—
419C2×C3×Dic3—41no—
420C2×C3×Dic3—42no—
421C2×C3×Dic3—42no—
422C2×C3×Dic3—61no—
423C2×C3×Dic3—61no—
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C2×C3×Dic3C22×D311yescharacteristic
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C23×C311yescharacteristic
433C2×C3×Dic3C23×C311yescharacteristic
434C2×C3×Dic3C23×C311yescharacteristic
435C2×C3×Dic3C23×C311yescharacteristic
436C2×C3×Dic3C23×C311yescharacteristic
437C2×C3×Dic3C23×C311yescharacteristic
438C2×C3×Dic3C23×C311yescharacteristic
439C2×C3×Dic3C23×C311yescharacteristic
440C3×C4×D3—62no—
441C3×C4×D3—62no—
442C3×C4×D3—121no—
443C3×C4×D3—121no—
444C3×Dic6—121no—
445C3×Dic6—121no—
446#627—41no—
447#624—22no—
448#624—41no—
449#551—91noSylow
450C2×C33—22no—
451C2×C33—41no—
452C2×C33C2×#4111yescharacteristic
453C2×C33C2×#4111yescharacteristic
454C2×C33H(5,𝔽2)11yescharacteristic
455C3×C3⋊D3—22no—
456C3×C3⋊D3—41no—
457C24×C3—91no—
458C23×D3—31no—
459C23×D3—31no—
460C23×D3—61no—
461C2×C3×Q8—91no—
462C2×C3×D4—21no—
463C2×C3×D4—21no—
464C2×C3×D4—21no—
465C2×C3×D4—41no—
466C2×C3×D4—91no—
467C2×C3×D4—91no—
468C2×C3×D4D3211yescharacteristic
469C2×C3×D4C2×C3×D311yescharacteristic
470C2×C3×D4C2×C3×D311yescharacteristic
471C22×C3×C4—31no—
472C22×C3×C4—31no—
473C22×C3×C4—31no—
474C22×C3×C4—31no—
475C22×C3×C4—31no—
476C22×C3×C4—31no—
477C22×C3×C4—61no—
478C22×C3×C4—61no—
479C22×C3×C4—61no—
480C22×C3×C4—91no—
481C22×C3×C4—91no—
482C2×#67—31no—
483C2×#67—31no—
484C2×#67—31no—
485C2×#67—31no—
486C2×#67—61no—
487C2×#67—61no—
488C22×Dic3C2×C3×D311yescharacteristic
489C22×Dic3C2×C3×D311yescharacteristic
490C22×Dic3C2×C3×D311yescharacteristic, complemented
491C2×C4×D3—31no—
492C2×C4×D3—31no—
493C2×C4×D3—31no—
494C2×C4×D3—31no—
495C2×Dic6—31no—
496C2×Dic6—31no—
497C3×C4⋊C4—31no—
498C3×C4⋊C4—31no—
499C3×C4⋊C4—31no—
500C3×C4⋊C4—31no—
501C3×C4⋊C4—31no—
502C3×C4⋊C4—31no—
503C3×C4⋊C4—61no—
504C3×C4⋊C4—61no—
505C3×C4⋊C4—61no—
506C3×C4⋊C4—91no—
507C3×C4⋊C4—91no—
508C3×C4⋊C4—91no—
509C3×C4⋊C4—91no—
510C3×C4⋊C4—91no—
511C3×C22⋊C4—31no—
512C3×C22⋊C4—31no—
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—61no—
522C3×C22⋊C4—61no—
523C3×C22⋊C4—61no—
524C3×C22⋊C4—61no—
525C3×C22⋊C4—61no—
526C3×C22⋊C4—91no—
527C3×C22⋊C4—91no—
528C3×C22⋊C4—91no—
529C3×C22⋊C4—91no—
530C3×C22⋊C4—91no—
531C3×C22⋊C4—91no—
532C3×C22⋊C4—91no—
533C3×C22⋊C4—91no—
534C3×C22⋊C4—91no—
535C3×C42—31no—
536C3×C42—31no—
537C3×C42—61no—
538C3×C42—91no—
539C3×C42—91no—
540#217—31no—
541#217—31no—
542#217—61no—
543#217C2×C3×D311yescharacteristic
544#217C2×C3×D311yescharacteristic
545#217C2×C3×D311yescharacteristic, complemented
546#217C2×C3×D311yescharacteristic, complemented
547#217C2×C3×D311yescharacteristic, complemented
548(C2×D3)⋊C4—31no—
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—31no—
558(C2×D3)⋊C4—31no—
559(C2×D3)⋊C4—31no—
560(C2×D3)⋊C4—31no—
561(C2×D3)⋊C4—31no—
562(C2×D3)⋊C4—31no—
563(C2×D3)⋊C4—31no—
564(C2×D3)⋊C4—61no—
565(C2×D3)⋊C4—61no—
566C4⋊Dic3—31no—
567C4⋊Dic3—31no—
568C4⋊Dic3—31no—
569C4⋊Dic3—31no—
570C4⋊Dic3C2×C3×D311yescharacteristic, complemented
571Dic3⋊C4—31no—
572Dic3⋊C4—31no—
573Dic3⋊C4—31no—
574Dic3⋊C4—31no—
575Dic3⋊C4—31no—
576Dic3⋊C4—31no—
577Dic3⋊C4C2×C3×D311yescharacteristic, complemented
578Dic3⋊C4C2×C3×D311yescharacteristic, complemented
579C4×Dic3—31no—
580C4×Dic3—31no—
581C4×Dic3—31no—
582C4×Dic3—31no—
583C4×Dic3C2×C3×D311yescharacteristic, complemented
584C22×C32—21no—
585C22×C32—21no—
586C22×C32—21no—
587C22×C32—21no—
588C22×C32—21no—
589C22×C32—21no—
590C22×C32—21no—
591C22×C32—22no—
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—21no—
603C22×C32—22no—
604C22×C32—22no—
605C22×C32—22no—
606C22×C32—41no—
607C22×C32—42no—
608C22×C32—41no—
609C22×C32—41no—
610C22×C32—42no—
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—41no—
623C22×C32—81no—
624C22×C32—81no—
625C22×C32—81no—
626C22×C32—81no—
627C22×C32#23512yes—
628C22×C32#23712yes—
629C22×C32C3×#4112yes—
630C22×C32C23×D311yescharacteristic
631C22×C32C23×D311yescharacteristic
632C22×C32C24×C311yescharacteristic
633C2×C3⋊D3—21no—
634C2×C3⋊D3—21no—
635C2×C3⋊D3—21no—
636C2×C3⋊D3—21no—
637C2×C3⋊D3—21no—
638C2×C3⋊D3—44no—
639C2×C3⋊D3C3×#4112yes—
640C2×C3×D3—32no—
641C2×C3×D3—32no—
642C2×C3×D3—62no—
643C2×C3×D3—61no—
644C2×C3×D3—61no—
645C2×C3×D3—61no—
646C2×C3×D3—61no—
647C2×C3×D3—62no—
648C2×C3×D3—61no—
649C2×C3×D3—61no—
650C2×C3×D3—61no—
651C2×C3×D3—61no—
652C2×C3×D3—61no—
653C2×C3×D3—61no—
654C2×C3×D3—121no—
655C2×C3×D3—121no—
656C2×C3×D3—121no—
657C2×C3×D3—121no—
658C2×C3×D3—124no—
659C2×C3×D3—124no—
660C2×C3×D3—128no—
661C32×C4—21no—
662C32×C4—22no—
663C32×C4—21no—
664C32×C4—21no—
665C32×C4—41no—
666C32×C4—41no—
667C32×C4—42no—
668C32×C4—61no—
669C32×C4—61no—
670C32×C4—61no—
671C32×C4—61no—
672C32×C4—61no—
673C32×C4—61no—
674C32×C4—61no—
675C32×C4—61no—
676C3⋊Dic3—21no—
677C3⋊Dic3—21no—
678C3×Dic3—22no—
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—21no—
690C3×Dic3—21no—
691C3×Dic3—21no—
692C3×Dic3—21no—
693C3×Dic3—21no—
694C3×Dic3—21no—
695C3×Dic3—41no—
696C3×Dic3—41no—
697C3×Dic3—41no—
698C3×Dic3—41no—
699C3×Dic3—41no—
700C3×Dic3—41no—
701C3×Dic3—41no—
702C3×Dic3—61no—
703C3×Dic3—61no—
704C3×Dic3—61no—
705C3×Dic3—61no—
706C3×Dic3—121no—
707C3×Dic3—121no—
708#126—91no—
709#126—91no—
710#124—91no—
711#123—31no—
712#123—91no—
713#123—91no—
714C22⋊Q8—91no—
715C22⋊Q8—91no—
716#120—91no—
717C4×D4—31no—
718C4×D4—91no—
719#117—91no—
720#117—91no—
721C2×C22⋊C4—91no—
722C2×C22⋊C4—91no—
723C33#55111yescharacteristic, complemented, Sylow
724C23×C3—21no—
725C23×C3—21no—
726C23×C3—21no—
727C23×C3—21no—
728C23×C3—21no—
729C23×C3—21no—
730C23×C3—41no—
731C23×C3—41no—
732C23×C3—91no—
733C23×C3—91no—
734C23×C3—182no—
735C23×C3—182no—
736C23×C3—361no—
737C23×C3C2×D3211yescharacteristic
738C23×C3C2×D3211yescharacteristic
739C23×C3C22×C3×D311yescharacteristic
740C23×C3C22×C3×D311yescharacteristic
741C23×C3C22×C3×D311yescharacteristic
742C23×C3C22×C3×D311yescharacteristic
743C22×D3—31no—
744C22×D3—31no—
745C22×D3—31no—
746C22×D3—31no—
747C22×D3—61no—
748C22×D3—61no—
749C22×D3—62no—
750C22×D3—62no—
751C22×D3—62no—
752C22×D3—62no—
753C22×D3—122no—
754C22×D3—122no—
755C22×D3—121no—
756C22×D3—121no—
757C22×D3—122no—
758C3×Q8—361no—
759C3×D4—24no—
760C3×D4—22no—
761C3×D4—22no—
762C3×D4—22no—
763C3×D4—42no—
764C3×D4—42no—
765C3×D4—44no—
766C3×D4—182no—
767C3×D4—361no—
768C2×C3×C4—21no—
769C2×C3×C4—21no—
770C2×C3×C4—21no—
771C2×C3×C4—31no—
772C2×C3×C4—31no—
773C2×C3×C4—31no—
774C2×C3×C4—31no—
775C2×C3×C4—31no—
776C2×C3×C4—31no—
777C2×C3×C4—31no—
778C2×C3×C4—31no—
779C2×C3×C4—31no—
780C2×C3×C4—31no—
781C2×C3×C4—31no—
782C2×C3×C4—31no—
783C2×C3×C4—31no—
784C2×C3×C4—31no—
785C2×C3×C4—31no—
786C2×C3×C4—31no—
787C2×C3×C4—41no—
788C2×C3×C4—61no—
789C2×C3×C4—61no—
790C2×C3×C4—61no—
791C2×C3×C4—61no—
792C2×C3×C4—61no—
793C2×C3×C4—61no—
794C2×C3×C4—61no—
795C2×C3×C4—61no—
796C2×C3×C4—62no—
797C2×C3×C4—62no—
798C2×C3×C4—91no—
799C2×C3×C4—91no—
800C2×C3×C4—122no—
801C2×C3×C4—121no—
802C2×C3×C4—121no—
803C2×C3×C4—121no—
804C2×C3×C4—121no—
805C2×C3×C4—122no—
806C2×C3×C4—122no—
807C2×C3×C4—182no—
808C2×C3×C4—361no—
809C2×C3×C4C2×D3211yescharacteristic
810C2×C3×C4C22×C3×D311yescharacteristic
811C2×C3×C4C22×C3×D311yescharacteristic
812#67—62no—
813#67—62no—
814#67—122no—
815#67—121no—
816#67—121no—
817#67—122no—
818C2×Dic3—22no—
819C2×Dic3—31no—
820C2×Dic3—31no—
821C2×Dic3—31no—
822C2×Dic3—31no—
823C2×Dic3—41no—
824C2×Dic3—41no—
825C2×Dic3—61no—
826C2×Dic3—61no—
827C2×Dic3C22×C3×D311yescharacteristic
828C2×Dic3C22×C3×D311yescharacteristic
829C2×Dic3C22×C3×D311yescharacteristic
830C2×Dic3C22×C3×D311yescharacteristic
831C2×Dic3C22×C3×D311yescharacteristic
832C2×Dic3C22×C3×D311yescharacteristic
833C2×Dic3C22×C3×D311yescharacteristic
834C2×Dic3C22×C3×D311yescharacteristic
835C4×D3—62no—
836C4×D3—62no—
837C4×D3—121no—
838C4×D3—121no—
839Dic6—121no—
840Dic6—121no—
841C2×C32—22no—
842C2×C32—22no—
843C2×C32—22no—
844C2×C32—21no—
845C2×C32—21no—
846C2×C32—21no—
847C2×C32—21no—
848C2×C32—21no—
849C2×C32—21no—
850C2×C32—21no—
851C2×C32—21no—
852C2×C32—21no—
853C2×C32—41no—
854C2×C32—41no—
855C2×C32—41no—
856C2×C32—42no—
857C2×C32—42no—
858C2×C32—42no—
859C2×C32—41no—
860C2×C32—42no—
861C2×C32—41no—
862C2×C32—41no—
863C2×C32—82no—
864C2×C32—81no—
865C2×C32—81no—
866C2×C32—82no—
867C2×C32C2×#23511yescharacteristic
868C2×C32C2×#23711yescharacteristic
869C2×C32#100411yescharacteristic
870C2×C32D3×#4111yescharacteristic
871C2×C32D3×#4111yescharacteristic
872C2×C32#100911yescharacteristic
873C2×C32C2×C3×#4111yescharacteristic
874C2×C32C2×C3×#4111yescharacteristic
875C2×C32C3×H(5,𝔽2)11yescharacteristic
876C3⋊D3—22no—
877C3⋊D3—41no—
878C3×D3—62no—
879C3×D3—62no—
880C3×D3—122no—
881C3×D3—122no—
882C3×D3—121no—
883C3×D3—121no—
884C24—91no—
885C2×Q8—91no—
886C2×D4—91no—
887C2×D4—91no—
888C2×D4C3×D3211yescharacteristic
889C22×C4—31no—
890C22×C4—31no—
891C22×C4—31no—
892C22×C4—91no—
893C22×C4—91no—
894C4⋊C4—31no—
895C4⋊C4—31no—
896C4⋊C4—31no—
897C4⋊C4—91no—
898C4⋊C4—91no—
899C4⋊C4—91no—
900C4⋊C4—91no—
901C4⋊C4—91no—
902C22⋊C4—31no—
903C22⋊C4—31no—
904C22⋊C4—31no—
905C22⋊C4—31no—
906C22⋊C4—31no—
907C22⋊C4—91no—
908C22⋊C4—91no—
909C22⋊C4—91no—
910C22⋊C4—91no—
911C22⋊C4—91no—
912C22⋊C4—91no—
913C22⋊C4—91no—
914C22⋊C4—91no—
915C22⋊C4—91no—
916C42—31no—
917C42—91no—
918C42—91no—
919C22×C3—21no—
920C22×C3—21no—
921C22×C3—21no—
922C22×C3—21no—
923C22×C3—21no—
924C22×C3—21no—
925C22×C3—22no—
926C22×C3—21no—
927C22×C3—21no—
928C22×C3—21no—
929C22×C3—21no—
930C22×C3—21no—
931C22×C3—21no—
932C22×C3—21no—
933C22×C3—21no—
934C22×C3—21no—
935C22×C3—21no—
936C22×C3—21no—
937C22×C3—21no—
938C22×C3—22no—
939C22×C3—22no—
940C22×C3—22no—
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—41no—
951C22×C3—41no—
952C22×C3—41no—
953C22×C3—41no—
954C22×C3—41no—
955C22×C3—42no—
956C22×C3—41no—
957C22×C3—42no—
958C22×C3—81no—
959C22×C3—81no—
960C22×C3—81no—
961C22×C3—81no—
962C22×C3—92no—
963C22×C3—181no—
964C22×C3—181no—
965C22×C3—181no—
966C22×C3—181no—
967C22×C3—181no—
968C22×C3—364no—
969C22×C3#380412yes—
970C22×C3C3×#23512yes—
971C22×C3C3×#23712yes—
972C22×C3C22×D3211yescharacteristic
973C22×C3C23×C3×D311yescharacteristic
974C22×C3C23×C3×D311yescharacteristic
975C2×D3—32no—
976C2×D3—32no—
977C2×D3—62no—
978C2×D3—61no—
979C2×D3—61no—
980C2×D3—61no—
981C2×D3—61no—
982C2×D3—62no—
983C2×D3—61no—
984C2×D3—61no—
985C2×D3—61no—
986C2×D3—61no—
987C2×D3—61no—
988C2×D3—61no—
989C2×D3—121no—
990C2×D3—121no—
991C2×D3—121no—
992C2×D3—121no—
993C2×D3—124no—
994C2×D3—124no—
995C2×D3—128no—
996C3×C4—22no—
997C3×C4—21no—
998C3×C4—21no—
999C3×C4—21no—
1000C3×C4—41no—
1001C3×C4—41no—
1002C3×C4—42no—
1003C3×C4—62no—
1004C3×C4—61no—
1005C3×C4—61no—
1006C3×C4—61no—
1007C3×C4—61no—
1008C3×C4—61no—
1009C3×C4—61no—
1010C3×C4—61no—
1011C3×C4—61no—
1012C3×C4—61no—
1013C3×C4—61no—
1014C3×C4—61no—
1015C3×C4—61no—
1016C3×C4—61no—
1017C3×C4—61no—
1018C3×C4—61no—
1019C3×C4—61no—
1020C3×C4—121no—
1021C3×C4—121no—
1022C3×C4—121no—
1023C3×C4—121no—
1024C3×C4—121no—
1025C3×C4—121no—
1026C3×C4—121no—
1027C3×C4—181no—
1028C3×C4—181no—
1029Dic3—21no—
1030Dic3—21no—
1031Dic3—21no—
1032Dic3—21no—
1033Dic3—21no—
1034Dic3—21no—
1035Dic3—21no—
1036Dic3—21no—
1037Dic3—61no—
1038Dic3—61no—
1039Dic3—61no—
1040Dic3—61no—
1041Dic3—121no—
1042Dic3—121no—
1043C32—21no—
1044C32—21no—
1045C32—21no—
1046C32—41no—
1047C32#555611yescharacteristic, complemented
1048C32#565811yescharacteristic, complemented
1049C32C3×#55111yescharacteristic, complemented
1050C23—91no—
1051C23—91no—
1052C23—182no—
1053C23—182no—
1054C23—361no—
1055C23C2×C3×D3211yescharacteristic
1056C23C2×C3×D3211yescharacteristic
1057Q8—361no—
1058D4—22no—
1059D4—182no—
1060D4—361no—
1061C2×C4—31no—
1062C2×C4—31no—
1063C2×C4—31no—
1064C2×C4—31no—
1065C2×C4—31no—
1066C2×C4—31no—
1067C2×C4—31no—
1068C2×C4—31no—
1069C2×C4—62no—
1070C2×C4—91no—
1071C2×C4—91no—
1072C2×C4—121no—
1073C2×C4—121no—
1074C2×C4—182no—
1075C2×C4—361no—
1076C2×C4C2×C3×D3211yescharacteristic
1077C2×C3—22no—
1078C2×C3—22no—
1079C2×C3—22no—
1080C2×C3—21no—
1081C2×C3—21no—
1082C2×C3—21no—
1083C2×C3—21no—
1084C2×C3—21no—
1085C2×C3—21no—
1086C2×C3—21no—
1087C2×C3—21no—
1088C2×C3—21no—
1089C2×C3—42no—
1090C2×C3—42no—
1091C2×C3—42no—
1092C2×C3—42no—
1093C2×C3—41no—
1094C2×C3—41no—
1095C2×C3—41no—
1096C2×C3—41no—
1097C2×C3—41no—
1098C2×C3—41no—
1099C2×C3—82no—
1100C2×C3—81no—
1101C2×C3—81no—
1102C2×C3—82no—
1103C2×C3—182no—
1104C2×C3—361no—
1105C2×C3#6431211yescharacteristic
1106C2×C3#6431411yescharacteristic
1107C2×C3C2×#380411yescharacteristic
1108C2×C3C2×C3×#23511yescharacteristic
1109C2×C3C2×C3×#23711yescharacteristic
1110C2×C3C3×#100411yescharacteristic
1111C2×C3C3×D3×#4111yescharacteristic
1112C2×C3C3×D3×#4111yescharacteristic
1113C2×C3C3×#100911yescharacteristic
1114D3—62no—
1115D3—62no—
1116D3—122no—
1117D3—122no—
1118D3—121no—
1119D3—121no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—92no—
1126C22—181no—
1127C22—181no—
1128C22—181no—
1129C22—181no—
1130C22—181no—
1131C22—364no—
1132C22C3×#380412yes—
1133C22C22×C3×D3211yescharacteristic
1134C4—21no—
1135C4—61no—
1136C4—61no—
1137C4—61no—
1138C4—61no—
1139C4—61no—
1140C4—61no—
1141C4—61no—
1142C4—61no—
1143C4—181no—
1144C4—181no—
1145C3—21no—
1146C3—21no—
1147C3—21no—
1148C3—41no—
1149C3#1059511811yescharacteristic, direct product factor
1150C3C3×#555611yescharacteristic, complemented
1151C3C3×#565811yescharacteristic, complemented
1152C2—22no—
1153C2—41no—
1154C2—182no—
1155C2—361no—
1156C2C3×#6431211yescharacteristic
1157C2C3×#6431411yescharacteristic
1158C2C2×C3×#380411yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
prime radicalC3×#64146C2
hypercenterC2×C3×D4D32
hypocenterC32C3×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
2. C32×#935C2semidirect
3. C32×D4×Dic3C2semidirect
4. C3×#63975C2semidirect
5. C3×#63974C2semidirect
6. C3×#63966C2semidirect
7. C3×#63964C2semidirect
8. C2×C3×#3722C2semidirect
9. C3×#63955C2semidirect
10. C3×#63953C2semidirect
11. C3×#63952C2semidirect
12. C3×#63895C2semidirect
13. C3×#63868C2semidirect
14. C3×#63848C2semidirect
15. C3×#63836C2semidirect
18. #10595118C3direct (N × H)
25. C22×C32×Dic3C22semidirect
26. C2×C3×#627C22semidirect
34. C32×#217C22semidirect
35. C32×#217C22semidirect
36. C32×#217C22semidirect
37. C32×C4⋊Dic3C22semidirect
38. C32×Dic3⋊C4C22semidirect
39. C32×Dic3⋊C4C22semidirect
40. C32×C4×Dic3C22semidirect
41. C3×#3724C22semidirect
42. C3×Dic3⋊Dic3C22semidirect
43. C3×Dic3⋊Dic3C22semidirect
44. C3×Dic3⋊Dic3C22semidirect
45. C3×Dic3⋊Dic3C22semidirect
52. C3×Dic32C22semidirect
53. C3×Dic32C22semidirect
61. C3×#935D3semidirect
62. C3×#935C2×C3semidirect
64. C3×D4×Dic3D3semidirect
65. C3×D4×Dic3C2×C3semidirect
90. #63975C2×C3semidirect
91. #63974C2×C3semidirect
92. #63966C2×C3semidirect
93. #63964C2×C3semidirect
94. C2×#3722C2×C3semidirect
95. #63955C2×C3semidirect
96. #63953C2×C3semidirect
97. #63952C2×C3semidirect
98. #63895C2×C3semidirect
99. #63868C2×C3semidirect
100. #63848C2×C3semidirect
101. #63836C2×C3semidirect
159. C22×C3×Dic3C2×D3semidirect
162. C22×C3×Dic3C22×C3semidirect
169. C2×#627C22×C3semidirect
194. C3×#217C2×D3semidirect
195. C3×#217C2×D3semidirect
196. C3×#217C2×D3semidirect
199. C3×#217C22×C3semidirect
200. C3×#217C22×C3semidirect
201. C3×#217C22×C3semidirect
225. C3×C4⋊Dic3C2×D3semidirect
226. C3×C4⋊Dic3C22×C3semidirect
235. C3×Dic3⋊C4C2×D3semidirect
236. C3×Dic3⋊C4C2×D3semidirect
237. C3×Dic3⋊C4C22×C3semidirect
238. C3×Dic3⋊C4C22×C3semidirect
244. C3×C4×Dic3C2×D3semidirect
245. C3×C4×Dic3C22×C3semidirect
246. #3724C22×C3semidirect
247. Dic3⋊Dic3C22×C3semidirect
248. Dic3⋊Dic3C22×C3semidirect
249. Dic3⋊Dic3C22×C3semidirect
250. Dic3⋊Dic3C22×C3semidirect
257. Dic32C22×C3semidirect
258. Dic32C22×C3semidirect
306. #935C3×D3semidirect
307. D4×Dic3C3×D3semidirect
490. C22×Dic3C2×C3×D3semidirect
545. #217C2×C3×D3semidirect
546. #217C2×C3×D3semidirect
547. #217C2×C3×D3semidirect
570. C4⋊Dic3C2×C3×D3semidirect
577. Dic3⋊C4C2×C3×D3semidirect
578. Dic3⋊C4C2×C3×D3semidirect
583. C4×Dic3C2×C3×D3semidirect
723. C33#551semidirect
1047. C32#5556semidirect
1048. C32#5658semidirect
1049. C32C3×#551semidirect
1149. C3#10595118direct (N × H)
1150. C3C3×#5556semidirect
1151. C3C3×#5658semidirect

Maximal subgroups

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

subgroupindex
C3×#641462
C32×#9352
C32×D4×Dic32
C3×#639752
C3×#639742
C3×#639662
C3×#639642
C2×C3×#37222
C3×#639552
C3×#639532
C3×#639522
C3×#638952
C3×#638682
C3×#638482
C3×#638362
C3×#56583
C3×#55563
#105951183