Finite Group Databasebeta

← C3×#10595035 #13174611

Subgroups — C3×#10595035 #13174611

Order 1728.

1346 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3752C211yesmaximal, characteristic, complemented
2C32×C4×#67C211yesmaximal, characteristic, complemented
3C32×#924C211yesmaximal, characteristic, complemented
4C3×#63981C211yesmaximal, characteristic
5C3×#63974C211yesmaximal, characteristic, complemented
6C3×#63962C211yesmaximal, characteristic, complemented
7C3×#63957C211yesmaximal, characteristic, complemented
8C3×#63907C211yesmaximal, characteristic, complemented
9C3×#63904C211yesmaximal, characteristic, complemented
10C3×#63888C211yesmaximal, characteristic, complemented
11C3×#63868C211yesmaximal, characteristic, complemented
12C3×#63854C211yesmaximal, characteristic, complemented
13C3×#63850C211yesmaximal, characteristic, complemented
14C3×#63848C211yesmaximal, characteristic, complemented
15C3×#63836C211yesmaximal, characteristic, complemented
16C3×#5637—31nomaximal
17C3×#5556—31nomaximal
18#10595035C311yesmaximal, characteristic, direct product factor
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×C4×D3C2211yescharacteristic, complemented
24C2×C32×Dic6C2211yescharacteristic, complemented
25C2×C3×#626C2211yescharacteristic
26C2×C3×#626C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28C2×C3×#624C2211yescharacteristic
29C3×#3752C2211yescharacteristic
30C3×#3752C2211yescharacteristic
31C3×#3752C2211yescharacteristic
32C3×#3752C2211yescharacteristic
33C32×#217C2211yescharacteristic
34C32×#217C2211yescharacteristic
35C32×#217C2211yescharacteristic
36C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
37C32×C4⋊Dic3C2211yescharacteristic, complemented
38C32×Dic3⋊C4C2211yescharacteristic, complemented
39C32×Dic3⋊C4C2211yescharacteristic, complemented
40C32×Dic3⋊C4C2211yescharacteristic, complemented
41C32×C4×Dic3C2211yescharacteristic, complemented
42C3×#3724C2211yescharacteristic, complemented
43C3×#3724C2211yescharacteristic, complemented
44C3×Dic3⋊Dic3C2211yescharacteristic, complemented
45C3×Dic3⋊Dic3C2211yescharacteristic, complemented
46C3×#3722C2211yescharacteristic
47C3×#3722C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
51C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52C3×Dic32C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54C32×C22⋊Q8—31no—
55C32×C4×D4—31no—
56C2×#3752C2×C311yescharacteristic, complemented
57C3×#947—31no—
58C3×#946—31no—
59C3×#937—31no—
60C3×#935—31no—
61C3×#929—31no—
62C3×C4×#67—21no—
63C3×C4×#67—31no—
64C3×C4×#67D311yescharacteristic, complemented
65C3×C4×#67C2×C311yescharacteristic, complemented
66C2×C3×(C2×D3)⋊C4—31no—
67C2×C3×(C2×D3)⋊C4—31no—
68C2×C3×(C2×D3)⋊C4—61no—
69C3×#924—21no—
70C3×#924D311yescharacteristic, complemented
71C3×#924C2×C311yescharacteristic, complemented
72C3×#898—31no—
73C3×#898—31no—
74C3×#898—31no—
75C3×#896—31no—
76C3×#894—31no—
77C3×#894—31no—
78C3×#893—31no—
79C3×#892—31no—
80C3×#886—31no—
81C3×#885—31no—
82C3×#883—31no—
83C3×#882—31no—
84C3×D3×C22⋊C4—31no—
85C3×D3×C22⋊C4—31no—
86C3×#877—31no—
87C3×#877—31no—
88C3×#876—31no—
89C3×#872—31no—
90#63981C2×C311yescharacteristic
91#63974C2×C311yescharacteristic, complemented
92#63962C2×C311yescharacteristic, complemented
93#63957C2×C311yescharacteristic, complemented
94#63907C2×C311yescharacteristic, complemented
95#63904C2×C311yescharacteristic, complemented
96#63888C2×C311yescharacteristic, complemented
97#63868C2×C311yescharacteristic, complemented
98#63854C2×C311yescharacteristic, complemented
99#63850C2×C311yescharacteristic, complemented
100#63848C2×C311yescharacteristic, complemented
101#63836C2×C311yescharacteristic, complemented
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3—22no—
104C22×C3×C3⋊D3—22no—
105C22×C3×C3⋊D3—41no—
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×C33×C4—41no—
110C2×C33×C4C2311yescharacteristic
111C2×C33×C4C2311yescharacteristic
112C2×C3×C3⋊Dic3—22no—
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C32×#67—22no—
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C32×C4×D3—41no—
124C32×Dic6—41no—
125C3×#626—22no—
126C3×#626—41no—
127C3×#624—22no—
128C3×#624—41no—
129C3×#551—91no—
130#5637—31no—
131#5556—31no—
132C23×C3⋊D3C22×C311yescharacteristic
133C23×C3×D3—31no—
134C23×C3×D3—31no—
135C23×C3×D3—61no—
136C2×C32×Q8—31no—
137C2×C32×D4—31no—
138C22×C32×C4—21no—
139C22×C32×C4—21no—
140C22×C32×C4—21no—
141C22×C32×C4—31no—
142C22×C32×C4—41no—
143C22×C32×C4C2×D311yescharacteristic
144C22×C32×C4C2×D311yescharacteristic
145C22×C32×C4C22×C311yescharacteristic
146C22×C3⋊Dic3C22×C311yescharacteristic
147C2×C3×#67—21no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67C2×D311yescharacteristic
151C2×C3×#67C22×C311yescharacteristic
152C22×C3×Dic3—31no—
153C22×C3×Dic3—31no—
154C22×C3×Dic3—61no—
155C2×C3×D12—31no—
156C2×C3×D12—31no—
157C2×C3×C4×D3—21no—
158C2×C3×C4×D3—31no—
159C2×C3×C4×D3—31no—
160C2×C3×C4×D3—31no—
161C2×C3×C4×D3—31no—
162C2×C3×C4×D3C2×D311yescharacteristic, complemented
163C2×C3×C4×D3C22×C311yescharacteristic, complemented
164C2×C3×Dic6—21no—
165C2×C3×Dic6C2×D311yescharacteristic, complemented
166C2×C3×Dic6C22×C311yescharacteristic, complemented
167C2×#626C22×C311yescharacteristic
168C2×#626C22×C311yescharacteristic
169C2×#624C22×C311yescharacteristic
170C2×#624C22×C311yescharacteristic
171C32×C4⋊C4—31no—
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×C42—31no—
180#3752C22×C311yescharacteristic
181#3752C22×C311yescharacteristic
182#3752C22×C311yescharacteristic
183#3752C22×C311yescharacteristic
184C3×#217—21no—
185C3×#217—21no—
186C3×#217—21no—
187C3×#217—31no—
188C3×#217—31no—
189C3×#217C2×D311yescharacteristic
190C3×#217C2×D311yescharacteristic
191C3×#217C2×D311yescharacteristic
192C3×#217C22×C311yescharacteristic
193C3×#217C22×C311yescharacteristic
194C3×#217C22×C311yescharacteristic
195C3×(C2×D3)⋊C4—21no—
196C3×(C2×D3)⋊C4—31no—
197C3×(C2×D3)⋊C4—31no—
198C3×(C2×D3)⋊C4—31no—
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—31no—
201C3×(C2×D3)⋊C4—31no—
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—61no—
215C3×(C2×D3)⋊C4—61no—
216C3×(C2×D3)⋊C4—61no—
217C3×(C2×D3)⋊C4—61no—
218C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
219C3×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
220C3×C4⋊Dic3—21no—
221C3×C4⋊Dic3—31no—
222C3×C4⋊Dic3—31no—
223C3×C4⋊Dic3C2×D311yescharacteristic, complemented
224C3×C4⋊Dic3C22×C311yescharacteristic, complemented
225C3×Dic3⋊C4—21no—
226C3×Dic3⋊C4—21no—
227C3×Dic3⋊C4—21no—
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⋊C4C2×D311yescharacteristic, complemented
235C3×Dic3⋊C4C2×D311yescharacteristic, complemented
236C3×Dic3⋊C4C2×D311yescharacteristic, complemented
237C3×Dic3⋊C4C22×C311yescharacteristic, complemented
238C3×Dic3⋊C4C22×C311yescharacteristic, complemented
239C3×Dic3⋊C4C22×C311yescharacteristic, complemented
240C3×C4×Dic3—21no—
241C3×C4×Dic3—31no—
242C3×C4×Dic3—31no—
243C3×C4×Dic3—31no—
244C3×C4×Dic3—31no—
245C3×C4×Dic3C2×D311yescharacteristic, complemented
246C3×C4×Dic3C22×C311yescharacteristic, complemented
247#3724C22×C311yescharacteristic, complemented
248#3724C22×C311yescharacteristic, complemented
249Dic3⋊Dic3C22×C311yescharacteristic, complemented
250Dic3⋊Dic3C22×C311yescharacteristic, complemented
251#3722C22×C311yescharacteristic
252#3722C22×C311yescharacteristic
253#3722C22×C311yescharacteristic
254#3722C22×C311yescharacteristic
255(C2×D3)⋊Dic3C22×C311yescharacteristic, complemented
256(C2×D3)⋊Dic3C22×C311yescharacteristic, complemented
257Dic32C22×C311yescharacteristic, complemented
258Dic32C22×C311yescharacteristic, complemented
259C22×C33—21no—
260C22×C33—21no—
261C22×C33#4112yes—
262C22×C33C2411yescharacteristic
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊D3—21no—
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3—44no—
269C2×C3×C3⋊D3#4112yes—
270C2×C32×D3—21no—
271C2×C32×D3—21no—
272C2×C32×D3—21no—
273C33×C4—21no—
274C33×C4—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—31no—
291C3×C22⋊Q8—31no—
292C3×C22⋊Q8—61no—
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#947—31no—
304#946—31no—
305#937—31no—
306#935—31no—
307#929—31no—
308C4×#67—31no—
309C4×#67C3×D311yescharacteristic, complemented
310C2×(C2×D3)⋊C4—31no—
311C2×(C2×D3)⋊C4—31no—
312C2×(C2×D3)⋊C4—61no—
313#924C3×D311yescharacteristic, complemented
314#898—31no—
315#898—31no—
316#898—31no—
317#896—31no—
318#894—31no—
319#894—31no—
320#893—31no—
321#892—31no—
322#886—31no—
323#885—31no—
324#883—31no—
325#882—31no—
326D3×C22⋊C4—31no—
327D3×C22⋊C4—31no—
328#877—31no—
329#877—31no—
330#876—31no—
331#872—31no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—21no—
335C23×C32—31no—
336C23×C32—41no—
337C23×C32C22×D311yescharacteristic
338C23×C32C22×D311yescharacteristic
339C23×C32C23×C311yescharacteristic
340C22×C3⋊D3—22no—
341C22×C3⋊D3—22no—
342C22×C3⋊D3—41no—
343C22×C3⋊D3C23×C311yescharacteristic
344C22×C3⋊D3C23×C311yescharacteristic
345C22×C3×D3—21no—
346C22×C3×D3—31no—
347C22×C3×D3—31no—
348C22×C3×D3—31no—
349C22×C3×D3—31no—
350C22×C3×D3—61no—
351C22×C3×D3—61no—
352C22×C3×D3—62no—
353C22×C3×D3—62no—
354C22×C3×D3—64no—
355C22×C3×D3—62no—
356C22×C3×D3—62no—
357C22×C3×D3—122no—
358C22×C3×D3—121no—
359C22×C3×D3—121no—
360C22×C3×D3—122no—
361C22×C3×D3C22×D311yescharacteristic
362C22×C3×D3C23×C311yescharacteristic
363C32×Q8—121no—
364C32×D4—62no—
365C2×C32×C4—21no—
366C2×C32×C4—21no—
367C2×C32×C4—21no—
368C2×C32×C4—21no—
369C2×C32×C4—21no—
370C2×C32×C4—21no—
371C2×C32×C4—31no—
372C2×C32×C4—31no—
373C2×C32×C4—31no—
374C2×C32×C4—31no—
375C2×C32×C4—31no—
376C2×C32×C4—31no—
377C2×C32×C4—31no—
378C2×C32×C4—41no—
379C2×C32×C4—41no—
380C2×C32×C4—41no—
381C2×C32×C4—41no—
382C2×C32×C4—41no—
383C2×C32×C4—42no—
384C2×C32×C4—42no—
385C2×C32×C4—42no—
386C2×C32×C4—44no—
387C2×C32×C4—121no—
388C2×C32×C4C22×D311yescharacteristic
389C2×C32×C4C22×D311yescharacteristic
390C2×C32×C4C22×D311yescharacteristic
391C2×C32×C4C22×D311yescharacteristic
392C2×C32×C4C23×C311yescharacteristic
393C2×C32×C4C23×C311yescharacteristic
394C2×C3⋊Dic3—22no—
395C2×C3⋊Dic3C23×C311yescharacteristic
396C2×C3⋊Dic3C23×C311yescharacteristic
397C3×#67—24no—
398C3×#67—22no—
399C3×#67—22no—
400C3×#67—62no—
401C3×#67—121no—
402C2×C3×Dic3—21no—
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—31no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3—62no—
416C2×C3×Dic3—62no—
417C2×C3×Dic3—122no—
418C2×C3×Dic3C22×D311yescharacteristic
419C2×C3×Dic3C22×D311yescharacteristic
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C23×C311yescharacteristic
426C2×C3×Dic3C23×C311yescharacteristic
427C2×C3×Dic3C23×C311yescharacteristic
428C2×C3×Dic3C23×C311yescharacteristic
429C2×C3×Dic3C23×C311yescharacteristic
430C2×C3×Dic3C23×C311yescharacteristic
431C2×C3×Dic3C23×C311yescharacteristic
432C3×D12—62no—
433C3×D12—121no—
434C3×C4×D3—41no—
435C3×C4×D3—41no—
436C3×C4×D3—42no—
437C3×C4×D3—62no—
438C3×C4×D3—62no—
439C3×C4×D3—121no—
440C3×C4×D3—121no—
441C3×Dic6—41no—
442C3×Dic6—41no—
443C3×Dic6—42no—
444#626—22no—
445#626—41no—
446#624—22no—
447#624—41no—
448#551—91noSylow
449C2×C33—22no—
450C2×C33C2×#4111yescharacteristic
451C2×C33C2×#4111yescharacteristic
452C2×C33H(5,𝔽2)11yescharacteristic
453C3×C3⋊D3—22no—
454C3×C3⋊D3—41no—
455C32×D3—41no—
456C24×C3—91no—
457C23×D3—31no—
458C23×D3—31no—
459C23×D3—61no—
460C2×C3×Q8—31no—
461C2×C3×Q8—31no—
462C2×C3×Q8—61no—
463C2×C3×D4—31no—
464C2×C3×D4—31no—
465C2×C3×D4—61no—
466C2×C3×D4—91no—
467C2×C3×D4—91no—
468C22×C3×C4—21no—
469C22×C3×C4—21no—
470C22×C3×C4—21no—
471C22×C3×C4—31no—
472C22×C3×C4—31no—
473C22×C3×C4—41no—
474C22×C3×C4—61no—
475C22×C3×C4—91no—
476C22×C3×C4—91no—
477C22×C3×C4—91no—
478C22×C3×C4D3211yescharacteristic
479C22×C3×C4C2×C3×D311yescharacteristic
480C22×C3×C4C2×C3×D311yescharacteristic
481C2×#67—31no—
482C2×#67—31no—
483C2×#67C2×C3×D311yescharacteristic
484C22×Dic3—31no—
485C22×Dic3—31no—
486C22×Dic3—61no—
487C2×D12—31no—
488C2×D12—31no—
489C2×C4×D3—31no—
490C2×C4×D3—31no—
491C2×C4×D3—31no—
492C2×C4×D3—31no—
493C2×C4×D3C2×C3×D311yescharacteristic, complemented
494C2×Dic6C2×C3×D311yescharacteristic, complemented
495C3×C4⋊C4—31no—
496C3×C4⋊C4—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—61no—
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—61no—
520C3×C22⋊C4—61no—
521C3×C22⋊C4—61no—
522C3×C22⋊C4—61no—
523C3×C22⋊C4—91no—
524C3×C22⋊C4—91no—
525C3×C22⋊C4—91no—
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×C42—31no—
534C3×C42—31no—
535C3×C42—61no—
536C3×C42—91no—
537C3×C42—91no—
538#217—31no—
539#217—31no—
540#217C2×C3×D311yescharacteristic
541#217C2×C3×D311yescharacteristic
542#217C2×C3×D311yescharacteristic
543(C2×D3)⋊C4—31no—
544(C2×D3)⋊C4—31no—
545(C2×D3)⋊C4—31no—
546(C2×D3)⋊C4—31no—
547(C2×D3)⋊C4—31no—
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—61no—
562(C2×D3)⋊C4—61no—
563(C2×D3)⋊C4—61no—
564(C2×D3)⋊C4—61no—
565(C2×D3)⋊C4C2×C3×D311yescharacteristic, complemented
566C4⋊Dic3—31no—
567C4⋊Dic3—31no—
568C4⋊Dic3C2×C3×D311yescharacteristic, complemented
569Dic3⋊C4—31no—
570Dic3⋊C4—31no—
571Dic3⋊C4—31no—
572Dic3⋊C4—31no—
573Dic3⋊C4—31no—
574Dic3⋊C4—31no—
575Dic3⋊C4C2×C3×D311yescharacteristic, complemented
576Dic3⋊C4C2×C3×D311yescharacteristic, complemented
577Dic3⋊C4C2×C3×D311yescharacteristic, complemented
578C4×Dic3—31no—
579C4×Dic3—31no—
580C4×Dic3—31no—
581C4×Dic3—31no—
582C4×Dic3C2×C3×D311yescharacteristic, complemented
583C22×C32—21no—
584C22×C32—21no—
585C22×C32—22no—
586C22×C32—22no—
587C22×C32—21no—
588C22×C32—21no—
589C22×C32—21no—
590C22×C32—21no—
591C22×C32—21no—
592C22×C32—21no—
593C22×C32—21no—
594C22×C32—22no—
595C22×C32—22no—
596C22×C32—22no—
597C22×C32—42no—
598C22×C32—41no—
599C22×C32—41no—
600C22×C32—41no—
601C22×C32—41no—
602C22×C32—41no—
603C22×C32—42no—
604C22×C32—42no—
605C22×C32—61no—
606C22×C32—61no—
607C22×C32—61no—
608C22×C32#23512yes—
609C22×C32#23912yes—
610C22×C32C3×#4112yes—
611C22×C32C23×D311yescharacteristic
612C22×C32C23×D311yescharacteristic
613C22×C32C24×C311yescharacteristic
614C2×C3⋊D3—21no—
615C2×C3⋊D3—21no—
616C2×C3⋊D3—21no—
617C2×C3⋊D3—21no—
618C2×C3⋊D3—21no—
619C2×C3⋊D3—44no—
620C2×C3⋊D3C3×#4112yes—
621C2×C3×D3—22no—
622C2×C3×D3—21no—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—21no—
626C2×C3×D3—21no—
627C2×C3×D3—21no—
628C2×C3×D3—32no—
629C2×C3×D3—32no—
630C2×C3×D3—41no—
631C2×C3×D3—41no—
632C2×C3×D3—62no—
633C2×C3×D3—61no—
634C2×C3×D3—61no—
635C2×C3×D3—61no—
636C2×C3×D3—61no—
637C2×C3×D3—62no—
638C2×C3×D3—61no—
639C2×C3×D3—61no—
640C2×C3×D3—61no—
641C2×C3×D3—61no—
642C2×C3×D3—61no—
643C2×C3×D3—61no—
644C2×C3×D3—121no—
645C2×C3×D3—121no—
646C2×C3×D3—121no—
647C2×C3×D3—121no—
648C2×C3×D3—124no—
649C2×C3×D3—124no—
650C2×C3×D3—128no—
651C32×C4—21no—
652C32×C4—21no—
653C32×C4—22no—
654C32×C4—22no—
655C32×C4—21no—
656C32×C4—21no—
657C32×C4—21no—
658C32×C4—21no—
659C32×C4—41no—
660C32×C4—41no—
661C32×C4—41no—
662C32×C4—41no—
663C32×C4—42no—
664C32×C4—42no—
665C32×C4—61no—
666C32×C4—61no—
667C32×C4—61no—
668C32×C4—61no—
669C32×C4—61no—
670C32×C4—61no—
671C32×C4—61no—
672C3⋊Dic3—21no—
673C3⋊Dic3—21no—
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—41no—
690C3×Dic3—41no—
691C3×Dic3—41no—
692C3×Dic3—41no—
693C3×Dic3—41no—
694C3×Dic3—41no—
695C3×Dic3—61no—
696C3×Dic3—61no—
697C3×Dic3—61no—
698C3×Dic3—61no—
699C3×Dic3—121no—
700C3×Dic3—121no—
701#126—91no—
702#126—91no—
703#124—91no—
704#123—91no—
705#123—91no—
706#123—91no—
707C22⋊Q8—31no—
708C22⋊Q8—91no—
709#120—91no—
710C4×D4—31no—
711C4×D4—91no—
712#117—91no—
713#117—91no—
714C2×C22⋊C4—91no—
715C2×C22⋊C4—91no—
716C33#55111yescharacteristic, complemented, Sylow
717C23×C3—21no—
718C23×C3—21no—
719C23×C3—21no—
720C23×C3—31no—
721C23×C3—31no—
722C23×C3—41no—
723C23×C3—61no—
724C23×C3—91no—
725C23×C3—91no—
726C23×C3—182no—
727C23×C3—182no—
728C23×C3—361no—
729C23×C3C2×D3211yescharacteristic
730C23×C3C22×C3×D311yescharacteristic
731C23×C3C22×C3×D311yescharacteristic
732C22×D3—31no—
733C22×D3—31no—
734C22×D3—31no—
735C22×D3—31no—
736C22×D3—61no—
737C22×D3—61no—
738C22×D3—62no—
739C22×D3—62no—
740C22×D3—64no—
741C22×D3—62no—
742C22×D3—62no—
743C22×D3—122no—
744C22×D3—121no—
745C22×D3—121no—
746C22×D3—122no—
747C22×D3C22×C3×D311yescharacteristic
748C3×Q8—121no—
749C3×Q8—121no—
750C3×Q8—122no—
751C3×D4—64no—
752C3×D4—62no—
753C3×D4—62no—
754C3×D4—182no—
755C3×D4—361no—
756C2×C3×C4—21no—
757C2×C3×C4—21no—
758C2×C3×C4—21no—
759C2×C3×C4—21no—
760C2×C3×C4—21no—
761C2×C3×C4—21no—
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—31no—
775C2×C3×C4—31no—
776C2×C3×C4—41no—
777C2×C3×C4—41no—
778C2×C3×C4—41no—
779C2×C3×C4—42no—
780C2×C3×C4—42no—
781C2×C3×C4—42no—
782C2×C3×C4—44no—
783C2×C3×C4—41no—
784C2×C3×C4—41no—
785C2×C3×C4—61no—
786C2×C3×C4—61no—
787C2×C3×C4—61no—
788C2×C3×C4—61no—
789C2×C3×C4—61no—
790C2×C3×C4—61no—
791C2×C3×C4—61no—
792C2×C3×C4—91no—
793C2×C3×C4—91no—
794C2×C3×C4—121no—
795C2×C3×C4—121no—
796C2×C3×C4—122no—
797C2×C3×C4—182no—
798C2×C3×C4—182no—
799C2×C3×C4—361no—
800C2×C3×C4C2×D3211yescharacteristic
801C2×C3×C4C2×D3211yescharacteristic
802C2×C3×C4C22×C3×D311yescharacteristic
803C2×C3×C4C22×C3×D311yescharacteristic
804C2×C3×C4C22×C3×D311yescharacteristic
805C2×C3×C4C22×C3×D311yescharacteristic
806#67—22no—
807#67—62no—
808#67—121no—
809C2×Dic3—31no—
810C2×Dic3—31no—
811C2×Dic3—31no—
812C2×Dic3—31no—
813C2×Dic3—61no—
814C2×Dic3—61no—
815C2×Dic3—62no—
816C2×Dic3—62no—
817C2×Dic3—122no—
818C2×Dic3C22×C3×D311yescharacteristic
819C2×Dic3C22×C3×D311yescharacteristic
820C2×Dic3C22×C3×D311yescharacteristic
821C2×Dic3C22×C3×D311yescharacteristic
822C2×Dic3C22×C3×D311yescharacteristic
823C2×Dic3C22×C3×D311yescharacteristic
824C2×Dic3C22×C3×D311yescharacteristic
825D12—62no—
826D12—121no—
827C4×D3—41no—
828C4×D3—62no—
829C4×D3—62no—
830C4×D3—121no—
831C4×D3—121no—
832Dic6—41no—
833C2×C32—22no—
834C2×C32—24no—
835C2×C32—22no—
836C2×C32—22no—
837C2×C32—21no—
838C2×C32—21no—
839C2×C32—21no—
840C2×C32—21no—
841C2×C32—21no—
842C2×C32—21no—
843C2×C32—21no—
844C2×C32—21no—
845C2×C32—21no—
846C2×C32—41no—
847C2×C32—41no—
848C2×C32—41no—
849C2×C32—42no—
850C2×C32—42no—
851C2×C32—44no—
852C2×C32—121no—
853C2×C32C2×#23511yescharacteristic
854C2×C32#100411yescharacteristic
855C2×C32#100411yescharacteristic
856C2×C32C2×#23911yescharacteristic
857C2×C32D3×#4111yescharacteristic
858C2×C32D3×#4111yescharacteristic
859C2×C32C2×C3×#4111yescharacteristic
860C2×C32C2×C3×#4111yescharacteristic
861C2×C32C3×H(5,𝔽2)11yescharacteristic
862C3⋊D3—22no—
863C3⋊D3—41no—
864C3×D3—42no—
865C3×D3—41no—
866C3×D3—41no—
867C3×D3—62no—
868C3×D3—62no—
869C3×D3—122no—
870C3×D3—122no—
871C3×D3—121no—
872C3×D3—121no—
873C24—91no—
874C2×Q8—31no—
875C2×D4—31no—
876C2×D4—91no—
877C2×D4—91no—
878C22×C4—31no—
879C22×C4—91no—
880C22×C4—91no—
881C22×C4—91no—
882C22×C4C3×D3211yescharacteristic
883C4⋊C4—31no—
884C4⋊C4—31no—
885C4⋊C4—31no—
886C4⋊C4—31no—
887C4⋊C4—91no—
888C4⋊C4—91no—
889C4⋊C4—91no—
890C4⋊C4—91no—
891C22⋊C4—31no—
892C22⋊C4—31no—
893C22⋊C4—31no—
894C22⋊C4—31no—
895C22⋊C4—91no—
896C22⋊C4—91no—
897C22⋊C4—91no—
898C22⋊C4—91no—
899C22⋊C4—91no—
900C22⋊C4—91no—
901C22⋊C4—91no—
902C22⋊C4—91no—
903C22⋊C4—91no—
904C22⋊C4—91no—
905C42—31no—
906C42—91no—
907C42—91no—
908C22×C3—22no—
909C22×C3—22no—
910C22×C3—21no—
911C22×C3—21no—
912C22×C3—21no—
913C22×C3—21no—
914C22×C3—21no—
915C22×C3—21no—
916C22×C3—21no—
917C22×C3—21no—
918C22×C3—21no—
919C22×C3—22no—
920C22×C3—22no—
921C22×C3—22no—
922C22×C3—41no—
923C22×C3—41no—
924C22×C3—41no—
925C22×C3—41no—
926C22×C3—42no—
927C22×C3—42no—
928C22×C3—41no—
929C22×C3—42no—
930C22×C3—62no—
931C22×C3—61no—
932C22×C3—61no—
933C22×C3—61no—
934C22×C3—61no—
935C22×C3—61no—
936C22×C3—61no—
937C22×C3—92no—
938C22×C3—121no—
939C22×C3—121no—
940C22×C3—181no—
941C22×C3—181no—
942C22×C3—181no—
943C22×C3—181no—
944C22×C3—181no—
945C22×C3—364no—
946C22×C3#379912yes—
947C22×C3C3×#23512yes—
948C22×C3C3×#23912yes—
949C22×C3C22×D3211yescharacteristic
950C22×C3C23×C3×D311yescharacteristic
951C22×C3C23×C3×D311yescharacteristic
952C2×D3—21no—
953C2×D3—21no—
954C2×D3—21no—
955C2×D3—32no—
956C2×D3—32no—
957C2×D3—62no—
958C2×D3—61no—
959C2×D3—61no—
960C2×D3—61no—
961C2×D3—61no—
962C2×D3—62no—
963C2×D3—61no—
964C2×D3—61no—
965C2×D3—61no—
966C2×D3—61no—
967C2×D3—61no—
968C2×D3—61no—
969C2×D3—121no—
970C2×D3—121no—
971C2×D3—121no—
972C2×D3—121no—
973C2×D3—124no—
974C2×D3—124no—
975C2×D3—128no—
976C3×C4—22no—
977C3×C4—22no—
978C3×C4—21no—
979C3×C4—21no—
980C3×C4—21no—
981C3×C4—21no—
982C3×C4—21no—
983C3×C4—21no—
984C3×C4—41no—
985C3×C4—41no—
986C3×C4—41no—
987C3×C4—41no—
988C3×C4—42no—
989C3×C4—42no—
990C3×C4—62no—
991C3×C4—61no—
992C3×C4—61no—
993C3×C4—61no—
994C3×C4—61no—
995C3×C4—61no—
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—121no—
1006C3×C4—121no—
1007C3×C4—121no—
1008C3×C4—121no—
1009C3×C4—121no—
1010C3×C4—121no—
1011C3×C4—181no—
1012C3×C4—181no—
1013Dic3—21no—
1014Dic3—21no—
1015Dic3—21no—
1016Dic3—21no—
1017Dic3—21no—
1018Dic3—21no—
1019Dic3—21no—
1020Dic3—61no—
1021Dic3—61no—
1022Dic3—61no—
1023Dic3—61no—
1024Dic3—121no—
1025Dic3—121no—
1026C32—21no—
1027C32—21no—
1028C32—21no—
1029C32—41no—
1030C32#555611yescharacteristic, complemented
1031C32#563711yescharacteristic, complemented
1032C32C3×#55111yescharacteristic, complemented
1033C23—31no—
1034C23—91no—
1035C23—91no—
1036C23—182no—
1037C23—182no—
1038C23—361no—
1039C23C2×C3×D3211yescharacteristic
1040Q8—121no—
1041D4—62no—
1042D4—182no—
1043D4—361no—
1044C2×C4—31no—
1045C2×C4—31no—
1046C2×C4—31no—
1047C2×C4—31no—
1048C2×C4—31no—
1049C2×C4—31no—
1050C2×C4—31no—
1051C2×C4—41no—
1052C2×C4—91no—
1053C2×C4—91no—
1054C2×C4—121no—
1055C2×C4—182no—
1056C2×C4—182no—
1057C2×C4—361no—
1058C2×C4C2×C3×D3211yescharacteristic
1059C2×C4C2×C3×D3211yescharacteristic
1060C2×C3—24no—
1061C2×C3—22no—
1062C2×C3—22no—
1063C2×C3—22no—
1064C2×C3—21no—
1065C2×C3—21no—
1066C2×C3—21no—
1067C2×C3—21no—
1068C2×C3—21no—
1069C2×C3—21no—
1070C2×C3—21no—
1071C2×C3—21no—
1072C2×C3—21no—
1073C2×C3—42no—
1074C2×C3—42no—
1075C2×C3—44no—
1076C2×C3—41no—
1077C2×C3—41no—
1078C2×C3—41no—
1079C2×C3—122no—
1080C2×C3—121no—
1081C2×C3—121no—
1082C2×C3—182no—
1083C2×C3—361no—
1084C2×C3C2×#379911yescharacteristic
1085C2×C3#6430611yescharacteristic
1086C2×C3#6433011yescharacteristic
1087C2×C3C2×C3×#23511yescharacteristic
1088C2×C3C3×#100411yescharacteristic
1089C2×C3C3×#100411yescharacteristic
1090C2×C3C2×C3×#23911yescharacteristic
1091C2×C3C3×D3×#4111yescharacteristic
1092C2×C3C3×D3×#4111yescharacteristic
1093D3—41no—
1094D3—62no—
1095D3—62no—
1096D3—122no—
1097D3—122no—
1098D3—121no—
1099D3—121no—
1100C22—21no—
1101C22—21no—
1102C22—61no—
1103C22—61no—
1104C22—61no—
1105C22—92no—
1106C22—181no—
1107C22—181no—
1108C22—181no—
1109C22—181no—
1110C22—181no—
1111C22—364no—
1112C22C3×#379912yes—
1113C22C22×C3×D3211yescharacteristic
1114C4—21no—
1115C4—21no—
1116C4—61no—
1117C4—61no—
1118C4—61no—
1119C4—61no—
1120C4—61no—
1121C4—61no—
1122C4—61no—
1123C4—181no—
1124C4—181no—
1125C3—21no—
1126C3—21no—
1127C3—21no—
1128C3—41no—
1129C3#1059503511yescharacteristic, direct product factor
1130C3C3×#555611yescharacteristic, complemented
1131C3C3×#563711yescharacteristic, complemented
1132C2—22no—
1133C2—121no—
1134C2—182no—
1135C2—361no—
1136C2C2×C3×#379911yescharacteristic
1137C2C3×#6430611yescharacteristic
1138C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
prime radicalC3×#63981C2
hypercenterC22×C3×C4D32
hypocenterC32C3×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3752C2semidirect
2. C32×C4×#67C2semidirect
3. C32×#924C2semidirect
5. C3×#63974C2semidirect
6. C3×#63962C2semidirect
7. C3×#63957C2semidirect
8. C3×#63907C2semidirect
9. C3×#63904C2semidirect
10. C3×#63888C2semidirect
11. C3×#63868C2semidirect
12. C3×#63854C2semidirect
13. C3×#63850C2semidirect
14. C3×#63848C2semidirect
15. C3×#63836C2semidirect
18. #10595035C3direct (N × H)
23. C2×C32×C4×D3C22semidirect
24. C2×C32×Dic6C22semidirect
36. C32×(C2×D3)⋊C4C22semidirect
37. C32×C4⋊Dic3C22semidirect
38. C32×Dic3⋊C4C22semidirect
39. C32×Dic3⋊C4C22semidirect
40. C32×Dic3⋊C4C22semidirect
41. C32×C4×Dic3C22semidirect
42. C3×#3724C22semidirect
43. C3×#3724C22semidirect
44. C3×Dic3⋊Dic3C22semidirect
45. C3×Dic3⋊Dic3C22semidirect
50. C3×(C2×D3)⋊Dic3C22semidirect
51. C3×(C2×D3)⋊Dic3C22semidirect
52. C3×Dic32C22semidirect
53. C3×Dic32C22semidirect
56. C2×#3752C2×C3semidirect
64. C3×C4×#67D3semidirect
65. C3×C4×#67C2×C3semidirect
70. C3×#924D3semidirect
71. C3×#924C2×C3semidirect
91. #63974C2×C3semidirect
92. #63962C2×C3semidirect
93. #63957C2×C3semidirect
94. #63907C2×C3semidirect
95. #63904C2×C3semidirect
96. #63888C2×C3semidirect
97. #63868C2×C3semidirect
98. #63854C2×C3semidirect
99. #63850C2×C3semidirect
100. #63848C2×C3semidirect
101. #63836C2×C3semidirect
162. C2×C3×C4×D3C2×D3semidirect
163. C2×C3×C4×D3C22×C3semidirect
165. C2×C3×Dic6C2×D3semidirect
166. C2×C3×Dic6C22×C3semidirect
218. C3×(C2×D3)⋊C4C2×D3semidirect
219. C3×(C2×D3)⋊C4C22×C3semidirect
223. C3×C4⋊Dic3C2×D3semidirect
224. C3×C4⋊Dic3C22×C3semidirect
234. C3×Dic3⋊C4C2×D3semidirect
235. C3×Dic3⋊C4C2×D3semidirect
236. C3×Dic3⋊C4C2×D3semidirect
237. C3×Dic3⋊C4C22×C3semidirect
238. C3×Dic3⋊C4C22×C3semidirect
239. C3×Dic3⋊C4C22×C3semidirect
245. C3×C4×Dic3C2×D3semidirect
246. C3×C4×Dic3C22×C3semidirect
247. #3724C22×C3semidirect
248. #3724C22×C3semidirect
249. Dic3⋊Dic3C22×C3semidirect
250. Dic3⋊Dic3C22×C3semidirect
255. (C2×D3)⋊Dic3C22×C3semidirect
256. (C2×D3)⋊Dic3C22×C3semidirect
257. Dic32C22×C3semidirect
258. Dic32C22×C3semidirect
309. C4×#67C3×D3semidirect
313. #924C3×D3semidirect
493. C2×C4×D3C2×C3×D3semidirect
494. C2×Dic6C2×C3×D3semidirect
565. (C2×D3)⋊C4C2×C3×D3semidirect
568. C4⋊Dic3C2×C3×D3semidirect
575. Dic3⋊C4C2×C3×D3semidirect
576. Dic3⋊C4C2×C3×D3semidirect
577. Dic3⋊C4C2×C3×D3semidirect
582. C4×Dic3C2×C3×D3semidirect
716. C33#551semidirect
1030. C32#5556semidirect
1031. C32#5637semidirect
1032. C32C3×#551semidirect
1129. C3#10595035direct (N × H)
1130. C3C3×#5556semidirect
1131. C3C3×#5637semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37522
C32×C4×#672
C32×#9242
C3×#639812
C3×#639742
C3×#639622
C3×#639572
C3×#639072
C3×#639042
C3×#638882
C3×#638682
C3×#638542
C3×#638502
C3×#638482
C3×#638362
C3×#56373
C3×#55563
#105950353