Finite Group Databasebeta

← C3×#10594544 #13173976

Subgroups — C3×#10594544 #13173976

Order 1728.

1208 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64107C211yesmaximal, characteristic, complemented
2C32×#894C211yesmaximal, characteristic, complemented
3C32×D3×C4⋊C4C211yesmaximal, characteristic, complemented
4C3×#63908C211yesmaximal, characteristic, complemented
5C3×#63906C211yesmaximal, characteristic, complemented
6C3×#63906C211yesmaximal, characteristic, complemented
7C3×#63904C211yesmaximal, characteristic, complemented
8C3×#63904C211yesmaximal, characteristic, complemented
9C3×C4×#625C211yesmaximal, characteristic, complemented
10C3×#63886C211yesmaximal, characteristic, complemented
11C3×#63879C211yesmaximal, characteristic, complemented
12C3×#63878C211yesmaximal, characteristic, complemented
13C3×#63858C211yesmaximal, characteristic, complemented
14C3×#63854C211yesmaximal, characteristic, complemented
15C3×#63845C211yesmaximal, characteristic, complemented
16C3×#5661—31nomaximal
17C3×#5514—31nomaximal
18#10594544C311yesmaximal, characteristic, direct product factor
19C2×C32×D12C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×C32×C4×D3C2211yescharacteristic
22C2×C32×C4×D3C2211yescharacteristic
23C2×C32×C4×D3C2211yescharacteristic
24C2×C3×#626C2211yescharacteristic
25C2×C3×#626C2211yescharacteristic
26C2×C3×#626C2211yescharacteristic
27C2×C3×#625C2211yescharacteristic
28C2×C3×#625C2211yescharacteristic
29C2×C3×#624C2211yescharacteristic
30C2×C3×D3×Dic3C2211yescharacteristic
31C33×C4⋊C4C2211yescharacteristic
32C3×#3752C2211yescharacteristic
33C3×#3752C2211yescharacteristic
34C3×#3752C2211yescharacteristic
35C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
36C3×#3750C2211yescharacteristic
37C3×C4×C3⋊Dic3C2211yescharacteristic
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×C4⋊Dic3C2211yescharacteristic
42C32×Dic3⋊C4C2211yescharacteristic
43C32×Dic3⋊C4C2211yescharacteristic
44C32×Dic3⋊C4C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C32×#123—31no—
55C2×C32×C4⋊C4—31no—
56#64107C2×C311yescharacteristic, complemented
57C3×#939—31no—
58C3×#938—31no—
59C3×#930—31no—
60C3×#930—31no—
61C3×#930—31no—
62C3×C4×#67—31no—
63C3×C4×#67—31no—
64C3×C4×#67—31no—
65C3×C4×#67—31no—
66C3×C4×#67—31no—
67C3×#898—31no—
68C3×#898—31no—
69C3×#898—31no—
70C3×#898—61no—
71C3×#895—31no—
72C3×#894—21no—
73C3×#894—31no—
74C3×#894D311yescharacteristic, complemented
75C3×#894C2×C311yescharacteristic, complemented
76C3×#893—31no—
77C3×#893—31no—
78C3×#892—31no—
79C3×D3×C4⋊C4—21no—
80C3×D3×C4⋊C4D311yescharacteristic, complemented
81C3×D3×C4⋊C4C2×C311yescharacteristic, complemented
82C3×#890—31no—
83C3×#889—31no—
84C3×#884—31no—
85C3×#884—31no—
86C3×#883—31no—
87C3×#67⋊C4—31no—
88C3×#879—31no—
89C3×#877—31no—
90#63908C2×C311yescharacteristic, complemented
91#63906C2×C311yescharacteristic, complemented
92#63906C2×C311yescharacteristic, complemented
93#63904C2×C311yescharacteristic, complemented
94#63904C2×C311yescharacteristic, complemented
95C4×#625C2×C311yescharacteristic, complemented
96#63886C2×C311yescharacteristic, complemented
97#63879C2×C311yescharacteristic, complemented
98#63878C2×C311yescharacteristic, complemented
99#63858C2×C311yescharacteristic, complemented
100#63854C2×C311yescharacteristic, complemented
101#63845C2×C311yescharacteristic, complemented
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×C33×C4C2311yescharacteristic
107C2×C33×C4C2311yescharacteristic
108C2×C33×C4C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C32×D12—41no—
118C32×C4×D3—22no—
119C32×C4×D3—41no—
120C32×C4×D3—41no—
121C32×C4×D3—41no—
122C3×#626—22no—
123C3×#626—22no—
124C3×#626—41no—
125C3×#625—22no—
126C3×#625—22no—
127C3×#624—41no—
128C3×D3×Dic3—22no—
129C3×#553—91no—
130#5661—31no—
131#5514—31no—
132C2×C32×D4—31no—
133C22×C32×C4—31no—
134C22×C32×C4—31no—
135C22×C32×C4—31no—
136C22×C32×C4—31no—
137C2×C3×#67—31no—
138C2×C3×#67—31no—
139C2×C3×#67—31no—
140C2×C3×#67—31no—
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C22×C3×Dic3—31no—
145C2×C3×D12—21no—
146C2×C3×D12—31no—
147C2×C3×D12—31no—
148C2×C3×D12—31no—
149C2×C3×D12C2×D311yescharacteristic
150C2×C3×D12C22×C311yescharacteristic
151C2×C3×C4×D3—21no—
152C2×C3×C4×D3—21no—
153C2×C3×C4×D3—21no—
154C2×C3×C4×D3—21no—
155C2×C3×C4×D3—31no—
156C2×C3×C4×D3—31no—
157C2×C3×C4×D3—31no—
158C2×C3×C4×D3C2×D311yescharacteristic
159C2×C3×C4×D3C2×D311yescharacteristic
160C2×C3×C4×D3C2×D311yescharacteristic
161C2×C3×C4×D3C2×D311yescharacteristic
162C2×C3×C4×D3C22×C311yescharacteristic
163C2×C3×C4×D3C22×C311yescharacteristic
164C2×C3×C4×D3C22×C311yescharacteristic
165C2×C3×C4×D3C22×C311yescharacteristic
166C2×#626C22×C311yescharacteristic
167C2×#626C22×C311yescharacteristic
168C2×#626C22×C311yescharacteristic
169C2×#625C22×C311yescharacteristic
170C2×#625C22×C311yescharacteristic
171C2×#624C22×C311yescharacteristic
172C2×D3×Dic3C22×C311yescharacteristic
173C32×C4⋊C4—21no—
174C32×C4⋊C4—21no—
175C32×C4⋊C4—21no—
176C32×C4⋊C4—31no—
177C32×C4⋊C4—31no—
178C32×C4⋊C4—31no—
179C32×C4⋊C4—31no—
180C32×C4⋊C4—41no—
181C32×C4⋊C4C2×D311yescharacteristic
182C32×C4⋊C4C2×D311yescharacteristic
183C32×C4⋊C4C22×C311yescharacteristic
184C32×C22⋊C4—31no—
185C32×C22⋊C4—31no—
186C32×C22⋊C4—31no—
187#3752C22×C311yescharacteristic
188#3752C22×C311yescharacteristic
189#3752C22×C311yescharacteristic
190C4⋊(C3⋊Dic3)C22×C311yescharacteristic
191#3750C22×C311yescharacteristic
192C4×C3⋊Dic3C22×C311yescharacteristic
193C3×#217—31no—
194C3×#217—31no—
195C3×#217—31no—
196C3×#217—31no—
197C3×(C2×D3)⋊C4—21no—
198C3×(C2×D3)⋊C4—21no—
199C3×(C2×D3)⋊C4—21no—
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—61no—
211C3×(C2×D3)⋊C4—61no—
212C3×(C2×D3)⋊C4—61no—
213C3×(C2×D3)⋊C4C2×D311yescharacteristic
214C3×(C2×D3)⋊C4C2×D311yescharacteristic
215C3×(C2×D3)⋊C4C2×D311yescharacteristic
216C3×(C2×D3)⋊C4C22×C311yescharacteristic
217C3×(C2×D3)⋊C4C22×C311yescharacteristic
218C3×(C2×D3)⋊C4C22×C311yescharacteristic
219C3×C4⋊Dic3—21no—
220C3×C4⋊Dic3—31no—
221C3×C4⋊Dic3—31no—
222C3×C4⋊Dic3—31no—
223C3×C4⋊Dic3—31no—
224C3×C4⋊Dic3—61no—
225C3×C4⋊Dic3C2×D311yescharacteristic
226C3×C4⋊Dic3C22×C311yescharacteristic
227C3×Dic3⋊C4—21no—
228C3×Dic3⋊C4—21no—
229C3×Dic3⋊C4—21no—
230C3×Dic3⋊C4—31no—
231C3×Dic3⋊C4—31no—
232C3×Dic3⋊C4—31no—
233C3×Dic3⋊C4—31no—
234C3×Dic3⋊C4—31no—
235C3×Dic3⋊C4—31no—
236C3×Dic3⋊C4—61no—
237C3×Dic3⋊C4C2×D311yescharacteristic
238C3×Dic3⋊C4C2×D311yescharacteristic
239C3×Dic3⋊C4C2×D311yescharacteristic
240C3×Dic3⋊C4C22×C311yescharacteristic
241C3×Dic3⋊C4C22×C311yescharacteristic
242C3×Dic3⋊C4C22×C311yescharacteristic
243C3×C4×Dic3—31no—
244C3×C4×Dic3—31no—
245C3×C4×Dic3—31no—
246C3×C4×Dic3—31no—
247C3×C4×Dic3—31no—
248C3×C4×Dic3—31no—
249C3×C4×Dic3—61no—
250#3724C22×C311yescharacteristic
251Dic3⋊Dic3C22×C311yescharacteristic
252Dic3⋊Dic3C22×C311yescharacteristic
253(C2×D3)⋊Dic3C22×C311yescharacteristic
254(C2×D3)⋊Dic3C22×C311yescharacteristic
255(C2×D3)⋊Dic3C22×C311yescharacteristic
256(C2×D3)⋊Dic3C22×C311yescharacteristic
257Dic32C22×C311yescharacteristic
258Dic32C22×C311yescharacteristic
259C22×C33C2411yescharacteristic
260C2×C3×C3⋊D3—21no—
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊D3—21no—
263C2×C32×D3—21no—
264C2×C32×D3—21no—
265C2×C32×D3—21no—
266C2×C32×D3—21no—
267C2×C32×D3—21no—
268C2×C32×D3—21no—
269C2×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3#4112yes—
272C33×C4—21no—
273C33×C4—21no—
274C33×C4—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C32×Dic3—21no—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3#4112yes—
283C3×#126—91no—
284C3×#126—91no—
285C3×#125—91no—
286C3×#123—31no—
287C3×#123—31no—
288C3×#123—61no—
289C3×#123—91no—
290C3×#121—91no—
291C3×#121—91no—
292C3×#121—91no—
293C3×#121—91no—
294C3×C4×D4—91no—
295C3×C4×D4—91no—
296C3×C4×D4—91no—
297C3×C4×D4—91no—
298C3×#117—91no—
299C2×C3×C4⋊C4—31no—
300C2×C3×C4⋊C4—31no—
301C2×C3×C4⋊C4—61no—
302#939—31no—
303#938—31no—
304#930—31no—
305#930—31no—
306#930—31no—
307C4×#67—31no—
308C4×#67—31no—
309C4×#67—31no—
310C4×#67—31no—
311C4×#67—31no—
312#898—31no—
313#898—31no—
314#898—31no—
315#898—61no—
316#895—31no—
317#894—31no—
318#894C3×D311yescharacteristic, complemented
319#893—31no—
320#893—31no—
321#892—31no—
322D3×C4⋊C4C3×D311yescharacteristic, complemented
323#890—31no—
324#889—31no—
325#884—31no—
326#884—31no—
327#883—31no—
328#67⋊C4—31no—
329#879—31no—
330#877—31no—
331C23×C32—31no—
332C23×C32—31no—
333C23×C32—31no—
334C22×C3⋊D3C23×C311yescharacteristic
335C22×C3×D3—21no—
336C22×C3×D3—21no—
337C22×C3×D3—21no—
338C22×C3×D3—31no—
339C22×C3×D3—31no—
340C22×C3×D3—61no—
341C22×C3×D3C22×D311yescharacteristic
342C22×C3×D3C22×D311yescharacteristic
343C22×C3×D3C22×D311yescharacteristic
344C22×C3×D3C23×C311yescharacteristic
345C22×C3×D3C23×C311yescharacteristic
346C22×C3×D3C23×C311yescharacteristic
347C32×D4—121no—
348C2×C32×C4—21no—
349C2×C32×C4—21no—
350C2×C32×C4—21no—
351C2×C32×C4—21no—
352C2×C32×C4—21no—
353C2×C32×C4—21no—
354C2×C32×C4—21no—
355C2×C32×C4—21no—
356C2×C32×C4—21no—
357C2×C32×C4—31no—
358C2×C32×C4—31no—
359C2×C32×C4—31no—
360C2×C32×C4—31no—
361C2×C32×C4—31no—
362C2×C32×C4—41no—
363C2×C32×C4—41no—
364C2×C32×C4—41no—
365C2×C32×C4—62no—
366C2×C32×C4—121no—
367C2×C32×C4—121no—
368C2×C32×C4—121no—
369C2×C32×C4C22×D311yescharacteristic
370C2×C32×C4C22×D311yescharacteristic
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×C32×C4C23×C311yescharacteristic
378C2×C3⋊Dic3C23×C311yescharacteristic
379C2×C3⋊Dic3C23×C311yescharacteristic
380C2×C3⋊Dic3C23×C311yescharacteristic
381C3×#67—62no—
382C3×#67—62no—
383C3×#67—62no—
384C3×#67—62no—
385C3×#67—62no—
386C3×#67—62no—
387C3×#67—121no—
388C2×C3×Dic3—21no—
389C2×C3×Dic3—21no—
390C2×C3×Dic3—21no—
391C2×C3×Dic3—21no—
392C2×C3×Dic3—21no—
393C2×C3×Dic3—31no—
394C2×C3×Dic3—31no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—31no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—31no—
399C2×C3×Dic3—61no—
400C2×C3×Dic3—61no—
401C2×C3×Dic3—61no—
402C2×C3×Dic3—62no—
403C2×C3×Dic3C22×D311yescharacteristic
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C23×C311yescharacteristic
409C2×C3×Dic3C23×C311yescharacteristic
410C2×C3×Dic3C23×C311yescharacteristic
411C2×C3×Dic3C23×C311yescharacteristic
412C2×C3×Dic3C23×C311yescharacteristic
413C3×D12—41no—
414C3×D12—41no—
415C3×D12—42no—
416C3×D12—62no—
417C3×D12—62no—
418C3×D12—121no—
419C3×C4×D3—24no—
420C3×C4×D3—22no—
421C3×C4×D3—22no—
422C3×C4×D3—41no—
423C3×C4×D3—41no—
424C3×C4×D3—41no—
425C3×C4×D3—41no—
426C3×C4×D3—41no—
427C3×C4×D3—41no—
428C3×C4×D3—42no—
429C3×C4×D3—42no—
430C3×C4×D3—42no—
431C3×C4×D3—62no—
432C3×C4×D3—121no—
433C3×C4×D3—121no—
434#626—22no—
435#626—22no—
436#626—41no—
437#625—22no—
438#625—22no—
439#624—41no—
440D3×Dic3—22no—
441#553—91noSylow
442C2×C33C2×#4111yescharacteristic
443C2×C33C2×#4111yescharacteristic
444C2×C33H(5,𝔽2)11yescharacteristic
445C3×C3⋊D3—41no—
446C32×D3—22no—
447C32×D3—41no—
448C32×D3—41no—
449C2×C3×D4—31no—
450C2×C3×D4—31no—
451C2×C3×D4—61no—
452C2×C3×D4—91no—
453C2×C3×D4—91no—
454C2×C3×D4—91no—
455C2×C3×D4—91no—
456C2×C3×D4—91no—
457C22×C3×C4—31no—
458C22×C3×C4—31no—
459C22×C3×C4—31no—
460C22×C3×C4—31no—
461C22×C3×C4—31no—
462C22×C3×C4—31no—
463C22×C3×C4—31no—
464C22×C3×C4—31no—
465C22×C3×C4—61no—
466C22×C3×C4—61no—
467C22×C3×C4—61no—
468C22×C3×C4—61no—
469C22×C3×C4—91no—
470C22×C3×C4—91no—
471C2×#67—31no—
472C2×#67—31no—
473C2×#67—31no—
474C2×#67—31no—
475C2×#67—31no—
476C2×#67—31no—
477C2×#67—31no—
478C22×Dic3—31no—
479C2×D12—31no—
480C2×D12—31no—
481C2×D12—31no—
482C2×D12C2×C3×D311yescharacteristic
483C2×C4×D3—31no—
484C2×C4×D3—31no—
485C2×C4×D3—31no—
486C2×C4×D3C2×C3×D311yescharacteristic
487C2×C4×D3C2×C3×D311yescharacteristic
488C2×C4×D3C2×C3×D311yescharacteristic
489C2×C4×D3C2×C3×D311yescharacteristic
490C3×C4⋊C4—21no—
491C3×C4⋊C4—21no—
492C3×C4⋊C4—21no—
493C3×C4⋊C4—31no—
494C3×C4⋊C4—31no—
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—41no—
502C3×C4⋊C4—61no—
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×C4⋊C4D3211yescharacteristic
512C3×C4⋊C4C2×C3×D311yescharacteristic
513C3×C4⋊C4C2×C3×D311yescharacteristic
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—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×C42—91no—
531C3×C42—91no—
532C3×C42—91no—
533#217—31no—
534#217—31no—
535#217—31no—
536#217—31no—
537(C2×D3)⋊C4—31no—
538(C2×D3)⋊C4—31no—
539(C2×D3)⋊C4—31no—
540(C2×D3)⋊C4—31no—
541(C2×D3)⋊C4—31no—
542(C2×D3)⋊C4—31no—
543(C2×D3)⋊C4—31no—
544(C2×D3)⋊C4—31no—
545(C2×D3)⋊C4—31no—
546(C2×D3)⋊C4—31no—
547(C2×D3)⋊C4—61no—
548(C2×D3)⋊C4—61no—
549(C2×D3)⋊C4—61no—
550(C2×D3)⋊C4C2×C3×D311yescharacteristic
551(C2×D3)⋊C4C2×C3×D311yescharacteristic
552(C2×D3)⋊C4C2×C3×D311yescharacteristic
553C4⋊Dic3—31no—
554C4⋊Dic3—31no—
555C4⋊Dic3—31no—
556C4⋊Dic3—31no—
557C4⋊Dic3—61no—
558C4⋊Dic3C2×C3×D311yescharacteristic
559Dic3⋊C4—31no—
560Dic3⋊C4—31no—
561Dic3⋊C4—31no—
562Dic3⋊C4—31no—
563Dic3⋊C4—31no—
564Dic3⋊C4—31no—
565Dic3⋊C4—61no—
566Dic3⋊C4C2×C3×D311yescharacteristic
567Dic3⋊C4C2×C3×D311yescharacteristic
568Dic3⋊C4C2×C3×D311yescharacteristic
569C4×Dic3—31no—
570C4×Dic3—31no—
571C4×Dic3—31no—
572C4×Dic3—31no—
573C4×Dic3—31no—
574C4×Dic3—31no—
575C4×Dic3—61no—
576C22×C32—21no—
577C22×C32—21no—
578C22×C32—21no—
579C22×C32—32no—
580C22×C32—41no—
581C22×C32—61no—
582C22×C32—61no—
583C22×C32—61no—
584C22×C32—61no—
585C22×C32—61no—
586C22×C32—61no—
587C22×C32—61no—
588C22×C32—61no—
589C22×C32C23×D311yescharacteristic
590C22×C32C23×D311yescharacteristic
591C22×C32C24×C311yescharacteristic
592C2×C3⋊D3—21no—
593C2×C3⋊D3—21no—
594C2×C3⋊D3—21no—
595C2×C3×D3—22no—
596C2×C3×D3—22no—
597C2×C3×D3—21no—
598C2×C3×D3—21no—
599C2×C3×D3—21no—
600C2×C3×D3—21no—
601C2×C3×D3—22no—
602C2×C3×D3—21no—
603C2×C3×D3—21no—
604C2×C3×D3—21no—
605C2×C3×D3—21no—
606C2×C3×D3—21no—
607C2×C3×D3—21no—
608C2×C3×D3—21no—
609C2×C3×D3—21no—
610C2×C3×D3—21no—
611C2×C3×D3—21no—
612C2×C3×D3—21no—
613C2×C3×D3—21no—
614C2×C3×D3—22no—
615C2×C3×D3—41no—
616C2×C3×D3—41no—
617C2×C3×D3—41no—
618C2×C3×D3—41no—
619C2×C3×D3—41no—
620C2×C3×D3—61no—
621C2×C3×D3—61no—
622C2×C3×D3—61no—
623C2×C3×D3—61no—
624C2×C3×D3—61no—
625C2×C3×D3—61no—
626C2×C3×D3—121no—
627C2×C3×D3—121no—
628C2×C3×D3—121no—
629C2×C3×D3#23912yes—
630C2×C3×D3C3×#4112yes—
631C32×C4—21no—
632C32×C4—22no—
633C32×C4—21no—
634C32×C4—21no—
635C32×C4—21no—
636C32×C4—21no—
637C32×C4—21no—
638C32×C4—21no—
639C32×C4—21no—
640C32×C4—21no—
641C32×C4—32no—
642C32×C4—41no—
643C32×C4—41no—
644C32×C4—42no—
645C32×C4—41no—
646C32×C4—41no—
647C32×C4—41no—
648C32×C4—41no—
649C32×C4—41no—
650C32×C4—41no—
651C32×C4—61no—
652C32×C4—61no—
653C32×C4—61no—
654C32×C4—61no—
655C32×C4—81no—
656C32×C4—81no—
657C3⋊Dic3—21no—
658C3⋊Dic3—21no—
659C3⋊Dic3—21no—
660C3×Dic3—21no—
661C3×Dic3—21no—
662C3×Dic3—21no—
663C3×Dic3—21no—
664C3×Dic3—21no—
665C3×Dic3—21no—
666C3×Dic3—21no—
667C3×Dic3—21no—
668C3×Dic3—22no—
669C3×Dic3—41no—
670C3×Dic3—41no—
671C3×Dic3—41no—
672C3×Dic3—41no—
673C3×Dic3—61no—
674C3×Dic3—61no—
675C3×Dic3—61no—
676C3×Dic3—61no—
677C3×Dic3—61no—
678C3×Dic3—61no—
679C3×Dic3—121no—
680C3×Dic3—121no—
681C3×Dic3—121no—
682C3×Dic3#23512yes—
683C3×Dic3C3×#4112yes—
684#126—91no—
685#126—91no—
686#125—91no—
687#123—31no—
688#123—91no—
689#121—91no—
690#121—91no—
691#121—91no—
692#121—91no—
693C4×D4—91no—
694C4×D4—91no—
695C4×D4—91no—
696C4×D4—91no—
697#117—91no—
698C2×C4⋊C4—31no—
699C33#55311yescharacteristic, complemented, Sylow
700C23×C3—31no—
701C23×C3—31no—
702C23×C3—31no—
703C23×C3—31no—
704C23×C3—31no—
705C23×C3—31no—
706C23×C3—61no—
707C23×C3—61no—
708C23×C3—61no—
709C23×C3—91no—
710C22×D3—31no—
711C22×D3—31no—
712C22×D3—61no—
713C22×D3C22×C3×D311yescharacteristic
714C22×D3C22×C3×D311yescharacteristic
715C22×D3C22×C3×D311yescharacteristic
716C3×D4—121no—
717C3×D4—121no—
718C3×D4—122no—
719C3×D4—182no—
720C3×D4—182no—
721C3×D4—182no—
722C3×D4—182no—
723C3×D4—361no—
724C2×C3×C4—21no—
725C2×C3×C4—21no—
726C2×C3×C4—21no—
727C2×C3×C4—21no—
728C2×C3×C4—21no—
729C2×C3×C4—21no—
730C2×C3×C4—21no—
731C2×C3×C4—21no—
732C2×C3×C4—21no—
733C2×C3×C4—31no—
734C2×C3×C4—31no—
735C2×C3×C4—31no—
736C2×C3×C4—31no—
737C2×C3×C4—31no—
738C2×C3×C4—31no—
739C2×C3×C4—31no—
740C2×C3×C4—31no—
741C2×C3×C4—31no—
742C2×C3×C4—31no—
743C2×C3×C4—41no—
744C2×C3×C4—41no—
745C2×C3×C4—41no—
746C2×C3×C4—61no—
747C2×C3×C4—61no—
748C2×C3×C4—61no—
749C2×C3×C4—61no—
750C2×C3×C4—61no—
751C2×C3×C4—62no—
752C2×C3×C4—62no—
753C2×C3×C4—64no—
754C2×C3×C4—91no—
755C2×C3×C4—91no—
756C2×C3×C4—91no—
757C2×C3×C4—121no—
758C2×C3×C4—121no—
759C2×C3×C4—121no—
760C2×C3×C4—121no—
761C2×C3×C4—121no—
762C2×C3×C4—121no—
763C2×C3×C4—122no—
764C2×C3×C4—122no—
765C2×C3×C4—122no—
766C2×C3×C4—182no—
767C2×C3×C4—361no—
768C2×C3×C4C2×D3211yescharacteristic
769C2×C3×C4C2×D3211yescharacteristic
770C2×C3×C4C2×D3211yescharacteristic
771C2×C3×C4C22×C3×D311yescharacteristic
772C2×C3×C4C22×C3×D311yescharacteristic
773C2×C3×C4C22×C3×D311yescharacteristic
774C2×C3×C4C22×C3×D311yescharacteristic
775C2×C3×C4C22×C3×D311yescharacteristic
776C2×C3×C4C22×C3×D311yescharacteristic
777#67—62no—
778#67—62no—
779#67—62no—
780#67—62no—
781#67—62no—
782#67—62no—
783#67—121no—
784C2×Dic3—31no—
785C2×Dic3—31no—
786C2×Dic3—31no—
787C2×Dic3—31no—
788C2×Dic3—31no—
789C2×Dic3—31no—
790C2×Dic3—61no—
791C2×Dic3—61no—
792C2×Dic3—61no—
793C2×Dic3—62no—
794C2×Dic3C22×C3×D311yescharacteristic
795C2×Dic3C22×C3×D311yescharacteristic
796C2×Dic3C22×C3×D311yescharacteristic
797C2×Dic3C22×C3×D311yescharacteristic
798C2×Dic3C22×C3×D311yescharacteristic
799D12—41no—
800D12—62no—
801D12—62no—
802D12—121no—
803C4×D3—22no—
804C4×D3—41no—
805C4×D3—41no—
806C4×D3—41no—
807C4×D3—62no—
808C4×D3—121no—
809C4×D3—121no—
810C2×C32—21no—
811C2×C32—21no—
812C2×C32—21no—
813C2×C32—21no—
814C2×C32—21no—
815C2×C32—21no—
816C2×C32—21no—
817C2×C32—21no—
818C2×C32—21no—
819C2×C32—41no—
820C2×C32—41no—
821C2×C32—41no—
822C2×C32—62no—
823C2×C32—121no—
824C2×C32—121no—
825C2×C32C2×#23511yescharacteristic
826C2×C32#100411yescharacteristic
827C2×C32#100411yescharacteristic
828C2×C32C2×#23911yescharacteristic
829C2×C32D3×#4111yescharacteristic
830C2×C32D3×#4111yescharacteristic
831C2×C32C2×C3×#4111yescharacteristic
832C2×C32C2×C3×#4111yescharacteristic
833C2×C32C3×H(5,𝔽2)11yescharacteristic
834C3⋊D3—41no—
835C3×D3—24no—
836C3×D3—22no—
837C3×D3—22no—
838C3×D3—42no—
839C3×D3—41no—
840C3×D3—41no—
841C3×D3—41no—
842C3×D3—41no—
843C3×D3—81no—
844C3×D3—121no—
845C3×D3—121no—
846C3×D3—241no—
847C2×D4—31no—
848C2×D4—91no—
849C2×D4—91no—
850C2×D4—91no—
851C2×D4—91no—
852C2×D4—91no—
853C22×C4—31no—
854C22×C4—31no—
855C22×C4—31no—
856C22×C4—31no—
857C22×C4—91no—
858C22×C4—91no—
859C4⋊C4—31no—
860C4⋊C4—31no—
861C4⋊C4—31no—
862C4⋊C4—31no—
863C4⋊C4—91no—
864C4⋊C4—91no—
865C4⋊C4—91no—
866C4⋊C4—91no—
867C4⋊C4—91no—
868C4⋊C4C3×D3211yescharacteristic
869C22⋊C4—31no—
870C22⋊C4—31no—
871C22⋊C4—31no—
872C22⋊C4—91no—
873C22⋊C4—91no—
874C22⋊C4—91no—
875C22⋊C4—91no—
876C22⋊C4—91no—
877C22⋊C4—91no—
878C22⋊C4—91no—
879C42—91no—
880C42—91no—
881C42—91no—
882C22×C3—21no—
883C22×C3—21no—
884C22×C3—21no—
885C22×C3—32no—
886C22×C3—32no—
887C22×C3—41no—
888C22×C3—62no—
889C22×C3—62no—
890C22×C3—62no—
891C22×C3—62no—
892C22×C3—61no—
893C22×C3—61no—
894C22×C3—61no—
895C22×C3—61no—
896C22×C3—61no—
897C22×C3—61no—
898C22×C3—61no—
899C22×C3—61no—
900C22×C3—61no—
901C22×C3—61no—
902C22×C3—61no—
903C22×C3—61no—
904C22×C3—61no—
905C22×C3—61no—
906C22×C3—61no—
907C22×C3—61no—
908C22×C3—121no—
909C22×C3—121no—
910C22×C3—121no—
911C22×C3—121no—
912C22×C3—121no—
913C22×C3—181no—
914C22×C3—181no—
915C22×C3—181no—
916C22×C3C22×D3211yescharacteristic
917C22×C3C23×C3×D311yescharacteristic
918C22×C3C23×C3×D311yescharacteristic
919C2×D3—21no—
920C2×D3—21no—
921C2×D3—21no—
922C2×D3—21no—
923C2×D3—21no—
924C2×D3—21no—
925C2×D3—21no—
926C2×D3—21no—
927C2×D3—61no—
928C2×D3—61no—
929C2×D3—61no—
930C2×D3—61no—
931C2×D3—61no—
932C2×D3—61no—
933C2×D3—121no—
934C2×D3—121no—
935C2×D3—121no—
936C2×D3C3×#23912yes—
937C3×C4—22no—
938C3×C4—21no—
939C3×C4—21no—
940C3×C4—21no—
941C3×C4—21no—
942C3×C4—21no—
943C3×C4—21no—
944C3×C4—21no—
945C3×C4—21no—
946C3×C4—21no—
947C3×C4—32no—
948C3×C4—32no—
949C3×C4—41no—
950C3×C4—41no—
951C3×C4—41no—
952C3×C4—41no—
953C3×C4—41no—
954C3×C4—41no—
955C3×C4—41no—
956C3×C4—41no—
957C3×C4—42no—
958C3×C4—62no—
959C3×C4—61no—
960C3×C4—61no—
961C3×C4—61no—
962C3×C4—61no—
963C3×C4—61no—
964C3×C4—61no—
965C3×C4—61no—
966C3×C4—61no—
967C3×C4—81no—
968C3×C4—81no—
969C3×C4—121no—
970C3×C4—121no—
971C3×C4—121no—
972C3×C4—121no—
973C3×C4—181no—
974C3×C4—181no—
975C3×C4—181no—
976Dic3—21no—
977Dic3—21no—
978Dic3—21no—
979Dic3—21no—
980Dic3—61no—
981Dic3—61no—
982Dic3—61no—
983Dic3—61no—
984Dic3—61no—
985Dic3—61no—
986Dic3—121no—
987Dic3—121no—
988Dic3—121no—
989Dic3C3×#23512yes—
990C32—21no—
991C32—21no—
992C32—21no—
993C32—41no—
994C32#551411yescharacteristic, complemented
995C32#566111yescharacteristic, complemented
996C32C3×#55311yescharacteristic, complemented
997C23—31no—
998C23—31no—
999C23—31no—
1000C23—91no—
1001D4—121no—
1002D4—182no—
1003D4—182no—
1004D4—182no—
1005D4—182no—
1006D4—361no—
1007C2×C4—31no—
1008C2×C4—31no—
1009C2×C4—31no—
1010C2×C4—31no—
1011C2×C4—31no—
1012C2×C4—62no—
1013C2×C4—91no—
1014C2×C4—91no—
1015C2×C4—91no—
1016C2×C4—121no—
1017C2×C4—121no—
1018C2×C4—121no—
1019C2×C4—182no—
1020C2×C4—361no—
1021C2×C4C2×C3×D3211yescharacteristic
1022C2×C4C2×C3×D3211yescharacteristic
1023C2×C4C2×C3×D3211yescharacteristic
1024C2×C3—21no—
1025C2×C3—21no—
1026C2×C3—21no—
1027C2×C3—21no—
1028C2×C3—21no—
1029C2×C3—21no—
1030C2×C3—21no—
1031C2×C3—21no—
1032C2×C3—21no—
1033C2×C3—41no—
1034C2×C3—41no—
1035C2×C3—41no—
1036C2×C3—64no—
1037C2×C3—62no—
1038C2×C3—62no—
1039C2×C3—122no—
1040C2×C3—121no—
1041C2×C3—121no—
1042C2×C3—121no—
1043C2×C3—121no—
1044C2×C3—241no—
1045C2×C3—361no—
1046C2×C3D3×#23511yescharacteristic
1047C2×C3#6431311yescharacteristic
1048C2×C3D3×#23911yescharacteristic
1049C2×C3C2×C3×#23511yescharacteristic
1050C2×C3C3×#100411yescharacteristic
1051C2×C3C3×#100411yescharacteristic
1052C2×C3C2×C3×#23911yescharacteristic
1053C2×C3C3×D3×#4111yescharacteristic
1054C2×C3C3×D3×#4111yescharacteristic
1055D3—22no—
1056D3—41no—
1057D3—41no—
1058D3—121no—
1059D3—121no—
1060D3—241no—
1061C22—32no—
1062C22—61no—
1063C22—61no—
1064C22—61no—
1065C22—61no—
1066C22—61no—
1067C22—61no—
1068C22—61no—
1069C22—61no—
1070C22—181no—
1071C22—181no—
1072C22—181no—
1073C22C22×C3×D3211yescharacteristic
1074C4—21no—
1075C4—21no—
1076C4—21no—
1077C4—32no—
1078C4—61no—
1079C4—61no—
1080C4—61no—
1081C4—61no—
1082C4—181no—
1083C4—181no—
1084C4—181no—
1085C3—21no—
1086C3—21no—
1087C3—21no—
1088C3—41no—
1089C3#1059454411yescharacteristic, direct product factor
1090C3C3×#551411yescharacteristic, complemented
1091C3C3×#566111yescharacteristic, complemented
1092C2—62no—
1093C2—121no—
1094C2—121no—
1095C2—361no—
1096C2C3×D3×#23511yescharacteristic
1097C2C3×#6431311yescharacteristic
1098C2C3×D3×#23911yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#553
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64107C2semidirect
2. C32×#894C2semidirect
3. C32×D3×C4⋊C4C2semidirect
4. C3×#63908C2semidirect
5. C3×#63906C2semidirect
6. C3×#63906C2semidirect
7. C3×#63904C2semidirect
8. C3×#63904C2semidirect
9. C3×C4×#625C2semidirect
10. C3×#63886C2semidirect
11. C3×#63879C2semidirect
12. C3×#63878C2semidirect
13. C3×#63858C2semidirect
14. C3×#63854C2semidirect
15. C3×#63845C2semidirect
18. #10594544C3direct (N × H)
56. #64107C2×C3semidirect
74. C3×#894D3semidirect
75. C3×#894C2×C3semidirect
80. C3×D3×C4⋊C4D3semidirect
81. C3×D3×C4⋊C4C2×C3semidirect
90. #63908C2×C3semidirect
91. #63906C2×C3semidirect
92. #63906C2×C3semidirect
93. #63904C2×C3semidirect
94. #63904C2×C3semidirect
95. C4×#625C2×C3semidirect
96. #63886C2×C3semidirect
97. #63879C2×C3semidirect
98. #63878C2×C3semidirect
99. #63858C2×C3semidirect
100. #63854C2×C3semidirect
101. #63845C2×C3semidirect
318. #894C3×D3semidirect
322. D3×C4⋊C4C3×D3semidirect
699. C33#553semidirect
994. C32#5514semidirect
995. C32#5661semidirect
996. C32C3×#553semidirect
1089. C3#10594544direct (N × H)
1090. C3C3×#5514semidirect
1091. C3C3×#5661semidirect

Maximal subgroups

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

subgroupindex
C3×#641072
C32×#8942
C32×D3×C4⋊C42
C3×#639082
C3×#639062
C3×#639042
C3×C4×#6252
C3×#638862
C3×#638792
C3×#638782
C3×#638582
C3×#638542
C3×#638452
C3×#56613
C3×#55143
#105945443