Finite Group Databasebeta

← C3×#10594943 #13174599

Subgroups — C3×#10594943 #13174599

Order 1728.

1272 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64138C211yesmaximal, characteristic, complemented
2C32×C4×#67C211yesmaximal, characteristic, complemented
3C32×C4×#67C211yesmaximal, characteristic, complemented
4C3×#63971C211yesmaximal, characteristic, complemented
5C3×#63970C211yesmaximal, characteristic, complemented
6C3×#63958C211yesmaximal, characteristic, complemented
7C3×#63956C211yesmaximal, characteristic, complemented
8C3×#63906C211yesmaximal, characteristic, complemented
9C3×#63880C211yesmaximal, characteristic, complemented
10C3×#63879C211yesmaximal, characteristic, complemented
11C3×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
12C3×#63867C211yesmaximal, characteristic, complemented
13C3×#63859C211yesmaximal, characteristic, complemented
14C3×#63850C211yesmaximal, characteristic, complemented
15C3×#63836C211yesmaximal, characteristic, complemented
16C3×#5558—31nomaximal
17C3×#5540—31nomaximal
18#10594943C311yesmaximal, characteristic, direct product factor
19C22×C33×C4C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×C4×D3C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic
25C2×C3×#626C2211yescharacteristic
26C2×C3×#626C2211yescharacteristic
27C2×C3×#625C2211yescharacteristic
28C2×C3×#624C2211yescharacteristic
29C2×C3×D3×Dic3C2211yescharacteristic
30C2×C3×D3×Dic3C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32C3×#3752C2211yescharacteristic
33C3×#3752C2211yescharacteristic
34C3×#3750C2211yescharacteristic
35C3×#3750C2211yescharacteristic
36C32×#217C2211yescharacteristic
37C32×#217C2211yescharacteristic
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×Dic3⋊C4C2211yescharacteristic
41C32×Dic3⋊C4C2211yescharacteristic
42C32×C4×Dic3C2211yescharacteristic
43C32×C4×Dic3C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C32×C4×D4—31no—
55C32×C4×D4—31no—
56#64138C2×C311yescharacteristic, complemented
57C3×#939—31no—
58C3×#939—31no—
59C3×#938—31no—
60C3×#938—31no—
61C3×#930—31no—
62C3×#929—31no—
63C3×#929—31no—
64C3×#929—31no—
65C3×#929—61no—
66C3×C4×#67—21no—
67C3×C4×#67—21no—
68C3×C4×#67—31no—
69C3×C4×#67D311yescharacteristic, complemented
70C3×C4×#67D311yescharacteristic, complemented
71C3×C4×#67C2×C311yescharacteristic, complemented
72C3×C4×#67C2×C311yescharacteristic, complemented
73C2×C3×Dic3⋊C4—31no—
74C3×#894—31no—
75C3×#892—31no—
76C3×D3×C4⋊C4—31no—
77C3×#889—31no—
78C3×#884—31no—
79C3×#884—31no—
80C3×#884—31no—
81C3×#67⋊C4—31no—
82C3×#67⋊C4—31no—
83C3×#879—31no—
84C3×#879—31no—
85C3×#879—31no—
86C3×#876—31no—
87C3×C4×D12—31no—
88C3×#872—31no—
89C3×#870—31no—
90#63971C2×C311yescharacteristic, complemented
91#63970C2×C311yescharacteristic, complemented
92#63958C2×C311yescharacteristic, complemented
93#63956C2×C311yescharacteristic, complemented
94#63906C2×C311yescharacteristic, complemented
95#63880C2×C311yescharacteristic, complemented
96#63879C2×C311yescharacteristic, complemented
97D3×Dic3⋊C4C2×C311yescharacteristic, complemented
98#63867C2×C311yescharacteristic, complemented
99#63859C2×C311yescharacteristic, complemented
100#63850C2×C311yescharacteristic, complemented
101#63836C2×C311yescharacteristic, complemented
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×C33×C4—41no—
107C2×C33×C4C2311yescharacteristic
108C2×C33×C4C2311yescharacteristic
109C3×#638—41no—
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C32×#67—22no—
114C32×#67—22no—
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C32×C4×D3—41no—
122C32×C4×D3—41no—
123C3×#626—22no—
124C3×#626—41no—
125C3×#625—22no—
126C3×#624—22no—
127C3×D3×Dic3—22no—
128C3×D3×Dic3—41no—
129C3×#553—91no—
130#5558—31no—
131#5540—31no—
132C2×C32×D4—31no—
133C2×C32×D4—31no—
134C22×C32×C4—21no—
135C22×C32×C4—21no—
136C22×C32×C4—21no—
137C22×C32×C4—31no—
138C22×C32×C4—31no—
139C22×C32×C4—41no—
140C22×C32×C4C2×D311yescharacteristic
141C22×C32×C4C2×D311yescharacteristic
142C22×C32×C4C22×C311yescharacteristic
143C2×#638C22×C311yescharacteristic
144C2×C3×#67—21no—
145C2×C3×#67—21no—
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—31no—
152C2×C3×#67—61no—
153C2×C3×#67C2×D311yescharacteristic
154C2×C3×#67C2×D311yescharacteristic
155C2×C3×#67C22×C311yescharacteristic
156C2×C3×#67C22×C311yescharacteristic
157C22×C3×Dic3—31no—
158C22×C3×Dic3—31no—
159C2×C3×D12—31no—
160C2×C3×D12—31no—
161C2×C3×C4×D3—21no—
162C2×C3×C4×D3—21no—
163C2×C3×C4×D3—31no—
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—31no—
166C2×C3×C4×D3—31no—
167C2×C3×C4×D3C2×D311yescharacteristic
168C2×C3×C4×D3C2×D311yescharacteristic
169C2×C3×C4×D3C22×C311yescharacteristic
170C2×C3×C4×D3C22×C311yescharacteristic
171C2×#626C22×C311yescharacteristic
172C2×#626C22×C311yescharacteristic
173C2×#625C22×C311yescharacteristic
174C2×#624C22×C311yescharacteristic
175C2×D3×Dic3C22×C311yescharacteristic
176C2×D3×Dic3C22×C311yescharacteristic
177C32×C4⋊C4—31no—
178C32×C4⋊C4—31no—
179C32×C22⋊C4—31no—
180C32×C22⋊C4—31no—
181C32×C22⋊C4—31no—
182C32×C22⋊C4—31no—
183C32×C42—31no—
184C32×C42—31no—
185#3757C22×C311yescharacteristic
186#3752C22×C311yescharacteristic
187#3752C22×C311yescharacteristic
188#3750C22×C311yescharacteristic
189#3750C22×C311yescharacteristic
190C3×#217—21no—
191C3×#217—21no—
192C3×#217—31no—
193C3×#217—31no—
194C3×#217—31no—
195C3×#217—31no—
196C3×#217—61no—
197C3×#217C2×D311yescharacteristic
198C3×#217C2×D311yescharacteristic
199C3×#217C22×C311yescharacteristic
200C3×#217C22×C311yescharacteristic
201C3×(C2×D3)⋊C4—21no—
202C3×(C2×D3)⋊C4—21no—
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—61no—
212C3×(C2×D3)⋊C4—61no—
213C3×(C2×D3)⋊C4C2×D311yescharacteristic
214C3×(C2×D3)⋊C4C2×D311yescharacteristic
215C3×(C2×D3)⋊C4C22×C311yescharacteristic
216C3×(C2×D3)⋊C4C22×C311yescharacteristic
217C3×C4⋊Dic3—31no—
218C3×C4⋊Dic3—31no—
219C3×C4⋊Dic3—31no—
220C3×C4⋊Dic3—31no—
221C3×Dic3⋊C4—21no—
222C3×Dic3⋊C4—21no—
223C3×Dic3⋊C4—31no—
224C3×Dic3⋊C4—31no—
225C3×Dic3⋊C4—31no—
226C3×Dic3⋊C4—31no—
227C3×Dic3⋊C4—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—61no—
236C3×Dic3⋊C4—61no—
237C3×Dic3⋊C4C2×D311yescharacteristic
238C3×Dic3⋊C4C2×D311yescharacteristic
239C3×Dic3⋊C4C22×C311yescharacteristic
240C3×Dic3⋊C4C22×C311yescharacteristic
241C3×C4×Dic3—21no—
242C3×C4×Dic3—21no—
243C3×C4×Dic3—31no—
244C3×C4×Dic3—31no—
245C3×C4×Dic3C2×D311yescharacteristic
246C3×C4×Dic3C2×D311yescharacteristic
247C3×C4×Dic3C22×C311yescharacteristic
248C3×C4×Dic3C22×C311yescharacteristic
249#3724C22×C311yescharacteristic
250#3724C22×C311yescharacteristic
251Dic3⋊Dic3C22×C311yescharacteristic
252Dic3⋊Dic3C22×C311yescharacteristic
253Dic3⋊Dic3C22×C311yescharacteristic
254Dic3⋊Dic3C22×C311yescharacteristic
255#3722C22×C311yescharacteristic
256(C2×D3)⋊Dic3C22×C311yescharacteristic
257(C2×D3)⋊Dic3C22×C311yescharacteristic
258Dic32C22×C311yescharacteristic
259C22×C33—21no—
260C22×C33—21no—
261C22×C33—21no—
262C22×C33C2411yescharacteristic
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊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—
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#4112yes—
283C3×#126—91no—
284C3×#126—91no—
285C3×#125—91no—
286C3×#123—91no—
287C3×#123—91no—
288C3×#121—91no—
289C3×#121—91no—
290C3×#121—91no—
291C3×#121—91no—
292C3×C4×D4—31no—
293C3×C4×D4—31no—
294C3×C4×D4—31no—
295C3×C4×D4—31no—
296C3×C4×D4—61no—
297C3×C4×D4—61no—
298C3×C4×D4—91no—
299C3×C4×D4—91no—
300C3×#117—91no—
301C2×C3×C4⋊C4—91no—
302#939—31no—
303#939—31no—
304#938—31no—
305#938—31no—
306#930—31no—
307#929—31no—
308#929—31no—
309#929—31no—
310#929—61no—
311C4×#67—31no—
312C4×#67C3×D311yescharacteristic, complemented
313C4×#67C3×D311yescharacteristic, complemented
314C2×Dic3⋊C4—31no—
315#894—31no—
316#892—31no—
317D3×C4⋊C4—31no—
318#889—31no—
319#884—31no—
320#884—31no—
321#884—31no—
322#67⋊C4—31no—
323#67⋊C4—31no—
324#879—31no—
325#879—31no—
326#879—31no—
327#876—31no—
328C4×D12—31no—
329#872—31no—
330#870—31no—
331C23×C32—21no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—31no—
335C23×C32—31no—
336C23×C32—41no—
337C23×C32C22×D311yescharacteristic
338C23×C32C22×D311yescharacteristic
339C23×C32C23×C311yescharacteristic
340C22×C3⋊D3C23×C311yescharacteristic
341C22×C3×D3—21no—
342C22×C3×D3—21no—
343C22×C3×D3—31no—
344C22×C3×D3—31no—
345C22×C3×D3—61no—
346C22×C3×D3C22×D311yescharacteristic
347C22×C3×D3C22×D311yescharacteristic
348C22×C3×D3C23×C311yescharacteristic
349C22×C3×D3C23×C311yescharacteristic
350C32×D4—62no—
351C32×D4—62no—
352C2×C32×C4—21no—
353C2×C32×C4—21no—
354C2×C32×C4—21no—
355C2×C32×C4—21no—
356C2×C32×C4—21no—
357C2×C32×C4—21no—
358C2×C32×C4—31no—
359C2×C32×C4—31no—
360C2×C32×C4—31no—
361C2×C32×C4—31no—
362C2×C32×C4—31no—
363C2×C32×C4—31no—
364C2×C32×C4—41no—
365C2×C32×C4—41no—
366C2×C32×C4—41no—
367C2×C32×C4—41no—
368C2×C32×C4—41no—
369C2×C32×C4—42no—
370C2×C32×C4—42no—
371C2×C32×C4—42no—
372C2×C32×C4—44no—
373C2×C32×C4—121no—
374C2×C32×C4—121no—
375C2×C32×C4C22×D311yescharacteristic
376C2×C32×C4C22×D311yescharacteristic
377C2×C32×C4C22×D311yescharacteristic
378C2×C32×C4C22×D311yescharacteristic
379C2×C32×C4C23×C311yescharacteristic
380C2×C32×C4C23×C311yescharacteristic
381#638—41no—
382C2×C3⋊Dic3C23×C311yescharacteristic
383C2×C3⋊Dic3C23×C311yescharacteristic
384C2×C3⋊Dic3C23×C311yescharacteristic
385C3×#67—24no—
386C3×#67—24no—
387C3×#67—22no—
388C3×#67—22no—
389C3×#67—22no—
390C3×#67—22no—
391C3×#67—62no—
392C3×#67—62no—
393C3×#67—62no—
394C3×#67—121no—
395C3×#67—121no—
396C3×#67—121no—
397C3×#67—122no—
398C2×C3×Dic3—21no—
399C2×C3×Dic3—21no—
400C2×C3×Dic3—21no—
401C2×C3×Dic3—21no—
402C2×C3×Dic3—21no—
403C2×C3×Dic3—21no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—31no—
410C2×C3×Dic3—61no—
411C2×C3×Dic3—61no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—62no—
414C2×C3×Dic3—121no—
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C2×C3×Dic3C22×D311yescharacteristic
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C23×C311yescharacteristic
422C2×C3×Dic3C23×C311yescharacteristic
423C2×C3×Dic3C23×C311yescharacteristic
424C2×C3×Dic3C23×C311yescharacteristic
425C2×C3×Dic3C23×C311yescharacteristic
426C2×C3×Dic3C23×C311yescharacteristic
427C3×D12—62no—
428C3×D12—121no—
429C3×C4×D3—41no—
430C3×C4×D3—41no—
431C3×C4×D3—41no—
432C3×C4×D3—41no—
433C3×C4×D3—42no—
434C3×C4×D3—42no—
435C3×C4×D3—62no—
436C3×C4×D3—62no—
437C3×C4×D3—62no—
438C3×C4×D3—121no—
439#626—22no—
440#626—41no—
441#625—22no—
442#624—22no—
443D3×Dic3—22no—
444D3×Dic3—41no—
445#553—91noSylow
446C2×C33—41no—
447C2×C33C2×#4111yescharacteristic
448C2×C33C2×#4111yescharacteristic
449C2×C33H(5,𝔽2)11yescharacteristic
450C3×C3⋊D3—41no—
451C32×D3—22no—
452C32×D3—41no—
453C2×C3×D4—31no—
454C2×C3×D4—31no—
455C2×C3×D4—31no—
456C2×C3×D4—31no—
457C2×C3×D4—61no—
458C2×C3×D4—61no—
459C2×C3×D4—91no—
460C2×C3×D4—91no—
461C2×C3×D4—91no—
462C2×C3×D4—91no—
463C22×C3×C4—21no—
464C22×C3×C4—21no—
465C22×C3×C4—21no—
466C22×C3×C4—31no—
467C22×C3×C4—31no—
468C22×C3×C4—31no—
469C22×C3×C4—31no—
470C22×C3×C4—41no—
471C22×C3×C4—61no—
472C22×C3×C4—61no—
473C22×C3×C4—91no—
474C22×C3×C4—91no—
475C22×C3×C4—91no—
476C22×C3×C4D3211yescharacteristic
477C22×C3×C4C2×C3×D311yescharacteristic
478C22×C3×C4C2×C3×D311yescharacteristic
479C2×#67—31no—
480C2×#67—31no—
481C2×#67—31no—
482C2×#67—31no—
483C2×#67—31no—
484C2×#67—31no—
485C2×#67—61no—
486C2×#67C2×C3×D311yescharacteristic
487C2×#67C2×C3×D311yescharacteristic
488C22×Dic3—31no—
489C22×Dic3—31no—
490C2×D12—31no—
491C2×D12—31no—
492C2×C4×D3—31no—
493C2×C4×D3—31no—
494C2×C4×D3—31no—
495C2×C4×D3—31no—
496C2×C4×D3C2×C3×D311yescharacteristic
497C2×C4×D3C2×C3×D311yescharacteristic
498C3×C4⋊C4—31no—
499C3×C4⋊C4—31no—
500C3×C4⋊C4—31no—
501C3×C4⋊C4—31no—
502C3×C4⋊C4—61no—
503C3×C4⋊C4—61no—
504C3×C4⋊C4—91no—
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×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—61no—
521C3×C22⋊C4—61no—
522C3×C22⋊C4—61no—
523C3×C22⋊C4—61no—
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—31no—
531C3×C42—31no—
532C3×C42—31no—
533C3×C42—31no—
534C3×C42—61no—
535C3×C42—61no—
536C3×C42—91no—
537#217—31no—
538#217—31no—
539#217—31no—
540#217—31no—
541#217—61no—
542#217C2×C3×D311yescharacteristic
543#217C2×C3×D311yescharacteristic
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—61no—
553(C2×D3)⋊C4—61no—
554(C2×D3)⋊C4C2×C3×D311yescharacteristic
555(C2×D3)⋊C4C2×C3×D311yescharacteristic
556C4⋊Dic3—31no—
557C4⋊Dic3—31no—
558C4⋊Dic3—31no—
559C4⋊Dic3—31no—
560Dic3⋊C4—31no—
561Dic3⋊C4—31no—
562Dic3⋊C4—31no—
563Dic3⋊C4—31no—
564Dic3⋊C4—31no—
565Dic3⋊C4—31no—
566Dic3⋊C4—31no—
567Dic3⋊C4—31no—
568Dic3⋊C4—31no—
569Dic3⋊C4—31no—
570Dic3⋊C4—31no—
571Dic3⋊C4—31no—
572Dic3⋊C4—61no—
573Dic3⋊C4—61no—
574Dic3⋊C4C2×C3×D311yescharacteristic
575Dic3⋊C4C2×C3×D311yescharacteristic
576C4×Dic3—31no—
577C4×Dic3—31no—
578C4×Dic3C2×C3×D311yescharacteristic
579C4×Dic3C2×C3×D311yescharacteristic
580C22×C32—21no—
581C22×C32—21no—
582C22×C32—21no—
583C22×C32—22no—
584C22×C32—22no—
585C22×C32—22no—
586C22×C32—21no—
587C22×C32—21no—
588C22×C32—21no—
589C22×C32—21no—
590C22×C32—21no—
591C22×C32—21no—
592C22×C32—21no—
593C22×C32—21no—
594C22×C32—21no—
595C22×C32—32no—
596C22×C32—41no—
597C22×C32—41no—
598C22×C32—41no—
599C22×C32—41no—
600C22×C32—41no—
601C22×C32—41no—
602C22×C32—41no—
603C22×C32—42no—
604C22×C32—42no—
605C22×C32—42no—
606C22×C32—61no—
607C22×C32—61no—
608C22×C32—61no—
609C22×C32—61no—
610C22×C32—61no—
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—21no—
620C2×C3×D3—21no—
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—22no—
629C2×C3×D3—41no—
630C2×C3×D3—41no—
631C2×C3×D3—41no—
632C2×C3×D3—41no—
633C2×C3×D3—61no—
634C2×C3×D3—61no—
635C2×C3×D3—61no—
636C2×C3×D3—61no—
637C2×C3×D3—61no—
638C2×C3×D3—61no—
639C2×C3×D3—121no—
640C2×C3×D3—121no—
641C2×C3×D3—121no—
642C2×C3×D3#23512yes—
643C2×C3×D3C3×#4112yes—
644C32×C4—21no—
645C32×C4—21no—
646C32×C4—22no—
647C32×C4—22no—
648C32×C4—21no—
649C32×C4—21no—
650C32×C4—21no—
651C32×C4—21no—
652C32×C4—32no—
653C32×C4—41no—
654C32×C4—41no—
655C32×C4—41no—
656C32×C4—41no—
657C32×C4—42no—
658C32×C4—42no—
659C32×C4—61no—
660C32×C4—61no—
661C32×C4—61no—
662C32×C4—61no—
663C32×C4—61no—
664C3⋊Dic3—21no—
665C3⋊Dic3—21no—
666C3⋊Dic3—21no—
667C3×Dic3—22no—
668C3×Dic3—21no—
669C3×Dic3—21no—
670C3×Dic3—21no—
671C3×Dic3—21no—
672C3×Dic3—21no—
673C3×Dic3—21no—
674C3×Dic3—21no—
675C3×Dic3—21no—
676C3×Dic3—21no—
677C3×Dic3—21no—
678C3×Dic3—22no—
679C3×Dic3—41no—
680C3×Dic3—41no—
681C3×Dic3—41no—
682C3×Dic3—41no—
683C3×Dic3—61no—
684C3×Dic3—61no—
685C3×Dic3—61no—
686C3×Dic3—61no—
687C3×Dic3—61no—
688C3×Dic3—61no—
689C3×Dic3—121no—
690C3×Dic3—121no—
691C3×Dic3—121no—
692C3×Dic3#23512yes—
693C3×Dic3C3×#4112yes—
694#126—91no—
695#126—91no—
696#125—91no—
697#123—91no—
698#123—91no—
699#121—91no—
700#121—91no—
701#121—91no—
702#121—91no—
703C4×D4—31no—
704C4×D4—31no—
705C4×D4—91no—
706C4×D4—91no—
707#117—91no—
708C2×C4⋊C4—91no—
709C33#55311yescharacteristic, complemented, Sylow
710C23×C3—21no—
711C23×C3—21no—
712C23×C3—21no—
713C23×C3—31no—
714C23×C3—31no—
715C23×C3—31no—
716C23×C3—31no—
717C23×C3—41no—
718C23×C3—61no—
719C23×C3—61no—
720C23×C3—91no—
721C23×C3C2×D3211yescharacteristic
722C23×C3C22×C3×D311yescharacteristic
723C23×C3C22×C3×D311yescharacteristic
724C22×D3—31no—
725C22×D3—31no—
726C22×D3—61no—
727C22×D3C22×C3×D311yescharacteristic
728C22×D3C22×C3×D311yescharacteristic
729C3×D4—62no—
730C3×D4—62no—
731C3×D4—62no—
732C3×D4—62no—
733C3×D4—64no—
734C3×D4—64no—
735C3×D4—182no—
736C3×D4—182no—
737C3×D4—361no—
738C3×D4—361no—
739C2×C3×C4—21no—
740C2×C3×C4—21no—
741C2×C3×C4—21no—
742C2×C3×C4—21no—
743C2×C3×C4—21no—
744C2×C3×C4—21no—
745C2×C3×C4—31no—
746C2×C3×C4—31no—
747C2×C3×C4—31no—
748C2×C3×C4—31no—
749C2×C3×C4—31no—
750C2×C3×C4—31no—
751C2×C3×C4—31no—
752C2×C3×C4—31no—
753C2×C3×C4—31no—
754C2×C3×C4—31no—
755C2×C3×C4—31no—
756C2×C3×C4—31no—
757C2×C3×C4—41no—
758C2×C3×C4—41no—
759C2×C3×C4—41no—
760C2×C3×C4—42no—
761C2×C3×C4—42no—
762C2×C3×C4—42no—
763C2×C3×C4—44no—
764C2×C3×C4—41no—
765C2×C3×C4—41no—
766C2×C3×C4—61no—
767C2×C3×C4—61no—
768C2×C3×C4—61no—
769C2×C3×C4—61no—
770C2×C3×C4—61no—
771C2×C3×C4—61no—
772C2×C3×C4—91no—
773C2×C3×C4—91no—
774C2×C3×C4—91no—
775C2×C3×C4—121no—
776C2×C3×C4—121no—
777C2×C3×C4—121no—
778C2×C3×C4—121no—
779C2×C3×C4—122no—
780C2×C3×C4—122no—
781C2×C3×C4—182no—
782C2×C3×C4—182no—
783C2×C3×C4—361no—
784C2×C3×C4C2×D3211yescharacteristic
785C2×C3×C4C2×D3211yescharacteristic
786C2×C3×C4C22×C3×D311yescharacteristic
787C2×C3×C4C22×C3×D311yescharacteristic
788C2×C3×C4C22×C3×D311yescharacteristic
789C2×C3×C4C22×C3×D311yescharacteristic
790#67—22no—
791#67—22no—
792#67—62no—
793#67—62no—
794#67—62no—
795#67—121no—
796#67—121no—
797#67—121no—
798#67—122no—
799C2×Dic3—31no—
800C2×Dic3—31no—
801C2×Dic3—31no—
802C2×Dic3—31no—
803C2×Dic3—31no—
804C2×Dic3—31no—
805C2×Dic3—61no—
806C2×Dic3—61no—
807C2×Dic3—61no—
808C2×Dic3—62no—
809C2×Dic3—121no—
810C2×Dic3C22×C3×D311yescharacteristic
811C2×Dic3C22×C3×D311yescharacteristic
812C2×Dic3C22×C3×D311yescharacteristic
813C2×Dic3C22×C3×D311yescharacteristic
814C2×Dic3C22×C3×D311yescharacteristic
815C2×Dic3C22×C3×D311yescharacteristic
816D12—62no—
817D12—121no—
818C4×D3—41no—
819C4×D3—41no—
820C4×D3—62no—
821C4×D3—62no—
822C4×D3—62no—
823C4×D3—121no—
824C2×C32—21no—
825C2×C32—21no—
826C2×C32—21no—
827C2×C32—21no—
828C2×C32—21no—
829C2×C32—21no—
830C2×C32—21no—
831C2×C32—21no—
832C2×C32—21no—
833C2×C32—41no—
834C2×C32—41no—
835C2×C32—41no—
836C2×C32—42no—
837C2×C32—42no—
838C2×C32—42no—
839C2×C32—44no—
840C2×C32—41no—
841C2×C32—41no—
842C2×C32—41no—
843C2×C32—62no—
844C2×C32—121no—
845C2×C32C2×#23511yescharacteristic
846C2×C32C2×#23511yescharacteristic
847C2×C32#100411yescharacteristic
848C2×C32#100411yescharacteristic
849C2×C32D3×#4111yescharacteristic
850C2×C32D3×#4111yescharacteristic
851C2×C32C2×C3×#4111yescharacteristic
852C2×C32C2×C3×#4111yescharacteristic
853C2×C32C3×H(5,𝔽2)11yescharacteristic
854C3⋊D3—41no—
855C3×D3—22no—
856C3×D3—22no—
857C3×D3—42no—
858C3×D3—42no—
859C3×D3—41no—
860C3×D3—41no—
861C3×D3—121no—
862C3×D3—121no—
863C3×D3—241no—
864C2×D4—31no—
865C2×D4—31no—
866C2×D4—91no—
867C2×D4—91no—
868C2×D4—91no—
869C2×D4—91no—
870C22×C4—31no—
871C22×C4—31no—
872C22×C4—91no—
873C22×C4—91no—
874C22×C4—91no—
875C22×C4C3×D3211yescharacteristic
876C4⋊C4—31no—
877C4⋊C4—31no—
878C4⋊C4—91no—
879C4⋊C4—91no—
880C4⋊C4—91no—
881C4⋊C4—91no—
882C4⋊C4—91no—
883C4⋊C4—91no—
884C4⋊C4—91no—
885C4⋊C4—91no—
886C22⋊C4—31no—
887C22⋊C4—31no—
888C22⋊C4—31no—
889C22⋊C4—31no—
890C22⋊C4—91no—
891C22⋊C4—91no—
892C22⋊C4—91no—
893C22⋊C4—91no—
894C22⋊C4—91no—
895C22⋊C4—91no—
896C42—31no—
897C42—31no—
898C42—91no—
899C22×C3—22no—
900C22×C3—22no—
901C22×C3—22no—
902C22×C3—21no—
903C22×C3—21no—
904C22×C3—21no—
905C22×C3—21no—
906C22×C3—21no—
907C22×C3—21no—
908C22×C3—21no—
909C22×C3—21no—
910C22×C3—21no—
911C22×C3—21no—
912C22×C3—21no—
913C22×C3—21no—
914C22×C3—32no—
915C22×C3—32no—
916C22×C3—41no—
917C22×C3—41no—
918C22×C3—41no—
919C22×C3—41no—
920C22×C3—41no—
921C22×C3—41no—
922C22×C3—42no—
923C22×C3—42no—
924C22×C3—42no—
925C22×C3—41no—
926C22×C3—62no—
927C22×C3—62no—
928C22×C3—61no—
929C22×C3—61no—
930C22×C3—61no—
931C22×C3—61no—
932C22×C3—61no—
933C22×C3—61no—
934C22×C3—61no—
935C22×C3—61no—
936C22×C3—61no—
937C22×C3—61no—
938C22×C3—121no—
939C22×C3—121no—
940C22×C3—121no—
941C22×C3—121no—
942C22×C3—181no—
943C22×C3—181no—
944C22×C3—181no—
945C22×C3C22×D3211yescharacteristic
946C22×C3C23×C3×D311yescharacteristic
947C22×C3C23×C3×D311yescharacteristic
948C2×D3—21no—
949C2×D3—21no—
950C2×D3—21no—
951C2×D3—21no—
952C2×D3—21no—
953C2×D3—61no—
954C2×D3—61no—
955C2×D3—61no—
956C2×D3—61no—
957C2×D3—61no—
958C2×D3—61no—
959C2×D3—121no—
960C2×D3—121no—
961C2×D3—121no—
962C2×D3C3×#23512yes—
963C3×C4—22no—
964C3×C4—22no—
965C3×C4—21no—
966C3×C4—21no—
967C3×C4—21no—
968C3×C4—21no—
969C3×C4—21no—
970C3×C4—21no—
971C3×C4—32no—
972C3×C4—32no—
973C3×C4—41no—
974C3×C4—41no—
975C3×C4—41no—
976C3×C4—41no—
977C3×C4—42no—
978C3×C4—42no—
979C3×C4—62no—
980C3×C4—62no—
981C3×C4—61no—
982C3×C4—61no—
983C3×C4—61no—
984C3×C4—61no—
985C3×C4—61no—
986C3×C4—61no—
987C3×C4—61no—
988C3×C4—61no—
989C3×C4—61no—
990C3×C4—61no—
991C3×C4—121no—
992C3×C4—121no—
993C3×C4—121no—
994C3×C4—121no—
995C3×C4—181no—
996C3×C4—181no—
997C3×C4—181no—
998Dic3—21no—
999Dic3—21no—
1000Dic3—21no—
1001Dic3—21no—
1002Dic3—21no—
1003Dic3—61no—
1004Dic3—61no—
1005Dic3—61no—
1006Dic3—61no—
1007Dic3—61no—
1008Dic3—61no—
1009Dic3—121no—
1010Dic3—121no—
1011Dic3—121no—
1012Dic3C3×#23512yes—
1013C32—21no—
1014C32—21no—
1015C32—21no—
1016C32—41no—
1017C32#554011yescharacteristic, complemented
1018C32#555811yescharacteristic, complemented
1019C32C3×#55311yescharacteristic, complemented
1020C23—31no—
1021C23—31no—
1022C23—91no—
1023C23C2×C3×D3211yescharacteristic
1024D4—62no—
1025D4—62no—
1026D4—182no—
1027D4—182no—
1028D4—361no—
1029D4—361no—
1030C2×C4—31no—
1031C2×C4—31no—
1032C2×C4—31no—
1033C2×C4—31no—
1034C2×C4—31no—
1035C2×C4—31no—
1036C2×C4—41no—
1037C2×C4—91no—
1038C2×C4—91no—
1039C2×C4—91no—
1040C2×C4—121no—
1041C2×C4—121no—
1042C2×C4—182no—
1043C2×C4—182no—
1044C2×C4—361no—
1045C2×C4C2×C3×D3211yescharacteristic
1046C2×C4C2×C3×D3211yescharacteristic
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—21no—
1051C2×C3—21no—
1052C2×C3—21no—
1053C2×C3—21no—
1054C2×C3—21no—
1055C2×C3—21no—
1056C2×C3—42no—
1057C2×C3—42no—
1058C2×C3—42no—
1059C2×C3—44no—
1060C2×C3—41no—
1061C2×C3—41no—
1062C2×C3—41no—
1063C2×C3—41no—
1064C2×C3—41no—
1065C2×C3—41no—
1066C2×C3—62no—
1067C2×C3—62no—
1068C2×C3—122no—
1069C2×C3—122no—
1070C2×C3—121no—
1071C2×C3—121no—
1072C2×C3—361no—
1073C2×C3D3×#23511yescharacteristic
1074C2×C3D3×#23511yescharacteristic
1075C2×C3#6433011yescharacteristic
1076C2×C3C2×C3×#23511yescharacteristic
1077C2×C3C2×C3×#23511yescharacteristic
1078C2×C3C3×#100411yescharacteristic
1079C2×C3C3×#100411yescharacteristic
1080C2×C3C3×D3×#4111yescharacteristic
1081C2×C3C3×D3×#4111yescharacteristic
1082D3—22no—
1083D3—41no—
1084D3—121no—
1085D3—121no—
1086D3—241no—
1087C22—21no—
1088C22—21no—
1089C22—21no—
1090C22—32no—
1091C22—61no—
1092C22—61no—
1093C22—61no—
1094C22—61no—
1095C22—61no—
1096C22—181no—
1097C22—181no—
1098C22—181no—
1099C22C22×C3×D3211yescharacteristic
1100C4—21no—
1101C4—21no—
1102C4—32no—
1103C4—61no—
1104C4—61no—
1105C4—61no—
1106C4—61no—
1107C4—61no—
1108C4—181no—
1109C4—181no—
1110C4—181no—
1111C3—21no—
1112C3—21no—
1113C3—21no—
1114C3—41no—
1115C3#1059494311yescharacteristic, direct product factor
1116C3C3×#554011yescharacteristic, complemented
1117C3C3×#555811yescharacteristic, complemented
1118C2—41no—
1119C2—62no—
1120C2—121no—
1121C2—361no—
1122C2C3×D3×#23511yescharacteristic
1123C2C3×D3×#23511yescharacteristic
1124C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C3×#553
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. C3×#64138C2semidirect
2. C32×C4×#67C2semidirect
3. C32×C4×#67C2semidirect
4. C3×#63971C2semidirect
5. C3×#63970C2semidirect
6. C3×#63958C2semidirect
7. C3×#63956C2semidirect
8. C3×#63906C2semidirect
9. C3×#63880C2semidirect
10. C3×#63879C2semidirect
11. C3×D3×Dic3⋊C4C2semidirect
12. C3×#63867C2semidirect
13. C3×#63859C2semidirect
14. C3×#63850C2semidirect
15. C3×#63836C2semidirect
18. #10594943C3direct (N × H)
56. #64138C2×C3semidirect
69. C3×C4×#67D3semidirect
70. C3×C4×#67D3semidirect
71. C3×C4×#67C2×C3semidirect
72. C3×C4×#67C2×C3semidirect
90. #63971C2×C3semidirect
91. #63970C2×C3semidirect
92. #63958C2×C3semidirect
93. #63956C2×C3semidirect
94. #63906C2×C3semidirect
95. #63880C2×C3semidirect
96. #63879C2×C3semidirect
97. D3×Dic3⋊C4C2×C3semidirect
98. #63867C2×C3semidirect
99. #63859C2×C3semidirect
100. #63850C2×C3semidirect
101. #63836C2×C3semidirect
312. C4×#67C3×D3semidirect
313. C4×#67C3×D3semidirect
709. C33#553semidirect
1017. C32#5540semidirect
1018. C32#5558semidirect
1019. C32C3×#553semidirect
1115. C3#10594943direct (N × H)
1116. C3C3×#5540semidirect
1117. C3C3×#5558semidirect

Maximal subgroups

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

subgroupindex
C3×#641382
C32×C4×#672
C3×#639712
C3×#639702
C3×#639582
C3×#639562
C3×#639062
C3×#638802
C3×#638792
C3×D3×Dic3⋊C42
C3×#638672
C3×#638592
C3×#638502
C3×#638362
C3×#55583
C3×#55403
#105949433