Finite Group Databasebeta

← C3×#10595090 #13174687

Subgroups — C3×#10595090 #13174687

Order 1728.

1328 conjugacy classes of subgroups.

The subgroup lattice has 1246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64139C211yesmaximal, characteristic, complemented
2C32×#930C211yesmaximal, characteristic, complemented
3C32×#929C211yesmaximal, characteristic, complemented
4C3×#63983C211yesmaximal, characteristic, complemented
5C3×#63979C211yesmaximal, characteristic, complemented
6C3×#63971C211yesmaximal, characteristic, complemented
7C3×#63958C211yesmaximal, characteristic, complemented
8C3×#63923C211yesmaximal, characteristic, complemented
9C3×#63922C211yesmaximal, characteristic, complemented
10C3×#63910C211yesmaximal, characteristic, complemented
11C3×#63891C211yesmaximal, characteristic, complemented
12C3×#63886C211yesmaximal, characteristic, complemented
13C3×#63861C211yesmaximal, characteristic, complemented
14C3×#63854C211yesmaximal, characteristic, complemented
15C3×#63848C211yesmaximal, characteristic, complemented
16C3×#5666—31nomaximal
17C3×#5620—31nomaximal
18#10595090C311yesmaximal, characteristic, direct product factor
19C22×C3×D32C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic, complemented
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic, complemented
23C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C2×C32×#67C2211yescharacteristic, complemented
27C2×C32×D12C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#626C2211yescharacteristic
30C2×C3×#626C2211yescharacteristic
31C2×C3×#626C2211yescharacteristic, complemented
32C2×C3×#625C2211yescharacteristic
33C2×C3×#624C2211yescharacteristic, complemented
34C2×C3×D3×Dic3C2211yescharacteristic, complemented
35C3×#3752C2211yescharacteristic
36C3×#3752C2211yescharacteristic, complemented
37C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
38C32×#217C2211yescharacteristic, complemented
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C32×C4⋊Dic3C2211yescharacteristic, complemented
44C32×Dic3⋊C4C2211yescharacteristic, complemented
45C32×Dic3⋊C4C2211yescharacteristic, complemented
46C3×#3724C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic, complemented
54C32×#123—31no—
55C32×#121—31no—
56#64139C2×C311yescharacteristic, complemented
57C3×#940—31no—
58C3×#940—31no—
59C3×#939—31no—
60C3×#939—31no—
61C3×#938—31no—
62C3×#937—31no—
63C3×#937—31no—
64C3×#937—31no—
65C3×#930—21no—
66C3×#930—31no—
67C3×#930—31no—
68C3×#930—61no—
69C3×#930D311yescharacteristic, complemented
70C3×#930C2×C311yescharacteristic, complemented
71C3×#929—21no—
72C3×#929D311yescharacteristic, complemented
73C3×#929C2×C311yescharacteristic, complemented
74C3×#898—31no—
75C3×#898—31no—
76C3×#898—31no—
77C3×#895—31no—
78C3×#895—31no—
79C3×#894—31no—
80C3×#886—31no—
81C3×#884—31no—
82C3×#884—31no—
83C3×#884—31no—
84C3×#883—31no—
85C3×#883—31no—
86C3×#882—31no—
87C3×#882—31no—
88C3×#882—31no—
89C3×#879—31no—
90#63983C2×C311yescharacteristic, complemented
91#63979C2×C311yescharacteristic, complemented
92#63971C2×C311yescharacteristic, complemented
93#63958C2×C311yescharacteristic, complemented
94#63923C2×C311yescharacteristic, complemented
95#63922C2×C311yescharacteristic, complemented
96#63910C2×C311yescharacteristic, complemented
97#63891C2×C311yescharacteristic, complemented
98#63886C2×C311yescharacteristic, complemented
99#63861C2×C311yescharacteristic, complemented
100#63854C2×C311yescharacteristic, complemented
101#63848C2×C311yescharacteristic, complemented
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C2×C3×D32—41no—
109C2×C3×D32—41no—
110C2×C3×D32—41no—
111C2×C33×C4—41no—
112C2×C33×C4C2311yescharacteristic
113C2×C33×C4C2311yescharacteristic
114C3×#638—41no—
115C3×#638—41no—
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C3×C4⋊(C3⋊D3)—41no—
119C32×#67—41no—
120C32×#67—41no—
121C32×#67—41no—
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C2×C32×Dic3C2311yescharacteristic
127C32×D12—41no—
128C3×#626—41no—
129C3×#626—41no—
130C3×#626—41no—
131C3×#626—41no—
132C3×#625—41no—
133C3×#624—41no—
134C3×D3×Dic3—41no—
135C3×#560—91no—
136#5666—31no—
137#5620—31no—
138C23×C3×D3—31no—
139C23×C3×D3—31no—
140C22×D32C22×C311yescharacteristic
141C2×C32×D4—31no—
142C2×C32×D4—31no—
143C2×C32×D4—31no—
144C2×C32×D4—31no—
145C22×C32×C4—21no—
146C22×C32×C4—21no—
147C22×C32×C4—21no—
148C22×C32×C4—41no—
149C22×C32×C4C2×D311yescharacteristic, complemented
150C22×C32×C4C2×D311yescharacteristic, complemented
151C22×C32×C4C22×C311yescharacteristic, complemented
152C2×#638C22×C311yescharacteristic
153C2×#638C22×C311yescharacteristic, complemented
154C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
155C2×C3×#67—21no—
156C2×C3×#67—21no—
157C2×C3×#67—21no—
158C2×C3×#67—31no—
159C2×C3×#67—31no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C2×C3×#67—31no—
163C2×C3×#67—31no—
164C2×C3×#67—31no—
165C2×C3×#67—31no—
166C2×C3×#67—31no—
167C2×C3×#67—31no—
168C2×C3×#67—61no—
169C2×C3×#67—61no—
170C2×C3×#67C2×D311yescharacteristic
171C2×C3×#67C2×D311yescharacteristic
172C2×C3×#67C2×D311yescharacteristic, complemented
173C2×C3×#67C22×C311yescharacteristic
174C2×C3×#67C22×C311yescharacteristic
175C2×C3×#67C22×C311yescharacteristic, complemented
176C22×C3×Dic3—31no—
177C2×C3×D12—21no—
178C2×C3×D12—31no—
179C2×C3×D12—31no—
180C2×C3×D12—31no—
181C2×C3×D12—31no—
182C2×C3×D12—31no—
183C2×C3×D12—31no—
184C2×C3×D12—61no—
185C2×C3×D12C2×D311yescharacteristic
186C2×C3×D12C22×C311yescharacteristic
187C2×C3×C4×D3—31no—
188C2×C3×C4×D3—31no—
189C2×C3×C4×D3—31no—
190C2×#626C22×C311yescharacteristic
191C2×#626C22×C311yescharacteristic
192C2×#626C22×C311yescharacteristic
193C2×#626C22×C311yescharacteristic, complemented
194C2×#625C22×C311yescharacteristic
195C2×#624C22×C311yescharacteristic, complemented
196C2×D3×Dic3C22×C311yescharacteristic, complemented
197C32×C4⋊C4—31no—
198C32×C4⋊C4—31no—
199C32×C4⋊C4—31no—
200C32×C22⋊C4—31no—
201C32×C22⋊C4—31no—
202C32×C22⋊C4—31no—
203C32×C22⋊C4—31no—
204C32×C22⋊C4—31no—
205#3752C22×C311yescharacteristic
206#3752C22×C311yescharacteristic, complemented
207C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
208C3×#217—21no—
209C3×#217—31no—
210C3×#217—31no—
211C3×#217—31no—
212C3×#217C2×D311yescharacteristic, complemented
213C3×#217C22×C311yescharacteristic, complemented
214C3×(C2×D3)⋊C4—21no—
215C3×(C2×D3)⋊C4—21no—
216C3×(C2×D3)⋊C4—21no—
217C3×(C2×D3)⋊C4—21no—
218C3×(C2×D3)⋊C4—31no—
219C3×(C2×D3)⋊C4—31no—
220C3×(C2×D3)⋊C4—31no—
221C3×(C2×D3)⋊C4—31no—
222C3×(C2×D3)⋊C4—31no—
223C3×(C2×D3)⋊C4—31no—
224C3×(C2×D3)⋊C4—31no—
225C3×(C2×D3)⋊C4—31no—
226C3×(C2×D3)⋊C4—31no—
227C3×(C2×D3)⋊C4—31no—
228C3×(C2×D3)⋊C4—31no—
229C3×(C2×D3)⋊C4—61no—
230C3×(C2×D3)⋊C4—61no—
231C3×(C2×D3)⋊C4C2×D311yescharacteristic
232C3×(C2×D3)⋊C4C2×D311yescharacteristic
233C3×(C2×D3)⋊C4C2×D311yescharacteristic
234C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
235C3×(C2×D3)⋊C4C22×C311yescharacteristic
236C3×(C2×D3)⋊C4C22×C311yescharacteristic
237C3×(C2×D3)⋊C4C22×C311yescharacteristic
238C3×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
239C3×C4⋊Dic3—21no—
240C3×C4⋊Dic3—31no—
241C3×C4⋊Dic3—31no—
242C3×C4⋊Dic3—31no—
243C3×C4⋊Dic3—61no—
244C3×C4⋊Dic3C2×D311yescharacteristic, complemented
245C3×C4⋊Dic3C22×C311yescharacteristic, complemented
246C3×Dic3⋊C4—21no—
247C3×Dic3⋊C4—21no—
248C3×Dic3⋊C4—31no—
249C3×Dic3⋊C4—31no—
250C3×Dic3⋊C4—31no—
251C3×Dic3⋊C4C2×D311yescharacteristic, complemented
252C3×Dic3⋊C4C2×D311yescharacteristic, complemented
253C3×Dic3⋊C4C22×C311yescharacteristic, complemented
254C3×Dic3⋊C4C22×C311yescharacteristic, complemented
255C3×C4×Dic3—31no—
256C3×C4×Dic3—31no—
257#3724C22×C311yescharacteristic, complemented
258Dic3⋊Dic3C22×C311yescharacteristic, complemented
259#3722C22×C311yescharacteristic
260#3722C22×C311yescharacteristic
261(C2×D3)⋊Dic3C22×C311yescharacteristic
262(C2×D3)⋊Dic3C22×C311yescharacteristic
263(C2×D3)⋊Dic3C22×C311yescharacteristic
264Dic32C22×C311yescharacteristic, complemented
265C22×C33—21no—
266C22×C33—21no—
267C22×C33—21no—
268C22×C33C2411yescharacteristic
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3—21no—
272C2×C3×C3⋊D3—21no—
273C2×C3×C3⋊D3—21no—
274C2×C3×C3⋊D3—21no—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3—21no—
278C2×C32×D3—21no—
279C2×C32×D3—21no—
280C2×C32×D3—21no—
281C2×C32×D3—21no—
282C2×C32×D3—21no—
283C2×C32×D3—21no—
284C3×D32—44no—
285C33×C4—21no—
286C33×C4—21no—
287C3×C3⋊Dic3—21no—
288C3×C3⋊Dic3—21no—
289C32×Dic3—21no—
290C32×Dic3—21no—
291C32×Dic3—21no—
292C32×Dic3—21no—
293C32×Dic3—21no—
294C3×#127—91no—
295C3×#126—91no—
296C3×#126—91no—
297C3×#123—31no—
298C3×#123—31no—
299C3×#123—61no—
300C3×#123—91no—
301C3×#123—91no—
302C3×#121—31no—
303C3×#121—31no—
304C3×#121—61no—
305C3×#121—91no—
306C3×#121—91no—
307C3×#121—91no—
308C3×#121—91no—
309C3×#121—91no—
310C3×#120—91no—
311C3×#120—91no—
312C3×#120—91no—
313#940—31no—
314#940—31no—
315#939—31no—
316#939—31no—
317#938—31no—
318#937—31no—
319#937—31no—
320#937—31no—
321#930—31no—
322#930—31no—
323#930—61no—
324#930C3×D311yescharacteristic, complemented
325#929C3×D311yescharacteristic, complemented
326#898—31no—
327#898—31no—
328#898—31no—
329#895—31no—
330#895—31no—
331#894—31no—
332#886—31no—
333#884—31no—
334#884—31no—
335#884—31no—
336#883—31no—
337#883—31no—
338#882—31no—
339#882—31no—
340#882—31no—
341#879—31no—
342C23×C32—21no—
343C23×C32—21no—
344C23×C32—21no—
345C23×C32—31no—
346C23×C32—31no—
347C23×C32—31no—
348C23×C32—41no—
349C23×C32C22×D311yescharacteristic
350C23×C32C22×D311yescharacteristic
351C23×C32C23×C311yescharacteristic
352C22×C3⋊D3C23×C311yescharacteristic
353C22×C3⋊D3C23×C311yescharacteristic
354C22×C3×D3—21no—
355C22×C3×D3—21no—
356C22×C3×D3—21no—
357C22×C3×D3—31no—
358C22×C3×D3—31no—
359C22×C3×D3—31no—
360C22×C3×D3—31no—
361C22×C3×D3—61no—
362C22×C3×D3—61no—
363C22×C3×D3—121no—
364C22×C3×D3—121no—
365C22×C3×D3—121no—
366C22×C3×D3—121no—
367C22×C3×D3—121no—
368C22×C3×D3—121no—
369C22×C3×D3C22×D311yescharacteristic
370C22×C3×D3C22×D311yescharacteristic
371C22×C3×D3C22×D311yescharacteristic
372C22×C3×D3C23×C311yescharacteristic
373C22×C3×D3C23×C311yescharacteristic
374C22×C3×D3C23×C311yescharacteristic
375C2×D32—41no—
376C2×D32—41no—
377C2×D32—41no—
378C32×D4—121no—
379C32×D4—121no—
380C32×D4—121no—
381C32×D4—121no—
382C2×C32×C4—21no—
383C2×C32×C4—21no—
384C2×C32×C4—21no—
385C2×C32×C4—21no—
386C2×C32×C4—21no—
387C2×C32×C4—21no—
388C2×C32×C4—31no—
389C2×C32×C4—31no—
390C2×C32×C4—31no—
391C2×C32×C4—31no—
392C2×C32×C4—31no—
393C2×C32×C4—41no—
394C2×C32×C4—41no—
395C2×C32×C4—41no—
396C2×C32×C4—41no—
397C2×C32×C4—41no—
398C2×C32×C4—42no—
399C2×C32×C4—42no—
400C2×C32×C4—42no—
401C2×C32×C4—44no—
402C2×C32×C4C22×D311yescharacteristic
403C2×C32×C4C22×D311yescharacteristic
404C2×C32×C4C22×D311yescharacteristic
405C2×C32×C4C22×D311yescharacteristic
406C2×C32×C4C23×C311yescharacteristic
407C2×C32×C4C23×C311yescharacteristic
408#638—41no—
409#638—41no—
410C2×C3⋊Dic3C23×C311yescharacteristic
411C2×C3⋊Dic3C23×C311yescharacteristic
412C4⋊(C3⋊D3)—41no—
413C3×#67—41no—
414C3×#67—41no—
415C3×#67—41no—
416C3×#67—41no—
417C3×#67—41no—
418C3×#67—41no—
419C3×#67—42no—
420C3×#67—42no—
421C3×#67—42no—
422C3×#67—121no—
423C3×#67—121no—
424C3×#67—121no—
425C3×#67—121no—
426C3×#67—121no—
427C3×#67—121no—
428C3×#67—121no—
429C3×#67—121no—
430C3×#67—121no—
431C3×#67—121no—
432C3×#67—122no—
433C3×#67—122no—
434C2×C3×Dic3—21no—
435C2×C3×Dic3—21no—
436C2×C3×Dic3—21no—
437C2×C3×Dic3—21no—
438C2×C3×Dic3—21no—
439C2×C3×Dic3—31no—
440C2×C3×Dic3—31no—
441C2×C3×Dic3—31no—
442C2×C3×Dic3—31no—
443C2×C3×Dic3—61no—
444C2×C3×Dic3—61no—
445C2×C3×Dic3—121no—
446C2×C3×Dic3C22×D311yescharacteristic
447C2×C3×Dic3C22×D311yescharacteristic
448C2×C3×Dic3C22×D311yescharacteristic
449C2×C3×Dic3C22×D311yescharacteristic
450C2×C3×Dic3C22×D311yescharacteristic
451C2×C3×Dic3C23×C311yescharacteristic
452C2×C3×Dic3C23×C311yescharacteristic
453C2×C3×Dic3C23×C311yescharacteristic
454C2×C3×Dic3C23×C311yescharacteristic
455C2×C3×Dic3C23×C311yescharacteristic
456C3×D12—41no—
457C3×D12—41no—
458C3×D12—42no—
459C3×D12—121no—
460C3×D12—121no—
461C3×D12—122no—
462C3×D12—121no—
463C3×D12—121no—
464C3×D12—121no—
465C3×D12—121no—
466C3×C4×D3—121no—
467C3×C4×D3—121no—
468C3×C4×D3—121no—
469#626—41no—
470#626—41no—
471#626—41no—
472#626—41no—
473#625—41no—
474#624—41no—
475D3×Dic3—41no—
476#560—91noSylow
477C2×C33—41no—
478C2×C33H(5,𝔽2)11yescharacteristic
479C2×C33H(5,𝔽2)11yescharacteristic
480C2×C33H(5,𝔽2)11yescharacteristic
481C3×C3⋊D3—41no—
482C3×C3⋊D3—41no—
483C32×D3—41no—
484C32×D3—41no—
485C32×D3—41no—
486C24×C3—91no—
487C23×D3—31no—
488C23×D3—31no—
489C2×C3×D4—31no—
490C2×C3×D4—31no—
491C2×C3×D4—31no—
492C2×C3×D4—31no—
493C2×C3×D4—31no—
494C2×C3×D4—31no—
495C2×C3×D4—31no—
496C2×C3×D4—31no—
497C2×C3×D4—61no—
498C2×C3×D4—61no—
499C2×C3×D4—61no—
500C2×C3×D4—61no—
501C2×C3×D4—91no—
502C2×C3×D4—91no—
503C2×C3×D4—91no—
504C2×C3×D4—91no—
505C2×C3×D4—91no—
506C2×C3×D4—91no—
507C2×C3×D4—91no—
508C2×C3×D4—91no—
509C22×C3×C4—21no—
510C22×C3×C4—21no—
511C22×C3×C4—21no—
512C22×C3×C4—41no—
513C22×C3×C4—91no—
514C22×C3×C4—91no—
515C22×C3×C4D3211yescharacteristic, complemented
516C22×C3×C4C2×C3×D311yescharacteristic, complemented
517C22×C3×C4C2×C3×D311yescharacteristic, complemented
518C2×#67—31no—
519C2×#67—31no—
520C2×#67—31no—
521C2×#67—31no—
522C2×#67—31no—
523C2×#67—31no—
524C2×#67—31no—
525C2×#67—31no—
526C2×#67—31no—
527C2×#67—31no—
528C2×#67—61no—
529C2×#67—61no—
530C2×#67C2×C3×D311yescharacteristic
531C2×#67C2×C3×D311yescharacteristic
532C2×#67C2×C3×D311yescharacteristic, complemented
533C22×Dic3—31no—
534C2×D12—31no—
535C2×D12—31no—
536C2×D12—31no—
537C2×D12—31no—
538C2×D12—31no—
539C2×D12—31no—
540C2×D12—61no—
541C2×D12C2×C3×D311yescharacteristic
542C2×C4×D3—31no—
543C2×C4×D3—31no—
544C2×C4×D3—31no—
545C3×C4⋊C4—31no—
546C3×C4⋊C4—31no—
547C3×C4⋊C4—31no—
548C3×C4⋊C4—31no—
549C3×C4⋊C4—31no—
550C3×C4⋊C4—31no—
551C3×C4⋊C4—61no—
552C3×C4⋊C4—61no—
553C3×C4⋊C4—61no—
554C3×C4⋊C4—91no—
555C3×C4⋊C4—91no—
556C3×C4⋊C4—91no—
557C3×C22⋊C4—31no—
558C3×C22⋊C4—31no—
559C3×C22⋊C4—31no—
560C3×C22⋊C4—31no—
561C3×C22⋊C4—31no—
562C3×C22⋊C4—31no—
563C3×C22⋊C4—31no—
564C3×C22⋊C4—31no—
565C3×C22⋊C4—31no—
566C3×C22⋊C4—31no—
567C3×C22⋊C4—61no—
568C3×C22⋊C4—61no—
569C3×C22⋊C4—61no—
570C3×C22⋊C4—61no—
571C3×C22⋊C4—61no—
572C3×C22⋊C4—91no—
573C3×C22⋊C4—91no—
574C3×C22⋊C4—91no—
575C3×C22⋊C4—91no—
576C3×C22⋊C4—91no—
577C3×C22⋊C4—91no—
578C3×C22⋊C4—91no—
579C3×C42—91no—
580#217—31no—
581#217—31no—
582#217—31no—
583#217C2×C3×D311yescharacteristic, complemented
584(C2×D3)⋊C4—31no—
585(C2×D3)⋊C4—31no—
586(C2×D3)⋊C4—31no—
587(C2×D3)⋊C4—31no—
588(C2×D3)⋊C4—31no—
589(C2×D3)⋊C4—31no—
590(C2×D3)⋊C4—31no—
591(C2×D3)⋊C4—31no—
592(C2×D3)⋊C4—31no—
593(C2×D3)⋊C4—31no—
594(C2×D3)⋊C4—31no—
595(C2×D3)⋊C4—61no—
596(C2×D3)⋊C4—61no—
597(C2×D3)⋊C4C2×C3×D311yescharacteristic
598(C2×D3)⋊C4C2×C3×D311yescharacteristic
599(C2×D3)⋊C4C2×C3×D311yescharacteristic
600(C2×D3)⋊C4C2×C3×D311yescharacteristic, complemented
601C4⋊Dic3—31no—
602C4⋊Dic3—31no—
603C4⋊Dic3—31no—
604C4⋊Dic3—61no—
605C4⋊Dic3C2×C3×D311yescharacteristic, complemented
606Dic3⋊C4—31no—
607Dic3⋊C4—31no—
608Dic3⋊C4—31no—
609Dic3⋊C4C2×C3×D311yescharacteristic, complemented
610Dic3⋊C4C2×C3×D311yescharacteristic, complemented
611C4×Dic3—31no—
612C4×Dic3—31no—
613C22×C32—21no—
614C22×C32—21no—
615C22×C32—21no—
616C22×C32—22no—
617C22×C32—22no—
618C22×C32—22no—
619C22×C32—21no—
620C22×C32—21no—
621C22×C32—21no—
622C22×C32—21no—
623C22×C32—21no—
624C22×C32—21no—
625C22×C32—21no—
626C22×C32—21no—
627C22×C32—21no—
628C22×C32—41no—
629C22×C32—41no—
630C22×C32—41no—
631C22×C32—41no—
632C22×C32—41no—
633C22×C32—41no—
634C22×C32—41no—
635C22×C32—42no—
636C22×C32—42no—
637C22×C32—42no—
638C22×C32—61no—
639C22×C32—61no—
640C22×C32—61no—
641C22×C32—61no—
642C22×C32—61no—
643C22×C32—61no—
644C22×C32—61no—
645C22×C32—61no—
646C22×C32—61no—
647C22×C32C23×D311yescharacteristic
648C22×C32C23×D311yescharacteristic
649C22×C32C24×C311yescharacteristic
650C2×C3⋊D3—21no—
651C2×C3⋊D3—21no—
652C2×C3⋊D3—21no—
653C2×C3⋊D3—21no—
654C2×C3⋊D3—21no—
655C2×C3⋊D3—21no—
656C2×C3×D3—21no—
657C2×C3×D3—21no—
658C2×C3×D3—21no—
659C2×C3×D3—21no—
660C2×C3×D3—21no—
661C2×C3×D3—21no—
662C2×C3×D3—21no—
663C2×C3×D3—21no—
664C2×C3×D3—21no—
665C2×C3×D3—21no—
666C2×C3×D3—21no—
667C2×C3×D3—21no—
668C2×C3×D3—21no—
669C2×C3×D3—21no—
670C2×C3×D3—21no—
671C2×C3×D3—21no—
672C2×C3×D3—21no—
673C2×C3×D3—21no—
674C2×C3×D3—41no—
675C2×C3×D3—41no—
676C2×C3×D3—41no—
677C2×C3×D3—41no—
678C2×C3×D3—41no—
679C2×C3×D3—41no—
680C2×C3×D3—41no—
681C2×C3×D3—41no—
682C2×C3×D3—41no—
683C2×C3×D3—61no—
684C2×C3×D3—61no—
685C2×C3×D3—61no—
686C2×C3×D3—61no—
687C2×C3×D3—61no—
688C2×C3×D3—61no—
689C2×C3×D3—61no—
690C2×C3×D3—61no—
691C2×C3×D3—61no—
692C2×C3×D3—61no—
693C2×C3×D3—61no—
694C2×C3×D3—61no—
695C2×C3×D3—121no—
696C2×C3×D3—121no—
697C2×C3×D3—121no—
698C2×C3×D3—121no—
699C2×C3×D3—121no—
700C2×C3×D3—121no—
701C2×C3×D3—124no—
702C2×C3×D3—124no—
703D32—44no—
704C32×C4—21no—
705C32×C4—21no—
706C32×C4—22no—
707C32×C4—22no—
708C32×C4—21no—
709C32×C4—21no—
710C32×C4—21no—
711C32×C4—21no—
712C32×C4—41no—
713C32×C4—41no—
714C32×C4—41no—
715C32×C4—41no—
716C32×C4—42no—
717C32×C4—42no—
718C32×C4—61no—
719C32×C4—61no—
720C32×C4—61no—
721C32×C4—61no—
722C32×C4—61no—
723C3⋊Dic3—21no—
724C3⋊Dic3—21no—
725C3×Dic3—21no—
726C3×Dic3—21no—
727C3×Dic3—21no—
728C3×Dic3—21no—
729C3×Dic3—21no—
730C3×Dic3—21no—
731C3×Dic3—21no—
732C3×Dic3—21no—
733C3×Dic3—21no—
734C3×Dic3—21no—
735C3×Dic3—41no—
736C3×Dic3—41no—
737C3×Dic3—41no—
738C3×Dic3—41no—
739C3×Dic3—41no—
740C3×Dic3—61no—
741C3×Dic3—61no—
742C3×Dic3—61no—
743C3×Dic3—61no—
744C3×Dic3—121no—
745C3×Dic3—121no—
746#127—91no—
747#126—91no—
748#126—91no—
749#123—31no—
750#123—91no—
751#123—91no—
752#121—31no—
753#121—91no—
754#121—91no—
755#121—91no—
756#121—91no—
757#121—91no—
758#120—91no—
759#120—91no—
760#120—91no—
761C33#56011yescharacteristic, complemented, Sylow
762C23×C3—21no—
763C23×C3—21no—
764C23×C3—21no—
765C23×C3—31no—
766C23×C3—31no—
767C23×C3—31no—
768C23×C3—31no—
769C23×C3—31no—
770C23×C3—31no—
771C23×C3—41no—
772C23×C3—61no—
773C23×C3—61no—
774C23×C3—61no—
775C23×C3—91no—
776C23×C3—91no—
777C23×C3—361no—
778C23×C3—361no—
779C23×C3—361no—
780C23×C3C2×D3211yescharacteristic
781C23×C3C22×C3×D311yescharacteristic
782C23×C3C22×C3×D311yescharacteristic
783C22×D3—31no—
784C22×D3—31no—
785C22×D3—31no—
786C22×D3—31no—
787C22×D3—61no—
788C22×D3—61no—
789C22×D3—121no—
790C22×D3—121no—
791C22×D3—121no—
792C22×D3—121no—
793C22×D3—121no—
794C22×D3—121no—
795C22×D3C22×C3×D311yescharacteristic
796C22×D3C22×C3×D311yescharacteristic
797C22×D3C22×C3×D311yescharacteristic
798C3×D4—121no—
799C3×D4—121no—
800C3×D4—122no—
801C3×D4—121no—
802C3×D4—121no—
803C3×D4—121no—
804C3×D4—121no—
805C3×D4—121no—
806C3×D4—121no—
807C3×D4—122no—
808C3×D4—122no—
809C3×D4—122no—
810C3×D4—361no—
811C3×D4—361no—
812C3×D4—361no—
813C3×D4—361no—
814C3×D4—361no—
815C3×D4—361no—
816C3×D4—361no—
817C3×D4—361no—
818C2×C3×C4—21no—
819C2×C3×C4—21no—
820C2×C3×C4—21no—
821C2×C3×C4—21no—
822C2×C3×C4—21no—
823C2×C3×C4—21no—
824C2×C3×C4—31no—
825C2×C3×C4—31no—
826C2×C3×C4—31no—
827C2×C3×C4—31no—
828C2×C3×C4—31no—
829C2×C3×C4—31no—
830C2×C3×C4—31no—
831C2×C3×C4—31no—
832C2×C3×C4—31no—
833C2×C3×C4—31no—
834C2×C3×C4—41no—
835C2×C3×C4—41no—
836C2×C3×C4—41no—
837C2×C3×C4—42no—
838C2×C3×C4—42no—
839C2×C3×C4—42no—
840C2×C3×C4—44no—
841C2×C3×C4—41no—
842C2×C3×C4—41no—
843C2×C3×C4—61no—
844C2×C3×C4—61no—
845C2×C3×C4—61no—
846C2×C3×C4—61no—
847C2×C3×C4—61no—
848C2×C3×C4—91no—
849C2×C3×C4—91no—
850C2×C3×C4—361no—
851C2×C3×C4—361no—
852C2×C3×C4C2×D3211yescharacteristic
853C2×C3×C4C2×D3211yescharacteristic
854C2×C3×C4C22×C3×D311yescharacteristic
855C2×C3×C4C22×C3×D311yescharacteristic
856C2×C3×C4C22×C3×D311yescharacteristic
857C2×C3×C4C22×C3×D311yescharacteristic
858#67—41no—
859#67—41no—
860#67—41no—
861#67—121no—
862#67—121no—
863#67—121no—
864#67—121no—
865#67—121no—
866#67—121no—
867#67—121no—
868#67—121no—
869#67—121no—
870#67—121no—
871#67—122no—
872#67—122no—
873C2×Dic3—31no—
874C2×Dic3—31no—
875C2×Dic3—31no—
876C2×Dic3—31no—
877C2×Dic3—61no—
878C2×Dic3—61no—
879C2×Dic3—121no—
880C2×Dic3C22×C3×D311yescharacteristic
881C2×Dic3C22×C3×D311yescharacteristic
882C2×Dic3C22×C3×D311yescharacteristic
883C2×Dic3C22×C3×D311yescharacteristic
884C2×Dic3C22×C3×D311yescharacteristic
885D12—41no—
886D12—121no—
887D12—121no—
888D12—122no—
889D12—121no—
890D12—121no—
891D12—121no—
892D12—121no—
893C4×D3—121no—
894C4×D3—121no—
895C4×D3—121no—
896C2×C32—21no—
897C2×C32—21no—
898C2×C32—21no—
899C2×C32—21no—
900C2×C32—21no—
901C2×C32—21no—
902C2×C32—21no—
903C2×C32—21no—
904C2×C32—21no—
905C2×C32—41no—
906C2×C32—41no—
907C2×C32—41no—
908C2×C32—42no—
909C2×C32—42no—
910C2×C32—42no—
911C2×C32—44no—
912C2×C32—41no—
913C2×C32—41no—
914C2×C32—41no—
915C2×C32—121no—
916C2×C32—121no—
917C2×C32—121no—
918C2×C32#100411yescharacteristic
919C2×C32#100411yescharacteristic
920C2×C32#100411yescharacteristic
921C2×C32#100911yescharacteristic
922C2×C32#100911yescharacteristic
923C2×C32#100911yescharacteristic
924C2×C32C3×H(5,𝔽2)11yescharacteristic
925C2×C32C3×H(5,𝔽2)11yescharacteristic
926C2×C32C3×H(5,𝔽2)11yescharacteristic
927C3⋊D3—41no—
928C3⋊D3—41no—
929C3×D3—41no—
930C3×D3—41no—
931C3×D3—41no—
932C3×D3—41no—
933C3×D3—41no—
934C3×D3—41no—
935C3×D3—81no—
936C3×D3—81no—
937C3×D3—81no—
938C3×D3—121no—
939C3×D3—121no—
940C3×D3—121no—
941C3×D3—121no—
942C3×D3—241no—
943C3×D3—241no—
944C24—91no—
945C2×D4—31no—
946C2×D4—31no—
947C2×D4—31no—
948C2×D4—31no—
949C2×D4—91no—
950C2×D4—91no—
951C2×D4—91no—
952C2×D4—91no—
953C2×D4—91no—
954C2×D4—91no—
955C2×D4—91no—
956C2×D4—91no—
957C22×C4—91no—
958C22×C4—91no—
959C22×C4C3×D3211yescharacteristic, complemented
960C4⋊C4—31no—
961C4⋊C4—31no—
962C4⋊C4—31no—
963C4⋊C4—91no—
964C4⋊C4—91no—
965C4⋊C4—91no—
966C22⋊C4—31no—
967C22⋊C4—31no—
968C22⋊C4—31no—
969C22⋊C4—31no—
970C22⋊C4—31no—
971C22⋊C4—91no—
972C22⋊C4—91no—
973C22⋊C4—91no—
974C22⋊C4—91no—
975C22⋊C4—91no—
976C22⋊C4—91no—
977C22⋊C4—91no—
978C42—91no—
979C22×C3—22no—
980C22×C3—22no—
981C22×C3—22no—
982C22×C3—21no—
983C22×C3—21no—
984C22×C3—21no—
985C22×C3—21no—
986C22×C3—21no—
987C22×C3—21no—
988C22×C3—21no—
989C22×C3—21no—
990C22×C3—21no—
991C22×C3—21no—
992C22×C3—21no—
993C22×C3—21no—
994C22×C3—41no—
995C22×C3—41no—
996C22×C3—41no—
997C22×C3—41no—
998C22×C3—41no—
999C22×C3—41no—
1000C22×C3—42no—
1001C22×C3—42no—
1002C22×C3—42no—
1003C22×C3—41no—
1004C22×C3—61no—
1005C22×C3—61no—
1006C22×C3—61no—
1007C22×C3—61no—
1008C22×C3—61no—
1009C22×C3—61no—
1010C22×C3—61no—
1011C22×C3—61no—
1012C22×C3—61no—
1013C22×C3—61no—
1014C22×C3—61no—
1015C22×C3—61no—
1016C22×C3—61no—
1017C22×C3—61no—
1018C22×C3—61no—
1019C22×C3—61no—
1020C22×C3—61no—
1021C22×C3—61no—
1022C22×C3—121no—
1023C22×C3—121no—
1024C22×C3—121no—
1025C22×C3—121no—
1026C22×C3—121no—
1027C22×C3—121no—
1028C22×C3—121no—
1029C22×C3—121no—
1030C22×C3—121no—
1031C22×C3—181no—
1032C22×C3—181no—
1033C22×C3—181no—
1034C22×C3—181no—
1035C22×C3—181no—
1036C22×C3—181no—
1037C22×C3—364no—
1038C22×C3C22×D3211yescharacteristic
1039C22×C3C23×C3×D311yescharacteristic
1040C22×C3C23×C3×D311yescharacteristic
1041C2×D3—21no—
1042C2×D3—21no—
1043C2×D3—21no—
1044C2×D3—21no—
1045C2×D3—21no—
1046C2×D3—21no—
1047C2×D3—21no—
1048C2×D3—21no—
1049C2×D3—21no—
1050C2×D3—61no—
1051C2×D3—61no—
1052C2×D3—61no—
1053C2×D3—61no—
1054C2×D3—61no—
1055C2×D3—61no—
1056C2×D3—61no—
1057C2×D3—61no—
1058C2×D3—61no—
1059C2×D3—61no—
1060C2×D3—61no—
1061C2×D3—61no—
1062C2×D3—121no—
1063C2×D3—121no—
1064C2×D3—121no—
1065C2×D3—121no—
1066C2×D3—121no—
1067C2×D3—121no—
1068C2×D3—124no—
1069C2×D3—124no—
1070C3×C4—22no—
1071C3×C4—22no—
1072C3×C4—21no—
1073C3×C4—21no—
1074C3×C4—21no—
1075C3×C4—21no—
1076C3×C4—21no—
1077C3×C4—21no—
1078C3×C4—41no—
1079C3×C4—41no—
1080C3×C4—41no—
1081C3×C4—41no—
1082C3×C4—42no—
1083C3×C4—42no—
1084C3×C4—61no—
1085C3×C4—61no—
1086C3×C4—61no—
1087C3×C4—61no—
1088C3×C4—61no—
1089C3×C4—61no—
1090C3×C4—61no—
1091C3×C4—61no—
1092C3×C4—61no—
1093C3×C4—61no—
1094C3×C4—121no—
1095C3×C4—121no—
1096C3×C4—121no—
1097C3×C4—121no—
1098C3×C4—121no—
1099C3×C4—181no—
1100C3×C4—181no—
1101Dic3—21no—
1102Dic3—21no—
1103Dic3—21no—
1104Dic3—21no—
1105Dic3—21no—
1106Dic3—61no—
1107Dic3—61no—
1108Dic3—61no—
1109Dic3—61no—
1110Dic3—121no—
1111Dic3—121no—
1112C32—21no—
1113C32—21no—
1114C32—21no—
1115C32—41no—
1116C32#562011yescharacteristic, complemented
1117C32#566611yescharacteristic, complemented
1118C32C3×#56011yescharacteristic, complemented
1119C23—31no—
1120C23—31no—
1121C23—31no—
1122C23—91no—
1123C23—91no—
1124C23—361no—
1125C23—361no—
1126C23—361no—
1127C23C2×C3×D3211yescharacteristic
1128D4—121no—
1129D4—121no—
1130D4—121no—
1131D4—121no—
1132D4—361no—
1133D4—361no—
1134D4—361no—
1135D4—361no—
1136D4—361no—
1137D4—361no—
1138D4—361no—
1139D4—361no—
1140C2×C4—31no—
1141C2×C4—31no—
1142C2×C4—31no—
1143C2×C4—31no—
1144C2×C4—31no—
1145C2×C4—41no—
1146C2×C4—91no—
1147C2×C4—91no—
1148C2×C4—361no—
1149C2×C4—361no—
1150C2×C4C2×C3×D3211yescharacteristic
1151C2×C4C2×C3×D3211yescharacteristic
1152C2×C3—21no—
1153C2×C3—21no—
1154C2×C3—21no—
1155C2×C3—21no—
1156C2×C3—21no—
1157C2×C3—21no—
1158C2×C3—21no—
1159C2×C3—21no—
1160C2×C3—21no—
1161C2×C3—42no—
1162C2×C3—42no—
1163C2×C3—42no—
1164C2×C3—44no—
1165C2×C3—41no—
1166C2×C3—41no—
1167C2×C3—41no—
1168C2×C3—41no—
1169C2×C3—41no—
1170C2×C3—41no—
1171C2×C3—121no—
1172C2×C3—121no—
1173C2×C3—121no—
1174C2×C3—121no—
1175C2×C3—121no—
1176C2×C3—121no—
1177C2×C3—241no—
1178C2×C3—241no—
1179C2×C3—241no—
1180C2×C3—361no—
1181C2×C3—361no—
1182C2×C3#6430711yescharacteristic
1183C2×C3#6430811yescharacteristic
1184C2×C3#6433011yescharacteristic
1185C2×C3C3×#100411yescharacteristic
1186C2×C3C3×#100411yescharacteristic
1187C2×C3C3×#100411yescharacteristic
1188C2×C3C3×#100911yescharacteristic
1189C2×C3C3×#100911yescharacteristic
1190C2×C3C3×#100911yescharacteristic
1191D3—41no—
1192D3—41no—
1193D3—41no—
1194D3—121no—
1195D3—121no—
1196D3—121no—
1197D3—121no—
1198D3—241no—
1199D3—241no—
1200C22—21no—
1201C22—21no—
1202C22—21no—
1203C22—61no—
1204C22—61no—
1205C22—61no—
1206C22—61no—
1207C22—61no—
1208C22—61no—
1209C22—61no—
1210C22—61no—
1211C22—61no—
1212C22—181no—
1213C22—181no—
1214C22—181no—
1215C22—181no—
1216C22—181no—
1217C22—181no—
1218C22—364no—
1219C22C22×C3×D3211yescharacteristic
1220C4—21no—
1221C4—21no—
1222C4—61no—
1223C4—61no—
1224C4—61no—
1225C4—61no—
1226C4—61no—
1227C4—181no—
1228C4—181no—
1229C3—21no—
1230C3—21no—
1231C3—21no—
1232C3—41no—
1233C3#1059509011yescharacteristic, direct product factor
1234C3C3×#562011yescharacteristic, complemented
1235C3C3×#566611yescharacteristic, complemented
1236C2—41no—
1237C2—121no—
1238C2—121no—
1239C2—121no—
1240C2—361no—
1241C2—361no—
1242C2C3×#6430711yescharacteristic
1243C2C3×#6430811yescharacteristic
1244C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C3×#560
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×#64139C2semidirect
2. C32×#930C2semidirect
3. C32×#929C2semidirect
4. C3×#63983C2semidirect
5. C3×#63979C2semidirect
6. C3×#63971C2semidirect
7. C3×#63958C2semidirect
8. C3×#63923C2semidirect
9. C3×#63922C2semidirect
10. C3×#63910C2semidirect
11. C3×#63891C2semidirect
12. C3×#63886C2semidirect
13. C3×#63861C2semidirect
14. C3×#63854C2semidirect
15. C3×#63848C2semidirect
18. #10595090C3direct (N × H)
20. C22×C33×C4C22semidirect
22. C2×C3×#638C22semidirect
26. C2×C32×#67C22semidirect
31. C2×C3×#626C22semidirect
33. C2×C3×#624C22semidirect
34. C2×C3×D3×Dic3C22semidirect
36. C3×#3752C22semidirect
37. C3×C4⋊(C3⋊Dic3)C22semidirect
38. C32×#217C22semidirect
42. C32×(C2×D3)⋊C4C22semidirect
43. C32×C4⋊Dic3C22semidirect
44. C32×Dic3⋊C4C22semidirect
45. C32×Dic3⋊C4C22semidirect
46. C3×#3724C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
56. #64139C2×C3semidirect
69. C3×#930D3semidirect
70. C3×#930C2×C3semidirect
72. C3×#929D3semidirect
73. C3×#929C2×C3semidirect
90. #63983C2×C3semidirect
91. #63979C2×C3semidirect
92. #63971C2×C3semidirect
93. #63958C2×C3semidirect
94. #63923C2×C3semidirect
95. #63922C2×C3semidirect
96. #63910C2×C3semidirect
97. #63891C2×C3semidirect
98. #63886C2×C3semidirect
99. #63861C2×C3semidirect
100. #63854C2×C3semidirect
101. #63848C2×C3semidirect
149. C22×C32×C4C2×D3semidirect
150. C22×C32×C4C2×D3semidirect
151. C22×C32×C4C22×C3semidirect
153. C2×#638C22×C3semidirect
172. C2×C3×#67C2×D3semidirect
175. C2×C3×#67C22×C3semidirect
193. C2×#626C22×C3semidirect
195. C2×#624C22×C3semidirect
196. C2×D3×Dic3C22×C3semidirect
206. #3752C22×C3semidirect
207. C4⋊(C3⋊Dic3)C22×C3semidirect
212. C3×#217C2×D3semidirect
213. C3×#217C22×C3semidirect
234. C3×(C2×D3)⋊C4C2×D3semidirect
238. C3×(C2×D3)⋊C4C22×C3semidirect
244. C3×C4⋊Dic3C2×D3semidirect
245. C3×C4⋊Dic3C22×C3semidirect
251. C3×Dic3⋊C4C2×D3semidirect
252. C3×Dic3⋊C4C2×D3semidirect
253. C3×Dic3⋊C4C22×C3semidirect
254. C3×Dic3⋊C4C22×C3semidirect
257. #3724C22×C3semidirect
258. Dic3⋊Dic3C22×C3semidirect
264. Dic32C22×C3semidirect
324. #930C3×D3semidirect
325. #929C3×D3semidirect
515. C22×C3×C4D32semidirect
516. C22×C3×C4C2×C3×D3semidirect
517. C22×C3×C4C2×C3×D3semidirect
532. C2×#67C2×C3×D3semidirect
583. #217C2×C3×D3semidirect
600. (C2×D3)⋊C4C2×C3×D3semidirect
605. C4⋊Dic3C2×C3×D3semidirect
609. Dic3⋊C4C2×C3×D3semidirect
610. Dic3⋊C4C2×C3×D3semidirect
761. C33#560semidirect
959. C22×C4C3×D32semidirect
1116. C32#5620semidirect
1117. C32#5666semidirect
1118. C32C3×#560semidirect
1233. C3#10595090direct (N × H)
1234. C3C3×#5620semidirect
1235. C3C3×#5666semidirect

Maximal subgroups

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

subgroupindex
C3×#641392
C32×#9302
C32×#9292
C3×#639832
C3×#639792
C3×#639712
C3×#639582
C3×#639232
C3×#639222
C3×#639102
C3×#638912
C3×#638862
C3×#638612
C3×#638542
C3×#638482
C3×#56663
C3×#56203
#105950903