Finite Group Databasebeta

← C3×#10595089 #13174686

Subgroups — C3×#10595089 #13174686

Order 1728.

1320 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#638C211yesmaximal, characteristic, complemented
2C32×#930C211yesmaximal, characteristic, complemented
3C32×#929C211yesmaximal, characteristic, complemented
4C3×#63983C211yesmaximal, characteristic, complemented
5C3×#63970C211yesmaximal, characteristic, complemented
6C3×#63959C211yesmaximal, characteristic, complemented
7C3×#63958C211yesmaximal, characteristic, complemented
8C3×#63922C211yesmaximal, characteristic, complemented
9C3×#63921C211yesmaximal, characteristic, complemented
10C3×#63915C211yesmaximal, characteristic, complemented
11C3×#63895C211yesmaximal, characteristic, complemented
12C3×#63884C211yesmaximal, characteristic, complemented
13C3×#63881C211yesmaximal, characteristic, complemented
14C3×#63862C211yesmaximal, characteristic, complemented
15C3×#63858C211yesmaximal, characteristic, complemented
16C3×#5657—31nomaximal
17C3×#5613—31nomaximal
18#10595089C311yesmaximal, characteristic, direct product factor
19C22×C3×D32C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic, complemented
21C2×C3×#638C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic, complemented
26C2×C32×D12C2211yescharacteristic
27C2×C3×#627C2211yescharacteristic, complemented
28C2×C3×#626C2211yescharacteristic
29C2×C3×#625C2211yescharacteristic
30C2×C3×#624C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic, complemented
32C3×#3757C2211yescharacteristic, complemented
33C3×#3752C2211yescharacteristic
34C3×#3750C2211yescharacteristic, complemented
35C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
36C32×#217C2211yescharacteristic, complemented
37C32×(C2×D3)⋊C4C2211yescharacteristic
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C32×C4⋊Dic3C2211yescharacteristic, complemented
42C32×Dic3⋊C4C2211yescharacteristic, complemented
43C32×Dic3⋊C4C2211yescharacteristic, complemented
44C3×Dic3⋊Dic3C2211yescharacteristic, complemented
45C3×Dic3⋊Dic3C2211yescharacteristic, complemented
46C3×#3722C2211yescharacteristic
47C3×(C2×D3)⋊Dic3C2211yescharacteristic
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54C32×#123—31no—
55C32×#121—31no—
56C4×#638C2×C311yescharacteristic, complemented
57C3×#939—31no—
58C3×#938—31no—
59C3×#938—31no—
60C3×#937—31no—
61C3×#937—31no—
62C3×#937—31no—
63C3×#936—31no—
64C3×#935—31no—
65C3×#930—21no—
66C3×#930D311yescharacteristic, complemented
67C3×#930C2×C311yescharacteristic, complemented
68C3×#929—21no—
69C3×#929D311yescharacteristic, complemented
70C3×#929C2×C311yescharacteristic, complemented
71C3×C4×#67—31no—
72C3×C4×#67—31no—
73C3×C4×#67—61no—
74C3×#898—31no—
75C3×#898—31no—
76C3×#897—31no—
77C3×#896—31no—
78C3×#894—31no—
79C3×#893—31no—
80C3×#885—31no—
81C3×#885—31no—
82C3×#885—31no—
83C3×#884—31no—
84C3×#882—31no—
85C3×#67⋊C4—31no—
86C3×D3×C22⋊C4—31no—
87C3×D3×C22⋊C4—31no—
88C3×#879—31no—
89C3×#879—31no—
90#63983C2×C311yescharacteristic, complemented
91#63970C2×C311yescharacteristic, complemented
92#63959C2×C311yescharacteristic, complemented
93#63958C2×C311yescharacteristic, complemented
94#63922C2×C311yescharacteristic, complemented
95#63921C2×C311yescharacteristic, complemented
96#63915C2×C311yescharacteristic, complemented
97#63895C2×C311yescharacteristic, complemented
98#63884C2×C311yescharacteristic, complemented
99#63881C2×C311yescharacteristic, complemented
100#63862C2×C311yescharacteristic, complemented
101#63858C2×C311yescharacteristic, complemented
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×C3×D32—22no—
108C2×C3×D32—41no—
109C2×C3×D32—41no—
110C2×C33×C4—41no—
111C2×C33×C4C2311yescharacteristic
112C2×C33×C4C2311yescharacteristic
113C3×#638—22no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C3×C4×C3⋊D3—41no—
118C32×#67—41no—
119C32×#67—41no—
120C32×#67—41no—
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126C32×D12—41no—
127C3×#627—41no—
128C3×#626—22no—
129C3×#625—41no—
130C3×#624—41no—
131C3×D3×Dic3—41no—
132C3×#538—91no—
133#5657—31no—
134#5613—31no—
135C23×C3×D3—31no—
136C23×C3×D3—31no—
137C22×D32C22×C311yescharacteristic
138C2×C32×D4—31no—
139C2×C32×D4—31no—
140C2×C32×D4—31no—
141C2×C32×D4—31no—
142C22×C32×C4—21no—
143C22×C32×C4—21no—
144C22×C32×C4—21no—
145C22×C32×C4—41no—
146C22×C32×C4C2×D311yescharacteristic, complemented
147C22×C32×C4C2×D311yescharacteristic, complemented
148C22×C32×C4C22×C311yescharacteristic, complemented
149C2×#638C22×C311yescharacteristic
150C2×C4×C3⋊D3C22×C311yescharacteristic
151C2×C3×#67—21no—
152C2×C3×#67—21no—
153C2×C3×#67—21no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C2×C3×#67—31no—
159C2×C3×#67—61no—
160C2×C3×#67C2×D311yescharacteristic
161C2×C3×#67C2×D311yescharacteristic
162C2×C3×#67C2×D311yescharacteristic, complemented
163C2×C3×#67C22×C311yescharacteristic
164C2×C3×#67C22×C311yescharacteristic
165C2×C3×#67C22×C311yescharacteristic, complemented
166C22×C3×Dic3—31no—
167C2×C3×D12—21no—
168C2×C3×D12—31no—
169C2×C3×D12C2×D311yescharacteristic
170C2×C3×D12C22×C311yescharacteristic
171C2×C3×C4×D3—31no—
172C2×C3×C4×D3—31no—
173C2×C3×C4×D3—31no—
174C2×C3×C4×D3—31no—
175C2×C3×C4×D3—31no—
176C2×C3×C4×D3—61no—
177C2×C3×Dic6—31no—
178C2×C3×Dic6—31no—
179C2×#627C22×C311yescharacteristic, complemented
180C2×#626C22×C311yescharacteristic
181C2×#625C22×C311yescharacteristic
182C2×#624C22×C311yescharacteristic
183C2×D3×Dic3C22×C311yescharacteristic, complemented
184C32×C4⋊C4—31no—
185C32×C4⋊C4—31no—
186C32×C4⋊C4—31no—
187C32×C22⋊C4—31no—
188C32×C22⋊C4—31no—
189C32×C22⋊C4—31no—
190C32×C22⋊C4—31no—
191C32×C22⋊C4—31no—
192#3757C22×C311yescharacteristic, complemented
193#3752C22×C311yescharacteristic
194#3750C22×C311yescharacteristic, complemented
195C4×C3⋊Dic3C22×C311yescharacteristic, complemented
196C3×#217—21no—
197C3×#217—31no—
198C3×#217—31no—
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—31no—
202C3×#217—31no—
203C3×#217—31no—
204C3×#217—31no—
205C3×#217—61no—
206C3×#217C2×D311yescharacteristic, complemented
207C3×#217C22×C311yescharacteristic, complemented
208C3×(C2×D3)⋊C4—21no—
209C3×(C2×D3)⋊C4—21no—
210C3×(C2×D3)⋊C4—21no—
211C3×(C2×D3)⋊C4—21no—
212C3×(C2×D3)⋊C4—31no—
213C3×(C2×D3)⋊C4—31no—
214C3×(C2×D3)⋊C4—31no—
215C3×(C2×D3)⋊C4—31no—
216C3×(C2×D3)⋊C4—31no—
217C3×(C2×D3)⋊C4—31no—
218C3×(C2×D3)⋊C4—31no—
219C3×(C2×D3)⋊C4—31no—
220C3×(C2×D3)⋊C4—31no—
221C3×(C2×D3)⋊C4—31no—
222C3×(C2×D3)⋊C4—61no—
223C3×(C2×D3)⋊C4C2×D311yescharacteristic
224C3×(C2×D3)⋊C4C2×D311yescharacteristic
225C3×(C2×D3)⋊C4C2×D311yescharacteristic
226C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
227C3×(C2×D3)⋊C4C22×C311yescharacteristic
228C3×(C2×D3)⋊C4C22×C311yescharacteristic
229C3×(C2×D3)⋊C4C22×C311yescharacteristic
230C3×(C2×D3)⋊C4C22×C311yescharacteristic, complemented
231C3×C4⋊Dic3—21no—
232C3×C4⋊Dic3—31no—
233C3×C4⋊Dic3—31no—
234C3×C4⋊Dic3C2×D311yescharacteristic, complemented
235C3×C4⋊Dic3C22×C311yescharacteristic, complemented
236C3×Dic3⋊C4—21no—
237C3×Dic3⋊C4—21no—
238C3×Dic3⋊C4—31no—
239C3×Dic3⋊C4—31no—
240C3×Dic3⋊C4—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—61no—
243C3×Dic3⋊C4C2×D311yescharacteristic, complemented
244C3×Dic3⋊C4C2×D311yescharacteristic, complemented
245C3×Dic3⋊C4C22×C311yescharacteristic, complemented
246C3×Dic3⋊C4C22×C311yescharacteristic, complemented
247C3×C4×Dic3—31no—
248C3×C4×Dic3—31no—
249C3×C4×Dic3—31no—
250C3×C4×Dic3—31no—
251C3×C4×Dic3—61no—
252Dic3⋊Dic3C22×C311yescharacteristic, complemented
253Dic3⋊Dic3C22×C311yescharacteristic, complemented
254#3722C22×C311yescharacteristic
255(C2×D3)⋊Dic3C22×C311yescharacteristic
256(C2×D3)⋊Dic3C22×C311yescharacteristic
257(C2×D3)⋊Dic3C22×C311yescharacteristic
258(C2×D3)⋊Dic3C22×C311yescharacteristic
259(C2×D3)⋊Dic3C22×C311yescharacteristic
260(C2×D3)⋊Dic3C22×C311yescharacteristic, complemented
261Dic32C22×C311yescharacteristic, complemented
262C22×C33—21no—
263C22×C33—21no—
264C22×C33—21no—
265C22×C33C2411yescharacteristic
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3#4112yes—
269C2×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3—21no—
272C2×C32×D3—21no—
273C2×C32×D3—21no—
274C2×C32×D3—21no—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3—21no—
278C3×D32—44no—
279C33×C4—21no—
280C33×C4—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C32×Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#126—91no—
290C3×#126—91no—
291C3×#124—91no—
292C3×#124—91no—
293C3×#123—31no—
294C3×#123—31no—
295C3×#123—61no—
296C3×#123—91no—
297C3×C22⋊Q8—91no—
298C3×#121—31no—
299C3×#121—31no—
300C3×#121—61no—
301C3×#121—91no—
302C3×#121—91no—
303C3×#120—91no—
304C3×#120—91no—
305C3×C4×D4—91no—
306C3×C4×D4—91no—
307C2×C3×C22⋊C4—91no—
308#939—31no—
309#938—31no—
310#938—31no—
311#937—31no—
312#937—31no—
313#937—31no—
314#936—31no—
315#935—31no—
316#930C3×D311yescharacteristic, complemented
317#929C3×D311yescharacteristic, complemented
318C4×#67—31no—
319C4×#67—31no—
320C4×#67—61no—
321#898—31no—
322#898—31no—
323#897—31no—
324#896—31no—
325#894—31no—
326#893—31no—
327#885—31no—
328#885—31no—
329#885—31no—
330#884—31no—
331#882—31no—
332#67⋊C4—31no—
333D3×C22⋊C4—31no—
334D3×C22⋊C4—31no—
335#879—31no—
336#879—31no—
337C23×C32—21no—
338C23×C32—21no—
339C23×C32—21no—
340C23×C32—31no—
341C23×C32—31no—
342C23×C32—31no—
343C23×C32—41no—
344C23×C32C22×D311yescharacteristic
345C23×C32C22×D311yescharacteristic
346C23×C32C23×C311yescharacteristic
347C22×C3⋊D3C23×C311yescharacteristic
348C22×C3×D3—21no—
349C22×C3×D3—21no—
350C22×C3×D3—21no—
351C22×C3×D3—31no—
352C22×C3×D3—31no—
353C22×C3×D3—61no—
354C22×C3×D3—62no—
355C22×C3×D3—62no—
356C22×C3×D3—121no—
357C22×C3×D3—121no—
358C22×C3×D3—121no—
359C22×C3×D3—121no—
360C22×C3×D3C22×D311yescharacteristic
361C22×C3×D3C22×D311yescharacteristic
362C22×C3×D3C22×D311yescharacteristic
363C22×C3×D3C23×C311yescharacteristic
364C22×C3×D3C23×C311yescharacteristic
365C22×C3×D3C23×C311yescharacteristic
366C2×D32—22no—
367C2×D32—41no—
368C2×D32—41no—
369C32×D4—121no—
370C32×D4—121no—
371C32×D4—121no—
372C32×D4—121no—
373C2×C32×C4—21no—
374C2×C32×C4—21no—
375C2×C32×C4—21no—
376C2×C32×C4—21no—
377C2×C32×C4—21no—
378C2×C32×C4—21no—
379C2×C32×C4—31no—
380C2×C32×C4—31no—
381C2×C32×C4—31no—
382C2×C32×C4—31no—
383C2×C32×C4—31no—
384C2×C32×C4—41no—
385C2×C32×C4—41no—
386C2×C32×C4—41no—
387C2×C32×C4—41no—
388C2×C32×C4—41no—
389C2×C32×C4—42no—
390C2×C32×C4—42no—
391C2×C32×C4—42no—
392C2×C32×C4—44no—
393C2×C32×C4C22×D311yescharacteristic
394C2×C32×C4C22×D311yescharacteristic
395C2×C32×C4C22×D311yescharacteristic
396C2×C32×C4C22×D311yescharacteristic
397C2×C32×C4C23×C311yescharacteristic
398C2×C32×C4C23×C311yescharacteristic
399#638—22no—
400C2×C3⋊Dic3C23×C311yescharacteristic
401C2×C3⋊Dic3C23×C311yescharacteristic
402C2×C3⋊Dic3C23×C311yescharacteristic
403C4×C3⋊D3—41no—
404C3×#67—41no—
405C3×#67—41no—
406C3×#67—41no—
407C3×#67—41no—
408C3×#67—41no—
409C3×#67—41no—
410C3×#67—42no—
411C3×#67—42no—
412C3×#67—42no—
413C3×#67—62no—
414C3×#67—62no—
415C3×#67—62no—
416C3×#67—64no—
417C3×#67—121no—
418C3×#67—121no—
419C2×C3×Dic3—21no—
420C2×C3×Dic3—21no—
421C2×C3×Dic3—21no—
422C2×C3×Dic3—21no—
423C2×C3×Dic3—21no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—31no—
426C2×C3×Dic3—31no—
427C2×C3×Dic3—31no—
428C2×C3×Dic3—31no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—61no—
431C2×C3×Dic3—61no—
432C2×C3×Dic3—61no—
433C2×C3×Dic3—121no—
434C2×C3×Dic3C22×D311yescharacteristic
435C2×C3×Dic3C22×D311yescharacteristic
436C2×C3×Dic3C22×D311yescharacteristic
437C2×C3×Dic3C22×D311yescharacteristic
438C2×C3×Dic3C22×D311yescharacteristic
439C2×C3×Dic3C23×C311yescharacteristic
440C2×C3×Dic3C23×C311yescharacteristic
441C2×C3×Dic3C23×C311yescharacteristic
442C2×C3×Dic3C23×C311yescharacteristic
443C2×C3×Dic3C23×C311yescharacteristic
444C3×D12—41no—
445C3×D12—41no—
446C3×D12—42no—
447C3×D12—62no—
448C3×C4×D3—121no—
449C3×C4×D3—121no—
450C3×C4×D3—121no—
451C3×C4×D3—121no—
452C3×C4×D3—121no—
453C3×C4×D3—122no—
454C3×Dic6—121no—
455C3×Dic6—121no—
456#627—41no—
457#626—22no—
458#625—41no—
459#624—41no—
460D3×Dic3—41no—
461#538—91noSylow
462C2×C33—41no—
463C2×C33C2×#4111yescharacteristic
464C2×C33H(5,𝔽2)11yescharacteristic
465C2×C33H(5,𝔽2)11yescharacteristic
466C3×C3⋊D3—22no—
467C32×D3—41no—
468C32×D3—41no—
469C32×D3—41no—
470C24×C3—91no—
471C23×D3—31no—
472C23×D3—31no—
473C2×C3×Q8—91no—
474C2×C3×D4—31no—
475C2×C3×D4—31no—
476C2×C3×D4—31no—
477C2×C3×D4—31no—
478C2×C3×D4—31no—
479C2×C3×D4—31no—
480C2×C3×D4—31no—
481C2×C3×D4—31no—
482C2×C3×D4—61no—
483C2×C3×D4—61no—
484C2×C3×D4—61no—
485C2×C3×D4—61no—
486C2×C3×D4—91no—
487C2×C3×D4—91no—
488C2×C3×D4—91no—
489C22×C3×C4—21no—
490C22×C3×C4—21no—
491C22×C3×C4—21no—
492C22×C3×C4—41no—
493C22×C3×C4—91no—
494C22×C3×C4—91no—
495C22×C3×C4—91no—
496C22×C3×C4D3211yescharacteristic, complemented
497C22×C3×C4C2×C3×D311yescharacteristic, complemented
498C22×C3×C4C2×C3×D311yescharacteristic, complemented
499C2×#67—31no—
500C2×#67—31no—
501C2×#67—31no—
502C2×#67—31no—
503C2×#67—31no—
504C2×#67—61no—
505C2×#67C2×C3×D311yescharacteristic
506C2×#67C2×C3×D311yescharacteristic
507C2×#67C2×C3×D311yescharacteristic, complemented
508C22×Dic3—31no—
509C2×D12—31no—
510C2×D12C2×C3×D311yescharacteristic
511C2×C4×D3—31no—
512C2×C4×D3—31no—
513C2×C4×D3—31no—
514C2×C4×D3—31no—
515C2×C4×D3—31no—
516C2×C4×D3—61no—
517C2×Dic6—31no—
518C2×Dic6—31no—
519C3×C4⋊C4—31no—
520C3×C4⋊C4—31no—
521C3×C4⋊C4—31no—
522C3×C4⋊C4—31no—
523C3×C4⋊C4—31no—
524C3×C4⋊C4—31no—
525C3×C4⋊C4—61no—
526C3×C4⋊C4—61no—
527C3×C4⋊C4—61no—
528C3×C4⋊C4—91no—
529C3×C4⋊C4—91no—
530C3×C4⋊C4—91no—
531C3×C22⋊C4—31no—
532C3×C22⋊C4—31no—
533C3×C22⋊C4—31no—
534C3×C22⋊C4—31no—
535C3×C22⋊C4—31no—
536C3×C22⋊C4—31no—
537C3×C22⋊C4—31no—
538C3×C22⋊C4—31no—
539C3×C22⋊C4—31no—
540C3×C22⋊C4—31no—
541C3×C22⋊C4—61no—
542C3×C22⋊C4—61no—
543C3×C22⋊C4—61no—
544C3×C22⋊C4—61no—
545C3×C22⋊C4—61no—
546C3×C22⋊C4—91no—
547C3×C22⋊C4—91no—
548C3×C22⋊C4—91no—
549C3×C22⋊C4—91no—
550C3×C22⋊C4—91no—
551C3×C22⋊C4—91no—
552C3×C22⋊C4—91no—
553C3×C22⋊C4—91no—
554C3×C22⋊C4—91no—
555C3×C42—91no—
556C3×C42—91no—
557#217—31no—
558#217—31no—
559#217—31no—
560#217—31no—
561#217—31no—
562#217—31no—
563#217—31no—
564#217—31no—
565#217—61no—
566#217C2×C3×D311yescharacteristic, complemented
567(C2×D3)⋊C4—31no—
568(C2×D3)⋊C4—31no—
569(C2×D3)⋊C4—31no—
570(C2×D3)⋊C4—31no—
571(C2×D3)⋊C4—31no—
572(C2×D3)⋊C4—31no—
573(C2×D3)⋊C4—31no—
574(C2×D3)⋊C4—31no—
575(C2×D3)⋊C4—31no—
576(C2×D3)⋊C4—31no—
577(C2×D3)⋊C4—61no—
578(C2×D3)⋊C4C2×C3×D311yescharacteristic
579(C2×D3)⋊C4C2×C3×D311yescharacteristic
580(C2×D3)⋊C4C2×C3×D311yescharacteristic
581(C2×D3)⋊C4C2×C3×D311yescharacteristic, complemented
582C4⋊Dic3—31no—
583C4⋊Dic3—31no—
584C4⋊Dic3C2×C3×D311yescharacteristic, complemented
585Dic3⋊C4—31no—
586Dic3⋊C4—31no—
587Dic3⋊C4—31no—
588Dic3⋊C4—31no—
589Dic3⋊C4—61no—
590Dic3⋊C4C2×C3×D311yescharacteristic, complemented
591Dic3⋊C4C2×C3×D311yescharacteristic, complemented
592C4×Dic3—31no—
593C4×Dic3—31no—
594C4×Dic3—31no—
595C4×Dic3—31no—
596C4×Dic3—61no—
597C22×C32—21no—
598C22×C32—21no—
599C22×C32—21no—
600C22×C32—22no—
601C22×C32—22no—
602C22×C32—22no—
603C22×C32—21no—
604C22×C32—21no—
605C22×C32—21no—
606C22×C32—21no—
607C22×C32—21no—
608C22×C32—21no—
609C22×C32—21no—
610C22×C32—21no—
611C22×C32—21no—
612C22×C32—41no—
613C22×C32—41no—
614C22×C32—41no—
615C22×C32—41no—
616C22×C32—41no—
617C22×C32—41no—
618C22×C32—41no—
619C22×C32—42no—
620C22×C32—42no—
621C22×C32—42no—
622C22×C32—61no—
623C22×C32—61no—
624C22×C32—61no—
625C22×C32—61no—
626C22×C32—61no—
627C22×C32—61no—
628C22×C32—61no—
629C22×C32—61no—
630C22×C32—61no—
631C22×C32C23×D311yescharacteristic
632C22×C32C23×D311yescharacteristic
633C22×C32C24×C311yescharacteristic
634C2×C3⋊D3—21no—
635C2×C3⋊D3—21no—
636C2×C3⋊D3C3×#4112yes—
637C2×C3×D3—21no—
638C2×C3×D3—21no—
639C2×C3×D3—21no—
640C2×C3×D3—21no—
641C2×C3×D3—21no—
642C2×C3×D3—21no—
643C2×C3×D3—21no—
644C2×C3×D3—21no—
645C2×C3×D3—21no—
646C2×C3×D3—21no—
647C2×C3×D3—21no—
648C2×C3×D3—21no—
649C2×C3×D3—21no—
650C2×C3×D3—21no—
651C2×C3×D3—21no—
652C2×C3×D3—21no—
653C2×C3×D3—21no—
654C2×C3×D3—21no—
655C2×C3×D3—32no—
656C2×C3×D3—32no—
657C2×C3×D3—41no—
658C2×C3×D3—41no—
659C2×C3×D3—41no—
660C2×C3×D3—41no—
661C2×C3×D3—41no—
662C2×C3×D3—41no—
663C2×C3×D3—41no—
664C2×C3×D3—41no—
665C2×C3×D3—41no—
666C2×C3×D3—62no—
667C2×C3×D3—61no—
668C2×C3×D3—61no—
669C2×C3×D3—61no—
670C2×C3×D3—61no—
671C2×C3×D3—121no—
672C2×C3×D3—121no—
673C2×C3×D3—124no—
674C2×C3×D3—124no—
675D32—44no—
676C32×C4—21no—
677C32×C4—21no—
678C32×C4—22no—
679C32×C4—22no—
680C32×C4—21no—
681C32×C4—21no—
682C32×C4—21no—
683C32×C4—21no—
684C32×C4—41no—
685C32×C4—41no—
686C32×C4—41no—
687C32×C4—41no—
688C32×C4—42no—
689C32×C4—42no—
690C32×C4—61no—
691C32×C4—61no—
692C32×C4—61no—
693C32×C4—61no—
694C32×C4—61no—
695C3⋊Dic3—21no—
696C3⋊Dic3—21no—
697C3⋊Dic3—21no—
698C3×Dic3—21no—
699C3×Dic3—21no—
700C3×Dic3—21no—
701C3×Dic3—21no—
702C3×Dic3—21no—
703C3×Dic3—21no—
704C3×Dic3—21no—
705C3×Dic3—21no—
706C3×Dic3—21no—
707C3×Dic3—21no—
708C3×Dic3—41no—
709C3×Dic3—41no—
710C3×Dic3—41no—
711C3×Dic3—41no—
712C3×Dic3—41no—
713C3×Dic3—62no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—61no—
717C3×Dic3—61no—
718C3×Dic3—61no—
719C3×Dic3—61no—
720C3×Dic3—121no—
721C3×Dic3—121no—
722#126—91no—
723#126—91no—
724#124—91no—
725#124—91no—
726#123—31no—
727#123—91no—
728C22⋊Q8—91no—
729#121—31no—
730#121—91no—
731#121—91no—
732#120—91no—
733#120—91no—
734C4×D4—91no—
735C4×D4—91no—
736C2×C22⋊C4—91no—
737C33#53811yescharacteristic, complemented, Sylow
738C23×C3—21no—
739C23×C3—21no—
740C23×C3—21no—
741C23×C3—31no—
742C23×C3—31no—
743C23×C3—31no—
744C23×C3—31no—
745C23×C3—31no—
746C23×C3—31no—
747C23×C3—41no—
748C23×C3—61no—
749C23×C3—61no—
750C23×C3—61no—
751C23×C3—91no—
752C23×C3—182no—
753C23×C3—361no—
754C23×C3—361no—
755C23×C3C2×D3211yescharacteristic
756C23×C3C22×C3×D311yescharacteristic
757C23×C3C22×C3×D311yescharacteristic
758C22×D3—31no—
759C22×D3—31no—
760C22×D3—61no—
761C22×D3—62no—
762C22×D3—62no—
763C22×D3—121no—
764C22×D3—121no—
765C22×D3—121no—
766C22×D3—121no—
767C22×D3C22×C3×D311yescharacteristic
768C22×D3C22×C3×D311yescharacteristic
769C22×D3C22×C3×D311yescharacteristic
770C3×Q8—361no—
771C3×D4—121no—
772C3×D4—121no—
773C3×D4—122no—
774C3×D4—121no—
775C3×D4—121no—
776C3×D4—121no—
777C3×D4—121no—
778C3×D4—121no—
779C3×D4—121no—
780C3×D4—122no—
781C3×D4—122no—
782C3×D4—122no—
783C3×D4—182no—
784C3×D4—182no—
785C3×D4—361no—
786C2×C3×C4—21no—
787C2×C3×C4—21no—
788C2×C3×C4—21no—
789C2×C3×C4—21no—
790C2×C3×C4—21no—
791C2×C3×C4—21no—
792C2×C3×C4—31no—
793C2×C3×C4—31no—
794C2×C3×C4—31no—
795C2×C3×C4—31no—
796C2×C3×C4—31no—
797C2×C3×C4—31no—
798C2×C3×C4—31no—
799C2×C3×C4—31no—
800C2×C3×C4—31no—
801C2×C3×C4—31no—
802C2×C3×C4—41no—
803C2×C3×C4—41no—
804C2×C3×C4—41no—
805C2×C3×C4—42no—
806C2×C3×C4—42no—
807C2×C3×C4—42no—
808C2×C3×C4—44no—
809C2×C3×C4—41no—
810C2×C3×C4—41no—
811C2×C3×C4—61no—
812C2×C3×C4—61no—
813C2×C3×C4—61no—
814C2×C3×C4—61no—
815C2×C3×C4—61no—
816C2×C3×C4—91no—
817C2×C3×C4—91no—
818C2×C3×C4—91no—
819C2×C3×C4—361no—
820C2×C3×C4—361no—
821C2×C3×C4—361no—
822C2×C3×C4C2×D3211yescharacteristic
823C2×C3×C4C2×D3211yescharacteristic
824C2×C3×C4C22×C3×D311yescharacteristic
825C2×C3×C4C22×C3×D311yescharacteristic
826C2×C3×C4C22×C3×D311yescharacteristic
827C2×C3×C4C22×C3×D311yescharacteristic
828#67—41no—
829#67—41no—
830#67—41no—
831#67—62no—
832#67—62no—
833#67—62no—
834#67—64no—
835#67—121no—
836#67—121no—
837C2×Dic3—31no—
838C2×Dic3—31no—
839C2×Dic3—31no—
840C2×Dic3—31no—
841C2×Dic3—31no—
842C2×Dic3—31no—
843C2×Dic3—61no—
844C2×Dic3—61no—
845C2×Dic3—61no—
846C2×Dic3—121no—
847C2×Dic3C22×C3×D311yescharacteristic
848C2×Dic3C22×C3×D311yescharacteristic
849C2×Dic3C22×C3×D311yescharacteristic
850C2×Dic3C22×C3×D311yescharacteristic
851C2×Dic3C22×C3×D311yescharacteristic
852D12—41no—
853D12—62no—
854C4×D3—121no—
855C4×D3—121no—
856C4×D3—121no—
857C4×D3—121no—
858C4×D3—121no—
859C4×D3—122no—
860Dic6—121no—
861Dic6—121no—
862C2×C32—21no—
863C2×C32—21no—
864C2×C32—21no—
865C2×C32—21no—
866C2×C32—21no—
867C2×C32—21no—
868C2×C32—21no—
869C2×C32—21no—
870C2×C32—21no—
871C2×C32—41no—
872C2×C32—41no—
873C2×C32—41no—
874C2×C32—42no—
875C2×C32—42no—
876C2×C32—42no—
877C2×C32—44no—
878C2×C32—41no—
879C2×C32—41no—
880C2×C32—41no—
881C2×C32—121no—
882C2×C32—121no—
883C2×C32—121no—
884C2×C32#100411yescharacteristic
885C2×C32#100411yescharacteristic
886C2×C32#100411yescharacteristic
887C2×C32D3×#4111yescharacteristic
888C2×C32D3×#4111yescharacteristic
889C2×C32#100911yescharacteristic
890C2×C32C2×C3×#4111yescharacteristic
891C2×C32C3×H(5,𝔽2)11yescharacteristic
892C2×C32C3×H(5,𝔽2)11yescharacteristic
893C3⋊D3—22no—
894C3×D3—41no—
895C3×D3—41no—
896C3×D3—41no—
897C3×D3—41no—
898C3×D3—41no—
899C3×D3—41no—
900C3×D3—62no—
901C3×D3—62no—
902C3×D3—81no—
903C3×D3—81no—
904C3×D3—81no—
905C3×D3—122no—
906C24—91no—
907C2×Q8—91no—
908C2×D4—31no—
909C2×D4—31no—
910C2×D4—31no—
911C2×D4—31no—
912C2×D4—91no—
913C2×D4—91no—
914C2×D4—91no—
915C22×C4—91no—
916C22×C4—91no—
917C22×C4—91no—
918C22×C4C3×D3211yescharacteristic, complemented
919C4⋊C4—31no—
920C4⋊C4—31no—
921C4⋊C4—31no—
922C4⋊C4—91no—
923C4⋊C4—91no—
924C4⋊C4—91no—
925C22⋊C4—31no—
926C22⋊C4—31no—
927C22⋊C4—31no—
928C22⋊C4—31no—
929C22⋊C4—31no—
930C22⋊C4—91no—
931C22⋊C4—91no—
932C22⋊C4—91no—
933C22⋊C4—91no—
934C22⋊C4—91no—
935C22⋊C4—91no—
936C22⋊C4—91no—
937C22⋊C4—91no—
938C22⋊C4—91no—
939C42—91no—
940C42—91no—
941C22×C3—22no—
942C22×C3—22no—
943C22×C3—22no—
944C22×C3—21no—
945C22×C3—21no—
946C22×C3—21no—
947C22×C3—21no—
948C22×C3—21no—
949C22×C3—21no—
950C22×C3—21no—
951C22×C3—21no—
952C22×C3—21no—
953C22×C3—21no—
954C22×C3—21no—
955C22×C3—21no—
956C22×C3—41no—
957C22×C3—41no—
958C22×C3—41no—
959C22×C3—41no—
960C22×C3—41no—
961C22×C3—41no—
962C22×C3—42no—
963C22×C3—42no—
964C22×C3—42no—
965C22×C3—41no—
966C22×C3—61no—
967C22×C3—61no—
968C22×C3—61no—
969C22×C3—61no—
970C22×C3—61no—
971C22×C3—61no—
972C22×C3—61no—
973C22×C3—61no—
974C22×C3—61no—
975C22×C3—61no—
976C22×C3—61no—
977C22×C3—61no—
978C22×C3—61no—
979C22×C3—61no—
980C22×C3—61no—
981C22×C3—61no—
982C22×C3—61no—
983C22×C3—61no—
984C22×C3—92no—
985C22×C3—121no—
986C22×C3—121no—
987C22×C3—121no—
988C22×C3—121no—
989C22×C3—121no—
990C22×C3—121no—
991C22×C3—121no—
992C22×C3—121no—
993C22×C3—121no—
994C22×C3—181no—
995C22×C3—181no—
996C22×C3—364no—
997C22×C3C22×D3211yescharacteristic
998C22×C3C23×C3×D311yescharacteristic
999C22×C3C23×C3×D311yescharacteristic
1000C2×D3—21no—
1001C2×D3—21no—
1002C2×D3—21no—
1003C2×D3—21no—
1004C2×D3—21no—
1005C2×D3—21no—
1006C2×D3—21no—
1007C2×D3—21no—
1008C2×D3—21no—
1009C2×D3—32no—
1010C2×D3—32no—
1011C2×D3—62no—
1012C2×D3—61no—
1013C2×D3—61no—
1014C2×D3—61no—
1015C2×D3—61no—
1016C2×D3—121no—
1017C2×D3—121no—
1018C2×D3—124no—
1019C2×D3—124no—
1020C3×C4—22no—
1021C3×C4—22no—
1022C3×C4—21no—
1023C3×C4—21no—
1024C3×C4—21no—
1025C3×C4—21no—
1026C3×C4—21no—
1027C3×C4—21no—
1028C3×C4—41no—
1029C3×C4—41no—
1030C3×C4—41no—
1031C3×C4—41no—
1032C3×C4—42no—
1033C3×C4—42no—
1034C3×C4—61no—
1035C3×C4—61no—
1036C3×C4—61no—
1037C3×C4—61no—
1038C3×C4—61no—
1039C3×C4—61no—
1040C3×C4—61no—
1041C3×C4—61no—
1042C3×C4—61no—
1043C3×C4—61no—
1044C3×C4—121no—
1045C3×C4—121no—
1046C3×C4—121no—
1047C3×C4—121no—
1048C3×C4—121no—
1049C3×C4—181no—
1050C3×C4—181no—
1051C3×C4—181no—
1052Dic3—21no—
1053Dic3—21no—
1054Dic3—21no—
1055Dic3—21no—
1056Dic3—21no—
1057Dic3—62no—
1058Dic3—61no—
1059Dic3—61no—
1060Dic3—61no—
1061Dic3—61no—
1062Dic3—61no—
1063Dic3—61no—
1064Dic3—121no—
1065Dic3—121no—
1066C32—21no—
1067C32—21no—
1068C32—21no—
1069C32—41no—
1070C32#561311yescharacteristic, complemented
1071C32#565711yescharacteristic, complemented
1072C32C3×#53811yescharacteristic, complemented
1073C23—31no—
1074C23—31no—
1075C23—31no—
1076C23—91no—
1077C23—182no—
1078C23—361no—
1079C23—361no—
1080C23C2×C3×D3211yescharacteristic
1081Q8—361no—
1082D4—121no—
1083D4—121no—
1084D4—121no—
1085D4—121no—
1086D4—182no—
1087D4—182no—
1088D4—361no—
1089C2×C4—31no—
1090C2×C4—31no—
1091C2×C4—31no—
1092C2×C4—31no—
1093C2×C4—31no—
1094C2×C4—41no—
1095C2×C4—91no—
1096C2×C4—91no—
1097C2×C4—91no—
1098C2×C4—361no—
1099C2×C4—361no—
1100C2×C4—361no—
1101C2×C4C2×C3×D3211yescharacteristic
1102C2×C4C2×C3×D3211yescharacteristic
1103C2×C3—21no—
1104C2×C3—21no—
1105C2×C3—21no—
1106C2×C3—21no—
1107C2×C3—21no—
1108C2×C3—21no—
1109C2×C3—21no—
1110C2×C3—21no—
1111C2×C3—21no—
1112C2×C3—42no—
1113C2×C3—42no—
1114C2×C3—42no—
1115C2×C3—44no—
1116C2×C3—41no—
1117C2×C3—41no—
1118C2×C3—41no—
1119C2×C3—41no—
1120C2×C3—41no—
1121C2×C3—41no—
1122C2×C3—121no—
1123C2×C3—121no—
1124C2×C3—121no—
1125C2×C3—121no—
1126C2×C3—121no—
1127C2×C3—121no—
1128C2×C3—182no—
1129C2×C3—241no—
1130C2×C3—241no—
1131C2×C3—241no—
1132C2×C3#6430611yescharacteristic
1133C2×C3#6430711yescharacteristic
1134C2×C3#6433011yescharacteristic
1135C2×C3C3×#100411yescharacteristic
1136C2×C3C3×#100411yescharacteristic
1137C2×C3C3×#100411yescharacteristic
1138C2×C3C3×D3×#4111yescharacteristic
1139C2×C3C3×D3×#4111yescharacteristic
1140C2×C3C3×#100911yescharacteristic
1141D3—41no—
1142D3—41no—
1143D3—41no—
1144D3—62no—
1145D3—62no—
1146D3—122no—
1147C22—21no—
1148C22—21no—
1149C22—21no—
1150C22—61no—
1151C22—61no—
1152C22—61no—
1153C22—61no—
1154C22—61no—
1155C22—61no—
1156C22—61no—
1157C22—61no—
1158C22—61no—
1159C22—92no—
1160C22—181no—
1161C22—181no—
1162C22—364no—
1163C22C22×C3×D3211yescharacteristic
1164C4—21no—
1165C4—21no—
1166C4—61no—
1167C4—61no—
1168C4—61no—
1169C4—61no—
1170C4—61no—
1171C4—181no—
1172C4—181no—
1173C4—181no—
1174C3—21no—
1175C3—21no—
1176C3—21no—
1177C3—41no—
1178C3#1059508911yescharacteristic, direct product factor
1179C3C3×#561311yescharacteristic, complemented
1180C3C3×#565711yescharacteristic, complemented
1181C2—41no—
1182C2—121no—
1183C2—121no—
1184C2—121no—
1185C2—182no—
1186C2C3×#6430611yescharacteristic
1187C2C3×#6430711yescharacteristic
1188C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C3×#538
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×C4×#638C2semidirect
2. C32×#930C2semidirect
3. C32×#929C2semidirect
4. C3×#63983C2semidirect
5. C3×#63970C2semidirect
6. C3×#63959C2semidirect
7. C3×#63958C2semidirect
8. C3×#63922C2semidirect
9. C3×#63921C2semidirect
10. C3×#63915C2semidirect
11. C3×#63895C2semidirect
12. C3×#63884C2semidirect
13. C3×#63881C2semidirect
14. C3×#63862C2semidirect
15. C3×#63858C2semidirect
18. #10595089C3direct (N × H)
20. C22×C33×C4C22semidirect
25. C2×C32×#67C22semidirect
27. C2×C3×#627C22semidirect
31. C2×C3×D3×Dic3C22semidirect
32. C3×#3757C22semidirect
34. C3×#3750C22semidirect
35. C3×C4×C3⋊Dic3C22semidirect
36. C32×#217C22semidirect
40. C32×(C2×D3)⋊C4C22semidirect
41. C32×C4⋊Dic3C22semidirect
42. C32×Dic3⋊C4C22semidirect
43. C32×Dic3⋊C4C22semidirect
44. C3×Dic3⋊Dic3C22semidirect
45. C3×Dic3⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
56. C4×#638C2×C3semidirect
66. C3×#930D3semidirect
67. C3×#930C2×C3semidirect
69. C3×#929D3semidirect
70. C3×#929C2×C3semidirect
90. #63983C2×C3semidirect
91. #63970C2×C3semidirect
92. #63959C2×C3semidirect
93. #63958C2×C3semidirect
94. #63922C2×C3semidirect
95. #63921C2×C3semidirect
96. #63915C2×C3semidirect
97. #63895C2×C3semidirect
98. #63884C2×C3semidirect
99. #63881C2×C3semidirect
100. #63862C2×C3semidirect
101. #63858C2×C3semidirect
146. C22×C32×C4C2×D3semidirect
147. C22×C32×C4C2×D3semidirect
148. C22×C32×C4C22×C3semidirect
162. C2×C3×#67C2×D3semidirect
165. C2×C3×#67C22×C3semidirect
179. C2×#627C22×C3semidirect
183. C2×D3×Dic3C22×C3semidirect
192. #3757C22×C3semidirect
194. #3750C22×C3semidirect
195. C4×C3⋊Dic3C22×C3semidirect
206. C3×#217C2×D3semidirect
207. C3×#217C22×C3semidirect
226. C3×(C2×D3)⋊C4C2×D3semidirect
230. C3×(C2×D3)⋊C4C22×C3semidirect
234. C3×C4⋊Dic3C2×D3semidirect
235. C3×C4⋊Dic3C22×C3semidirect
243. C3×Dic3⋊C4C2×D3semidirect
244. C3×Dic3⋊C4C2×D3semidirect
245. C3×Dic3⋊C4C22×C3semidirect
246. C3×Dic3⋊C4C22×C3semidirect
252. Dic3⋊Dic3C22×C3semidirect
253. Dic3⋊Dic3C22×C3semidirect
260. (C2×D3)⋊Dic3C22×C3semidirect
261. Dic32C22×C3semidirect
316. #930C3×D3semidirect
317. #929C3×D3semidirect
496. C22×C3×C4D32semidirect
497. C22×C3×C4C2×C3×D3semidirect
498. C22×C3×C4C2×C3×D3semidirect
507. C2×#67C2×C3×D3semidirect
566. #217C2×C3×D3semidirect
581. (C2×D3)⋊C4C2×C3×D3semidirect
584. C4⋊Dic3C2×C3×D3semidirect
590. Dic3⋊C4C2×C3×D3semidirect
591. Dic3⋊C4C2×C3×D3semidirect
737. C33#538semidirect
918. C22×C4C3×D32semidirect
1070. C32#5613semidirect
1071. C32#5657semidirect
1072. C32C3×#538semidirect
1178. C3#10595089direct (N × H)
1179. C3C3×#5613semidirect
1180. C3C3×#5657semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#6382
C32×#9302
C32×#9292
C3×#639832
C3×#639702
C3×#639592
C3×#639582
C3×#639222
C3×#639212
C3×#639152
C3×#638952
C3×#638842
C3×#638812
C3×#638622
C3×#638582
C3×#56573
C3×#56133
#105950893