Finite Group Databasebeta

← C32×#5678 #13179056

Subgroups — C32×#5678 #13179056

Order 1728.

1804 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×#124C211yesmaximal, characteristic, complemented
2C32×#947C211yesmaximal, characteristic, complemented
3C32×#946C211yesmaximal, characteristic, complemented
4C32×#939C211yesmaximal, characteristic, complemented
5C32×#937C211yesmaximal, characteristic, complemented
6C32×#886C211yesmaximal, characteristic, complemented
7C32×#884C211yesmaximal, characteristic, complemented
8C32×#884C211yesmaximal, characteristic, complemented
9C32×#883C211yesmaximal, characteristic, complemented
10C32×#882C211yesmaximal, characteristic, complemented
11C32×#67⋊C4C211yesmaximal, characteristic, complemented
12C32×D3×C22⋊C4C211yesmaximal, characteristic, complemented
13C32×#879C211yesmaximal, characteristic, complemented
14C32×#876C211yesmaximal, characteristic, complemented
15C32×C4×D12C211yesmaximal, characteristic, complemented
16C32×#538—31nomaximal
17C3×#5678C314yesmaximal, direct product factor
18C23×C32×D3C2211yescharacteristic
19C2×C33×Q8C2211yescharacteristic, complemented
20C2×C33×D4C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic, complemented
25C22×C32×Dic3C2211yescharacteristic, complemented
26C2×C32×D12C2211yescharacteristic
27C2×C32×D12C2211yescharacteristic
28C2×C32×C4×D3C2211yescharacteristic
29C2×C32×C4×D3C2211yescharacteristic
30C2×C32×C4×D3C2211yescharacteristic, complemented
31C33×C22⋊C4C2211yescharacteristic
32C33×C22⋊C4C2211yescharacteristic
33C33×C22⋊C4C2211yescharacteristic, complemented
34C33×C22⋊C4C2211yescharacteristic, complemented
35C33×C42C2211yescharacteristic, complemented
36C32×#217C2211yescharacteristic
37C32×#217C2211yescharacteristic
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C32×C4⋊Dic3C2211yescharacteristic, complemented
47C32×C4⋊Dic3C2211yescharacteristic, complemented
48C32×Dic3⋊C4C2211yescharacteristic, complemented
49C32×Dic3⋊C4C2211yescharacteristic, complemented
50C32×Dic3⋊C4C2211yescharacteristic, complemented
51C32×Dic3⋊C4C2211yescharacteristic, complemented
52C32×C4×Dic3C2211yescharacteristic, complemented
53C32×#126—31no—
54C32×#126—31no—
55C32×#124—24no—
56C32×#124—31no—
57C32×#124D311yescharacteristic, complemented
58C32×#124C2×C314yescomplemented
59C32×#123—31no—
60C32×#123—31no—
61C32×C22⋊Q8—31no—
62C32×#121—31no—
63C32×#121—31no—
64C32×#121—31no—
65C32×#120—31no—
66C32×#120—31no—
67C32×C4×D4—31no—
68C32×C4×D4—31no—
69C2×C32×C22⋊C4—31no—
70C3×#947C2×C314yescomplemented
71C3×#946C2×C314yescomplemented
72C3×#939C2×C314yescomplemented
73C3×#937C2×C314yescomplemented
74C3×#886C2×C314yescomplemented
75C3×#884C2×C314yescomplemented
76C3×#884C2×C314yescomplemented
77C3×#883C2×C314yescomplemented
78C3×#882C2×C314yescomplemented
79C3×#67⋊C4C2×C314yescomplemented
80C3×D3×C22⋊C4C2×C314yescomplemented
81C3×#879C2×C314yescomplemented
82C3×#876C2×C314yescomplemented
83C3×C4×D12C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C22×C32×D3—22no—
87C22×C32×D3—41no—
88C22×C32×D3—41no—
89C22×C32×D3C2311yescharacteristic
90C22×C32×D3C2311yescharacteristic
91C22×C32×D3C2311yescharacteristic
92C33×Q8—41no—
93C33×D4—41no—
94C2×C33×C4C2311yescharacteristic
95C2×C33×C4C2311yescharacteristic
96C2×C33×C4C2311yescharacteristic
97C2×C33×C4C2311yescharacteristic
98C2×C33×C4C2311yescharacteristic
99C32×#67—22no—
100C32×#67—41no—
101C32×#67—41no—
102C32×#67—41no—
103C2×C32×Dic3—41no—
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109C32×D12—22no—
110C32×D12—41no—
111C32×C4×D3—41no—
112C32×C4×D3—41no—
113C32×C4×D3—41no—
114C3×#538—34no—
115#5678C3211yescharacteristic, direct product factor
116C24×C32—31no—
117C23×C3×D3C22×C314yes—
118C2×C32×Q8—24no—
119C2×C32×Q8C2×D311yescharacteristic, complemented
120C2×C32×Q8C22×C314yescomplemented
121C2×C32×D4—24no—
122C2×C32×D4—31no—
123C2×C32×D4—31no—
124C2×C32×D4—31no—
125C2×C32×D4—31no—
126C2×C32×D4—31no—
127C2×C32×D4—31no—
128C2×C32×D4C2×D311yescharacteristic
129C2×C32×D4C22×C314yes—
130C22×C32×C4—31no—
131C22×C32×C4—31no—
132C22×C32×C4—31no—
133C22×C32×C4—31no—
134C2×C3×#67C22×C314yes—
135C2×C3×#67C22×C314yes—
136C2×C3×#67C22×C314yes—
137C2×C3×#67C22×C314yescomplemented
138C22×C3×Dic3C22×C314yescomplemented
139C2×C3×D12C22×C314yes—
140C2×C3×D12C22×C314yes—
141C2×C3×C4×D3C22×C314yes—
142C2×C3×C4×D3C22×C314yes—
143C2×C3×C4×D3C22×C314yescomplemented
144C32×C4⋊C4—31no—
145C32×C4⋊C4—31no—
146C32×C4⋊C4—31no—
147C32×C4⋊C4—31no—
148C32×C4⋊C4—31no—
149C32×C4⋊C4—31no—
150C32×C22⋊C4—24no—
151C32×C22⋊C4—24no—
152C32×C22⋊C4—24no—
153C32×C22⋊C4—24no—
154C32×C22⋊C4—31no—
155C32×C22⋊C4—31no—
156C32×C22⋊C4—31no—
157C32×C22⋊C4—31no—
158C32×C22⋊C4—31no—
159C32×C22⋊C4—31no—
160C32×C22⋊C4—31no—
161C32×C22⋊C4—31no—
162C32×C22⋊C4—31no—
163C32×C22⋊C4—31no—
164C32×C22⋊C4C2×D311yescharacteristic
165C32×C22⋊C4C2×D311yescharacteristic
166C32×C22⋊C4C2×D311yescharacteristic, complemented
167C32×C22⋊C4C2×D311yescharacteristic, complemented
168C32×C22⋊C4C22×C314yes—
169C32×C22⋊C4C22×C314yes—
170C32×C22⋊C4C22×C314yescomplemented
171C32×C22⋊C4C22×C314yescomplemented
172C32×C42—24no—
173C32×C42—31no—
174C32×C42C2×D311yescharacteristic, complemented
175C32×C42C22×C314yescomplemented
176C3×#217C22×C314yes—
177C3×#217C22×C314yes—
178C3×(C2×D3)⋊C4C22×C314yes—
179C3×(C2×D3)⋊C4C22×C314yes—
180C3×(C2×D3)⋊C4C22×C314yes—
181C3×(C2×D3)⋊C4C22×C314yes—
182C3×(C2×D3)⋊C4C22×C314yes—
183C3×(C2×D3)⋊C4C22×C314yes—
184C3×(C2×D3)⋊C4C22×C314yescomplemented
185C3×(C2×D3)⋊C4C22×C314yescomplemented
186C3×C4⋊Dic3C22×C314yescomplemented
187C3×C4⋊Dic3C22×C314yescomplemented
188C3×Dic3⋊C4C22×C314yescomplemented
189C3×Dic3⋊C4C22×C314yescomplemented
190C3×Dic3⋊C4C22×C314yescomplemented
191C3×Dic3⋊C4C22×C314yescomplemented
192C3×C4×Dic3C22×C314yescomplemented
193C22×C33—21no—
194C22×C33—21no—
195C22×C33—21no—
196C22×C33—21no—
197C22×C33—21no—
198C22×C33—21no—
199C22×C33C2411yescharacteristic
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3—21no—
203C2×C32×D3—21no—
204C2×C32×D3—21no—
205C2×C32×D3—21no—
206C2×C32×D3—21no—
207C2×C32×D3—21no—
208C2×C32×D3—44no—
209C2×C32×D3#4112yes—
210C33×C4—21no—
211C33×C4—21no—
212C33×C4—21no—
213C33×C4—21no—
214C33×C4—21no—
215C32×Dic3—21no—
216C32×Dic3—21no—
217C32×Dic3—21no—
218C32×Dic3—21no—
219C32×Dic3—21no—
220C3×#126—34no—
221C3×#126—34no—
222C3×#124—24no—
223C3×#124—34no—
224C3×#124C3×D314yescomplemented
225C3×#124C2×C3211yescharacteristic, complemented
226C3×#123—34no—
227C3×#123—34no—
228C3×C22⋊Q8—34no—
229C3×#121—34no—
230C3×#121—34no—
231C3×#121—34no—
232C3×#120—34no—
233C3×#120—34no—
234C3×C4×D4—34no—
235C3×C4×D4—34no—
236C2×C3×C22⋊C4—34no—
237#947C2×C3211yescharacteristic, complemented
238#946C2×C3211yescharacteristic, complemented
239#939C2×C3211yescharacteristic, complemented
240#937C2×C3211yescharacteristic, complemented
241#886C2×C3211yescharacteristic, complemented
242#884C2×C3211yescharacteristic, complemented
243#884C2×C3211yescharacteristic, complemented
244#883C2×C3211yescharacteristic, complemented
245#882C2×C3211yescharacteristic, complemented
246#67⋊C4C2×C3211yescharacteristic, complemented
247D3×C22⋊C4C2×C3211yescharacteristic, complemented
248#879C2×C3211yescharacteristic, complemented
249#876C2×C3211yescharacteristic, complemented
250C4×D12C2×C3211yescharacteristic, complemented
251C23×C32—24no—
252C23×C32—24no—
253C23×C32—31no—
254C23×C32—31no—
255C23×C32—31no—
256C23×C32—62no—
257C23×C32—121no—
258C23×C32—121no—
259C23×C32C22×D311yescharacteristic
260C23×C32C22×D311yescharacteristic
261C23×C32C23×C314yes—
262C23×C32C23×C314yes—
263C22×C3×D3—28no—
264C22×C3×D3—44no—
265C22×C3×D3—44no—
266C22×C3×D3C23×C314yes—
267C22×C3×D3C23×C314yes—
268C22×C3×D3C23×C314yes—
269C32×Q8—41no—
270C32×Q8—44no—
271C32×Q8—48no—
272C32×D4—41no—
273C32×D4—44no—
274C32×D4—48no—
275C32×D4—62no—
276C32×D4—62no—
277C32×D4—121no—
278C32×D4—121no—
279C32×D4—121no—
280C32×D4—121no—
281C2×C32×C4—24no—
282C2×C32×C4—24no—
283C2×C32×C4—24no—
284C2×C32×C4—24no—
285C2×C32×C4—24no—
286C2×C32×C4—31no—
287C2×C32×C4—31no—
288C2×C32×C4—31no—
289C2×C32×C4—31no—
290C2×C32×C4—31no—
291C2×C32×C4—121no—
292C2×C32×C4—121no—
293C2×C32×C4—121no—
294C2×C32×C4—121no—
295C2×C32×C4C22×D311yescharacteristic
296C2×C32×C4C22×D311yescharacteristic
297C2×C32×C4C22×D311yescharacteristic
298C2×C32×C4C22×D311yescharacteristic
299C2×C32×C4C22×D311yescharacteristic
300C2×C32×C4C23×C314yes—
301C2×C32×C4C23×C314yes—
302C2×C32×C4C23×C314yes—
303C2×C32×C4C23×C314yes—
304C2×C32×C4C23×C314yes—
305C3×#67—28no—
306C3×#67—44no—
307C3×#67—44no—
308C3×#67—44no—
309C2×C3×Dic3—44no—
310C2×C3×Dic3C23×C314yes—
311C2×C3×Dic3C23×C314yes—
312C2×C3×Dic3C23×C314yes—
313C2×C3×Dic3C23×C314yes—
314C2×C3×Dic3C23×C314yes—
315C3×D12—28no—
316C3×D12—44no—
317C3×C4×D3—44no—
318C3×C4×D3—44no—
319C3×C4×D3—44no—
320#538—31noSylow
321C2×C33—41no—
322C2×C33—41no—
323C2×C33C2×#4111yescharacteristic
324C2×C33H(5,𝔽2)11yescharacteristic
325C2×C33H(5,𝔽2)11yescharacteristic
326C32×D3—22no—
327C32×D3—41no—
328C32×D3—41no—
329C24×C3—34no—
330C23×D3C22×C3211yescharacteristic
331C2×C3×Q8—24no—
332C2×C3×Q8C2×C3×D314yescomplemented
333C2×C3×Q8C22×C3211yescharacteristic, complemented
334C2×C3×D4—24no—
335C2×C3×D4—34no—
336C2×C3×D4—34no—
337C2×C3×D4—34no—
338C2×C3×D4—34no—
339C2×C3×D4—34no—
340C2×C3×D4—34no—
341C2×C3×D4C2×C3×D314yes—
342C2×C3×D4C22×C3211yescharacteristic
343C22×C3×C4—34no—
344C22×C3×C4—34no—
345C22×C3×C4—34no—
346C22×C3×C4—34no—
347C2×#67C22×C3211yescharacteristic
348C2×#67C22×C3211yescharacteristic
349C2×#67C22×C3211yescharacteristic
350C2×#67C22×C3211yescharacteristic, complemented
351C22×Dic3C22×C3211yescharacteristic, complemented
352C2×D12C22×C3211yescharacteristic
353C2×D12C22×C3211yescharacteristic
354C2×C4×D3C22×C3211yescharacteristic
355C2×C4×D3C22×C3211yescharacteristic
356C2×C4×D3C22×C3211yescharacteristic, complemented
357C3×C4⋊C4—34no—
358C3×C4⋊C4—34no—
359C3×C4⋊C4—34no—
360C3×C4⋊C4—34no—
361C3×C4⋊C4—34no—
362C3×C4⋊C4—34no—
363C3×C22⋊C4—24no—
364C3×C22⋊C4—24no—
365C3×C22⋊C4—24no—
366C3×C22⋊C4—24no—
367C3×C22⋊C4—34no—
368C3×C22⋊C4—34no—
369C3×C22⋊C4—34no—
370C3×C22⋊C4—34no—
371C3×C22⋊C4—34no—
372C3×C22⋊C4—34no—
373C3×C22⋊C4—34no—
374C3×C22⋊C4—34no—
375C3×C22⋊C4—34no—
376C3×C22⋊C4—34no—
377C3×C22⋊C4C2×C3×D314yes—
378C3×C22⋊C4C2×C3×D314yes—
379C3×C22⋊C4C2×C3×D314yescomplemented
380C3×C22⋊C4C2×C3×D314yescomplemented
381C3×C22⋊C4C22×C3211yescharacteristic
382C3×C22⋊C4C22×C3211yescharacteristic
383C3×C22⋊C4C22×C3211yescharacteristic, complemented
384C3×C22⋊C4C22×C3211yescharacteristic, complemented
385C3×C42—24no—
386C3×C42—34no—
387C3×C42C2×C3×D314yescomplemented
388C3×C42C22×C3211yescharacteristic, complemented
389#217C22×C3211yescharacteristic
390#217C22×C3211yescharacteristic
391(C2×D3)⋊C4C22×C3211yescharacteristic
392(C2×D3)⋊C4C22×C3211yescharacteristic
393(C2×D3)⋊C4C22×C3211yescharacteristic
394(C2×D3)⋊C4C22×C3211yescharacteristic
395(C2×D3)⋊C4C22×C3211yescharacteristic
396(C2×D3)⋊C4C22×C3211yescharacteristic
397(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
398(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
399C4⋊Dic3C22×C3211yescharacteristic, complemented
400C4⋊Dic3C22×C3211yescharacteristic, complemented
401Dic3⋊C4C22×C3211yescharacteristic, complemented
402Dic3⋊C4C22×C3211yescharacteristic, complemented
403Dic3⋊C4C22×C3211yescharacteristic, complemented
404Dic3⋊C4C22×C3211yescharacteristic, complemented
405C4×Dic3C22×C3211yescharacteristic, complemented
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—24no—
413C22×C32—24no—
414C22×C32—24no—
415C22×C32—24no—
416C22×C32—24no—
417C22×C32—24no—
418C22×C32—24no—
419C22×C32—32no—
420C22×C32—44no—
421C22×C32—44no—
422C22×C32—44no—
423C22×C32—44no—
424C22×C32—44no—
425C22×C32—44no—
426C22×C32—61no—
427C22×C32—61no—
428C22×C32—61no—
429C22×C32—61no—
430C22×C32—61no—
431C22×C32—61no—
432C22×C32—61no—
433C22×C32—61no—
434C22×C32—124no—
435C22×C32C23×D311yescharacteristic
436C22×C32C24×C314yes—
437C2×C3×D3—24no—
438C2×C3×D3—24no—
439C2×C3×D3—24no—
440C2×C3×D3—24no—
441C2×C3×D3—24no—
442C2×C3×D3—24no—
443C2×C3×D3—24no—
444C2×C3×D3—24no—
445C2×C3×D3—416no—
446C2×C3×D3C3×#4118yes—
447C32×C4—28no—
448C32×C4—21no—
449C32×C4—21no—
450C32×C4—21no—
451C32×C4—21no—
452C32×C4—21no—
453C32×C4—24no—
454C32×C4—24no—
455C32×C4—24no—
456C32×C4—24no—
457C32×C4—24no—
458C32×C4—44no—
459C32×C4—44no—
460C32×C4—44no—
461C32×C4—44no—
462C32×C4—61no—
463C32×C4—61no—
464C32×C4—61no—
465C32×C4—61no—
466C32×C4—61no—
467C3×Dic3—24no—
468C3×Dic3—24no—
469C3×Dic3—24no—
470C3×Dic3—24no—
471C3×Dic3—24no—
472#126—31no—
473#126—31no—
474#124—31no—
475#124C32×D311yescharacteristic, complemented
476#123—31no—
477#123—31no—
478C22⋊Q8—31no—
479#121—31no—
480#121—31no—
481#121—31no—
482#120—31no—
483#120—31no—
484C4×D4—31no—
485C4×D4—31no—
486C2×C22⋊C4—31no—
487C33#53811yescharacteristic, complemented, Sylow
488C23×C3—24no—
489C23×C3—24no—
490C23×C3—34no—
491C23×C3—34no—
492C23×C3—34no—
493C23×C3—68no—
494C23×C3—124no—
495C23×C3—124no—
496C23×C3C22×C3×D314yes—
497C23×C3C22×C3×D314yes—
498C23×C3C23×C3211yescharacteristic
499C23×C3C23×C3211yescharacteristic
500C22×D3—22no—
501C22×D3—41no—
502C22×D3—41no—
503C22×D3C23×C3211yescharacteristic
504C22×D3C23×C3211yescharacteristic
505C22×D3C23×C3211yescharacteristic
506C3×Q8—44no—
507C3×Q8—41no—
508C3×Q8—48no—
509C3×D4—44no—
510C3×D4—41no—
511C3×D4—48no—
512C3×D4—68no—
513C3×D4—68no—
514C3×D4—124no—
515C3×D4—124no—
516C3×D4—124no—
517C3×D4—124no—
518C2×C3×C4—24no—
519C2×C3×C4—24no—
520C2×C3×C4—24no—
521C2×C3×C4—24no—
522C2×C3×C4—24no—
523C2×C3×C4—34no—
524C2×C3×C4—34no—
525C2×C3×C4—34no—
526C2×C3×C4—34no—
527C2×C3×C4—34no—
528C2×C3×C4—124no—
529C2×C3×C4—124no—
530C2×C3×C4—124no—
531C2×C3×C4—124no—
532C2×C3×C4C22×C3×D314yes—
533C2×C3×C4C22×C3×D314yes—
534C2×C3×C4C22×C3×D314yes—
535C2×C3×C4C22×C3×D314yes—
536C2×C3×C4C22×C3×D314yes—
537C2×C3×C4C23×C3211yescharacteristic
538C2×C3×C4C23×C3211yescharacteristic
539C2×C3×C4C23×C3211yescharacteristic
540C2×C3×C4C23×C3211yescharacteristic
541C2×C3×C4C23×C3211yescharacteristic
542#67—22no—
543#67—41no—
544#67—41no—
545#67—41no—
546C2×Dic3—41no—
547C2×Dic3C23×C3211yescharacteristic
548C2×Dic3C23×C3211yescharacteristic
549C2×Dic3C23×C3211yescharacteristic
550C2×Dic3C23×C3211yescharacteristic
551C2×Dic3C23×C3211yescharacteristic
552D12—22no—
553D12—41no—
554C4×D3—41no—
555C4×D3—41no—
556C4×D3—41no—
557C2×C32—24no—
558C2×C32—24no—
559C2×C32—24no—
560C2×C32—41no—
561C2×C32—41no—
562C2×C32—44no—
563C2×C32—44no—
564C2×C32—62no—
565C2×C32—84no—
566C2×C32—84no—
567C2×C32—121no—
568C2×C32—121no—
569C2×C32#100411yescharacteristic
570C2×C32D3×#4111yescharacteristic
571C2×C32#100911yescharacteristic
572C2×C32C2×C3×#4114yes—
573C2×C32C3×H(5,𝔽2)14yes—
574C2×C32C3×H(5,𝔽2)14yes—
575C3×D3—28no—
576C3×D3—44no—
577C3×D3—44no—
578C24—31no—
579C2×Q8C2×C32×D311yescharacteristic, complemented
580C2×D4—31no—
581C2×D4—31no—
582C2×D4—31no—
583C2×D4—31no—
584C2×D4—31no—
585C2×D4—31no—
586C2×D4C2×C32×D311yescharacteristic
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—31no—
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C22⋊C4—31no—
598C22⋊C4—31no—
599C22⋊C4—31no—
600C22⋊C4—31no—
601C22⋊C4—31no—
602C22⋊C4—31no—
603C22⋊C4—31no—
604C22⋊C4—31no—
605C22⋊C4—31no—
606C22⋊C4—31no—
607C22⋊C4C2×C32×D311yescharacteristic
608C22⋊C4C2×C32×D311yescharacteristic
609C22⋊C4C2×C32×D311yescharacteristic, complemented
610C22⋊C4C2×C32×D311yescharacteristic, complemented
611C42—31no—
612C42C2×C32×D311yescharacteristic, complemented
613C22×C3—24no—
614C22×C3—24no—
615C22×C3—24no—
616C22×C3—24no—
617C22×C3—24no—
618C22×C3—24no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—24no—
626C22×C3—38no—
627C22×C3—44no—
628C22×C3—44no—
629C22×C3—44no—
630C22×C3—44no—
631C22×C3—44no—
632C22×C3—44no—
633C22×C3—64no—
634C22×C3—64no—
635C22×C3—64no—
636C22×C3—64no—
637C22×C3—64no—
638C22×C3—64no—
639C22×C3—64no—
640C22×C3—64no—
641C22×C3—1216no—
642C22×C3C23×C3×D314yes—
643C22×C3C24×C3211yescharacteristic
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—44no—
653C2×D3C32×#4112yes—
654C3×C4—28no—
655C3×C4—24no—
656C3×C4—24no—
657C3×C4—24no—
658C3×C4—24no—
659C3×C4—24no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—44no—
666C3×C4—44no—
667C3×C4—44no—
668C3×C4—44no—
669C3×C4—64no—
670C3×C4—64no—
671C3×C4—64no—
672C3×C4—64no—
673C3×C4—64no—
674Dic3—21no—
675Dic3—21no—
676Dic3—21no—
677Dic3—21no—
678Dic3—21no—
679C32—24no—
680C32#567811yescharacteristic, direct product factor
681C32C3×#53814yescomplemented
682C23—31no—
683C23—31no—
684C23—31no—
685C23—62no—
686C23—121no—
687C23—121no—
688C23C22×C32×D311yescharacteristic
689C23C22×C32×D311yescharacteristic
690Q8—41no—
691D4—41no—
692D4—62no—
693D4—62no—
694D4—121no—
695D4—121no—
696D4—121no—
697D4—121no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4C22×C32×D311yescharacteristic
708C2×C4C22×C32×D311yescharacteristic
709C2×C4C22×C32×D311yescharacteristic
710C2×C4C22×C32×D311yescharacteristic
711C2×C4C22×C32×D311yescharacteristic
712C2×C3—24no—
713C2×C3—24no—
714C2×C3—24no—
715C2×C3—44no—
716C2×C3—44no—
717C2×C3—41no—
718C2×C3—41no—
719C2×C3—68no—
720C2×C3—84no—
721C2×C3—84no—
722C2×C3—124no—
723C2×C3—124no—
724C2×C3C3×#100414yes—
725C2×C3C3×D3×#4114yes—
726C2×C3C3×#100914yes—
727C2×C3C2×C32×#4111yescharacteristic
728C2×C3C32×H(5,𝔽2)11yescharacteristic
729C2×C3C32×H(5,𝔽2)11yescharacteristic
730D3—22no—
731D3—41no—
732D3—41no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—32no—
740C22—61no—
741C22—61no—
742C22—61no—
743C22—61no—
744C22—61no—
745C22—61no—
746C22—61no—
747C22—61no—
748C22—124no—
749C22C23×C32×D311yescharacteristic
750C4—21no—
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—61no—
756C4—61no—
757C4—61no—
758C4—61no—
759C4—61no—
760C3—24no—
761C3C3×#567814yesdirect product factor
762C3C32×#53811yescharacteristic, complemented
763C2—41no—
764C2—41no—
765C2—62no—
766C2—121no—
767C2—121no—
768C2C32×#100411yescharacteristic
769C2C32×D3×#4111yescharacteristic
770C2C32×#100911yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#124C2
socleC22×C33C24
hypercenterC32×#124D3
hypocenterC3C32×#538
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×#124

Complements

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

NH ≅ G/Ntype
1. C33×#124C2semidirect
2. C32×#947C2semidirect
3. C32×#946C2semidirect
4. C32×#939C2semidirect
5. C32×#937C2semidirect
6. C32×#886C2semidirect
7. C32×#884C2semidirect
8. C32×#884C2semidirect
9. C32×#883C2semidirect
10. C32×#882C2semidirect
11. C32×#67⋊C4C2semidirect
12. C32×D3×C22⋊C4C2semidirect
13. C32×#879C2semidirect
14. C32×#876C2semidirect
15. C32×C4×D12C2semidirect
17. C3×#5678C3direct (N × H)
19. C2×C33×Q8C22semidirect
24. C2×C32×#67C22semidirect
25. C22×C32×Dic3C22semidirect
30. C2×C32×C4×D3C22semidirect
33. C33×C22⋊C4C22semidirect
34. C33×C22⋊C4C22semidirect
35. C33×C42C22semidirect
44. C32×(C2×D3)⋊C4C22semidirect
45. C32×(C2×D3)⋊C4C22semidirect
46. C32×C4⋊Dic3C22semidirect
47. C32×C4⋊Dic3C22semidirect
48. C32×Dic3⋊C4C22semidirect
49. C32×Dic3⋊C4C22semidirect
50. C32×Dic3⋊C4C22semidirect
51. C32×Dic3⋊C4C22semidirect
52. C32×C4×Dic3C22semidirect
57. C32×#124D3semidirect
58. C32×#124C2×C3semidirect
70. C3×#947C2×C3semidirect
71. C3×#946C2×C3semidirect
72. C3×#939C2×C3semidirect
73. C3×#937C2×C3semidirect
74. C3×#886C2×C3semidirect
75. C3×#884C2×C3semidirect
76. C3×#884C2×C3semidirect
77. C3×#883C2×C3semidirect
78. C3×#882C2×C3semidirect
79. C3×#67⋊C4C2×C3semidirect
80. C3×D3×C22⋊C4C2×C3semidirect
81. C3×#879C2×C3semidirect
82. C3×#876C2×C3semidirect
83. C3×C4×D12C2×C3semidirect
115. #5678C32direct (N × H)
119. C2×C32×Q8C2×D3semidirect
120. C2×C32×Q8C22×C3semidirect
137. C2×C3×#67C22×C3semidirect
138. C22×C3×Dic3C22×C3semidirect
143. C2×C3×C4×D3C22×C3semidirect
166. C32×C22⋊C4C2×D3semidirect
167. C32×C22⋊C4C2×D3semidirect
170. C32×C22⋊C4C22×C3semidirect
171. C32×C22⋊C4C22×C3semidirect
174. C32×C42C2×D3semidirect
175. C32×C42C22×C3semidirect
184. C3×(C2×D3)⋊C4C22×C3semidirect
185. C3×(C2×D3)⋊C4C22×C3semidirect
186. C3×C4⋊Dic3C22×C3semidirect
187. C3×C4⋊Dic3C22×C3semidirect
188. C3×Dic3⋊C4C22×C3semidirect
189. C3×Dic3⋊C4C22×C3semidirect
190. C3×Dic3⋊C4C22×C3semidirect
191. C3×Dic3⋊C4C22×C3semidirect
192. C3×C4×Dic3C22×C3semidirect
224. C3×#124C3×D3semidirect
225. C3×#124C2×C32semidirect
237. #947C2×C32semidirect
238. #946C2×C32semidirect
239. #939C2×C32semidirect
240. #937C2×C32semidirect
241. #886C2×C32semidirect
242. #884C2×C32semidirect
243. #884C2×C32semidirect
244. #883C2×C32semidirect
245. #882C2×C32semidirect
246. #67⋊C4C2×C32semidirect
247. D3×C22⋊C4C2×C32semidirect
248. #879C2×C32semidirect
249. #876C2×C32semidirect
250. C4×D12C2×C32semidirect
332. C2×C3×Q8C2×C3×D3semidirect
333. C2×C3×Q8C22×C32semidirect
350. C2×#67C22×C32semidirect
351. C22×Dic3C22×C32semidirect
356. C2×C4×D3C22×C32semidirect
379. C3×C22⋊C4C2×C3×D3semidirect
380. C3×C22⋊C4C2×C3×D3semidirect
383. C3×C22⋊C4C22×C32semidirect
384. C3×C22⋊C4C22×C32semidirect
387. C3×C42C2×C3×D3semidirect
388. C3×C42C22×C32semidirect
397. (C2×D3)⋊C4C22×C32semidirect
398. (C2×D3)⋊C4C22×C32semidirect
399. C4⋊Dic3C22×C32semidirect
400. C4⋊Dic3C22×C32semidirect
401. Dic3⋊C4C22×C32semidirect
402. Dic3⋊C4C22×C32semidirect
403. Dic3⋊C4C22×C32semidirect
404. Dic3⋊C4C22×C32semidirect
405. C4×Dic3C22×C32semidirect
475. #124C32×D3semidirect
487. C33#538semidirect
579. C2×Q8C2×C32×D3semidirect
609. C22⋊C4C2×C32×D3semidirect
610. C22⋊C4C2×C32×D3semidirect
612. C42C2×C32×D3semidirect
680. C32#5678direct (N × H)
681. C32C3×#538semidirect
761. C3C3×#5678direct (N × H)
762. C3C32×#538semidirect

Maximal subgroups

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

subgroupindex
C33×#1242
C32×#9472
C32×#9462
C32×#9392
C32×#9372
C32×#8862
C32×#8842
C32×#8832
C32×#8822
C32×#67⋊C42
C32×D3×C22⋊C42
C32×#8792
C32×#8762
C32×C4×D122
C32×#5383
C3×#56783