Finite Group Databasebeta

← C32×#5560 #13178937

Subgroups — C32×#5560 #13178937

Order 1728.

1876 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×C4×D4C211yesmaximal, characteristic, complemented
2C32×#939C211yesmaximal, characteristic, complemented
3C32×#937C211yesmaximal, characteristic, complemented
4C32×#930C211yesmaximal, characteristic, complemented
5C32×#929C211yesmaximal, characteristic, complemented
6C32×C4×#67C211yesmaximal, characteristic, complemented
7C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
8C32×#898C211yesmaximal, characteristic, complemented
9C32×#894C211yesmaximal, characteristic, complemented
10C32×#885C211yesmaximal, characteristic, complemented
11C32×#884C211yesmaximal, characteristic, complemented
12C32×#882C211yesmaximal, characteristic, complemented
13C32×#878C211yesmaximal, characteristic, complemented
14C32×#876C211yesmaximal, characteristic, complemented
15C32×#875C211yesmaximal, characteristic, complemented
16C32×#538—31nomaximal
17C3×#5560C314yesmaximal, direct product factor
18C23×C32×D3C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic
21C22×C33×C4C2211yescharacteristic, complemented
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic, complemented
26C22×C32×Dic3C2211yescharacteristic
27C2×C32×D12C2211yescharacteristic
28C2×C32×D12C2211yescharacteristic
29C2×C32×C4×D3C2211yescharacteristic, complemented
30C2×C32×Dic6C2211yescharacteristic, complemented
31C33×C4⋊C4C2211yescharacteristic, complemented
32C33×C22⋊C4C2211yescharacteristic
33C33×C22⋊C4C2211yescharacteristic, complemented
34C33×C42C2211yescharacteristic, complemented
35C32×#217C2211yescharacteristic
36C32×#217C2211yescharacteristic, complemented
37C32×(C2×D3)⋊C4C2211yescharacteristic
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
45C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic, 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—31no—
56C32×#124—31no—
57C32×#123—31no—
58C32×#123—31no—
59C32×C22⋊Q8—31no—
60C32×#121—31no—
61C32×#121—31no—
62C32×#121—31no—
63C32×#120—31no—
64C32×#120—31no—
65C32×C4×D4—24no—
66C32×C4×D4—31no—
67C32×C4×D4D311yescharacteristic, complemented
68C32×C4×D4C2×C314yescomplemented
69C2×C32×C22⋊C4—31no—
70C3×#939C2×C314yescomplemented
71C3×#937C2×C314yescomplemented
72C3×#930C2×C314yescomplemented
73C3×#929C2×C314yescomplemented
74C3×C4×#67C2×C314yescomplemented
75C2×C3×(C2×D3)⋊C4C2×C314yescomplemented
76C3×#898C2×C314yescomplemented
77C3×#894C2×C314yescomplemented
78C3×#885C2×C314yescomplemented
79C3×#884C2×C314yescomplemented
80C3×#882C2×C314yescomplemented
81C3×#878C2×C314yescomplemented
82C3×#876C2×C314yescomplemented
83C3×#875C2×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×D4—22no—
93C2×C33×C4—41no—
94C2×C33×C4—41no—
95C2×C33×C4C2311yescharacteristic
96C2×C33×C4C2311yescharacteristic
97C2×C33×C4C2311yescharacteristic
98C2×C33×C4C2311yescharacteristic
99C2×C33×C4C2311yescharacteristic
100C32×#67—22no—
101C32×#67—41no—
102C32×#67—41no—
103C32×#67—41no—
104C2×C32×Dic3—41no—
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109C2×C32×Dic3C2311yescharacteristic
110C32×D12—41no—
111C32×D12—41no—
112C32×C4×D3—41no—
113C32×Dic6—41no—
114C3×#538—34no—
115#5560C3211yescharacteristic, direct product factor
116C24×C32—31no—
117C23×C3×D3C22×C314yes—
118C2×C32×Q8—31no—
119C2×C32×D4—24no—
120C2×C32×D4—31no—
121C2×C32×D4—31no—
122C2×C32×D4—31no—
123C2×C32×D4—31no—
124C2×C32×D4—31no—
125C2×C32×D4—31no—
126C2×C32×D4C2×D311yescharacteristic
127C2×C32×D4C22×C314yes—
128C22×C32×C4—24no—
129C22×C32×C4—24no—
130C22×C32×C4—31no—
131C22×C32×C4—31no—
132C22×C32×C4C2×D311yescharacteristic
133C22×C32×C4C2×D311yescharacteristic, complemented
134C22×C32×C4C22×C314yes—
135C22×C32×C4C22×C314yescomplemented
136C2×C3×#67C22×C314yes—
137C2×C3×#67C22×C314yes—
138C2×C3×#67C22×C314yes—
139C2×C3×#67C22×C314yescomplemented
140C22×C3×Dic3C22×C314yes—
141C2×C3×D12C22×C314yes—
142C2×C3×D12C22×C314yes—
143C2×C3×C4×D3C22×C314yescomplemented
144C2×C3×Dic6C22×C314yescomplemented
145C32×C4⋊C4—24no—
146C32×C4⋊C4—31no—
147C32×C4⋊C4—31no—
148C32×C4⋊C4—31no—
149C32×C4⋊C4—31no—
150C32×C4⋊C4—31no—
151C32×C4⋊C4C2×D311yescharacteristic, complemented
152C32×C4⋊C4C22×C314yescomplemented
153C32×C22⋊C4—24no—
154C32×C22⋊C4—24no—
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⋊C4—31no—
165C32×C22⋊C4—31no—
166C32×C22⋊C4—31no—
167C32×C22⋊C4C2×D311yescharacteristic
168C32×C22⋊C4C2×D311yescharacteristic, complemented
169C32×C22⋊C4C22×C314yes—
170C32×C22⋊C4C22×C314yescomplemented
171C32×C42—24no—
172C32×C42—31no—
173C32×C42C2×D311yescharacteristic, complemented
174C32×C42C22×C314yescomplemented
175C3×#217C22×C314yes—
176C3×#217C22×C314yescomplemented
177C3×(C2×D3)⋊C4C22×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×C314yes—
185C3×(C2×D3)⋊C4C22×C314yescomplemented
186C3×(C2×D3)⋊C4C22×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#4112yes—
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—21no—
209C2×C32×D3—44no—
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—34no—
223C3×#124—34no—
224C3×#123—34no—
225C3×#123—34no—
226C3×C22⋊Q8—34no—
227C3×#121—34no—
228C3×#121—34no—
229C3×#121—34no—
230C3×#120—34no—
231C3×#120—34no—
232C3×C4×D4—24no—
233C3×C4×D4—34no—
234C3×C4×D4C3×D314yescomplemented
235C3×C4×D4C2×C3211yescharacteristic, complemented
236C2×C3×C22⋊C4—34no—
237#939C2×C3211yescharacteristic, complemented
238#937C2×C3211yescharacteristic, complemented
239#930C2×C3211yescharacteristic, complemented
240#929C2×C3211yescharacteristic, complemented
241C4×#67C2×C3211yescharacteristic, complemented
242C2×(C2×D3)⋊C4C2×C3211yescharacteristic, complemented
243#898C2×C3211yescharacteristic, complemented
244#894C2×C3211yescharacteristic, complemented
245#885C2×C3211yescharacteristic, complemented
246#884C2×C3211yescharacteristic, complemented
247#882C2×C3211yescharacteristic, complemented
248#878C2×C3211yescharacteristic, complemented
249#876C2×C3211yescharacteristic, complemented
250#875C2×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—121no—
270C32×D4—216no—
271C32×D4—22no—
272C32×D4—28no—
273C32×D4—62no—
274C32×D4—121no—
275C32×D4—121no—
276C32×D4—121no—
277C32×D4—121no—
278C32×D4—121no—
279C2×C32×C4—24no—
280C2×C32×C4—24no—
281C2×C32×C4—24no—
282C2×C32×C4—24no—
283C2×C32×C4—24no—
284C2×C32×C4—31no—
285C2×C32×C4—31no—
286C2×C32×C4—31no—
287C2×C32×C4—31no—
288C2×C32×C4—31no—
289C2×C32×C4—41no—
290C2×C32×C4—41no—
291C2×C32×C4—44no—
292C2×C32×C4—44no—
293C2×C32×C4—48no—
294C2×C32×C4—48no—
295C2×C32×C4—121no—
296C2×C32×C4—121no—
297C2×C32×C4C22×D311yescharacteristic
298C2×C32×C4C22×D311yescharacteristic
299C2×C32×C4C22×D311yescharacteristic
300C2×C32×C4C22×D311yescharacteristic
301C2×C32×C4C22×D311yescharacteristic
302C2×C32×C4C23×C314yes—
303C2×C32×C4C23×C314yes—
304C2×C32×C4C23×C314yes—
305C2×C32×C4C23×C314yes—
306C2×C32×C4C23×C314yes—
307C3×#67—28no—
308C3×#67—44no—
309C3×#67—44no—
310C3×#67—44no—
311C2×C3×Dic3—44no—
312C2×C3×Dic3C23×C314yes—
313C2×C3×Dic3C23×C314yes—
314C2×C3×Dic3C23×C314yes—
315C2×C3×Dic3C23×C314yes—
316C2×C3×Dic3C23×C314yes—
317C3×D12—44no—
318C3×D12—44no—
319C3×C4×D3—44no—
320C3×Dic6—44no—
321#538—31noSylow
322C2×C33—22no—
323C2×C33—41no—
324C2×C33C2×#4111yescharacteristic
325C2×C33H(5,𝔽2)11yescharacteristic
326C2×C33H(5,𝔽2)11yescharacteristic
327C32×D3—41no—
328C32×D3—41no—
329C32×D3—41no—
330C24×C3—34no—
331C23×D3C22×C3211yescharacteristic
332C2×C3×Q8—34no—
333C2×C3×D4—24no—
334C2×C3×D4—34no—
335C2×C3×D4—34no—
336C2×C3×D4—34no—
337C2×C3×D4—34no—
338C2×C3×D4—34no—
339C2×C3×D4—34no—
340C2×C3×D4C2×C3×D314yes—
341C2×C3×D4C22×C3211yescharacteristic
342C22×C3×C4—24no—
343C22×C3×C4—24no—
344C22×C3×C4—34no—
345C22×C3×C4—34no—
346C22×C3×C4C2×C3×D314yes—
347C22×C3×C4C2×C3×D314yescomplemented
348C22×C3×C4C22×C3211yescharacteristic
349C22×C3×C4C22×C3211yescharacteristic, complemented
350C2×#67C22×C3211yescharacteristic
351C2×#67C22×C3211yescharacteristic
352C2×#67C22×C3211yescharacteristic
353C2×#67C22×C3211yescharacteristic, complemented
354C22×Dic3C22×C3211yescharacteristic
355C2×D12C22×C3211yescharacteristic
356C2×D12C22×C3211yescharacteristic
357C2×C4×D3C22×C3211yescharacteristic, complemented
358C2×Dic6C22×C3211yescharacteristic, complemented
359C3×C4⋊C4—24no—
360C3×C4⋊C4—34no—
361C3×C4⋊C4—34no—
362C3×C4⋊C4—34no—
363C3×C4⋊C4—34no—
364C3×C4⋊C4—34no—
365C3×C4⋊C4C2×C3×D314yescomplemented
366C3×C4⋊C4C22×C3211yescharacteristic, complemented
367C3×C22⋊C4—24no—
368C3×C22⋊C4—24no—
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⋊C4—34no—
378C3×C22⋊C4—34no—
379C3×C22⋊C4—34no—
380C3×C22⋊C4—34no—
381C3×C22⋊C4C2×C3×D314yes—
382C3×C22⋊C4C2×C3×D314yescomplemented
383C3×C22⋊C4C22×C3211yescharacteristic
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, complemented
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
398(C2×D3)⋊C4C22×C3211yescharacteristic
399(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
400(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
401C4⋊Dic3C22×C3211yescharacteristic, complemented
402Dic3⋊C4C22×C3211yescharacteristic, complemented
403Dic3⋊C4C22×C3211yescharacteristic, complemented
404Dic3⋊C4C22×C3211yescharacteristic, complemented
405Dic3⋊C4C22×C3211yescharacteristic, complemented
406C4×Dic3C22×C3211yescharacteristic, complemented
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—28no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—24no—
414C22×C32—24no—
415C22×C32—28no—
416C22×C32—24no—
417C22×C32—24no—
418C22×C32—24no—
419C22×C32—24no—
420C22×C32—44no—
421C22×C32—44no—
422C22×C32—44no—
423C22×C32—44no—
424C22×C32—61no—
425C22×C32—61no—
426C22×C32—61no—
427C22×C32—61no—
428C22×C32—61no—
429C22×C32—61no—
430C22×C32—61no—
431C22×C32—61no—
432C22×C32—61no—
433C22×C32—124no—
434C22×C32#23512yes—
435C22×C32C3×#4118yes—
436C22×C32C23×D311yescharacteristic
437C22×C32C24×C314yes—
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—24no—
446C2×C3×D3—24no—
447C2×C3×D3—416no—
448C32×C4—28no—
449C32×C4—28no—
450C32×C4—21no—
451C32×C4—21no—
452C32×C4—21no—
453C32×C4—21no—
454C32×C4—21no—
455C32×C4—24no—
456C32×C4—24no—
457C32×C4—24no—
458C32×C4—24no—
459C32×C4—24no—
460C32×C4—44no—
461C32×C4—44no—
462C32×C4—44no—
463C32×C4—61no—
464C32×C4—61no—
465C32×C4—61no—
466C32×C4—61no—
467C32×C4—61no—
468C3×Dic3—24no—
469C3×Dic3—24no—
470C3×Dic3—24no—
471C3×Dic3—24no—
472C3×Dic3—24no—
473#126—31no—
474#126—31no—
475#124—31no—
476#124—31no—
477#123—31no—
478#123—31no—
479C22⋊Q8—31no—
480#121—31no—
481#121—31no—
482#121—31no—
483#120—31no—
484#120—31no—
485C4×D4—31no—
486C4×D4C32×D311yescharacteristic, complemented
487C2×C22⋊C4—31no—
488C33#53811yescharacteristic, complemented, Sylow
489C23×C3—24no—
490C23×C3—24no—
491C23×C3—34no—
492C23×C3—34no—
493C23×C3—34no—
494C23×C3—68no—
495C23×C3—124no—
496C23×C3—124no—
497C23×C3C22×C3×D314yes—
498C23×C3C22×C3×D314yes—
499C23×C3C23×C3211yescharacteristic
500C23×C3C23×C3211yescharacteristic
501C22×D3—22no—
502C22×D3—41no—
503C22×D3—41no—
504C22×D3C23×C3211yescharacteristic
505C22×D3C23×C3211yescharacteristic
506C22×D3C23×C3211yescharacteristic
507C3×Q8—124no—
508C3×D4—216no—
509C3×D4—28no—
510C3×D4—22no—
511C3×D4—68no—
512C3×D4—124no—
513C3×D4—124no—
514C3×D4—124no—
515C3×D4—124no—
516C3×D4—124no—
517C2×C3×C4—24no—
518C2×C3×C4—24no—
519C2×C3×C4—24no—
520C2×C3×C4—24no—
521C2×C3×C4—24no—
522C2×C3×C4—34no—
523C2×C3×C4—34no—
524C2×C3×C4—34no—
525C2×C3×C4—34no—
526C2×C3×C4—34no—
527C2×C3×C4—44no—
528C2×C3×C4—44no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—48no—
532C2×C3×C4—48no—
533C2×C3×C4—124no—
534C2×C3×C4—124no—
535C2×C3×C4C22×C3×D314yes—
536C2×C3×C4C22×C3×D314yes—
537C2×C3×C4C22×C3×D314yes—
538C2×C3×C4C22×C3×D314yes—
539C2×C3×C4C22×C3×D314yes—
540C2×C3×C4C23×C3211yescharacteristic
541C2×C3×C4C23×C3211yescharacteristic
542C2×C3×C4C23×C3211yescharacteristic
543C2×C3×C4C23×C3211yescharacteristic
544C2×C3×C4C23×C3211yescharacteristic
545#67—22no—
546#67—41no—
547#67—41no—
548#67—41no—
549C2×Dic3—41no—
550C2×Dic3C23×C3211yescharacteristic
551C2×Dic3C23×C3211yescharacteristic
552C2×Dic3C23×C3211yescharacteristic
553C2×Dic3C23×C3211yescharacteristic
554C2×Dic3C23×C3211yescharacteristic
555D12—41no—
556D12—41no—
557C4×D3—41no—
558Dic6—41no—
559C2×C32—22no—
560C2×C32—24no—
561C2×C32—24no—
562C2×C32—24no—
563C2×C32—28no—
564C2×C32—48no—
565C2×C32—48no—
566C2×C32—41no—
567C2×C32—44no—
568C2×C32—121no—
569C2×C32—121no—
570C2×C32—121no—
571C2×C32C2×#23511yescharacteristic
572C2×C32#100411yescharacteristic
573C2×C32#100911yescharacteristic
574C2×C32C2×C3×#4114yes—
575C2×C32C3×H(5,𝔽2)14yes—
576C2×C32C3×H(5,𝔽2)14yes—
577C3×D3—44no—
578C3×D3—44no—
579C3×D3—44no—
580C24—31no—
581C2×Q8—31no—
582C2×D4—31no—
583C2×D4—31no—
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—31no—
587C2×D4—31no—
588C2×D4C2×C32×D311yescharacteristic
589C22×C4—31no—
590C22×C4—31no—
591C22×C4C2×C32×D311yescharacteristic
592C22×C4C2×C32×D311yescharacteristic, complemented
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4C2×C32×D311yescharacteristic, complemented
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⋊C4—31no—
608C22⋊C4—31no—
609C22⋊C4—31no—
610C22⋊C4—31no—
611C22⋊C4C2×C32×D311yescharacteristic
612C22⋊C4C2×C32×D311yescharacteristic, complemented
613C42—31no—
614C42C2×C32×D311yescharacteristic, complemented
615C22×C3—24no—
616C22×C3—24no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—28no—
620C22×C3—24no—
621C22×C3—24no—
622C22×C3—24no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—24no—
627C22×C3—28no—
628C22×C3—44no—
629C22×C3—44no—
630C22×C3—44no—
631C22×C3—44no—
632C22×C3—64no—
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×C3C3×#23518yes—
643C22×C3C32×#4112yes—
644C22×C3C23×C3×D314yes—
645C22×C3C24×C3211yescharacteristic
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—44no—
656C3×C4—28no—
657C3×C4—28no—
658C3×C4—24no—
659C3×C4—24no—
660C3×C4—24no—
661C3×C4—24no—
662C3×C4—24no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—44no—
669C3×C4—44no—
670C3×C4—44no—
671C3×C4—64no—
672C3×C4—64no—
673C3×C4—64no—
674C3×C4—64no—
675C3×C4—64no—
676Dic3—21no—
677Dic3—21no—
678Dic3—21no—
679Dic3—21no—
680Dic3—21no—
681C32—24no—
682C32#556011yescharacteristic, direct product factor
683C32C3×#53814yescomplemented
684C23—31no—
685C23—31no—
686C23—31no—
687C23—62no—
688C23—121no—
689C23—121no—
690C23C22×C32×D311yescharacteristic
691C23C22×C32×D311yescharacteristic
692Q8—121no—
693D4—22no—
694D4—62no—
695D4—121no—
696D4—121no—
697D4—121no—
698D4—121no—
699D4—121no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4C22×C32×D311yescharacteristic
710C2×C4C22×C32×D311yescharacteristic
711C2×C4C22×C32×D311yescharacteristic
712C2×C4C22×C32×D311yescharacteristic
713C2×C4C22×C32×D311yescharacteristic
714C2×C3—28no—
715C2×C3—22no—
716C2×C3—24no—
717C2×C3—24no—
718C2×C3—24no—
719C2×C3—48no—
720C2×C3—48no—
721C2×C3—44no—
722C2×C3—41no—
723C2×C3—124no—
724C2×C3—124no—
725C2×C3—124no—
726C2×C3C2×C3×#23514yes—
727C2×C3C3×#100414yes—
728C2×C3C3×#100914yes—
729C2×C3C2×C32×#4111yescharacteristic
730C2×C3C32×H(5,𝔽2)11yescharacteristic
731C2×C3C32×H(5,𝔽2)11yescharacteristic
732D3—41no—
733D3—41no—
734D3—41no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—61no—
741C22—61no—
742C22—61no—
743C22—61no—
744C22—61no—
745C22—61no—
746C22—61no—
747C22—61no—
748C22—61no—
749C22—124no—
750C22C32×#23512yes—
751C22C23×C32×D311yescharacteristic
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—61no—
758C4—61no—
759C4—61no—
760C4—61no—
761C4—61no—
762C3—24no—
763C3C3×#556014yesdirect product factor
764C3C32×#53811yescharacteristic, complemented
765C2—22no—
766C2—41no—
767C2—121no—
768C2—121no—
769C2—121no—
770C2C2×C32×#23511yescharacteristic
771C2C32×#100411yescharacteristic
772C2C32×#100911yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×C4×D4C2
socleC22×C33C24
hypercenterC32×C4×D4D3
hypocenterC3C32×#538
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×C4×D4

Complements

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

NH ≅ G/Ntype
1. C33×C4×D4C2semidirect
2. C32×#939C2semidirect
3. C32×#937C2semidirect
4. C32×#930C2semidirect
5. C32×#929C2semidirect
6. C32×C4×#67C2semidirect
7. C2×C32×(C2×D3)⋊C4C2semidirect
8. C32×#898C2semidirect
9. C32×#894C2semidirect
10. C32×#885C2semidirect
11. C32×#884C2semidirect
12. C32×#882C2semidirect
13. C32×#878C2semidirect
14. C32×#876C2semidirect
15. C32×#875C2semidirect
17. C3×#5560C3direct (N × H)
21. C22×C33×C4C22semidirect
25. C2×C32×#67C22semidirect
29. C2×C32×C4×D3C22semidirect
30. C2×C32×Dic6C22semidirect
31. C33×C4⋊C4C22semidirect
33. C33×C22⋊C4C22semidirect
34. C33×C42C22semidirect
36. C32×#217C22semidirect
45. C32×(C2×D3)⋊C4C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. C32×C4⋊Dic3C22semidirect
48. C32×Dic3⋊C4C22semidirect
49. C32×Dic3⋊C4C22semidirect
50. C32×Dic3⋊C4C22semidirect
51. C32×Dic3⋊C4C22semidirect
52. C32×C4×Dic3C22semidirect
67. C32×C4×D4D3semidirect
68. C32×C4×D4C2×C3semidirect
70. C3×#939C2×C3semidirect
71. C3×#937C2×C3semidirect
72. C3×#930C2×C3semidirect
73. C3×#929C2×C3semidirect
74. C3×C4×#67C2×C3semidirect
75. C2×C3×(C2×D3)⋊C4C2×C3semidirect
76. C3×#898C2×C3semidirect
77. C3×#894C2×C3semidirect
78. C3×#885C2×C3semidirect
79. C3×#884C2×C3semidirect
80. C3×#882C2×C3semidirect
81. C3×#878C2×C3semidirect
82. C3×#876C2×C3semidirect
83. C3×#875C2×C3semidirect
115. #5560C32direct (N × H)
133. C22×C32×C4C2×D3semidirect
135. C22×C32×C4C22×C3semidirect
139. C2×C3×#67C22×C3semidirect
143. C2×C3×C4×D3C22×C3semidirect
144. C2×C3×Dic6C22×C3semidirect
151. C32×C4⋊C4C2×D3semidirect
152. C32×C4⋊C4C22×C3semidirect
168. C32×C22⋊C4C2×D3semidirect
170. C32×C22⋊C4C22×C3semidirect
173. C32×C42C2×D3semidirect
174. C32×C42C22×C3semidirect
176. C3×#217C22×C3semidirect
185. C3×(C2×D3)⋊C4C22×C3semidirect
186. C3×(C2×D3)⋊C4C22×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
234. C3×C4×D4C3×D3semidirect
235. C3×C4×D4C2×C32semidirect
237. #939C2×C32semidirect
238. #937C2×C32semidirect
239. #930C2×C32semidirect
240. #929C2×C32semidirect
241. C4×#67C2×C32semidirect
242. C2×(C2×D3)⋊C4C2×C32semidirect
243. #898C2×C32semidirect
244. #894C2×C32semidirect
245. #885C2×C32semidirect
246. #884C2×C32semidirect
247. #882C2×C32semidirect
248. #878C2×C32semidirect
249. #876C2×C32semidirect
250. #875C2×C32semidirect
347. C22×C3×C4C2×C3×D3semidirect
349. C22×C3×C4C22×C32semidirect
353. C2×#67C22×C32semidirect
357. C2×C4×D3C22×C32semidirect
358. C2×Dic6C22×C32semidirect
365. C3×C4⋊C4C2×C3×D3semidirect
366. C3×C4⋊C4C22×C32semidirect
382. C3×C22⋊C4C2×C3×D3semidirect
384. C3×C22⋊C4C22×C32semidirect
387. C3×C42C2×C3×D3semidirect
388. C3×C42C22×C32semidirect
390. #217C22×C32semidirect
399. (C2×D3)⋊C4C22×C32semidirect
400. (C2×D3)⋊C4C22×C32semidirect
401. C4⋊Dic3C22×C32semidirect
402. Dic3⋊C4C22×C32semidirect
403. Dic3⋊C4C22×C32semidirect
404. Dic3⋊C4C22×C32semidirect
405. Dic3⋊C4C22×C32semidirect
406. C4×Dic3C22×C32semidirect
486. C4×D4C32×D3semidirect
488. C33#538semidirect
592. C22×C4C2×C32×D3semidirect
598. C4⋊C4C2×C32×D3semidirect
612. C22⋊C4C2×C32×D3semidirect
614. C42C2×C32×D3semidirect
682. C32#5560direct (N × H)
683. C32C3×#538semidirect
763. C3C3×#5560direct (N × H)
764. C3C32×#538semidirect

Maximal subgroups

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

subgroupindex
C33×C4×D42
C32×#9392
C32×#9372
C32×#9302
C32×#9292
C32×C4×#672
C2×C32×(C2×D3)⋊C42
C32×#8982
C32×#8942
C32×#8852
C32×#8842
C32×#8822
C32×#8782
C32×#8762
C32×#8752
C32×#5383
C3×#55603