Finite Group Databasebeta

← C32×#5591 #13178969

Subgroups — C32×#5591 #13178969

Order 1728.

2524 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×#67C211yesmaximal, characteristic, complemented
2C2×C32×#237C211yesmaximal, characteristic, complemented
3C33×#120C211yesmaximal, characteristic, complemented
4C2×C32×#217C211yesmaximal, characteristic, complemented
5C32×#939C211yesmaximal, characteristic, complemented
6C32×#939C211yesmaximal, characteristic, complemented
7C32×#938C211yesmaximal, characteristic, complemented
8C32×#937C211yesmaximal, characteristic, complemented
9C32×D4×Dic3C211yesmaximal, characteristic, complemented
10C32×#886C211yesmaximal, characteristic, complemented
11C32×#885C211yesmaximal, characteristic, complemented
12C32×#883C211yesmaximal, characteristic, complemented
13C32×#67⋊C4C211yesmaximal, characteristic, complemented
14C32×D3×C22⋊C4C211yesmaximal, characteristic, complemented
15C32×#878C211yesmaximal, characteristic, complemented
16C32×#546—31nomaximal
17C3×#5591C314yesmaximal, direct product factor
18C24×C33C2211yescharacteristic
19C23×C32×D3C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic
21C2×C33×D4C2211yescharacteristic, complemented
22C2×C33×D4C2211yescharacteristic, complemented
23C2×C32×#67—24no—
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C2×C32×#67C2211yescharacteristic
27C2×C32×#67C2211yescharacteristic
28C2×C32×#67C2211yescharacteristic, complemented
29C2×C32×#67C2211yescharacteristic, complemented
30C22×C32×Dic3C2211yescharacteristic
31C22×C32×Dic3C2211yescharacteristic, complemented
32C22×C32×Dic3C2211yescharacteristic, complemented
33C22×C32×Dic3C2211yescharacteristic, complemented
34C32×#237—24no—
35C2×C32×C4×D3C2211yescharacteristic, complemented
36C2×C32×C4×D3C2211yescharacteristic, complemented
37C2×C32×Dic6C2211yescharacteristic, complemented
38C33×C22⋊C4C2211yescharacteristic
39C33×C22⋊C4C2211yescharacteristic, complemented
40C33×C22⋊C4C2211yescharacteristic, complemented
41C32×#217C2211yescharacteristic
42C32×#217C2211yescharacteristic
43C32×#217C2211yescharacteristic, complemented
44C32×#217C2211yescharacteristic, complemented
45C32×#217C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C32×C4⋊Dic3C2211yescharacteristic, complemented
51C32×C4⋊Dic3C2211yescharacteristic, complemented
52C32×Dic3⋊C4C2211yescharacteristic, complemented
53C32×Dic3⋊C4C2211yescharacteristic, complemented
54C32×C4×Dic3C2211yescharacteristic, complemented
55C2×C32×#41—31no—
56C22×C32×D4—31no—
57C22×C3×#67C2×C314yescomplemented
58C2×C3×#237C2×C314yescomplemented
59C32×#124—31no—
60C32×#123—31no—
61C32×#123—31no—
62C32×C22⋊Q8—31no—
63C32×#121—31no—
64C32×#121—31no—
65C32×#121—31no—
66C32×#120—24no—
67C32×#120—31no—
68C32×#120D311yescharacteristic, complemented
69C32×#120C2×C314yescomplemented
70C32×C4×D4—31no—
71C32×C4×D4—31no—
72C2×C32×C22⋊C4—31no—
73C2×C32×C22⋊C4—31no—
74C2×C3×#217C2×C314yescomplemented
75C3×#939C2×C314yescomplemented
76C3×#939C2×C314yescomplemented
77C3×#938C2×C314yescomplemented
78C3×#937C2×C314yescomplemented
79C3×D4×Dic3C2×C314yescomplemented
80C3×#886C2×C314yescomplemented
81C3×#885C2×C314yescomplemented
82C3×#883C2×C314yescomplemented
83C3×#67⋊C4C2×C314yescomplemented
84C3×D3×C22⋊C4C2×C314yescomplemented
85C3×#878C2×C314yescomplemented
86C23×C33—22no—
87C23×C33—22no—
88C23×C33—41no—
89C23×C33C2311yescharacteristic
90C23×C33C2311yescharacteristic
91C23×C33C2311yescharacteristic
92C23×C33C2311yescharacteristic
93C22×C32×D3—22no—
94C22×C32×D3—22no—
95C22×C32×D3—41no—
96C22×C32×D3C2311yescharacteristic
97C22×C32×D3C2311yescharacteristic
98C33×D4—22no—
99C33×D4—22no—
100C33×D4—41no—
101C2×C33×C4C2311yescharacteristic
102C2×C33×C4C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104C32×#67—22no—
105C32×#67—22no—
106C32×#67—22no—
107C32×#67—22no—
108C32×#67—41no—
109C32×#67D414yescomplemented
110C2×C32×Dic3—22no—
111C2×C32×Dic3—22no—
112C2×C32×Dic3—22no—
113C2×C32×Dic3—41no—
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C32×C4×D3—22no—
121C32×C4×D3—41no—
122C32×Dic6—22no—
123C3×#546—34no—
124#5591C3211yescharacteristic, direct product factor
125C24×C32—24no—
126C24×C32—31no—
127C24×C32C2×D311yescharacteristic
128C24×C32C22×C314yes—
129C23×C3×D3C22×C314yes—
130C32×#41—64no—
131C2×C32×Q8—31no—
132C2×C32×D4—24no—
133C2×C32×D4—24no—
134C2×C32×D4—24no—
135C2×C32×D4—31no—
136C2×C32×D4—31no—
137C2×C32×D4—31no—
138C2×C32×D4—31no—
139C2×C32×D4—31no—
140C2×C32×D4—31no—
141C2×C32×D4—64no—
142C2×C32×D4C2×D311yescharacteristic
143C2×C32×D4C2×D311yescharacteristic, complemented
144C2×C32×D4C2×D311yescharacteristic, complemented
145C2×C32×D4C22×C314yes—
146C2×C32×D4C22×C314yescomplemented
147C2×C32×D4C22×C314yescomplemented
148C22×C32×C4—31no—
149C22×C32×C4—31no—
150C22×C32×C4—31no—
151C22×C32×C4—31no—
152C22×C32×C4—31no—
153C22×C32×C4—31no—
154C2×C3×#67—216no—
155C2×C3×#67C22×C314yes—
156C2×C3×#67C22×C314yes—
157C2×C3×#67C22×C314yes—
158C2×C3×#67C22×C314yes—
159C2×C3×#67C22×C314yescomplemented
160C2×C3×#67C22×C314yescomplemented
161C22×C3×Dic3C22×C314yes—
162C22×C3×Dic3C22×C314yescomplemented
163C22×C3×Dic3C22×C314yescomplemented
164C22×C3×Dic3C22×C314yescomplemented
165C3×#237—216no—
166C2×C3×C4×D3C22×C314yescomplemented
167C2×C3×C4×D3C22×C314yescomplemented
168C2×C3×Dic6C22×C314yescomplemented
169C32×C4⋊C4—31no—
170C32×C4⋊C4—31no—
171C32×C4⋊C4—31no—
172C32×C4⋊C4—31no—
173C32×C22⋊C4—24no—
174C32×C22⋊C4—24no—
175C32×C22⋊C4—24no—
176C32×C22⋊C4—31no—
177C32×C22⋊C4—31no—
178C32×C22⋊C4—31no—
179C32×C22⋊C4—31no—
180C32×C22⋊C4—31no—
181C32×C22⋊C4—31no—
182C32×C22⋊C4—31no—
183C32×C22⋊C4—31no—
184C32×C22⋊C4—31no—
185C32×C22⋊C4C2×D311yescharacteristic
186C32×C22⋊C4C2×D311yescharacteristic, complemented
187C32×C22⋊C4C2×D311yescharacteristic, complemented
188C32×C22⋊C4C22×C314yes—
189C32×C22⋊C4C22×C314yescomplemented
190C32×C22⋊C4C22×C314yescomplemented
191C32×C42—31no—
192C3×#217C22×C314yes—
193C3×#217C22×C314yes—
194C3×#217C22×C314yescomplemented
195C3×#217C22×C314yescomplemented
196C3×#217C22×C314yescomplemented
197C3×(C2×D3)⋊C4C22×C314yescomplemented
198C3×(C2×D3)⋊C4C22×C314yescomplemented
199C3×(C2×D3)⋊C4C22×C314yescomplemented
200C3×(C2×D3)⋊C4C22×C314yescomplemented
201C3×C4⋊Dic3C22×C314yescomplemented
202C3×C4⋊Dic3C22×C314yescomplemented
203C3×Dic3⋊C4C22×C314yescomplemented
204C3×Dic3⋊C4C22×C314yescomplemented
205C3×C4×Dic3C22×C314yescomplemented
206C22×C33—21no—
207C22×C33—21no—
208C22×C33—21no—
209C22×C33—21no—
210C22×C33—21no—
211C22×C33—21no—
212C22×C33—21no—
213C22×C33—21no—
214C22×C33—21no—
215C22×C33—21no—
216C22×C33—44no—
217C22×C33C2×D412yes—
218C22×C33#4112yescomplemented
219C22×C33C2411yescharacteristic
220C2×C32×D3—21no—
221C2×C32×D3—21no—
222C2×C32×D3—21no—
223C2×C32×D3—21no—
224C2×C32×D3—21no—
225C2×C32×D3—44no—
226C2×C32×D3C2×D412yes—
227C33×C4—21no—
228C33×C4—21no—
229C33×C4—21no—
230C32×Dic3—21no—
231C32×Dic3—21no—
232C32×Dic3—21no—
233C32×Dic3—21no—
234C32×Dic3—21no—
235C32×Dic3C2×D412yes—
236C2×C3×#41—34no—
237C22×C3×D4—34no—
238C22×#67C2×C3211yescharacteristic, complemented
239C2×#237C2×C3211yescharacteristic, complemented
240C3×#124—34no—
241C3×#123—34no—
242C3×#123—34no—
243C3×C22⋊Q8—34no—
244C3×#121—34no—
245C3×#121—34no—
246C3×#121—34no—
247C3×#120—24no—
248C3×#120—34no—
249C3×#120C3×D314yescomplemented
250C3×#120C2×C3211yescharacteristic, complemented
251C3×C4×D4—34no—
252C3×C4×D4—34no—
253C2×C3×C22⋊C4—34no—
254C2×C3×C22⋊C4—34no—
255C2×#217C2×C3211yescharacteristic, complemented
256#939C2×C3211yescharacteristic, complemented
257#939C2×C3211yescharacteristic, complemented
258#938C2×C3211yescharacteristic, complemented
259#937C2×C3211yescharacteristic, complemented
260D4×Dic3C2×C3211yescharacteristic, complemented
261#886C2×C3211yescharacteristic, complemented
262#885C2×C3211yescharacteristic, complemented
263#883C2×C3211yescharacteristic, complemented
264#67⋊C4C2×C3211yescharacteristic, complemented
265D3×C22⋊C4C2×C3211yescharacteristic, complemented
266#878C2×C3211yescharacteristic, complemented
267C23×C32—22no—
268C23×C32—22no—
269C23×C32—24no—
270C23×C32—24no—
271C23×C32—24no—
272C23×C32—24no—
273C23×C32—28no—
274C23×C32—28no—
275C23×C32—31no—
276C23×C32—31no—
277C23×C32—48no—
278C23×C32—48no—
279C23×C32—41no—
280C23×C32—44no—
281C23×C32—48no—
282C23×C32—62no—
283C23×C32—62no—
284C23×C32—121no—
285C23×C32C22×D311yescharacteristic
286C23×C32C22×D311yescharacteristic
287C23×C32C22×D311yescharacteristic
288C23×C32C22×D311yescharacteristic
289C23×C32C23×C314yes—
290C23×C32C23×C314yes—
291C23×C32C23×C314yes—
292C23×C32C23×C314yes—
293C22×C3×D3—28no—
294C22×C3×D3—28no—
295C22×C3×D3—44no—
296C22×C3×D3C23×C314yes—
297C22×C3×D3C23×C314yes—
298C32×Q8—62no—
299C32×D4—22no—
300C32×D4—22no—
301C32×D4—28no—
302C32×D4—28no—
303C32×D4—34no—
304C32×D4—48no—
305C32×D4—48no—
306C32×D4—41no—
307C32×D4—44no—
308C32×D4—48no—
309C32×D4—62no—
310C32×D4—62no—
311C32×D4—62no—
312C32×D4—62no—
313C32×D4—121no—
314C2×C32×C4—24no—
315C2×C32×C4—24no—
316C2×C32×C4—24no—
317C2×C32×C4—31no—
318C2×C32×C4—31no—
319C2×C32×C4—31no—
320C2×C32×C4—31no—
321C2×C32×C4—31no—
322C2×C32×C4—31no—
323C2×C32×C4—62no—
324C2×C32×C4—62no—
325C2×C32×C4—62no—
326C2×C32×C4—62no—
327C2×C32×C4—121no—
328C2×C32×C4—121no—
329C2×C32×C4C22×D311yescharacteristic
330C2×C32×C4C22×D311yescharacteristic
331C2×C32×C4C22×D311yescharacteristic
332C2×C32×C4C23×C314yes—
333C2×C32×C4C23×C314yes—
334C2×C32×C4C23×C314yes—
335C3×#67—28no—
336C3×#67—28no—
337C3×#67—28no—
338C3×#67—28no—
339C3×#67—44no—
340C3×#67C3×D4116yescomplemented
341C2×C3×Dic3—28no—
342C2×C3×Dic3—28no—
343C2×C3×Dic3—28no—
344C2×C3×Dic3—44no—
345C2×C3×Dic3C23×C314yes—
346C2×C3×Dic3C23×C314yes—
347C2×C3×Dic3C23×C314yes—
348C2×C3×Dic3C23×C314yes—
349C2×C3×Dic3C23×C314yes—
350C2×C3×Dic3C23×C314yes—
351C3×C4×D3—28no—
352C3×C4×D3—44no—
353C3×Dic6—28no—
354#546—31noSylow
355C2×C33—22no—
356C2×C33—22no—
357C2×C33—41no—
358C2×C33—41no—
359C2×C33C22×D411yescharacteristic
360C2×C33C2×#4111yescharacteristic
361C2×C33H(5,𝔽2)11yescharacteristic
362C32×D3—22no—
363C32×D3—41no—
364C24×C3—24no—
365C24×C3—34no—
366C24×C3C2×C3×D314yes—
367C24×C3C22×C3211yescharacteristic
368C23×D3C22×C3211yescharacteristic
369C3×#41—616no—
370C2×C3×Q8—34no—
371C2×C3×D4—24no—
372C2×C3×D4—24no—
373C2×C3×D4—24no—
374C2×C3×D4—34no—
375C2×C3×D4—34no—
376C2×C3×D4—34no—
377C2×C3×D4—34no—
378C2×C3×D4—34no—
379C2×C3×D4—34no—
380C2×C3×D4—616no—
381C2×C3×D4C2×C3×D314yes—
382C2×C3×D4C2×C3×D314yescomplemented
383C2×C3×D4C2×C3×D314yescomplemented
384C2×C3×D4C22×C3211yescharacteristic
385C2×C3×D4C22×C3211yescharacteristic, complemented
386C2×C3×D4C22×C3211yescharacteristic, complemented
387C22×C3×C4—34no—
388C22×C3×C4—34no—
389C22×C3×C4—34no—
390C22×C3×C4—34no—
391C22×C3×C4—34no—
392C22×C3×C4—34no—
393C2×#67—24no—
394C2×#67C22×C3211yescharacteristic
395C2×#67C22×C3211yescharacteristic
396C2×#67C22×C3211yescharacteristic
397C2×#67C22×C3211yescharacteristic
398C2×#67C22×C3211yescharacteristic, complemented
399C2×#67C22×C3211yescharacteristic, complemented
400C22×Dic3C22×C3211yescharacteristic
401C22×Dic3C22×C3211yescharacteristic, complemented
402C22×Dic3C22×C3211yescharacteristic, complemented
403C22×Dic3C22×C3211yescharacteristic, complemented
404#237—24no—
405C2×C4×D3C22×C3211yescharacteristic, complemented
406C2×C4×D3C22×C3211yescharacteristic, complemented
407C2×Dic6C22×C3211yescharacteristic, complemented
408C3×C4⋊C4—34no—
409C3×C4⋊C4—34no—
410C3×C4⋊C4—34no—
411C3×C4⋊C4—34no—
412C3×C22⋊C4—24no—
413C3×C22⋊C4—24no—
414C3×C22⋊C4—24no—
415C3×C22⋊C4—34no—
416C3×C22⋊C4—34no—
417C3×C22⋊C4—34no—
418C3×C22⋊C4—34no—
419C3×C22⋊C4—34no—
420C3×C22⋊C4—34no—
421C3×C22⋊C4—34no—
422C3×C22⋊C4—34no—
423C3×C22⋊C4—34no—
424C3×C22⋊C4C2×C3×D314yes—
425C3×C22⋊C4C2×C3×D314yescomplemented
426C3×C22⋊C4C2×C3×D314yescomplemented
427C3×C22⋊C4C22×C3211yescharacteristic
428C3×C22⋊C4C22×C3211yescharacteristic, complemented
429C3×C22⋊C4C22×C3211yescharacteristic, complemented
430C3×C42—34no—
431#217C22×C3211yescharacteristic
432#217C22×C3211yescharacteristic
433#217C22×C3211yescharacteristic, complemented
434#217C22×C3211yescharacteristic, complemented
435#217C22×C3211yescharacteristic, complemented
436(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
437(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
438(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
439(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
440C4⋊Dic3C22×C3211yescharacteristic, complemented
441C4⋊Dic3C22×C3211yescharacteristic, complemented
442Dic3⋊C4C22×C3211yescharacteristic, complemented
443Dic3⋊C4C22×C3211yescharacteristic, complemented
444C4×Dic3C22×C3211yescharacteristic, complemented
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—28no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—24no—
457C22×C32—24no—
458C22×C32—28no—
459C22×C32—28no—
460C22×C32—24no—
461C22×C32—24no—
462C22×C32—24no—
463C22×C32—24no—
464C22×C32—24no—
465C22×C32—24no—
466C22×C32—24no—
467C22×C32—24no—
468C22×C32—24no—
469C22×C32—32no—
470C22×C32—44no—
471C22×C32—44no—
472C22×C32—44no—
473C22×C32—44no—
474C22×C32—44no—
475C22×C32—44no—
476C22×C32—44no—
477C22×C32—44no—
478C22×C32—44no—
479C22×C32—44no—
480C22×C32—416no—
481C22×C32—432no—
482C22×C32—61no—
483C22×C32—61no—
484C22×C32—61no—
485C22×C32—61no—
486C22×C32—61no—
487C22×C32—124no—
488C22×C32D3×D412yes—
489C22×C32#23712yescomplemented
490C22×C32C2×C3×D418yes—
491C22×C32C3×#4118yescomplemented
492C22×C32C23×D311yescharacteristic
493C22×C32C24×C314yes—
494C2×C3×D3—24no—
495C2×C3×D3—24no—
496C2×C3×D3—24no—
497C2×C3×D3—24no—
498C2×C3×D3—24no—
499C2×C3×D3—416no—
500C2×C3×D3C2×C3×D418yes—
501C32×C4—21no—
502C32×C4—21no—
503C32×C4—21no—
504C32×C4—24no—
505C32×C4—24no—
506C32×C4—24no—
507C32×C4—32no—
508C32×C4—44no—
509C32×C4—44no—
510C32×C4—44no—
511C32×C4—61no—
512C32×C4—61no—
513C32×C4—61no—
514C32×C4—61no—
515C32×C4—61no—
516C3×Dic3—24no—
517C3×Dic3—24no—
518C3×Dic3—24no—
519C3×Dic3—24no—
520C3×Dic3—24no—
521C3×Dic3C2×C3×D418yes—
522C2×#41—31no—
523C22×D4—31no—
524#124—31no—
525#123—31no—
526#123—31no—
527C22⋊Q8—31no—
528#121—31no—
529#121—31no—
530#121—31no—
531#120—31no—
532#120C32×D311yescharacteristic, complemented
533C4×D4—31no—
534C4×D4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C33#54611yescharacteristic, complemented, Sylow
538C23×C3—28no—
539C23×C3—28no—
540C23×C3—22no—
541C23×C3—22no—
542C23×C3—24no—
543C23×C3—24no—
544C23×C3—24no—
545C23×C3—24no—
546C23×C3—34no—
547C23×C3—34no—
548C23×C3—48no—
549C23×C3—48no—
550C23×C3—44no—
551C23×C3—41no—
552C23×C3—48no—
553C23×C3—68no—
554C23×C3—68no—
555C23×C3—124no—
556C23×C3C22×C3×D314yes—
557C23×C3C22×C3×D314yes—
558C23×C3C22×C3×D314yes—
559C23×C3C22×C3×D314yes—
560C23×C3C23×C3211yescharacteristic
561C23×C3C23×C3211yescharacteristic
562C23×C3C23×C3211yescharacteristic
563C23×C3C23×C3211yescharacteristic
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—41no—
567C22×D3C23×C3211yescharacteristic
568C22×D3C23×C3211yescharacteristic
569C3×Q8—68no—
570C3×D4—28no—
571C3×D4—28no—
572C3×D4—22no—
573C3×D4—22no—
574C3×D4—316no—
575C3×D4—48no—
576C3×D4—48no—
577C3×D4—44no—
578C3×D4—41no—
579C3×D4—48no—
580C3×D4—68no—
581C3×D4—68no—
582C3×D4—68no—
583C3×D4—68no—
584C3×D4—124no—
585C2×C3×C4—24no—
586C2×C3×C4—24no—
587C2×C3×C4—24no—
588C2×C3×C4—34no—
589C2×C3×C4—34no—
590C2×C3×C4—34no—
591C2×C3×C4—34no—
592C2×C3×C4—34no—
593C2×C3×C4—34no—
594C2×C3×C4—68no—
595C2×C3×C4—68no—
596C2×C3×C4—68no—
597C2×C3×C4—68no—
598C2×C3×C4—124no—
599C2×C3×C4—124no—
600C2×C3×C4C22×C3×D314yes—
601C2×C3×C4C22×C3×D314yes—
602C2×C3×C4C22×C3×D314yes—
603C2×C3×C4C23×C3211yescharacteristic
604C2×C3×C4C23×C3211yescharacteristic
605C2×C3×C4C23×C3211yescharacteristic
606#67—22no—
607#67—22no—
608#67—22no—
609#67—22no—
610#67—41no—
611#67C32×D414yescomplemented
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—41no—
616C2×Dic3C23×C3211yescharacteristic
617C2×Dic3C23×C3211yescharacteristic
618C2×Dic3C23×C3211yescharacteristic
619C2×Dic3C23×C3211yescharacteristic
620C2×Dic3C23×C3211yescharacteristic
621C2×Dic3C23×C3211yescharacteristic
622C4×D3—22no—
623C4×D3—41no—
624Dic6—22no—
625C2×C32—22no—
626C2×C32—22no—
627C2×C32—24no—
628C2×C32—24no—
629C2×C32—24no—
630C2×C32—28no—
631C2×C32—28no—
632C2×C32—48no—
633C2×C32—48no—
634C2×C32—48no—
635C2×C32—41no—
636C2×C32—41no—
637C2×C32—44no—
638C2×C32—44no—
639C2×C32—62no—
640C2×C32—84no—
641C2×C32—121no—
642C2×C32C2×D3×D411yescharacteristic
643C2×C32C2×#23711yescharacteristic
644C2×C32#100411yescharacteristic
645C2×C32C22×C3×D414yes—
646C2×C32C2×C3×#4114yes—
647C2×C32C3×H(5,𝔽2)14yes—
648C3×D3—28no—
649C3×D3—44no—
650C24—31no—
651C24C2×C32×D311yescharacteristic
652#41—64no—
653C2×Q8—31no—
654C2×D4—31no—
655C2×D4—31no—
656C2×D4—31no—
657C2×D4—31no—
658C2×D4—31no—
659C2×D4—31no—
660C2×D4—64no—
661C2×D4C2×C32×D311yescharacteristic
662C2×D4C2×C32×D311yescharacteristic, complemented
663C2×D4C2×C32×D311yescharacteristic, complemented
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—31no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—31no—
670C4⋊C4—31no—
671C4⋊C4—31no—
672C4⋊C4—31no—
673C4⋊C4—31no—
674C22⋊C4—31no—
675C22⋊C4—31no—
676C22⋊C4—31no—
677C22⋊C4—31no—
678C22⋊C4—31no—
679C22⋊C4—31no—
680C22⋊C4—31no—
681C22⋊C4—31no—
682C22⋊C4—31no—
683C22⋊C4C2×C32×D311yescharacteristic
684C22⋊C4C2×C32×D311yescharacteristic, complemented
685C22⋊C4C2×C32×D311yescharacteristic, complemented
686C42—31no—
687C22×C3—24no—
688C22×C3—24no—
689C22×C3—24no—
690C22×C3—24no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—28no—
696C22×C3—24no—
697C22×C3—24no—
698C22×C3—24no—
699C22×C3—24no—
700C22×C3—24no—
701C22×C3—24no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—24no—
709C22×C3—28no—
710C22×C3—28no—
711C22×C3—38no—
712C22×C3—44no—
713C22×C3—44no—
714C22×C3—44no—
715C22×C3—44no—
716C22×C3—44no—
717C22×C3—44no—
718C22×C3—44no—
719C22×C3—44no—
720C22×C3—44no—
721C22×C3—416no—
722C22×C3—44no—
723C22×C3—432no—
724C22×C3—64no—
725C22×C3—64no—
726C22×C3—64no—
727C22×C3—64no—
728C22×C3—64no—
729C22×C3—1216no—
730C22×C3C3×D3×D418yes—
731C22×C3C3×#23718yescomplemented
732C22×C3C2×C32×D412yes—
733C22×C3C32×#4112yescomplemented
734C22×C3C23×C3×D314yes—
735C22×C3C24×C3211yescharacteristic
736C2×D3—21no—
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—44no—
742C2×D3C2×C32×D412yes—
743C3×C4—24no—
744C3×C4—24no—
745C3×C4—24no—
746C3×C4—21no—
747C3×C4—21no—
748C3×C4—21no—
749C3×C4—38no—
750C3×C4—44no—
751C3×C4—44no—
752C3×C4—44no—
753C3×C4—64no—
754C3×C4—64no—
755C3×C4—64no—
756C3×C4—64no—
757C3×C4—64no—
758Dic3—21no—
759Dic3—21no—
760Dic3—21no—
761Dic3—21no—
762Dic3—21no—
763Dic3C2×C32×D412yes—
764C32—24no—
765C32#559111yescharacteristic, direct product factor
766C32C3×#54614yescomplemented
767C23—22no—
768C23—22no—
769C23—31no—
770C23—31no—
771C23—41no—
772C23—62no—
773C23—62no—
774C23—121no—
775C23C22×C32×D311yescharacteristic
776C23C22×C32×D311yescharacteristic
777C23C22×C32×D311yescharacteristic
778C23C22×C32×D311yescharacteristic
779Q8—62no—
780D4—22no—
781D4—22no—
782D4—34no—
783D4—41no—
784D4—62no—
785D4—62no—
786D4—62no—
787D4—62no—
788D4—121no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—31no—
792C2×C4—31no—
793C2×C4—31no—
794C2×C4—31no—
795C2×C4—62no—
796C2×C4—62no—
797C2×C4—62no—
798C2×C4—62no—
799C2×C4—121no—
800C2×C4—121no—
801C2×C4C22×C32×D311yescharacteristic
802C2×C4C22×C32×D311yescharacteristic
803C2×C4C22×C32×D311yescharacteristic
804C2×C3—28no—
805C2×C3—28no—
806C2×C3—22no—
807C2×C3—22no—
808C2×C3—24no—
809C2×C3—24no—
810C2×C3—24no—
811C2×C3—48no—
812C2×C3—48no—
813C2×C3—48no—
814C2×C3—44no—
815C2×C3—44no—
816C2×C3—41no—
817C2×C3—41no—
818C2×C3—68no—
819C2×C3—84no—
820C2×C3—124no—
821C2×C3C2×C3×D3×D414yes—
822C2×C3C2×C3×#23714yes—
823C2×C3C3×#100414yes—
824C2×C3C22×C32×D411yescharacteristic
825C2×C3C2×C32×#4111yescharacteristic
826C2×C3C32×H(5,𝔽2)11yescharacteristic
827D3—22no—
828D3—41no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—32no—
840C22—44no—
841C22—61no—
842C22—61no—
843C22—61no—
844C22—61no—
845C22—61no—
846C22—124no—
847C22C32×D3×D412yes—
848C22C32×#23712yescomplemented
849C22C23×C32×D311yescharacteristic
850C4—21no—
851C4—21no—
852C4—21no—
853C4—32no—
854C4—61no—
855C4—61no—
856C4—61no—
857C4—61no—
858C4—61no—
859C3—24no—
860C3C3×#559114yesdirect product factor
861C3C32×#54611yescharacteristic, complemented
862C2—22no—
863C2—22no—
864C2—41no—
865C2—41no—
866C2—62no—
867C2—121no—
868C2C2×C32×D3×D411yescharacteristic
869C2C2×C32×#23711yescharacteristic
870C2C32×#100411yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#120C2
socleC22×C33C24
hypercenterC32×#120D3
hypocenterC3C32×#546
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×#120

Complements

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

NH ≅ G/Ntype
1. C22×C32×#67C2semidirect
2. C2×C32×#237C2semidirect
3. C33×#120C2semidirect
4. C2×C32×#217C2semidirect
5. C32×#939C2semidirect
6. C32×#939C2semidirect
7. C32×#938C2semidirect
8. C32×#937C2semidirect
9. C32×D4×Dic3C2semidirect
10. C32×#886C2semidirect
11. C32×#885C2semidirect
12. C32×#883C2semidirect
13. C32×#67⋊C4C2semidirect
14. C32×D3×C22⋊C4C2semidirect
15. C32×#878C2semidirect
17. C3×#5591C3direct (N × H)
21. C2×C33×D4C22semidirect
22. C2×C33×D4C22semidirect
28. C2×C32×#67C22semidirect
29. C2×C32×#67C22semidirect
31. C22×C32×Dic3C22semidirect
32. C22×C32×Dic3C22semidirect
33. C22×C32×Dic3C22semidirect
35. C2×C32×C4×D3C22semidirect
36. C2×C32×C4×D3C22semidirect
37. C2×C32×Dic6C22semidirect
39. C33×C22⋊C4C22semidirect
40. C33×C22⋊C4C22semidirect
43. C32×#217C22semidirect
44. C32×#217C22semidirect
45. C32×#217C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. C32×(C2×D3)⋊C4C22semidirect
48. C32×(C2×D3)⋊C4C22semidirect
49. C32×(C2×D3)⋊C4C22semidirect
50. C32×C4⋊Dic3C22semidirect
51. C32×C4⋊Dic3C22semidirect
52. C32×Dic3⋊C4C22semidirect
53. C32×Dic3⋊C4C22semidirect
54. C32×C4×Dic3C22semidirect
57. C22×C3×#67C2×C3semidirect
58. C2×C3×#237C2×C3semidirect
68. C32×#120D3semidirect
69. C32×#120C2×C3semidirect
74. C2×C3×#217C2×C3semidirect
75. C3×#939C2×C3semidirect
76. C3×#939C2×C3semidirect
77. C3×#938C2×C3semidirect
78. C3×#937C2×C3semidirect
79. C3×D4×Dic3C2×C3semidirect
80. C3×#886C2×C3semidirect
81. C3×#885C2×C3semidirect
82. C3×#883C2×C3semidirect
83. C3×#67⋊C4C2×C3semidirect
84. C3×D3×C22⋊C4C2×C3semidirect
85. C3×#878C2×C3semidirect
109. C32×#67D4semidirect
124. #5591C32direct (N × H)
143. C2×C32×D4C2×D3semidirect
144. C2×C32×D4C2×D3semidirect
146. C2×C32×D4C22×C3semidirect
147. C2×C32×D4C22×C3semidirect
159. C2×C3×#67C22×C3semidirect
160. C2×C3×#67C22×C3semidirect
162. C22×C3×Dic3C22×C3semidirect
163. C22×C3×Dic3C22×C3semidirect
164. C22×C3×Dic3C22×C3semidirect
166. C2×C3×C4×D3C22×C3semidirect
167. C2×C3×C4×D3C22×C3semidirect
168. C2×C3×Dic6C22×C3semidirect
186. C32×C22⋊C4C2×D3semidirect
187. C32×C22⋊C4C2×D3semidirect
189. C32×C22⋊C4C22×C3semidirect
190. C32×C22⋊C4C22×C3semidirect
194. C3×#217C22×C3semidirect
195. C3×#217C22×C3semidirect
196. C3×#217C22×C3semidirect
197. C3×(C2×D3)⋊C4C22×C3semidirect
198. C3×(C2×D3)⋊C4C22×C3semidirect
199. C3×(C2×D3)⋊C4C22×C3semidirect
200. C3×(C2×D3)⋊C4C22×C3semidirect
201. C3×C4⋊Dic3C22×C3semidirect
202. C3×C4⋊Dic3C22×C3semidirect
203. C3×Dic3⋊C4C22×C3semidirect
204. C3×Dic3⋊C4C22×C3semidirect
205. C3×C4×Dic3C22×C3semidirect
218. C22×C33#41semidirect
238. C22×#67C2×C32semidirect
239. C2×#237C2×C32semidirect
249. C3×#120C3×D3semidirect
250. C3×#120C2×C32semidirect
255. C2×#217C2×C32semidirect
256. #939C2×C32semidirect
257. #939C2×C32semidirect
258. #938C2×C32semidirect
259. #937C2×C32semidirect
260. D4×Dic3C2×C32semidirect
261. #886C2×C32semidirect
262. #885C2×C32semidirect
263. #883C2×C32semidirect
264. #67⋊C4C2×C32semidirect
265. D3×C22⋊C4C2×C32semidirect
266. #878C2×C32semidirect
340. C3×#67C3×D4semidirect
382. C2×C3×D4C2×C3×D3semidirect
383. C2×C3×D4C2×C3×D3semidirect
385. C2×C3×D4C22×C32semidirect
386. C2×C3×D4C22×C32semidirect
398. C2×#67C22×C32semidirect
399. C2×#67C22×C32semidirect
401. C22×Dic3C22×C32semidirect
402. C22×Dic3C22×C32semidirect
403. C22×Dic3C22×C32semidirect
405. C2×C4×D3C22×C32semidirect
406. C2×C4×D3C22×C32semidirect
407. C2×Dic6C22×C32semidirect
425. C3×C22⋊C4C2×C3×D3semidirect
426. C3×C22⋊C4C2×C3×D3semidirect
428. C3×C22⋊C4C22×C32semidirect
429. C3×C22⋊C4C22×C32semidirect
433. #217C22×C32semidirect
434. #217C22×C32semidirect
435. #217C22×C32semidirect
436. (C2×D3)⋊C4C22×C32semidirect
437. (C2×D3)⋊C4C22×C32semidirect
438. (C2×D3)⋊C4C22×C32semidirect
439. (C2×D3)⋊C4C22×C32semidirect
440. C4⋊Dic3C22×C32semidirect
441. C4⋊Dic3C22×C32semidirect
442. Dic3⋊C4C22×C32semidirect
443. Dic3⋊C4C22×C32semidirect
444. C4×Dic3C22×C32semidirect
489. C22×C32#237semidirect
491. C22×C32C3×#41semidirect
532. #120C32×D3semidirect
537. C33#546semidirect
611. #67C32×D4semidirect
662. C2×D4C2×C32×D3semidirect
663. C2×D4C2×C32×D3semidirect
684. C22⋊C4C2×C32×D3semidirect
685. C22⋊C4C2×C32×D3semidirect
731. C22×C3C3×#237semidirect
733. C22×C3C32×#41semidirect
765. C32#5591direct (N × H)
766. C32C3×#546semidirect
848. C22C32×#237semidirect
860. C3C3×#5591direct (N × H)
861. C3C32×#546semidirect

Maximal subgroups

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

subgroupindex
C22×C32×#672
C2×C32×#2372
C33×#1202
C2×C32×#2172
C32×#9392
C32×#9382
C32×#9372
C32×D4×Dic32
C32×#8862
C32×#8852
C32×#8832
C32×#67⋊C42
C32×D3×C22⋊C42
C32×#8782
C32×#5463
C3×#55913