Finite Group Databasebeta

← C32×#5610 #13178989

Subgroups — C32×#5610 #13178989

Order 1728.

2380 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#237C211yesmaximal, characteristic, complemented
2C2×C32×D3×D4C211yesmaximal, characteristic, complemented
3C33×#121C211yesmaximal, characteristic, complemented
4C32×#939C211yesmaximal, characteristic, complemented
5C32×#937C211yesmaximal, characteristic, complemented
6C32×#937C211yesmaximal, characteristic, complemented
7C32×#935C211yesmaximal, characteristic, complemented
8C32×C4×#67C211yesmaximal, characteristic, complemented
9C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C32×#896C211yesmaximal, characteristic, complemented
11C32×#894C211yesmaximal, characteristic, complemented
12C32×#885C211yesmaximal, characteristic, complemented
13C32×#884C211yesmaximal, characteristic, complemented
14C32×#67⋊C4C211yesmaximal, characteristic, complemented
15C32×D3×C22⋊C4C211yesmaximal, characteristic, complemented
16C32×#546—31nomaximal
17C3×#5610C314yesmaximal, direct product factor
18C23×C32×D3C2211yescharacteristic
19C23×C32×D3C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic
21C2×C33×D4C2211yescharacteristic, complemented
22C2×C33×D4C2211yescharacteristic, complemented
23C22×C33×C4C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C2×C32×#67C2211yescharacteristic
27C2×C32×#67C2211yescharacteristic, complemented
28C2×C32×#67C2211yescharacteristic, complemented
29C22×C32×Dic3C2211yescharacteristic, complemented
30C22×C32×Dic3C2211yescharacteristic, complemented
31C32×#237—24no—
32C32×D3×D4—24no—
33C2×C32×D12C2211yescharacteristic
34C2×C32×C4×D3C2211yescharacteristic
35C2×C32×C4×D3C2211yescharacteristic, complemented
36C2×C32×C4×D3C2211yescharacteristic, complemented
37C2×C32×Dic6C2211yescharacteristic, complemented
38C33×C4⋊C4C2211yescharacteristic, complemented
39C33×C22⋊C4C2211yescharacteristic, complemented
40C33×C22⋊C4C2211yescharacteristic, complemented
41C32×#217C2211yescharacteristic, complemented
42C32×#217C2211yescharacteristic, complemented
43C32×#217C2211yescharacteristic, complemented
44C32×(C2×D3)⋊C4C2211yescharacteristic
45C32×(C2×D3)⋊C4C2211yescharacteristic
46C32×(C2×D3)⋊C4C2211yescharacteristic
47C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C32×Dic3⋊C4C2211yescharacteristic, complemented
52C32×Dic3⋊C4C2211yescharacteristic, complemented
53C32×Dic3⋊C4C2211yescharacteristic, complemented
54C32×C4×Dic3C2211yescharacteristic, complemented
55C2×C32×#41—31no—
56C22×C32×D4—31no—
57C2×C3×#237C2×C314yescomplemented
58C2×C3×D3×D4C2×C314yescomplemented
59C32×#124—31no—
60C32×#123—31no—
61C32×#123—31no—
62C32×C22⋊Q8—31no—
63C32×#121—24no—
64C32×#121—31no—
65C32×#121—31no—
66C32×#121D311yescharacteristic, complemented
67C32×#121C2×C314yescomplemented
68C32×#120—31no—
69C32×#120—31no—
70C32×C4×D4—31no—
71C32×C4×D4—31no—
72C2×C32×C22⋊C4—31no—
73C2×C32×C22⋊C4—31no—
74C3×#939C2×C314yescomplemented
75C3×#937C2×C314yescomplemented
76C3×#937C2×C314yescomplemented
77C3×#935C2×C314yescomplemented
78C3×C4×#67C2×C314yescomplemented
79C2×C3×(C2×D3)⋊C4C2×C314yescomplemented
80C3×#896C2×C314yescomplemented
81C3×#894C2×C314yescomplemented
82C3×#885C2×C314yescomplemented
83C3×#884C2×C314yescomplemented
84C3×#67⋊C4C2×C314yescomplemented
85C3×D3×C22⋊C4C2×C314yescomplemented
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C23×C33C2311yescharacteristic
89C22×C32×D3—22no—
90C22×C32×D3—22no—
91C22×C32×D3—22no—
92C22×C32×D3—22no—
93C22×C32×D3—41no—
94C22×C32×D3—41no—
95C22×C32×D3C2311yescharacteristic
96C22×C32×D3C2311yescharacteristic
97C22×C32×D3C2311yescharacteristic
98C33×D4—22no—
99C33×D4—22no—
100C33×D4—41no—
101C2×C33×C4—41no—
102C2×C33×C4C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C32×#67—22no—
107C32×#67—22no—
108C32×#67—22no—
109C32×#67—41no—
110C32×#67D414yescomplemented
111C2×C32×Dic3—22no—
112C2×C32×Dic3—22no—
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C32×D12—22no—
119C32×C4×D3—22no—
120C32×C4×D3—22no—
121C32×C4×D3—41no—
122C32×Dic6—22no—
123C3×#546—34no—
124#5610C3211yescharacteristic, direct product factor
125C24×C32—31no—
126C24×C32—31no—
127C23×C3×D3C22×C314yes—
128C23×C3×D3C22×C314yes—
129C32×#41—64no—
130C2×C32×Q8—31no—
131C2×C32×D4—24no—
132C2×C32×D4—24no—
133C2×C32×D4—24no—
134C2×C32×D4—31no—
135C2×C32×D4—31no—
136C2×C32×D4—31no—
137C2×C32×D4—31no—
138C2×C32×D4—31no—
139C2×C32×D4—31no—
140C2×C32×D4—64no—
141C2×C32×D4C2×D311yescharacteristic
142C2×C32×D4C2×D311yescharacteristic, complemented
143C2×C32×D4C2×D311yescharacteristic, complemented
144C2×C32×D4C22×C314yes—
145C2×C32×D4C22×C314yescomplemented
146C2×C32×D4C22×C314yescomplemented
147C22×C32×C4—24no—
148C22×C32×C4—31no—
149C22×C32×C4—31no—
150C22×C32×C4—31no—
151C22×C32×C4—31no—
152C22×C32×C4—31no—
153C22×C32×C4C2×D311yescharacteristic, complemented
154C22×C32×C4C22×C314yescomplemented
155C2×C3×#67C22×C314yes—
156C2×C3×#67C22×C314yes—
157C2×C3×#67C22×C314yes—
158C2×C3×#67C22×C314yescomplemented
159C2×C3×#67C22×C314yescomplemented
160C22×C3×Dic3C22×C314yescomplemented
161C22×C3×Dic3C22×C314yescomplemented
162C3×#237—216no—
163C3×D3×D4—216no—
164C2×C3×D12C22×C314yes—
165C2×C3×C4×D3C22×C314yes—
166C2×C3×C4×D3C22×C314yescomplemented
167C2×C3×C4×D3C22×C314yescomplemented
168C2×C3×Dic6C22×C314yescomplemented
169C32×C4⋊C4—24no—
170C32×C4⋊C4—31no—
171C32×C4⋊C4—31no—
172C32×C4⋊C4—31no—
173C32×C4⋊C4C2×D311yescharacteristic, complemented
174C32×C4⋊C4C22×C314yescomplemented
175C32×C22⋊C4—24no—
176C32×C22⋊C4—24no—
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⋊C4—31no—
186C32×C22⋊C4—31no—
187C32×C22⋊C4C2×D311yescharacteristic, complemented
188C32×C22⋊C4C2×D311yescharacteristic, complemented
189C32×C22⋊C4C22×C314yescomplemented
190C32×C22⋊C4C22×C314yescomplemented
191C32×C42—31no—
192C3×#217C22×C314yescomplemented
193C3×#217C22×C314yescomplemented
194C3×#217C22×C314yescomplemented
195C3×(C2×D3)⋊C4C22×C314yes—
196C3×(C2×D3)⋊C4C22×C314yes—
197C3×(C2×D3)⋊C4C22×C314yes—
198C3×(C2×D3)⋊C4C22×C314yescomplemented
199C3×(C2×D3)⋊C4C22×C314yescomplemented
200C3×(C2×D3)⋊C4C22×C314yescomplemented
201C3×(C2×D3)⋊C4C22×C314yescomplemented
202C3×Dic3⋊C4C22×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×C33C2×D412yes—
215C22×C33C2411yescharacteristic
216C2×C32×D3—21no—
217C2×C32×D3—21no—
218C2×C32×D3—21no—
219C2×C32×D3—21no—
220C2×C32×D3—21no—
221C2×C32×D3—21no—
222C2×C32×D3—21no—
223C2×C32×D3—44no—
224C2×C32×D3—44no—
225C2×C32×D3C2×D412yes—
226C2×C32×D3#4112yescomplemented
227C33×C4—21no—
228C33×C4—21no—
229C33×C4—21no—
230C33×C4—21no—
231C32×Dic3—21no—
232C32×Dic3—21no—
233C32×Dic3—21no—
234C32×Dic3—21no—
235C32×Dic3C2×D412yes—
236C2×C3×#41—34no—
237C22×C3×D4—34no—
238C2×#237C2×C3211yescharacteristic, complemented
239C2×D3×D4C2×C3211yescharacteristic, complemented
240C3×#124—34no—
241C3×#123—34no—
242C3×#123—34no—
243C3×C22⋊Q8—34no—
244C3×#121—24no—
245C3×#121—34no—
246C3×#121—34no—
247C3×#121C3×D314yescomplemented
248C3×#121C2×C3211yescharacteristic, complemented
249C3×#120—34no—
250C3×#120—34no—
251C3×C4×D4—34no—
252C3×C4×D4—34no—
253C2×C3×C22⋊C4—34no—
254C2×C3×C22⋊C4—34no—
255#939C2×C3211yescharacteristic, complemented
256#937C2×C3211yescharacteristic, complemented
257#937C2×C3211yescharacteristic, complemented
258#935C2×C3211yescharacteristic, complemented
259C4×#67C2×C3211yescharacteristic, complemented
260C2×(C2×D3)⋊C4C2×C3211yescharacteristic, complemented
261#896C2×C3211yescharacteristic, complemented
262#894C2×C3211yescharacteristic, complemented
263#885C2×C3211yescharacteristic, complemented
264#884C2×C3211yescharacteristic, complemented
265#67⋊C4C2×C3211yescharacteristic, complemented
266D3×C22⋊C4C2×C3211yescharacteristic, complemented
267C23×C32—24no—
268C23×C32—24no—
269C23×C32—24no—
270C23×C32—31no—
271C23×C32—31no—
272C23×C32—31no—
273C23×C32—62no—
274C23×C32—62no—
275C23×C32—62no—
276C23×C32—62no—
277C23×C32—121no—
278C23×C32—121no—
279C23×C32C22×D311yescharacteristic
280C23×C32C22×D311yescharacteristic
281C23×C32C22×D311yescharacteristic
282C23×C32C23×C314yes—
283C23×C32C23×C314yes—
284C23×C32C23×C314yes—
285C22×C3×D3—28no—
286C22×C3×D3—28no—
287C22×C3×D3—28no—
288C22×C3×D3—28no—
289C22×C3×D3—44no—
290C22×C3×D3—44no—
291C22×C3×D3C23×C314yes—
292C22×C3×D3C23×C314yes—
293C22×C3×D3C23×C314yes—
294C32×Q8—62no—
295C32×D4—22no—
296C32×D4—22no—
297C32×D4—28no—
298C32×D4—28no—
299C32×D4—34no—
300C32×D4—48no—
301C32×D4—48no—
302C32×D4—41no—
303C32×D4—44no—
304C32×D4—48no—
305C32×D4—62no—
306C32×D4—62no—
307C32×D4—62no—
308C32×D4—62no—
309C32×D4—121no—
310C2×C32×C4—24no—
311C2×C32×C4—24no—
312C2×C32×C4—24no—
313C2×C32×C4—24no—
314C2×C32×C4—31no—
315C2×C32×C4—31no—
316C2×C32×C4—31no—
317C2×C32×C4—31no—
318C2×C32×C4—31no—
319C2×C32×C4—41no—
320C2×C32×C4—44no—
321C2×C32×C4—48no—
322C2×C32×C4—62no—
323C2×C32×C4—62no—
324C2×C32×C4—62no—
325C2×C32×C4—62no—
326C2×C32×C4—121no—
327C2×C32×C4C22×D311yescharacteristic
328C2×C32×C4C22×D311yescharacteristic
329C2×C32×C4C22×D311yescharacteristic
330C2×C32×C4C22×D311yescharacteristic
331C2×C32×C4C23×C314yes—
332C2×C32×C4C23×C314yes—
333C2×C32×C4C23×C314yes—
334C2×C32×C4C23×C314yes—
335C3×#67—28no—
336C3×#67—28no—
337C3×#67—28no—
338C3×#67—44no—
339C3×#67C3×D4116yescomplemented
340C2×C3×Dic3—28no—
341C2×C3×Dic3—28no—
342C2×C3×Dic3C23×C314yes—
343C2×C3×Dic3C23×C314yes—
344C2×C3×Dic3C23×C314yes—
345C2×C3×Dic3C23×C314yes—
346C2×C3×Dic3C23×C314yes—
347C3×D12—28no—
348C3×C4×D3—28no—
349C3×C4×D3—28no—
350C3×C4×D3—44no—
351C3×Dic6—28no—
352#546—31noSylow
353C2×C33—22no—
354C2×C33—41no—
355C2×C33—41no—
356C2×C33C22×D411yescharacteristic
357C2×C33C2×#4111yescharacteristic
358C2×C33H(5,𝔽2)11yescharacteristic
359C32×D3—22no—
360C32×D3—22no—
361C32×D3—41no—
362C24×C3—34no—
363C24×C3—34no—
364C23×D3C22×C3211yescharacteristic
365C23×D3C22×C3211yescharacteristic
366C3×#41—616no—
367C2×C3×Q8—34no—
368C2×C3×D4—24no—
369C2×C3×D4—24no—
370C2×C3×D4—24no—
371C2×C3×D4—34no—
372C2×C3×D4—34no—
373C2×C3×D4—34no—
374C2×C3×D4—34no—
375C2×C3×D4—34no—
376C2×C3×D4—34no—
377C2×C3×D4—616no—
378C2×C3×D4C2×C3×D314yes—
379C2×C3×D4C2×C3×D314yescomplemented
380C2×C3×D4C2×C3×D314yescomplemented
381C2×C3×D4C22×C3211yescharacteristic
382C2×C3×D4C22×C3211yescharacteristic, complemented
383C2×C3×D4C22×C3211yescharacteristic, complemented
384C22×C3×C4—24no—
385C22×C3×C4—34no—
386C22×C3×C4—34no—
387C22×C3×C4—34no—
388C22×C3×C4—34no—
389C22×C3×C4—34no—
390C22×C3×C4C2×C3×D314yescomplemented
391C22×C3×C4C22×C3211yescharacteristic, complemented
392C2×#67C22×C3211yescharacteristic
393C2×#67C22×C3211yescharacteristic
394C2×#67C22×C3211yescharacteristic
395C2×#67C22×C3211yescharacteristic, complemented
396C2×#67C22×C3211yescharacteristic, complemented
397C22×Dic3C22×C3211yescharacteristic, complemented
398C22×Dic3C22×C3211yescharacteristic, complemented
399#237—24no—
400D3×D4—24no—
401C2×D12C22×C3211yescharacteristic
402C2×C4×D3C22×C3211yescharacteristic
403C2×C4×D3C22×C3211yescharacteristic, complemented
404C2×C4×D3C22×C3211yescharacteristic, complemented
405C2×Dic6C22×C3211yescharacteristic, complemented
406C3×C4⋊C4—24no—
407C3×C4⋊C4—34no—
408C3×C4⋊C4—34no—
409C3×C4⋊C4—34no—
410C3×C4⋊C4C2×C3×D314yescomplemented
411C3×C4⋊C4C22×C3211yescharacteristic, complemented
412C3×C22⋊C4—24no—
413C3×C22⋊C4—24no—
414C3×C22⋊C4—34no—
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×D314yescomplemented
425C3×C22⋊C4C2×C3×D314yescomplemented
426C3×C22⋊C4C22×C3211yescharacteristic, complemented
427C3×C22⋊C4C22×C3211yescharacteristic, complemented
428C3×C42—34no—
429#217C22×C3211yescharacteristic, complemented
430#217C22×C3211yescharacteristic, complemented
431#217C22×C3211yescharacteristic, complemented
432(C2×D3)⋊C4C22×C3211yescharacteristic
433(C2×D3)⋊C4C22×C3211yescharacteristic
434(C2×D3)⋊C4C22×C3211yescharacteristic
435(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
436(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
437(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
438(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
439Dic3⋊C4C22×C3211yescharacteristic, complemented
440Dic3⋊C4C22×C3211yescharacteristic, complemented
441Dic3⋊C4C22×C3211yescharacteristic, complemented
442C4×Dic3C22×C3211yescharacteristic, complemented
443C22×C32—21no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—24no—
452C22×C32—28no—
453C22×C32—24no—
454C22×C32—24no—
455C22×C32—24no—
456C22×C32—24no—
457C22×C32—24no—
458C22×C32—24no—
459C22×C32—24no—
460C22×C32—24no—
461C22×C32—32no—
462C22×C32—32no—
463C22×C32—44no—
464C22×C32—44no—
465C22×C32—44no—
466C22×C32—44no—
467C22×C32—44no—
468C22×C32—44no—
469C22×C32—44no—
470C22×C32—44no—
471C22×C32—61no—
472C22×C32—61no—
473C22×C32—61no—
474C22×C32—61no—
475C22×C32—61no—
476C22×C32—61no—
477C22×C32—61no—
478C22×C32—124no—
479C22×C32—124no—
480C22×C32D3×D412yes—
481C22×C32C2×C3×D418yes—
482C22×C32C23×D311yescharacteristic
483C22×C32C24×C314yes—
484C2×C3×D3—24no—
485C2×C3×D3—24no—
486C2×C3×D3—24no—
487C2×C3×D3—24no—
488C2×C3×D3—24no—
489C2×C3×D3—24no—
490C2×C3×D3—24no—
491C2×C3×D3—416no—
492C2×C3×D3—416no—
493C2×C3×D3C2×C3×D418yes—
494C2×C3×D3C3×#4118yescomplemented
495C32×C4—28no—
496C32×C4—21no—
497C32×C4—21no—
498C32×C4—21no—
499C32×C4—21no—
500C32×C4—24no—
501C32×C4—24no—
502C32×C4—24no—
503C32×C4—24no—
504C32×C4—32no—
505C32×C4—44no—
506C32×C4—44no—
507C32×C4—44no—
508C32×C4—61no—
509C32×C4—61no—
510C32×C4—61no—
511C32×C4—61no—
512C3×Dic3—24no—
513C3×Dic3—24no—
514C3×Dic3—24no—
515C3×Dic3—24no—
516C3×Dic3C2×C3×D418yes—
517C2×#41—31no—
518C22×D4—31no—
519#124—31no—
520#123—31no—
521#123—31no—
522C22⋊Q8—31no—
523#121—31no—
524#121—31no—
525#121C32×D311yescharacteristic, complemented
526#120—31no—
527#120—31no—
528C4×D4—31no—
529C4×D4—31no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—31no—
532C33#54611yescharacteristic, complemented, Sylow
533C23×C3—24no—
534C23×C3—24no—
535C23×C3—24no—
536C23×C3—34no—
537C23×C3—34no—
538C23×C3—34no—
539C23×C3—68no—
540C23×C3—68no—
541C23×C3—68no—
542C23×C3—68no—
543C23×C3—124no—
544C23×C3—124no—
545C23×C3C22×C3×D314yes—
546C23×C3C22×C3×D314yes—
547C23×C3C22×C3×D314yes—
548C23×C3C23×C3211yescharacteristic
549C23×C3C23×C3211yescharacteristic
550C23×C3C23×C3211yescharacteristic
551C22×D3—22no—
552C22×D3—22no—
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—41no—
556C22×D3—41no—
557C22×D3C23×C3211yescharacteristic
558C22×D3C23×C3211yescharacteristic
559C22×D3C23×C3211yescharacteristic
560C3×Q8—68no—
561C3×D4—28no—
562C3×D4—28no—
563C3×D4—22no—
564C3×D4—22no—
565C3×D4—316no—
566C3×D4—48no—
567C3×D4—48no—
568C3×D4—44no—
569C3×D4—41no—
570C3×D4—48no—
571C3×D4—68no—
572C3×D4—68no—
573C3×D4—68no—
574C3×D4—68no—
575C3×D4—124no—
576C2×C3×C4—24no—
577C2×C3×C4—24no—
578C2×C3×C4—24no—
579C2×C3×C4—24no—
580C2×C3×C4—34no—
581C2×C3×C4—34no—
582C2×C3×C4—34no—
583C2×C3×C4—34no—
584C2×C3×C4—34no—
585C2×C3×C4—44no—
586C2×C3×C4—41no—
587C2×C3×C4—48no—
588C2×C3×C4—68no—
589C2×C3×C4—68no—
590C2×C3×C4—68no—
591C2×C3×C4—68no—
592C2×C3×C4—124no—
593C2×C3×C4C22×C3×D314yes—
594C2×C3×C4C22×C3×D314yes—
595C2×C3×C4C22×C3×D314yes—
596C2×C3×C4C22×C3×D314yes—
597C2×C3×C4C23×C3211yescharacteristic
598C2×C3×C4C23×C3211yescharacteristic
599C2×C3×C4C23×C3211yescharacteristic
600C2×C3×C4C23×C3211yescharacteristic
601#67—22no—
602#67—22no—
603#67—22no—
604#67—41no—
605#67C32×D414yescomplemented
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3C23×C3211yescharacteristic
609C2×Dic3C23×C3211yescharacteristic
610C2×Dic3C23×C3211yescharacteristic
611C2×Dic3C23×C3211yescharacteristic
612C2×Dic3C23×C3211yescharacteristic
613D12—22no—
614C4×D3—22no—
615C4×D3—22no—
616C4×D3—41no—
617Dic6—22no—
618C2×C32—22no—
619C2×C32—24no—
620C2×C32—24no—
621C2×C32—24no—
622C2×C32—28no—
623C2×C32—48no—
624C2×C32—41no—
625C2×C32—41no—
626C2×C32—44no—
627C2×C32—44no—
628C2×C32—62no—
629C2×C32—62no—
630C2×C32—84no—
631C2×C32—84no—
632C2×C32—121no—
633C2×C32C2×D3×D411yescharacteristic
634C2×C32#100411yescharacteristic
635C2×C32D3×#4111yescharacteristic
636C2×C32C22×C3×D414yes—
637C2×C32C2×C3×#4114yes—
638C2×C32C3×H(5,𝔽2)14yes—
639C3×D3—28no—
640C3×D3—28no—
641C3×D3—44no—
642C24—31no—
643C24—31no—
644#41—64no—
645C2×Q8—31no—
646C2×D4—31no—
647C2×D4—31no—
648C2×D4—31no—
649C2×D4—31no—
650C2×D4—31no—
651C2×D4—31no—
652C2×D4—64no—
653C2×D4C2×C32×D311yescharacteristic
654C2×D4C2×C32×D311yescharacteristic, complemented
655C2×D4C2×C32×D311yescharacteristic, complemented
656C22×C4—31no—
657C22×C4—31no—
658C22×C4—31no—
659C22×C4—31no—
660C22×C4—31no—
661C22×C4C2×C32×D311yescharacteristic, complemented
662C4⋊C4—31no—
663C4⋊C4—31no—
664C4⋊C4—31no—
665C4⋊C4C2×C32×D311yescharacteristic, complemented
666C22⋊C4—31no—
667C22⋊C4—31no—
668C22⋊C4—31no—
669C22⋊C4—31no—
670C22⋊C4—31no—
671C22⋊C4—31no—
672C22⋊C4—31no—
673C22⋊C4—31no—
674C22⋊C4—31no—
675C22⋊C4—31no—
676C22⋊C4C2×C32×D311yescharacteristic, complemented
677C22⋊C4C2×C32×D311yescharacteristic, complemented
678C42—31no—
679C22×C3—24no—
680C22×C3—24no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—24no—
684C22×C3—24no—
685C22×C3—24no—
686C22×C3—24no—
687C22×C3—24no—
688C22×C3—24no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—24no—
696C22×C3—28no—
697C22×C3—38no—
698C22×C3—38no—
699C22×C3—44no—
700C22×C3—44no—
701C22×C3—44no—
702C22×C3—44no—
703C22×C3—44no—
704C22×C3—44no—
705C22×C3—44no—
706C22×C3—44no—
707C22×C3—64no—
708C22×C3—64no—
709C22×C3—64no—
710C22×C3—64no—
711C22×C3—64no—
712C22×C3—64no—
713C22×C3—64no—
714C22×C3—1216no—
715C22×C3—1216no—
716C22×C3C3×D3×D418yes—
717C22×C3C2×C32×D412yes—
718C22×C3C23×C3×D314yes—
719C22×C3C24×C3211yescharacteristic
720C2×D3—21no—
721C2×D3—21no—
722C2×D3—21no—
723C2×D3—21no—
724C2×D3—21no—
725C2×D3—21no—
726C2×D3—21no—
727C2×D3—44no—
728C2×D3—44no—
729C2×D3C2×C32×D412yes—
730C2×D3C32×#4112yescomplemented
731C3×C4—28no—
732C3×C4—24no—
733C3×C4—24no—
734C3×C4—24no—
735C3×C4—24no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—21no—
740C3×C4—38no—
741C3×C4—44no—
742C3×C4—44no—
743C3×C4—44no—
744C3×C4—64no—
745C3×C4—64no—
746C3×C4—64no—
747C3×C4—64no—
748Dic3—21no—
749Dic3—21no—
750Dic3—21no—
751Dic3—21no—
752Dic3C2×C32×D412yes—
753C32—24no—
754C32#561011yescharacteristic, direct product factor
755C32C3×#54614yescomplemented
756C23—31no—
757C23—31no—
758C23—31no—
759C23—62no—
760C23—62no—
761C23—62no—
762C23—62no—
763C23—121no—
764C23—121no—
765C23C22×C32×D311yescharacteristic
766C23C22×C32×D311yescharacteristic
767C23C22×C32×D311yescharacteristic
768Q8—62no—
769D4—22no—
770D4—22no—
771D4—34no—
772D4—41no—
773D4—62no—
774D4—62no—
775D4—62no—
776D4—62no—
777D4—121no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—31no—
781C2×C4—31no—
782C2×C4—31no—
783C2×C4—41no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—121no—
789C2×C4C22×C32×D311yescharacteristic
790C2×C4C22×C32×D311yescharacteristic
791C2×C4C22×C32×D311yescharacteristic
792C2×C4C22×C32×D311yescharacteristic
793C2×C3—28no—
794C2×C3—22no—
795C2×C3—24no—
796C2×C3—24no—
797C2×C3—24no—
798C2×C3—48no—
799C2×C3—44no—
800C2×C3—44no—
801C2×C3—41no—
802C2×C3—41no—
803C2×C3—68no—
804C2×C3—68no—
805C2×C3—84no—
806C2×C3—84no—
807C2×C3—124no—
808C2×C3C2×C3×D3×D414yes—
809C2×C3C3×#100414yes—
810C2×C3C3×D3×#4114yes—
811C2×C3C22×C32×D411yescharacteristic
812C2×C3C2×C32×#4111yescharacteristic
813C2×C3C32×H(5,𝔽2)11yescharacteristic
814D3—22no—
815D3—22no—
816D3—41no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—32no—
826C22—32no—
827C22—61no—
828C22—61no—
829C22—61no—
830C22—61no—
831C22—61no—
832C22—61no—
833C22—61no—
834C22—124no—
835C22—124no—
836C22C32×D3×D412yes—
837C22C23×C32×D311yescharacteristic
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—32no—
843C4—61no—
844C4—61no—
845C4—61no—
846C4—61no—
847C3—24no—
848C3C3×#561014yesdirect product factor
849C3C32×#54611yescharacteristic, complemented
850C2—22no—
851C2—41no—
852C2—41no—
853C2—62no—
854C2—62no—
855C2—121no—
856C2C2×C32×D3×D411yescharacteristic
857C2C32×#100411yescharacteristic
858C2C32×D3×#4111yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#121C2
socleC22×C33C24
hypercenterC32×#121D3
hypocenterC3C32×#546
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×#121

Complements

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

NH ≅ G/Ntype
1. C2×C32×#237C2semidirect
2. C2×C32×D3×D4C2semidirect
3. C33×#121C2semidirect
4. C32×#939C2semidirect
5. C32×#937C2semidirect
6. C32×#937C2semidirect
7. C32×#935C2semidirect
8. C32×C4×#67C2semidirect
9. C2×C32×(C2×D3)⋊C4C2semidirect
10. C32×#896C2semidirect
11. C32×#894C2semidirect
12. C32×#885C2semidirect
13. C32×#884C2semidirect
14. C32×#67⋊C4C2semidirect
15. C32×D3×C22⋊C4C2semidirect
17. C3×#5610C3direct (N × H)
21. C2×C33×D4C22semidirect
22. C2×C33×D4C22semidirect
23. C22×C33×C4C22semidirect
27. C2×C32×#67C22semidirect
28. C2×C32×#67C22semidirect
29. C22×C32×Dic3C22semidirect
30. C22×C32×Dic3C22semidirect
35. C2×C32×C4×D3C22semidirect
36. C2×C32×C4×D3C22semidirect
37. C2×C32×Dic6C22semidirect
38. C33×C4⋊C4C22semidirect
39. C33×C22⋊C4C22semidirect
40. C33×C22⋊C4C22semidirect
41. C32×#217C22semidirect
42. C32×#217C22semidirect
43. C32×#217C22semidirect
47. C32×(C2×D3)⋊C4C22semidirect
48. C32×(C2×D3)⋊C4C22semidirect
49. C32×(C2×D3)⋊C4C22semidirect
50. C32×(C2×D3)⋊C4C22semidirect
51. C32×Dic3⋊C4C22semidirect
52. C32×Dic3⋊C4C22semidirect
53. C32×Dic3⋊C4C22semidirect
54. C32×C4×Dic3C22semidirect
57. C2×C3×#237C2×C3semidirect
58. C2×C3×D3×D4C2×C3semidirect
66. C32×#121D3semidirect
67. C32×#121C2×C3semidirect
74. C3×#939C2×C3semidirect
75. C3×#937C2×C3semidirect
76. C3×#937C2×C3semidirect
77. C3×#935C2×C3semidirect
78. C3×C4×#67C2×C3semidirect
79. C2×C3×(C2×D3)⋊C4C2×C3semidirect
80. C3×#896C2×C3semidirect
81. C3×#894C2×C3semidirect
82. C3×#885C2×C3semidirect
83. C3×#884C2×C3semidirect
84. C3×#67⋊C4C2×C3semidirect
85. C3×D3×C22⋊C4C2×C3semidirect
110. C32×#67D4semidirect
124. #5610C32direct (N × H)
142. C2×C32×D4C2×D3semidirect
143. C2×C32×D4C2×D3semidirect
145. C2×C32×D4C22×C3semidirect
146. C2×C32×D4C22×C3semidirect
153. C22×C32×C4C2×D3semidirect
154. C22×C32×C4C22×C3semidirect
158. C2×C3×#67C22×C3semidirect
159. C2×C3×#67C22×C3semidirect
160. C22×C3×Dic3C22×C3semidirect
161. C22×C3×Dic3C22×C3semidirect
166. C2×C3×C4×D3C22×C3semidirect
167. C2×C3×C4×D3C22×C3semidirect
168. C2×C3×Dic6C22×C3semidirect
173. C32×C4⋊C4C2×D3semidirect
174. C32×C4⋊C4C22×C3semidirect
187. C32×C22⋊C4C2×D3semidirect
188. C32×C22⋊C4C2×D3semidirect
189. C32×C22⋊C4C22×C3semidirect
190. C32×C22⋊C4C22×C3semidirect
192. C3×#217C22×C3semidirect
193. C3×#217C22×C3semidirect
194. C3×#217C22×C3semidirect
198. C3×(C2×D3)⋊C4C22×C3semidirect
199. C3×(C2×D3)⋊C4C22×C3semidirect
200. C3×(C2×D3)⋊C4C22×C3semidirect
201. C3×(C2×D3)⋊C4C22×C3semidirect
202. C3×Dic3⋊C4C22×C3semidirect
203. C3×Dic3⋊C4C22×C3semidirect
204. C3×Dic3⋊C4C22×C3semidirect
205. C3×C4×Dic3C22×C3semidirect
226. C2×C32×D3#41semidirect
238. C2×#237C2×C32semidirect
239. C2×D3×D4C2×C32semidirect
247. C3×#121C3×D3semidirect
248. C3×#121C2×C32semidirect
255. #939C2×C32semidirect
256. #937C2×C32semidirect
257. #937C2×C32semidirect
258. #935C2×C32semidirect
259. C4×#67C2×C32semidirect
260. C2×(C2×D3)⋊C4C2×C32semidirect
261. #896C2×C32semidirect
262. #894C2×C32semidirect
263. #885C2×C32semidirect
264. #884C2×C32semidirect
265. #67⋊C4C2×C32semidirect
266. D3×C22⋊C4C2×C32semidirect
339. C3×#67C3×D4semidirect
379. C2×C3×D4C2×C3×D3semidirect
380. C2×C3×D4C2×C3×D3semidirect
382. C2×C3×D4C22×C32semidirect
383. C2×C3×D4C22×C32semidirect
390. C22×C3×C4C2×C3×D3semidirect
391. C22×C3×C4C22×C32semidirect
395. C2×#67C22×C32semidirect
396. C2×#67C22×C32semidirect
397. C22×Dic3C22×C32semidirect
398. C22×Dic3C22×C32semidirect
403. C2×C4×D3C22×C32semidirect
404. C2×C4×D3C22×C32semidirect
405. C2×Dic6C22×C32semidirect
410. C3×C4⋊C4C2×C3×D3semidirect
411. C3×C4⋊C4C22×C32semidirect
424. C3×C22⋊C4C2×C3×D3semidirect
425. C3×C22⋊C4C2×C3×D3semidirect
426. C3×C22⋊C4C22×C32semidirect
427. C3×C22⋊C4C22×C32semidirect
429. #217C22×C32semidirect
430. #217C22×C32semidirect
431. #217C22×C32semidirect
435. (C2×D3)⋊C4C22×C32semidirect
436. (C2×D3)⋊C4C22×C32semidirect
437. (C2×D3)⋊C4C22×C32semidirect
438. (C2×D3)⋊C4C22×C32semidirect
439. Dic3⋊C4C22×C32semidirect
440. Dic3⋊C4C22×C32semidirect
441. Dic3⋊C4C22×C32semidirect
442. C4×Dic3C22×C32semidirect
494. C2×C3×D3C3×#41semidirect
525. #121C32×D3semidirect
532. C33#546semidirect
605. #67C32×D4semidirect
654. C2×D4C2×C32×D3semidirect
655. C2×D4C2×C32×D3semidirect
661. C22×C4C2×C32×D3semidirect
665. C4⋊C4C2×C32×D3semidirect
676. C22⋊C4C2×C32×D3semidirect
677. C22⋊C4C2×C32×D3semidirect
730. C2×D3C32×#41semidirect
754. C32#5610direct (N × H)
755. C32C3×#546semidirect
848. C3C3×#5610direct (N × H)
849. C3C32×#546semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2372
C2×C32×D3×D42
C33×#1212
C32×#9392
C32×#9372
C32×#9352
C32×C4×#672
C2×C32×(C2×D3)⋊C42
C32×#8962
C32×#8942
C32×#8852
C32×#8842
C32×#67⋊C42
C32×D3×C22⋊C42
C32×#5463
C3×#56103