Finite Group Databasebeta

← C32×#5654 #13179035

Subgroups — C32×#5654 #13179035

Order 1728.

2316 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×D3×D4C211yesmaximal, characteristic, complemented
2C2×C32×#235C211yesmaximal, characteristic, complemented
3C33×#123C211yesmaximal, characteristic, complemented
4C32×#939C211yesmaximal, characteristic, complemented
5C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C32×#896C211yesmaximal, characteristic, complemented
7C32×#895C211yesmaximal, characteristic, complemented
8C32×#894C211yesmaximal, characteristic, complemented
9C32×#893C211yesmaximal, characteristic, complemented
10C32×#885C211yesmaximal, characteristic, complemented
11C32×#884C211yesmaximal, characteristic, complemented
12C32×#882C211yesmaximal, characteristic, complemented
13C32×#882C211yesmaximal, characteristic, complemented
14C32×#67⋊C4C211yesmaximal, characteristic, complemented
15C32×D3×C22⋊C4C211yesmaximal, characteristic, complemented
16C32×#546—31nomaximal
17C3×#5654C314yesmaximal, direct product factor
18C23×C32×D3C2211yescharacteristic
19C23×C32×D3C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic
21C22×C33×C4C2211yescharacteristic, complemented
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic, complemented
26C22×C32×Dic3C2211yescharacteristic, complemented
27C32×D3×D4—24no—
28C32×#235—24no—
29C2×C32×D12C2211yescharacteristic
30C2×C32×D12C2211yescharacteristic
31C2×C32×D12C2211yescharacteristic, complemented
32C2×C32×D12C2211yescharacteristic, complemented
33C2×C32×C4×D3C2211yescharacteristic
34C2×C32×C4×D3C2211yescharacteristic, complemented
35C2×C32×C4×D3C2211yescharacteristic, complemented
36C2×C32×C4×D3C2211yescharacteristic, complemented
37C2×C32×Dic6C2211yescharacteristic, complemented
38C33×C4⋊C4C2211yescharacteristic, complemented
39C33×C4⋊C4C2211yescharacteristic, complemented
40C33×C22⋊C4C2211yescharacteristic, complemented
41C33×C22⋊C4C2211yescharacteristic, complemented
42C33×C22⋊C4C2211yescharacteristic, 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×(C2×D3)⋊C4C2211yescharacteristic, complemented
52C32×Dic3⋊C4C2211yescharacteristic, complemented
53C32×Dic3⋊C4C2211yescharacteristic, complemented
54C32×C4×Dic3C2211yescharacteristic, complemented
55C2×C32×#41—31no—
56C22×C32×D4—31no—
57C2×C3×D3×D4C2×C314yescomplemented
58C2×C3×#235C2×C314yescomplemented
59C32×#124—31no—
60C32×#123—24no—
61C32×#123—31no—
62C32×#123D311yescharacteristic, complemented
63C32×#123C2×C314yescomplemented
64C32×C22⋊Q8—31no—
65C32×#121—31no—
66C32×#121—31no—
67C32×#121—31no—
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
75C2×C3×(C2×D3)⋊C4C2×C314yescomplemented
76C3×#896C2×C314yescomplemented
77C3×#895C2×C314yescomplemented
78C3×#894C2×C314yescomplemented
79C3×#893C2×C314yescomplemented
80C3×#885C2×C314yescomplemented
81C3×#884C2×C314yescomplemented
82C3×#882C2×C314yescomplemented
83C3×#882C2×C314yescomplemented
84C3×#67⋊C4C2×C314yescomplemented
85C3×D3×C22⋊C4C2×C314yescomplemented
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C32×D3—22no—
89C22×C32×D3—22no—
90C22×C32×D3—22no—
91C22×C32×D3—22no—
92C22×C32×D3—41no—
93C22×C32×D3—41no—
94C22×C32×D3C2311yescharacteristic
95C22×C32×D3C2311yescharacteristic
96C22×C32×D3C2311yescharacteristic
97C22×C32×D3C2311yescharacteristic
98C33×D4—22no—
99C2×C33×C4—22no—
100C2×C33×C4C2311yescharacteristic
101C2×C33×C4C2311yescharacteristic
102C2×C33×C4C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C32×#67—22no—
106C32×#67—22no—
107C32×#67—41no—
108C32×#67D414yescomplemented
109C2×C32×Dic3—41no—
110C2×C32×Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C32×D12—22no—
115C32×D12—22no—
116C32×D12—22no—
117C32×D12—41no—
118C32×C4×D3—22no—
119C32×C4×D3—22no—
120C32×C4×D3—22no—
121C32×C4×D3—41no—
122C32×Dic6—22no—
123C3×#546—34no—
124#5654C3211yescharacteristic, 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—31no—
133C2×C32×D4—31no—
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×D4C22×C314yes—
143C22×C32×C4—24no—
144C22×C32×C4—31no—
145C22×C32×C4—31no—
146C22×C32×C4—31no—
147C22×C32×C4—31no—
148C22×C32×C4—31no—
149C22×C32×C4C2×D311yescharacteristic, complemented
150C22×C32×C4C22×C314yescomplemented
151C2×C3×#67C22×C314yes—
152C2×C3×#67C22×C314yes—
153C2×C3×#67C22×C314yescomplemented
154C2×C3×#67C22×C314yescomplemented
155C22×C3×Dic3C22×C314yescomplemented
156C3×D3×D4—216no—
157C3×#235—216no—
158C2×C3×D12C22×C314yes—
159C2×C3×D12C22×C314yes—
160C2×C3×D12C22×C314yescomplemented
161C2×C3×D12C22×C314yescomplemented
162C2×C3×C4×D3C22×C314yes—
163C2×C3×C4×D3C22×C314yescomplemented
164C2×C3×C4×D3C22×C314yescomplemented
165C2×C3×C4×D3C22×C314yescomplemented
166C2×C3×Dic6C22×C314yescomplemented
167C32×C4⋊C4—24no—
168C32×C4⋊C4—24no—
169C32×C4⋊C4—31no—
170C32×C4⋊C4—31no—
171C32×C4⋊C4C2×D311yescharacteristic, complemented
172C32×C4⋊C4C2×D311yescharacteristic, complemented
173C32×C4⋊C4C22×C314yescomplemented
174C32×C4⋊C4C22×C314yescomplemented
175C32×C22⋊C4—24no—
176C32×C22⋊C4—24no—
177C32×C22⋊C4—24no—
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⋊C4C2×D311yescharacteristic, complemented
190C32×C22⋊C4C22×C314yescomplemented
191C32×C22⋊C4C22×C314yescomplemented
192C32×C22⋊C4C22×C314yescomplemented
193C32×C42—31no—
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×(C2×D3)⋊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×C33C2×D412yes—
212C22×C33C2411yescharacteristic
213C2×C32×D3—21no—
214C2×C32×D3—21no—
215C2×C32×D3—21no—
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—
231C33×C4—21no—
232C32×Dic3—21no—
233C32×Dic3—21no—
234C32×Dic3—21no—
235C32×Dic3C2×D412yes—
236C2×C3×#41—34no—
237C22×C3×D4—34no—
238C2×D3×D4C2×C3211yescharacteristic, complemented
239C2×#235C2×C3211yescharacteristic, complemented
240C3×#124—34no—
241C3×#123—24no—
242C3×#123—34no—
243C3×#123C3×D314yescomplemented
244C3×#123C2×C3211yescharacteristic, complemented
245C3×C22⋊Q8—34no—
246C3×#121—34no—
247C3×#121—34no—
248C3×#121—34no—
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
256C2×(C2×D3)⋊C4C2×C3211yescharacteristic, complemented
257#896C2×C3211yescharacteristic, complemented
258#895C2×C3211yescharacteristic, complemented
259#894C2×C3211yescharacteristic, complemented
260#893C2×C3211yescharacteristic, complemented
261#885C2×C3211yescharacteristic, complemented
262#884C2×C3211yescharacteristic, complemented
263#882C2×C3211yescharacteristic, complemented
264#882C2×C3211yescharacteristic, complemented
265#67⋊C4C2×C3211yescharacteristic, complemented
266D3×C22⋊C4C2×C3211yescharacteristic, complemented
267C23×C32—24no—
268C23×C32—24no—
269C23×C32—31no—
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×C32C23×C314yes—
282C23×C32C23×C314yes—
283C22×C3×D3—28no—
284C22×C3×D3—28no—
285C22×C3×D3—28no—
286C22×C3×D3—28no—
287C22×C3×D3—44no—
288C22×C3×D3—44no—
289C22×C3×D3C23×C314yes—
290C22×C3×D3C23×C314yes—
291C22×C3×D3C23×C314yes—
292C22×C3×D3C23×C314yes—
293C32×Q8—62no—
294C32×D4—22no—
295C32×D4—28no—
296C32×D4—34no—
297C32×D4—48no—
298C32×D4—62no—
299C32×D4—62no—
300C32×D4—62no—
301C32×D4—62no—
302C32×D4—62no—
303C32×D4—121no—
304C32×D4—121no—
305C2×C32×C4—22no—
306C2×C32×C4—24no—
307C2×C32×C4—24no—
308C2×C32×C4—24no—
309C2×C32×C4—24no—
310C2×C32×C4—24no—
311C2×C32×C4—28no—
312C2×C32×C4—31no—
313C2×C32×C4—31no—
314C2×C32×C4—31no—
315C2×C32×C4—31no—
316C2×C32×C4—48no—
317C2×C32×C4—62no—
318C2×C32×C4—62no—
319C2×C32×C4—62no—
320C2×C32×C4—121no—
321C2×C32×C4—121no—
322C2×C32×C4C22×D311yescharacteristic
323C2×C32×C4C22×D311yescharacteristic
324C2×C32×C4C22×D311yescharacteristic
325C2×C32×C4C22×D311yescharacteristic
326C2×C32×C4C22×D311yescharacteristic
327C2×C32×C4C23×C314yes—
328C2×C32×C4C23×C314yes—
329C2×C32×C4C23×C314yes—
330C2×C32×C4C23×C314yes—
331C2×C32×C4C23×C314yes—
332C3×#67—28no—
333C3×#67—28no—
334C3×#67—44no—
335C3×#67C3×D4116yescomplemented
336C2×C3×Dic3—44no—
337C2×C3×Dic3C23×C314yes—
338C2×C3×Dic3C23×C314yes—
339C2×C3×Dic3C23×C314yes—
340C2×C3×Dic3C23×C314yes—
341C3×D12—28no—
342C3×D12—28no—
343C3×D12—28no—
344C3×D12—44no—
345C3×C4×D3—28no—
346C3×C4×D3—28no—
347C3×C4×D3—28no—
348C3×C4×D3—44no—
349C3×Dic6—28no—
350#546—31noSylow
351C2×C33—22no—
352C2×C33—41no—
353C2×C33C22×D411yescharacteristic
354C2×C33C2×#4111yescharacteristic
355C2×C33H(5,𝔽2)11yescharacteristic
356C32×D3—22no—
357C32×D3—22no—
358C32×D3—41no—
359C32×D3—41no—
360C24×C3—34no—
361C24×C3—34no—
362C23×D3C22×C3211yescharacteristic
363C23×D3C22×C3211yescharacteristic
364C3×#41—616no—
365C2×C3×Q8—34no—
366C2×C3×D4—24no—
367C2×C3×D4—34no—
368C2×C3×D4—34no—
369C2×C3×D4—34no—
370C2×C3×D4—34no—
371C2×C3×D4—34no—
372C2×C3×D4—34no—
373C2×C3×D4—34no—
374C2×C3×D4—34no—
375C2×C3×D4—616no—
376C2×C3×D4C2×C3×D314yes—
377C2×C3×D4C22×C3211yescharacteristic
378C22×C3×C4—24no—
379C22×C3×C4—34no—
380C22×C3×C4—34no—
381C22×C3×C4—34no—
382C22×C3×C4—34no—
383C22×C3×C4—34no—
384C22×C3×C4C2×C3×D314yescomplemented
385C22×C3×C4C22×C3211yescharacteristic, complemented
386C2×#67C22×C3211yescharacteristic
387C2×#67C22×C3211yescharacteristic
388C2×#67C22×C3211yescharacteristic, complemented
389C2×#67C22×C3211yescharacteristic, complemented
390C22×Dic3C22×C3211yescharacteristic, complemented
391D3×D4—24no—
392#235—24no—
393C2×D12C22×C3211yescharacteristic
394C2×D12C22×C3211yescharacteristic
395C2×D12C22×C3211yescharacteristic, complemented
396C2×D12C22×C3211yescharacteristic, complemented
397C2×C4×D3C22×C3211yescharacteristic
398C2×C4×D3C22×C3211yescharacteristic, complemented
399C2×C4×D3C22×C3211yescharacteristic, complemented
400C2×C4×D3C22×C3211yescharacteristic, complemented
401C2×Dic6C22×C3211yescharacteristic, complemented
402C3×C4⋊C4—24no—
403C3×C4⋊C4—24no—
404C3×C4⋊C4—34no—
405C3×C4⋊C4—34no—
406C3×C4⋊C4C2×C3×D314yescomplemented
407C3×C4⋊C4C2×C3×D314yescomplemented
408C3×C4⋊C4C22×C3211yescharacteristic, complemented
409C3×C4⋊C4C22×C3211yescharacteristic, complemented
410C3×C22⋊C4—24no—
411C3×C22⋊C4—24no—
412C3×C22⋊C4—24no—
413C3×C22⋊C4—34no—
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⋊C4C2×C3×D314yescomplemented
423C3×C22⋊C4C2×C3×D314yescomplemented
424C3×C22⋊C4C2×C3×D314yescomplemented
425C3×C22⋊C4C22×C3211yescharacteristic, complemented
426C3×C22⋊C4C22×C3211yescharacteristic, complemented
427C3×C22⋊C4C22×C3211yescharacteristic, complemented
428C3×C42—34no—
429#217C22×C3211yescharacteristic, complemented
430(C2×D3)⋊C4C22×C3211yescharacteristic
431(C2×D3)⋊C4C22×C3211yescharacteristic
432(C2×D3)⋊C4C22×C3211yescharacteristic
433(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
434(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
435(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
436(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
437(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
438Dic3⋊C4C22×C3211yescharacteristic, complemented
439Dic3⋊C4C22×C3211yescharacteristic, complemented
440C4×Dic3C22×C3211yescharacteristic, complemented
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—24no—
447C22×C32—28no—
448C22×C32—24no—
449C22×C32—24no—
450C22×C32—24no—
451C22×C32—24no—
452C22×C32—24no—
453C22×C32—32no—
454C22×C32—32no—
455C22×C32—44no—
456C22×C32—44no—
457C22×C32—44no—
458C22×C32—44no—
459C22×C32—44no—
460C22×C32—61no—
461C22×C32—61no—
462C22×C32—61no—
463C22×C32—61no—
464C22×C32—61no—
465C22×C32—61no—
466C22×C32—61no—
467C22×C32—61no—
468C22×C32—61no—
469C22×C32—61no—
470C22×C32—124no—
471C22×C32—124no—
472C22×C32D3×D412yes—
473C22×C32C2×C3×D418yes—
474C22×C32C23×D311yescharacteristic
475C22×C32C24×C314yes—
476C2×C3×D3—24no—
477C2×C3×D3—24no—
478C2×C3×D3—24no—
479C2×C3×D3—24no—
480C2×C3×D3—24no—
481C2×C3×D3—24no—
482C2×C3×D3—24no—
483C2×C3×D3—24no—
484C2×C3×D3—24no—
485C2×C3×D3—24no—
486C2×C3×D3—416no—
487C2×C3×D3—416no—
488C2×C3×D3C2×C3×D418yes—
489C2×C3×D3C3×#4118yescomplemented
490C32×C4—21no—
491C32×C4—21no—
492C32×C4—21no—
493C32×C4—21no—
494C32×C4—21no—
495C32×C4—24no—
496C32×C4—24no—
497C32×C4—24no—
498C32×C4—24no—
499C32×C4—24no—
500C32×C4—32no—
501C32×C4—44no—
502C32×C4—44no—
503C32×C4—44no—
504C32×C4—44no—
505C32×C4—44no—
506C32×C4—61no—
507C32×C4—61no—
508C32×C4—61no—
509C3×Dic3—24no—
510C3×Dic3—24no—
511C3×Dic3—24no—
512C3×Dic3C2×C3×D418yes—
513C2×#41—31no—
514C22×D4—31no—
515#124—31no—
516#123—31no—
517#123C32×D311yescharacteristic, complemented
518C22⋊Q8—31no—
519#121—31no—
520#121—31no—
521#121—31no—
522#120—31no—
523#120—31no—
524C4×D4—31no—
525C4×D4—31no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—31no—
528C33#54611yescharacteristic, complemented, Sylow
529C23×C3—24no—
530C23×C3—24no—
531C23×C3—34no—
532C23×C3—34no—
533C23×C3—34no—
534C23×C3—34no—
535C23×C3—68no—
536C23×C3—68no—
537C23×C3—68no—
538C23×C3—68no—
539C23×C3—124no—
540C23×C3—124no—
541C23×C3C22×C3×D314yes—
542C23×C3C22×C3×D314yes—
543C23×C3C23×C3211yescharacteristic
544C23×C3C23×C3211yescharacteristic
545C22×D3—22no—
546C22×D3—22no—
547C22×D3—22no—
548C22×D3—22no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3C23×C3211yescharacteristic
552C22×D3C23×C3211yescharacteristic
553C22×D3C23×C3211yescharacteristic
554C22×D3C23×C3211yescharacteristic
555C3×Q8—68no—
556C3×D4—28no—
557C3×D4—22no—
558C3×D4—316no—
559C3×D4—48no—
560C3×D4—68no—
561C3×D4—68no—
562C3×D4—68no—
563C3×D4—68no—
564C3×D4—68no—
565C3×D4—124no—
566C3×D4—124no—
567C2×C3×C4—28no—
568C2×C3×C4—22no—
569C2×C3×C4—24no—
570C2×C3×C4—24no—
571C2×C3×C4—24no—
572C2×C3×C4—24no—
573C2×C3×C4—24no—
574C2×C3×C4—34no—
575C2×C3×C4—34no—
576C2×C3×C4—34no—
577C2×C3×C4—34no—
578C2×C3×C4—48no—
579C2×C3×C4—68no—
580C2×C3×C4—68no—
581C2×C3×C4—68no—
582C2×C3×C4—124no—
583C2×C3×C4—124no—
584C2×C3×C4C22×C3×D314yes—
585C2×C3×C4C22×C3×D314yes—
586C2×C3×C4C22×C3×D314yes—
587C2×C3×C4C22×C3×D314yes—
588C2×C3×C4C22×C3×D314yes—
589C2×C3×C4C23×C3211yescharacteristic
590C2×C3×C4C23×C3211yescharacteristic
591C2×C3×C4C23×C3211yescharacteristic
592C2×C3×C4C23×C3211yescharacteristic
593C2×C3×C4C23×C3211yescharacteristic
594#67—22no—
595#67—22no—
596#67—41no—
597#67C32×D414yescomplemented
598C2×Dic3—41no—
599C2×Dic3C23×C3211yescharacteristic
600C2×Dic3C23×C3211yescharacteristic
601C2×Dic3C23×C3211yescharacteristic
602C2×Dic3C23×C3211yescharacteristic
603D12—22no—
604D12—22no—
605D12—22no—
606D12—41no—
607C4×D3—22no—
608C4×D3—22no—
609C4×D3—22no—
610C4×D3—41no—
611Dic6—22no—
612C2×C32—22no—
613C2×C32—24no—
614C2×C32—24no—
615C2×C32—24no—
616C2×C32—28no—
617C2×C32—48no—
618C2×C32—41no—
619C2×C32—44no—
620C2×C32—62no—
621C2×C32—62no—
622C2×C32—84no—
623C2×C32—121no—
624C2×C32—121no—
625C2×C32C2×D3×D411yescharacteristic
626C2×C32D3×#4111yescharacteristic
627C2×C32#100911yescharacteristic
628C2×C32C22×C3×D414yes—
629C2×C32C2×C3×#4114yes—
630C2×C32C3×H(5,𝔽2)14yes—
631C3×D3—28no—
632C3×D3—28no—
633C3×D3—44no—
634C3×D3—44no—
635C24—31no—
636C24—31no—
637#41—64no—
638C2×Q8—31no—
639C2×D4—31no—
640C2×D4—31no—
641C2×D4—31no—
642C2×D4—31no—
643C2×D4—31no—
644C2×D4—31no—
645C2×D4—31no—
646C2×D4—31no—
647C2×D4—64no—
648C2×D4C2×C32×D311yescharacteristic
649C22×C4—31no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—31no—
653C22×C4—31no—
654C22×C4C2×C32×D311yescharacteristic, complemented
655C4⋊C4—31no—
656C4⋊C4—31no—
657C4⋊C4C2×C32×D311yescharacteristic, complemented
658C4⋊C4C2×C32×D311yescharacteristic, complemented
659C22⋊C4—31no—
660C22⋊C4—31no—
661C22⋊C4—31no—
662C22⋊C4—31no—
663C22⋊C4—31no—
664C22⋊C4—31no—
665C22⋊C4—31no—
666C22⋊C4—31no—
667C22⋊C4—31no—
668C22⋊C4C2×C32×D311yescharacteristic, complemented
669C22⋊C4C2×C32×D311yescharacteristic, complemented
670C22⋊C4C2×C32×D311yescharacteristic, complemented
671C42—31no—
672C22×C3—24no—
673C22×C3—24no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—24no—
677C22×C3—24no—
678C22×C3—24no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—24no—
683C22×C3—28no—
684C22×C3—38no—
685C22×C3—38no—
686C22×C3—44no—
687C22×C3—44no—
688C22×C3—44no—
689C22×C3—44no—
690C22×C3—44no—
691C22×C3—64no—
692C22×C3—64no—
693C22×C3—64no—
694C22×C3—64no—
695C22×C3—64no—
696C22×C3—64no—
697C22×C3—64no—
698C22×C3—64no—
699C22×C3—64no—
700C22×C3—64no—
701C22×C3—1216no—
702C22×C3—1216no—
703C22×C3C3×D3×D418yes—
704C22×C3C2×C32×D412yes—
705C22×C3C23×C3×D314yes—
706C22×C3C24×C3211yescharacteristic
707C2×D3—21no—
708C2×D3—21no—
709C2×D3—21no—
710C2×D3—21no—
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—21no—
714C2×D3—21no—
715C2×D3—21no—
716C2×D3—21no—
717C2×D3—44no—
718C2×D3—44no—
719C2×D3C2×C32×D412yes—
720C2×D3C32×#4112yescomplemented
721C3×C4—24no—
722C3×C4—24no—
723C3×C4—24no—
724C3×C4—24no—
725C3×C4—24no—
726C3×C4—21no—
727C3×C4—21no—
728C3×C4—21no—
729C3×C4—21no—
730C3×C4—21no—
731C3×C4—38no—
732C3×C4—44no—
733C3×C4—44no—
734C3×C4—44no—
735C3×C4—44no—
736C3×C4—44no—
737C3×C4—64no—
738C3×C4—64no—
739C3×C4—64no—
740Dic3—21no—
741Dic3—21no—
742Dic3—21no—
743Dic3C2×C32×D412yes—
744C32—24no—
745C32#565411yescharacteristic, direct product factor
746C32C3×#54614yescomplemented
747C23—31no—
748C23—31no—
749C23—31no—
750C23—31no—
751C23—62no—
752C23—62no—
753C23—62no—
754C23—62no—
755C23—121no—
756C23—121no—
757C23C22×C32×D311yescharacteristic
758C23C22×C32×D311yescharacteristic
759Q8—62no—
760D4—22no—
761D4—34no—
762D4—62no—
763D4—62no—
764D4—62no—
765D4—62no—
766D4—62no—
767D4—121no—
768D4—121no—
769C2×C4—22no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—31no—
773C2×C4—31no—
774C2×C4—62no—
775C2×C4—62no—
776C2×C4—62no—
777C2×C4—121no—
778C2×C4—121no—
779C2×C4C22×C32×D311yescharacteristic
780C2×C4C22×C32×D311yescharacteristic
781C2×C4C22×C32×D311yescharacteristic
782C2×C4C22×C32×D311yescharacteristic
783C2×C4C22×C32×D311yescharacteristic
784C2×C3—28no—
785C2×C3—22no—
786C2×C3—24no—
787C2×C3—24no—
788C2×C3—24no—
789C2×C3—48no—
790C2×C3—44no—
791C2×C3—41no—
792C2×C3—68no—
793C2×C3—68no—
794C2×C3—84no—
795C2×C3—124no—
796C2×C3—124no—
797C2×C3C2×C3×D3×D414yes—
798C2×C3C3×D3×#4114yes—
799C2×C3C3×#100914yes—
800C2×C3C22×C32×D411yescharacteristic
801C2×C3C2×C32×#4111yescharacteristic
802C2×C3C32×H(5,𝔽2)11yescharacteristic
803D3—22no—
804D3—22no—
805D3—41no—
806D3—41no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—32no—
813C22—32no—
814C22—61no—
815C22—61no—
816C22—61no—
817C22—61no—
818C22—61no—
819C22—61no—
820C22—61no—
821C22—61no—
822C22—61no—
823C22—61no—
824C22—124no—
825C22—124no—
826C22C32×D3×D412yes—
827C22C23×C32×D311yescharacteristic
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—32no—
834C4—61no—
835C4—61no—
836C4—61no—
837C3—24no—
838C3C3×#565414yesdirect product factor
839C3C32×#54611yescharacteristic, complemented
840C2—22no—
841C2—41no—
842C2—62no—
843C2—62no—
844C2—121no—
845C2—121no—
846C2C2×C32×D3×D411yescharacteristic
847C2C32×D3×#4111yescharacteristic
848C2C32×#100911yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#123C2
socleC22×C33C24
hypercenterC32×#123D3
hypocenterC3C32×#546
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×#123

Complements

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

NH ≅ G/Ntype
1. C2×C32×D3×D4C2semidirect
2. C2×C32×#235C2semidirect
3. C33×#123C2semidirect
4. C32×#939C2semidirect
5. C2×C32×(C2×D3)⋊C4C2semidirect
6. C32×#896C2semidirect
7. C32×#895C2semidirect
8. C32×#894C2semidirect
9. C32×#893C2semidirect
10. C32×#885C2semidirect
11. C32×#884C2semidirect
12. C32×#882C2semidirect
13. C32×#882C2semidirect
14. C32×#67⋊C4C2semidirect
15. C32×D3×C22⋊C4C2semidirect
17. C3×#5654C3direct (N × H)
21. C22×C33×C4C22semidirect
24. C2×C32×#67C22semidirect
25. C2×C32×#67C22semidirect
26. C22×C32×Dic3C22semidirect
31. C2×C32×D12C22semidirect
32. C2×C32×D12C22semidirect
34. C2×C32×C4×D3C22semidirect
35. C2×C32×C4×D3C22semidirect
36. C2×C32×C4×D3C22semidirect
37. C2×C32×Dic6C22semidirect
38. C33×C4⋊C4C22semidirect
39. C33×C4⋊C4C22semidirect
40. C33×C22⋊C4C22semidirect
41. C33×C22⋊C4C22semidirect
42. C33×C22⋊C4C22semidirect
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×(C2×D3)⋊C4C22semidirect
52. C32×Dic3⋊C4C22semidirect
53. C32×Dic3⋊C4C22semidirect
54. C32×C4×Dic3C22semidirect
57. C2×C3×D3×D4C2×C3semidirect
58. C2×C3×#235C2×C3semidirect
62. C32×#123D3semidirect
63. C32×#123C2×C3semidirect
74. C3×#939C2×C3semidirect
75. C2×C3×(C2×D3)⋊C4C2×C3semidirect
76. C3×#896C2×C3semidirect
77. C3×#895C2×C3semidirect
78. C3×#894C2×C3semidirect
79. C3×#893C2×C3semidirect
80. C3×#885C2×C3semidirect
81. C3×#884C2×C3semidirect
82. C3×#882C2×C3semidirect
83. C3×#882C2×C3semidirect
84. C3×#67⋊C4C2×C3semidirect
85. C3×D3×C22⋊C4C2×C3semidirect
108. C32×#67D4semidirect
124. #5654C32direct (N × H)
149. C22×C32×C4C2×D3semidirect
150. C22×C32×C4C22×C3semidirect
153. C2×C3×#67C22×C3semidirect
154. C2×C3×#67C22×C3semidirect
155. C22×C3×Dic3C22×C3semidirect
160. C2×C3×D12C22×C3semidirect
161. C2×C3×D12C22×C3semidirect
163. C2×C3×C4×D3C22×C3semidirect
164. C2×C3×C4×D3C22×C3semidirect
165. C2×C3×C4×D3C22×C3semidirect
166. C2×C3×Dic6C22×C3semidirect
171. C32×C4⋊C4C2×D3semidirect
172. C32×C4⋊C4C2×D3semidirect
173. C32×C4⋊C4C22×C3semidirect
174. C32×C4⋊C4C22×C3semidirect
187. C32×C22⋊C4C2×D3semidirect
188. C32×C22⋊C4C2×D3semidirect
189. C32×C22⋊C4C2×D3semidirect
190. C32×C22⋊C4C22×C3semidirect
191. C32×C22⋊C4C22×C3semidirect
192. C32×C22⋊C4C22×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×(C2×D3)⋊C4C22×C3semidirect
203. C3×Dic3⋊C4C22×C3semidirect
204. C3×Dic3⋊C4C22×C3semidirect
205. C3×C4×Dic3C22×C3semidirect
226. C2×C32×D3#41semidirect
238. C2×D3×D4C2×C32semidirect
239. C2×#235C2×C32semidirect
243. C3×#123C3×D3semidirect
244. C3×#123C2×C32semidirect
255. #939C2×C32semidirect
256. C2×(C2×D3)⋊C4C2×C32semidirect
257. #896C2×C32semidirect
258. #895C2×C32semidirect
259. #894C2×C32semidirect
260. #893C2×C32semidirect
261. #885C2×C32semidirect
262. #884C2×C32semidirect
263. #882C2×C32semidirect
264. #882C2×C32semidirect
265. #67⋊C4C2×C32semidirect
266. D3×C22⋊C4C2×C32semidirect
335. C3×#67C3×D4semidirect
384. C22×C3×C4C2×C3×D3semidirect
385. C22×C3×C4C22×C32semidirect
388. C2×#67C22×C32semidirect
389. C2×#67C22×C32semidirect
390. C22×Dic3C22×C32semidirect
395. C2×D12C22×C32semidirect
396. C2×D12C22×C32semidirect
398. C2×C4×D3C22×C32semidirect
399. C2×C4×D3C22×C32semidirect
400. C2×C4×D3C22×C32semidirect
401. C2×Dic6C22×C32semidirect
406. C3×C4⋊C4C2×C3×D3semidirect
407. C3×C4⋊C4C2×C3×D3semidirect
408. C3×C4⋊C4C22×C32semidirect
409. C3×C4⋊C4C22×C32semidirect
422. C3×C22⋊C4C2×C3×D3semidirect
423. C3×C22⋊C4C2×C3×D3semidirect
424. C3×C22⋊C4C2×C3×D3semidirect
425. C3×C22⋊C4C22×C32semidirect
426. C3×C22⋊C4C22×C32semidirect
427. C3×C22⋊C4C22×C32semidirect
429. #217C22×C32semidirect
433. (C2×D3)⋊C4C22×C32semidirect
434. (C2×D3)⋊C4C22×C32semidirect
435. (C2×D3)⋊C4C22×C32semidirect
436. (C2×D3)⋊C4C22×C32semidirect
437. (C2×D3)⋊C4C22×C32semidirect
438. Dic3⋊C4C22×C32semidirect
439. Dic3⋊C4C22×C32semidirect
440. C4×Dic3C22×C32semidirect
489. C2×C3×D3C3×#41semidirect
517. #123C32×D3semidirect
528. C33#546semidirect
597. #67C32×D4semidirect
654. C22×C4C2×C32×D3semidirect
657. C4⋊C4C2×C32×D3semidirect
658. C4⋊C4C2×C32×D3semidirect
668. C22⋊C4C2×C32×D3semidirect
669. C22⋊C4C2×C32×D3semidirect
670. C22⋊C4C2×C32×D3semidirect
720. C2×D3C32×#41semidirect
745. C32#5654direct (N × H)
746. C32C3×#546semidirect
838. C3C3×#5654direct (N × H)
839. C3C32×#546semidirect

Maximal subgroups

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

subgroupindex
C2×C32×D3×D42
C2×C32×#2352
C33×#1232
C32×#9392
C2×C32×(C2×D3)⋊C42
C32×#8962
C32×#8952
C32×#8942
C32×#8932
C32×#8852
C32×#8842
C32×#8822
C32×#67⋊C42
C32×D3×C22⋊C42
C32×#5463
C3×#56543