Finite Group Databasebeta

← C32×#5640 #13179004

Subgroups — C32×#5640 #13179004

Order 1728.

1592 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×C22⋊Q8C211yesmaximal, characteristic, complemented
2C32×#947C211yesmaximal, characteristic, complemented
3C32×#944C211yesmaximal, characteristic, complemented
4C32×#929C211yesmaximal, characteristic, complemented
5C32×C4×#67C211yesmaximal, characteristic, complemented
6C32×#898C211yesmaximal, characteristic, complemented
7C32×#896C211yesmaximal, characteristic, complemented
8C32×#896C211yesmaximal, characteristic, complemented
9C32×#894C211yesmaximal, characteristic, complemented
10C32×#892C211yesmaximal, characteristic, complemented
11C32×#887C211yesmaximal, characteristic, complemented
12C32×#885C211yesmaximal, characteristic, complemented
13C32×#885C211yesmaximal, characteristic, complemented
14C32×#884C211yesmaximal, characteristic
15C32×#879C211yesmaximal, characteristic, complemented
16C32×#542—31nomaximal
17C3×#5640C314yesmaximal, direct product factor
18C2×C33×Q8C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C2×C32×D12C2211yescharacteristic
23C2×C32×C4×D3C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic
25C2×C32×Dic6C2211yescharacteristic
26C2×C32×Dic6C2211yescharacteristic
27C33×C4⋊C4C2211yescharacteristic
28C33×C4⋊C4C2211yescharacteristic
29C33×C4⋊C4C2211yescharacteristic
30C33×C22⋊C4C2211yescharacteristic
31C33×C22⋊C4C2211yescharacteristic
32C32×#217C2211yescharacteristic
33C32×#217C2211yescharacteristic
34C32×(C2×D3)⋊C4C2211yescharacteristic
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×(C2×D3)⋊C4C2211yescharacteristic
37C32×(C2×D3)⋊C4C2211yescharacteristic
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×(C2×D3)⋊C4C2211yescharacteristic
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×C4⋊Dic3C2211yescharacteristic
43C32×Dic3⋊C4C2211yescharacteristic
44C32×Dic3⋊C4C2211yescharacteristic
45C32×Dic3⋊C4C2211yescharacteristic
46C32×Dic3⋊C4C2211yescharacteristic
47C32×Dic3⋊C4C2211yescharacteristic
48C32×Dic3⋊C4C2211yescharacteristic
49C32×C4×Dic3C2211yescharacteristic
50C32×C4×Dic3C2211yescharacteristic
51C32×C4×Dic3C2211yescharacteristic
52C32×C4×Dic3C2211yescharacteristic
53C32×C4⋊Q8—31no—
54C32×#126—31no—
55C32×#126—31no—
56C32×#124—31no—
57C32×#124—31no—
58C32×#124—31no—
59C32×#123—31no—
60C32×#123—31no—
61C32×C22⋊Q8—24no—
62C32×C22⋊Q8—31no—
63C32×C22⋊Q8—31no—
64C32×C22⋊Q8D311yescharacteristic, complemented
65C32×C22⋊Q8C2×C314yescomplemented
66C32×#121—31no—
67C32×C4×Q8—31no—
68C32×C4×D4—31no—
69C32×#117—31no—
70C3×#947C2×C314yescomplemented
71C3×#944C2×C314yescomplemented
72C3×#929C2×C314yescomplemented
73C3×C4×#67C2×C314yescomplemented
74C3×#898C2×C314yescomplemented
75C3×#896C2×C314yescomplemented
76C3×#896C2×C314yescomplemented
77C3×#894C2×C314yescomplemented
78C3×#892C2×C314yescomplemented
79C3×#887C2×C314yescomplemented
80C3×#885C2×C314yescomplemented
81C3×#885C2×C314yescomplemented
82C3×#884C2×C314yes—
83C3×#879C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C22×C32×D3C2311yescharacteristic
86C22×C32×D3C2311yescharacteristic
87C33×Q8—41no—
88C2×C33×C4—41no—
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C32×#67—22no—
96C32×#67—41no—
97C2×C32×Dic3C2311yescharacteristic
98C2×C32×Dic3C2311yescharacteristic
99C2×C32×Dic3C2311yescharacteristic
100C2×C32×Dic3C2311yescharacteristic
101C2×C32×Dic3C2311yescharacteristic
102C2×C32×Dic3C2311yescharacteristic
103C32×D12—41no—
104C32×C4×D3—22no—
105C32×C4×D3—41no—
106C32×Dic6—22no—
107C32×Dic6—41no—
108C3×#542—34no—
109#5640C3211yescharacteristic, direct product factor
110C2×C32×Q8—24no—
111C2×C32×Q8—31no—
112C2×C32×Q8—31no—
113C2×C32×Q8C2×D311yescharacteristic
114C2×C32×Q8C22×C314yes—
115C2×C32×D4—31no—
116C2×C32×D4—31no—
117C2×C32×D4—31no—
118C22×C32×C4—24no—
119C22×C32×C4—31no—
120C22×C32×C4—31no—
121C22×C32×C4C2×D311yescharacteristic
122C22×C32×C4C22×C314yes—
123C2×C3×#67C22×C314yes—
124C2×C3×#67C22×C314yes—
125C2×C3×D12C22×C314yes—
126C2×C3×C4×D3C22×C314yes—
127C2×C3×C4×D3C22×C314yes—
128C2×C3×Dic6C22×C314yes—
129C2×C3×Dic6C22×C314yes—
130C32×C4⋊C4—24no—
131C32×C4⋊C4—24no—
132C32×C4⋊C4—24no—
133C32×C4⋊C4—31no—
134C32×C4⋊C4—31no—
135C32×C4⋊C4—31no—
136C32×C4⋊C4—31no—
137C32×C4⋊C4—31no—
138C32×C4⋊C4—31no—
139C32×C4⋊C4—31no—
140C32×C4⋊C4C2×D311yescharacteristic
141C32×C4⋊C4C2×D311yescharacteristic
142C32×C4⋊C4C2×D311yescharacteristic
143C32×C4⋊C4C22×C314yes—
144C32×C4⋊C4C22×C314yes—
145C32×C4⋊C4C22×C314yes—
146C32×C22⋊C4—24no—
147C32×C22⋊C4—24no—
148C32×C22⋊C4—31no—
149C32×C22⋊C4—31no—
150C32×C22⋊C4—31no—
151C32×C22⋊C4—31no—
152C32×C22⋊C4—31no—
153C32×C22⋊C4—31no—
154C32×C22⋊C4—31no—
155C32×C22⋊C4—31no—
156C32×C22⋊C4—31no—
157C32×C22⋊C4—31no—
158C32×C22⋊C4C2×D311yescharacteristic
159C32×C22⋊C4C2×D311yescharacteristic
160C32×C22⋊C4C22×C314yes—
161C32×C22⋊C4C22×C314yes—
162C32×C42—31no—
163C32×C42—31no—
164C32×C42—31no—
165C32×C42—31no—
166C3×#217C22×C314yes—
167C3×#217C22×C314yes—
168C3×(C2×D3)⋊C4C22×C314yes—
169C3×(C2×D3)⋊C4C22×C314yes—
170C3×(C2×D3)⋊C4C22×C314yes—
171C3×(C2×D3)⋊C4C22×C314yes—
172C3×(C2×D3)⋊C4C22×C314yes—
173C3×(C2×D3)⋊C4C22×C314yes—
174C3×(C2×D3)⋊C4C22×C314yes—
175C3×(C2×D3)⋊C4C22×C314yes—
176C3×C4⋊Dic3C22×C314yes—
177C3×Dic3⋊C4C22×C314yes—
178C3×Dic3⋊C4C22×C314yes—
179C3×Dic3⋊C4C22×C314yes—
180C3×Dic3⋊C4C22×C314yes—
181C3×Dic3⋊C4C22×C314yes—
182C3×Dic3⋊C4C22×C314yes—
183C3×C4×Dic3C22×C314yes—
184C3×C4×Dic3C22×C314yes—
185C3×C4×Dic3C22×C314yes—
186C3×C4×Dic3C22×C314yes—
187C22×C33—21no—
188C22×C33—21no—
189C22×C33—21no—
190C22×C33C2411yescharacteristic
191C2×C32×D3—21no—
192C2×C32×D3—21no—
193C2×C32×D3—21no—
194C2×C32×D3—21no—
195C2×C32×D3—21no—
196C2×C32×D3—21no—
197C33×C4—21no—
198C33×C4—21no—
199C33×C4—21no—
200C33×C4—21no—
201C33×C4—21no—
202C33×C4—21no—
203C32×Dic3—21no—
204C32×Dic3—21no—
205C32×Dic3—21no—
206C32×Dic3—21no—
207C32×Dic3—21no—
208C32×Dic3#4112yes—
209C3×C4⋊Q8—34no—
210C3×#126—34no—
211C3×#126—34no—
212C3×#124—34no—
213C3×#124—34no—
214C3×#124—34no—
215C3×#123—34no—
216C3×#123—34no—
217C3×C22⋊Q8—24no—
218C3×C22⋊Q8—34no—
219C3×C22⋊Q8—34no—
220C3×C22⋊Q8C3×D314yescomplemented
221C3×C22⋊Q8C2×C3211yescharacteristic, complemented
222C3×#121—34no—
223C3×C4×Q8—34no—
224C3×C4×D4—34no—
225C3×#117—34no—
226#947C2×C3211yescharacteristic, complemented
227#944C2×C3211yescharacteristic, complemented
228#929C2×C3211yescharacteristic, complemented
229C4×#67C2×C3211yescharacteristic, complemented
230#898C2×C3211yescharacteristic, complemented
231#896C2×C3211yescharacteristic, complemented
232#896C2×C3211yescharacteristic, complemented
233#894C2×C3211yescharacteristic, complemented
234#892C2×C3211yescharacteristic, complemented
235#887C2×C3211yescharacteristic, complemented
236#885C2×C3211yescharacteristic, complemented
237#885C2×C3211yescharacteristic, complemented
238#884C2×C3211yescharacteristic
239#879C2×C3211yescharacteristic, complemented
240C23×C32—24no—
241C23×C32—31no—
242C23×C32—31no—
243C23×C32C22×D311yescharacteristic
244C23×C32C23×C314yes—
245C22×C3×D3C23×C314yes—
246C22×C3×D3C23×C314yes—
247C32×Q8—41no—
248C32×Q8—44no—
249C32×Q8—48no—
250C32×Q8—62no—
251C32×Q8—121no—
252C32×D4—62no—
253C32×D4—121no—
254C32×D4—121no—
255C2×C32×C4—24no—
256C2×C32×C4—24no—
257C2×C32×C4—24no—
258C2×C32×C4—24no—
259C2×C32×C4—24no—
260C2×C32×C4—24no—
261C2×C32×C4—31no—
262C2×C32×C4—31no—
263C2×C32×C4—31no—
264C2×C32×C4—31no—
265C2×C32×C4—31no—
266C2×C32×C4—31no—
267C2×C32×C4—41no—
268C2×C32×C4—44no—
269C2×C32×C4—48no—
270C2×C32×C4—62no—
271C2×C32×C4—121no—
272C2×C32×C4C22×D311yescharacteristic
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C22×D311yescharacteristic
275C2×C32×C4C22×D311yescharacteristic
276C2×C32×C4C22×D311yescharacteristic
277C2×C32×C4C22×D311yescharacteristic
278C2×C32×C4C23×C314yes—
279C2×C32×C4C23×C314yes—
280C2×C32×C4C23×C314yes—
281C2×C32×C4C23×C314yes—
282C2×C32×C4C23×C314yes—
283C2×C32×C4C23×C314yes—
284C3×#67—28no—
285C3×#67—44no—
286C2×C3×Dic3C23×C314yes—
287C2×C3×Dic3C23×C314yes—
288C2×C3×Dic3C23×C314yes—
289C2×C3×Dic3C23×C314yes—
290C2×C3×Dic3C23×C314yes—
291C2×C3×Dic3C23×C314yes—
292C3×D12—44no—
293C3×C4×D3—28no—
294C3×C4×D3—44no—
295C3×Dic6—28no—
296C3×Dic6—44no—
297#542—31noSylow
298C2×C33—41no—
299C2×C33C2×#4111yescharacteristic
300C2×C33H(5,𝔽2)11yescharacteristic
301C2×C332−1+411yescharacteristic
302C32×D3—41no—
303C32×D3—41no—
304C2×C3×Q8—24no—
305C2×C3×Q8—34no—
306C2×C3×Q8—34no—
307C2×C3×Q8C2×C3×D314yes—
308C2×C3×Q8C22×C3211yescharacteristic
309C2×C3×D4—34no—
310C2×C3×D4—34no—
311C2×C3×D4—34no—
312C22×C3×C4—24no—
313C22×C3×C4—34no—
314C22×C3×C4—34no—
315C22×C3×C4C2×C3×D314yes—
316C22×C3×C4C22×C3211yescharacteristic
317C2×#67C22×C3211yescharacteristic
318C2×#67C22×C3211yescharacteristic
319C2×D12C22×C3211yescharacteristic
320C2×C4×D3C22×C3211yescharacteristic
321C2×C4×D3C22×C3211yescharacteristic
322C2×Dic6C22×C3211yescharacteristic
323C2×Dic6C22×C3211yescharacteristic
324C3×C4⋊C4—24no—
325C3×C4⋊C4—24no—
326C3×C4⋊C4—24no—
327C3×C4⋊C4—34no—
328C3×C4⋊C4—34no—
329C3×C4⋊C4—34no—
330C3×C4⋊C4—34no—
331C3×C4⋊C4—34no—
332C3×C4⋊C4—34no—
333C3×C4⋊C4—34no—
334C3×C4⋊C4C2×C3×D314yes—
335C3×C4⋊C4C2×C3×D314yes—
336C3×C4⋊C4C2×C3×D314yes—
337C3×C4⋊C4C22×C3211yescharacteristic
338C3×C4⋊C4C22×C3211yescharacteristic
339C3×C4⋊C4C22×C3211yescharacteristic
340C3×C22⋊C4—24no—
341C3×C22⋊C4—24no—
342C3×C22⋊C4—34no—
343C3×C22⋊C4—34no—
344C3×C22⋊C4—34no—
345C3×C22⋊C4—34no—
346C3×C22⋊C4—34no—
347C3×C22⋊C4—34no—
348C3×C22⋊C4—34no—
349C3×C22⋊C4—34no—
350C3×C22⋊C4—34no—
351C3×C22⋊C4—34no—
352C3×C22⋊C4C2×C3×D314yes—
353C3×C22⋊C4C2×C3×D314yes—
354C3×C22⋊C4C22×C3211yescharacteristic
355C3×C22⋊C4C22×C3211yescharacteristic
356C3×C42—34no—
357C3×C42—34no—
358C3×C42—34no—
359C3×C42—34no—
360#217C22×C3211yescharacteristic
361#217C22×C3211yescharacteristic
362(C2×D3)⋊C4C22×C3211yescharacteristic
363(C2×D3)⋊C4C22×C3211yescharacteristic
364(C2×D3)⋊C4C22×C3211yescharacteristic
365(C2×D3)⋊C4C22×C3211yescharacteristic
366(C2×D3)⋊C4C22×C3211yescharacteristic
367(C2×D3)⋊C4C22×C3211yescharacteristic
368(C2×D3)⋊C4C22×C3211yescharacteristic
369(C2×D3)⋊C4C22×C3211yescharacteristic
370C4⋊Dic3C22×C3211yescharacteristic
371Dic3⋊C4C22×C3211yescharacteristic
372Dic3⋊C4C22×C3211yescharacteristic
373Dic3⋊C4C22×C3211yescharacteristic
374Dic3⋊C4C22×C3211yescharacteristic
375Dic3⋊C4C22×C3211yescharacteristic
376Dic3⋊C4C22×C3211yescharacteristic
377C4×Dic3C22×C3211yescharacteristic
378C4×Dic3C22×C3211yescharacteristic
379C4×Dic3C22×C3211yescharacteristic
380C4×Dic3C22×C3211yescharacteristic
381C22×C32—28no—
382C22×C32—21no—
383C22×C32—21no—
384C22×C32—21no—
385C22×C32—24no—
386C22×C32—24no—
387C22×C32—24no—
388C22×C32—24no—
389C22×C32—44no—
390C22×C32—44no—
391C22×C32—61no—
392C22×C32—61no—
393C22×C32—61no—
394C22×C32—61no—
395C22×C32—61no—
396C22×C32—61no—
397C22×C32C23×D311yescharacteristic
398C22×C32C24×C314yes—
399C2×C3×D3—24no—
400C2×C3×D3—24no—
401C2×C3×D3—24no—
402C2×C3×D3—24no—
403C2×C3×D3—24no—
404C2×C3×D3—24no—
405C32×C4—28no—
406C32×C4—21no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—21no—
411C32×C4—21no—
412C32×C4—24no—
413C32×C4—24no—
414C32×C4—24no—
415C32×C4—24no—
416C32×C4—24no—
417C32×C4—24no—
418C32×C4—32no—
419C32×C4—44no—
420C32×C4—44no—
421C32×C4—44no—
422C32×C4—44no—
423C32×C4—44no—
424C32×C4—61no—
425C32×C4—61no—
426C32×C4—61no—
427C32×C4—61no—
428C32×C4—61no—
429C3×Dic3—24no—
430C3×Dic3—24no—
431C3×Dic3—24no—
432C3×Dic3—24no—
433C3×Dic3—24no—
434C3×Dic3C3×#4118yes—
435C4⋊Q8—31no—
436#126—31no—
437#126—31no—
438#124—31no—
439#124—31no—
440#124—31no—
441#123—31no—
442#123—31no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8C32×D311yescharacteristic, complemented
446#121—31no—
447C4×Q8—31no—
448C4×D4—31no—
449#117—31no—
450C33#54211yescharacteristic, complemented, Sylow
451C23×C3—24no—
452C23×C3—34no—
453C23×C3—34no—
454C23×C3C22×C3×D314yes—
455C23×C3C23×C3211yescharacteristic
456C22×D3C23×C3211yescharacteristic
457C22×D3C23×C3211yescharacteristic
458C3×Q8—44no—
459C3×Q8—41no—
460C3×Q8—48no—
461C3×Q8—68no—
462C3×Q8—124no—
463C3×D4—68no—
464C3×D4—124no—
465C3×D4—124no—
466C2×C3×C4—24no—
467C2×C3×C4—24no—
468C2×C3×C4—24no—
469C2×C3×C4—24no—
470C2×C3×C4—24no—
471C2×C3×C4—24no—
472C2×C3×C4—34no—
473C2×C3×C4—34no—
474C2×C3×C4—34no—
475C2×C3×C4—34no—
476C2×C3×C4—34no—
477C2×C3×C4—34no—
478C2×C3×C4—44no—
479C2×C3×C4—41no—
480C2×C3×C4—48no—
481C2×C3×C4—68no—
482C2×C3×C4—124no—
483C2×C3×C4C22×C3×D314yes—
484C2×C3×C4C22×C3×D314yes—
485C2×C3×C4C22×C3×D314yes—
486C2×C3×C4C22×C3×D314yes—
487C2×C3×C4C22×C3×D314yes—
488C2×C3×C4C22×C3×D314yes—
489C2×C3×C4C23×C3211yescharacteristic
490C2×C3×C4C23×C3211yescharacteristic
491C2×C3×C4C23×C3211yescharacteristic
492C2×C3×C4C23×C3211yescharacteristic
493C2×C3×C4C23×C3211yescharacteristic
494C2×C3×C4C23×C3211yescharacteristic
495#67—22no—
496#67—41no—
497C2×Dic3C23×C3211yescharacteristic
498C2×Dic3C23×C3211yescharacteristic
499C2×Dic3C23×C3211yescharacteristic
500C2×Dic3C23×C3211yescharacteristic
501C2×Dic3C23×C3211yescharacteristic
502C2×Dic3C23×C3211yescharacteristic
503D12—41no—
504C4×D3—22no—
505C4×D3—41no—
506Dic6—22no—
507Dic6—41no—
508C2×C32—24no—
509C2×C32—24no—
510C2×C32—24no—
511C2×C32—48no—
512C2×C32—41no—
513C2×C32—44no—
514C2×C32—121no—
515C2×C32—121no—
516C2×C32#100411yescharacteristic
517C2×C32#100711yescharacteristic
518C2×C32D3×#4111yescharacteristic
519C2×C32C2×C3×#4114yes—
520C2×C32C3×H(5,𝔽2)14yes—
521C2×C32C3×2−1+414yes—
522C3×D3—44no—
523C3×D3—44no—
524C2×Q8—31no—
525C2×Q8—31no—
526C2×Q8C2×C32×D311yescharacteristic
527C2×D4—31no—
528C2×D4—31no—
529C2×D4—31no—
530C22×C4—31no—
531C22×C4—31no—
532C22×C4C2×C32×D311yescharacteristic
533C4⋊C4—31no—
534C4⋊C4—31no—
535C4⋊C4—31no—
536C4⋊C4—31no—
537C4⋊C4—31no—
538C4⋊C4—31no—
539C4⋊C4—31no—
540C4⋊C4C2×C32×D311yescharacteristic
541C4⋊C4C2×C32×D311yescharacteristic
542C4⋊C4C2×C32×D311yescharacteristic
543C22⋊C4—31no—
544C22⋊C4—31no—
545C22⋊C4—31no—
546C22⋊C4—31no—
547C22⋊C4—31no—
548C22⋊C4—31no—
549C22⋊C4—31no—
550C22⋊C4—31no—
551C22⋊C4—31no—
552C22⋊C4—31no—
553C22⋊C4C2×C32×D311yescharacteristic
554C22⋊C4C2×C32×D311yescharacteristic
555C42—31no—
556C42—31no—
557C42—31no—
558C42—31no—
559C22×C3—28no—
560C22×C3—24no—
561C22×C3—24no—
562C22×C3—24no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—24no—
567C22×C3—44no—
568C22×C3—44no—
569C22×C3—64no—
570C22×C3—64no—
571C22×C3—64no—
572C22×C3—64no—
573C22×C3—64no—
574C22×C3—64no—
575C22×C3C23×C3×D314yes—
576C22×C3C24×C3211yescharacteristic
577C2×D3—21no—
578C2×D3—21no—
579C2×D3—21no—
580C2×D3—21no—
581C2×D3—21no—
582C2×D3—21no—
583C3×C4—28no—
584C3×C4—24no—
585C3×C4—24no—
586C3×C4—24no—
587C3×C4—24no—
588C3×C4—24no—
589C3×C4—24no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—38no—
597C3×C4—44no—
598C3×C4—44no—
599C3×C4—44no—
600C3×C4—44no—
601C3×C4—44no—
602C3×C4—64no—
603C3×C4—64no—
604C3×C4—64no—
605C3×C4—64no—
606C3×C4—64no—
607Dic3—21no—
608Dic3—21no—
609Dic3—21no—
610Dic3—21no—
611Dic3—21no—
612Dic3C32×#4112yes—
613C32—24no—
614C32#564011yescharacteristic, direct product factor
615C32C3×#54214yescomplemented
616C23—31no—
617C23—31no—
618C23C22×C32×D311yescharacteristic
619Q8—41no—
620Q8—62no—
621Q8—121no—
622D4—62no—
623D4—121no—
624D4—121no—
625C2×C4—31no—
626C2×C4—31no—
627C2×C4—31no—
628C2×C4—31no—
629C2×C4—31no—
630C2×C4—31no—
631C2×C4—41no—
632C2×C4—62no—
633C2×C4—121no—
634C2×C4C22×C32×D311yescharacteristic
635C2×C4C22×C32×D311yescharacteristic
636C2×C4C22×C32×D311yescharacteristic
637C2×C4C22×C32×D311yescharacteristic
638C2×C4C22×C32×D311yescharacteristic
639C2×C4C22×C32×D311yescharacteristic
640C2×C3—24no—
641C2×C3—24no—
642C2×C3—24no—
643C2×C3—48no—
644C2×C3—44no—
645C2×C3—41no—
646C2×C3—124no—
647C2×C3—124no—
648C2×C3C3×#100414yes—
649C2×C3C3×#100714yes—
650C2×C3C3×D3×#4114yes—
651C2×C3C2×C32×#4111yescharacteristic
652C2×C3C32×H(5,𝔽2)11yescharacteristic
653C2×C3C32×2−1+411yescharacteristic
654D3—41no—
655D3—41no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—61no—
660C22—61no—
661C22—61no—
662C22—61no—
663C22—61no—
664C22—61no—
665C22C23×C32×D311yescharacteristic
666C4—21no—
667C4—21no—
668C4—21no—
669C4—21no—
670C4—21no—
671C4—21no—
672C4—32no—
673C4—61no—
674C4—61no—
675C4—61no—
676C4—61no—
677C4—61no—
678C3—24no—
679C3C3×#564014yesdirect product factor
680C3C32×#54211yescharacteristic, complemented
681C2—41no—
682C2—121no—
683C2—121no—
684C2C32×#100411yescharacteristic
685C2C32×#100711yescharacteristic
686C2C32×D3×#4111yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×C22⋊Q8C2
socleC22×C33C24
prime radicalC32×#884C2
hypercenterC32×C22⋊Q8D3
hypocenterC3C32×#542
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C33×C22⋊Q8C2semidirect
2. C32×#947C2semidirect
3. C32×#944C2semidirect
4. C32×#929C2semidirect
5. C32×C4×#67C2semidirect
6. C32×#898C2semidirect
7. C32×#896C2semidirect
8. C32×#896C2semidirect
9. C32×#894C2semidirect
10. C32×#892C2semidirect
11. C32×#887C2semidirect
12. C32×#885C2semidirect
13. C32×#885C2semidirect
15. C32×#879C2semidirect
17. C3×#5640C3direct (N × H)
64. C32×C22⋊Q8D3semidirect
65. C32×C22⋊Q8C2×C3semidirect
70. C3×#947C2×C3semidirect
71. C3×#944C2×C3semidirect
72. C3×#929C2×C3semidirect
73. C3×C4×#67C2×C3semidirect
74. C3×#898C2×C3semidirect
75. C3×#896C2×C3semidirect
76. C3×#896C2×C3semidirect
77. C3×#894C2×C3semidirect
78. C3×#892C2×C3semidirect
79. C3×#887C2×C3semidirect
80. C3×#885C2×C3semidirect
81. C3×#885C2×C3semidirect
83. C3×#879C2×C3semidirect
109. #5640C32direct (N × H)
220. C3×C22⋊Q8C3×D3semidirect
221. C3×C22⋊Q8C2×C32semidirect
226. #947C2×C32semidirect
227. #944C2×C32semidirect
228. #929C2×C32semidirect
229. C4×#67C2×C32semidirect
230. #898C2×C32semidirect
231. #896C2×C32semidirect
232. #896C2×C32semidirect
233. #894C2×C32semidirect
234. #892C2×C32semidirect
235. #887C2×C32semidirect
236. #885C2×C32semidirect
237. #885C2×C32semidirect
239. #879C2×C32semidirect
445. C22⋊Q8C32×D3semidirect
450. C33#542semidirect
614. C32#5640direct (N × H)
615. C32C3×#542semidirect
679. C3C3×#5640direct (N × H)
680. C3C32×#542semidirect

Maximal subgroups

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

subgroupindex
C33×C22⋊Q82
C32×#9472
C32×#9442
C32×#9292
C32×C4×#672
C32×#8982
C32×#8962
C32×#8942
C32×#8922
C32×#8872
C32×#8852
C32×#8842
C32×#8792
C32×#5423
C3×#56403