Finite Group Databasebeta

← C32×#5706 #13179084

Subgroups — C32×#5706 #13179084

Order 1728.

1644 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×#126C211yesmaximal, characteristic, complemented
2C32×#896C211yesmaximal, characteristic, complemented
3C32×#894C211yesmaximal, characteristic, complemented
4C32×#893C211yesmaximal, characteristic, complemented
5C32×#892C211yesmaximal, characteristic, complemented
6C32×#889C211yesmaximal, characteristic, complemented
7C32×#887C211yesmaximal, characteristic, complemented
8C32×#885C211yesmaximal, characteristic, complemented
9C32×#884C211yesmaximal, characteristic
10C32×#883C211yesmaximal, characteristic, complemented
11C32×#67⋊C4C211yesmaximal, characteristic, complemented
12C32×#67⋊C4C211yesmaximal, characteristic, complemented
13C32×#877C211yesmaximal, characteristic, complemented
14C32×#876C211yesmaximal, characteristic, complemented
15C32×C42×D3C211yesmaximal, characteristic, complemented
16C32×#529—31nomaximal
17C3×#5706C314yesmaximal, direct product factor
18C2×C32×#67C2211yescharacteristic
19C2×C32×#67C2211yescharacteristic
20C22×C32×Dic3C2211yescharacteristic
21C2×C32×D12C2211yescharacteristic
22C2×C32×C4×D3C2211yescharacteristic
23C2×C32×C4×D3C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic
26C2×C32×Dic6C2211yescharacteristic
27C33×C4⋊C4C2211yescharacteristic
28C33×C4⋊C4C2211yescharacteristic
29C33×C4⋊C4C2211yescharacteristic
30C33×C22⋊C4C2211yescharacteristic
31C33×C22⋊C4C2211yescharacteristic
32C33×C22⋊C4C2211yescharacteristic
33C33×C42C2211yescharacteristic
34C32×#217C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
42C32×Dic3⋊C4C2211yescharacteristic
43C32×Dic3⋊C4C2211yescharacteristic
44C32×Dic3⋊C4C2211yescharacteristic
45C32×Dic3⋊C4C2211yescharacteristic
46C32×Dic3⋊C4C2211yescharacteristic
47C32×Dic3⋊C4C2211yescharacteristic
48C32×C4×Dic3C2211yescharacteristic
49C32×C4×Dic3C2211yescharacteristic
50C32×C4×Dic3C2211yescharacteristic
51C32×C4×Dic3C2211yescharacteristic
52C32×C4×Dic3C2211yescharacteristic
53C32×#126—24no—
54C32×#126—31no—
55C32×#126D311yescharacteristic, complemented
56C32×#126C2×C314yescomplemented
57C32×#125—31no—
58C32×#124—31no—
59C32×#123—31no—
60C32×#123—31no—
61C32×C22⋊Q8—31no—
62C32×#121—31no—
63C32×C4×Q8—31no—
64C32×C4×D4—31no—
65C32×C4×D4—31no—
66C32×C4×D4—31no—
67C32×#117—31no—
68C32×#117—31no—
69C2×C32×C42—31no—
70C3×#896C2×C314yescomplemented
71C3×#894C2×C314yescomplemented
72C3×#893C2×C314yescomplemented
73C3×#892C2×C314yescomplemented
74C3×#889C2×C314yescomplemented
75C3×#887C2×C314yescomplemented
76C3×#885C2×C314yescomplemented
77C3×#884C2×C314yes—
78C3×#883C2×C314yescomplemented
79C3×#67⋊C4C2×C314yescomplemented
80C3×#67⋊C4C2×C314yescomplemented
81C3×#877C2×C314yescomplemented
82C3×#876C2×C314yescomplemented
83C3×C42×D3C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C22×C32×D3C2311yescharacteristic
86C22×C32×D3C2311yescharacteristic
87C2×C33×C4C2311yescharacteristic
88C2×C33×C4C2311yescharacteristic
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C32×#67—22no—
94C32×#67—22no—
95C2×C32×Dic3—22no—
96C2×C32×Dic3C2311yescharacteristic
97C2×C32×Dic3C2311yescharacteristic
98C2×C32×Dic3C2311yescharacteristic
99C2×C32×Dic3C2311yescharacteristic
100C2×C32×Dic3C2311yescharacteristic
101C2×C32×Dic3C2311yescharacteristic
102C32×D12—22no—
103C32×C4×D3—22no—
104C32×C4×D3—22no—
105C32×C4×D3—22no—
106C32×C4×D3—22no—
107C32×Dic6—22no—
108C3×#529—34no—
109#5706C3211yescharacteristic, direct product factor
110C2×C32×Q8—31no—
111C2×C32×D4—31no—
112C2×C32×D4—31no—
113C2×C32×D4—31no—
114C22×C32×C4—31no—
115C22×C32×C4—31no—
116C22×C32×C4—31no—
117C22×C32×C4—31no—
118C22×C32×C4—31no—
119C2×C3×#67C22×C314yes—
120C2×C3×#67C22×C314yes—
121C22×C3×Dic3C22×C314yes—
122C2×C3×D12C22×C314yes—
123C2×C3×C4×D3C22×C314yes—
124C2×C3×C4×D3C22×C314yes—
125C2×C3×C4×D3C22×C314yes—
126C2×C3×C4×D3C22×C314yes—
127C2×C3×Dic6C22×C314yes—
128C32×C4⋊C4—24no—
129C32×C4⋊C4—24no—
130C32×C4⋊C4—24no—
131C32×C4⋊C4—31no—
132C32×C4⋊C4—31no—
133C32×C4⋊C4—31no—
134C32×C4⋊C4—31no—
135C32×C4⋊C4—31no—
136C32×C4⋊C4—31no—
137C32×C4⋊C4—31no—
138C32×C4⋊C4C2×D311yescharacteristic
139C32×C4⋊C4C2×D311yescharacteristic
140C32×C4⋊C4C2×D311yescharacteristic
141C32×C4⋊C4C22×C314yes—
142C32×C4⋊C4C22×C314yes—
143C32×C4⋊C4C22×C314yes—
144C32×C22⋊C4—24no—
145C32×C22⋊C4—24no—
146C32×C22⋊C4—24no—
147C32×C22⋊C4—31no—
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⋊C4C2×D311yescharacteristic
155C32×C22⋊C4C2×D311yescharacteristic
156C32×C22⋊C4C2×D311yescharacteristic
157C32×C22⋊C4C22×C314yes—
158C32×C22⋊C4C22×C314yes—
159C32×C22⋊C4C22×C314yes—
160C32×C42—24no—
161C32×C42—31no—
162C32×C42—31no—
163C32×C42—31no—
164C32×C42—31no—
165C32×C42—31no—
166C32×C42C2×D311yescharacteristic
167C32×C42C22×C314yes—
168C3×#217C22×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×C4⋊Dic3C22×C314yes—
176C3×Dic3⋊C4C22×C314yes—
177C3×Dic3⋊C4C22×C314yes—
178C3×Dic3⋊C4C22×C314yes—
179C3×Dic3⋊C4C22×C314yes—
180C3×Dic3⋊C4C22×C314yes—
181C3×Dic3⋊C4C22×C314yes—
182C3×C4×Dic3C22×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#4112yes—
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#4112yes—
208C32×Dic3#4112yes—
209C3×#126—24no—
210C3×#126—34no—
211C3×#126C3×D314yescomplemented
212C3×#126C2×C3211yescharacteristic, complemented
213C3×#125—34no—
214C3×#124—34no—
215C3×#123—34no—
216C3×#123—34no—
217C3×C22⋊Q8—34no—
218C3×#121—34no—
219C3×C4×Q8—34no—
220C3×C4×D4—34no—
221C3×C4×D4—34no—
222C3×C4×D4—34no—
223C3×#117—34no—
224C3×#117—34no—
225C2×C3×C42—34no—
226#896C2×C3211yescharacteristic, complemented
227#894C2×C3211yescharacteristic, complemented
228#893C2×C3211yescharacteristic, complemented
229#892C2×C3211yescharacteristic, complemented
230#889C2×C3211yescharacteristic, complemented
231#887C2×C3211yescharacteristic, complemented
232#885C2×C3211yescharacteristic, complemented
233#884C2×C3211yescharacteristic
234#883C2×C3211yescharacteristic, complemented
235#67⋊C4C2×C3211yescharacteristic, complemented
236#67⋊C4C2×C3211yescharacteristic, complemented
237#877C2×C3211yescharacteristic, complemented
238#876C2×C3211yescharacteristic, complemented
239C42×D3C2×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—62no—
248C32×D4—62no—
249C32×D4—62no—
250C32×D4—62no—
251C2×C32×C4—24no—
252C2×C32×C4—24no—
253C2×C32×C4—24no—
254C2×C32×C4—24no—
255C2×C32×C4—24no—
256C2×C32×C4—24no—
257C2×C32×C4—31no—
258C2×C32×C4—31no—
259C2×C32×C4—31no—
260C2×C32×C4—31no—
261C2×C32×C4—31no—
262C2×C32×C4—31no—
263C2×C32×C4—62no—
264C2×C32×C4—62no—
265C2×C32×C4—62no—
266C2×C32×C4—62no—
267C2×C32×C4—62no—
268C2×C32×C4C22×D311yescharacteristic
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C22×D311yescharacteristic
272C2×C32×C4C22×D311yescharacteristic
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C23×C314yes—
275C2×C32×C4C23×C314yes—
276C2×C32×C4C23×C314yes—
277C2×C32×C4C23×C314yes—
278C2×C32×C4C23×C314yes—
279C2×C32×C4C23×C314yes—
280C3×#67—28no—
281C3×#67—28no—
282C2×C3×Dic3—28no—
283C2×C3×Dic3C23×C314yes—
284C2×C3×Dic3C23×C314yes—
285C2×C3×Dic3C23×C314yes—
286C2×C3×Dic3C23×C314yes—
287C2×C3×Dic3C23×C314yes—
288C2×C3×Dic3C23×C314yes—
289C3×D12—28no—
290C3×C4×D3—28no—
291C3×C4×D3—28no—
292C3×C4×D3—28no—
293C3×C4×D3—28no—
294C3×Dic6—28no—
295#529—31noSylow
296C2×C33—41no—
297C2×C33C2×#4111yescharacteristic
298C2×C33C2×#4111yescharacteristic
299C2×C33C2×#4111yescharacteristic
300C32×D3—22no—
301C32×D3—41no—
302C2×C3×Q8—34no—
303C2×C3×D4—34no—
304C2×C3×D4—34no—
305C2×C3×D4—34no—
306C22×C3×C4—34no—
307C22×C3×C4—34no—
308C22×C3×C4—34no—
309C22×C3×C4—34no—
310C22×C3×C4—34no—
311C2×#67C22×C3211yescharacteristic
312C2×#67C22×C3211yescharacteristic
313C22×Dic3C22×C3211yescharacteristic
314C2×D12C22×C3211yescharacteristic
315C2×C4×D3C22×C3211yescharacteristic
316C2×C4×D3C22×C3211yescharacteristic
317C2×C4×D3C22×C3211yescharacteristic
318C2×C4×D3C22×C3211yescharacteristic
319C2×Dic6C22×C3211yescharacteristic
320C3×C4⋊C4—24no—
321C3×C4⋊C4—24no—
322C3×C4⋊C4—24no—
323C3×C4⋊C4—34no—
324C3×C4⋊C4—34no—
325C3×C4⋊C4—34no—
326C3×C4⋊C4—34no—
327C3×C4⋊C4—34no—
328C3×C4⋊C4—34no—
329C3×C4⋊C4—34no—
330C3×C4⋊C4C2×C3×D314yes—
331C3×C4⋊C4C2×C3×D314yes—
332C3×C4⋊C4C2×C3×D314yes—
333C3×C4⋊C4C22×C3211yescharacteristic
334C3×C4⋊C4C22×C3211yescharacteristic
335C3×C4⋊C4C22×C3211yescharacteristic
336C3×C22⋊C4—24no—
337C3×C22⋊C4—24no—
338C3×C22⋊C4—24no—
339C3×C22⋊C4—34no—
340C3×C22⋊C4—34no—
341C3×C22⋊C4—34no—
342C3×C22⋊C4—34no—
343C3×C22⋊C4—34no—
344C3×C22⋊C4—34no—
345C3×C22⋊C4—34no—
346C3×C22⋊C4C2×C3×D314yes—
347C3×C22⋊C4C2×C3×D314yes—
348C3×C22⋊C4C2×C3×D314yes—
349C3×C22⋊C4C22×C3211yescharacteristic
350C3×C22⋊C4C22×C3211yescharacteristic
351C3×C22⋊C4C22×C3211yescharacteristic
352C3×C42—24no—
353C3×C42—34no—
354C3×C42—34no—
355C3×C42—34no—
356C3×C42—34no—
357C3×C42—34no—
358C3×C42C2×C3×D314yes—
359C3×C42C22×C3211yescharacteristic
360#217C22×C3211yescharacteristic
361(C2×D3)⋊C4C22×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
367C4⋊Dic3C22×C3211yescharacteristic
368Dic3⋊C4C22×C3211yescharacteristic
369Dic3⋊C4C22×C3211yescharacteristic
370Dic3⋊C4C22×C3211yescharacteristic
371Dic3⋊C4C22×C3211yescharacteristic
372Dic3⋊C4C22×C3211yescharacteristic
373Dic3⋊C4C22×C3211yescharacteristic
374C4×Dic3C22×C3211yescharacteristic
375C4×Dic3C22×C3211yescharacteristic
376C4×Dic3C22×C3211yescharacteristic
377C4×Dic3C22×C3211yescharacteristic
378C4×Dic3C22×C3211yescharacteristic
379C22×C32—21no—
380C22×C32—21no—
381C22×C32—21no—
382C22×C32—24no—
383C22×C32—24no—
384C22×C32—24no—
385C22×C32—24no—
386C22×C32—32no—
387C22×C32—44no—
388C22×C32—44no—
389C22×C32—44no—
390C22×C32—61no—
391C22×C32—61no—
392C22×C32—61no—
393C22×C32—61no—
394C22×C32—61no—
395C22×C32C23×D311yescharacteristic
396C22×C32C24×C314yes—
397C2×C3×D3—24no—
398C2×C3×D3—24no—
399C2×C3×D3—24no—
400C2×C3×D3—24no—
401C2×C3×D3—24no—
402C2×C3×D3C3×#4118yes—
403C32×C4—21no—
404C32×C4—21no—
405C32×C4—21no—
406C32×C4—21no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—24no—
410C32×C4—24no—
411C32×C4—24no—
412C32×C4—24no—
413C32×C4—24no—
414C32×C4—24no—
415C32×C4—32no—
416C32×C4—32no—
417C32×C4—44no—
418C32×C4—44no—
419C32×C4—44no—
420C32×C4—44no—
421C32×C4—44no—
422C32×C4—44no—
423C32×C4—61no—
424C32×C4—61no—
425C32×C4—61no—
426C32×C4—61no—
427C3×Dic3—24no—
428C3×Dic3—24no—
429C3×Dic3—24no—
430C3×Dic3—24no—
431C3×Dic3C3×#4118yes—
432C3×Dic3C3×#4118yes—
433#126—31no—
434#126C32×D311yescharacteristic, complemented
435#125—31no—
436#124—31no—
437#123—31no—
438#123—31no—
439C22⋊Q8—31no—
440#121—31no—
441C4×Q8—31no—
442C4×D4—31no—
443C4×D4—31no—
444C4×D4—31no—
445#117—31no—
446#117—31no—
447C2×C42—31no—
448C33#52911yescharacteristic, complemented, Sylow
449C23×C3—24no—
450C23×C3—34no—
451C23×C3—34no—
452C23×C3C22×C3×D314yes—
453C23×C3C23×C3211yescharacteristic
454C22×D3C23×C3211yescharacteristic
455C22×D3C23×C3211yescharacteristic
456C3×Q8—68no—
457C3×D4—68no—
458C3×D4—68no—
459C3×D4—68no—
460C2×C3×C4—24no—
461C2×C3×C4—24no—
462C2×C3×C4—24no—
463C2×C3×C4—24no—
464C2×C3×C4—24no—
465C2×C3×C4—24no—
466C2×C3×C4—34no—
467C2×C3×C4—34no—
468C2×C3×C4—34no—
469C2×C3×C4—34no—
470C2×C3×C4—34no—
471C2×C3×C4—34no—
472C2×C3×C4—68no—
473C2×C3×C4—68no—
474C2×C3×C4—68no—
475C2×C3×C4—68no—
476C2×C3×C4—68no—
477C2×C3×C4C22×C3×D314yes—
478C2×C3×C4C22×C3×D314yes—
479C2×C3×C4C22×C3×D314yes—
480C2×C3×C4C22×C3×D314yes—
481C2×C3×C4C22×C3×D314yes—
482C2×C3×C4C22×C3×D314yes—
483C2×C3×C4C23×C3211yescharacteristic
484C2×C3×C4C23×C3211yescharacteristic
485C2×C3×C4C23×C3211yescharacteristic
486C2×C3×C4C23×C3211yescharacteristic
487C2×C3×C4C23×C3211yescharacteristic
488C2×C3×C4C23×C3211yescharacteristic
489#67—22no—
490#67—22no—
491C2×Dic3—22no—
492C2×Dic3C23×C3211yescharacteristic
493C2×Dic3C23×C3211yescharacteristic
494C2×Dic3C23×C3211yescharacteristic
495C2×Dic3C23×C3211yescharacteristic
496C2×Dic3C23×C3211yescharacteristic
497C2×Dic3C23×C3211yescharacteristic
498D12—22no—
499C4×D3—22no—
500C4×D3—22no—
501C4×D3—22no—
502C4×D3—22no—
503Dic6—22no—
504C2×C32—24no—
505C2×C32—24no—
506C2×C32—24no—
507C2×C32—41no—
508C2×C32—44no—
509C2×C32—62no—
510C2×C32—84no—
511C2×C32—121no—
512C2×C32D3×#4111yescharacteristic
513C2×C32D3×#4111yescharacteristic
514C2×C32D3×#4111yescharacteristic
515C2×C32C2×C3×#4114yes—
516C2×C32C2×C3×#4114yes—
517C2×C32C2×C3×#4114yes—
518C3×D3—28no—
519C3×D3—44no—
520C2×Q8—31no—
521C2×D4—31no—
522C2×D4—31no—
523C2×D4—31no—
524C22×C4—31no—
525C22×C4—31no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—31no—
529C4⋊C4—31no—
530C4⋊C4—31no—
531C4⋊C4—31no—
532C4⋊C4—31no—
533C4⋊C4—31no—
534C4⋊C4—31no—
535C4⋊C4—31no—
536C4⋊C4C2×C32×D311yescharacteristic
537C4⋊C4C2×C32×D311yescharacteristic
538C4⋊C4C2×C32×D311yescharacteristic
539C22⋊C4—31no—
540C22⋊C4—31no—
541C22⋊C4—31no—
542C22⋊C4—31no—
543C22⋊C4—31no—
544C22⋊C4—31no—
545C22⋊C4—31no—
546C22⋊C4C2×C32×D311yescharacteristic
547C22⋊C4C2×C32×D311yescharacteristic
548C22⋊C4C2×C32×D311yescharacteristic
549C42—31no—
550C42—31no—
551C42—31no—
552C42—31no—
553C42—31no—
554C42C2×C32×D311yescharacteristic
555C22×C3—24no—
556C22×C3—24no—
557C22×C3—24no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—24no—
562C22×C3—38no—
563C22×C3—44no—
564C22×C3—44no—
565C22×C3—44no—
566C22×C3—64no—
567C22×C3—64no—
568C22×C3—64no—
569C22×C3—64no—
570C22×C3—64no—
571C22×C3C23×C3×D314yes—
572C22×C3C24×C3211yescharacteristic
573C2×D3—21no—
574C2×D3—21no—
575C2×D3—21no—
576C2×D3—21no—
577C2×D3—21no—
578C2×D3C32×#4112yes—
579C3×C4—24no—
580C3×C4—24no—
581C3×C4—24no—
582C3×C4—24no—
583C3×C4—24no—
584C3×C4—24no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—38no—
592C3×C4—38no—
593C3×C4—44no—
594C3×C4—44no—
595C3×C4—44no—
596C3×C4—44no—
597C3×C4—44no—
598C3×C4—44no—
599C3×C4—64no—
600C3×C4—64no—
601C3×C4—64no—
602C3×C4—64no—
603Dic3—21no—
604Dic3—21no—
605Dic3—21no—
606Dic3—21no—
607Dic3C32×#4112yes—
608Dic3C32×#4112yes—
609C32—24no—
610C32#570611yescharacteristic, direct product factor
611C32C3×#52914yescomplemented
612C23—31no—
613C23—31no—
614C23C22×C32×D311yescharacteristic
615Q8—62no—
616D4—62no—
617D4—62no—
618D4—62no—
619C2×C4—31no—
620C2×C4—31no—
621C2×C4—31no—
622C2×C4—31no—
623C2×C4—31no—
624C2×C4—31no—
625C2×C4—62no—
626C2×C4—62no—
627C2×C4—62no—
628C2×C4—62no—
629C2×C4—62no—
630C2×C4C22×C32×D311yescharacteristic
631C2×C4C22×C32×D311yescharacteristic
632C2×C4C22×C32×D311yescharacteristic
633C2×C4C22×C32×D311yescharacteristic
634C2×C4C22×C32×D311yescharacteristic
635C2×C4C22×C32×D311yescharacteristic
636C2×C3—24no—
637C2×C3—24no—
638C2×C3—24no—
639C2×C3—44no—
640C2×C3—41no—
641C2×C3—68no—
642C2×C3—84no—
643C2×C3—124no—
644C2×C3C3×D3×#4114yes—
645C2×C3C3×D3×#4114yes—
646C2×C3C3×D3×#4114yes—
647C2×C3C2×C32×#4111yescharacteristic
648C2×C3C2×C32×#4111yescharacteristic
649C2×C3C2×C32×#4111yescharacteristic
650D3—22no—
651D3—41no—
652C22—21no—
653C22—21no—
654C22—21no—
655C22—32no—
656C22—61no—
657C22—61no—
658C22—61no—
659C22—61no—
660C22—61no—
661C22C23×C32×D311yescharacteristic
662C4—21no—
663C4—21no—
664C4—21no—
665C4—21no—
666C4—21no—
667C4—21no—
668C4—32no—
669C4—32no—
670C4—61no—
671C4—61no—
672C4—61no—
673C4—61no—
674C3—24no—
675C3C3×#570614yesdirect product factor
676C3C32×#52911yescharacteristic, complemented
677C2—41no—
678C2—62no—
679C2—121no—
680C2C32×D3×#4111yescharacteristic
681C2C32×D3×#4111yescharacteristic
682C2C32×D3×#4111yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#126C2
socleC22×C33C24
prime radicalC32×#884C2
hypercenterC32×#126D3
hypocenterC3C32×#529
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×#126

Complements

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

NH ≅ G/Ntype
1. C33×#126C2semidirect
2. C32×#896C2semidirect
3. C32×#894C2semidirect
4. C32×#893C2semidirect
5. C32×#892C2semidirect
6. C32×#889C2semidirect
7. C32×#887C2semidirect
8. C32×#885C2semidirect
10. C32×#883C2semidirect
11. C32×#67⋊C4C2semidirect
12. C32×#67⋊C4C2semidirect
13. C32×#877C2semidirect
14. C32×#876C2semidirect
15. C32×C42×D3C2semidirect
17. C3×#5706C3direct (N × H)
55. C32×#126D3semidirect
56. C32×#126C2×C3semidirect
70. C3×#896C2×C3semidirect
71. C3×#894C2×C3semidirect
72. C3×#893C2×C3semidirect
73. C3×#892C2×C3semidirect
74. C3×#889C2×C3semidirect
75. C3×#887C2×C3semidirect
76. C3×#885C2×C3semidirect
78. C3×#883C2×C3semidirect
79. C3×#67⋊C4C2×C3semidirect
80. C3×#67⋊C4C2×C3semidirect
81. C3×#877C2×C3semidirect
82. C3×#876C2×C3semidirect
83. C3×C42×D3C2×C3semidirect
109. #5706C32direct (N × H)
211. C3×#126C3×D3semidirect
212. C3×#126C2×C32semidirect
226. #896C2×C32semidirect
227. #894C2×C32semidirect
228. #893C2×C32semidirect
229. #892C2×C32semidirect
230. #889C2×C32semidirect
231. #887C2×C32semidirect
232. #885C2×C32semidirect
234. #883C2×C32semidirect
235. #67⋊C4C2×C32semidirect
236. #67⋊C4C2×C32semidirect
237. #877C2×C32semidirect
238. #876C2×C32semidirect
239. C42×D3C2×C32semidirect
434. #126C32×D3semidirect
448. C33#529semidirect
610. C32#5706direct (N × H)
611. C32C3×#529semidirect
675. C3C3×#5706direct (N × H)
676. C3C32×#529semidirect

Maximal subgroups

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

subgroupindex
C33×#1262
C32×#8962
C32×#8942
C32×#8932
C32×#8922
C32×#8892
C32×#8872
C32×#8852
C32×#8842
C32×#8832
C32×#67⋊C42
C32×#8772
C32×#8762
C32×C42×D32
C32×#5293
C3×#57063