Finite Group Databasebeta

← C32×#5646 #13179023

Subgroups — C32×#5646 #13179023

Order 1728.

1472 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×C22⋊Q8C211yesmaximal, characteristic, complemented
2C32×#946C211yesmaximal, characteristic, complemented
3C32×#944C211yesmaximal, characteristic, complemented
4C32×#929C211yesmaximal, characteristic
5C32×#924C211yesmaximal, characteristic, complemented
6C32×#898C211yesmaximal, characteristic, complemented
7C32×#898C211yesmaximal, characteristic, complemented
8C32×#896C211yesmaximal, characteristic, complemented
9C32×#890C211yesmaximal, characteristic, complemented
10C32×#889C211yesmaximal, characteristic, complemented
11C32×#888C211yesmaximal, characteristic, complemented
12C32×#885C211yesmaximal, characteristic
13C32×#883C211yesmaximal, characteristic
14C32×#879C211yesmaximal, characteristic, complemented
15C32×#879C211yesmaximal, characteristic, complemented
16C32×#563—31nomaximal
17C3×#5646C314yesmaximal, direct product factor
18C2×C33×Q8C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C2×C32×C4×D3C2211yescharacteristic
22C2×C32×Dic6C2211yescharacteristic
23C2×C32×Dic6C2211yescharacteristic
24C33×C4⋊C4C2211yescharacteristic
25C33×C4⋊C4C2211yescharacteristic
26C33×C4⋊C4C2211yescharacteristic
27C33×C22⋊C4C2211yescharacteristic
28C33×C22⋊C4C2211yescharacteristic
29C32×#217C2211yescharacteristic
30C32×#217C2211yescharacteristic
31C32×#217C2211yescharacteristic
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×(C2×D3)⋊C4C2211yescharacteristic
34C32×(C2×D3)⋊C4C2211yescharacteristic
35C32×(C2×D3)⋊C4C2211yescharacteristic
36C32×(C2×D3)⋊C4C2211yescharacteristic
37C32×C4⋊Dic3C2211yescharacteristic
38C32×C4⋊Dic3C2211yescharacteristic
39C32×C4⋊Dic3C2211yescharacteristic
40C32×C4⋊Dic3C2211yescharacteristic
41C32×Dic3⋊C4C2211yescharacteristic
42C32×Dic3⋊C4C2211yescharacteristic
43C32×Dic3⋊C4C2211yescharacteristic
44C32×Dic3⋊C4C2211yescharacteristic
45C32×Dic3⋊C4C2211yescharacteristic
46C32×Dic3⋊C4C2211yescharacteristic
47C32×Dic3⋊C4C2211yescharacteristic
48C32×Dic3⋊C4C2211yescharacteristic
49C32×Dic3⋊C4C2211yescharacteristic
50C32×C4×Dic3C2211yescharacteristic
51C32×C4×Dic3C2211yescharacteristic
52C32×C4×Dic3C2211yescharacteristic
53C32×C4⋊Q8—31no—
54C32×C4⋊Q8—31no—
55C32×#126—31no—
56C32×#126—31no—
57C32×#126—31no—
58C32×#126—31no—
59C32×#125—31no—
60C32×#125—31no—
61C32×#124—31no—
62C32×#123—31no—
63C32×#123—31no—
64C32×C22⋊Q8—24no—
65C32×C22⋊Q8—31no—
66C32×C22⋊Q8—31no—
67C32×C22⋊Q8—31no—
68C32×C22⋊Q8D311yescharacteristic, complemented
69C32×C22⋊Q8C2×C314yescomplemented
70C3×#946C2×C314yescomplemented
71C3×#944C2×C314yescomplemented
72C3×#929C2×C314yes—
73C3×#924C2×C314yescomplemented
74C3×#898C2×C314yescomplemented
75C3×#898C2×C314yescomplemented
76C3×#896C2×C314yescomplemented
77C3×#890C2×C314yescomplemented
78C3×#889C2×C314yescomplemented
79C3×#888C2×C314yescomplemented
80C3×#885C2×C314yes—
81C3×#883C2×C314yes—
82C3×#879C2×C314yescomplemented
83C3×#879C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C22×C32×D3C2311yescharacteristic
86C33×Q8—41no—
87C2×C33×C4—41no—
88C2×C33×C4C2311yescharacteristic
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C32×#67—41no—
95C2×C32×Dic3C2311yescharacteristic
96C2×C32×Dic3C2311yescharacteristic
97C2×C32×Dic3C2311yescharacteristic
98C2×C32×Dic3C2311yescharacteristic
99C2×C32×Dic3C2311yescharacteristic
100C2×C32×Dic3C2311yescharacteristic
101C2×C32×Dic3C2311yescharacteristic
102C32×C4×D3—41no—
103C32×Dic6—41no—
104C32×Dic6—41no—
105C3×#563—34no—
106#5646C3211yescharacteristic, direct product factor
107C2×C32×Q8—24no—
108C2×C32×Q8—31no—
109C2×C32×Q8—31no—
110C2×C32×Q8C2×D311yescharacteristic
111C2×C32×Q8C22×C314yes—
112C2×C32×D4—31no—
113C22×C32×C4—24no—
114C22×C32×C4—31no—
115C22×C32×C4C2×D311yescharacteristic
116C22×C32×C4C22×C314yes—
117C2×C3×#67C22×C314yes—
118C2×C3×C4×D3C22×C314yes—
119C2×C3×Dic6C22×C314yes—
120C2×C3×Dic6C22×C314yes—
121C32×C4⋊C4—24no—
122C32×C4⋊C4—24no—
123C32×C4⋊C4—24no—
124C32×C4⋊C4—31no—
125C32×C4⋊C4—31no—
126C32×C4⋊C4—31no—
127C32×C4⋊C4—31no—
128C32×C4⋊C4—31no—
129C32×C4⋊C4—31no—
130C32×C4⋊C4—31no—
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⋊C4C2×D311yescharacteristic
138C32×C4⋊C4C2×D311yescharacteristic
139C32×C4⋊C4C2×D311yescharacteristic
140C32×C4⋊C4C22×C314yes—
141C32×C4⋊C4C22×C314yes—
142C32×C4⋊C4C22×C314yes—
143C32×C22⋊C4—24no—
144C32×C22⋊C4—24no—
145C32×C22⋊C4—31no—
146C32×C22⋊C4—31no—
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⋊C4C2×D311yescharacteristic
154C32×C22⋊C4C2×D311yescharacteristic
155C32×C22⋊C4C22×C314yes—
156C32×C22⋊C4C22×C314yes—
157C32×C42—31no—
158C32×C42—31no—
159C32×C42—31no—
160C3×#217C22×C314yes—
161C3×#217C22×C314yes—
162C3×#217C22×C314yes—
163C3×(C2×D3)⋊C4C22×C314yes—
164C3×(C2×D3)⋊C4C22×C314yes—
165C3×(C2×D3)⋊C4C22×C314yes—
166C3×(C2×D3)⋊C4C22×C314yes—
167C3×(C2×D3)⋊C4C22×C314yes—
168C3×C4⋊Dic3C22×C314yes—
169C3×C4⋊Dic3C22×C314yes—
170C3×C4⋊Dic3C22×C314yes—
171C3×C4⋊Dic3C22×C314yes—
172C3×Dic3⋊C4C22×C314yes—
173C3×Dic3⋊C4C22×C314yes—
174C3×Dic3⋊C4C22×C314yes—
175C3×Dic3⋊C4C22×C314yes—
176C3×Dic3⋊C4C22×C314yes—
177C3×Dic3⋊C4C22×C314yes—
178C3×Dic3⋊C4C22×C314yes—
179C3×Dic3⋊C4C22×C314yes—
180C3×Dic3⋊C4C22×C314yes—
181C3×C4×Dic3C22×C314yes—
182C3×C4×Dic3C22×C314yes—
183C3×C4×Dic3C22×C314yes—
184C22×C33—21no—
185C22×C33—21no—
186C22×C33—21no—
187C22×C33C2411yescharacteristic
188C2×C32×D3—21no—
189C2×C32×D3—21no—
190C2×C32×D3—21no—
191C33×C4—21no—
192C33×C4—21no—
193C33×C4—21no—
194C33×C4—21no—
195C33×C4—21no—
196C33×C4—21no—
197C32×Dic3—21no—
198C32×Dic3—21no—
199C32×Dic3—21no—
200C32×Dic3—21no—
201C32×Dic3—21no—
202C32×Dic3—21no—
203C32×Dic3—21no—
204C3×C4⋊Q8—34no—
205C3×C4⋊Q8—34no—
206C3×#126—34no—
207C3×#126—34no—
208C3×#126—34no—
209C3×#126—34no—
210C3×#125—34no—
211C3×#125—34no—
212C3×#124—34no—
213C3×#123—34no—
214C3×#123—34no—
215C3×C22⋊Q8—24no—
216C3×C22⋊Q8—34no—
217C3×C22⋊Q8—34no—
218C3×C22⋊Q8—34no—
219C3×C22⋊Q8C3×D314yescomplemented
220C3×C22⋊Q8C2×C3211yescharacteristic, complemented
221#946C2×C3211yescharacteristic, complemented
222#944C2×C3211yescharacteristic, complemented
223#929C2×C3211yescharacteristic
224#924C2×C3211yescharacteristic, complemented
225#898C2×C3211yescharacteristic, complemented
226#898C2×C3211yescharacteristic, complemented
227#896C2×C3211yescharacteristic, complemented
228#890C2×C3211yescharacteristic, complemented
229#889C2×C3211yescharacteristic, complemented
230#888C2×C3211yescharacteristic, complemented
231#885C2×C3211yescharacteristic
232#883C2×C3211yescharacteristic
233#879C2×C3211yescharacteristic, complemented
234#879C2×C3211yescharacteristic, complemented
235C23×C32—24no—
236C23×C32—31no—
237C23×C32C22×D311yescharacteristic
238C23×C32C23×C314yes—
239C22×C3×D3C23×C314yes—
240C32×Q8—41no—
241C32×Q8—44no—
242C32×Q8—48no—
243C32×Q8—121no—
244C32×Q8—121no—
245C32×D4—121no—
246C2×C32×C4—24no—
247C2×C32×C4—24no—
248C2×C32×C4—24no—
249C2×C32×C4—24no—
250C2×C32×C4—24no—
251C2×C32×C4—24no—
252C2×C32×C4—31no—
253C2×C32×C4—31no—
254C2×C32×C4—31no—
255C2×C32×C4—31no—
256C2×C32×C4—31no—
257C2×C32×C4—31no—
258C2×C32×C4—31no—
259C2×C32×C4—41no—
260C2×C32×C4—44no—
261C2×C32×C4—48no—
262C2×C32×C4—121no—
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267C2×C32×C4C22×D311yescharacteristic
268C2×C32×C4C22×D311yescharacteristic
269C2×C32×C4C23×C314yes—
270C2×C32×C4C23×C314yes—
271C2×C32×C4C23×C314yes—
272C2×C32×C4C23×C314yes—
273C2×C32×C4C23×C314yes—
274C2×C32×C4C23×C314yes—
275C3×#67—44no—
276C2×C3×Dic3C23×C314yes—
277C2×C3×Dic3C23×C314yes—
278C2×C3×Dic3C23×C314yes—
279C2×C3×Dic3C23×C314yes—
280C2×C3×Dic3C23×C314yes—
281C2×C3×Dic3C23×C314yes—
282C2×C3×Dic3C23×C314yes—
283C3×C4×D3—44no—
284C3×Dic6—44no—
285C3×Dic6—44no—
286#563—31noSylow
287C2×C33—41no—
288C2×C33H(5,𝔽2)11yescharacteristic
289C2×C332−1+411yescharacteristic
290C2×C332−1+411yescharacteristic
291C32×D3—41no—
292C2×C3×Q8—24no—
293C2×C3×Q8—34no—
294C2×C3×Q8—34no—
295C2×C3×Q8C2×C3×D314yes—
296C2×C3×Q8C22×C3211yescharacteristic
297C2×C3×D4—34no—
298C22×C3×C4—24no—
299C22×C3×C4—34no—
300C22×C3×C4C2×C3×D314yes—
301C22×C3×C4C22×C3211yescharacteristic
302C2×#67C22×C3211yescharacteristic
303C2×C4×D3C22×C3211yescharacteristic
304C2×Dic6C22×C3211yescharacteristic
305C2×Dic6C22×C3211yescharacteristic
306C3×C4⋊C4—24no—
307C3×C4⋊C4—24no—
308C3×C4⋊C4—24no—
309C3×C4⋊C4—34no—
310C3×C4⋊C4—34no—
311C3×C4⋊C4—34no—
312C3×C4⋊C4—34no—
313C3×C4⋊C4—34no—
314C3×C4⋊C4—34no—
315C3×C4⋊C4—34no—
316C3×C4⋊C4—34no—
317C3×C4⋊C4—34no—
318C3×C4⋊C4—34no—
319C3×C4⋊C4—34no—
320C3×C4⋊C4—34no—
321C3×C4⋊C4—34no—
322C3×C4⋊C4C2×C3×D314yes—
323C3×C4⋊C4C2×C3×D314yes—
324C3×C4⋊C4C2×C3×D314yes—
325C3×C4⋊C4C22×C3211yescharacteristic
326C3×C4⋊C4C22×C3211yescharacteristic
327C3×C4⋊C4C22×C3211yescharacteristic
328C3×C22⋊C4—24no—
329C3×C22⋊C4—24no—
330C3×C22⋊C4—34no—
331C3×C22⋊C4—34no—
332C3×C22⋊C4—34no—
333C3×C22⋊C4—34no—
334C3×C22⋊C4—34no—
335C3×C22⋊C4—34no—
336C3×C22⋊C4—34no—
337C3×C22⋊C4—34no—
338C3×C22⋊C4C2×C3×D314yes—
339C3×C22⋊C4C2×C3×D314yes—
340C3×C22⋊C4C22×C3211yescharacteristic
341C3×C22⋊C4C22×C3211yescharacteristic
342C3×C42—34no—
343C3×C42—34no—
344C3×C42—34no—
345#217C22×C3211yescharacteristic
346#217C22×C3211yescharacteristic
347#217C22×C3211yescharacteristic
348(C2×D3)⋊C4C22×C3211yescharacteristic
349(C2×D3)⋊C4C22×C3211yescharacteristic
350(C2×D3)⋊C4C22×C3211yescharacteristic
351(C2×D3)⋊C4C22×C3211yescharacteristic
352(C2×D3)⋊C4C22×C3211yescharacteristic
353C4⋊Dic3C22×C3211yescharacteristic
354C4⋊Dic3C22×C3211yescharacteristic
355C4⋊Dic3C22×C3211yescharacteristic
356C4⋊Dic3C22×C3211yescharacteristic
357Dic3⋊C4C22×C3211yescharacteristic
358Dic3⋊C4C22×C3211yescharacteristic
359Dic3⋊C4C22×C3211yescharacteristic
360Dic3⋊C4C22×C3211yescharacteristic
361Dic3⋊C4C22×C3211yescharacteristic
362Dic3⋊C4C22×C3211yescharacteristic
363Dic3⋊C4C22×C3211yescharacteristic
364Dic3⋊C4C22×C3211yescharacteristic
365Dic3⋊C4C22×C3211yescharacteristic
366C4×Dic3C22×C3211yescharacteristic
367C4×Dic3C22×C3211yescharacteristic
368C4×Dic3C22×C3211yescharacteristic
369C22×C32—28no—
370C22×C32—21no—
371C22×C32—21no—
372C22×C32—21no—
373C22×C32—24no—
374C22×C32—24no—
375C22×C32—24no—
376C22×C32—24no—
377C22×C32—44no—
378C22×C32—44no—
379C22×C32—61no—
380C22×C32—61no—
381C22×C32—61no—
382C22×C32C23×D311yescharacteristic
383C22×C32C24×C314yes—
384C2×C3×D3—24no—
385C2×C3×D3—24no—
386C2×C3×D3—24no—
387C32×C4—28no—
388C32×C4—21no—
389C32×C4—21no—
390C32×C4—21no—
391C32×C4—21no—
392C32×C4—21no—
393C32×C4—21no—
394C32×C4—24no—
395C32×C4—24no—
396C32×C4—24no—
397C32×C4—24no—
398C32×C4—24no—
399C32×C4—24no—
400C32×C4—44no—
401C32×C4—44no—
402C32×C4—44no—
403C32×C4—44no—
404C32×C4—44no—
405C32×C4—61no—
406C32×C4—61no—
407C32×C4—61no—
408C32×C4—61no—
409C32×C4—61no—
410C32×C4—61no—
411C32×C4—61no—
412C3×Dic3—24no—
413C3×Dic3—24no—
414C3×Dic3—24no—
415C3×Dic3—24no—
416C3×Dic3—24no—
417C3×Dic3—24no—
418C3×Dic3—24no—
419C4⋊Q8—31no—
420C4⋊Q8—31no—
421#126—31no—
422#126—31no—
423#126—31no—
424#126—31no—
425#125—31no—
426#125—31no—
427#124—31no—
428#123—31no—
429#123—31no—
430C22⋊Q8—31no—
431C22⋊Q8—31no—
432C22⋊Q8—31no—
433C22⋊Q8C32×D311yescharacteristic, complemented
434C33#56311yescharacteristic, complemented, Sylow
435C23×C3—24no—
436C23×C3—34no—
437C23×C3C22×C3×D314yes—
438C23×C3C23×C3211yescharacteristic
439C22×D3C23×C3211yescharacteristic
440C3×Q8—44no—
441C3×Q8—41no—
442C3×Q8—48no—
443C3×Q8—124no—
444C3×Q8—124no—
445C3×D4—124no—
446C2×C3×C4—24no—
447C2×C3×C4—24no—
448C2×C3×C4—24no—
449C2×C3×C4—24no—
450C2×C3×C4—24no—
451C2×C3×C4—24no—
452C2×C3×C4—34no—
453C2×C3×C4—34no—
454C2×C3×C4—34no—
455C2×C3×C4—34no—
456C2×C3×C4—34no—
457C2×C3×C4—34no—
458C2×C3×C4—34no—
459C2×C3×C4—44no—
460C2×C3×C4—41no—
461C2×C3×C4—48no—
462C2×C3×C4—124no—
463C2×C3×C4C22×C3×D314yes—
464C2×C3×C4C22×C3×D314yes—
465C2×C3×C4C22×C3×D314yes—
466C2×C3×C4C22×C3×D314yes—
467C2×C3×C4C22×C3×D314yes—
468C2×C3×C4C22×C3×D314yes—
469C2×C3×C4C23×C3211yescharacteristic
470C2×C3×C4C23×C3211yescharacteristic
471C2×C3×C4C23×C3211yescharacteristic
472C2×C3×C4C23×C3211yescharacteristic
473C2×C3×C4C23×C3211yescharacteristic
474C2×C3×C4C23×C3211yescharacteristic
475#67—41no—
476C2×Dic3C23×C3211yescharacteristic
477C2×Dic3C23×C3211yescharacteristic
478C2×Dic3C23×C3211yescharacteristic
479C2×Dic3C23×C3211yescharacteristic
480C2×Dic3C23×C3211yescharacteristic
481C2×Dic3C23×C3211yescharacteristic
482C2×Dic3C23×C3211yescharacteristic
483C4×D3—41no—
484Dic6—41no—
485Dic6—41no—
486C2×C32—24no—
487C2×C32—24no—
488C2×C32—24no—
489C2×C32—48no—
490C2×C32—44no—
491C2×C32—41no—
492C2×C32—121no—
493C2×C32#100411yescharacteristic
494C2×C32#100711yescharacteristic
495C2×C32#101011yescharacteristic
496C2×C32C3×H(5,𝔽2)14yes—
497C2×C32C3×2−1+414yes—
498C2×C32C3×2−1+414yes—
499C3×D3—44no—
500C2×Q8—31no—
501C2×Q8—31no—
502C2×Q8C2×C32×D311yescharacteristic
503C2×D4—31no—
504C22×C4—31no—
505C22×C4C2×C32×D311yescharacteristic
506C4⋊C4—31no—
507C4⋊C4—31no—
508C4⋊C4—31no—
509C4⋊C4—31no—
510C4⋊C4—31no—
511C4⋊C4—31no—
512C4⋊C4—31no—
513C4⋊C4—31no—
514C4⋊C4—31no—
515C4⋊C4—31no—
516C4⋊C4—31no—
517C4⋊C4—31no—
518C4⋊C4—31no—
519C4⋊C4C2×C32×D311yescharacteristic
520C4⋊C4C2×C32×D311yescharacteristic
521C4⋊C4C2×C32×D311yescharacteristic
522C22⋊C4—31no—
523C22⋊C4—31no—
524C22⋊C4—31no—
525C22⋊C4—31no—
526C22⋊C4—31no—
527C22⋊C4—31no—
528C22⋊C4—31no—
529C22⋊C4—31no—
530C22⋊C4C2×C32×D311yescharacteristic
531C22⋊C4C2×C32×D311yescharacteristic
532C42—31no—
533C42—31no—
534C42—31no—
535C22×C3—28no—
536C22×C3—24no—
537C22×C3—24no—
538C22×C3—24no—
539C22×C3—21no—
540C22×C3—21no—
541C22×C3—21no—
542C22×C3—24no—
543C22×C3—44no—
544C22×C3—44no—
545C22×C3—64no—
546C22×C3—64no—
547C22×C3—64no—
548C22×C3C23×C3×D314yes—
549C22×C3C24×C3211yescharacteristic
550C2×D3—21no—
551C2×D3—21no—
552C2×D3—21no—
553C3×C4—28no—
554C3×C4—24no—
555C3×C4—24no—
556C3×C4—24no—
557C3×C4—24no—
558C3×C4—24no—
559C3×C4—24no—
560C3×C4—21no—
561C3×C4—21no—
562C3×C4—21no—
563C3×C4—21no—
564C3×C4—21no—
565C3×C4—21no—
566C3×C4—44no—
567C3×C4—44no—
568C3×C4—44no—
569C3×C4—44no—
570C3×C4—44no—
571C3×C4—64no—
572C3×C4—64no—
573C3×C4—64no—
574C3×C4—64no—
575C3×C4—64no—
576C3×C4—64no—
577C3×C4—64no—
578Dic3—21no—
579Dic3—21no—
580Dic3—21no—
581Dic3—21no—
582Dic3—21no—
583Dic3—21no—
584Dic3—21no—
585C32—24no—
586C32#564611yescharacteristic, direct product factor
587C32C3×#56314yescomplemented
588C23—31no—
589C23C22×C32×D311yescharacteristic
590Q8—41no—
591Q8—121no—
592Q8—121no—
593D4—121no—
594C2×C4—31no—
595C2×C4—31no—
596C2×C4—31no—
597C2×C4—31no—
598C2×C4—31no—
599C2×C4—31no—
600C2×C4—31no—
601C2×C4—41no—
602C2×C4—121no—
603C2×C4C22×C32×D311yescharacteristic
604C2×C4C22×C32×D311yescharacteristic
605C2×C4C22×C32×D311yescharacteristic
606C2×C4C22×C32×D311yescharacteristic
607C2×C4C22×C32×D311yescharacteristic
608C2×C4C22×C32×D311yescharacteristic
609C2×C3—24no—
610C2×C3—24no—
611C2×C3—24no—
612C2×C3—48no—
613C2×C3—41no—
614C2×C3—44no—
615C2×C3—124no—
616C2×C3C3×#100414yes—
617C2×C3C3×#100714yes—
618C2×C3C3×#101014yes—
619C2×C3C32×H(5,𝔽2)11yescharacteristic
620C2×C3C32×2−1+411yescharacteristic
621C2×C3C32×2−1+411yescharacteristic
622D3—41no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—61no—
627C22—61no—
628C22—61no—
629C22C23×C32×D311yescharacteristic
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—61no—
637C4—61no—
638C4—61no—
639C4—61no—
640C4—61no—
641C4—61no—
642C4—61no—
643C3—24no—
644C3C3×#564614yesdirect product factor
645C3C32×#56311yescharacteristic, complemented
646C2—41no—
647C2—121no—
648C2C32×#100411yescharacteristic
649C2C32×#100711yescharacteristic
650C2C32×#101011yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×C22⋊Q8C2
socleC22×C33C24
prime radicalC2×C32×#67C22
hypercenterC32×C22⋊Q8D3
hypocenterC3C32×#563
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×#946C2semidirect
3. C32×#944C2semidirect
5. C32×#924C2semidirect
6. C32×#898C2semidirect
7. C32×#898C2semidirect
8. C32×#896C2semidirect
9. C32×#890C2semidirect
10. C32×#889C2semidirect
11. C32×#888C2semidirect
14. C32×#879C2semidirect
15. C32×#879C2semidirect
17. C3×#5646C3direct (N × H)
68. C32×C22⋊Q8D3semidirect
69. C32×C22⋊Q8C2×C3semidirect
70. C3×#946C2×C3semidirect
71. C3×#944C2×C3semidirect
73. C3×#924C2×C3semidirect
74. C3×#898C2×C3semidirect
75. C3×#898C2×C3semidirect
76. C3×#896C2×C3semidirect
77. C3×#890C2×C3semidirect
78. C3×#889C2×C3semidirect
79. C3×#888C2×C3semidirect
82. C3×#879C2×C3semidirect
83. C3×#879C2×C3semidirect
106. #5646C32direct (N × H)
219. C3×C22⋊Q8C3×D3semidirect
220. C3×C22⋊Q8C2×C32semidirect
221. #946C2×C32semidirect
222. #944C2×C32semidirect
224. #924C2×C32semidirect
225. #898C2×C32semidirect
226. #898C2×C32semidirect
227. #896C2×C32semidirect
228. #890C2×C32semidirect
229. #889C2×C32semidirect
230. #888C2×C32semidirect
233. #879C2×C32semidirect
234. #879C2×C32semidirect
433. C22⋊Q8C32×D3semidirect
434. C33#563semidirect
586. C32#5646direct (N × H)
587. C32C3×#563semidirect
644. C3C3×#5646direct (N × H)
645. C3C32×#563semidirect

Maximal subgroups

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

subgroupindex
C33×C22⋊Q82
C32×#9462
C32×#9442
C32×#9292
C32×#9242
C32×#8982
C32×#8962
C32×#8902
C32×#8892
C32×#8882
C32×#8852
C32×#8832
C32×#8792
C32×#5633
C3×#56463