Finite Group Databasebeta

← C32×#5650 #13179029

Subgroups — C32×#5650 #13179029

Order 1728.

1596 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×#123C211yesmaximal, characteristic
2C32×#935C211yesmaximal, characteristic
3C32×D4×Dic3C211yesmaximal, characteristic
4C32×#926C211yesmaximal, characteristic, complemented
5C2×C32×Dic3⋊C4C211yesmaximal, characteristic, complemented
6C32×#890C211yesmaximal, characteristic, complemented
7C32×#889C211yesmaximal, characteristic, complemented
8C32×#889C211yesmaximal, characteristic, complemented
9C32×#887C211yesmaximal, characteristic, complemented
10C32×#879C211yesmaximal, characteristic, complemented
11C32×#879C211yesmaximal, characteristic, complemented
12C32×#878C211yesmaximal, characteristic, complemented
13C32×#878C211yesmaximal, characteristic, complemented
14C32×#877C211yesmaximal, characteristic, complemented
15C32×#877C211yesmaximal, characteristic, complemented
16C32×#552—31nomaximal
17C3×#5650C314yesmaximal, direct product factor
18C2×C33×D4C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic
20C22×C32×Dic3C2211yescharacteristic
21C22×C32×Dic3C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C2×C32×Dic6C2211yescharacteristic
24C33×C4⋊C4C2211yescharacteristic
25C33×C4⋊C4C2211yescharacteristic
26C33×C22⋊C4C2211yescharacteristic
27C33×C22⋊C4C2211yescharacteristic
28C33×C22⋊C4C2211yescharacteristic
29C32×#217C2211yescharacteristic
30C32×#217C2211yescharacteristic
31C32×#217C2211yescharacteristic
32C32×#217C2211yescharacteristic
33C32×#217C2211yescharacteristic
34C32×C4⋊Dic3C2211yescharacteristic
35C32×C4⋊Dic3C2211yescharacteristic
36C32×C4⋊Dic3C2211yescharacteristic
37C32×C4⋊Dic3C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic
39C32×Dic3⋊C4C2211yescharacteristic
40C32×Dic3⋊C4C2211yescharacteristic
41C32×Dic3⋊C4C2211yescharacteristic
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—31no—
54C32×#126—31no—
55C32×#125—31no—
56C32×#125—31no—
57C32×#125—31no—
58C32×#123—24no—
59C32×#123—31no—
60C32×#123D311yescharacteristic
61C32×#123C2×C314yes—
62C32×C22⋊Q8—31no—
63C32×C22⋊Q8—31no—
64C32×C4×Q8—31no—
65C32×C4×D4—31no—
66C32×#117—31no—
67C32×#117—31no—
68C32×#117—31no—
69C2×C32×C4⋊C4—31no—
70C3×#935C2×C314yes—
71C3×D4×Dic3C2×C314yes—
72C3×#926C2×C314yescomplemented
73C2×C3×Dic3⋊C4C2×C314yescomplemented
74C3×#890C2×C314yescomplemented
75C3×#889C2×C314yescomplemented
76C3×#889C2×C314yescomplemented
77C3×#887C2×C314yescomplemented
78C3×#879C2×C314yescomplemented
79C3×#879C2×C314yescomplemented
80C3×#878C2×C314yescomplemented
81C3×#878C2×C314yescomplemented
82C3×#877C2×C314yescomplemented
83C3×#877C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C33×D4—22no—
87C2×C33×C4—22no—
88C2×C33×C4C2311yescharacteristic
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C32×Dic3—22no—
94C2×C32×Dic3—22no—
95C2×C32×Dic3—22no—
96C2×C32×Dic3C2311yescharacteristic
97C2×C32×Dic3C2311yescharacteristic
98C2×C32×Dic3C2311yescharacteristic
99C2×C32×Dic3C2311yescharacteristic
100C2×C32×Dic3C2311yescharacteristic
101C2×C32×Dic3C2311yescharacteristic
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C32×Dic6—22no—
105C3×#552—34no—
106#5650C3211yescharacteristic, direct product factor
107C2×C32×Q8—31no—
108C2×C32×D4—24no—
109C2×C32×D4C2×D311yescharacteristic
110C2×C32×D4C22×C314yes—
111C22×C32×C4—24no—
112C22×C32×C4—31no—
113C22×C32×C4—31no—
114C22×C32×C4—31no—
115C22×C32×C4C2×D311yescharacteristic
116C22×C32×C4C22×C314yes—
117C22×C3×Dic3C22×C314yes—
118C22×C3×Dic3C22×C314yes—
119C22×C3×Dic3C22×C314yes—
120C2×C3×Dic6C22×C314yes—
121C32×C4⋊C4—24no—
122C32×C4⋊C4—24no—
123C32×C4⋊C4—31no—
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⋊C4C22×C314yes—
140C32×C4⋊C4C22×C314yes—
141C32×C22⋊C4—24no—
142C32×C22⋊C4—24no—
143C32×C22⋊C4—24no—
144C32×C22⋊C4—31no—
145C32×C22⋊C4—31no—
146C32×C22⋊C4—31no—
147C32×C22⋊C4—31no—
148C32×C22⋊C4—31no—
149C32×C22⋊C4C2×D311yescharacteristic
150C32×C22⋊C4C2×D311yescharacteristic
151C32×C22⋊C4C2×D311yescharacteristic
152C32×C22⋊C4C22×C314yes—
153C32×C22⋊C4C22×C314yes—
154C32×C22⋊C4C22×C314yes—
155C32×C42—31no—
156C32×C42—31no—
157C32×C42—31no—
158C32×C42—31no—
159C32×C42—31no—
160C3×#217C22×C314yes—
161C3×#217C22×C314yes—
162C3×#217C22×C314yes—
163C3×#217C22×C314yes—
164C3×#217C22×C314yes—
165C3×C4⋊Dic3C22×C314yes—
166C3×C4⋊Dic3C22×C314yes—
167C3×C4⋊Dic3C22×C314yes—
168C3×C4⋊Dic3C22×C314yes—
169C3×Dic3⋊C4C22×C314yes—
170C3×Dic3⋊C4C22×C314yes—
171C3×Dic3⋊C4C22×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×C4×Dic3C22×C314yes—
180C3×C4×Dic3C22×C314yes—
181C3×C4×Dic3C22×C314yes—
182C3×C4×Dic3C22×C314yes—
183C3×C4×Dic3C22×C314yes—
184C22×C33—21no—
185C22×C33—21no—
186C22×C33—21no—
187C22×C33—21no—
188C22×C33—21no—
189C22×C33#4112yes—
190C22×C33C2411yescharacteristic
191C33×C4—21no—
192C33×C4—21no—
193C33×C4—21no—
194C33×C4—21no—
195C33×C4—21no—
196C32×Dic3—21no—
197C32×Dic3—21no—
198C32×Dic3—21no—
199C32×Dic3—21no—
200C32×Dic3—21no—
201C32×Dic3—21no—
202C32×Dic3—21no—
203C32×Dic3#4112yes—
204C3×#126—34no—
205C3×#126—34no—
206C3×#125—34no—
207C3×#125—34no—
208C3×#125—34no—
209C3×#123—24no—
210C3×#123—34no—
211C3×#123C3×D314yes—
212C3×#123C2×C3211yescharacteristic
213C3×C22⋊Q8—34no—
214C3×C22⋊Q8—34no—
215C3×C4×Q8—34no—
216C3×C4×D4—34no—
217C3×#117—34no—
218C3×#117—34no—
219C3×#117—34no—
220C2×C3×C4⋊C4—34no—
221#935C2×C3211yescharacteristic
222D4×Dic3C2×C3211yescharacteristic
223#926C2×C3211yescharacteristic, complemented
224C2×Dic3⋊C4C2×C3211yescharacteristic, complemented
225#890C2×C3211yescharacteristic, complemented
226#889C2×C3211yescharacteristic, complemented
227#889C2×C3211yescharacteristic, complemented
228#887C2×C3211yescharacteristic, complemented
229#879C2×C3211yescharacteristic, complemented
230#879C2×C3211yescharacteristic, complemented
231#878C2×C3211yescharacteristic, complemented
232#878C2×C3211yescharacteristic, complemented
233#877C2×C3211yescharacteristic, complemented
234#877C2×C3211yescharacteristic, complemented
235C23×C32—24no—
236C23×C32—24no—
237C23×C32C22×D311yescharacteristic
238C23×C32C22×D311yescharacteristic
239C23×C32C23×C314yes—
240C23×C32C23×C314yes—
241C32×Q8—62no—
242C32×D4—22no—
243C32×D4—28no—
244C32×D4—48no—
245C2×C32×C4—22no—
246C2×C32×C4—24no—
247C2×C32×C4—24no—
248C2×C32×C4—24no—
249C2×C32×C4—24no—
250C2×C32×C4—24no—
251C2×C32×C4—28no—
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—31no—
260C2×C32×C4—48no—
261C2×C32×C4—62no—
262C2×C32×C4—62no—
263C2×C32×C4—62no—
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×C3×Dic3—28no—
275C2×C3×Dic3—28no—
276C2×C3×Dic3—28no—
277C2×C3×Dic3C23×C314yes—
278C2×C3×Dic3C23×C314yes—
279C2×C3×Dic3C23×C314yes—
280C2×C3×Dic3C23×C314yes—
281C2×C3×Dic3C23×C314yes—
282C2×C3×Dic3C23×C314yes—
283C2×C3×Dic3C23×C314yes—
284C2×C3×Dic3C23×C314yes—
285C3×Dic6—28no—
286#552—31noSylow
287C2×C33—22no—
288C2×C33—41no—
289C2×C33C2×#4111yescharacteristic
290C2×C33C2×#4111yescharacteristic
291C2×C332−1+411yescharacteristic
292C2×C3×Q8—34no—
293C2×C3×D4—24no—
294C2×C3×D4C2×C3×D314yes—
295C2×C3×D4C22×C3211yescharacteristic
296C22×C3×C4—24no—
297C22×C3×C4—34no—
298C22×C3×C4—34no—
299C22×C3×C4—34no—
300C22×C3×C4C2×C3×D314yes—
301C22×C3×C4C22×C3211yescharacteristic
302C22×Dic3C22×C3211yescharacteristic
303C22×Dic3C22×C3211yescharacteristic
304C22×Dic3C22×C3211yescharacteristic
305C2×Dic6C22×C3211yescharacteristic
306C3×C4⋊C4—24no—
307C3×C4⋊C4—24no—
308C3×C4⋊C4—34no—
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⋊C4C22×C3211yescharacteristic
325C3×C4⋊C4C22×C3211yescharacteristic
326C3×C22⋊C4—24no—
327C3×C22⋊C4—24no—
328C3×C22⋊C4—24no—
329C3×C22⋊C4—34no—
330C3×C22⋊C4—34no—
331C3×C22⋊C4—34no—
332C3×C22⋊C4—34no—
333C3×C22⋊C4—34no—
334C3×C22⋊C4C2×C3×D314yes—
335C3×C22⋊C4C2×C3×D314yes—
336C3×C22⋊C4C2×C3×D314yes—
337C3×C22⋊C4C22×C3211yescharacteristic
338C3×C22⋊C4C22×C3211yescharacteristic
339C3×C22⋊C4C22×C3211yescharacteristic
340C3×C42—34no—
341C3×C42—34no—
342C3×C42—34no—
343C3×C42—34no—
344C3×C42—34no—
345#217C22×C3211yescharacteristic
346#217C22×C3211yescharacteristic
347#217C22×C3211yescharacteristic
348#217C22×C3211yescharacteristic
349#217C22×C3211yescharacteristic
350C4⋊Dic3C22×C3211yescharacteristic
351C4⋊Dic3C22×C3211yescharacteristic
352C4⋊Dic3C22×C3211yescharacteristic
353C4⋊Dic3C22×C3211yescharacteristic
354Dic3⋊C4C22×C3211yescharacteristic
355Dic3⋊C4C22×C3211yescharacteristic
356Dic3⋊C4C22×C3211yescharacteristic
357Dic3⋊C4C22×C3211yescharacteristic
358Dic3⋊C4C22×C3211yescharacteristic
359Dic3⋊C4C22×C3211yescharacteristic
360Dic3⋊C4C22×C3211yescharacteristic
361Dic3⋊C4C22×C3211yescharacteristic
362Dic3⋊C4C22×C3211yescharacteristic
363Dic3⋊C4C22×C3211yescharacteristic
364C4×Dic3C22×C3211yescharacteristic
365C4×Dic3C22×C3211yescharacteristic
366C4×Dic3C22×C3211yescharacteristic
367C4×Dic3C22×C3211yescharacteristic
368C4×Dic3C22×C3211yescharacteristic
369C22×C32—21no—
370C22×C32—21no—
371C22×C32—21no—
372C22×C32—21no—
373C22×C32—21no—
374C22×C32—24no—
375C22×C32—28no—
376C22×C32—24no—
377C22×C32—24no—
378C22×C32—24no—
379C22×C32—24no—
380C22×C32—24no—
381C22×C32—44no—
382C22×C32—44no—
383C22×C32—44no—
384C22×C32—44no—
385C22×C32—44no—
386C22×C32#23712yes—
387C22×C32C3×#4118yes—
388C22×C32C23×D311yescharacteristic
389C22×C32C24×C314yes—
390C32×C4—21no—
391C32×C4—21no—
392C32×C4—21no—
393C32×C4—21no—
394C32×C4—21no—
395C32×C4—24no—
396C32×C4—24no—
397C32×C4—24no—
398C32×C4—24no—
399C32×C4—24no—
400C32×C4—32no—
401C32×C4—44no—
402C32×C4—44no—
403C32×C4—44no—
404C32×C4—44no—
405C32×C4—44no—
406C32×C4—61no—
407C32×C4—61no—
408C32×C4—61no—
409C32×C4—61no—
410C32×C4—61no—
411C32×C4—61no—
412C32×C4—61no—
413C3×Dic3—24no—
414C3×Dic3—24no—
415C3×Dic3—24no—
416C3×Dic3—24no—
417C3×Dic3—24no—
418C3×Dic3—24no—
419C3×Dic3—24no—
420C3×Dic3C3×#4118yes—
421#126—31no—
422#126—31no—
423#125—31no—
424#125—31no—
425#125—31no—
426#123—31no—
427#123C32×D311yescharacteristic
428C22⋊Q8—31no—
429C22⋊Q8—31no—
430C4×Q8—31no—
431C4×D4—31no—
432#117—31no—
433#117—31no—
434#117—31no—
435C2×C4⋊C4—31no—
436C33#55211yescharacteristic, complemented, Sylow
437C23×C3—24no—
438C23×C3—24no—
439C23×C3C22×C3×D314yes—
440C23×C3C22×C3×D314yes—
441C23×C3C23×C3211yescharacteristic
442C23×C3C23×C3211yescharacteristic
443C3×Q8—68no—
444C3×D4—28no—
445C3×D4—22no—
446C3×D4—48no—
447C2×C3×C4—28no—
448C2×C3×C4—22no—
449C2×C3×C4—24no—
450C2×C3×C4—24no—
451C2×C3×C4—24no—
452C2×C3×C4—24no—
453C2×C3×C4—24no—
454C2×C3×C4—34no—
455C2×C3×C4—34no—
456C2×C3×C4—34no—
457C2×C3×C4—34no—
458C2×C3×C4—34no—
459C2×C3×C4—34no—
460C2×C3×C4—34no—
461C2×C3×C4—34no—
462C2×C3×C4—48no—
463C2×C3×C4—68no—
464C2×C3×C4—68no—
465C2×C3×C4—68no—
466C2×C3×C4C22×C3×D314yes—
467C2×C3×C4C22×C3×D314yes—
468C2×C3×C4C22×C3×D314yes—
469C2×C3×C4C22×C3×D314yes—
470C2×C3×C4C22×C3×D314yes—
471C2×C3×C4C23×C3211yescharacteristic
472C2×C3×C4C23×C3211yescharacteristic
473C2×C3×C4C23×C3211yescharacteristic
474C2×C3×C4C23×C3211yescharacteristic
475C2×C3×C4C23×C3211yescharacteristic
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3C23×C3211yescharacteristic
480C2×Dic3C23×C3211yescharacteristic
481C2×Dic3C23×C3211yescharacteristic
482C2×Dic3C23×C3211yescharacteristic
483C2×Dic3C23×C3211yescharacteristic
484C2×Dic3C23×C3211yescharacteristic
485C2×Dic3C23×C3211yescharacteristic
486C2×Dic3C23×C3211yescharacteristic
487Dic6—22no—
488C2×C32—22no—
489C2×C32—24no—
490C2×C32—24no—
491C2×C32—24no—
492C2×C32—28no—
493C2×C32—48no—
494C2×C32—41no—
495C2×C32—44no—
496C2×C32—84no—
497C2×C32C2×#23711yescharacteristic
498C2×C32D3×#4111yescharacteristic
499C2×C32#101011yescharacteristic
500C2×C32C2×C3×#4114yes—
501C2×C32C2×C3×#4114yes—
502C2×C32C3×2−1+414yes—
503C2×Q8—31no—
504C2×D4C2×C32×D311yescharacteristic
505C22×C4—31no—
506C22×C4—31no—
507C22×C4—31no—
508C22×C4C2×C32×D311yescharacteristic
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⋊C4—31no—
520C4⋊C4—31no—
521C4⋊C4—31no—
522C4⋊C4—31no—
523C4⋊C4C2×C32×D311yescharacteristic
524C4⋊C4C2×C32×D311yescharacteristic
525C22⋊C4—31no—
526C22⋊C4—31no—
527C22⋊C4—31no—
528C22⋊C4—31no—
529C22⋊C4—31no—
530C22⋊C4C2×C32×D311yescharacteristic
531C22⋊C4C2×C32×D311yescharacteristic
532C22⋊C4C2×C32×D311yescharacteristic
533C42—31no—
534C42—31no—
535C42—31no—
536C42—31no—
537C42—31no—
538C22×C3—24no—
539C22×C3—24no—
540C22×C3—21no—
541C22×C3—21no—
542C22×C3—24no—
543C22×C3—24no—
544C22×C3—24no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—24no—
549C22×C3—28no—
550C22×C3—44no—
551C22×C3—44no—
552C22×C3—44no—
553C22×C3—44no—
554C22×C3—44no—
555C22×C3C3×#23718yes—
556C22×C3C32×#4112yes—
557C22×C3C23×C3×D314yes—
558C22×C3C24×C3211yescharacteristic
559C3×C4—24no—
560C3×C4—24no—
561C3×C4—24no—
562C3×C4—24no—
563C3×C4—24no—
564C3×C4—21no—
565C3×C4—21no—
566C3×C4—21no—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—38no—
570C3×C4—44no—
571C3×C4—44no—
572C3×C4—44no—
573C3×C4—44no—
574C3×C4—44no—
575C3×C4—64no—
576C3×C4—64no—
577C3×C4—64no—
578C3×C4—64no—
579C3×C4—64no—
580C3×C4—64no—
581C3×C4—64no—
582Dic3—21no—
583Dic3—21no—
584Dic3—21no—
585Dic3—21no—
586Dic3—21no—
587Dic3—21no—
588Dic3—21no—
589Dic3C32×#4112yes—
590C32—24no—
591C32#565011yescharacteristic, direct product factor
592C32C3×#55214yescomplemented
593C23C22×C32×D311yescharacteristic
594C23C22×C32×D311yescharacteristic
595Q8—62no—
596D4—22no—
597C2×C4—22no—
598C2×C4—31no—
599C2×C4—31no—
600C2×C4—31no—
601C2×C4—31no—
602C2×C4—31no—
603C2×C4—31no—
604C2×C4—31no—
605C2×C4—31no—
606C2×C4—62no—
607C2×C4—62no—
608C2×C4—62no—
609C2×C4C22×C32×D311yescharacteristic
610C2×C4C22×C32×D311yescharacteristic
611C2×C4C22×C32×D311yescharacteristic
612C2×C4C22×C32×D311yescharacteristic
613C2×C4C22×C32×D311yescharacteristic
614C2×C3—22no—
615C2×C3—28no—
616C2×C3—24no—
617C2×C3—24no—
618C2×C3—24no—
619C2×C3—48no—
620C2×C3—41no—
621C2×C3—44no—
622C2×C3—84no—
623C2×C3C2×C3×#23714yes—
624C2×C3C3×D3×#4114yes—
625C2×C3C3×#101014yes—
626C2×C3C2×C32×#4111yescharacteristic
627C2×C3C2×C32×#4111yescharacteristic
628C2×C3C32×2−1+411yescharacteristic
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22C32×#23712yes—
635C22C23×C32×D311yescharacteristic
636C4—21no—
637C4—21no—
638C4—21no—
639C4—21no—
640C4—21no—
641C4—32no—
642C4—61no—
643C4—61no—
644C4—61no—
645C4—61no—
646C4—61no—
647C4—61no—
648C4—61no—
649C3—24no—
650C3C3×#565014yesdirect product factor
651C3C32×#55211yescharacteristic, complemented
652C2—22no—
653C2—41no—
654C2C2×C32×#23711yescharacteristic
655C2C32×D3×#4111yescharacteristic
656C2C32×#101011yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#123C2
socleC22×C33C24
prime radicalC2×C33×D4C22
hypercenterC32×#123D3
hypocenterC3C32×#552
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×#123

Complements

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

NH ≅ G/Ntype
4. C32×#926C2semidirect
5. C2×C32×Dic3⋊C4C2semidirect
6. C32×#890C2semidirect
7. C32×#889C2semidirect
8. C32×#889C2semidirect
9. C32×#887C2semidirect
10. C32×#879C2semidirect
11. C32×#879C2semidirect
12. C32×#878C2semidirect
13. C32×#878C2semidirect
14. C32×#877C2semidirect
15. C32×#877C2semidirect
17. C3×#5650C3direct (N × H)
72. C3×#926C2×C3semidirect
73. C2×C3×Dic3⋊C4C2×C3semidirect
74. C3×#890C2×C3semidirect
75. C3×#889C2×C3semidirect
76. C3×#889C2×C3semidirect
77. C3×#887C2×C3semidirect
78. C3×#879C2×C3semidirect
79. C3×#879C2×C3semidirect
80. C3×#878C2×C3semidirect
81. C3×#878C2×C3semidirect
82. C3×#877C2×C3semidirect
83. C3×#877C2×C3semidirect
106. #5650C32direct (N × H)
223. #926C2×C32semidirect
224. C2×Dic3⋊C4C2×C32semidirect
225. #890C2×C32semidirect
226. #889C2×C32semidirect
227. #889C2×C32semidirect
228. #887C2×C32semidirect
229. #879C2×C32semidirect
230. #879C2×C32semidirect
231. #878C2×C32semidirect
232. #878C2×C32semidirect
233. #877C2×C32semidirect
234. #877C2×C32semidirect
436. C33#552semidirect
591. C32#5650direct (N × H)
592. C32C3×#552semidirect
650. C3C3×#5650direct (N × H)
651. C3C32×#552semidirect

Maximal subgroups

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

subgroupindex
C33×#1232
C32×#9352
C32×D4×Dic32
C32×#9262
C2×C32×Dic3⋊C42
C32×#8902
C32×#8892
C32×#8872
C32×#8792
C32×#8782
C32×#8772
C32×#5523
C3×#56503