Finite Group Databasebeta

← C32×#5701 #13179078

Subgroups — C32×#5701 #13179078

Order 1728.

1392 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×#126C211yesmaximal, characteristic
2C32×#890C211yesmaximal, characteristic, complemented
3C32×#889C211yesmaximal, characteristic, complemented
4C32×#889C211yesmaximal, characteristic, complemented
5C32×#889C211yesmaximal, characteristic, complemented
6C32×#888C211yesmaximal, characteristic, complemented
7C32×#887C211yesmaximal, characteristic, complemented
8C32×#879C211yesmaximal, characteristic
9C32×#879C211yesmaximal, characteristic
10C32×#879C211yesmaximal, characteristic
11C32×#878C211yesmaximal, characteristic
12C32×#878C211yesmaximal, characteristic
13C32×#877C211yesmaximal, characteristic
14C32×#870C211yesmaximal, characteristic, complemented
15C32×C4×Dic6C211yesmaximal, characteristic, complemented
16C32×#541—31nomaximal
17C3×#5701C314yesmaximal, direct product factor
18C22×C32×Dic3C2211yescharacteristic
19C2×C32×Dic6C2211yescharacteristic
20C2×C32×Dic6C2211yescharacteristic
21C33×C4⋊C4C2211yescharacteristic
22C33×C4⋊C4C2211yescharacteristic
23C33×C4⋊C4C2211yescharacteristic
24C33×C22⋊C4C2211yescharacteristic
25C33×C22⋊C4C2211yescharacteristic
26C33×C22⋊C4C2211yescharacteristic
27C33×C42C2211yescharacteristic
28C32×#217C2211yescharacteristic
29C32×#217C2211yescharacteristic
30C32×#217C2211yescharacteristic
31C32×C4⋊Dic3C2211yescharacteristic
32C32×C4⋊Dic3C2211yescharacteristic
33C32×C4⋊Dic3C2211yescharacteristic
34C32×C4⋊Dic3C2211yescharacteristic
35C32×C4⋊Dic3C2211yescharacteristic
36C32×Dic3⋊C4C2211yescharacteristic
37C32×Dic3⋊C4C2211yescharacteristic
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×C4⋊Q8—31no—
54C32×#126—24no—
55C32×#126—31no—
56C32×#126—31no—
57C32×#126—31no—
58C32×#126D311yescharacteristic
59C32×#126C2×C314yes—
60C32×#125—31no—
61C32×#125—31no—
62C32×#125—31no—
63C32×#125—31no—
64C32×#125—31no—
65C32×C22⋊Q8—31no—
66C32×C22⋊Q8—31no—
67C32×C4×Q8—31no—
68C32×C4×Q8—31no—
69C32×#117—31no—
70C3×#890C2×C314yescomplemented
71C3×#889C2×C314yescomplemented
72C3×#889C2×C314yescomplemented
73C3×#889C2×C314yescomplemented
74C3×#888C2×C314yescomplemented
75C3×#887C2×C314yescomplemented
76C3×#879C2×C314yes—
77C3×#879C2×C314yes—
78C3×#879C2×C314yes—
79C3×#878C2×C314yes—
80C3×#878C2×C314yes—
81C3×#877C2×C314yes—
82C3×#870C2×C314yescomplemented
83C3×C4×Dic6C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C2×C33×C4C2311yescharacteristic
86C2×C33×C4C2311yescharacteristic
87C2×C33×C4C2311yescharacteristic
88C2×C33×C4C2311yescharacteristic
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C32×Dic3—22no—
92C2×C32×Dic3C2311yescharacteristic
93C2×C32×Dic3C2311yescharacteristic
94C2×C32×Dic3C2311yescharacteristic
95C2×C32×Dic3C2311yescharacteristic
96C2×C32×Dic3C2311yescharacteristic
97C2×C32×Dic3C2311yescharacteristic
98C2×C32×Dic3C2311yescharacteristic
99C2×C32×Dic3C2311yescharacteristic
100C32×Dic6—22no—
101C32×Dic6—22no—
102C3×#541—34no—
103#5701C3211yescharacteristic, direct product factor
104C2×C32×Q8—31no—
105C2×C32×Q8—31no—
106C22×C32×C4—31no—
107C22×C3×Dic3C22×C314yes—
108C2×C3×Dic6C22×C314yes—
109C2×C3×Dic6C22×C314yes—
110C32×C4⋊C4—24no—
111C32×C4⋊C4—24no—
112C32×C4⋊C4—24no—
113C32×C4⋊C4—31no—
114C32×C4⋊C4—31no—
115C32×C4⋊C4—31no—
116C32×C4⋊C4—31no—
117C32×C4⋊C4—31no—
118C32×C4⋊C4—31no—
119C32×C4⋊C4—31no—
120C32×C4⋊C4—31no—
121C32×C4⋊C4—31no—
122C32×C4⋊C4—31no—
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⋊C4C2×D311yescharacteristic
131C32×C4⋊C4C2×D311yescharacteristic
132C32×C4⋊C4C2×D311yescharacteristic
133C32×C4⋊C4C22×C314yes—
134C32×C4⋊C4C22×C314yes—
135C32×C4⋊C4C22×C314yes—
136C32×C22⋊C4—24no—
137C32×C22⋊C4—24no—
138C32×C22⋊C4—24no—
139C32×C22⋊C4—31no—
140C32×C22⋊C4—31no—
141C32×C22⋊C4—31no—
142C32×C22⋊C4C2×D311yescharacteristic
143C32×C22⋊C4C2×D311yescharacteristic
144C32×C22⋊C4C2×D311yescharacteristic
145C32×C22⋊C4C22×C314yes—
146C32×C22⋊C4C22×C314yes—
147C32×C22⋊C4C22×C314yes—
148C32×C42—24no—
149C32×C42—31no—
150C32×C42—31no—
151C32×C42—31no—
152C32×C42—31no—
153C32×C42—31no—
154C32×C42C2×D311yescharacteristic
155C32×C42C22×C314yes—
156C3×#217C22×C314yes—
157C3×#217C22×C314yes—
158C3×#217C22×C314yes—
159C3×C4⋊Dic3C22×C314yes—
160C3×C4⋊Dic3C22×C314yes—
161C3×C4⋊Dic3C22×C314yes—
162C3×C4⋊Dic3C22×C314yes—
163C3×C4⋊Dic3C22×C314yes—
164C3×Dic3⋊C4C22×C314yes—
165C3×Dic3⋊C4C22×C314yes—
166C3×Dic3⋊C4C22×C314yes—
167C3×Dic3⋊C4C22×C314yes—
168C3×Dic3⋊C4C22×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×C4×Dic3C22×C314yes—
177C3×C4×Dic3C22×C314yes—
178C3×C4×Dic3C22×C314yes—
179C3×C4×Dic3C22×C314yes—
180C3×C4×Dic3C22×C314yes—
181C22×C33—21no—
182C22×C33—21no—
183C22×C33—21no—
184C22×C33C2411yescharacteristic
185C33×C4—21no—
186C33×C4—21no—
187C33×C4—21no—
188C33×C4—21no—
189C33×C4—21no—
190C33×C4—21no—
191C32×Dic3—21no—
192C32×Dic3—21no—
193C32×Dic3—21no—
194C32×Dic3—21no—
195C32×Dic3—21no—
196C32×Dic3—21no—
197C32×Dic3—21no—
198C32×Dic3#4112yes—
199C3×C4⋊Q8—34no—
200C3×#126—24no—
201C3×#126—34no—
202C3×#126—34no—
203C3×#126—34no—
204C3×#126C3×D314yes—
205C3×#126C2×C3211yescharacteristic
206C3×#125—34no—
207C3×#125—34no—
208C3×#125—34no—
209C3×#125—34no—
210C3×#125—34no—
211C3×C22⋊Q8—34no—
212C3×C22⋊Q8—34no—
213C3×C4×Q8—34no—
214C3×C4×Q8—34no—
215C3×#117—34no—
216#890C2×C3211yescharacteristic, complemented
217#889C2×C3211yescharacteristic, complemented
218#889C2×C3211yescharacteristic, complemented
219#889C2×C3211yescharacteristic, complemented
220#888C2×C3211yescharacteristic, complemented
221#887C2×C3211yescharacteristic, complemented
222#879C2×C3211yescharacteristic
223#879C2×C3211yescharacteristic
224#879C2×C3211yescharacteristic
225#878C2×C3211yescharacteristic
226#878C2×C3211yescharacteristic
227#877C2×C3211yescharacteristic
228#870C2×C3211yescharacteristic, complemented
229C4×Dic6C2×C3211yescharacteristic, complemented
230C23×C32—24no—
231C23×C32C22×D311yescharacteristic
232C23×C32C23×C314yes—
233C32×Q8—62no—
234C32×Q8—62no—
235C2×C32×C4—24no—
236C2×C32×C4—24no—
237C2×C32×C4—24no—
238C2×C32×C4—24no—
239C2×C32×C4—24no—
240C2×C32×C4—24no—
241C2×C32×C4—31no—
242C2×C32×C4—31no—
243C2×C32×C4—31no—
244C2×C32×C4—31no—
245C2×C32×C4—31no—
246C2×C32×C4—31no—
247C2×C32×C4—31no—
248C2×C32×C4—31no—
249C2×C32×C4—62no—
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C23×C314yes—
257C2×C32×C4C23×C314yes—
258C2×C32×C4C23×C314yes—
259C2×C32×C4C23×C314yes—
260C2×C32×C4C23×C314yes—
261C2×C32×C4C23×C314yes—
262C2×C3×Dic3—28no—
263C2×C3×Dic3C23×C314yes—
264C2×C3×Dic3C23×C314yes—
265C2×C3×Dic3C23×C314yes—
266C2×C3×Dic3C23×C314yes—
267C2×C3×Dic3C23×C314yes—
268C2×C3×Dic3C23×C314yes—
269C2×C3×Dic3C23×C314yes—
270C2×C3×Dic3C23×C314yes—
271C3×Dic6—28no—
272C3×Dic6—28no—
273#541—31noSylow
274C2×C33—41no—
275C2×C33C2×#4111yescharacteristic
276C2×C332−1+411yescharacteristic
277C2×C332−1+411yescharacteristic
278C2×C3×Q8—34no—
279C2×C3×Q8—34no—
280C22×C3×C4—34no—
281C22×Dic3C22×C3211yescharacteristic
282C2×Dic6C22×C3211yescharacteristic
283C2×Dic6C22×C3211yescharacteristic
284C3×C4⋊C4—24no—
285C3×C4⋊C4—24no—
286C3×C4⋊C4—24no—
287C3×C4⋊C4—34no—
288C3×C4⋊C4—34no—
289C3×C4⋊C4—34no—
290C3×C4⋊C4—34no—
291C3×C4⋊C4—34no—
292C3×C4⋊C4—34no—
293C3×C4⋊C4—34no—
294C3×C4⋊C4—34no—
295C3×C4⋊C4—34no—
296C3×C4⋊C4—34no—
297C3×C4⋊C4—34no—
298C3×C4⋊C4—34no—
299C3×C4⋊C4—34no—
300C3×C4⋊C4—34no—
301C3×C4⋊C4—34no—
302C3×C4⋊C4—34no—
303C3×C4⋊C4—34no—
304C3×C4⋊C4C2×C3×D314yes—
305C3×C4⋊C4C2×C3×D314yes—
306C3×C4⋊C4C2×C3×D314yes—
307C3×C4⋊C4C22×C3211yescharacteristic
308C3×C4⋊C4C22×C3211yescharacteristic
309C3×C4⋊C4C22×C3211yescharacteristic
310C3×C22⋊C4—24no—
311C3×C22⋊C4—24no—
312C3×C22⋊C4—24no—
313C3×C22⋊C4—34no—
314C3×C22⋊C4—34no—
315C3×C22⋊C4—34no—
316C3×C22⋊C4C2×C3×D314yes—
317C3×C22⋊C4C2×C3×D314yes—
318C3×C22⋊C4C2×C3×D314yes—
319C3×C22⋊C4C22×C3211yescharacteristic
320C3×C22⋊C4C22×C3211yescharacteristic
321C3×C22⋊C4C22×C3211yescharacteristic
322C3×C42—24no—
323C3×C42—34no—
324C3×C42—34no—
325C3×C42—34no—
326C3×C42—34no—
327C3×C42—34no—
328C3×C42C2×C3×D314yes—
329C3×C42C22×C3211yescharacteristic
330#217C22×C3211yescharacteristic
331#217C22×C3211yescharacteristic
332#217C22×C3211yescharacteristic
333C4⋊Dic3C22×C3211yescharacteristic
334C4⋊Dic3C22×C3211yescharacteristic
335C4⋊Dic3C22×C3211yescharacteristic
336C4⋊Dic3C22×C3211yescharacteristic
337C4⋊Dic3C22×C3211yescharacteristic
338Dic3⋊C4C22×C3211yescharacteristic
339Dic3⋊C4C22×C3211yescharacteristic
340Dic3⋊C4C22×C3211yescharacteristic
341Dic3⋊C4C22×C3211yescharacteristic
342Dic3⋊C4C22×C3211yescharacteristic
343Dic3⋊C4C22×C3211yescharacteristic
344Dic3⋊C4C22×C3211yescharacteristic
345Dic3⋊C4C22×C3211yescharacteristic
346Dic3⋊C4C22×C3211yescharacteristic
347Dic3⋊C4C22×C3211yescharacteristic
348Dic3⋊C4C22×C3211yescharacteristic
349Dic3⋊C4C22×C3211yescharacteristic
350C4×Dic3C22×C3211yescharacteristic
351C4×Dic3C22×C3211yescharacteristic
352C4×Dic3C22×C3211yescharacteristic
353C4×Dic3C22×C3211yescharacteristic
354C4×Dic3C22×C3211yescharacteristic
355C22×C32—21no—
356C22×C32—21no—
357C22×C32—21no—
358C22×C32—24no—
359C22×C32—24no—
360C22×C32—24no—
361C22×C32—24no—
362C22×C32—44no—
363C22×C32—44no—
364C22×C32—44no—
365C22×C32C23×D311yescharacteristic
366C22×C32C24×C314yes—
367C32×C4—21no—
368C32×C4—21no—
369C32×C4—21no—
370C32×C4—21no—
371C32×C4—21no—
372C32×C4—21no—
373C32×C4—24no—
374C32×C4—24no—
375C32×C4—24no—
376C32×C4—24no—
377C32×C4—24no—
378C32×C4—24no—
379C32×C4—32no—
380C32×C4—44no—
381C32×C4—44no—
382C32×C4—44no—
383C32×C4—44no—
384C32×C4—44no—
385C32×C4—44no—
386C32×C4—61no—
387C32×C4—61no—
388C32×C4—61no—
389C32×C4—61no—
390C32×C4—61no—
391C32×C4—61no—
392C32×C4—61no—
393C3×Dic3—24no—
394C3×Dic3—24no—
395C3×Dic3—24no—
396C3×Dic3—24no—
397C3×Dic3—24no—
398C3×Dic3—24no—
399C3×Dic3—24no—
400C3×Dic3C3×#4118yes—
401C4⋊Q8—31no—
402#126—31no—
403#126—31no—
404#126—31no—
405#126C32×D311yescharacteristic
406#125—31no—
407#125—31no—
408#125—31no—
409#125—31no—
410#125—31no—
411C22⋊Q8—31no—
412C22⋊Q8—31no—
413C4×Q8—31no—
414C4×Q8—31no—
415#117—31no—
416C33#54111yescharacteristic, complemented, Sylow
417C23×C3—24no—
418C23×C3C22×C3×D314yes—
419C23×C3C23×C3211yescharacteristic
420C3×Q8—68no—
421C3×Q8—68no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
425C2×C3×C4—24no—
426C2×C3×C4—24no—
427C2×C3×C4—24no—
428C2×C3×C4—34no—
429C2×C3×C4—34no—
430C2×C3×C4—34no—
431C2×C3×C4—34no—
432C2×C3×C4—34no—
433C2×C3×C4—34no—
434C2×C3×C4—34no—
435C2×C3×C4—34no—
436C2×C3×C4—68no—
437C2×C3×C4C22×C3×D314yes—
438C2×C3×C4C22×C3×D314yes—
439C2×C3×C4C22×C3×D314yes—
440C2×C3×C4C22×C3×D314yes—
441C2×C3×C4C22×C3×D314yes—
442C2×C3×C4C22×C3×D314yes—
443C2×C3×C4C23×C3211yescharacteristic
444C2×C3×C4C23×C3211yescharacteristic
445C2×C3×C4C23×C3211yescharacteristic
446C2×C3×C4C23×C3211yescharacteristic
447C2×C3×C4C23×C3211yescharacteristic
448C2×C3×C4C23×C3211yescharacteristic
449C2×Dic3—22no—
450C2×Dic3C23×C3211yescharacteristic
451C2×Dic3C23×C3211yescharacteristic
452C2×Dic3C23×C3211yescharacteristic
453C2×Dic3C23×C3211yescharacteristic
454C2×Dic3C23×C3211yescharacteristic
455C2×Dic3C23×C3211yescharacteristic
456C2×Dic3C23×C3211yescharacteristic
457C2×Dic3C23×C3211yescharacteristic
458Dic6—22no—
459Dic6—22no—
460C2×C32—24no—
461C2×C32—24no—
462C2×C32—24no—
463C2×C32—41no—
464C2×C32—44no—
465C2×C32—84no—
466C2×C32D3×#4111yescharacteristic
467C2×C32#101011yescharacteristic
468C2×C32#101011yescharacteristic
469C2×C32C2×C3×#4114yes—
470C2×C32C3×2−1+414yes—
471C2×C32C3×2−1+414yes—
472C2×Q8—31no—
473C2×Q8—31no—
474C22×C4—31no—
475C4⋊C4—31no—
476C4⋊C4—31no—
477C4⋊C4—31no—
478C4⋊C4—31no—
479C4⋊C4—31no—
480C4⋊C4—31no—
481C4⋊C4—31no—
482C4⋊C4—31no—
483C4⋊C4—31no—
484C4⋊C4—31no—
485C4⋊C4—31no—
486C4⋊C4—31no—
487C4⋊C4—31no—
488C4⋊C4—31no—
489C4⋊C4—31no—
490C4⋊C4—31no—
491C4⋊C4—31no—
492C4⋊C4C2×C32×D311yescharacteristic
493C4⋊C4C2×C32×D311yescharacteristic
494C4⋊C4C2×C32×D311yescharacteristic
495C22⋊C4—31no—
496C22⋊C4—31no—
497C22⋊C4—31no—
498C22⋊C4C2×C32×D311yescharacteristic
499C22⋊C4C2×C32×D311yescharacteristic
500C22⋊C4C2×C32×D311yescharacteristic
501C42—31no—
502C42—31no—
503C42—31no—
504C42—31no—
505C42—31no—
506C42C2×C32×D311yescharacteristic
507C22×C3—24no—
508C22×C3—24no—
509C22×C3—24no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—24no—
514C22×C3—44no—
515C22×C3—44no—
516C22×C3—44no—
517C22×C3C23×C3×D314yes—
518C22×C3C24×C3211yescharacteristic
519C3×C4—24no—
520C3×C4—24no—
521C3×C4—24no—
522C3×C4—24no—
523C3×C4—24no—
524C3×C4—24no—
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—21no—
528C3×C4—21no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—38no—
532C3×C4—44no—
533C3×C4—44no—
534C3×C4—44no—
535C3×C4—44no—
536C3×C4—44no—
537C3×C4—44no—
538C3×C4—64no—
539C3×C4—64no—
540C3×C4—64no—
541C3×C4—64no—
542C3×C4—64no—
543C3×C4—64no—
544C3×C4—64no—
545Dic3—21no—
546Dic3—21no—
547Dic3—21no—
548Dic3—21no—
549Dic3—21no—
550Dic3—21no—
551Dic3—21no—
552Dic3C32×#4112yes—
553C32—24no—
554C32#570111yescharacteristic, direct product factor
555C32C3×#54114yescomplemented
556C23C22×C32×D311yescharacteristic
557Q8—62no—
558Q8—62no—
559C2×C4—31no—
560C2×C4—31no—
561C2×C4—31no—
562C2×C4—31no—
563C2×C4—31no—
564C2×C4—31no—
565C2×C4—31no—
566C2×C4—31no—
567C2×C4—62no—
568C2×C4C22×C32×D311yescharacteristic
569C2×C4C22×C32×D311yescharacteristic
570C2×C4C22×C32×D311yescharacteristic
571C2×C4C22×C32×D311yescharacteristic
572C2×C4C22×C32×D311yescharacteristic
573C2×C4C22×C32×D311yescharacteristic
574C2×C3—24no—
575C2×C3—24no—
576C2×C3—24no—
577C2×C3—44no—
578C2×C3—41no—
579C2×C3—84no—
580C2×C3C3×D3×#4114yes—
581C2×C3C3×#101014yes—
582C2×C3C3×#101014yes—
583C2×C3C2×C32×#4111yescharacteristic
584C2×C3C32×2−1+411yescharacteristic
585C2×C3C32×2−1+411yescharacteristic
586C22—21no—
587C22—21no—
588C22—21no—
589C22C23×C32×D311yescharacteristic
590C4—21no—
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—21no—
596C4—32no—
597C4—61no—
598C4—61no—
599C4—61no—
600C4—61no—
601C4—61no—
602C4—61no—
603C4—61no—
604C3—24no—
605C3C3×#570114yesdirect product factor
606C3C32×#54111yescharacteristic, complemented
607C2—41no—
608C2C32×D3×#4111yescharacteristic
609C2C32×#101011yescharacteristic
610C2C32×#101011yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#126C2
socleC22×C33C24
prime radicalC23×C33C23
hypercenterC32×#126D3
hypocenterC3C32×#541
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×#126

Complements

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

NH ≅ G/Ntype
2. C32×#890C2semidirect
3. C32×#889C2semidirect
4. C32×#889C2semidirect
5. C32×#889C2semidirect
6. C32×#888C2semidirect
7. C32×#887C2semidirect
14. C32×#870C2semidirect
15. C32×C4×Dic6C2semidirect
17. C3×#5701C3direct (N × H)
70. C3×#890C2×C3semidirect
71. C3×#889C2×C3semidirect
72. C3×#889C2×C3semidirect
73. C3×#889C2×C3semidirect
74. C3×#888C2×C3semidirect
75. C3×#887C2×C3semidirect
82. C3×#870C2×C3semidirect
83. C3×C4×Dic6C2×C3semidirect
103. #5701C32direct (N × H)
216. #890C2×C32semidirect
217. #889C2×C32semidirect
218. #889C2×C32semidirect
219. #889C2×C32semidirect
220. #888C2×C32semidirect
221. #887C2×C32semidirect
228. #870C2×C32semidirect
229. C4×Dic6C2×C32semidirect
416. C33#541semidirect
554. C32#5701direct (N × H)
555. C32C3×#541semidirect
605. C3C3×#5701direct (N × H)
606. C3C32×#541semidirect

Maximal subgroups

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

subgroupindex
C33×#1262
C32×#8902
C32×#8892
C32×#8882
C32×#8872
C32×#8792
C32×#8782
C32×#8772
C32×#8702
C32×C4×Dic62
C32×#5413
C3×#57013