Finite Group Databasebeta

← C32×#5647 #13179024

Subgroups — C32×#5647 #13179024

Order 1728.

1616 conjugacy classes of subgroups.

The subgroup lattice has 724 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×#946C211yesmaximal, characteristic, complemented
4C32×#930C211yesmaximal, characteristic, complemented
5C32×#929C211yesmaximal, characteristic, complemented
6C32×#897C211yesmaximal, characteristic, complemented
7C32×#896C211yesmaximal, characteristic, complemented
8C32×#895C211yesmaximal, characteristic, complemented
9C32×#894C211yesmaximal, characteristic, complemented
10C32×#894C211yesmaximal, characteristic, complemented
11C32×#889C211yesmaximal, characteristic, complemented
12C32×#885C211yesmaximal, characteristic, complemented
13C32×#884C211yesmaximal, characteristic, complemented
14C32×#884C211yesmaximal, characteristic, complemented
15C32×#883C211yesmaximal, characteristic, complemented
16C32×#562—31nomaximal
17C3×#5647C314yesmaximal, direct product factor
18C2×C33×Q8C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×D12C2211yescharacteristic
24C2×C32×D12C2211yescharacteristic
25C2×C32×D12C2211yescharacteristic
26C2×C32×C4×D3C2211yescharacteristic
27C2×C32×C4×D3C2211yescharacteristic
28C2×C32×C4×D3C2211yescharacteristic
29C2×C32×Dic6C2211yescharacteristic
30C33×C4⋊C4C2211yescharacteristic
31C33×C4⋊C4C2211yescharacteristic
32C33×C4⋊C4C2211yescharacteristic
33C33×C22⋊C4C2211yescharacteristic
34C33×C22⋊C4C2211yescharacteristic
35C32×#217C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×(C2×D3)⋊C4C2211yescharacteristic
45C32×C4⋊Dic3C2211yescharacteristic
46C32×C4⋊Dic3C2211yescharacteristic
47C32×Dic3⋊C4C2211yescharacteristic
48C32×Dic3⋊C4C2211yescharacteristic
49C32×Dic3⋊C4C2211yescharacteristic
50C32×Dic3⋊C4C2211yescharacteristic
51C32×Dic3⋊C4C2211yescharacteristic
52C32×C4×Dic3C2211yescharacteristic
53C32×#125—31no—
54C32×#124—31no—
55C32×#124—31no—
56C32×#123—31no—
57C32×#123—31no—
58C32×#123—31no—
59C32×#123—31no—
60C32×C22⋊Q8—24no—
61C32×C22⋊Q8—31no—
62C32×C22⋊Q8—31no—
63C32×C22⋊Q8—31no—
64C32×C22⋊Q8D311yescharacteristic, complemented
65C32×C22⋊Q8C2×C314yescomplemented
66C32×#121—31no—
67C32×#121—31no—
68C32×#121—31no—
69C32×#121—31no—
70C3×#947C2×C314yescomplemented
71C3×#946C2×C314yescomplemented
72C3×#930C2×C314yescomplemented
73C3×#929C2×C314yescomplemented
74C3×#897C2×C314yescomplemented
75C3×#896C2×C314yescomplemented
76C3×#895C2×C314yescomplemented
77C3×#894C2×C314yescomplemented
78C3×#894C2×C314yescomplemented
79C3×#889C2×C314yescomplemented
80C3×#885C2×C314yescomplemented
81C3×#884C2×C314yescomplemented
82C3×#884C2×C314yescomplemented
83C3×#883C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C22×C32×D3C2311yescharacteristic
86C22×C32×D3C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C33×Q8—41no—
89C2×C33×C4—41no—
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C2×C33×C4C2311yescharacteristic
96C32×#67—41no—
97C32×#67—41no—
98C32×#67—41no—
99C2×C32×Dic3C2311yescharacteristic
100C2×C32×Dic3C2311yescharacteristic
101C2×C32×Dic3C2311yescharacteristic
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C32×D12—41no—
105C32×D12—41no—
106C32×D12—41no—
107C32×C4×D3—41no—
108C32×C4×D3—41no—
109C32×C4×D3—41no—
110C32×Dic6—41no—
111C3×#562—34no—
112#5647C3211yescharacteristic, direct product factor
113C2×C32×Q8—24no—
114C2×C32×Q8—31no—
115C2×C32×Q8C2×D311yescharacteristic
116C2×C32×Q8C22×C314yes—
117C2×C32×D4—31no—
118C2×C32×D4—31no—
119C2×C32×D4—31no—
120C2×C32×D4—31no—
121C2×C32×D4—31no—
122C2×C32×D4—31no—
123C22×C32×C4—24no—
124C22×C32×C4—31no—
125C22×C32×C4—31no—
126C22×C32×C4—31no—
127C22×C32×C4C2×D311yescharacteristic
128C22×C32×C4C22×C314yes—
129C2×C3×#67C22×C314yes—
130C2×C3×#67C22×C314yes—
131C2×C3×#67C22×C314yes—
132C2×C3×D12C22×C314yes—
133C2×C3×D12C22×C314yes—
134C2×C3×D12C22×C314yes—
135C2×C3×C4×D3C22×C314yes—
136C2×C3×C4×D3C22×C314yes—
137C2×C3×C4×D3C22×C314yes—
138C2×C3×Dic6C22×C314yes—
139C32×C4⋊C4—24no—
140C32×C4⋊C4—24no—
141C32×C4⋊C4—24no—
142C32×C4⋊C4—31no—
143C32×C4⋊C4—31no—
144C32×C4⋊C4—31no—
145C32×C4⋊C4—31no—
146C32×C4⋊C4—31no—
147C32×C4⋊C4—31no—
148C32×C4⋊C4—31no—
149C32×C4⋊C4C2×D311yescharacteristic
150C32×C4⋊C4C2×D311yescharacteristic
151C32×C4⋊C4C2×D311yescharacteristic
152C32×C4⋊C4C22×C314yes—
153C32×C4⋊C4C22×C314yes—
154C32×C4⋊C4C22×C314yes—
155C32×C22⋊C4—24no—
156C32×C22⋊C4—24no—
157C32×C22⋊C4—31no—
158C32×C22⋊C4—31no—
159C32×C22⋊C4—31no—
160C32×C22⋊C4—31no—
161C32×C22⋊C4—31no—
162C32×C22⋊C4—31no—
163C32×C22⋊C4—31no—
164C32×C22⋊C4—31no—
165C32×C22⋊C4—31no—
166C32×C22⋊C4—31no—
167C32×C22⋊C4C2×D311yescharacteristic
168C32×C22⋊C4C2×D311yescharacteristic
169C32×C22⋊C4C22×C314yes—
170C32×C22⋊C4C22×C314yes—
171C32×C42—31no—
172C3×#217C22×C314yes—
173C3×(C2×D3)⋊C4C22×C314yes—
174C3×(C2×D3)⋊C4C22×C314yes—
175C3×(C2×D3)⋊C4C22×C314yes—
176C3×(C2×D3)⋊C4C22×C314yes—
177C3×(C2×D3)⋊C4C22×C314yes—
178C3×(C2×D3)⋊C4C22×C314yes—
179C3×(C2×D3)⋊C4C22×C314yes—
180C3×(C2×D3)⋊C4C22×C314yes—
181C3×(C2×D3)⋊C4C22×C314yes—
182C3×C4⋊Dic3C22×C314yes—
183C3×C4⋊Dic3C22×C314yes—
184C3×Dic3⋊C4C22×C314yes—
185C3×Dic3⋊C4C22×C314yes—
186C3×Dic3⋊C4C22×C314yes—
187C3×Dic3⋊C4C22×C314yes—
188C3×Dic3⋊C4C22×C314yes—
189C3×C4×Dic3C22×C314yes—
190C22×C33—21no—
191C22×C33—21no—
192C22×C33—21no—
193C22×C33C2411yescharacteristic
194C2×C32×D3—21no—
195C2×C32×D3—21no—
196C2×C32×D3—21no—
197C2×C32×D3—21no—
198C2×C32×D3—21no—
199C2×C32×D3—21no—
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3—21no—
203C33×C4—21no—
204C33×C4—21no—
205C33×C4—21no—
206C33×C4—21no—
207C33×C4—21no—
208C33×C4—21no—
209C32×Dic3—21no—
210C32×Dic3—21no—
211C32×Dic3—21no—
212C32×Dic3—21no—
213C32×Dic3—21no—
214C3×#125—34no—
215C3×#124—34no—
216C3×#124—34no—
217C3×#123—34no—
218C3×#123—34no—
219C3×#123—34no—
220C3×#123—34no—
221C3×C22⋊Q8—24no—
222C3×C22⋊Q8—34no—
223C3×C22⋊Q8—34no—
224C3×C22⋊Q8—34no—
225C3×C22⋊Q8C3×D314yescomplemented
226C3×C22⋊Q8C2×C3211yescharacteristic, complemented
227C3×#121—34no—
228C3×#121—34no—
229C3×#121—34no—
230C3×#121—34no—
231#947C2×C3211yescharacteristic, complemented
232#946C2×C3211yescharacteristic, complemented
233#930C2×C3211yescharacteristic, complemented
234#929C2×C3211yescharacteristic, complemented
235#897C2×C3211yescharacteristic, complemented
236#896C2×C3211yescharacteristic, complemented
237#895C2×C3211yescharacteristic, complemented
238#894C2×C3211yescharacteristic, complemented
239#894C2×C3211yescharacteristic, complemented
240#889C2×C3211yescharacteristic, complemented
241#885C2×C3211yescharacteristic, complemented
242#884C2×C3211yescharacteristic, complemented
243#884C2×C3211yescharacteristic, complemented
244#883C2×C3211yescharacteristic, complemented
245C23×C32—24no—
246C23×C32—31no—
247C23×C32—31no—
248C23×C32—31no—
249C23×C32C22×D311yescharacteristic
250C23×C32C23×C314yes—
251C22×C3×D3C23×C314yes—
252C22×C3×D3C23×C314yes—
253C22×C3×D3C23×C314yes—
254C32×Q8—41no—
255C32×Q8—44no—
256C32×Q8—48no—
257C32×Q8—121no—
258C32×D4—121no—
259C32×D4—121no—
260C32×D4—121no—
261C32×D4—121no—
262C32×D4—121no—
263C32×D4—121no—
264C2×C32×C4—24no—
265C2×C32×C4—24no—
266C2×C32×C4—24no—
267C2×C32×C4—24no—
268C2×C32×C4—24no—
269C2×C32×C4—24no—
270C2×C32×C4—31no—
271C2×C32×C4—31no—
272C2×C32×C4—31no—
273C2×C32×C4—31no—
274C2×C32×C4—31no—
275C2×C32×C4—41no—
276C2×C32×C4—44no—
277C2×C32×C4—48no—
278C2×C32×C4—121no—
279C2×C32×C4—121no—
280C2×C32×C4—121no—
281C2×C32×C4C22×D311yescharacteristic
282C2×C32×C4C22×D311yescharacteristic
283C2×C32×C4C22×D311yescharacteristic
284C2×C32×C4C22×D311yescharacteristic
285C2×C32×C4C22×D311yescharacteristic
286C2×C32×C4C22×D311yescharacteristic
287C2×C32×C4C23×C314yes—
288C2×C32×C4C23×C314yes—
289C2×C32×C4C23×C314yes—
290C2×C32×C4C23×C314yes—
291C2×C32×C4C23×C314yes—
292C2×C32×C4C23×C314yes—
293C3×#67—44no—
294C3×#67—44no—
295C3×#67—44no—
296C2×C3×Dic3C23×C314yes—
297C2×C3×Dic3C23×C314yes—
298C2×C3×Dic3C23×C314yes—
299C2×C3×Dic3C23×C314yes—
300C2×C3×Dic3C23×C314yes—
301C3×D12—44no—
302C3×D12—44no—
303C3×D12—44no—
304C3×C4×D3—44no—
305C3×C4×D3—44no—
306C3×C4×D3—44no—
307C3×Dic6—44no—
308#562—31noSylow
309C2×C33—41no—
310C2×C33H(5,𝔽2)11yescharacteristic
311C2×C33H(5,𝔽2)11yescharacteristic
312C2×C332−1+411yescharacteristic
313C32×D3—41no—
314C32×D3—41no—
315C32×D3—41no—
316C2×C3×Q8—24no—
317C2×C3×Q8—34no—
318C2×C3×Q8C2×C3×D314yes—
319C2×C3×Q8C22×C3211yescharacteristic
320C2×C3×D4—34no—
321C2×C3×D4—34no—
322C2×C3×D4—34no—
323C2×C3×D4—34no—
324C2×C3×D4—34no—
325C2×C3×D4—34no—
326C22×C3×C4—24no—
327C22×C3×C4—34no—
328C22×C3×C4—34no—
329C22×C3×C4—34no—
330C22×C3×C4C2×C3×D314yes—
331C22×C3×C4C22×C3211yescharacteristic
332C2×#67C22×C3211yescharacteristic
333C2×#67C22×C3211yescharacteristic
334C2×#67C22×C3211yescharacteristic
335C2×D12C22×C3211yescharacteristic
336C2×D12C22×C3211yescharacteristic
337C2×D12C22×C3211yescharacteristic
338C2×C4×D3C22×C3211yescharacteristic
339C2×C4×D3C22×C3211yescharacteristic
340C2×C4×D3C22×C3211yescharacteristic
341C2×Dic6C22×C3211yescharacteristic
342C3×C4⋊C4—24no—
343C3×C4⋊C4—24no—
344C3×C4⋊C4—24no—
345C3×C4⋊C4—34no—
346C3×C4⋊C4—34no—
347C3×C4⋊C4—34no—
348C3×C4⋊C4—34no—
349C3×C4⋊C4—34no—
350C3×C4⋊C4—34no—
351C3×C4⋊C4—34no—
352C3×C4⋊C4C2×C3×D314yes—
353C3×C4⋊C4C2×C3×D314yes—
354C3×C4⋊C4C2×C3×D314yes—
355C3×C4⋊C4C22×C3211yescharacteristic
356C3×C4⋊C4C22×C3211yescharacteristic
357C3×C4⋊C4C22×C3211yescharacteristic
358C3×C22⋊C4—24no—
359C3×C22⋊C4—24no—
360C3×C22⋊C4—34no—
361C3×C22⋊C4—34no—
362C3×C22⋊C4—34no—
363C3×C22⋊C4—34no—
364C3×C22⋊C4—34no—
365C3×C22⋊C4—34no—
366C3×C22⋊C4—34no—
367C3×C22⋊C4—34no—
368C3×C22⋊C4—34no—
369C3×C22⋊C4—34no—
370C3×C22⋊C4C2×C3×D314yes—
371C3×C22⋊C4C2×C3×D314yes—
372C3×C22⋊C4C22×C3211yescharacteristic
373C3×C22⋊C4C22×C3211yescharacteristic
374C3×C42—34no—
375#217C22×C3211yescharacteristic
376(C2×D3)⋊C4C22×C3211yescharacteristic
377(C2×D3)⋊C4C22×C3211yescharacteristic
378(C2×D3)⋊C4C22×C3211yescharacteristic
379(C2×D3)⋊C4C22×C3211yescharacteristic
380(C2×D3)⋊C4C22×C3211yescharacteristic
381(C2×D3)⋊C4C22×C3211yescharacteristic
382(C2×D3)⋊C4C22×C3211yescharacteristic
383(C2×D3)⋊C4C22×C3211yescharacteristic
384(C2×D3)⋊C4C22×C3211yescharacteristic
385C4⋊Dic3C22×C3211yescharacteristic
386C4⋊Dic3C22×C3211yescharacteristic
387Dic3⋊C4C22×C3211yescharacteristic
388Dic3⋊C4C22×C3211yescharacteristic
389Dic3⋊C4C22×C3211yescharacteristic
390Dic3⋊C4C22×C3211yescharacteristic
391Dic3⋊C4C22×C3211yescharacteristic
392C4×Dic3C22×C3211yescharacteristic
393C22×C32—28no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—24no—
398C22×C32—24no—
399C22×C32—24no—
400C22×C32—24no—
401C22×C32—44no—
402C22×C32—44no—
403C22×C32—61no—
404C22×C32—61no—
405C22×C32—61no—
406C22×C32—61no—
407C22×C32—61no—
408C22×C32—61no—
409C22×C32—61no—
410C22×C32—61no—
411C22×C32—61no—
412C22×C32C23×D311yescharacteristic
413C22×C32C24×C314yes—
414C2×C3×D3—24no—
415C2×C3×D3—24no—
416C2×C3×D3—24no—
417C2×C3×D3—24no—
418C2×C3×D3—24no—
419C2×C3×D3—24no—
420C2×C3×D3—24no—
421C2×C3×D3—24no—
422C2×C3×D3—24no—
423C32×C4—28no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—21no—
428C32×C4—21no—
429C32×C4—21no—
430C32×C4—24no—
431C32×C4—24no—
432C32×C4—24no—
433C32×C4—24no—
434C32×C4—24no—
435C32×C4—24no—
436C32×C4—44no—
437C32×C4—44no—
438C32×C4—44no—
439C32×C4—44no—
440C32×C4—44no—
441C32×C4—61no—
442C32×C4—61no—
443C32×C4—61no—
444C32×C4—61no—
445C32×C4—61no—
446C3×Dic3—24no—
447C3×Dic3—24no—
448C3×Dic3—24no—
449C3×Dic3—24no—
450C3×Dic3—24no—
451#125—31no—
452#124—31no—
453#124—31no—
454#123—31no—
455#123—31no—
456#123—31no—
457#123—31no—
458C22⋊Q8—31no—
459C22⋊Q8—31no—
460C22⋊Q8—31no—
461C22⋊Q8C32×D311yescharacteristic, complemented
462#121—31no—
463#121—31no—
464#121—31no—
465#121—31no—
466C33#56211yescharacteristic, complemented, Sylow
467C23×C3—24no—
468C23×C3—34no—
469C23×C3—34no—
470C23×C3—34no—
471C23×C3C22×C3×D314yes—
472C23×C3C23×C3211yescharacteristic
473C22×D3C23×C3211yescharacteristic
474C22×D3C23×C3211yescharacteristic
475C22×D3C23×C3211yescharacteristic
476C3×Q8—44no—
477C3×Q8—41no—
478C3×Q8—48no—
479C3×Q8—124no—
480C3×D4—124no—
481C3×D4—124no—
482C3×D4—124no—
483C3×D4—124no—
484C3×D4—124no—
485C3×D4—124no—
486C2×C3×C4—24no—
487C2×C3×C4—24no—
488C2×C3×C4—24no—
489C2×C3×C4—24no—
490C2×C3×C4—24no—
491C2×C3×C4—24no—
492C2×C3×C4—34no—
493C2×C3×C4—34no—
494C2×C3×C4—34no—
495C2×C3×C4—34no—
496C2×C3×C4—34no—
497C2×C3×C4—44no—
498C2×C3×C4—41no—
499C2×C3×C4—48no—
500C2×C3×C4—124no—
501C2×C3×C4—124no—
502C2×C3×C4—124no—
503C2×C3×C4C22×C3×D314yes—
504C2×C3×C4C22×C3×D314yes—
505C2×C3×C4C22×C3×D314yes—
506C2×C3×C4C22×C3×D314yes—
507C2×C3×C4C22×C3×D314yes—
508C2×C3×C4C22×C3×D314yes—
509C2×C3×C4C23×C3211yescharacteristic
510C2×C3×C4C23×C3211yescharacteristic
511C2×C3×C4C23×C3211yescharacteristic
512C2×C3×C4C23×C3211yescharacteristic
513C2×C3×C4C23×C3211yescharacteristic
514C2×C3×C4C23×C3211yescharacteristic
515#67—41no—
516#67—41no—
517#67—41no—
518C2×Dic3C23×C3211yescharacteristic
519C2×Dic3C23×C3211yescharacteristic
520C2×Dic3C23×C3211yescharacteristic
521C2×Dic3C23×C3211yescharacteristic
522C2×Dic3C23×C3211yescharacteristic
523D12—41no—
524D12—41no—
525D12—41no—
526C4×D3—41no—
527C4×D3—41no—
528C4×D3—41no—
529Dic6—41no—
530C2×C32—24no—
531C2×C32—24no—
532C2×C32—24no—
533C2×C32—48no—
534C2×C32—44no—
535C2×C32—41no—
536C2×C32—121no—
537C2×C32—121no—
538C2×C32—121no—
539C2×C32#100411yescharacteristic
540C2×C32#100711yescharacteristic
541C2×C32#100911yescharacteristic
542C2×C32C3×H(5,𝔽2)14yes—
543C2×C32C3×H(5,𝔽2)14yes—
544C2×C32C3×2−1+414yes—
545C3×D3—44no—
546C3×D3—44no—
547C3×D3—44no—
548C2×Q8—31no—
549C2×Q8C2×C32×D311yescharacteristic
550C2×D4—31no—
551C2×D4—31no—
552C2×D4—31no—
553C2×D4—31no—
554C2×D4—31no—
555C2×D4—31no—
556C22×C4—31no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4C2×C32×D311yescharacteristic
560C4⋊C4—31no—
561C4⋊C4—31no—
562C4⋊C4—31no—
563C4⋊C4—31no—
564C4⋊C4—31no—
565C4⋊C4—31no—
566C4⋊C4—31no—
567C4⋊C4C2×C32×D311yescharacteristic
568C4⋊C4C2×C32×D311yescharacteristic
569C4⋊C4C2×C32×D311yescharacteristic
570C22⋊C4—31no—
571C22⋊C4—31no—
572C22⋊C4—31no—
573C22⋊C4—31no—
574C22⋊C4—31no—
575C22⋊C4—31no—
576C22⋊C4—31no—
577C22⋊C4—31no—
578C22⋊C4—31no—
579C22⋊C4—31no—
580C22⋊C4C2×C32×D311yescharacteristic
581C22⋊C4C2×C32×D311yescharacteristic
582C42—31no—
583C22×C3—28no—
584C22×C3—24no—
585C22×C3—24no—
586C22×C3—24no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—24no—
591C22×C3—44no—
592C22×C3—44no—
593C22×C3—64no—
594C22×C3—64no—
595C22×C3—64no—
596C22×C3—64no—
597C22×C3—64no—
598C22×C3—64no—
599C22×C3—64no—
600C22×C3—64no—
601C22×C3—64no—
602C22×C3C23×C3×D314yes—
603C22×C3C24×C3211yescharacteristic
604C2×D3—21no—
605C2×D3—21no—
606C2×D3—21no—
607C2×D3—21no—
608C2×D3—21no—
609C2×D3—21no—
610C2×D3—21no—
611C2×D3—21no—
612C2×D3—21no—
613C3×C4—28no—
614C3×C4—24no—
615C3×C4—24no—
616C3×C4—24no—
617C3×C4—24no—
618C3×C4—24no—
619C3×C4—24no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—44no—
627C3×C4—44no—
628C3×C4—44no—
629C3×C4—44no—
630C3×C4—44no—
631C3×C4—64no—
632C3×C4—64no—
633C3×C4—64no—
634C3×C4—64no—
635C3×C4—64no—
636Dic3—21no—
637Dic3—21no—
638Dic3—21no—
639Dic3—21no—
640Dic3—21no—
641C32—24no—
642C32#564711yescharacteristic, direct product factor
643C32C3×#56214yescomplemented
644C23—31no—
645C23—31no—
646C23—31no—
647C23C22×C32×D311yescharacteristic
648Q8—41no—
649Q8—121no—
650D4—121no—
651D4—121no—
652D4—121no—
653D4—121no—
654D4—121no—
655D4—121no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—31no—
661C2×C4—41no—
662C2×C4—121no—
663C2×C4—121no—
664C2×C4—121no—
665C2×C4C22×C32×D311yescharacteristic
666C2×C4C22×C32×D311yescharacteristic
667C2×C4C22×C32×D311yescharacteristic
668C2×C4C22×C32×D311yescharacteristic
669C2×C4C22×C32×D311yescharacteristic
670C2×C4C22×C32×D311yescharacteristic
671C2×C3—24no—
672C2×C3—24no—
673C2×C3—24no—
674C2×C3—48no—
675C2×C3—41no—
676C2×C3—44no—
677C2×C3—124no—
678C2×C3—124no—
679C2×C3—124no—
680C2×C3C3×#100414yes—
681C2×C3C3×#100714yes—
682C2×C3C3×#100914yes—
683C2×C3C32×H(5,𝔽2)11yescharacteristic
684C2×C3C32×H(5,𝔽2)11yescharacteristic
685C2×C3C32×2−1+411yescharacteristic
686D3—41no—
687D3—41no—
688D3—41no—
689C22—21no—
690C22—21no—
691C22—21no—
692C22—61no—
693C22—61no—
694C22—61no—
695C22—61no—
696C22—61no—
697C22—61no—
698C22—61no—
699C22—61no—
700C22—61no—
701C22C23×C32×D311yescharacteristic
702C4—21no—
703C4—21no—
704C4—21no—
705C4—21no—
706C4—21no—
707C4—21no—
708C4—61no—
709C4—61no—
710C4—61no—
711C4—61no—
712C4—61no—
713C3—24no—
714C3C3×#564714yesdirect product factor
715C3C32×#56211yescharacteristic, complemented
716C2—41no—
717C2—121no—
718C2—121no—
719C2—121no—
720C2C32×#100411yescharacteristic
721C2C32×#100711yescharacteristic
722C2C32×#100911yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×C22⋊Q8C2
socleC22×C33C24
hypercenterC32×C22⋊Q8D3
hypocenterC3C32×#562
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×#946C2semidirect
4. C32×#930C2semidirect
5. C32×#929C2semidirect
6. C32×#897C2semidirect
7. C32×#896C2semidirect
8. C32×#895C2semidirect
9. C32×#894C2semidirect
10. C32×#894C2semidirect
11. C32×#889C2semidirect
12. C32×#885C2semidirect
13. C32×#884C2semidirect
14. C32×#884C2semidirect
15. C32×#883C2semidirect
17. C3×#5647C3direct (N × H)
64. C32×C22⋊Q8D3semidirect
65. C32×C22⋊Q8C2×C3semidirect
70. C3×#947C2×C3semidirect
71. C3×#946C2×C3semidirect
72. C3×#930C2×C3semidirect
73. C3×#929C2×C3semidirect
74. C3×#897C2×C3semidirect
75. C3×#896C2×C3semidirect
76. C3×#895C2×C3semidirect
77. C3×#894C2×C3semidirect
78. C3×#894C2×C3semidirect
79. C3×#889C2×C3semidirect
80. C3×#885C2×C3semidirect
81. C3×#884C2×C3semidirect
82. C3×#884C2×C3semidirect
83. C3×#883C2×C3semidirect
112. #5647C32direct (N × H)
225. C3×C22⋊Q8C3×D3semidirect
226. C3×C22⋊Q8C2×C32semidirect
231. #947C2×C32semidirect
232. #946C2×C32semidirect
233. #930C2×C32semidirect
234. #929C2×C32semidirect
235. #897C2×C32semidirect
236. #896C2×C32semidirect
237. #895C2×C32semidirect
238. #894C2×C32semidirect
239. #894C2×C32semidirect
240. #889C2×C32semidirect
241. #885C2×C32semidirect
242. #884C2×C32semidirect
243. #884C2×C32semidirect
244. #883C2×C32semidirect
461. C22⋊Q8C32×D3semidirect
466. C33#562semidirect
642. C32#5647direct (N × H)
643. C32C3×#562semidirect
714. C3C3×#5647direct (N × H)
715. C3C32×#562semidirect

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×#9462
C32×#9302
C32×#9292
C32×#8972
C32×#8962
C32×#8952
C32×#8942
C32×#8892
C32×#8852
C32×#8842
C32×#8832
C32×#5623
C3×#56473