Finite Group Databasebeta

← C32×#5556 #13178934

Subgroups — C32×#5556 #13178934

Order 1728.

1864 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×C4×D4C211yesmaximal, characteristic, complemented
2C32×#937C211yesmaximal, characteristic
3C32×#935C211yesmaximal, characteristic, complemented
4C32×#929C211yesmaximal, characteristic, complemented
5C32×C4×#67C211yesmaximal, characteristic, complemented
6C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7C32×#924C211yesmaximal, characteristic, complemented
8C32×#898C211yesmaximal, characteristic, complemented
9C32×#896C211yesmaximal, characteristic, complemented
10C32×#885C211yesmaximal, characteristic, complemented
11C32×#883C211yesmaximal, characteristic, complemented
12C32×D3×C22⋊C4C211yesmaximal, characteristic, complemented
13C32×#877C211yesmaximal, characteristic, complemented
14C32×#876C211yesmaximal, characteristic, complemented
15C32×#872C211yesmaximal, characteristic, complemented
16C32×#551—31nomaximal
17C3×#5556C314yesmaximal, direct product factor
18C23×C32×D3C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic
21C22×C33×C4C2211yescharacteristic, complemented
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic
26C2×C32×C4×D3C2211yescharacteristic
27C2×C32×Dic6C2211yescharacteristic, complemented
28C33×C4⋊C4C2211yescharacteristic, complemented
29C33×C22⋊C4C2211yescharacteristic
30C33×C22⋊C4C2211yescharacteristic, complemented
31C33×C42C2211yescharacteristic, complemented
32C32×#217C2211yescharacteristic
33C32×#217C2211yescharacteristic
34C32×#217C2211yescharacteristic, complemented
35C32×#217C2211yescharacteristic, complemented
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×C4⋊Dic3C2211yescharacteristic, complemented
45C32×Dic3⋊C4C2211yescharacteristic, complemented
46C32×Dic3⋊C4C2211yescharacteristic, complemented
47C32×Dic3⋊C4C2211yescharacteristic, complemented
48C32×Dic3⋊C4C2211yescharacteristic, complemented
49C32×Dic3⋊C4C2211yescharacteristic, complemented
50C32×Dic3⋊C4C2211yescharacteristic, complemented
51C32×C4×Dic3C2211yescharacteristic, complemented
52C32×C4×Dic3C2211yescharacteristic, complemented
53C32×#126—31no—
54C32×#126—31no—
55C32×#124—31no—
56C32×#123—31no—
57C32×#123—31no—
58C32×#123—31no—
59C32×C22⋊Q8—31no—
60C32×C22⋊Q8—31no—
61C32×#120—31no—
62C32×C4×D4—24no—
63C32×C4×D4—31no—
64C32×C4×D4D311yescharacteristic, complemented
65C32×C4×D4C2×C314yescomplemented
66C32×#117—31no—
67C32×#117—31no—
68C2×C32×C22⋊C4—31no—
69C2×C32×C22⋊C4—31no—
70C3×#937C2×C314yes—
71C3×#935C2×C314yescomplemented
72C3×#929C2×C314yescomplemented
73C3×C4×#67C2×C314yescomplemented
74C2×C3×(C2×D3)⋊C4C2×C314yescomplemented
75C3×#924C2×C314yescomplemented
76C3×#898C2×C314yescomplemented
77C3×#896C2×C314yescomplemented
78C3×#885C2×C314yescomplemented
79C3×#883C2×C314yescomplemented
80C3×D3×C22⋊C4C2×C314yescomplemented
81C3×#877C2×C314yescomplemented
82C3×#876C2×C314yescomplemented
83C3×#872C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C22×C32×D3—22no—
87C22×C32×D3—22no—
88C22×C32×D3—41no—
89C22×C32×D3C2311yescharacteristic
90C22×C32×D3C2311yescharacteristic
91C33×D4—22no—
92C2×C33×C4—41no—
93C2×C33×C4—41no—
94C2×C33×C4C2311yescharacteristic
95C2×C33×C4C2311yescharacteristic
96C2×C33×C4C2311yescharacteristic
97C2×C33×C4C2311yescharacteristic
98C2×C33×C4C2311yescharacteristic
99C32×#67—22no—
100C32×#67—41no—
101C2×C32×Dic3—22no—
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C32×C4×D3—22no—
109C32×C4×D3—41no—
110C32×Dic6—41no—
111C3×#551—34no—
112#5556C3211yescharacteristic, direct product factor
113C24×C32—31no—
114C23×C3×D3C22×C314yes—
115C2×C32×Q8—31no—
116C2×C32×D4—24no—
117C2×C32×D4—31no—
118C2×C32×D4—31no—
119C2×C32×D4C2×D311yescharacteristic
120C2×C32×D4C22×C314yes—
121C22×C32×C4—24no—
122C22×C32×C4—24no—
123C22×C32×C4—31no—
124C22×C32×C4—31no—
125C22×C32×C4—31no—
126C22×C32×C4C2×D311yescharacteristic
127C22×C32×C4C2×D311yescharacteristic, complemented
128C22×C32×C4C22×C314yes—
129C22×C32×C4C22×C314yescomplemented
130C2×C3×#67C22×C314yes—
131C2×C3×#67C22×C314yes—
132C22×C3×Dic3C22×C314yes—
133C2×C3×C4×D3C22×C314yes—
134C2×C3×C4×D3C22×C314yes—
135C2×C3×Dic6C22×C314yescomplemented
136C32×C4⋊C4—24no—
137C32×C4⋊C4—31no—
138C32×C4⋊C4—31no—
139C32×C4⋊C4—31no—
140C32×C4⋊C4—31no—
141C32×C4⋊C4—31no—
142C32×C4⋊C4—31no—
143C32×C4⋊C4—31no—
144C32×C4⋊C4C2×D311yescharacteristic, complemented
145C32×C4⋊C4C22×C314yescomplemented
146C32×C22⋊C4—24no—
147C32×C22⋊C4—24no—
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⋊C4—31no—
155C32×C22⋊C4—31no—
156C32×C22⋊C4—31no—
157C32×C22⋊C4—31no—
158C32×C22⋊C4—31no—
159C32×C22⋊C4—31no—
160C32×C22⋊C4C2×D311yescharacteristic
161C32×C22⋊C4C2×D311yescharacteristic, complemented
162C32×C22⋊C4C22×C314yes—
163C32×C22⋊C4C22×C314yescomplemented
164C32×C42—24no—
165C32×C42—31no—
166C32×C42—31no—
167C32×C42C2×D311yescharacteristic, complemented
168C32×C42C22×C314yescomplemented
169C3×#217C22×C314yes—
170C3×#217C22×C314yes—
171C3×#217C22×C314yescomplemented
172C3×#217C22×C314yescomplemented
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×C4⋊Dic3C22×C314yescomplemented
182C3×Dic3⋊C4C22×C314yescomplemented
183C3×Dic3⋊C4C22×C314yescomplemented
184C3×Dic3⋊C4C22×C314yescomplemented
185C3×Dic3⋊C4C22×C314yescomplemented
186C3×Dic3⋊C4C22×C314yescomplemented
187C3×Dic3⋊C4C22×C314yescomplemented
188C3×C4×Dic3C22×C314yescomplemented
189C3×C4×Dic3C22×C314yescomplemented
190C22×C33—21no—
191C22×C33—21no—
192C22×C33—21no—
193C22×C33—21no—
194C22×C33—21no—
195C22×C33#4112yes—
196C22×C33C2411yescharacteristic
197C2×C32×D3—21no—
198C2×C32×D3—21no—
199C2×C32×D3—21no—
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3—44no—
203C2×C32×D3#4112yes—
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—
214C32×Dic3—21no—
215C3×#126—34no—
216C3×#126—34no—
217C3×#124—34no—
218C3×#123—34no—
219C3×#123—34no—
220C3×#123—34no—
221C3×C22⋊Q8—34no—
222C3×C22⋊Q8—34no—
223C3×#120—34no—
224C3×C4×D4—24no—
225C3×C4×D4—34no—
226C3×C4×D4C3×D314yescomplemented
227C3×C4×D4C2×C3211yescharacteristic, complemented
228C3×#117—34no—
229C3×#117—34no—
230C2×C3×C22⋊C4—34no—
231C2×C3×C22⋊C4—34no—
232#937C2×C3211yescharacteristic
233#935C2×C3211yescharacteristic, complemented
234#929C2×C3211yescharacteristic, complemented
235C4×#67C2×C3211yescharacteristic, complemented
236C2×(C2×D3)⋊C4C2×C3211yescharacteristic, complemented
237#924C2×C3211yescharacteristic, complemented
238#898C2×C3211yescharacteristic, complemented
239#896C2×C3211yescharacteristic, complemented
240#885C2×C3211yescharacteristic, complemented
241#883C2×C3211yescharacteristic, complemented
242D3×C22⋊C4C2×C3211yescharacteristic, complemented
243#877C2×C3211yescharacteristic, complemented
244#876C2×C3211yescharacteristic, complemented
245#872C2×C3211yescharacteristic, complemented
246C23×C32—24no—
247C23×C32—24no—
248C23×C32—31no—
249C23×C32—31no—
250C23×C32—62no—
251C23×C32—62no—
252C23×C32—121no—
253C23×C32C22×D311yescharacteristic
254C23×C32C22×D311yescharacteristic
255C23×C32C23×C314yes—
256C23×C32C23×C314yes—
257C22×C3×D3—28no—
258C22×C3×D3—28no—
259C22×C3×D3—44no—
260C22×C3×D3C23×C314yes—
261C22×C3×D3C23×C314yes—
262C32×Q8—121no—
263C32×D4—216no—
264C32×D4—22no—
265C32×D4—28no—
266C32×D4—62no—
267C32×D4—121no—
268C2×C32×C4—24no—
269C2×C32×C4—24no—
270C2×C32×C4—24no—
271C2×C32×C4—24no—
272C2×C32×C4—24no—
273C2×C32×C4—31no—
274C2×C32×C4—31no—
275C2×C32×C4—31no—
276C2×C32×C4—31no—
277C2×C32×C4—31no—
278C2×C32×C4—31no—
279C2×C32×C4—41no—
280C2×C32×C4—41no—
281C2×C32×C4—44no—
282C2×C32×C4—44no—
283C2×C32×C4—48no—
284C2×C32×C4—48no—
285C2×C32×C4—62no—
286C2×C32×C4—62no—
287C2×C32×C4—121no—
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291C2×C32×C4C22×D311yescharacteristic
292C2×C32×C4C22×D311yescharacteristic
293C2×C32×C4C23×C314yes—
294C2×C32×C4C23×C314yes—
295C2×C32×C4C23×C314yes—
296C2×C32×C4C23×C314yes—
297C2×C32×C4C23×C314yes—
298C3×#67—28no—
299C3×#67—44no—
300C2×C3×Dic3—28no—
301C2×C3×Dic3C23×C314yes—
302C2×C3×Dic3C23×C314yes—
303C2×C3×Dic3C23×C314yes—
304C2×C3×Dic3C23×C314yes—
305C2×C3×Dic3C23×C314yes—
306C2×C3×Dic3C23×C314yes—
307C3×C4×D3—28no—
308C3×C4×D3—44no—
309C3×Dic6—44no—
310#551—31noSylow
311C2×C33—22no—
312C2×C33—41no—
313C2×C33C2×#4111yescharacteristic
314C2×C33C2×#4111yescharacteristic
315C2×C33H(5,𝔽2)11yescharacteristic
316C32×D3—22no—
317C32×D3—41no—
318C24×C3—34no—
319C23×D3C22×C3211yescharacteristic
320C2×C3×Q8—34no—
321C2×C3×D4—24no—
322C2×C3×D4—34no—
323C2×C3×D4—34no—
324C2×C3×D4C2×C3×D314yes—
325C2×C3×D4C22×C3211yescharacteristic
326C22×C3×C4—24no—
327C22×C3×C4—24no—
328C22×C3×C4—34no—
329C22×C3×C4—34no—
330C22×C3×C4—34no—
331C22×C3×C4C2×C3×D314yes—
332C22×C3×C4C2×C3×D314yescomplemented
333C22×C3×C4C22×C3211yescharacteristic
334C22×C3×C4C22×C3211yescharacteristic, complemented
335C2×#67C22×C3211yescharacteristic
336C2×#67C22×C3211yescharacteristic
337C22×Dic3C22×C3211yescharacteristic
338C2×C4×D3C22×C3211yescharacteristic
339C2×C4×D3C22×C3211yescharacteristic
340C2×Dic6C22×C3211yescharacteristic, complemented
341C3×C4⋊C4—24no—
342C3×C4⋊C4—34no—
343C3×C4⋊C4—34no—
344C3×C4⋊C4—34no—
345C3×C4⋊C4—34no—
346C3×C4⋊C4—34no—
347C3×C4⋊C4—34no—
348C3×C4⋊C4—34no—
349C3×C4⋊C4C2×C3×D314yescomplemented
350C3×C4⋊C4C22×C3211yescharacteristic, complemented
351C3×C22⋊C4—24no—
352C3×C22⋊C4—24no—
353C3×C22⋊C4—34no—
354C3×C22⋊C4—34no—
355C3×C22⋊C4—34no—
356C3×C22⋊C4—34no—
357C3×C22⋊C4—34no—
358C3×C22⋊C4—34no—
359C3×C22⋊C4—34no—
360C3×C22⋊C4—34no—
361C3×C22⋊C4—34no—
362C3×C22⋊C4—34no—
363C3×C22⋊C4—34no—
364C3×C22⋊C4—34no—
365C3×C22⋊C4C2×C3×D314yes—
366C3×C22⋊C4C2×C3×D314yescomplemented
367C3×C22⋊C4C22×C3211yescharacteristic
368C3×C22⋊C4C22×C3211yescharacteristic, complemented
369C3×C42—24no—
370C3×C42—34no—
371C3×C42—34no—
372C3×C42C2×C3×D314yescomplemented
373C3×C42C22×C3211yescharacteristic, complemented
374#217C22×C3211yescharacteristic
375#217C22×C3211yescharacteristic
376#217C22×C3211yescharacteristic, complemented
377#217C22×C3211yescharacteristic, complemented
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
385(C2×D3)⋊C4C22×C3211yescharacteristic
386C4⋊Dic3C22×C3211yescharacteristic, complemented
387Dic3⋊C4C22×C3211yescharacteristic, complemented
388Dic3⋊C4C22×C3211yescharacteristic, complemented
389Dic3⋊C4C22×C3211yescharacteristic, complemented
390Dic3⋊C4C22×C3211yescharacteristic, complemented
391Dic3⋊C4C22×C3211yescharacteristic, complemented
392Dic3⋊C4C22×C3211yescharacteristic, complemented
393C4×Dic3C22×C3211yescharacteristic, complemented
394C4×Dic3C22×C3211yescharacteristic, complemented
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—28no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—24no—
402C22×C32—24no—
403C22×C32—28no—
404C22×C32—24no—
405C22×C32—24no—
406C22×C32—24no—
407C22×C32—24no—
408C22×C32—32no—
409C22×C32—44no—
410C22×C32—44no—
411C22×C32—44no—
412C22×C32—44no—
413C22×C32—61no—
414C22×C32—61no—
415C22×C32—61no—
416C22×C32—61no—
417C22×C32—61no—
418C22×C32—124no—
419C22×C32#23512yes—
420C22×C32C3×#4118yes—
421C22×C32C23×D311yescharacteristic
422C22×C32C24×C314yes—
423C2×C3×D3—24no—
424C2×C3×D3—24no—
425C2×C3×D3—24no—
426C2×C3×D3—24no—
427C2×C3×D3—24no—
428C2×C3×D3—416no—
429C2×C3×D3C3×#4118yes—
430C32×C4—28no—
431C32×C4—28no—
432C32×C4—21no—
433C32×C4—21no—
434C32×C4—21no—
435C32×C4—21no—
436C32×C4—21no—
437C32×C4—24no—
438C32×C4—24no—
439C32×C4—24no—
440C32×C4—24no—
441C32×C4—24no—
442C32×C4—44no—
443C32×C4—44no—
444C32×C4—44no—
445C32×C4—61no—
446C32×C4—61no—
447C32×C4—61no—
448C32×C4—61no—
449C32×C4—61no—
450C32×C4—61no—
451C3×Dic3—24no—
452C3×Dic3—24no—
453C3×Dic3—24no—
454C3×Dic3—24no—
455C3×Dic3—24no—
456C3×Dic3—24no—
457#126—31no—
458#126—31no—
459#124—31no—
460#123—31no—
461#123—31no—
462#123—31no—
463C22⋊Q8—31no—
464C22⋊Q8—31no—
465#120—31no—
466C4×D4—31no—
467C4×D4C32×D311yescharacteristic, complemented
468#117—31no—
469#117—31no—
470C2×C22⋊C4—31no—
471C2×C22⋊C4—31no—
472C33#55111yescharacteristic, complemented, Sylow
473C23×C3—24no—
474C23×C3—24no—
475C23×C3—34no—
476C23×C3—34no—
477C23×C3—68no—
478C23×C3—68no—
479C23×C3—124no—
480C23×C3C22×C3×D314yes—
481C23×C3C22×C3×D314yes—
482C23×C3C23×C3211yescharacteristic
483C23×C3C23×C3211yescharacteristic
484C22×D3—22no—
485C22×D3—22no—
486C22×D3—41no—
487C22×D3C23×C3211yescharacteristic
488C22×D3C23×C3211yescharacteristic
489C3×Q8—124no—
490C3×D4—216no—
491C3×D4—28no—
492C3×D4—22no—
493C3×D4—68no—
494C3×D4—124no—
495C2×C3×C4—24no—
496C2×C3×C4—24no—
497C2×C3×C4—24no—
498C2×C3×C4—24no—
499C2×C3×C4—24no—
500C2×C3×C4—34no—
501C2×C3×C4—34no—
502C2×C3×C4—34no—
503C2×C3×C4—34no—
504C2×C3×C4—34no—
505C2×C3×C4—34no—
506C2×C3×C4—44no—
507C2×C3×C4—44no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—48no—
511C2×C3×C4—48no—
512C2×C3×C4—68no—
513C2×C3×C4—68no—
514C2×C3×C4—124no—
515C2×C3×C4C22×C3×D314yes—
516C2×C3×C4C22×C3×D314yes—
517C2×C3×C4C22×C3×D314yes—
518C2×C3×C4C22×C3×D314yes—
519C2×C3×C4C22×C3×D314yes—
520C2×C3×C4C23×C3211yescharacteristic
521C2×C3×C4C23×C3211yescharacteristic
522C2×C3×C4C23×C3211yescharacteristic
523C2×C3×C4C23×C3211yescharacteristic
524C2×C3×C4C23×C3211yescharacteristic
525#67—22no—
526#67—41no—
527C2×Dic3—22no—
528C2×Dic3C23×C3211yescharacteristic
529C2×Dic3C23×C3211yescharacteristic
530C2×Dic3C23×C3211yescharacteristic
531C2×Dic3C23×C3211yescharacteristic
532C2×Dic3C23×C3211yescharacteristic
533C2×Dic3C23×C3211yescharacteristic
534C4×D3—22no—
535C4×D3—41no—
536Dic6—41no—
537C2×C32—22no—
538C2×C32—24no—
539C2×C32—24no—
540C2×C32—24no—
541C2×C32—28no—
542C2×C32—48no—
543C2×C32—48no—
544C2×C32—41no—
545C2×C32—44no—
546C2×C32—62no—
547C2×C32—121no—
548C2×C32C2×#23511yescharacteristic
549C2×C32#100411yescharacteristic
550C2×C32D3×#4111yescharacteristic
551C2×C32C2×C3×#4114yes—
552C2×C32C2×C3×#4114yes—
553C2×C32C3×H(5,𝔽2)14yes—
554C3×D3—28no—
555C3×D3—44no—
556C24—31no—
557C2×Q8—31no—
558C2×D4—31no—
559C2×D4—31no—
560C2×D4C2×C32×D311yescharacteristic
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4C2×C32×D311yescharacteristic
565C22×C4C2×C32×D311yescharacteristic, complemented
566C4⋊C4—31no—
567C4⋊C4—31no—
568C4⋊C4—31no—
569C4⋊C4—31no—
570C4⋊C4—31no—
571C4⋊C4—31no—
572C4⋊C4—31no—
573C4⋊C4C2×C32×D311yescharacteristic, complemented
574C22⋊C4—31no—
575C22⋊C4—31no—
576C22⋊C4—31no—
577C22⋊C4—31no—
578C22⋊C4—31no—
579C22⋊C4—31no—
580C22⋊C4—31no—
581C22⋊C4—31no—
582C22⋊C4—31no—
583C22⋊C4—31no—
584C22⋊C4—31no—
585C22⋊C4—31no—
586C22⋊C4C2×C32×D311yescharacteristic
587C22⋊C4C2×C32×D311yescharacteristic, complemented
588C42—31no—
589C42—31no—
590C42C2×C32×D311yescharacteristic, complemented
591C22×C3—24no—
592C22×C3—24no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—28no—
596C22×C3—24no—
597C22×C3—24no—
598C22×C3—24no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—24no—
603C22×C3—28no—
604C22×C3—38no—
605C22×C3—44no—
606C22×C3—44no—
607C22×C3—44no—
608C22×C3—44no—
609C22×C3—64no—
610C22×C3—64no—
611C22×C3—64no—
612C22×C3—64no—
613C22×C3—64no—
614C22×C3—1216no—
615C22×C3C3×#23518yes—
616C22×C3C32×#4112yes—
617C22×C3C23×C3×D314yes—
618C22×C3C24×C3211yescharacteristic
619C2×D3—21no—
620C2×D3—21no—
621C2×D3—21no—
622C2×D3—21no—
623C2×D3—21no—
624C2×D3—44no—
625C2×D3C32×#4112yes—
626C3×C4—28no—
627C3×C4—28no—
628C3×C4—24no—
629C3×C4—24no—
630C3×C4—24no—
631C3×C4—24no—
632C3×C4—24no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—44no—
639C3×C4—44no—
640C3×C4—44no—
641C3×C4—64no—
642C3×C4—64no—
643C3×C4—64no—
644C3×C4—64no—
645C3×C4—64no—
646C3×C4—64no—
647Dic3—21no—
648Dic3—21no—
649Dic3—21no—
650Dic3—21no—
651Dic3—21no—
652Dic3—21no—
653C32—24no—
654C32#555611yescharacteristic, direct product factor
655C32C3×#55114yescomplemented
656C23—31no—
657C23—31no—
658C23—62no—
659C23—62no—
660C23—121no—
661C23C22×C32×D311yescharacteristic
662C23C22×C32×D311yescharacteristic
663Q8—121no—
664D4—22no—
665D4—62no—
666D4—121no—
667C2×C4—31no—
668C2×C4—31no—
669C2×C4—31no—
670C2×C4—31no—
671C2×C4—31no—
672C2×C4—31no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—62no—
676C2×C4—62no—
677C2×C4—121no—
678C2×C4C22×C32×D311yescharacteristic
679C2×C4C22×C32×D311yescharacteristic
680C2×C4C22×C32×D311yescharacteristic
681C2×C4C22×C32×D311yescharacteristic
682C2×C4C22×C32×D311yescharacteristic
683C2×C3—22no—
684C2×C3—28no—
685C2×C3—24no—
686C2×C3—24no—
687C2×C3—24no—
688C2×C3—48no—
689C2×C3—48no—
690C2×C3—41no—
691C2×C3—44no—
692C2×C3—68no—
693C2×C3—124no—
694C2×C3C2×C3×#23514yes—
695C2×C3C3×#100414yes—
696C2×C3C3×D3×#4114yes—
697C2×C3C2×C32×#4111yescharacteristic
698C2×C3C2×C32×#4111yescharacteristic
699C2×C3C32×H(5,𝔽2)11yescharacteristic
700D3—22no—
701D3—41no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—32no—
708C22—61no—
709C22—61no—
710C22—61no—
711C22—61no—
712C22—61no—
713C22—124no—
714C22C32×#23512yes—
715C22C23×C32×D311yescharacteristic
716C4—21no—
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—61no—
722C4—61no—
723C4—61no—
724C4—61no—
725C4—61no—
726C4—61no—
727C3—24no—
728C3C3×#555614yesdirect product factor
729C3C32×#55111yescharacteristic, complemented
730C2—22no—
731C2—41no—
732C2—62no—
733C2—121no—
734C2C2×C32×#23511yescharacteristic
735C2C32×#100411yescharacteristic
736C2C32×D3×#4111yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×C4×D4C2
socleC22×C33C24
prime radicalC32×#937C2
hypercenterC32×C4×D4D3
hypocenterC3C32×#551
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×C4×D4

Complements

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

NH ≅ G/Ntype
1. C33×C4×D4C2semidirect
3. C32×#935C2semidirect
4. C32×#929C2semidirect
5. C32×C4×#67C2semidirect
6. C2×C32×(C2×D3)⋊C4C2semidirect
7. C32×#924C2semidirect
8. C32×#898C2semidirect
9. C32×#896C2semidirect
10. C32×#885C2semidirect
11. C32×#883C2semidirect
12. C32×D3×C22⋊C4C2semidirect
13. C32×#877C2semidirect
14. C32×#876C2semidirect
15. C32×#872C2semidirect
17. C3×#5556C3direct (N × H)
21. C22×C33×C4C22semidirect
27. C2×C32×Dic6C22semidirect
28. C33×C4⋊C4C22semidirect
30. C33×C22⋊C4C22semidirect
31. C33×C42C22semidirect
34. C32×#217C22semidirect
35. C32×#217C22semidirect
44. C32×C4⋊Dic3C22semidirect
45. C32×Dic3⋊C4C22semidirect
46. C32×Dic3⋊C4C22semidirect
47. C32×Dic3⋊C4C22semidirect
48. C32×Dic3⋊C4C22semidirect
49. C32×Dic3⋊C4C22semidirect
50. C32×Dic3⋊C4C22semidirect
51. C32×C4×Dic3C22semidirect
52. C32×C4×Dic3C22semidirect
64. C32×C4×D4D3semidirect
65. C32×C4×D4C2×C3semidirect
71. C3×#935C2×C3semidirect
72. C3×#929C2×C3semidirect
73. C3×C4×#67C2×C3semidirect
74. C2×C3×(C2×D3)⋊C4C2×C3semidirect
75. C3×#924C2×C3semidirect
76. C3×#898C2×C3semidirect
77. C3×#896C2×C3semidirect
78. C3×#885C2×C3semidirect
79. C3×#883C2×C3semidirect
80. C3×D3×C22⋊C4C2×C3semidirect
81. C3×#877C2×C3semidirect
82. C3×#876C2×C3semidirect
83. C3×#872C2×C3semidirect
112. #5556C32direct (N × H)
127. C22×C32×C4C2×D3semidirect
129. C22×C32×C4C22×C3semidirect
135. C2×C3×Dic6C22×C3semidirect
144. C32×C4⋊C4C2×D3semidirect
145. C32×C4⋊C4C22×C3semidirect
161. C32×C22⋊C4C2×D3semidirect
163. C32×C22⋊C4C22×C3semidirect
167. C32×C42C2×D3semidirect
168. C32×C42C22×C3semidirect
171. C3×#217C22×C3semidirect
172. C3×#217C22×C3semidirect
181. C3×C4⋊Dic3C22×C3semidirect
182. C3×Dic3⋊C4C22×C3semidirect
183. C3×Dic3⋊C4C22×C3semidirect
184. C3×Dic3⋊C4C22×C3semidirect
185. C3×Dic3⋊C4C22×C3semidirect
186. C3×Dic3⋊C4C22×C3semidirect
187. C3×Dic3⋊C4C22×C3semidirect
188. C3×C4×Dic3C22×C3semidirect
189. C3×C4×Dic3C22×C3semidirect
226. C3×C4×D4C3×D3semidirect
227. C3×C4×D4C2×C32semidirect
233. #935C2×C32semidirect
234. #929C2×C32semidirect
235. C4×#67C2×C32semidirect
236. C2×(C2×D3)⋊C4C2×C32semidirect
237. #924C2×C32semidirect
238. #898C2×C32semidirect
239. #896C2×C32semidirect
240. #885C2×C32semidirect
241. #883C2×C32semidirect
242. D3×C22⋊C4C2×C32semidirect
243. #877C2×C32semidirect
244. #876C2×C32semidirect
245. #872C2×C32semidirect
332. C22×C3×C4C2×C3×D3semidirect
334. C22×C3×C4C22×C32semidirect
340. C2×Dic6C22×C32semidirect
349. C3×C4⋊C4C2×C3×D3semidirect
350. C3×C4⋊C4C22×C32semidirect
366. C3×C22⋊C4C2×C3×D3semidirect
368. C3×C22⋊C4C22×C32semidirect
372. C3×C42C2×C3×D3semidirect
373. C3×C42C22×C32semidirect
376. #217C22×C32semidirect
377. #217C22×C32semidirect
386. C4⋊Dic3C22×C32semidirect
387. Dic3⋊C4C22×C32semidirect
388. Dic3⋊C4C22×C32semidirect
389. Dic3⋊C4C22×C32semidirect
390. Dic3⋊C4C22×C32semidirect
391. Dic3⋊C4C22×C32semidirect
392. Dic3⋊C4C22×C32semidirect
393. C4×Dic3C22×C32semidirect
394. C4×Dic3C22×C32semidirect
467. C4×D4C32×D3semidirect
472. C33#551semidirect
565. C22×C4C2×C32×D3semidirect
573. C4⋊C4C2×C32×D3semidirect
587. C22⋊C4C2×C32×D3semidirect
590. C42C2×C32×D3semidirect
654. C32#5556direct (N × H)
655. C32C3×#551semidirect
728. C3C3×#5556direct (N × H)
729. C3C32×#551semidirect

Maximal subgroups

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

subgroupindex
C33×C4×D42
C32×#9372
C32×#9352
C32×#9292
C32×C4×#672
C2×C32×(C2×D3)⋊C42
C32×#9242
C32×#8982
C32×#8962
C32×#8852
C32×#8832
C32×D3×C22⋊C42
C32×#8772
C32×#8762
C32×#8722
C32×#5513
C3×#55563