Finite Group Databasebeta

← C32×#5620 #13178997

Subgroups — C32×#5620 #13178997

Order 1728.

1888 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×#121C211yesmaximal, characteristic, complemented
2C32×#940C211yesmaximal, characteristic, complemented
3C32×#939C211yesmaximal, characteristic, complemented
4C32×#939C211yesmaximal, characteristic, complemented
5C32×#938C211yesmaximal, characteristic, complemented
6C32×#937C211yesmaximal, characteristic, complemented
7C32×#937C211yesmaximal, characteristic, complemented
8C32×#930C211yesmaximal, characteristic, complemented
9C32×#929C211yesmaximal, characteristic, complemented
10C32×#898C211yesmaximal, characteristic, complemented
11C32×#894C211yesmaximal, characteristic, complemented
12C32×#886C211yesmaximal, characteristic, complemented
13C32×#884C211yesmaximal, characteristic, complemented
14C32×#882C211yesmaximal, characteristic, complemented
15C32×#879C211yesmaximal, characteristic, complemented
16C32×#560—31nomaximal
17C3×#5620C314yesmaximal, direct product factor
18C23×C32×D3C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic
21C2×C33×D4C2211yescharacteristic, complemented
22C22×C33×C4C2211yescharacteristic, complemented
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C2×C32×#67C2211yescharacteristic
27C2×C32×#67C2211yescharacteristic
28C2×C32×#67C2211yescharacteristic, complemented
29C2×C32×#67C2211yescharacteristic, complemented
30C22×C32×Dic3C2211yescharacteristic, complemented
31C2×C32×D12C2211yescharacteristic
32C2×C32×D12C2211yescharacteristic
33C2×C32×C4×D3C2211yescharacteristic, complemented
34C33×C4⋊C4C2211yescharacteristic, complemented
35C33×C22⋊C4C2211yescharacteristic
36C33×C22⋊C4C2211yescharacteristic, complemented
37C32×#217C2211yescharacteristic
38C32×#217C2211yescharacteristic
39C32×#217C2211yescharacteristic, complemented
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×(C2×D3)⋊C4C2211yescharacteristic
45C32×(C2×D3)⋊C4C2211yescharacteristic
46C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C32×C4⋊Dic3C2211yescharacteristic, complemented
48C32×C4⋊Dic3C2211yescharacteristic, complemented
49C32×Dic3⋊C4C2211yescharacteristic, complemented
50C32×Dic3⋊C4C2211yescharacteristic, complemented
51C32×Dic3⋊C4C2211yescharacteristic, complemented
52C32×C4×Dic3C2211yescharacteristic, complemented
53C32×#127—31no—
54C32×#126—31no—
55C32×#126—31no—
56C32×#123—31no—
57C32×#123—31no—
58C32×#123—31no—
59C32×#121—24no—
60C32×#121—31no—
61C32×#121—31no—
62C32×#121—31no—
63C32×#121—31no—
64C32×#121—31no—
65C32×#121D311yescharacteristic, complemented
66C32×#121C2×C314yescomplemented
67C32×#120—31no—
68C32×#120—31no—
69C32×#120—31no—
70C3×#940C2×C314yescomplemented
71C3×#939C2×C314yescomplemented
72C3×#939C2×C314yescomplemented
73C3×#938C2×C314yescomplemented
74C3×#937C2×C314yescomplemented
75C3×#937C2×C314yescomplemented
76C3×#930C2×C314yescomplemented
77C3×#929C2×C314yescomplemented
78C3×#898C2×C314yescomplemented
79C3×#894C2×C314yescomplemented
80C3×#886C2×C314yescomplemented
81C3×#884C2×C314yescomplemented
82C3×#882C2×C314yescomplemented
83C3×#879C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C23×C33C2311yescharacteristic
87C22×C32×D3—41no—
88C22×C32×D3—41no—
89C22×C32×D3—41no—
90C22×C32×D3C2311yescharacteristic
91C22×C32×D3C2311yescharacteristic
92C22×C32×D3C2311yescharacteristic
93C33×D4—41no—
94C33×D4—41no—
95C33×D4—41no—
96C2×C33×C4—41no—
97C2×C33×C4C2311yescharacteristic
98C2×C33×C4C2311yescharacteristic
99C2×C33×C4C2311yescharacteristic
100C2×C33×C4C2311yescharacteristic
101C32×#67—41no—
102C32×#67—41no—
103C32×#67—41no—
104C32×#67—41no—
105C32×#67—41no—
106C32×#67—41no—
107C32×#67—41no—
108C2×C32×Dic3—41no—
109C2×C32×Dic3C2311yescharacteristic
110C2×C32×Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C32×D12—41no—
115C32×D12—41no—
116C32×C4×D3—41no—
117C3×#560—34no—
118#5620C3211yescharacteristic, direct product factor
119C24×C32—31no—
120C23×C3×D3C22×C314yes—
121C2×C32×D4—24no—
122C2×C32×D4—24no—
123C2×C32×D4—24no—
124C2×C32×D4—31no—
125C2×C32×D4—31no—
126C2×C32×D4—31no—
127C2×C32×D4—31no—
128C2×C32×D4—31no—
129C2×C32×D4—31no—
130C2×C32×D4—31no—
131C2×C32×D4—31no—
132C2×C32×D4—31no—
133C2×C32×D4C2×D311yescharacteristic
134C2×C32×D4C2×D311yescharacteristic
135C2×C32×D4C2×D311yescharacteristic, complemented
136C2×C32×D4C22×C314yes—
137C2×C32×D4C22×C314yes—
138C2×C32×D4C22×C314yescomplemented
139C22×C32×C4—24no—
140C22×C32×C4—31no—
141C22×C32×C4—31no—
142C22×C32×C4C2×D311yescharacteristic, complemented
143C22×C32×C4C22×C314yescomplemented
144C2×C3×#67C22×C314yes—
145C2×C3×#67C22×C314yes—
146C2×C3×#67C22×C314yes—
147C2×C3×#67C22×C314yes—
148C2×C3×#67C22×C314yes—
149C2×C3×#67C22×C314yescomplemented
150C2×C3×#67C22×C314yescomplemented
151C22×C3×Dic3C22×C314yescomplemented
152C2×C3×D12C22×C314yes—
153C2×C3×D12C22×C314yes—
154C2×C3×C4×D3C22×C314yescomplemented
155C32×C4⋊C4—24no—
156C32×C4⋊C4—31no—
157C32×C4⋊C4—31no—
158C32×C4⋊C4—31no—
159C32×C4⋊C4—31no—
160C32×C4⋊C4—31no—
161C32×C4⋊C4C2×D311yescharacteristic, complemented
162C32×C4⋊C4C22×C314yescomplemented
163C32×C22⋊C4—24no—
164C32×C22⋊C4—24no—
165C32×C22⋊C4—31no—
166C32×C22⋊C4—31no—
167C32×C22⋊C4—31no—
168C32×C22⋊C4—31no—
169C32×C22⋊C4—31no—
170C32×C22⋊C4—31no—
171C32×C22⋊C4—31no—
172C32×C22⋊C4—31no—
173C32×C22⋊C4—31no—
174C32×C22⋊C4—31no—
175C32×C22⋊C4C2×D311yescharacteristic
176C32×C22⋊C4C2×D311yescharacteristic, complemented
177C32×C22⋊C4C22×C314yes—
178C32×C22⋊C4C22×C314yescomplemented
179C32×C42—31no—
180C3×#217C22×C314yes—
181C3×#217C22×C314yes—
182C3×#217C22×C314yescomplemented
183C3×(C2×D3)⋊C4C22×C314yes—
184C3×(C2×D3)⋊C4C22×C314yes—
185C3×(C2×D3)⋊C4C22×C314yes—
186C3×(C2×D3)⋊C4C22×C314yes—
187C3×(C2×D3)⋊C4C22×C314yes—
188C3×(C2×D3)⋊C4C22×C314yes—
189C3×(C2×D3)⋊C4C22×C314yescomplemented
190C3×C4⋊Dic3C22×C314yescomplemented
191C3×C4⋊Dic3C22×C314yescomplemented
192C3×Dic3⋊C4C22×C314yescomplemented
193C3×Dic3⋊C4C22×C314yescomplemented
194C3×Dic3⋊C4C22×C314yescomplemented
195C3×C4×Dic3C22×C314yescomplemented
196C22×C33—21no—
197C22×C33—21no—
198C22×C33—21no—
199C22×C33—21no—
200C22×C33—21no—
201C22×C33—21no—
202C22×C33—21no—
203C22×C33—21no—
204C22×C33—21no—
205C22×C33C2411yescharacteristic
206C2×C32×D3—21no—
207C2×C32×D3—21no—
208C2×C32×D3—21no—
209C2×C32×D3—21no—
210C2×C32×D3—21no—
211C2×C32×D3—21no—
212C2×C32×D3—21no—
213C2×C32×D3—21no—
214C2×C32×D3—21no—
215C2×C32×D3—44no—
216C33×C4—21no—
217C33×C4—21no—
218C33×C4—21no—
219C33×C4—21no—
220C32×Dic3—21no—
221C32×Dic3—21no—
222C32×Dic3—21no—
223C32×Dic3—21no—
224C32×Dic3—21no—
225C3×#127—34no—
226C3×#126—34no—
227C3×#126—34no—
228C3×#123—34no—
229C3×#123—34no—
230C3×#123—34no—
231C3×#121—24no—
232C3×#121—34no—
233C3×#121—34no—
234C3×#121—34no—
235C3×#121—34no—
236C3×#121—34no—
237C3×#121C3×D314yescomplemented
238C3×#121C2×C3211yescharacteristic, complemented
239C3×#120—34no—
240C3×#120—34no—
241C3×#120—34no—
242#940C2×C3211yescharacteristic, complemented
243#939C2×C3211yescharacteristic, complemented
244#939C2×C3211yescharacteristic, complemented
245#938C2×C3211yescharacteristic, complemented
246#937C2×C3211yescharacteristic, complemented
247#937C2×C3211yescharacteristic, complemented
248#930C2×C3211yescharacteristic, complemented
249#929C2×C3211yescharacteristic, complemented
250#898C2×C3211yescharacteristic, complemented
251#894C2×C3211yescharacteristic, complemented
252#886C2×C3211yescharacteristic, complemented
253#884C2×C3211yescharacteristic, complemented
254#882C2×C3211yescharacteristic, complemented
255#879C2×C3211yescharacteristic, complemented
256C23×C32—24no—
257C23×C32—24no—
258C23×C32—24no—
259C23×C32—31no—
260C23×C32—31no—
261C23×C32—31no—
262C23×C32—121no—
263C23×C32—121no—
264C23×C32—121no—
265C23×C32C22×D311yescharacteristic
266C23×C32C22×D311yescharacteristic
267C23×C32C22×D311yescharacteristic
268C23×C32C23×C314yes—
269C23×C32C23×C314yes—
270C23×C32C23×C314yes—
271C22×C3×D3—44no—
272C22×C3×D3—44no—
273C22×C3×D3—44no—
274C22×C3×D3C23×C314yes—
275C22×C3×D3C23×C314yes—
276C22×C3×D3C23×C314yes—
277C32×D4—41no—
278C32×D4—41no—
279C32×D4—41no—
280C32×D4—44no—
281C32×D4—44no—
282C32×D4—44no—
283C32×D4—48no—
284C32×D4—48no—
285C32×D4—48no—
286C32×D4—121no—
287C32×D4—121no—
288C32×D4—121no—
289C32×D4—121no—
290C32×D4—121no—
291C32×D4—121no—
292C32×D4—121no—
293C32×D4—121no—
294C32×D4—121no—
295C2×C32×C4—24no—
296C2×C32×C4—24no—
297C2×C32×C4—24no—
298C2×C32×C4—24no—
299C2×C32×C4—31no—
300C2×C32×C4—31no—
301C2×C32×C4—31no—
302C2×C32×C4—31no—
303C2×C32×C4—31no—
304C2×C32×C4—41no—
305C2×C32×C4—44no—
306C2×C32×C4—48no—
307C2×C32×C4—121no—
308C2×C32×C4—121no—
309C2×C32×C4C22×D311yescharacteristic
310C2×C32×C4C22×D311yescharacteristic
311C2×C32×C4C22×D311yescharacteristic
312C2×C32×C4C22×D311yescharacteristic
313C2×C32×C4C23×C314yes—
314C2×C32×C4C23×C314yes—
315C2×C32×C4C23×C314yes—
316C2×C32×C4C23×C314yes—
317C3×#67—44no—
318C3×#67—44no—
319C3×#67—44no—
320C3×#67—44no—
321C3×#67—44no—
322C3×#67—44no—
323C3×#67—44no—
324C2×C3×Dic3—44no—
325C2×C3×Dic3C23×C314yes—
326C2×C3×Dic3C23×C314yes—
327C2×C3×Dic3C23×C314yes—
328C2×C3×Dic3C23×C314yes—
329C2×C3×Dic3C23×C314yes—
330C3×D12—44no—
331C3×D12—44no—
332C3×C4×D3—44no—
333#560—31noSylow
334C2×C33—41no—
335C2×C33—41no—
336C2×C33—41no—
337C2×C33H(5,𝔽2)11yescharacteristic
338C2×C33H(5,𝔽2)11yescharacteristic
339C2×C33H(5,𝔽2)11yescharacteristic
340C32×D3—41no—
341C32×D3—41no—
342C32×D3—41no—
343C24×C3—34no—
344C23×D3C22×C3211yescharacteristic
345C2×C3×D4—24no—
346C2×C3×D4—24no—
347C2×C3×D4—24no—
348C2×C3×D4—34no—
349C2×C3×D4—34no—
350C2×C3×D4—34no—
351C2×C3×D4—34no—
352C2×C3×D4—34no—
353C2×C3×D4—34no—
354C2×C3×D4—34no—
355C2×C3×D4—34no—
356C2×C3×D4—34no—
357C2×C3×D4C2×C3×D314yes—
358C2×C3×D4C2×C3×D314yes—
359C2×C3×D4C2×C3×D314yescomplemented
360C2×C3×D4C22×C3211yescharacteristic
361C2×C3×D4C22×C3211yescharacteristic
362C2×C3×D4C22×C3211yescharacteristic, complemented
363C22×C3×C4—24no—
364C22×C3×C4—34no—
365C22×C3×C4—34no—
366C22×C3×C4C2×C3×D314yescomplemented
367C22×C3×C4C22×C3211yescharacteristic, complemented
368C2×#67C22×C3211yescharacteristic
369C2×#67C22×C3211yescharacteristic
370C2×#67C22×C3211yescharacteristic
371C2×#67C22×C3211yescharacteristic
372C2×#67C22×C3211yescharacteristic
373C2×#67C22×C3211yescharacteristic, complemented
374C2×#67C22×C3211yescharacteristic, complemented
375C22×Dic3C22×C3211yescharacteristic, complemented
376C2×D12C22×C3211yescharacteristic
377C2×D12C22×C3211yescharacteristic
378C2×C4×D3C22×C3211yescharacteristic, complemented
379C3×C4⋊C4—24no—
380C3×C4⋊C4—34no—
381C3×C4⋊C4—34no—
382C3×C4⋊C4—34no—
383C3×C4⋊C4—34no—
384C3×C4⋊C4—34no—
385C3×C4⋊C4C2×C3×D314yescomplemented
386C3×C4⋊C4C22×C3211yescharacteristic, complemented
387C3×C22⋊C4—24no—
388C3×C22⋊C4—24no—
389C3×C22⋊C4—34no—
390C3×C22⋊C4—34no—
391C3×C22⋊C4—34no—
392C3×C22⋊C4—34no—
393C3×C22⋊C4—34no—
394C3×C22⋊C4—34no—
395C3×C22⋊C4—34no—
396C3×C22⋊C4—34no—
397C3×C22⋊C4—34no—
398C3×C22⋊C4—34no—
399C3×C22⋊C4C2×C3×D314yes—
400C3×C22⋊C4C2×C3×D314yescomplemented
401C3×C22⋊C4C22×C3211yescharacteristic
402C3×C22⋊C4C22×C3211yescharacteristic, complemented
403C3×C42—34no—
404#217C22×C3211yescharacteristic
405#217C22×C3211yescharacteristic
406#217C22×C3211yescharacteristic, complemented
407(C2×D3)⋊C4C22×C3211yescharacteristic
408(C2×D3)⋊C4C22×C3211yescharacteristic
409(C2×D3)⋊C4C22×C3211yescharacteristic
410(C2×D3)⋊C4C22×C3211yescharacteristic
411(C2×D3)⋊C4C22×C3211yescharacteristic
412(C2×D3)⋊C4C22×C3211yescharacteristic
413(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
414C4⋊Dic3C22×C3211yescharacteristic, complemented
415C4⋊Dic3C22×C3211yescharacteristic, complemented
416Dic3⋊C4C22×C3211yescharacteristic, complemented
417Dic3⋊C4C22×C3211yescharacteristic, complemented
418Dic3⋊C4C22×C3211yescharacteristic, complemented
419C4×Dic3C22×C3211yescharacteristic, complemented
420C22×C32—28no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—24no—
431C22×C32—24no—
432C22×C32—24no—
433C22×C32—24no—
434C22×C32—24no—
435C22×C32—24no—
436C22×C32—24no—
437C22×C32—24no—
438C22×C32—24no—
439C22×C32—24no—
440C22×C32—44no—
441C22×C32—44no—
442C22×C32—44no—
443C22×C32—44no—
444C22×C32—44no—
445C22×C32—44no—
446C22×C32—44no—
447C22×C32—44no—
448C22×C32—61no—
449C22×C32—61no—
450C22×C32—61no—
451C22×C32—61no—
452C22×C32—61no—
453C22×C32—61no—
454C22×C32—61no—
455C22×C32—61no—
456C22×C32—61no—
457C22×C32—124no—
458C22×C32C23×D311yescharacteristic
459C22×C32C24×C314yes—
460C2×C3×D3—24no—
461C2×C3×D3—24no—
462C2×C3×D3—24no—
463C2×C3×D3—24no—
464C2×C3×D3—24no—
465C2×C3×D3—24no—
466C2×C3×D3—24no—
467C2×C3×D3—24no—
468C2×C3×D3—24no—
469C2×C3×D3—416no—
470C32×C4—28no—
471C32×C4—21no—
472C32×C4—21no—
473C32×C4—21no—
474C32×C4—21no—
475C32×C4—24no—
476C32×C4—24no—
477C32×C4—24no—
478C32×C4—24no—
479C32×C4—44no—
480C32×C4—44no—
481C32×C4—44no—
482C32×C4—61no—
483C32×C4—61no—
484C32×C4—61no—
485C32×C4—61no—
486C32×C4—61no—
487C3×Dic3—24no—
488C3×Dic3—24no—
489C3×Dic3—24no—
490C3×Dic3—24no—
491C3×Dic3—24no—
492#127—31no—
493#126—31no—
494#126—31no—
495#123—31no—
496#123—31no—
497#123—31no—
498#121—31no—
499#121—31no—
500#121—31no—
501#121—31no—
502#121—31no—
503#121C32×D311yescharacteristic, complemented
504#120—31no—
505#120—31no—
506#120—31no—
507C33#56011yescharacteristic, complemented, Sylow
508C23×C3—24no—
509C23×C3—24no—
510C23×C3—24no—
511C23×C3—34no—
512C23×C3—34no—
513C23×C3—34no—
514C23×C3—124no—
515C23×C3—124no—
516C23×C3—124no—
517C23×C3C22×C3×D314yes—
518C23×C3C22×C3×D314yes—
519C23×C3C22×C3×D314yes—
520C23×C3C23×C3211yescharacteristic
521C23×C3C23×C3211yescharacteristic
522C23×C3C23×C3211yescharacteristic
523C22×D3—41no—
524C22×D3—41no—
525C22×D3—41no—
526C22×D3C23×C3211yescharacteristic
527C22×D3C23×C3211yescharacteristic
528C22×D3C23×C3211yescharacteristic
529C3×D4—44no—
530C3×D4—44no—
531C3×D4—44no—
532C3×D4—41no—
533C3×D4—41no—
534C3×D4—41no—
535C3×D4—48no—
536C3×D4—48no—
537C3×D4—48no—
538C3×D4—124no—
539C3×D4—124no—
540C3×D4—124no—
541C3×D4—124no—
542C3×D4—124no—
543C3×D4—124no—
544C3×D4—124no—
545C3×D4—124no—
546C3×D4—124no—
547C2×C3×C4—24no—
548C2×C3×C4—24no—
549C2×C3×C4—24no—
550C2×C3×C4—24no—
551C2×C3×C4—34no—
552C2×C3×C4—34no—
553C2×C3×C4—34no—
554C2×C3×C4—34no—
555C2×C3×C4—34no—
556C2×C3×C4—44no—
557C2×C3×C4—41no—
558C2×C3×C4—48no—
559C2×C3×C4—124no—
560C2×C3×C4—124no—
561C2×C3×C4C22×C3×D314yes—
562C2×C3×C4C22×C3×D314yes—
563C2×C3×C4C22×C3×D314yes—
564C2×C3×C4C22×C3×D314yes—
565C2×C3×C4C23×C3211yescharacteristic
566C2×C3×C4C23×C3211yescharacteristic
567C2×C3×C4C23×C3211yescharacteristic
568C2×C3×C4C23×C3211yescharacteristic
569#67—41no—
570#67—41no—
571#67—41no—
572#67—41no—
573#67—41no—
574#67—41no—
575#67—41no—
576C2×Dic3—41no—
577C2×Dic3C23×C3211yescharacteristic
578C2×Dic3C23×C3211yescharacteristic
579C2×Dic3C23×C3211yescharacteristic
580C2×Dic3C23×C3211yescharacteristic
581C2×Dic3C23×C3211yescharacteristic
582D12—41no—
583D12—41no—
584C4×D3—41no—
585C2×C32—24no—
586C2×C32—24no—
587C2×C32—24no—
588C2×C32—48no—
589C2×C32—44no—
590C2×C32—41no—
591C2×C32—41no—
592C2×C32—41no—
593C2×C32—44no—
594C2×C32—44no—
595C2×C32—84no—
596C2×C32—84no—
597C2×C32—121no—
598C2×C32—121no—
599C2×C32—121no—
600C2×C32#100411yescharacteristic
601C2×C32#100411yescharacteristic
602C2×C32#100911yescharacteristic
603C2×C32C3×H(5,𝔽2)14yes—
604C2×C32C3×H(5,𝔽2)14yes—
605C2×C32C3×H(5,𝔽2)14yes—
606C3×D3—44no—
607C3×D3—44no—
608C3×D3—44no—
609C24—31no—
610C2×D4—31no—
611C2×D4—31no—
612C2×D4—31no—
613C2×D4—31no—
614C2×D4—31no—
615C2×D4—31no—
616C2×D4—31no—
617C2×D4—31no—
618C2×D4—31no—
619C2×D4C2×C32×D311yescharacteristic
620C2×D4C2×C32×D311yescharacteristic
621C2×D4C2×C32×D311yescharacteristic, complemented
622C22×C4—31no—
623C22×C4—31no—
624C22×C4C2×C32×D311yescharacteristic, complemented
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4C2×C32×D311yescharacteristic, complemented
631C22⋊C4—31no—
632C22⋊C4—31no—
633C22⋊C4—31no—
634C22⋊C4—31no—
635C22⋊C4—31no—
636C22⋊C4—31no—
637C22⋊C4—31no—
638C22⋊C4—31no—
639C22⋊C4—31no—
640C22⋊C4—31no—
641C22⋊C4C2×C32×D311yescharacteristic
642C22⋊C4C2×C32×D311yescharacteristic, complemented
643C42—31no—
644C22×C3—28no—
645C22×C3—24no—
646C22×C3—24no—
647C22×C3—24no—
648C22×C3—24no—
649C22×C3—24no—
650C22×C3—24no—
651C22×C3—24no—
652C22×C3—24no—
653C22×C3—24no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—24no—
664C22×C3—44no—
665C22×C3—44no—
666C22×C3—44no—
667C22×C3—44no—
668C22×C3—44no—
669C22×C3—44no—
670C22×C3—44no—
671C22×C3—44no—
672C22×C3—64no—
673C22×C3—64no—
674C22×C3—64no—
675C22×C3—64no—
676C22×C3—64no—
677C22×C3—64no—
678C22×C3—64no—
679C22×C3—64no—
680C22×C3—64no—
681C22×C3—1216no—
682C22×C3C23×C3×D314yes—
683C22×C3C24×C3211yescharacteristic
684C2×D3—21no—
685C2×D3—21no—
686C2×D3—21no—
687C2×D3—21no—
688C2×D3—21no—
689C2×D3—21no—
690C2×D3—21no—
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—44no—
694C3×C4—28no—
695C3×C4—24no—
696C3×C4—24no—
697C3×C4—24no—
698C3×C4—24no—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—44no—
704C3×C4—44no—
705C3×C4—44no—
706C3×C4—64no—
707C3×C4—64no—
708C3×C4—64no—
709C3×C4—64no—
710C3×C4—64no—
711Dic3—21no—
712Dic3—21no—
713Dic3—21no—
714Dic3—21no—
715Dic3—21no—
716C32—24no—
717C32#562011yescharacteristic, direct product factor
718C32C3×#56014yescomplemented
719C23—31no—
720C23—31no—
721C23—31no—
722C23—121no—
723C23—121no—
724C23—121no—
725C23C22×C32×D311yescharacteristic
726C23C22×C32×D311yescharacteristic
727C23C22×C32×D311yescharacteristic
728D4—41no—
729D4—41no—
730D4—41no—
731D4—121no—
732D4—121no—
733D4—121no—
734D4—121no—
735D4—121no—
736D4—121no—
737D4—121no—
738D4—121no—
739D4—121no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—31no—
744C2×C4—31no—
745C2×C4—41no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4C22×C32×D311yescharacteristic
749C2×C4C22×C32×D311yescharacteristic
750C2×C4C22×C32×D311yescharacteristic
751C2×C4C22×C32×D311yescharacteristic
752C2×C3—24no—
753C2×C3—24no—
754C2×C3—24no—
755C2×C3—48no—
756C2×C3—41no—
757C2×C3—41no—
758C2×C3—41no—
759C2×C3—44no—
760C2×C3—44no—
761C2×C3—44no—
762C2×C3—84no—
763C2×C3—84no—
764C2×C3—124no—
765C2×C3—124no—
766C2×C3—124no—
767C2×C3C3×#100414yes—
768C2×C3C3×#100414yes—
769C2×C3C3×#100914yes—
770C2×C3C32×H(5,𝔽2)11yescharacteristic
771C2×C3C32×H(5,𝔽2)11yescharacteristic
772C2×C3C32×H(5,𝔽2)11yescharacteristic
773D3—41no—
774D3—41no—
775D3—41no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—61no—
786C22—61no—
787C22—61no—
788C22—61no—
789C22—61no—
790C22—61no—
791C22—61no—
792C22—61no—
793C22—61no—
794C22—124no—
795C22C23×C32×D311yescharacteristic
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—61no—
801C4—61no—
802C4—61no—
803C4—61no—
804C4—61no—
805C3—24no—
806C3C3×#562014yesdirect product factor
807C3C32×#56011yescharacteristic, complemented
808C2—41no—
809C2—41no—
810C2—41no—
811C2—121no—
812C2—121no—
813C2—121no—
814C2C32×#100411yescharacteristic
815C2C32×#100411yescharacteristic
816C2C32×#100911yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#121C2
socleC22×C33C24
hypercenterC32×#121D3
hypocenterC3C32×#560
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×#121

Complements

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

NH ≅ G/Ntype
1. C33×#121C2semidirect
2. C32×#940C2semidirect
3. C32×#939C2semidirect
4. C32×#939C2semidirect
5. C32×#938C2semidirect
6. C32×#937C2semidirect
7. C32×#937C2semidirect
8. C32×#930C2semidirect
9. C32×#929C2semidirect
10. C32×#898C2semidirect
11. C32×#894C2semidirect
12. C32×#886C2semidirect
13. C32×#884C2semidirect
14. C32×#882C2semidirect
15. C32×#879C2semidirect
17. C3×#5620C3direct (N × H)
21. C2×C33×D4C22semidirect
22. C22×C33×C4C22semidirect
28. C2×C32×#67C22semidirect
29. C2×C32×#67C22semidirect
30. C22×C32×Dic3C22semidirect
33. C2×C32×C4×D3C22semidirect
34. C33×C4⋊C4C22semidirect
36. C33×C22⋊C4C22semidirect
39. C32×#217C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. C32×C4⋊Dic3C22semidirect
48. C32×C4⋊Dic3C22semidirect
49. C32×Dic3⋊C4C22semidirect
50. C32×Dic3⋊C4C22semidirect
51. C32×Dic3⋊C4C22semidirect
52. C32×C4×Dic3C22semidirect
65. C32×#121D3semidirect
66. C32×#121C2×C3semidirect
70. C3×#940C2×C3semidirect
71. C3×#939C2×C3semidirect
72. C3×#939C2×C3semidirect
73. C3×#938C2×C3semidirect
74. C3×#937C2×C3semidirect
75. C3×#937C2×C3semidirect
76. C3×#930C2×C3semidirect
77. C3×#929C2×C3semidirect
78. C3×#898C2×C3semidirect
79. C3×#894C2×C3semidirect
80. C3×#886C2×C3semidirect
81. C3×#884C2×C3semidirect
82. C3×#882C2×C3semidirect
83. C3×#879C2×C3semidirect
118. #5620C32direct (N × H)
135. C2×C32×D4C2×D3semidirect
138. C2×C32×D4C22×C3semidirect
142. C22×C32×C4C2×D3semidirect
143. C22×C32×C4C22×C3semidirect
149. C2×C3×#67C22×C3semidirect
150. C2×C3×#67C22×C3semidirect
151. C22×C3×Dic3C22×C3semidirect
154. C2×C3×C4×D3C22×C3semidirect
161. C32×C4⋊C4C2×D3semidirect
162. C32×C4⋊C4C22×C3semidirect
176. C32×C22⋊C4C2×D3semidirect
178. C32×C22⋊C4C22×C3semidirect
182. C3×#217C22×C3semidirect
189. C3×(C2×D3)⋊C4C22×C3semidirect
190. C3×C4⋊Dic3C22×C3semidirect
191. C3×C4⋊Dic3C22×C3semidirect
192. C3×Dic3⋊C4C22×C3semidirect
193. C3×Dic3⋊C4C22×C3semidirect
194. C3×Dic3⋊C4C22×C3semidirect
195. C3×C4×Dic3C22×C3semidirect
237. C3×#121C3×D3semidirect
238. C3×#121C2×C32semidirect
242. #940C2×C32semidirect
243. #939C2×C32semidirect
244. #939C2×C32semidirect
245. #938C2×C32semidirect
246. #937C2×C32semidirect
247. #937C2×C32semidirect
248. #930C2×C32semidirect
249. #929C2×C32semidirect
250. #898C2×C32semidirect
251. #894C2×C32semidirect
252. #886C2×C32semidirect
253. #884C2×C32semidirect
254. #882C2×C32semidirect
255. #879C2×C32semidirect
359. C2×C3×D4C2×C3×D3semidirect
362. C2×C3×D4C22×C32semidirect
366. C22×C3×C4C2×C3×D3semidirect
367. C22×C3×C4C22×C32semidirect
373. C2×#67C22×C32semidirect
374. C2×#67C22×C32semidirect
375. C22×Dic3C22×C32semidirect
378. C2×C4×D3C22×C32semidirect
385. C3×C4⋊C4C2×C3×D3semidirect
386. C3×C4⋊C4C22×C32semidirect
400. C3×C22⋊C4C2×C3×D3semidirect
402. C3×C22⋊C4C22×C32semidirect
406. #217C22×C32semidirect
413. (C2×D3)⋊C4C22×C32semidirect
414. C4⋊Dic3C22×C32semidirect
415. C4⋊Dic3C22×C32semidirect
416. Dic3⋊C4C22×C32semidirect
417. Dic3⋊C4C22×C32semidirect
418. Dic3⋊C4C22×C32semidirect
419. C4×Dic3C22×C32semidirect
503. #121C32×D3semidirect
507. C33#560semidirect
621. C2×D4C2×C32×D3semidirect
624. C22×C4C2×C32×D3semidirect
630. C4⋊C4C2×C32×D3semidirect
642. C22⋊C4C2×C32×D3semidirect
717. C32#5620direct (N × H)
718. C32C3×#560semidirect
806. C3C3×#5620direct (N × H)
807. C3C32×#560semidirect

Maximal subgroups

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

subgroupindex
C33×#1212
C32×#9402
C32×#9392
C32×#9382
C32×#9372
C32×#9302
C32×#9292
C32×#8982
C32×#8942
C32×#8862
C32×#8842
C32×#8822
C32×#8792
C32×#5603
C3×#56203