Finite Group Databasebeta

← C32×#5704 #13179082

Subgroups — C32×#5704 #13179082

Order 1728.

1740 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×#126C211yesmaximal, characteristic, complemented
2C32×#898C211yesmaximal, characteristic, complemented
3C32×#896C211yesmaximal, characteristic, complemented
4C32×#895C211yesmaximal, characteristic, complemented
5C32×#895C211yesmaximal, characteristic, complemented
6C32×#894C211yesmaximal, characteristic, complemented
7C32×#893C211yesmaximal, characteristic, complemented
8C32×#885C211yesmaximal, characteristic, complemented
9C32×#884C211yesmaximal, characteristic, complemented
10C32×#883C211yesmaximal, characteristic, complemented
11C32×#882C211yesmaximal, characteristic, complemented
12C32×#882C211yesmaximal, characteristic, complemented
13C32×D3×C22⋊C4C211yesmaximal, characteristic, complemented
14C32×#875C211yesmaximal, characteristic, complemented
15C32×C4×D12C211yesmaximal, characteristic, complemented
16C32×#538—31nomaximal
17C3×#5704C314yesmaximal, direct product factor
18C23×C32×D3C2211yescharacteristic
19C2×C32×#67C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C2×C32×D12C2211yescharacteristic
22C2×C32×D12C2211yescharacteristic
23C2×C32×D12C2211yescharacteristic
24C2×C32×D12C2211yescharacteristic
25C2×C32×D12C2211yescharacteristic, complemented
26C2×C32×C4×D3C2211yescharacteristic
27C2×C32×C4×D3C2211yescharacteristic
28C2×C32×C4×D3C2211yescharacteristic, complemented
29C2×C32×C4×D3C2211yescharacteristic, complemented
30C2×C32×Dic6C2211yescharacteristic, complemented
31C33×C4⋊C4C2211yescharacteristic, complemented
32C33×C4⋊C4C2211yescharacteristic, complemented
33C33×C4⋊C4C2211yescharacteristic, complemented
34C33×C22⋊C4C2211yescharacteristic
35C33×C22⋊C4C2211yescharacteristic
36C33×C22⋊C4C2211yescharacteristic
37C33×C42C2211yescharacteristic, complemented
38C32×#217C2211yescharacteristic
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×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C32×C4⋊Dic3C2211yescharacteristic, complemented
50C32×Dic3⋊C4C2211yescharacteristic, complemented
51C32×Dic3⋊C4C2211yescharacteristic, complemented
52C32×C4×Dic3C2211yescharacteristic, complemented
53C32×#126—24no—
54C32×#126—31no—
55C32×#126D311yescharacteristic, complemented
56C32×#126C2×C314yescomplemented
57C32×#124—31no—
58C32×#124—31no—
59C32×#123—31no—
60C32×#123—31no—
61C32×C22⋊Q8—31no—
62C32×#121—31no—
63C32×#121—31no—
64C32×#121—31no—
65C32×#120—31no—
66C32×#120—31no—
67C32×C4×D4—31no—
68C32×C4×D4—31no—
69C2×C32×C22⋊C4—31no—
70C3×#898C2×C314yescomplemented
71C3×#896C2×C314yescomplemented
72C3×#895C2×C314yescomplemented
73C3×#895C2×C314yescomplemented
74C3×#894C2×C314yescomplemented
75C3×#893C2×C314yescomplemented
76C3×#885C2×C314yescomplemented
77C3×#884C2×C314yescomplemented
78C3×#883C2×C314yescomplemented
79C3×#882C2×C314yescomplemented
80C3×#882C2×C314yescomplemented
81C3×D3×C22⋊C4C2×C314yescomplemented
82C3×#875C2×C314yescomplemented
83C3×C4×D12C2×C314yescomplemented
84C23×C33C2311yescharacteristic
85C22×C32×D3—22no—
86C22×C32×D3—41no—
87C22×C32×D3—41no—
88C22×C32×D3C2311yescharacteristic
89C22×C32×D3C2311yescharacteristic
90C22×C32×D3C2311yescharacteristic
91C22×C32×D3C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C2×C33×C4C2311yescharacteristic
96C2×C33×C4C2311yescharacteristic
97C2×C33×C4C2311yescharacteristic
98C32×#67—41no—
99C32×#67—41no—
100C2×C32×Dic3C2311yescharacteristic
101C2×C32×Dic3C2311yescharacteristic
102C2×C32×Dic3C2311yescharacteristic
103C2×C32×Dic3C2311yescharacteristic
104C32×D12—22no—
105C32×D12—22no—
106C32×D12—41no—
107C32×D12—41no—
108C32×D12—41no—
109C32×C4×D3—41no—
110C32×C4×D3—41no—
111C32×C4×D3—41no—
112C32×C4×D3—41no—
113C32×Dic6—41no—
114C3×#538—34no—
115#5704C3211yescharacteristic, direct product factor
116C24×C32—31no—
117C23×C3×D3C22×C314yes—
118C2×C32×Q8—31no—
119C2×C32×D4—31no—
120C2×C32×D4—31no—
121C2×C32×D4—31no—
122C2×C32×D4—31no—
123C2×C32×D4—31no—
124C2×C32×D4—31no—
125C2×C32×D4—31no—
126C22×C32×C4—31no—
127C22×C32×C4—31no—
128C22×C32×C4—31no—
129C22×C32×C4—31no—
130C2×C3×#67C22×C314yes—
131C2×C3×#67C22×C314yes—
132C2×C3×D12C22×C314yes—
133C2×C3×D12C22×C314yes—
134C2×C3×D12C22×C314yes—
135C2×C3×D12C22×C314yes—
136C2×C3×D12C22×C314yescomplemented
137C2×C3×C4×D3C22×C314yes—
138C2×C3×C4×D3C22×C314yes—
139C2×C3×C4×D3C22×C314yescomplemented
140C2×C3×C4×D3C22×C314yescomplemented
141C2×C3×Dic6C22×C314yescomplemented
142C32×C4⋊C4—24no—
143C32×C4⋊C4—24no—
144C32×C4⋊C4—24no—
145C32×C4⋊C4—31no—
146C32×C4⋊C4—31no—
147C32×C4⋊C4—31no—
148C32×C4⋊C4C2×D311yescharacteristic, complemented
149C32×C4⋊C4C2×D311yescharacteristic, complemented
150C32×C4⋊C4C2×D311yescharacteristic, complemented
151C32×C4⋊C4C22×C314yescomplemented
152C32×C4⋊C4C22×C314yescomplemented
153C32×C4⋊C4C22×C314yescomplemented
154C32×C22⋊C4—24no—
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⋊C4—31no—
168C32×C22⋊C4C2×D311yescharacteristic
169C32×C22⋊C4C2×D311yescharacteristic
170C32×C22⋊C4C2×D311yescharacteristic
171C32×C22⋊C4C22×C314yes—
172C32×C22⋊C4C22×C314yes—
173C32×C22⋊C4C22×C314yes—
174C32×C42—24no—
175C32×C42—31no—
176C32×C42C2×D311yescharacteristic, complemented
177C32×C42C22×C314yescomplemented
178C3×#217C22×C314yes—
179C3×(C2×D3)⋊C4C22×C314yes—
180C3×(C2×D3)⋊C4C22×C314yes—
181C3×(C2×D3)⋊C4C22×C314yes—
182C3×(C2×D3)⋊C4C22×C314yes—
183C3×(C2×D3)⋊C4C22×C314yes—
184C3×(C2×D3)⋊C4C22×C314yes—
185C3×(C2×D3)⋊C4C22×C314yescomplemented
186C3×(C2×D3)⋊C4C22×C314yescomplemented
187C3×(C2×D3)⋊C4C22×C314yescomplemented
188C3×(C2×D3)⋊C4C22×C314yescomplemented
189C3×C4⋊Dic3C22×C314yescomplemented
190C3×Dic3⋊C4C22×C314yescomplemented
191C3×Dic3⋊C4C22×C314yescomplemented
192C3×C4×Dic3C22×C314yescomplemented
193C22×C33—21no—
194C22×C33—21no—
195C22×C33—21no—
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—21no—
203C2×C32×D3—21no—
204C2×C32×D3—21no—
205C2×C32×D3—21no—
206C2×C32×D3—21no—
207C2×C32×D3—21no—
208C2×C32×D3—44no—
209C2×C32×D3#4112yes—
210C33×C4—21no—
211C33×C4—21no—
212C33×C4—21no—
213C33×C4—21no—
214C33×C4—21no—
215C33×C4—21no—
216C32×Dic3—21no—
217C32×Dic3—21no—
218C32×Dic3—21no—
219C32×Dic3—21no—
220C3×#126—24no—
221C3×#126—34no—
222C3×#126C3×D314yescomplemented
223C3×#126C2×C3211yescharacteristic, complemented
224C3×#124—34no—
225C3×#124—34no—
226C3×#123—34no—
227C3×#123—34no—
228C3×C22⋊Q8—34no—
229C3×#121—34no—
230C3×#121—34no—
231C3×#121—34no—
232C3×#120—34no—
233C3×#120—34no—
234C3×C4×D4—34no—
235C3×C4×D4—34no—
236C2×C3×C22⋊C4—34no—
237#898C2×C3211yescharacteristic, complemented
238#896C2×C3211yescharacteristic, complemented
239#895C2×C3211yescharacteristic, complemented
240#895C2×C3211yescharacteristic, complemented
241#894C2×C3211yescharacteristic, complemented
242#893C2×C3211yescharacteristic, complemented
243#885C2×C3211yescharacteristic, complemented
244#884C2×C3211yescharacteristic, complemented
245#883C2×C3211yescharacteristic, complemented
246#882C2×C3211yescharacteristic, complemented
247#882C2×C3211yescharacteristic, complemented
248D3×C22⋊C4C2×C3211yescharacteristic, complemented
249#875C2×C3211yescharacteristic, complemented
250C4×D12C2×C3211yescharacteristic, complemented
251C23×C32—24no—
252C23×C32—31no—
253C23×C32—31no—
254C23×C32—31no—
255C23×C32—31no—
256C23×C32—62no—
257C23×C32—121no—
258C23×C32—121no—
259C23×C32C22×D311yescharacteristic
260C23×C32C23×C314yes—
261C22×C3×D3—28no—
262C22×C3×D3—44no—
263C22×C3×D3—44no—
264C22×C3×D3C23×C314yes—
265C22×C3×D3C23×C314yes—
266C22×C3×D3C23×C314yes—
267C22×C3×D3C23×C314yes—
268C32×Q8—121no—
269C32×D4—62no—
270C32×D4—62no—
271C32×D4—121no—
272C32×D4—121no—
273C32×D4—121no—
274C32×D4—121no—
275C32×D4—121no—
276C2×C32×C4—24no—
277C2×C32×C4—24no—
278C2×C32×C4—24no—
279C2×C32×C4—24no—
280C2×C32×C4—24no—
281C2×C32×C4—24no—
282C2×C32×C4—31no—
283C2×C32×C4—31no—
284C2×C32×C4—31no—
285C2×C32×C4—31no—
286C2×C32×C4—121no—
287C2×C32×C4—121no—
288C2×C32×C4—121no—
289C2×C32×C4—121no—
290C2×C32×C4C22×D311yescharacteristic
291C2×C32×C4C22×D311yescharacteristic
292C2×C32×C4C22×D311yescharacteristic
293C2×C32×C4C22×D311yescharacteristic
294C2×C32×C4C22×D311yescharacteristic
295C2×C32×C4C22×D311yescharacteristic
296C2×C32×C4C23×C314yes—
297C2×C32×C4C23×C314yes—
298C2×C32×C4C23×C314yes—
299C2×C32×C4C23×C314yes—
300C2×C32×C4C23×C314yes—
301C2×C32×C4C23×C314yes—
302C3×#67—44no—
303C3×#67—44no—
304C2×C3×Dic3C23×C314yes—
305C2×C3×Dic3C23×C314yes—
306C2×C3×Dic3C23×C314yes—
307C2×C3×Dic3C23×C314yes—
308C3×D12—28no—
309C3×D12—28no—
310C3×D12—44no—
311C3×D12—44no—
312C3×D12—44no—
313C3×C4×D3—44no—
314C3×C4×D3—44no—
315C3×C4×D3—44no—
316C3×C4×D3—44no—
317C3×Dic6—44no—
318#538—31noSylow
319C2×C33—41no—
320C2×C33C2×#4111yescharacteristic
321C2×C33H(5,𝔽2)11yescharacteristic
322C2×C33H(5,𝔽2)11yescharacteristic
323C32×D3—22no—
324C32×D3—41no—
325C32×D3—41no—
326C32×D3—41no—
327C24×C3—34no—
328C23×D3C22×C3211yescharacteristic
329C2×C3×Q8—34no—
330C2×C3×D4—34no—
331C2×C3×D4—34no—
332C2×C3×D4—34no—
333C2×C3×D4—34no—
334C2×C3×D4—34no—
335C2×C3×D4—34no—
336C2×C3×D4—34no—
337C22×C3×C4—34no—
338C22×C3×C4—34no—
339C22×C3×C4—34no—
340C22×C3×C4—34no—
341C2×#67C22×C3211yescharacteristic
342C2×#67C22×C3211yescharacteristic
343C2×D12C22×C3211yescharacteristic
344C2×D12C22×C3211yescharacteristic
345C2×D12C22×C3211yescharacteristic
346C2×D12C22×C3211yescharacteristic
347C2×D12C22×C3211yescharacteristic, complemented
348C2×C4×D3C22×C3211yescharacteristic
349C2×C4×D3C22×C3211yescharacteristic
350C2×C4×D3C22×C3211yescharacteristic, complemented
351C2×C4×D3C22×C3211yescharacteristic, complemented
352C2×Dic6C22×C3211yescharacteristic, complemented
353C3×C4⋊C4—24no—
354C3×C4⋊C4—24no—
355C3×C4⋊C4—24no—
356C3×C4⋊C4—34no—
357C3×C4⋊C4—34no—
358C3×C4⋊C4—34no—
359C3×C4⋊C4C2×C3×D314yescomplemented
360C3×C4⋊C4C2×C3×D314yescomplemented
361C3×C4⋊C4C2×C3×D314yescomplemented
362C3×C4⋊C4C22×C3211yescharacteristic, complemented
363C3×C4⋊C4C22×C3211yescharacteristic, complemented
364C3×C4⋊C4C22×C3211yescharacteristic, complemented
365C3×C22⋊C4—24no—
366C3×C22⋊C4—24no—
367C3×C22⋊C4—24no—
368C3×C22⋊C4—34no—
369C3×C22⋊C4—34no—
370C3×C22⋊C4—34no—
371C3×C22⋊C4—34no—
372C3×C22⋊C4—34no—
373C3×C22⋊C4—34no—
374C3×C22⋊C4—34no—
375C3×C22⋊C4—34no—
376C3×C22⋊C4—34no—
377C3×C22⋊C4—34no—
378C3×C22⋊C4—34no—
379C3×C22⋊C4C2×C3×D314yes—
380C3×C22⋊C4C2×C3×D314yes—
381C3×C22⋊C4C2×C3×D314yes—
382C3×C22⋊C4C22×C3211yescharacteristic
383C3×C22⋊C4C22×C3211yescharacteristic
384C3×C22⋊C4C22×C3211yescharacteristic
385C3×C42—24no—
386C3×C42—34no—
387C3×C42C2×C3×D314yescomplemented
388C3×C42C22×C3211yescharacteristic, complemented
389#217C22×C3211yescharacteristic
390(C2×D3)⋊C4C22×C3211yescharacteristic
391(C2×D3)⋊C4C22×C3211yescharacteristic
392(C2×D3)⋊C4C22×C3211yescharacteristic
393(C2×D3)⋊C4C22×C3211yescharacteristic
394(C2×D3)⋊C4C22×C3211yescharacteristic
395(C2×D3)⋊C4C22×C3211yescharacteristic
396(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
397(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
398(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
399(C2×D3)⋊C4C22×C3211yescharacteristic, complemented
400C4⋊Dic3C22×C3211yescharacteristic, complemented
401Dic3⋊C4C22×C3211yescharacteristic, complemented
402Dic3⋊C4C22×C3211yescharacteristic, complemented
403C4×Dic3C22×C3211yescharacteristic, complemented
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—21no—
407C22×C32—24no—
408C22×C32—24no—
409C22×C32—24no—
410C22×C32—24no—
411C22×C32—32no—
412C22×C32—44no—
413C22×C32—44no—
414C22×C32—44no—
415C22×C32—61no—
416C22×C32—61no—
417C22×C32—61no—
418C22×C32—61no—
419C22×C32—61no—
420C22×C32—61no—
421C22×C32—61no—
422C22×C32—61no—
423C22×C32—61no—
424C22×C32—61no—
425C22×C32—61no—
426C22×C32—124no—
427C22×C32C23×D311yescharacteristic
428C22×C32C24×C314yes—
429C2×C3×D3—24no—
430C2×C3×D3—24no—
431C2×C3×D3—24no—
432C2×C3×D3—24no—
433C2×C3×D3—24no—
434C2×C3×D3—24no—
435C2×C3×D3—24no—
436C2×C3×D3—24no—
437C2×C3×D3—24no—
438C2×C3×D3—24no—
439C2×C3×D3—24no—
440C2×C3×D3—416no—
441C2×C3×D3C3×#4118yes—
442C32×C4—21no—
443C32×C4—21no—
444C32×C4—21no—
445C32×C4—21no—
446C32×C4—21no—
447C32×C4—21no—
448C32×C4—24no—
449C32×C4—24no—
450C32×C4—24no—
451C32×C4—24no—
452C32×C4—24no—
453C32×C4—24no—
454C32×C4—44no—
455C32×C4—44no—
456C32×C4—44no—
457C32×C4—44no—
458C32×C4—44no—
459C32×C4—44no—
460C32×C4—61no—
461C32×C4—61no—
462C32×C4—61no—
463C32×C4—61no—
464C3×Dic3—24no—
465C3×Dic3—24no—
466C3×Dic3—24no—
467C3×Dic3—24no—
468#126—31no—
469#126C32×D311yescharacteristic, complemented
470#124—31no—
471#124—31no—
472#123—31no—
473#123—31no—
474C22⋊Q8—31no—
475#121—31no—
476#121—31no—
477#121—31no—
478#120—31no—
479#120—31no—
480C4×D4—31no—
481C4×D4—31no—
482C2×C22⋊C4—31no—
483C33#53811yescharacteristic, complemented, Sylow
484C23×C3—24no—
485C23×C3—34no—
486C23×C3—34no—
487C23×C3—34no—
488C23×C3—34no—
489C23×C3—68no—
490C23×C3—124no—
491C23×C3—124no—
492C23×C3C22×C3×D314yes—
493C23×C3C23×C3211yescharacteristic
494C22×D3—22no—
495C22×D3—41no—
496C22×D3—41no—
497C22×D3C23×C3211yescharacteristic
498C22×D3C23×C3211yescharacteristic
499C22×D3C23×C3211yescharacteristic
500C22×D3C23×C3211yescharacteristic
501C3×Q8—124no—
502C3×D4—68no—
503C3×D4—68no—
504C3×D4—124no—
505C3×D4—124no—
506C3×D4—124no—
507C3×D4—124no—
508C3×D4—124no—
509C2×C3×C4—24no—
510C2×C3×C4—24no—
511C2×C3×C4—24no—
512C2×C3×C4—24no—
513C2×C3×C4—24no—
514C2×C3×C4—24no—
515C2×C3×C4—34no—
516C2×C3×C4—34no—
517C2×C3×C4—34no—
518C2×C3×C4—34no—
519C2×C3×C4—124no—
520C2×C3×C4—124no—
521C2×C3×C4—124no—
522C2×C3×C4—124no—
523C2×C3×C4C22×C3×D314yes—
524C2×C3×C4C22×C3×D314yes—
525C2×C3×C4C22×C3×D314yes—
526C2×C3×C4C22×C3×D314yes—
527C2×C3×C4C22×C3×D314yes—
528C2×C3×C4C22×C3×D314yes—
529C2×C3×C4C23×C3211yescharacteristic
530C2×C3×C4C23×C3211yescharacteristic
531C2×C3×C4C23×C3211yescharacteristic
532C2×C3×C4C23×C3211yescharacteristic
533C2×C3×C4C23×C3211yescharacteristic
534C2×C3×C4C23×C3211yescharacteristic
535#67—41no—
536#67—41no—
537C2×Dic3C23×C3211yescharacteristic
538C2×Dic3C23×C3211yescharacteristic
539C2×Dic3C23×C3211yescharacteristic
540C2×Dic3C23×C3211yescharacteristic
541D12—22no—
542D12—22no—
543D12—41no—
544D12—41no—
545D12—41no—
546C4×D3—41no—
547C4×D3—41no—
548C4×D3—41no—
549C4×D3—41no—
550Dic6—41no—
551C2×C32—24no—
552C2×C32—24no—
553C2×C32—24no—
554C2×C32—41no—
555C2×C32—44no—
556C2×C32—62no—
557C2×C32—84no—
558C2×C32—121no—
559C2×C32—121no—
560C2×C32—121no—
561C2×C32D3×#4111yescharacteristic
562C2×C32#100911yescharacteristic
563C2×C32#100911yescharacteristic
564C2×C32C2×C3×#4114yes—
565C2×C32C3×H(5,𝔽2)14yes—
566C2×C32C3×H(5,𝔽2)14yes—
567C3×D3—28no—
568C3×D3—44no—
569C3×D3—44no—
570C3×D3—44no—
571C24—31no—
572C2×Q8—31no—
573C2×D4—31no—
574C2×D4—31no—
575C2×D4—31no—
576C2×D4—31no—
577C2×D4—31no—
578C2×D4—31no—
579C2×D4—31no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—31no—
583C22×C4—31no—
584C4⋊C4—31no—
585C4⋊C4—31no—
586C4⋊C4—31no—
587C4⋊C4C2×C32×D311yescharacteristic, complemented
588C4⋊C4C2×C32×D311yescharacteristic, complemented
589C4⋊C4C2×C32×D311yescharacteristic, complemented
590C22⋊C4—31no—
591C22⋊C4—31no—
592C22⋊C4—31no—
593C22⋊C4—31no—
594C22⋊C4—31no—
595C22⋊C4—31no—
596C22⋊C4—31no—
597C22⋊C4—31no—
598C22⋊C4—31no—
599C22⋊C4—31no—
600C22⋊C4—31no—
601C22⋊C4C2×C32×D311yescharacteristic
602C22⋊C4C2×C32×D311yescharacteristic
603C22⋊C4C2×C32×D311yescharacteristic
604C42—31no—
605C42C2×C32×D311yescharacteristic, complemented
606C22×C3—24no—
607C22×C3—24no—
608C22×C3—24no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—24no—
613C22×C3—38no—
614C22×C3—44no—
615C22×C3—44no—
616C22×C3—44no—
617C22×C3—64no—
618C22×C3—64no—
619C22×C3—64no—
620C22×C3—64no—
621C22×C3—64no—
622C22×C3—64no—
623C22×C3—64no—
624C22×C3—64no—
625C22×C3—64no—
626C22×C3—64no—
627C22×C3—64no—
628C22×C3—1216no—
629C22×C3C23×C3×D314yes—
630C22×C3C24×C3211yescharacteristic
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—44no—
643C2×D3C32×#4112yes—
644C3×C4—24no—
645C3×C4—24no—
646C3×C4—24no—
647C3×C4—24no—
648C3×C4—24no—
649C3×C4—24no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—44no—
657C3×C4—44no—
658C3×C4—44no—
659C3×C4—44no—
660C3×C4—44no—
661C3×C4—44no—
662C3×C4—64no—
663C3×C4—64no—
664C3×C4—64no—
665C3×C4—64no—
666Dic3—21no—
667Dic3—21no—
668Dic3—21no—
669Dic3—21no—
670C32—24no—
671C32#570411yescharacteristic, direct product factor
672C32C3×#53814yescomplemented
673C23—31no—
674C23—31no—
675C23—31no—
676C23—31no—
677C23—62no—
678C23—121no—
679C23—121no—
680C23C22×C32×D311yescharacteristic
681Q8—121no—
682D4—62no—
683D4—62no—
684D4—121no—
685D4—121no—
686D4—121no—
687D4—121no—
688D4—121no—
689C2×C4—31no—
690C2×C4—31no—
691C2×C4—31no—
692C2×C4—31no—
693C2×C4—121no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4C22×C32×D311yescharacteristic
698C2×C4C22×C32×D311yescharacteristic
699C2×C4C22×C32×D311yescharacteristic
700C2×C4C22×C32×D311yescharacteristic
701C2×C4C22×C32×D311yescharacteristic
702C2×C4C22×C32×D311yescharacteristic
703C2×C3—24no—
704C2×C3—24no—
705C2×C3—24no—
706C2×C3—44no—
707C2×C3—41no—
708C2×C3—68no—
709C2×C3—84no—
710C2×C3—124no—
711C2×C3—124no—
712C2×C3—124no—
713C2×C3C3×D3×#4114yes—
714C2×C3C3×#100914yes—
715C2×C3C3×#100914yes—
716C2×C3C2×C32×#4111yescharacteristic
717C2×C3C32×H(5,𝔽2)11yescharacteristic
718C2×C3C32×H(5,𝔽2)11yescharacteristic
719D3—22no—
720D3—41no—
721D3—41no—
722D3—41no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—32no—
727C22—61no—
728C22—61no—
729C22—61no—
730C22—61no—
731C22—61no—
732C22—61no—
733C22—61no—
734C22—61no—
735C22—61no—
736C22—61no—
737C22—61no—
738C22—124no—
739C22C23×C32×D311yescharacteristic
740C4—21no—
741C4—21no—
742C4—21no—
743C4—21no—
744C4—21no—
745C4—21no—
746C4—61no—
747C4—61no—
748C4—61no—
749C4—61no—
750C3—24no—
751C3C3×#570414yesdirect product factor
752C3C32×#53811yescharacteristic, complemented
753C2—41no—
754C2—62no—
755C2—121no—
756C2—121no—
757C2—121no—
758C2C32×D3×#4111yescharacteristic
759C2C32×#100911yescharacteristic
760C2C32×#100911yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#126C2
socleC22×C33C24
hypercenterC32×#126D3
hypocenterC3C32×#538
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×#126

Complements

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

NH ≅ G/Ntype
1. C33×#126C2semidirect
2. C32×#898C2semidirect
3. C32×#896C2semidirect
4. C32×#895C2semidirect
5. C32×#895C2semidirect
6. C32×#894C2semidirect
7. C32×#893C2semidirect
8. C32×#885C2semidirect
9. C32×#884C2semidirect
10. C32×#883C2semidirect
11. C32×#882C2semidirect
12. C32×#882C2semidirect
13. C32×D3×C22⋊C4C2semidirect
14. C32×#875C2semidirect
15. C32×C4×D12C2semidirect
17. C3×#5704C3direct (N × H)
25. C2×C32×D12C22semidirect
28. C2×C32×C4×D3C22semidirect
29. C2×C32×C4×D3C22semidirect
30. C2×C32×Dic6C22semidirect
31. C33×C4⋊C4C22semidirect
32. C33×C4⋊C4C22semidirect
33. C33×C4⋊C4C22semidirect
37. C33×C42C22semidirect
45. C32×(C2×D3)⋊C4C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. C32×(C2×D3)⋊C4C22semidirect
48. C32×(C2×D3)⋊C4C22semidirect
49. C32×C4⋊Dic3C22semidirect
50. C32×Dic3⋊C4C22semidirect
51. C32×Dic3⋊C4C22semidirect
52. C32×C4×Dic3C22semidirect
55. C32×#126D3semidirect
56. C32×#126C2×C3semidirect
70. C3×#898C2×C3semidirect
71. C3×#896C2×C3semidirect
72. C3×#895C2×C3semidirect
73. C3×#895C2×C3semidirect
74. C3×#894C2×C3semidirect
75. C3×#893C2×C3semidirect
76. C3×#885C2×C3semidirect
77. C3×#884C2×C3semidirect
78. C3×#883C2×C3semidirect
79. C3×#882C2×C3semidirect
80. C3×#882C2×C3semidirect
81. C3×D3×C22⋊C4C2×C3semidirect
82. C3×#875C2×C3semidirect
83. C3×C4×D12C2×C3semidirect
115. #5704C32direct (N × H)
136. C2×C3×D12C22×C3semidirect
139. C2×C3×C4×D3C22×C3semidirect
140. C2×C3×C4×D3C22×C3semidirect
141. C2×C3×Dic6C22×C3semidirect
148. C32×C4⋊C4C2×D3semidirect
149. C32×C4⋊C4C2×D3semidirect
150. C32×C4⋊C4C2×D3semidirect
151. C32×C4⋊C4C22×C3semidirect
152. C32×C4⋊C4C22×C3semidirect
153. C32×C4⋊C4C22×C3semidirect
176. C32×C42C2×D3semidirect
177. C32×C42C22×C3semidirect
185. C3×(C2×D3)⋊C4C22×C3semidirect
186. C3×(C2×D3)⋊C4C22×C3semidirect
187. C3×(C2×D3)⋊C4C22×C3semidirect
188. C3×(C2×D3)⋊C4C22×C3semidirect
189. C3×C4⋊Dic3C22×C3semidirect
190. C3×Dic3⋊C4C22×C3semidirect
191. C3×Dic3⋊C4C22×C3semidirect
192. C3×C4×Dic3C22×C3semidirect
222. C3×#126C3×D3semidirect
223. C3×#126C2×C32semidirect
237. #898C2×C32semidirect
238. #896C2×C32semidirect
239. #895C2×C32semidirect
240. #895C2×C32semidirect
241. #894C2×C32semidirect
242. #893C2×C32semidirect
243. #885C2×C32semidirect
244. #884C2×C32semidirect
245. #883C2×C32semidirect
246. #882C2×C32semidirect
247. #882C2×C32semidirect
248. D3×C22⋊C4C2×C32semidirect
249. #875C2×C32semidirect
250. C4×D12C2×C32semidirect
347. C2×D12C22×C32semidirect
350. C2×C4×D3C22×C32semidirect
351. C2×C4×D3C22×C32semidirect
352. C2×Dic6C22×C32semidirect
359. C3×C4⋊C4C2×C3×D3semidirect
360. C3×C4⋊C4C2×C3×D3semidirect
361. C3×C4⋊C4C2×C3×D3semidirect
362. C3×C4⋊C4C22×C32semidirect
363. C3×C4⋊C4C22×C32semidirect
364. C3×C4⋊C4C22×C32semidirect
387. C3×C42C2×C3×D3semidirect
388. C3×C42C22×C32semidirect
396. (C2×D3)⋊C4C22×C32semidirect
397. (C2×D3)⋊C4C22×C32semidirect
398. (C2×D3)⋊C4C22×C32semidirect
399. (C2×D3)⋊C4C22×C32semidirect
400. C4⋊Dic3C22×C32semidirect
401. Dic3⋊C4C22×C32semidirect
402. Dic3⋊C4C22×C32semidirect
403. C4×Dic3C22×C32semidirect
469. #126C32×D3semidirect
483. C33#538semidirect
587. C4⋊C4C2×C32×D3semidirect
588. C4⋊C4C2×C32×D3semidirect
589. C4⋊C4C2×C32×D3semidirect
605. C42C2×C32×D3semidirect
671. C32#5704direct (N × H)
672. C32C3×#538semidirect
751. C3C3×#5704direct (N × H)
752. C3C32×#538semidirect

Maximal subgroups

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

subgroupindex
C33×#1262
C32×#8982
C32×#8962
C32×#8952
C32×#8942
C32×#8932
C32×#8852
C32×#8842
C32×#8832
C32×#8822
C32×D3×C22⋊C42
C32×#8752
C32×C4×D122
C32×#5383
C3×#57043