Finite Group Databasebeta

← C32×#5692 #13179070

Subgroups — C32×#5692 #13179070

Order 1728.

1532 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×#125C211yesmaximal, characteristic, complemented
2C32×#898C211yesmaximal, characteristic, complemented
3C32×#897C211yesmaximal, characteristic, complemented
4C32×#896C211yesmaximal, characteristic, complemented
5C32×#896C211yesmaximal, characteristic, complemented
6C32×#895C211yesmaximal, characteristic
7C32×#894C211yesmaximal, characteristic, complemented
8C32×#894C211yesmaximal, characteristic, complemented
9C32×#894C211yesmaximal, characteristic, complemented
10C32×#894C211yesmaximal, characteristic, complemented
11C32×#893C211yesmaximal, characteristic, complemented
12C32×D3×C4⋊C4C211yesmaximal, characteristic, complemented
13C32×#889C211yesmaximal, characteristic, complemented
14C32×#876C211yesmaximal, characteristic, complemented
15C32×C4×D12C211yesmaximal, characteristic, complemented
16C32×#539—31nomaximal
17C3×#5692C314yesmaximal, direct product factor
18C2×C32×D12C2211yescharacteristic
19C2×C32×D12C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×C32×C4×D3C2211yescharacteristic
22C2×C32×C4×D3C2211yescharacteristic
23C2×C32×C4×D3C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic
26C2×C32×Dic6C2211yescharacteristic
27C33×C4⋊C4C2211yescharacteristic
28C33×C4⋊C4C2211yescharacteristic
29C33×C4⋊C4C2211yescharacteristic
30C33×C4⋊C4C2211yescharacteristic
31C33×C4⋊C4C2211yescharacteristic
32C33×C4⋊C4C2211yescharacteristic
33C33×C42C2211yescharacteristic
34C32×(C2×D3)⋊C4C2211yescharacteristic
35C32×(C2×D3)⋊C4C2211yescharacteristic
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
45C32×C4⋊Dic3C2211yescharacteristic
46C32×Dic3⋊C4C2211yescharacteristic
47C32×Dic3⋊C4C2211yescharacteristic
48C32×Dic3⋊C4C2211yescharacteristic
49C32×Dic3⋊C4C2211yescharacteristic
50C32×Dic3⋊C4C2211yescharacteristic
51C32×Dic3⋊C4C2211yescharacteristic
52C32×C4×Dic3C2211yescharacteristic
53C32×#126—31no—
54C32×#126—31no—
55C32×#125—24no—
56C32×#125—31no—
57C32×#125D311yescharacteristic, complemented
58C32×#125C2×C314yescomplemented
59C32×#123—31no—
60C32×#123—31no—
61C32×#123—31no—
62C32×#123—31no—
63C32×C22⋊Q8—31no—
64C32×C22⋊Q8—31no—
65C32×C22⋊Q8—31no—
66C32×#121—31no—
67C32×C4×D4—31no—
68C32×C4×D4—31no—
69C2×C32×C4⋊C4—31no—
70C3×#898C2×C314yescomplemented
71C3×#897C2×C314yescomplemented
72C3×#896C2×C314yescomplemented
73C3×#896C2×C314yescomplemented
74C3×#895C2×C314yes—
75C3×#894C2×C314yescomplemented
76C3×#894C2×C314yescomplemented
77C3×#894C2×C314yescomplemented
78C3×#894C2×C314yescomplemented
79C3×#893C2×C314yescomplemented
80C3×D3×C4⋊C4C2×C314yescomplemented
81C3×#889C2×C314yescomplemented
82C3×#876C2×C314yescomplemented
83C3×C4×D12C2×C314yescomplemented
84C22×C32×D3C2311yescharacteristic
85C22×C32×D3C2311yescharacteristic
86C22×C32×D3C2311yescharacteristic
87C2×C33×C4C2311yescharacteristic
88C2×C33×C4C2311yescharacteristic
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C2×C32×Dic3C2311yescharacteristic
95C2×C32×Dic3C2311yescharacteristic
96C2×C32×Dic3C2311yescharacteristic
97C2×C32×Dic3C2311yescharacteristic
98C2×C32×Dic3C2311yescharacteristic
99C32×D12—22no—
100C32×D12—22no—
101C32×D12—41no—
102C32×C4×D3—22no—
103C32×C4×D3—41no—
104C32×C4×D3—41no—
105C32×C4×D3—41no—
106C32×C4×D3—41no—
107C32×Dic6—41no—
108C3×#539—34no—
109#5692C3211yescharacteristic, direct product factor
110C2×C32×Q8—31no—
111C2×C32×D4—31no—
112C2×C32×D4—31no—
113C2×C32×D4—31no—
114C22×C32×C4—31no—
115C22×C32×C4—31no—
116C22×C32×C4—31no—
117C22×C32×C4—31no—
118C22×C32×C4—31no—
119C2×C3×D12C22×C314yes—
120C2×C3×D12C22×C314yes—
121C2×C3×D12C22×C314yes—
122C2×C3×C4×D3C22×C314yes—
123C2×C3×C4×D3C22×C314yes—
124C2×C3×C4×D3C22×C314yes—
125C2×C3×C4×D3C22×C314yes—
126C2×C3×C4×D3C22×C314yes—
127C2×C3×Dic6C22×C314yes—
128C32×C4⋊C4—24no—
129C32×C4⋊C4—24no—
130C32×C4⋊C4—24no—
131C32×C4⋊C4—24no—
132C32×C4⋊C4—24no—
133C32×C4⋊C4—24no—
134C32×C4⋊C4—31no—
135C32×C4⋊C4—31no—
136C32×C4⋊C4—31no—
137C32×C4⋊C4—31no—
138C32×C4⋊C4—31no—
139C32×C4⋊C4—31no—
140C32×C4⋊C4—31no—
141C32×C4⋊C4—31no—
142C32×C4⋊C4C2×D311yescharacteristic
143C32×C4⋊C4C2×D311yescharacteristic
144C32×C4⋊C4C2×D311yescharacteristic
145C32×C4⋊C4C2×D311yescharacteristic
146C32×C4⋊C4C2×D311yescharacteristic
147C32×C4⋊C4C2×D311yescharacteristic
148C32×C4⋊C4C22×C314yes—
149C32×C4⋊C4C22×C314yes—
150C32×C4⋊C4C22×C314yes—
151C32×C4⋊C4C22×C314yes—
152C32×C4⋊C4C22×C314yes—
153C32×C4⋊C4C22×C314yes—
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⋊C4—31no—
161C32×C22⋊C4—31no—
162C32×C22⋊C4—31no—
163C32×C22⋊C4—31no—
164C32×C42—24no—
165C32×C42—31no—
166C32×C42C2×D311yescharacteristic
167C32×C42C22×C314yes—
168C3×(C2×D3)⋊C4C22×C314yes—
169C3×(C2×D3)⋊C4C22×C314yes—
170C3×(C2×D3)⋊C4C22×C314yes—
171C3×(C2×D3)⋊C4C22×C314yes—
172C3×(C2×D3)⋊C4C22×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×C4⋊Dic3C22×C314yes—
179C3×C4⋊Dic3C22×C314yes—
180C3×Dic3⋊C4C22×C314yes—
181C3×Dic3⋊C4C22×C314yes—
182C3×Dic3⋊C4C22×C314yes—
183C3×Dic3⋊C4C22×C314yes—
184C3×Dic3⋊C4C22×C314yes—
185C3×Dic3⋊C4C22×C314yes—
186C3×C4×Dic3C22×C314yes—
187C22×C33C2411yescharacteristic
188C2×C32×D3—21no—
189C2×C32×D3—21no—
190C2×C32×D3—21no—
191C2×C32×D3—21no—
192C2×C32×D3—21no—
193C2×C32×D3—21no—
194C2×C32×D3—21no—
195C2×C32×D3—21no—
196C2×C32×D3#4112yes—
197C33×C4—21no—
198C33×C4—21no—
199C33×C4—21no—
200C33×C4—21no—
201C33×C4—21no—
202C33×C4—21no—
203C33×C4—21no—
204C32×Dic3—21no—
205C32×Dic3—21no—
206C32×Dic3—21no—
207C32×Dic3—21no—
208C32×Dic3—21no—
209C3×#126—34no—
210C3×#126—34no—
211C3×#125—24no—
212C3×#125—34no—
213C3×#125C3×D314yescomplemented
214C3×#125C2×C3211yescharacteristic, complemented
215C3×#123—34no—
216C3×#123—34no—
217C3×#123—34no—
218C3×#123—34no—
219C3×C22⋊Q8—34no—
220C3×C22⋊Q8—34no—
221C3×C22⋊Q8—34no—
222C3×#121—34no—
223C3×C4×D4—34no—
224C3×C4×D4—34no—
225C2×C3×C4⋊C4—34no—
226#898C2×C3211yescharacteristic, complemented
227#897C2×C3211yescharacteristic, complemented
228#896C2×C3211yescharacteristic, complemented
229#896C2×C3211yescharacteristic, complemented
230#895C2×C3211yescharacteristic
231#894C2×C3211yescharacteristic, complemented
232#894C2×C3211yescharacteristic, complemented
233#894C2×C3211yescharacteristic, complemented
234#894C2×C3211yescharacteristic, complemented
235#893C2×C3211yescharacteristic, complemented
236D3×C4⋊C4C2×C3211yescharacteristic, complemented
237#889C2×C3211yescharacteristic, complemented
238#876C2×C3211yescharacteristic, complemented
239C4×D12C2×C3211yescharacteristic, complemented
240C23×C32—31no—
241C23×C32—31no—
242C23×C32—31no—
243C22×C3×D3C23×C314yes—
244C22×C3×D3C23×C314yes—
245C22×C3×D3C23×C314yes—
246C32×Q8—121no—
247C32×D4—62no—
248C32×D4—62no—
249C32×D4—121no—
250C2×C32×C4—24no—
251C2×C32×C4—24no—
252C2×C32×C4—24no—
253C2×C32×C4—24no—
254C2×C32×C4—24no—
255C2×C32×C4—24no—
256C2×C32×C4—24no—
257C2×C32×C4—31no—
258C2×C32×C4—31no—
259C2×C32×C4—31no—
260C2×C32×C4—31no—
261C2×C32×C4—31no—
262C2×C32×C4—62no—
263C2×C32×C4—121no—
264C2×C32×C4—121no—
265C2×C32×C4—121no—
266C2×C32×C4—121no—
267C2×C32×C4C22×D311yescharacteristic
268C2×C32×C4C22×D311yescharacteristic
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C22×D311yescharacteristic
272C2×C32×C4C22×D311yescharacteristic
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C23×C314yes—
275C2×C32×C4C23×C314yes—
276C2×C32×C4C23×C314yes—
277C2×C32×C4C23×C314yes—
278C2×C32×C4C23×C314yes—
279C2×C32×C4C23×C314yes—
280C2×C32×C4C23×C314yes—
281C2×C3×Dic3C23×C314yes—
282C2×C3×Dic3C23×C314yes—
283C2×C3×Dic3C23×C314yes—
284C2×C3×Dic3C23×C314yes—
285C2×C3×Dic3C23×C314yes—
286C3×D12—28no—
287C3×D12—28no—
288C3×D12—44no—
289C3×C4×D3—28no—
290C3×C4×D3—44no—
291C3×C4×D3—44no—
292C3×C4×D3—44no—
293C3×C4×D3—44no—
294C3×Dic6—44no—
295#539—31noSylow
296C2×C33C2×#4111yescharacteristic
297C2×C33H(5,𝔽2)11yescharacteristic
298C2×C332−1+411yescharacteristic
299C32×D3—22no—
300C32×D3—41no—
301C32×D3—41no—
302C2×C3×Q8—34no—
303C2×C3×D4—34no—
304C2×C3×D4—34no—
305C2×C3×D4—34no—
306C22×C3×C4—34no—
307C22×C3×C4—34no—
308C22×C3×C4—34no—
309C22×C3×C4—34no—
310C22×C3×C4—34no—
311C2×D12C22×C3211yescharacteristic
312C2×D12C22×C3211yescharacteristic
313C2×D12C22×C3211yescharacteristic
314C2×C4×D3C22×C3211yescharacteristic
315C2×C4×D3C22×C3211yescharacteristic
316C2×C4×D3C22×C3211yescharacteristic
317C2×C4×D3C22×C3211yescharacteristic
318C2×C4×D3C22×C3211yescharacteristic
319C2×Dic6C22×C3211yescharacteristic
320C3×C4⋊C4—24no—
321C3×C4⋊C4—24no—
322C3×C4⋊C4—24no—
323C3×C4⋊C4—24no—
324C3×C4⋊C4—24no—
325C3×C4⋊C4—24no—
326C3×C4⋊C4—34no—
327C3×C4⋊C4—34no—
328C3×C4⋊C4—34no—
329C3×C4⋊C4—34no—
330C3×C4⋊C4—34no—
331C3×C4⋊C4—34no—
332C3×C4⋊C4—34no—
333C3×C4⋊C4—34no—
334C3×C4⋊C4C2×C3×D314yes—
335C3×C4⋊C4C2×C3×D314yes—
336C3×C4⋊C4C2×C3×D314yes—
337C3×C4⋊C4C2×C3×D314yes—
338C3×C4⋊C4C2×C3×D314yes—
339C3×C4⋊C4C2×C3×D314yes—
340C3×C4⋊C4C22×C3211yescharacteristic
341C3×C4⋊C4C22×C3211yescharacteristic
342C3×C4⋊C4C22×C3211yescharacteristic
343C3×C4⋊C4C22×C3211yescharacteristic
344C3×C4⋊C4C22×C3211yescharacteristic
345C3×C4⋊C4C22×C3211yescharacteristic
346C3×C22⋊C4—34no—
347C3×C22⋊C4—34no—
348C3×C22⋊C4—34no—
349C3×C22⋊C4—34no—
350C3×C22⋊C4—34no—
351C3×C22⋊C4—34no—
352C3×C22⋊C4—34no—
353C3×C22⋊C4—34no—
354C3×C22⋊C4—34no—
355C3×C22⋊C4—34no—
356C3×C42—24no—
357C3×C42—34no—
358C3×C42C2×C3×D314yes—
359C3×C42C22×C3211yescharacteristic
360(C2×D3)⋊C4C22×C3211yescharacteristic
361(C2×D3)⋊C4C22×C3211yescharacteristic
362(C2×D3)⋊C4C22×C3211yescharacteristic
363(C2×D3)⋊C4C22×C3211yescharacteristic
364(C2×D3)⋊C4C22×C3211yescharacteristic
365(C2×D3)⋊C4C22×C3211yescharacteristic
366(C2×D3)⋊C4C22×C3211yescharacteristic
367(C2×D3)⋊C4C22×C3211yescharacteristic
368(C2×D3)⋊C4C22×C3211yescharacteristic
369(C2×D3)⋊C4C22×C3211yescharacteristic
370C4⋊Dic3C22×C3211yescharacteristic
371C4⋊Dic3C22×C3211yescharacteristic
372Dic3⋊C4C22×C3211yescharacteristic
373Dic3⋊C4C22×C3211yescharacteristic
374Dic3⋊C4C22×C3211yescharacteristic
375Dic3⋊C4C22×C3211yescharacteristic
376Dic3⋊C4C22×C3211yescharacteristic
377Dic3⋊C4C22×C3211yescharacteristic
378C4×Dic3C22×C3211yescharacteristic
379C22×C32—24no—
380C22×C32—32no—
381C22×C32—61no—
382C22×C32—61no—
383C22×C32—61no—
384C22×C32—61no—
385C22×C32—61no—
386C22×C32—61no—
387C22×C32—61no—
388C22×C32—61no—
389C22×C32C23×D311yescharacteristic
390C22×C32C24×C314yes—
391C2×C3×D3—24no—
392C2×C3×D3—24no—
393C2×C3×D3—24no—
394C2×C3×D3—24no—
395C2×C3×D3—24no—
396C2×C3×D3—24no—
397C2×C3×D3—24no—
398C2×C3×D3—24no—
399C2×C3×D3C3×#4118yes—
400C32×C4—28no—
401C32×C4—21no—
402C32×C4—21no—
403C32×C4—21no—
404C32×C4—21no—
405C32×C4—21no—
406C32×C4—21no—
407C32×C4—21no—
408C32×C4—24no—
409C32×C4—24no—
410C32×C4—24no—
411C32×C4—24no—
412C32×C4—24no—
413C32×C4—24no—
414C32×C4—24no—
415C32×C4—44no—
416C32×C4—44no—
417C32×C4—44no—
418C32×C4—44no—
419C32×C4—44no—
420C32×C4—44no—
421C32×C4—61no—
422C32×C4—61no—
423C32×C4—61no—
424C32×C4—61no—
425C32×C4—61no—
426C3×Dic3—24no—
427C3×Dic3—24no—
428C3×Dic3—24no—
429C3×Dic3—24no—
430C3×Dic3—24no—
431#126—31no—
432#126—31no—
433#125—31no—
434#125C32×D311yescharacteristic, complemented
435#123—31no—
436#123—31no—
437#123—31no—
438#123—31no—
439C22⋊Q8—31no—
440C22⋊Q8—31no—
441C22⋊Q8—31no—
442#121—31no—
443C4×D4—31no—
444C4×D4—31no—
445C2×C4⋊C4—31no—
446C33#53911yescharacteristic, complemented, Sylow
447C23×C3—34no—
448C23×C3—34no—
449C23×C3—34no—
450C22×D3C23×C3211yescharacteristic
451C22×D3C23×C3211yescharacteristic
452C22×D3C23×C3211yescharacteristic
453C3×Q8—124no—
454C3×D4—68no—
455C3×D4—68no—
456C3×D4—124no—
457C2×C3×C4—24no—
458C2×C3×C4—24no—
459C2×C3×C4—24no—
460C2×C3×C4—24no—
461C2×C3×C4—24no—
462C2×C3×C4—24no—
463C2×C3×C4—24no—
464C2×C3×C4—34no—
465C2×C3×C4—34no—
466C2×C3×C4—34no—
467C2×C3×C4—34no—
468C2×C3×C4—34no—
469C2×C3×C4—68no—
470C2×C3×C4—124no—
471C2×C3×C4—124no—
472C2×C3×C4—124no—
473C2×C3×C4—124no—
474C2×C3×C4C22×C3×D314yes—
475C2×C3×C4C22×C3×D314yes—
476C2×C3×C4C22×C3×D314yes—
477C2×C3×C4C22×C3×D314yes—
478C2×C3×C4C22×C3×D314yes—
479C2×C3×C4C22×C3×D314yes—
480C2×C3×C4C22×C3×D314yes—
481C2×C3×C4C23×C3211yescharacteristic
482C2×C3×C4C23×C3211yescharacteristic
483C2×C3×C4C23×C3211yescharacteristic
484C2×C3×C4C23×C3211yescharacteristic
485C2×C3×C4C23×C3211yescharacteristic
486C2×C3×C4C23×C3211yescharacteristic
487C2×C3×C4C23×C3211yescharacteristic
488C2×Dic3C23×C3211yescharacteristic
489C2×Dic3C23×C3211yescharacteristic
490C2×Dic3C23×C3211yescharacteristic
491C2×Dic3C23×C3211yescharacteristic
492C2×Dic3C23×C3211yescharacteristic
493D12—22no—
494D12—22no—
495D12—41no—
496C4×D3—22no—
497C4×D3—41no—
498C4×D3—41no—
499C4×D3—41no—
500C4×D3—41no—
501Dic6—41no—
502C2×C32—24no—
503C2×C32—24no—
504C2×C32—24no—
505C2×C32—62no—
506C2×C32—121no—
507C2×C32—121no—
508C2×C32#100711yescharacteristic
509C2×C32D3×#4111yescharacteristic
510C2×C32#100911yescharacteristic
511C2×C32C2×C3×#4114yes—
512C2×C32C3×H(5,𝔽2)14yes—
513C2×C32C3×2−1+414yes—
514C3×D3—28no—
515C3×D3—44no—
516C3×D3—44no—
517C2×Q8—31no—
518C2×D4—31no—
519C2×D4—31no—
520C2×D4—31no—
521C22×C4—31no—
522C22×C4—31no—
523C22×C4—31no—
524C22×C4—31no—
525C22×C4—31no—
526C4⋊C4—31no—
527C4⋊C4—31no—
528C4⋊C4—31no—
529C4⋊C4—31no—
530C4⋊C4—31no—
531C4⋊C4—31no—
532C4⋊C4—31no—
533C4⋊C4—31no—
534C4⋊C4C2×C32×D311yescharacteristic
535C4⋊C4C2×C32×D311yescharacteristic
536C4⋊C4C2×C32×D311yescharacteristic
537C4⋊C4C2×C32×D311yescharacteristic
538C4⋊C4C2×C32×D311yescharacteristic
539C4⋊C4C2×C32×D311yescharacteristic
540C22⋊C4—31no—
541C22⋊C4—31no—
542C22⋊C4—31no—
543C22⋊C4—31no—
544C22⋊C4—31no—
545C22⋊C4—31no—
546C22⋊C4—31no—
547C22⋊C4—31no—
548C22⋊C4—31no—
549C22⋊C4—31no—
550C42—31no—
551C42C2×C32×D311yescharacteristic
552C22×C3—24no—
553C22×C3—38no—
554C22×C3—64no—
555C22×C3—64no—
556C22×C3—64no—
557C22×C3—64no—
558C22×C3—64no—
559C22×C3—64no—
560C22×C3—64no—
561C22×C3—64no—
562C22×C3C23×C3×D314yes—
563C22×C3C24×C3211yescharacteristic
564C2×D3—21no—
565C2×D3—21no—
566C2×D3—21no—
567C2×D3—21no—
568C2×D3—21no—
569C2×D3—21no—
570C2×D3—21no—
571C2×D3—21no—
572C2×D3C32×#4112yes—
573C3×C4—28no—
574C3×C4—24no—
575C3×C4—24no—
576C3×C4—24no—
577C3×C4—24no—
578C3×C4—24no—
579C3×C4—24no—
580C3×C4—24no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—44no—
589C3×C4—44no—
590C3×C4—44no—
591C3×C4—44no—
592C3×C4—44no—
593C3×C4—44no—
594C3×C4—64no—
595C3×C4—64no—
596C3×C4—64no—
597C3×C4—64no—
598C3×C4—64no—
599Dic3—21no—
600Dic3—21no—
601Dic3—21no—
602Dic3—21no—
603Dic3—21no—
604C32—24no—
605C32#569211yescharacteristic, direct product factor
606C32C3×#53914yescomplemented
607C23—31no—
608C23—31no—
609C23—31no—
610Q8—121no—
611D4—62no—
612D4—62no—
613D4—121no—
614C2×C4—31no—
615C2×C4—31no—
616C2×C4—31no—
617C2×C4—31no—
618C2×C4—31no—
619C2×C4—62no—
620C2×C4—121no—
621C2×C4—121no—
622C2×C4—121no—
623C2×C4—121no—
624C2×C4C22×C32×D311yescharacteristic
625C2×C4C22×C32×D311yescharacteristic
626C2×C4C22×C32×D311yescharacteristic
627C2×C4C22×C32×D311yescharacteristic
628C2×C4C22×C32×D311yescharacteristic
629C2×C4C22×C32×D311yescharacteristic
630C2×C4C22×C32×D311yescharacteristic
631C2×C3—24no—
632C2×C3—24no—
633C2×C3—24no—
634C2×C3—68no—
635C2×C3—124no—
636C2×C3—124no—
637C2×C3C3×#100714yes—
638C2×C3C3×D3×#4114yes—
639C2×C3C3×#100914yes—
640C2×C3C2×C32×#4111yescharacteristic
641C2×C3C32×H(5,𝔽2)11yescharacteristic
642C2×C3C32×2−1+411yescharacteristic
643D3—22no—
644D3—41no—
645D3—41no—
646C22—32no—
647C22—61no—
648C22—61no—
649C22—61no—
650C22—61no—
651C22—61no—
652C22—61no—
653C22—61no—
654C22—61no—
655C22C23×C32×D311yescharacteristic
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—21no—
661C4—21no—
662C4—21no—
663C4—61no—
664C4—61no—
665C4—61no—
666C4—61no—
667C4—61no—
668C3—24no—
669C3C3×#569214yesdirect product factor
670C3C32×#53911yescharacteristic, complemented
671C2—62no—
672C2—121no—
673C2—121no—
674C2C32×#100711yescharacteristic
675C2C32×D3×#4111yescharacteristic
676C2C32×#100911yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#125C2
socleC22×C33C24
prime radicalC32×#895C2
hypercenterC32×#125D3
hypocenterC3C32×#539
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×#125

Complements

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

NH ≅ G/Ntype
1. C33×#125C2semidirect
2. C32×#898C2semidirect
3. C32×#897C2semidirect
4. C32×#896C2semidirect
5. C32×#896C2semidirect
7. C32×#894C2semidirect
8. C32×#894C2semidirect
9. C32×#894C2semidirect
10. C32×#894C2semidirect
11. C32×#893C2semidirect
12. C32×D3×C4⋊C4C2semidirect
13. C32×#889C2semidirect
14. C32×#876C2semidirect
15. C32×C4×D12C2semidirect
17. C3×#5692C3direct (N × H)
57. C32×#125D3semidirect
58. C32×#125C2×C3semidirect
70. C3×#898C2×C3semidirect
71. C3×#897C2×C3semidirect
72. C3×#896C2×C3semidirect
73. C3×#896C2×C3semidirect
75. C3×#894C2×C3semidirect
76. C3×#894C2×C3semidirect
77. C3×#894C2×C3semidirect
78. C3×#894C2×C3semidirect
79. C3×#893C2×C3semidirect
80. C3×D3×C4⋊C4C2×C3semidirect
81. C3×#889C2×C3semidirect
82. C3×#876C2×C3semidirect
83. C3×C4×D12C2×C3semidirect
109. #5692C32direct (N × H)
213. C3×#125C3×D3semidirect
214. C3×#125C2×C32semidirect
226. #898C2×C32semidirect
227. #897C2×C32semidirect
228. #896C2×C32semidirect
229. #896C2×C32semidirect
231. #894C2×C32semidirect
232. #894C2×C32semidirect
233. #894C2×C32semidirect
234. #894C2×C32semidirect
235. #893C2×C32semidirect
236. D3×C4⋊C4C2×C32semidirect
237. #889C2×C32semidirect
238. #876C2×C32semidirect
239. C4×D12C2×C32semidirect
434. #125C32×D3semidirect
446. C33#539semidirect
605. C32#5692direct (N × H)
606. C32C3×#539semidirect
669. C3C3×#5692direct (N × H)
670. C3C32×#539semidirect

Maximal subgroups

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

subgroupindex
C33×#1252
C32×#8982
C32×#8972
C32×#8962
C32×#8952
C32×#8942
C32×#8932
C32×D3×C4⋊C42
C32×#8892
C32×#8762
C32×C4×D122
C32×#5393
C3×#56923