Finite Group Databasebeta

← C3×#10596009 #13179290

Subgroups — C3×#10596009 #13179290

Order 1728.

1780 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×C4×D4C211yesmaximal, characteristic, complemented
2C3×#64148C211yesmaximal, characteristic
3C3×#64144C211yesmaximal, characteristic, complemented
4C3×C4×#638C211yesmaximal, characteristic, complemented
5C3×C4×#638C211yesmaximal, characteristic, complemented
6C3×#64135C211yesmaximal, characteristic, complemented
7C2×C3×C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
8C3×#64107C211yesmaximal, characteristic, complemented
9C3×#64098C211yesmaximal, characteristic, complemented
10C3×#64095C211yesmaximal, characteristic, complemented
11C3×#64094C211yesmaximal, characteristic, complemented
12C3×#64088C211yesmaximal, characteristic, complemented
13C3×#64087C211yesmaximal, characteristic, complemented
14C3×#64081C211yesmaximal, characteristic, complemented
15C3×C4×#634C211yesmaximal, characteristic, complemented
16#10596009C311yesmaximal, characteristic, direct product factor
17C3×#5538—34nomaximal
18C2×C33×D4C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C22×C3×C3⋊Dic3C2211yescharacteristic
24C22×C3×C3⋊Dic3C2211yescharacteristic
25C2×C3×C4×C3⋊D3C2211yescharacteristic
26C2×C3×#634C2211yescharacteristic
27C33×C4⋊C4C2211yescharacteristic
28C33×C22⋊C4C2211yescharacteristic
29C33×C22⋊C4C2211yescharacteristic
30C33×C42C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32C3×#3757C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C3×#3757C2211yescharacteristic
35C3×#3752C2211yescharacteristic
36C3×#3752C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×#3752C2211yescharacteristic
39C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
40C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
41C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
42C3×#3750C2211yescharacteristic
43C3×#3750C2211yescharacteristic
44C3×#3750C2211yescharacteristic
45C3×#3750C2211yescharacteristic
46C3×#3750C2211yescharacteristic
47C3×#3750C2211yescharacteristic
48C3×C4×C3⋊Dic3C2211yescharacteristic
49C3×C4×C3⋊Dic3C2211yescharacteristic
50C3×C4×C3⋊Dic3C2211yescharacteristic
51C3×C4×C3⋊Dic3C2211yescharacteristic
52C3×C4×C3⋊Dic3C2211yescharacteristic
53C32×C4×D4—24no—
54C32×C4×D4D314yescomplemented
55C32×C4×D4C2×C311yescharacteristic, complemented
56#64148C2×C311yescharacteristic
57#64144C2×C311yescharacteristic, complemented
58C4×#638C2×C311yescharacteristic, complemented
59C4×#638C2×C311yescharacteristic, complemented
60#64135C2×C311yescharacteristic, complemented
61C2×C4×C3⋊Dic3C2×C311yescharacteristic, complemented
62#64107C2×C311yescharacteristic, complemented
63#64098C2×C311yescharacteristic, complemented
64#64095C2×C311yescharacteristic, complemented
65#64094C2×C311yescharacteristic, complemented
66#64088C2×C311yescharacteristic, complemented
67#64087C2×C311yescharacteristic, complemented
68#64081C2×C311yescharacteristic, complemented
69C4×#634C2×C311yescharacteristic, complemented
70C3×#939—34no—
71C3×#935—34no—
72C3×C4×#67—34no—
73C3×C4×#67—34no—
74C3×#926—34no—
75C2×C3×C4×Dic3—34no—
76C3×#898—34no—
77C3×#889—34no—
78C3×#886—34no—
79C3×#885—34no—
80C3×#879—34no—
81C3×#878—34no—
82C3×#872—34no—
83C3×C4×Dic6—34no—
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
87C33×D4—22no—
88C2×C33×C4—22no—
89C2×C33×C4—22no—
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C3×#638—22no—
96C3×#638—22no—
97C2×C3×C3⋊Dic3—22no—
98C2×C3×C3⋊Dic3—22no—
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C2×C3×C3⋊Dic3C2311yescharacteristic
105C2×C3×C3⋊Dic3C2311yescharacteristic
106C3×C4×C3⋊D3—22no—
107C3×#634—22no—
108C3×#529—91no—
109#5538—34no—
110C2×C32×D4—24no—
111C2×C32×D4C2×D314yes—
112C2×C32×D4C22×C311yescharacteristic
113C22×C32×C4—24no—
114C22×C32×C4—24no—
115C22×C32×C4C2×D314yes—
116C22×C32×C4C2×D314yes—
117C22×C32×C4C22×C311yescharacteristic
118C22×C32×C4C22×C311yescharacteristic
119C2×#638C22×C311yescharacteristic
120C2×#638C22×C311yescharacteristic
121C22×C3⋊Dic3C22×C311yescharacteristic
122C22×C3⋊Dic3C22×C311yescharacteristic
123C2×C4×C3⋊D3C22×C311yescharacteristic
124C2×#634C22×C311yescharacteristic
125C2×C3×#67—34no—
126C2×C3×#67—34no—
127C22×C3×Dic3—34no—
128C22×C3×Dic3—34no—
129C2×C3×C4×D3—34no—
130C2×C3×Dic6—34no—
131C32×C4⋊C4—24no—
132C32×C4⋊C4C2×D314yes—
133C32×C4⋊C4C22×C311yescharacteristic
134C32×C22⋊C4—24no—
135C32×C22⋊C4—24no—
136C32×C22⋊C4C2×D314yes—
137C32×C22⋊C4C2×D314yes—
138C32×C22⋊C4C22×C311yescharacteristic
139C32×C22⋊C4C22×C311yescharacteristic
140C32×C42—24no—
141C32×C42C2×D314yes—
142C32×C42C22×C311yescharacteristic
143#3757C22×C311yescharacteristic
144#3757C22×C311yescharacteristic
145#3757C22×C311yescharacteristic
146#3757C22×C311yescharacteristic
147#3752C22×C311yescharacteristic
148#3752C22×C311yescharacteristic
149#3752C22×C311yescharacteristic
150#3752C22×C311yescharacteristic
151C4⋊(C3⋊Dic3)C22×C311yescharacteristic
152C4⋊(C3⋊Dic3)C22×C311yescharacteristic
153C4⋊(C3⋊Dic3)C22×C311yescharacteristic
154#3750C22×C311yescharacteristic
155#3750C22×C311yescharacteristic
156#3750C22×C311yescharacteristic
157#3750C22×C311yescharacteristic
158#3750C22×C311yescharacteristic
159#3750C22×C311yescharacteristic
160C4×C3⋊Dic3C22×C311yescharacteristic
161C4×C3⋊Dic3C22×C311yescharacteristic
162C4×C3⋊Dic3C22×C311yescharacteristic
163C4×C3⋊Dic3C22×C311yescharacteristic
164C4×C3⋊Dic3C22×C311yescharacteristic
165C3×#217—34no—
166C3×#217—34no—
167C3×#217—34no—
168C3×#217—34no—
169C3×(C2×D3)⋊C4—34no—
170C3×(C2×D3)⋊C4—34no—
171C3×(C2×D3)⋊C4—34no—
172C3×(C2×D3)⋊C4—34no—
173C3×C4⋊Dic3—34no—
174C3×C4⋊Dic3—34no—
175C3×C4⋊Dic3—34no—
176C3×Dic3⋊C4—34no—
177C3×Dic3⋊C4—34no—
178C3×Dic3⋊C4—34no—
179C3×Dic3⋊C4—34no—
180C3×Dic3⋊C4—34no—
181C3×Dic3⋊C4—34no—
182C3×C4×Dic3—34no—
183C3×C4×Dic3—34no—
184C3×C4×Dic3—34no—
185C3×C4×Dic3—34no—
186C3×C4×Dic3—34no—
187C22×C33—21no—
188C22×C33—21no—
189C22×C33—21no—
190C22×C33—21no—
191C22×C33—21no—
192C22×C33#4112yes—
193C22×C33C2411yescharacteristic
194C2×C3×C3⋊D3—21no—
195C2×C3×C3⋊D3—21no—
196C2×C3×C3⋊D3—21no—
197C33×C4—21no—
198C33×C4—21no—
199C33×C4—21no—
200C33×C4—21no—
201C33×C4#4112yes—
202C3×C3⋊Dic3—21no—
203C3×C3⋊Dic3—21no—
204C3×C3⋊Dic3—21no—
205C3×C3⋊Dic3—21no—
206C3×C3⋊Dic3—21no—
207C3×C3⋊Dic3—21no—
208C3×C3⋊Dic3#4112yes—
209C3×#126—91no—
210C3×#126—91no—
211C3×#125—91no—
212C3×#124—91no—
213C3×#123—91no—
214C3×#123—91no—
215C3×C22⋊Q8—91no—
216C3×#121—91no—
217C3×C4×Q8—91no—
218C3×C4×D4—24no—
219C3×C4×D4—91no—
220C3×C4×D4—91no—
221C3×C4×D4C3×D314yescomplemented
222C3×C4×D4C3⋊D311yescharacteristic, complemented
223C3×#117—91no—
224C3×#117—91no—
225C2×C3×C42—91no—
226#939—34no—
227#935—34no—
228C4×#67—34no—
229C4×#67—34no—
230#926—34no—
231C2×C4×Dic3—34no—
232#898—34no—
233#889—34no—
234#886—34no—
235#885—34no—
236#879—34no—
237#878—34no—
238#872—34no—
239C4×Dic6—34no—
240C23×C32—24no—
241C23×C32—24no—
242C23×C32C22×D314yes—
243C23×C32C22×D314yes—
244C23×C32C23×C311yescharacteristic
245C23×C32C23×C311yescharacteristic
246C22×C3⋊D3C23×C311yescharacteristic
247C22×C3×D3—34no—
248C32×D4—216no—
249C32×D4—28no—
250C32×D4—22no—
251C2×C32×C4—22no—
252C2×C32×C4—22no—
253C2×C32×C4—24no—
254C2×C32×C4—24no—
255C2×C32×C4—24no—
256C2×C32×C4—24no—
257C2×C32×C4—24no—
258C2×C32×C4—28no—
259C2×C32×C4—28no—
260C2×C32×C4—48no—
261C2×C32×C4—48no—
262C2×C32×C4C22×D314yes—
263C2×C32×C4C22×D314yes—
264C2×C32×C4C22×D314yes—
265C2×C32×C4C22×D314yes—
266C2×C32×C4C22×D314yes—
267C2×C32×C4C23×C311yescharacteristic
268C2×C32×C4C23×C311yescharacteristic
269C2×C32×C4C23×C311yescharacteristic
270C2×C32×C4C23×C311yescharacteristic
271C2×C32×C4C23×C311yescharacteristic
272#638—22no—
273#638—22no—
274C2×C3⋊Dic3—22no—
275C2×C3⋊Dic3—22no—
276C2×C3⋊Dic3C23×C311yescharacteristic
277C2×C3⋊Dic3C23×C311yescharacteristic
278C2×C3⋊Dic3C23×C311yescharacteristic
279C2×C3⋊Dic3C23×C311yescharacteristic
280C2×C3⋊Dic3C23×C311yescharacteristic
281C2×C3⋊Dic3C23×C311yescharacteristic
282C2×C3⋊Dic3C23×C311yescharacteristic
283C4×C3⋊D3—22no—
284#634—22no—
285C3×#67—68no—
286C3×#67—68no—
287C2×C3×Dic3—34no—
288C2×C3×Dic3—34no—
289C2×C3×Dic3—34no—
290C2×C3×Dic3—34no—
291C2×C3×Dic3—34no—
292C2×C3×Dic3—34no—
293C2×C3×Dic3—34no—
294C2×C3×Dic3—68no—
295C2×C3×Dic3—68no—
296C3×C4×D3—68no—
297C3×Dic6—68no—
298#529—91noSylow
299C2×C33—22no—
300C2×C33—41no—
301C2×C33C2×#4111yescharacteristic
302C2×C33C2×#4111yescharacteristic
303C2×C33C2×#4111yescharacteristic
304C3×C3⋊D3—41no—
305C2×C3×Q8—91no—
306C2×C3×D4—24no—
307C2×C3×D4—91no—
308C2×C3×D4—91no—
309C2×C3×D4C2×C3×D314yes—
310C2×C3×D4C2×C3⋊D311yescharacteristic
311C22×C3×C4—24no—
312C22×C3×C4—24no—
313C22×C3×C4—91no—
314C22×C3×C4—91no—
315C22×C3×C4—91no—
316C22×C3×C4C2×C3×D314yes—
317C22×C3×C4C2×C3×D314yes—
318C22×C3×C4C2×C3⋊D311yescharacteristic
319C22×C3×C4C2×C3⋊D311yescharacteristic
320C2×#67—34no—
321C2×#67—34no—
322C22×Dic3—34no—
323C22×Dic3—34no—
324C2×C4×D3—34no—
325C2×Dic6—34no—
326C3×C4⋊C4—24no—
327C3×C4⋊C4—91no—
328C3×C4⋊C4—91no—
329C3×C4⋊C4—91no—
330C3×C4⋊C4—91no—
331C3×C4⋊C4—91no—
332C3×C4⋊C4—91no—
333C3×C4⋊C4—91no—
334C3×C4⋊C4—91no—
335C3×C4⋊C4—91no—
336C3×C4⋊C4C2×C3×D314yes—
337C3×C4⋊C4C2×C3⋊D311yescharacteristic
338C3×C22⋊C4—24no—
339C3×C22⋊C4—24no—
340C3×C22⋊C4—91no—
341C3×C22⋊C4—91no—
342C3×C22⋊C4—91no—
343C3×C22⋊C4—91no—
344C3×C22⋊C4—91no—
345C3×C22⋊C4—91no—
346C3×C22⋊C4—91no—
347C3×C22⋊C4—91no—
348C3×C22⋊C4C2×C3×D314yes—
349C3×C22⋊C4C2×C3×D314yes—
350C3×C22⋊C4C2×C3⋊D311yescharacteristic
351C3×C22⋊C4C2×C3⋊D311yescharacteristic
352C3×C42—24no—
353C3×C42—91no—
354C3×C42—91no—
355C3×C42—91no—
356C3×C42—91no—
357C3×C42—91no—
358C3×C42C2×C3×D314yes—
359C3×C42C2×C3⋊D311yescharacteristic
360#217—34no—
361#217—34no—
362#217—34no—
363#217—34no—
364(C2×D3)⋊C4—34no—
365(C2×D3)⋊C4—34no—
366(C2×D3)⋊C4—34no—
367(C2×D3)⋊C4—34no—
368C4⋊Dic3—34no—
369C4⋊Dic3—34no—
370C4⋊Dic3—34no—
371Dic3⋊C4—34no—
372Dic3⋊C4—34no—
373Dic3⋊C4—34no—
374Dic3⋊C4—34no—
375Dic3⋊C4—34no—
376Dic3⋊C4—34no—
377C4×Dic3—34no—
378C4×Dic3—34no—
379C4×Dic3—34no—
380C4×Dic3—34no—
381C4×Dic3—34no—
382C22×C32—21no—
383C22×C32—21no—
384C22×C32—28no—
385C22×C32—24no—
386C22×C32—21no—
387C22×C32—21no—
388C22×C32—21no—
389C22×C32—24no—
390C22×C32—28no—
391C22×C32—24no—
392C22×C32—24no—
393C22×C32—24no—
394C22×C32—24no—
395C22×C32—44no—
396C22×C32—44no—
397C22×C32—44no—
398C22×C32—44no—
399C22×C32#23518yes—
400C22×C32C3×#4112yes—
401C22×C32C23×D314yes—
402C22×C32C24×C311yescharacteristic
403C2×C3⋊D3—21no—
404C2×C3⋊D3—21no—
405C2×C3⋊D3—21no—
406C2×C3×D3—64no—
407C2×C3×D3—64no—
408C2×C3×D3—64no—
409C32×C4—28no—
410C32×C4—24no—
411C32×C4—21no—
412C32×C4—21no—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4—28no—
416C32×C4—24no—
417C32×C4—24no—
418C32×C4—24no—
419C32×C4—44no—
420C32×C4—44no—
421C32×C4—44no—
422C32×C4#23718yes—
423C32×C4C3×#4112yes—
424C3⋊Dic3—21no—
425C3⋊Dic3—21no—
426C3⋊Dic3—21no—
427C3⋊Dic3—21no—
428C3⋊Dic3—21no—
429C3⋊Dic3—21no—
430C3⋊Dic3C3×#4112yes—
431C3×Dic3—38no—
432C3×Dic3—64no—
433C3×Dic3—64no—
434C3×Dic3—64no—
435C3×Dic3—64no—
436C3×Dic3—64no—
437C3×Dic3—64no—
438#126—91no—
439#126—91no—
440#125—91no—
441#124—91no—
442#123—91no—
443#123—91no—
444C22⋊Q8—91no—
445#121—91no—
446C4×Q8—91no—
447C4×D4—91no—
448C4×D4—91no—
449C4×D4C3×C3⋊D311yescharacteristic, complemented
450#117—91no—
451#117—91no—
452C2×C42—91no—
453C33#52911yescharacteristic, complemented, Sylow
454C23×C3—24no—
455C23×C3—24no—
456C23×C3—91no—
457C23×C3C22×C3×D314yes—
458C23×C3C22×C3×D314yes—
459C23×C3C22×C3⋊D311yescharacteristic
460C23×C3C22×C3⋊D311yescharacteristic
461C22×D3—34no—
462C3×Q8—182no—
463C3×D4—216no—
464C3×D4—28no—
465C3×D4—22no—
466C3×D4—182no—
467C3×D4—182no—
468C2×C3×C4—28no—
469C2×C3×C4—28no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—24no—
473C2×C3×C4—24no—
474C2×C3×C4—24no—
475C2×C3×C4—24no—
476C2×C3×C4—24no—
477C2×C3×C4—48no—
478C2×C3×C4—48no—
479C2×C3×C4—91no—
480C2×C3×C4—91no—
481C2×C3×C4—91no—
482C2×C3×C4—91no—
483C2×C3×C4—91no—
484C2×C3×C4—91no—
485C2×C3×C4—91no—
486C2×C3×C4—182no—
487C2×C3×C4—182no—
488C2×C3×C4—182no—
489C2×C3×C4C22×C3×D314yes—
490C2×C3×C4C22×C3×D314yes—
491C2×C3×C4C22×C3×D314yes—
492C2×C3×C4C22×C3×D314yes—
493C2×C3×C4C22×C3×D314yes—
494C2×C3×C4C22×C3⋊D311yescharacteristic
495C2×C3×C4C22×C3⋊D311yescharacteristic
496C2×C3×C4C22×C3⋊D311yescharacteristic
497C2×C3×C4C22×C3⋊D311yescharacteristic
498C2×C3×C4C22×C3⋊D311yescharacteristic
499#67—68no—
500#67—68no—
501C2×Dic3—34no—
502C2×Dic3—34no—
503C2×Dic3—34no—
504C2×Dic3—34no—
505C2×Dic3—34no—
506C2×Dic3—34no—
507C2×Dic3—34no—
508C2×Dic3—68no—
509C2×Dic3—68no—
510C4×D3—68no—
511Dic6—68no—
512C2×C32—22no—
513C2×C32—24no—
514C2×C32—24no—
515C2×C32—24no—
516C2×C32—28no—
517C2×C32—48no—
518C2×C32—48no—
519C2×C32—44no—
520C2×C32—41no—
521C2×C32C2×#23514yes—
522C2×C32C2×#23714yes—
523C2×C32D3×#4114yes—
524C2×C32C2×C3×#4111yescharacteristic
525C2×C32C2×C3×#4111yescharacteristic
526C2×C32C2×C3×#4111yescharacteristic
527C3⋊D3—41no—
528C3×D3—124no—
529C2×Q8—91no—
530C2×D4—91no—
531C2×D4—91no—
532C2×D4C2×C3×C3⋊D311yescharacteristic
533C22×C4—91no—
534C22×C4—91no—
535C22×C4—91no—
536C22×C4C2×C3×C3⋊D311yescharacteristic
537C22×C4C2×C3×C3⋊D311yescharacteristic
538C4⋊C4—91no—
539C4⋊C4—91no—
540C4⋊C4—91no—
541C4⋊C4—91no—
542C4⋊C4—91no—
543C4⋊C4—91no—
544C4⋊C4—91no—
545C4⋊C4—91no—
546C4⋊C4—91no—
547C4⋊C4C2×C3×C3⋊D311yescharacteristic
548C22⋊C4—91no—
549C22⋊C4—91no—
550C22⋊C4—91no—
551C22⋊C4—91no—
552C22⋊C4—91no—
553C22⋊C4—91no—
554C22⋊C4—91no—
555C22⋊C4—91no—
556C22⋊C4C2×C3×C3⋊D311yescharacteristic
557C22⋊C4C2×C3×C3⋊D311yescharacteristic
558C42—91no—
559C42—91no—
560C42—91no—
561C42—91no—
562C42—91no—
563C42C2×C3×C3⋊D311yescharacteristic
564C22×C3—24no—
565C22×C3—24no—
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—28no—
569C22×C3—24no—
570C22×C3—24no—
571C22×C3—24no—
572C22×C3—21no—
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—24no—
576C22×C3—28no—
577C22×C3—44no—
578C22×C3—44no—
579C22×C3—44no—
580C22×C3—44no—
581C22×C3—181no—
582C22×C3—181no—
583C22×C3—181no—
584C22×C3C3×#23518yes—
585C22×C3#382812yes—
586C22×C3C23×C3×D314yes—
587C22×C3C23×C3⋊D311yescharacteristic
588C2×D3—64no—
589C2×D3—64no—
590C2×D3—64no—
591C3×C4—28no—
592C3×C4—24no—
593C3×C4—24no—
594C3×C4—24no—
595C3×C4—24no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—28no—
601C3×C4—44no—
602C3×C4—44no—
603C3×C4—44no—
604C3×C4—92no—
605C3×C4—181no—
606C3×C4—181no—
607C3×C4—181no—
608C3×C4—181no—
609C3×C4—181no—
610C3×C4—181no—
611C3×C4C3×#23718yes—
612C3×C4#383012yes—
613Dic3—38no—
614Dic3—64no—
615Dic3—64no—
616Dic3—64no—
617Dic3—64no—
618Dic3—64no—
619Dic3—64no—
620C32—24no—
621C32#553814yescomplemented
622C32C3×#52911yescharacteristic, complemented
623C23—91no—
624C23C22×C3×C3⋊D311yescharacteristic
625C23C22×C3×C3⋊D311yescharacteristic
626Q8—182no—
627D4—22no—
628D4—182no—
629D4—182no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—91no—
633C2×C4—91no—
634C2×C4—91no—
635C2×C4—91no—
636C2×C4—91no—
637C2×C4—91no—
638C2×C4—91no—
639C2×C4—182no—
640C2×C4—182no—
641C2×C4—182no—
642C2×C4C22×C3×C3⋊D311yescharacteristic
643C2×C4C22×C3×C3⋊D311yescharacteristic
644C2×C4C22×C3×C3⋊D311yescharacteristic
645C2×C4C22×C3×C3⋊D311yescharacteristic
646C2×C4C22×C3×C3⋊D311yescharacteristic
647C2×C3—28no—
648C2×C3—22no—
649C2×C3—24no—
650C2×C3—24no—
651C2×C3—24no—
652C2×C3—48no—
653C2×C3—48no—
654C2×C3—44no—
655C2×C3—41no—
656C2×C3—361no—
657C2×C3C2×C3×#23514yes—
658C2×C3C2×C3×#23714yes—
659C2×C3C3×D3×#4114yes—
660C2×C3C2×#382811yescharacteristic
661C2×C3C2×#383011yescharacteristic
662C2×C3#41×C3⋊D311yescharacteristic
663D3—124no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—181no—
670C22—181no—
671C22—181no—
672C22C3×#382812yes—
673C22C23×C3×C3⋊D311yescharacteristic
674C4—21no—
675C4—21no—
676C4—21no—
677C4—21no—
678C4—92no—
679C4—181no—
680C4—181no—
681C4—181no—
682C4—181no—
683C4—181no—
684C4—181no—
685C4C3×#383012yes—
686C3—24no—
687C3C3×#553814yescomplemented
688C3#1059600911yescharacteristic, direct product factor
689C2—22no—
690C2—41no—
691C2—361no—
692C2C2×C3×#382811yescharacteristic
693C2C2×C3×#383011yescharacteristic
694C2C3×#41×C3⋊D311yescharacteristic
subgroupG/H
centerC2×C3×C4C22×C3⋊D3
commutator, cosocleC22×C32C24×C3
FrattiniC22C23×C3×C3⋊D3
FittingC33×C4×D4C2
socleC22×C33C24
prime radicalC3×#64148C2
hypercenterC3×C4×D4C3⋊D3
hypocenterC32C3×#529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C33×C4×D4C2semidirect
3. C3×#64144C2semidirect
4. C3×C4×#638C2semidirect
5. C3×C4×#638C2semidirect
6. C3×#64135C2semidirect
7. C2×C3×C4×C3⋊Dic3C2semidirect
8. C3×#64107C2semidirect
9. C3×#64098C2semidirect
10. C3×#64095C2semidirect
11. C3×#64094C2semidirect
12. C3×#64088C2semidirect
13. C3×#64087C2semidirect
14. C3×#64081C2semidirect
15. C3×C4×#634C2semidirect
16. #10596009C3direct (N × H)
54. C32×C4×D4D3semidirect
55. C32×C4×D4C2×C3semidirect
57. #64144C2×C3semidirect
58. C4×#638C2×C3semidirect
59. C4×#638C2×C3semidirect
60. #64135C2×C3semidirect
61. C2×C4×C3⋊Dic3C2×C3semidirect
62. #64107C2×C3semidirect
63. #64098C2×C3semidirect
64. #64095C2×C3semidirect
65. #64094C2×C3semidirect
66. #64088C2×C3semidirect
67. #64087C2×C3semidirect
68. #64081C2×C3semidirect
69. C4×#634C2×C3semidirect
221. C3×C4×D4C3×D3semidirect
222. C3×C4×D4C3⋊D3semidirect
449. C4×D4C3×C3⋊D3semidirect
453. C33#529semidirect
621. C32#5538semidirect
622. C32C3×#529semidirect
687. C3C3×#5538semidirect
688. C3#10596009direct (N × H)

Maximal subgroups

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

subgroupindex
C33×C4×D42
C3×#641482
C3×#641442
C3×C4×#6382
C3×#641352
C2×C3×C4×C3⋊Dic32
C3×#641072
C3×#640982
C3×#640952
C3×#640942
C3×#640882
C3×#640872
C3×#640812
C3×C4×#6342
#105960093
C3×#55383