Finite Group Databasebeta

← C4×C3⋊D3×#67 #13177291

Subgroups — C4×C3⋊D3×#67 #13177291

Order 1728.

2932 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×#67C211yesmaximal, characteristic
3C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
4C4×#6312C211yesmaximal, characteristic, complemented
5C32×C4×#67C211yesmaximal, characteristic, complemented
6#11723622C211yesmaximal, characteristic, complemented
7C3⋊D3×#217C211yesmaximal, characteristic, complemented
8#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
9C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11723512C211yesmaximal, characteristic, complemented
11C4×#6292C211yesmaximal, characteristic, complemented
12#11723507C211yesmaximal, characteristic, complemented
13C4×#6290C211yesmaximal, characteristic, complemented
14C3⋊D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
15C4×Dic3×C3⋊D3C211yesmaximal, characteristic, complemented
16C4×D4×C3⋊D3—31nomaximal
17C4×D3×#67—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
23C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
24C2×C3×C4×C3⋊D3—24no—
25C2×C3×C4×C3⋊D3C2211yescharacteristic
26C2×C3×C4×C3⋊D3C2211yescharacteristic
27C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
28C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
29C2×C32×#67C2211yescharacteristic
30C2×C32×C4×D3C2211yescharacteristic, complemented
31C3⋊D3×#67C418yesdirect product factor
32C2×#6292C2211yescharacteristic
33C2×#6290C2211yescharacteristic
34C2×#6289C2211yescharacteristic, complemented
35C2×Dic3×C3⋊D3C2211yescharacteristic
36C2×Dic3×C3⋊D3C2211yescharacteristic
37C2×Dic3×C3⋊D3C2211yescharacteristic
38C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
39C4×D3×C3⋊D3—24no—
40#88864C2211yescharacteristic, complemented
41#88859C2211yescharacteristic, complemented
42#88857C2211yescharacteristic, complemented
43C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44C32×#217C2211yescharacteristic, complemented
45C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C32×Dic3⋊C4C2211yescharacteristic, complemented
47C32×C4×Dic3C2211yescharacteristic, complemented
48#88806C2211yescharacteristic, complemented
49Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
50#88804C2211yescharacteristic, complemented
51#88803C2211yescharacteristic, complemented
52#88803C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55Dic3×C3⋊Dic3C2211yescharacteristic, complemented
56C2×D4×C3⋊D3—31no—
57C22×C4×C3⋊D3—31no—
58C22×C4×C3⋊D3D311yescharacteristic, complemented
59C22×C3×C4×D3—34no—
60C2×D3×#67—34no—
61C2×C4×D32—34no—
62C32×C4×D4—31no—
63D4×C3⋊Dic3—31no—
64C4×#638—31no—
65C4×#638—31no—
66C4×#638—34no—
67C4×#638—64no—
68#64102—31no—
69C4⋊C4×C3⋊D3—31no—
70#64090—31no—
71#64090—31no—
72C22⋊C4×C3⋊D3—31no—
73C22⋊C4×C3⋊D3—31no—
74C4×C4⋊(C3⋊D3)—31no—
75C42×C3⋊D3—31no—
76C3×C4×#67D314yescomplemented
77Dic3×#67—34no—
78D3×#217—34no—
79#63952—34no—
80D3×(C2×D3)⋊C4—34no—
81#63904—34no—
82C4×#626—34no—
83C4×#625—34no—
84#63879—34no—
85D3×Dic3⋊C4—34no—
86C4×D3×Dic3—34no—
87C23×C33C2311yescharacteristic
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C3×C3⋊D3—22no—
90C22×C3×C3⋊D3—22no—
91C22×C3×C3⋊D3C2×C414yescomplemented
92C22×C3×C3⋊D3C2311yescharacteristic
93C22×C3×C3⋊D3C2311yescharacteristic
94C22×C32×D3C2311yescharacteristic
95C2×D3×C3⋊D3—22no—
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3C2×C414yescomplemented
98C2×C33×C4—22no—
99C2×C33×C4C2311yescharacteristic
100C2×C33×C4C2311yescharacteristic
101#6312C2×C414yescomplemented
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C4×C3⋊(C3⋊D3)—22no—
106C2×C3×C3⋊Dic3—22no—
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C3×C4×C3⋊D3—22no—
110C3×C4×C3⋊D3—22no—
111C3×C4×C3⋊D3—22no—
112C3×C4×C3⋊D3D414yescomplemented
113C32×#67C2×C414yescomplemented
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C32×C4×D3—22no—
118#6292C2×C414yescomplemented
119#6290C2×C414yescomplemented
120#6289—22no—
121Dic3×C3⋊D3—22no—
122Dic3×C3⋊D3—22no—
123Dic3×C3⋊D3C2×C414yescomplemented
124D3×C3⋊Dic3—22no—
125C2×C4×#67—91no—
126C4×D3×D4—94no—
127C23×C3⋊D3—31no—
128C23×C3⋊D3C2×D311yescharacteristic
129C23×C3×D3—34no—
130C22×D32—34no—
131C2×C32×D4—31no—
132C22×C32×C4—24no—
133C22×C32×C4—31no—
134C22×C32×C4C2×D314yescomplemented
135C22×C32×C4C2×D311yescharacteristic, complemented
136C2×#638—31no—
137C2×#638—34no—
138C2×#638—31no—
139C2×#638—64no—
140C22×C3⋊Dic3—31no—
141C22×C3⋊Dic3C2×D311yescharacteristic, complemented
142D4×C3⋊D3—38no—
143C2×C4⋊(C3⋊D3)—31no—
144C2×C4×C3⋊D3—24no—
145C2×C4×C3⋊D3—31no—
146C2×C4×C3⋊D3—31no—
147C2×C4×C3⋊D3—31no—
148C2×C4×C3⋊D3—31no—
149C2×C4×C3⋊D3—34no—
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3—64no—
152C2×C4×C3⋊D3—64no—
153C2×C4×C3⋊D3C2×D311yescharacteristic
154C2×C4×C3⋊D3C2×D311yescharacteristic
155C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
156C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
157C2×C3×#67C2×D314yes—
158C22×C3×Dic3—34no—
159C2×C3×C4×D3—34no—
160C2×C3×C4×D3—34no—
161C2×C3×C4×D3—34no—
162C2×C3×C4×D3—34no—
163C2×C3×C4×D3—616no—
164C2×C3×C4×D3C2×D314yescomplemented
165D3×#67—332no—
166C2×#626—34no—
167C2×#625—34no—
168C2×#624—34no—
169C2×D3×Dic3—34no—
170C2×D3×Dic3—34no—
171C2×D3×Dic3—34no—
172C2×D3×Dic3—34no—
173C4×D32—616no—
174C32×C4⋊C4—31no—
175C32×C22⋊C4—31no—
176C32×C22⋊C4—31no—
177C32×C42—31no—
178#3757—31no—
179#3757—34no—
180#3757—31no—
181#3757—64no—
182#3752—31no—
183#3752—31no—
184#3752—31no—
185#3752—34no—
186#3752—31no—
187#3752—64no—
188C4⋊(C3⋊Dic3)—31no—
189#3750—31no—
190#3750—34no—
191#3750—31no—
192#3750—64no—
193C4×C3⋊Dic3—31no—
194C4×C3⋊Dic3—34no—
195C4×C3⋊Dic3—31no—
196C4×C3⋊Dic3—31no—
197C4×C3⋊Dic3—64no—
198C3×#217C2×D314yescomplemented
199C3×(C2×D3)⋊C4C2×D314yescomplemented
200C3×Dic3⋊C4C2×D314yescomplemented
201C3×C4×Dic3C2×D314yescomplemented
202#3724—34no—
203Dic3⋊Dic3—34no—
204#3722—34no—
205(C2×D3)⋊Dic3—34no—
206(C2×D3)⋊Dic3—34no—
207(C2×D3)⋊Dic3—34no—
208Dic32—34no—
209Dic32—34no—
210C22×C33—21no—
211C22×C33—21no—
212C22×C33C22×C412yescomplemented
213C22×C33C2411yescharacteristic
214C2×C3⋊(C3⋊D3)—21no—
215C2×C3⋊(C3⋊D3)—21no—
216C2×C3⋊(C3⋊D3)C22×C412yescomplemented
217C2×C3×C3⋊D3—21no—
218C2×C3×C3⋊D3—21no—
219C2×C3×C3⋊D3—28no—
220C2×C3×C3⋊D3C22×C412yes—
221C2×C3×C3⋊D3C22×C412yescomplemented
222C2×C3×C3⋊D3C2×D412yes—
223C2×C3×C3⋊D3#4112yes—
224C2×C32×D3—21no—
225C2×C32×D3—21no—
226C2×C32×D3C22×C412yescomplemented
227D3×C3⋊D3—28no—
228C33×C4—21no—
229C33×C4C2×D412yescomplemented
230C3⋊(C3⋊Dic3)—21no—
231C3⋊(C3⋊Dic3)—21no—
232C3⋊(C3⋊Dic3)C22×C412yescomplemented
233C3×C3⋊Dic3—21no—
234C3×C3⋊Dic3C2×D412yescomplemented
235C32×Dic3—21no—
236C32×Dic3—21no—
237C32×Dic3C22×C412yescomplemented
238C23×C3×C4—91no—
239C22×#67—91no—
240C2×D3×D4—94no—
241C22×C4×D3—34no—
242C22×C4×D3—94no—
243C22×C4×D3—91no—
244C3×C4×D4—34no—
245C2×#217—91no—
246D4×Dic3—94no—
247C4×#67—94no—
248C4×#67—94no—
249C4×#67—91no—
250C4×#67—91no—
251C4×#67—91no—
252C4×#67—91no—
253C4×#67—91no—
254C4×#67—91no—
255C4×#67—91no—
256C4×#67—184no—
257C4×#67C3⋊D311yescharacteristic, direct product factor
258C2×(C2×D3)⋊C4—91no—
259C2×Dic3⋊C4—91no—
260C2×C4×Dic3—91no—
261#893—94no—
262D3×C4⋊C4—94no—
263#67⋊C4—94no—
264#67⋊C4—94no—
265D3×C22⋊C4—94no—
266D3×C22⋊C4—94no—
267C4×D12—94no—
268C42×D3—94no—
269C23×C32—24no—
270C23×C32—31no—
271C23×C32C22×D314yes—
272C23×C32C22×D311yescharacteristic
273C22×C3⋊D3—22no—
274C22×C3⋊D3—22no—
275C22×C3⋊D3—31no—
276C22×C3⋊D3—34no—
277C22×C3⋊D3—34no—
278C22×C3⋊D3—64no—
279C22×C3⋊D3—62no—
280C22×C3⋊D3—62no—
281C22×C3⋊D3C4×D314yescomplemented
282C22×C3⋊D3C22×D311yescharacteristic
283C22×C3⋊D3C22×D311yescharacteristic
284C22×C3×D3—34no—
285C22×C3×D3—316no—
286C22×C3×D3—34no—
287C22×C3×D3—68no—
288C22×C3×D3—68no—
289C22×C3×D3C22×D314yes—
290C2×D32—316no—
291C2×D32—68no—
292C2×D32—68no—
293C32×D4—34no—
294C2×C32×C4—22no—
295C2×C32×C4—24no—
296C2×C32×C4—24no—
297C2×C32×C4—28no—
298C2×C32×C4—31no—
299C2×C32×C4—31no—
300C2×C32×C4—31no—
301C2×C32×C4—48no—
302C2×C32×C4—62no—
303C2×C32×C4C22×D314yes—
304C2×C32×C4C22×D314yes—
305C2×C32×C4C22×D311yescharacteristic
306C2×C32×C4C22×D311yescharacteristic
307#638—34no—
308#638—34no—
309#638—316no—
310#638—616no—
311C2×C3⋊Dic3—22no—
312C2×C3⋊Dic3—31no—
313C2×C3⋊Dic3—31no—
314C2×C3⋊Dic3—31no—
315C2×C3⋊Dic3—34no—
316C2×C3⋊Dic3—34no—
317C2×C3⋊Dic3—34no—
318C2×C3⋊Dic3—64no—
319C2×C3⋊Dic3—64no—
320C2×C3⋊Dic3—64no—
321C2×C3⋊Dic3—62no—
322C2×C3⋊Dic3C22×D311yescharacteristic
323C2×C3⋊Dic3C22×D311yescharacteristic
324C4⋊(C3⋊D3)—34no—
325C4×C3⋊D3—22no—
326C4×C3⋊D3—22no—
327C4×C3⋊D3—22no—
328C4×C3⋊D3—34no—
329C4×C3⋊D3—62no—
330C4×C3⋊D3—62no—
331C4×C3⋊D3—62no—
332C4×C3⋊D3—62no—
333C4×C3⋊D3—68no—
334C4×C3⋊D3—128no—
335C4×C3⋊D3#6714yesdirect product factor
336C3×#67C4×D3116yescomplemented
337C2×C3×Dic3—34no—
338C2×C3×Dic3—34no—
339C2×C3×Dic3—68no—
340C2×C3×Dic3C22×D314yes—
341C2×C3×Dic3C22×D314yes—
342C2×C3×Dic3C22×D314yes—
343C3×C4×D3—28no—
344C3×C4×D3—316no—
345C3×C4×D3—68no—
346C3×C4×D3—68no—
347C3×C4×D3—68no—
348#626—316no—
349#625—316no—
350#624—68no—
351D3×Dic3—316no—
352D3×Dic3—68no—
353D3×Dic3—68no—
354D3×Dic3—68no—
355C2×C4×D4—271noSylow
356C2×C33—22no—
357C2×C33C23×C411yescharacteristic
358C2×C33C22×D411yescharacteristic
359C2×C33C2×#4111yescharacteristic
360C3⋊(C3⋊D3)—22no—
361C3×C3⋊D3—22no—
362C3×C3⋊D3C4×D414yescomplemented
363C32×D3—22no—
364C24×C3—91no—
365C23×D3—34no—
366C23×D3—94no—
367C23×D3—91no—
368C2×C3×D4—34no—
369C22×C3×C4—24no—
370C22×C3×C4—34no—
371C22×C3×C4—91no—
372C22×C3×C4—91no—
373C22×C3×C4—91no—
374C22×C3×C4—91no—
375C22×C3×C4—91no—
376C22×C3×C4—184no—
377C22×C3×C4D3214yescomplemented
378C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
379C2×#67—94no—
380C2×#67—94no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—98no—
384C2×#67—91no—
385C2×#67—184no—
386C2×#67C2×C3⋊D311yescharacteristic
387C22×Dic3—34no—
388C22×Dic3—94no—
389C22×Dic3—91no—
390C22×Dic3—91no—
391C22×Dic3—91no—
392D3×D4—932no—
393C2×D12—94no—
394C2×C4×D3—34no—
395C2×C4×D3—34no—
396C2×C4×D3—34no—
397C2×C4×D3—34no—
398C2×C4×D3—616no—
399C2×C4×D3—94no—
400C2×C4×D3—94no—
401C2×C4×D3—94no—
402C2×C4×D3—94no—
403C2×C4×D3—91no—
404C2×C4×D3—94no—
405C2×C4×D3—91no—
406C2×C4×D3—91no—
407C2×C4×D3—184no—
408C2×C4×D3—184no—
409C2×C4×D3—1816no—
410C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
411C3×C4⋊C4—34no—
412C3×C22⋊C4—34no—
413C3×C22⋊C4—34no—
414C3×C42—34no—
415#217—94no—
416#217—94no—
417#217—91no—
418#217—91no—
419#217—91no—
420#217—184no—
421#217C2×C3⋊D311yescharacteristic, complemented
422(C2×D3)⋊C4—94no—
423(C2×D3)⋊C4—94no—
424(C2×D3)⋊C4—94no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—94no—
427(C2×D3)⋊C4—91no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—184no—
430(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
431C4⋊Dic3—94no—
432Dic3⋊C4—94no—
433Dic3⋊C4—94no—
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—184no—
438Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
439C4×Dic3—94no—
440C4×Dic3—94no—
441C4×Dic3—94no—
442C4×Dic3—91no—
443C4×Dic3—91no—
444C4×Dic3—91no—
445C4×Dic3—184no—
446C4×Dic3C2×C3⋊D311yescharacteristic, complemented
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—24no—
450C22×C32—28no—
451C22×C32—24no—
452C22×C32—24no—
453C22×C32—32no—
454C22×C32—44no—
455C22×C32—44no—
456C22×C32—61no—
457C22×C32—61no—
458C22×C32C2×C4×D318yescomplemented
459C22×C32C2×C4×D312yescomplemented
460C22×C32C23×D314yes—
461C22×C32C23×D311yescharacteristic
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—28no—
465C2×C3⋊D3—32no—
466C2×C3⋊D3—38no—
467C2×C3⋊D3—68no—
468C2×C3⋊D3—61no—
469C2×C3⋊D3—61no—
470C2×C3⋊D3—68no—
471C2×C3⋊D3—64no—
472C2×C3⋊D3—64no—
473C2×C3⋊D3—124no—
474C2×C3⋊D3—124no—
475C2×C3⋊D3C2×C4×D312yes—
476C2×C3⋊D3C2×C4×D312yescomplemented
477C2×C3⋊D3#23512yes—
478C2×C3⋊D3C2×#6712yes—
479C2×C3×D3—24no—
480C2×C3×D3—24no—
481C2×C3×D3—38no—
482C2×C3×D3—38no—
483C2×C3×D3—38no—
484C2×C3×D3—38no—
485C2×C3×D3—632no—
486C2×C3×D3—64no—
487C2×C3×D3—64no—
488C2×C3×D3C2×C4×D318yescomplemented
489D32—632no—
490C32×C4—21no—
491C32×C4—28no—
492C32×C4—24no—
493C32×C4—32no—
494C32×C4—44no—
495C32×C4—61no—
496C32×C4—61no—
497C32×C4D3×D418yescomplemented
498C32×C4C2×#6712yescomplemented
499C3⋊Dic3—21no—
500C3⋊Dic3—32no—
501C3⋊Dic3—38no—
502C3⋊Dic3—68no—
503C3⋊Dic3—61no—
504C3⋊Dic3—61no—
505C3⋊Dic3—64no—
506C3⋊Dic3—64no—
507C3⋊Dic3—124no—
508C3⋊Dic3—124no—
509C3⋊Dic3C2×#6712yescomplemented
510C3×Dic3—24no—
511C3×Dic3—24no—
512C3×Dic3—38no—
513C3×Dic3—64no—
514C3×Dic3C2×C4×D318yescomplemented
515C22×D4—271no—
516C23×C4—91no—
517C23×C4—271no—
518C4×D4—31no—
519C4×D4—271no—
520C4×D4—271no—
521C4×D4—271no—
522C4×D4—271no—
523C4×D4—271no—
524C4×D4—271no—
525C4×D4—271no—
526C2×C4⋊C4—271no—
527C2×C22⋊C4—271no—
528C2×C22⋊C4—271no—
529C2×C42—271no—
530C33C2×C4×D411yescharacteristic, complemented, Sylow
531C23×C3—24no—
532C23×C3—34no—
533C23×C3—91no—
534C23×C3—91no—
535C23×C3—94no—
536C23×C3—182no—
537C23×C3—182no—
538C23×C3C2×D3214yes—
539C23×C3C22×C3⋊D311yescharacteristic
540C22×D3—34no—
541C22×D3—34no—
542C22×D3—316no—
543C22×D3—68no—
544C22×D3—68no—
545C22×D3—916no—
546C22×D3—94no—
547C22×D3—91no—
548C22×D3—94no—
549C22×D3—184no—
550C22×D3—182no—
551C22×D3—182no—
552C22×D3—188no—
553C22×D3—188no—
554C22×D3C22×C3⋊D311yescharacteristic
555C3×D4—316no—
556C2×C3×C4—28no—
557C2×C3×C4—22no—
558C2×C3×C4—24no—
559C2×C3×C4—24no—
560C2×C3×C4—34no—
561C2×C3×C4—34no—
562C2×C3×C4—34no—
563C2×C3×C4—48no—
564C2×C3×C4—68no—
565C2×C3×C4—91no—
566C2×C3×C4—94no—
567C2×C3×C4—91no—
568C2×C3×C4—182no—
569C2×C3×C4—182no—
570C2×C3×C4—182no—
571C2×C3×C4—182no—
572C2×C3×C4C2×D3214yes—
573C2×C3×C4C2×D3214yes—
574C2×C3×C4C22×C3⋊D311yescharacteristic
575C2×C3×C4C22×C3⋊D311yescharacteristic
576#67—916no—
577#67—916no—
578#67—94no—
579#67—94no—
580#67—94no—
581#67—1816no—
582#67C4×C3⋊D314yesdirect product factor
583C2×Dic3—34no—
584C2×Dic3—34no—
585C2×Dic3—68no—
586C2×Dic3—94no—
587C2×Dic3—91no—
588C2×Dic3—94no—
589C2×Dic3—94no—
590C2×Dic3—94no—
591C2×Dic3—91no—
592C2×Dic3—91no—
593C2×Dic3—184no—
594C2×Dic3—184no—
595C2×Dic3—184no—
596C2×Dic3—182no—
597C2×Dic3—182no—
598C2×Dic3—188no—
599C2×Dic3C22×C3⋊D311yescharacteristic
600C2×Dic3C22×C3⋊D311yescharacteristic
601C2×Dic3C22×C3⋊D311yescharacteristic
602D12—916no—
603C4×D3—22no—
604C4×D3—316no—
605C4×D3—68no—
606C4×D3—68no—
607C4×D3—68no—
608C4×D3—916no—
609C4×D3—182no—
610C4×D3—188no—
611C4×D3—188no—
612C4×D3—188no—
613C4×D3—182no—
614C4×D3—188no—
615C4×D3—182no—
616C4×D3—368no—
617C2×C32—22no—
618C2×C32—24no—
619C2×C32—24no—
620C2×C32—24no—
621C2×C32—28no—
622C2×C32—48no—
623C2×C32—62no—
624C2×C32C22×C4×D314yes—
625C2×C32C22×C4×D311yescharacteristic
626C2×C32C2×#23511yescharacteristic
627C2×C32C2×D3×D414yes—
628C2×C32D3×#4114yes—
629C2×C32C22×#6711yescharacteristic
630C3⋊D3—22no—
631C3⋊D3—62no—
632C3⋊D3—68no—
633C3⋊D3—128no—
634C3⋊D3C4×#6714yesdirect product factor
635C3×D3—28no—
636C3×D3—316no—
637C3×D3—68no—
638C24—91no—
639C24—271no—
640C2×D4—31no—
641C2×D4—271no—
642C2×D4—278no—
643C2×D4—271no—
644C2×D4—271no—
645C22×C4—31no—
646C22×C4—91no—
647C22×C4—91no—
648C22×C4—91no—
649C22×C4—91no—
650C22×C4—91no—
651C22×C4—184no—
652C22×C4—271no—
653C22×C4—271no—
654C22×C4—271no—
655C22×C4—271no—
656C22×C4—271no—
657C22×C4—271no—
658C22×C4—544no—
659C22×C4D3×C3⋊D311yescharacteristic, complemented
660C4⋊C4—31no—
661C4⋊C4—271no—
662C4⋊C4—271no—
663C4⋊C4—271no—
664C22⋊C4—31no—
665C22⋊C4—31no—
666C22⋊C4—271no—
667C22⋊C4—271no—
668C22⋊C4—271no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C22⋊C4—271no—
672C42—31no—
673C42—271no—
674C42—271no—
675C42—271no—
676C22×C3—24no—
677C22×C3—24no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—24no—
681C22×C3—28no—
682C22×C3—38no—
683C22×C3—44no—
684C22×C3—44no—
685C22×C3—64no—
686C22×C3—64no—
687C22×C3—92no—
688C22×C3—92no—
689C22×C3—92no—
690C22×C3—92no—
691C22×C3—188no—
692C22×C3—181no—
693C22×C3—181no—
694C22×C3C4×D3218yescomplemented
695C22×C3C2×C4×C3⋊D312yescomplemented
696C22×C3C22×D3214yes—
697C22×C3C23×C3⋊D311yescharacteristic
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—38no—
701C2×D3—38no—
702C2×D3—38no—
703C2×D3—38no—
704C2×D3—632no—
705C2×D3—64no—
706C2×D3—64no—
707C2×D3—98no—
708C2×D3—92no—
709C2×D3—188no—
710C2×D3—188no—
711C2×D3—1832no—
712C2×D3—184no—
713C2×D3—184no—
714C2×D3—181no—
715C2×D3—181no—
716C2×D3—364no—
717C2×D3—364no—
718C2×D3C2×C4×C3⋊D312yescomplemented
719C3×C4—24no—
720C3×C4—21no—
721C3×C4—28no—
722C3×C4—38no—
723C3×C4—44no—
724C3×C4—64no—
725C3×C4—64no—
726C3×C4—92no—
727C3×C4—181no—
728C3×C4D3×#6718yescomplemented
729C3×C4D4×C3⋊D312yescomplemented
730Dic3—21no—
731Dic3—21no—
732Dic3—38no—
733Dic3—64no—
734Dic3—98no—
735Dic3—92no—
736Dic3—188no—
737Dic3—184no—
738Dic3—184no—
739Dic3—181no—
740Dic3—181no—
741Dic3—364no—
742Dic3—364no—
743Dic3C2×C4×C3⋊D312yescomplemented
744C32—24no—
745C32C4×D3×D414yescomplemented
746C32C2×C4×#6711yescharacteristic, complemented
747C23—31no—
748C23—91no—
749C23—91no—
750C23—94no—
751C23—182no—
752C23—182no—
753C23—274no—
754C23—271no—
755C23—542no—
756C23—542no—
757C23C2×D3×C3⋊D311yescharacteristic
758D4—34no—
759D4—274no—
760D4—274no—
761D4—274no—
762C2×C4—22no—
763C2×C4—31no—
764C2×C4—31no—
765C2×C4—31no—
766C2×C4—62no—
767C2×C4—91no—
768C2×C4—94no—
769C2×C4—91no—
770C2×C4—182no—
771C2×C4—182no—
772C2×C4—182no—
773C2×C4—182no—
774C2×C4—274no—
775C2×C4—271no—
776C2×C4—271no—
777C2×C4—271no—
778C2×C4—542no—
779C2×C4—542no—
780C2×C4—542no—
781C2×C4—542no—
782C2×C4—542no—
783C2×C4C2×D3×C3⋊D311yescharacteristic
784C2×C4C2×D3×C3⋊D311yescharacteristic
785C2×C3—22no—
786C2×C3—28no—
787C2×C3—24no—
788C2×C3—24no—
789C2×C3—24no—
790C2×C3—48no—
791C2×C3—68no—
792C2×C3—94no—
793C2×C3—182no—
794C2×C3C2×C4×D3214yes—
795C2×C3D3×#23514yes—
796C2×C3C2×D3×#6714yes—
797C2×C3C22×C4×C3⋊D311yescharacteristic
798C2×C3C2×D4×C3⋊D311yescharacteristic
799C2×C3#41×C3⋊D311yescharacteristic
800D3—22no—
801D3—316no—
802D3—68no—
803D3—182no—
804D3—188no—
805D3—368no—
806C22—21no—
807C22—21no—
808C22—32no—
809C22—61no—
810C22—61no—
811C22—92no—
812C22—92no—
813C22—92no—
814C22—92no—
815C22—188no—
816C22—181no—
817C22—181no—
818C22—272no—
819C22—548no—
820C22—541no—
821C22—541no—
822C22C4×D3×C3⋊D312yescomplemented
823C22C22×D3×C3⋊D311yescharacteristic
824C4—21no—
825C4—32no—
826C4—61no—
827C4—61no—
828C4—92no—
829C4—181no—
830C4—272no—
831C4—541no—
832C4—541no—
833C4C3⋊D3×#6712yesdirect product factor
834C3—24no—
835C3C4×D3×#6714yescomplemented
836C3C4×D4×C3⋊D311yescharacteristic, complemented
837C2—22no—
838C2—62no—
839C2—94no—
840C2—182no—
841C2—542no—
842C2C2×C4×D3×C3⋊D311yescharacteristic
843C2C3⋊D3×#23511yescharacteristic
844C2C2×C3⋊D3×#6711yescharacteristic
subgroupG/H
centerC2×C4C2×D3×C3⋊D3
commutatorC2×C33C23×C4
FrattiniC22C22×D3×C3⋊D3
FittingC22×C33×C4C22
socle, cosocleC22×C33C24
prime radicalC2×C3⋊D3×#67C2
hypercenterC22×C4D3×C3⋊D3
hypocenterC33C2×C4×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4×C3⋊D3C2semidirect
3. C2×C4×D3×C3⋊D3C2semidirect
4. C4×#6312C2semidirect
5. C32×C4×#67C2semidirect
6. #11723622C2semidirect
7. C3⋊D3×#217C2semidirect
8. #67×C3⋊Dic3C2semidirect
9. C3⋊D3×(C2×D3)⋊C4C2semidirect
10. #11723512C2semidirect
11. C4×#6292C2semidirect
12. #11723507C2semidirect
13. C4×#6290C2semidirect
14. C3⋊D3×Dic3⋊C4C2semidirect
15. C4×Dic3×C3⋊D3C2semidirect
20. C22×C33×C4C22semidirect
22. C2×C4×C3⋊(C3⋊D3)C22semidirect
23. C22×C3×C3⋊Dic3C22semidirect
27. C2×C3×C4×C3⋊D3C22semidirect
28. C2×C3×C4×C3⋊D3C22semidirect
30. C2×C32×C4×D3C22semidirect
31. C3⋊D3×#67C4direct (N × H)
34. C2×#6289C22semidirect
38. C2×D3×C3⋊Dic3C22semidirect
40. #88864C22semidirect
41. #88859C22semidirect
42. #88857C22semidirect
43. C4×C3⋊(C3⋊Dic3)C22semidirect
44. C32×#217C22semidirect
45. C32×(C2×D3)⋊C4C22semidirect
46. C32×Dic3⋊C4C22semidirect
47. C32×C4×Dic3C22semidirect
48. #88806C22semidirect
49. Dic3⋊(C3⋊Dic3)C22semidirect
50. #88804C22semidirect
51. #88803C22semidirect
52. #88803C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
55. Dic3×C3⋊Dic3C22semidirect
58. C22×C4×C3⋊D3D3semidirect
76. C3×C4×#67D3semidirect
91. C22×C3×C3⋊D3C2×C4semidirect
97. C2×D3×C3⋊D3C2×C4semidirect
101. #6312C2×C4semidirect
112. C3×C4×C3⋊D3D4semidirect
113. C32×#67C2×C4semidirect
118. #6292C2×C4semidirect
119. #6290C2×C4semidirect
123. Dic3×C3⋊D3C2×C4semidirect
134. C22×C32×C4C2×D3semidirect
135. C22×C32×C4C2×D3semidirect
141. C22×C3⋊Dic3C2×D3semidirect
155. C2×C4×C3⋊D3C2×D3semidirect
156. C2×C4×C3⋊D3C2×D3semidirect
164. C2×C3×C4×D3C2×D3semidirect
198. C3×#217C2×D3semidirect
199. C3×(C2×D3)⋊C4C2×D3semidirect
200. C3×Dic3⋊C4C2×D3semidirect
201. C3×C4×Dic3C2×D3semidirect
212. C22×C33C22×C4semidirect
216. C2×C3⋊(C3⋊D3)C22×C4semidirect
221. C2×C3×C3⋊D3C22×C4semidirect
226. C2×C32×D3C22×C4semidirect
229. C33×C4C2×D4semidirect
232. C3⋊(C3⋊Dic3)C22×C4semidirect
234. C3×C3⋊Dic3C2×D4semidirect
237. C32×Dic3C22×C4semidirect
257. C4×#67C3⋊D3direct (N × H)
281. C22×C3⋊D3C4×D3semidirect
335. C4×C3⋊D3#67direct (N × H)
336. C3×#67C4×D3semidirect
362. C3×C3⋊D3C4×D4semidirect
377. C22×C3×C4D32semidirect
378. C22×C3×C4C2×C3⋊D3semidirect
410. C2×C4×D3C2×C3⋊D3semidirect
421. #217C2×C3⋊D3semidirect
430. (C2×D3)⋊C4C2×C3⋊D3semidirect
438. Dic3⋊C4C2×C3⋊D3semidirect
446. C4×Dic3C2×C3⋊D3semidirect
458. C22×C32C2×C4×D3semidirect
459. C22×C32C2×C4×D3semidirect
476. C2×C3⋊D3C2×C4×D3semidirect
488. C2×C3×D3C2×C4×D3semidirect
497. C32×C4D3×D4semidirect
498. C32×C4C2×#67semidirect
509. C3⋊Dic3C2×#67semidirect
514. C3×Dic3C2×C4×D3semidirect
530. C33C2×C4×D4semidirect
582. #67C4×C3⋊D3direct (N × H)
634. C3⋊D3C4×#67direct (N × H)
659. C22×C4D3×C3⋊D3semidirect
694. C22×C3C4×D32semidirect
695. C22×C3C2×C4×C3⋊D3semidirect
718. C2×D3C2×C4×C3⋊D3semidirect
728. C3×C4D3×#67semidirect
729. C3×C4D4×C3⋊D3semidirect
743. Dic3C2×C4×C3⋊D3semidirect
745. C32C4×D3×D4semidirect
746. C32C2×C4×#67semidirect
822. C22C4×D3×C3⋊D3semidirect
833. C4C3⋊D3×#67direct (N × H)
835. C3C4×D3×#67semidirect
836. C3C4×D4×C3⋊D3semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×C3⋊D32
C2×C3⋊D3×#672
C2×C4×D3×C3⋊D32
C4×#63122
C32×C4×#672
#117236222
C3⋊D3×#2172
#67×C3⋊Dic32
C3⋊D3×(C2×D3)⋊C42
#117235122
C4×#62922
#117235072
C4×#62902
C3⋊D3×Dic3⋊C42
C4×Dic3×C3⋊D32
C4×D4×C3⋊D33
C4×D3×#673