Finite Group Databasebeta

← C3⋊D3×#67⋊C4 #13175908

Subgroups — C3⋊D3×#67⋊C4 #13175908

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
1C2×C3⋊D3×#67C211yesmaximal, characteristic
2C22×Dic3×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
4#11723922C211yesmaximal, characteristic, complemented
5C3×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
6C32×#67⋊C4C211yesmaximal, characteristic, complemented
7#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
8#11723618C211yesmaximal, characteristic, complemented
9C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11723508C211yesmaximal, characteristic, complemented
11#11723506C211yesmaximal, characteristic, complemented
12#11723472C211yesmaximal, characteristic, complemented
13#11723471C211yesmaximal, characteristic, complemented
14C3⋊D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
15C4×Dic3×C3⋊D3C211yesmaximal, characteristic, complemented
16C4×D4×C3⋊D3—31nomaximal
17D3×#67⋊C4—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C3×C4×C3⋊D3C2211yescharacteristic
24C2×C3×C4×C3⋊D3C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C22×C32×Dic3C2211yescharacteristic, complemented
27C2×C32×C4×D3C2211yescharacteristic, complemented
28C3⋊D3×#67C418yescomplemented
29C2×#6292C2211yescharacteristic
30C2×#6290C2211yescharacteristic
31C2×#6289C2211yescharacteristic, complemented
32C2×Dic3×C3⋊D3—24no—
33C2×Dic3×C3⋊D3C2211yescharacteristic
34C2×Dic3×C3⋊D3C2211yescharacteristic
35C2×Dic3×C3⋊D3C2211yescharacteristic
36C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
37C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
38C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
39C4×D3×C3⋊D3—24no—
40C33×C22⋊C4C2211yescharacteristic, complemented
41#88859C2211yescharacteristic, complemented
42#88857C2211yescharacteristic, complemented
43C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44C3×#3757C2211yescharacteristic, complemented
45C3×#3752C2211yescharacteristic, complemented
46C3×#3752C2211yescharacteristic, complemented
47C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C32×Dic3⋊C4C2211yescharacteristic, complemented
49C32×C4×Dic3C2211yescharacteristic, complemented
50#88806C2211yescharacteristic, complemented
51Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
52#88804C2211yescharacteristic, 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⋊D3—31no—
59C2×D3×#67—34no—
60C22×D3×Dic3—34no—
61C2×C4×D32—34no—
62C32×C4×D4—31no—
63D4×C3⋊Dic3—31no—
64C4×#638—31no—
65C4×#638—31no—
66#64102—31no—
67C4⋊C4×C3⋊D3—31no—
68#64090—31no—
69#64090—31no—
70#64090—34no—
71#64090—64no—
72C22⋊C4×C3⋊D3—31no—
73C22⋊C4×C3⋊D3D311yescharacteristic, complemented
74C4×C4⋊(C3⋊D3)—31no—
75C42×C3⋊D3—31no—
76C3×#67⋊C4D314yescomplemented
77C3×D3×C22⋊C4—34no—
78#67⋊Dic3—34no—
79#63952—34no—
80D3×(C2×D3)⋊C4—34no—
81#63902—34no—
82#63881—34no—
83#63880—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×C4C2311yescharacteristic
99C2×C33×C4C2311yescharacteristic
100#6312C2×C414yescomplemented
101C2×C3⋊(C3⋊Dic3)—22no—
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C4×C3⋊(C3⋊D3)—22no—
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C3×C4×C3⋊D3—22no—
109C3×C4×C3⋊D3—22no—
110C32×#67C2×C414yescomplemented
111C2×C32×Dic3—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C32×C4×D3—22no—
116#6292C2×C414yescomplemented
117#6290C2×C414yescomplemented
118#6289—22no—
119Dic3×C3⋊D3—22no—
120Dic3×C3⋊D3—22no—
121Dic3×C3⋊D3—22no—
122Dic3×C3⋊D3C2×C414yescomplemented
123Dic3×C3⋊D3D414yescomplemented
124D3×C3⋊Dic3—22no—
125C4×D3×D4—94no—
126C2×#67⋊C4—91no—
127C23×C3⋊D3—31no—
128C23×C3⋊D3C2×D311yescharacteristic
129C23×C3×D3—34no—
130C22×D32—34no—
131C2×C32×D4—31no—
132C22×C32×C4—31no—
133C22×C32×C4—31no—
134C2×#638—31no—
135C2×#638—34no—
136C2×#638—31no—
137C2×#638—64no—
138C22×C3⋊Dic3—31no—
139C22×C3⋊Dic3—34no—
140C22×C3⋊Dic3—31no—
141C22×C3⋊Dic3—64no—
142D4×C3⋊D3—38no—
143C2×C4⋊(C3⋊D3)—31no—
144C2×C4×C3⋊D3—31no—
145C2×C4×C3⋊D3—31no—
146C2×C4×C3⋊D3—31no—
147C2×C4×C3⋊D3—31no—
148C2×C4×C3⋊D3—31no—
149C2×C4×C3⋊D3—31no—
150C2×C4×C3⋊D3—34no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—64no—
153C2×C4×C3⋊D3—64no—
154C2×C4×C3⋊D3—64no—
155C2×C4×C3⋊D3C2×D311yescharacteristic
156C2×C4×C3⋊D3C2×D311yescharacteristic
157C2×C3×#67C2×D314yes—
158C22×C3×Dic3C2×D314yescomplemented
159C2×C3×C4×D3—34no—
160C2×C3×C4×D3—34no—
161C2×C3×C4×D3C2×D314yescomplemented
162D3×#67—332no—
163C2×#626—34no—
164C2×#625—34no—
165C2×#624—34no—
166C2×D3×Dic3—34no—
167C2×D3×Dic3—34no—
168C2×D3×Dic3—34no—
169C2×D3×Dic3—34no—
170C2×D3×Dic3—34no—
171C2×D3×Dic3—34no—
172C2×D3×Dic3—616no—
173C4×D32—616no—
174C32×C4⋊C4—31no—
175C32×C22⋊C4—24no—
176C32×C22⋊C4—31no—
177C32×C22⋊C4C2×D314yescomplemented
178C32×C22⋊C4C2×D311yescharacteristic, complemented
179C32×C42—31no—
180#3757—31no—
181#3757C2×D311yescharacteristic, complemented
182#3752—31no—
183#3752—34no—
184#3752—31no—
185#3752—64no—
186#3752C2×D311yescharacteristic, complemented
187#3752C2×D311yescharacteristic, complemented
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×#217—34no—
199C3×(C2×D3)⋊C4—34no—
200C3×(C2×D3)⋊C4—34no—
201C3×(C2×D3)⋊C4C2×D314yescomplemented
202C3×Dic3⋊C4C2×D314yescomplemented
203C3×C4×Dic3C2×D314yescomplemented
204#3724—34no—
205Dic3⋊Dic3—34no—
206#3722—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×C4—21no—
230C3⋊(C3⋊Dic3)—21no—
231C3⋊(C3⋊Dic3)C22×C412yescomplemented
232C3⋊(C3⋊Dic3)C2×D412yescomplemented
233C3×C3⋊Dic3—21no—
234C3×C3⋊Dic3—21no—
235C32×Dic3—21no—
236C32×Dic3C22×C412yescomplemented
237C32×Dic3C2×D412yescomplemented
238C22×#67—91no—
239C23×Dic3—91no—
240C2×D3×D4—94no—
241C22×C4×D3—94no—
242C22×C4×D3—94no—
243C22×C4×D3—91no—
244C3×C4×D4—34no—
245C2×C3×C22⋊C4—91no—
246D4×Dic3—94no—
247C4×#67—94no—
248C4×#67—94no—
249C2×(C2×D3)⋊C4—91no—
250C2×Dic3⋊C4—91no—
251C2×C4×Dic3—91no—
252#893—94no—
253D3×C4⋊C4—94no—
254#67⋊C4—94no—
255#67⋊C4—91no—
256#67⋊C4—91no—
257#67⋊C4—91no—
258#67⋊C4—94no—
259#67⋊C4—91no—
260#67⋊C4—91no—
261#67⋊C4—91no—
262#67⋊C4—91no—
263#67⋊C4—184no—
264#67⋊C4C3⋊D311yescharacteristic, direct product factor
265D3×C22⋊C4—34no—
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—24no—
295C2×C32×C4—24no—
296C2×C32×C4—31no—
297C2×C32×C4—31no—
298C2×C32×C4—31no—
299C2×C32×C4—62no—
300C2×C32×C4—62no—
301C2×C32×C4C22×D314yes—
302C2×C32×C4C22×D314yes—
303C2×C32×C4C22×D311yescharacteristic
304C2×C32×C4C22×D311yescharacteristic
305#638—34no—
306#638—34no—
307#638—316no—
308#638—616no—
309C2×C3⋊Dic3—31no—
310C2×C3⋊Dic3—31no—
311C2×C3⋊Dic3—31no—
312C2×C3⋊Dic3—34no—
313C2×C3⋊Dic3—34no—
314C2×C3⋊Dic3—34no—
315C2×C3⋊Dic3—64no—
316C2×C3⋊Dic3—64no—
317C2×C3⋊Dic3—64no—
318C2×C3⋊Dic3—62no—
319C2×C3⋊Dic3—62no—
320C2×C3⋊Dic3—68no—
321C2×C3⋊Dic3—128no—
322C2×C3⋊Dic3C22×D311yescharacteristic
323C2×C3⋊Dic3C22×D311yescharacteristic
324C4⋊(C3⋊D3)—34no—
325C4×C3⋊D3—22no—
326C4×C3⋊D3—22no—
327C4×C3⋊D3—34no—
328C4×C3⋊D3—34no—
329C4×C3⋊D3—62no—
330C4×C3⋊D3—62no—
331C4×C3⋊D3—62no—
332C4×C3⋊D3—62no—
333C4×C3⋊D3—62no—
334C4×C3⋊D3—68no—
335C4×C3⋊D3—128no—
336C3×#67C4×D3116yescomplemented
337C2×C3×Dic3—28no—
338C2×C3×Dic3—34no—
339C2×C3×Dic3—34no—
340C2×C3×Dic3C22×D314yes—
341C2×C3×Dic3C22×D314yes—
342C2×C3×Dic3C22×D314yes—
343C3×C4×D3—28no—
344C3×C4×D3—68no—
345C3×C4×D3—68no—
346#626—316no—
347#625—316no—
348#624—68no—
349D3×Dic3—316no—
350D3×Dic3—316no—
351D3×Dic3—68no—
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—34no—
370C22×C3×C4—34no—
371C22×C3×C4—91no—
372C22×C3×C4—91no—
373C2×#67—94no—
374C2×#67—94no—
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—98no—
378C2×#67—91no—
379C2×#67—184no—
380C2×#67C2×C3⋊D311yescharacteristic
381C22×Dic3—94no—
382C22×Dic3—91no—
383C22×Dic3—91no—
384C22×Dic3—94no—
385C22×Dic3—91no—
386C22×Dic3—91no—
387C22×Dic3—91no—
388C22×Dic3—91no—
389C22×Dic3—184no—
390C22×Dic3—184no—
391C22×Dic3C2×C3⋊D311yescharacteristic, complemented
392D3×D4—932no—
393C2×D12—94no—
394C2×C4×D3—34no—
395C2×C4×D3—34no—
396C2×C4×D3—94no—
397C2×C4×D3—94no—
398C2×C4×D3—94no—
399C2×C4×D3—94no—
400C2×C4×D3—94no—
401C2×C4×D3—94no—
402C2×C4×D3—91no—
403C2×C4×D3—94no—
404C2×C4×D3—91no—
405C2×C4×D3—91no—
406C2×C4×D3—184no—
407C2×C4×D3—184no—
408C2×C4×D3—1816no—
409C2×C4×D3—1816no—
410C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
411C3×C4⋊C4—34no—
412C3×C22⋊C4—24no—
413C3×C22⋊C4—34no—
414C3×C22⋊C4—91no—
415C3×C22⋊C4—91no—
416C3×C22⋊C4—91no—
417C3×C22⋊C4D3214yescomplemented
418C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
419C3×C42—34no—
420#217—34no—
421#217—94no—
422(C2×D3)⋊C4—34no—
423(C2×D3)⋊C4—34no—
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⋊D3D3×D412yes—
478C2×C3⋊D3#23712yes—
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—21no—
492C32×C4—24no—
493C32×C4—24no—
494C32×C4—32no—
495C32×C4—32no—
496C32×C4—44no—
497C32×C4—44no—
498C32×C4—61no—
499C3⋊Dic3—21no—
500C3⋊Dic3—21no—
501C3⋊Dic3—32no—
502C3⋊Dic3—32no—
503C3⋊Dic3—38no—
504C3⋊Dic3—38no—
505C3⋊Dic3—68no—
506C3⋊Dic3—68no—
507C3⋊Dic3—61no—
508C3⋊Dic3—64no—
509C3⋊Dic3—124no—
510C3×Dic3—24no—
511C3×Dic3—64no—
512C3×Dic3—64no—
513C3×Dic3C2×C4×D318yescomplemented
514C3×Dic3D3×D418yescomplemented
515C22×D4—271no—
516C23×C4—271no—
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—91no—
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—24no—
557C2×C3×C4—24no—
558C2×C3×C4—34no—
559C2×C3×C4—34no—
560C2×C3×C4—34no—
561C2×C3×C4—68no—
562C2×C3×C4—68no—
563C2×C3×C4—91no—
564C2×C3×C4—91no—
565C2×C3×C4—182no—
566C2×C3×C4—182no—
567C2×C3×C4C2×D3214yes—
568C2×C3×C4C2×D3214yes—
569C2×C3×C4C22×C3⋊D311yescharacteristic
570C2×C3×C4C22×C3⋊D311yescharacteristic
571#67—916no—
572#67—916no—
573#67—94no—
574#67—94no—
575#67—94no—
576#67—1816no—
577#67C4×C3⋊D314yescomplemented
578C2×Dic3—22no—
579C2×Dic3—34no—
580C2×Dic3—34no—
581C2×Dic3—94no—
582C2×Dic3—94no—
583C2×Dic3—91no—
584C2×Dic3—91no—
585C2×Dic3—94no—
586C2×Dic3—94no—
587C2×Dic3—94no—
588C2×Dic3—91no—
589C2×Dic3—184no—
590C2×Dic3—184no—
591C2×Dic3—184no—
592C2×Dic3—182no—
593C2×Dic3—182no—
594C2×Dic3—188no—
595C2×Dic3—182no—
596C2×Dic3—188no—
597C2×Dic3—182no—
598C2×Dic3—368no—
599C2×Dic3C22×C3⋊D311yescharacteristic
600C2×Dic3C22×C3⋊D311yescharacteristic
601C2×Dic3C22×C3⋊D311yescharacteristic
602D12—916no—
603C4×D3—22no—
604C4×D3—68no—
605C4×D3—68no—
606C4×D3—916no—
607C4×D3—916no—
608C4×D3—188no—
609C4×D3—182no—
610C4×D3—188no—
611C4×D3—188no—
612C4×D3—182no—
613C4×D3—188no—
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×D3×D414yes—
627C2×C32C2×D3×D411yescharacteristic
628C2×C32C2×#23711yescharacteristic
629C2×C32D3×#4114yes—
630C3⋊D3—22no—
631C3⋊D3—62no—
632C3⋊D3—68no—
633C3⋊D3—128no—
634C3⋊D3#67⋊C414yesdirect 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—31no—
647C22×C4—91no—
648C22×C4—91no—
649C22×C4—271no—
650C22×C4—271no—
651C22×C4—271no—
652C22×C4—271no—
653C22×C4—271no—
654C22×C4—271no—
655C22×C4—271no—
656C22×C4—271no—
657C22×C4—271no—
658C22×C4—544no—
659C22×C4—544no—
660C4⋊C4—31no—
661C4⋊C4—271no—
662C4⋊C4—271no—
663C4⋊C4—271no—
664C22⋊C4—31no—
665C22⋊C4—91no—
666C22⋊C4—91no—
667C22⋊C4—91no—
668C22⋊C4—271no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C22⋊C4D3×C3⋊D311yescharacteristic, complemented
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—24no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—38no—
724C3×C4—38no—
725C3×C4—44no—
726C3×C4—44no—
727C3×C4—64no—
728C3×C4—181no—
729C3×C4—181no—
730Dic3—21no—
731Dic3—64no—
732Dic3—64no—
733Dic3—98no—
734Dic3—98no—
735Dic3—92no—
736Dic3—92no—
737Dic3—188no—
738Dic3—188no—
739Dic3—184no—
740Dic3—181no—
741Dic3—364no—
742Dic3C2×C4×C3⋊D312yescomplemented
743Dic3D4×C3⋊D312yescomplemented
744C32—24no—
745C32C2×#67⋊C411yescharacteristic, complemented
746C32C4×D3×D414yescomplemented
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—31no—
763C2×C4—31no—
764C2×C4—31no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—91no—
768C2×C4—91no—
769C2×C4—182no—
770C2×C4—182no—
771C2×C4—274no—
772C2×C4—274no—
773C2×C4—271no—
774C2×C4—271no—
775C2×C4—271no—
776C2×C4—542no—
777C2×C4—542no—
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×C3D32×D414yes—
796C2×C3D3×#23714yes—
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—21no—
826C4—32no—
827C4—32no—
828C4—61no—
829C4—181no—
830C4—181no—
831C4—272no—
832C4—272no—
833C4—541no—
834C3—24no—
835C3D3×#67⋊C414yescomplemented
836C3C4×D4×C3⋊D311yescharacteristic, complemented
837C2—22no—
838C2—62no—
839C2—94no—
840C2—182no—
841C2—542no—
842C2C2×C4×D3×C3⋊D311yescharacteristic
843C2D3×D4×C3⋊D311yescharacteristic
844C2C3⋊D3×#23711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutatorC2×C33C23×C4
FittingC33×C22⋊C4C22
socle, cosocleC22×C33C24
prime radicalC2×C3⋊D3×#67C2
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33C2×C4×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×Dic3×C3⋊D3C2semidirect
3. C2×C4×D3×C3⋊D3C2semidirect
4. #11723922C2semidirect
5. C3×C22⋊C4×C3⋊D3C2semidirect
6. C32×#67⋊C4C2semidirect
7. #67⋊(C3⋊Dic3)C2semidirect
8. #11723618C2semidirect
9. C3⋊D3×(C2×D3)⋊C4C2semidirect
10. #11723508C2semidirect
11. #11723506C2semidirect
12. #11723472C2semidirect
13. #11723471C2semidirect
14. C3⋊D3×Dic3⋊C4C2semidirect
15. C4×Dic3×C3⋊D3C2semidirect
21. C22×C3⋊(C3⋊Dic3)C22semidirect
22. C2×C4×C3⋊(C3⋊D3)C22semidirect
26. C22×C32×Dic3C22semidirect
27. C2×C32×C4×D3C22semidirect
28. C3⋊D3×#67C4semidirect
31. C2×#6289C22semidirect
36. C2×Dic3×C3⋊D3C22semidirect
37. C2×Dic3×C3⋊D3C22semidirect
38. C2×D3×C3⋊Dic3C22semidirect
40. C33×C22⋊C4C22semidirect
41. #88859C22semidirect
42. #88857C22semidirect
43. C4×C3⋊(C3⋊Dic3)C22semidirect
44. C3×#3757C22semidirect
45. C3×#3752C22semidirect
46. C3×#3752C22semidirect
47. C32×(C2×D3)⋊C4C22semidirect
48. C32×Dic3⋊C4C22semidirect
49. C32×C4×Dic3C22semidirect
50. #88806C22semidirect
51. Dic3⋊(C3⋊Dic3)C22semidirect
52. #88804C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
55. Dic3×C3⋊Dic3C22semidirect
73. C22⋊C4×C3⋊D3D3semidirect
76. C3×#67⋊C4D3semidirect
91. C22×C3×C3⋊D3C2×C4semidirect
97. C2×D3×C3⋊D3C2×C4semidirect
100. #6312C2×C4semidirect
110. C32×#67C2×C4semidirect
116. #6292C2×C4semidirect
117. #6290C2×C4semidirect
122. Dic3×C3⋊D3C2×C4semidirect
123. Dic3×C3⋊D3D4semidirect
158. C22×C3×Dic3C2×D3semidirect
161. C2×C3×C4×D3C2×D3semidirect
177. C32×C22⋊C4C2×D3semidirect
178. C32×C22⋊C4C2×D3semidirect
181. #3757C2×D3semidirect
186. #3752C2×D3semidirect
187. #3752C2×D3semidirect
201. C3×(C2×D3)⋊C4C2×D3semidirect
202. C3×Dic3⋊C4C2×D3semidirect
203. 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
231. C3⋊(C3⋊Dic3)C22×C4semidirect
232. C3⋊(C3⋊Dic3)C2×D4semidirect
236. C32×Dic3C22×C4semidirect
237. C32×Dic3C2×D4semidirect
264. #67⋊C4C3⋊D3direct (N × H)
281. C22×C3⋊D3C4×D3semidirect
336. C3×#67C4×D3semidirect
362. C3×C3⋊D3C4×D4semidirect
391. C22×Dic3C2×C3⋊D3semidirect
410. C2×C4×D3C2×C3⋊D3semidirect
417. C3×C22⋊C4D32semidirect
418. C3×C22⋊C4C2×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
513. C3×Dic3C2×C4×D3semidirect
514. C3×Dic3D3×D4semidirect
530. C33C2×C4×D4semidirect
577. #67C4×C3⋊D3semidirect
634. C3⋊D3#67⋊C4direct (N × H)
671. C22⋊C4D3×C3⋊D3semidirect
694. C22×C3C4×D32semidirect
695. C22×C3C2×C4×C3⋊D3semidirect
718. C2×D3C2×C4×C3⋊D3semidirect
742. Dic3C2×C4×C3⋊D3semidirect
743. Dic3D4×C3⋊D3semidirect
745. C32C2×#67⋊C4semidirect
746. C32C4×D3×D4semidirect
822. C22C4×D3×C3⋊D3semidirect
835. C3D3×#67⋊C4semidirect
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
C2×C3⋊D3×#672
C22×Dic3×C3⋊D32
C2×C4×D3×C3⋊D32
#117239222
C3×C22⋊C4×C3⋊D32
C32×#67⋊C42
#67⋊(C3⋊Dic3)2
#117236182
C3⋊D3×(C2×D3)⋊C42
#117235082
#117235062
#117234722
#117234712
C3⋊D3×Dic3⋊C42
C4×Dic3×C3⋊D32
C4×D4×C3⋊D33
D3×#67⋊C43