Finite Group Databasebeta

← #13175414

Subgroups — #13175414

Order 1728.

2284 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#89020C211yesmaximal, characteristic, complemented
3#11723913C211yesmaximal, characteristic, complemented
4C3×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
5C32×C4×D12C211yesmaximal, characteristic, complemented
6#11723541C211yesmaximal, characteristic, complemented
7#11723540C211yesmaximal, characteristic, complemented
8#11723519C211yesmaximal, characteristic, complemented
9C4×#6290C211yesmaximal, characteristic, complemented
10C4×#6290C211yesmaximal, characteristic, complemented
11#11723504C211yesmaximal, characteristic, complemented
12#11723502C211yesmaximal, characteristic, complemented
13#11723500C211yesmaximal, characteristic, complemented
14#11723474C211yesmaximal, characteristic, complemented
15#11723422C211yesmaximal, characteristic, complemented
16#10596018—31nomaximal
17#10594006—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
23C2×C32×D12C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic, complemented
26C2×#6293C2211yescharacteristic, complemented
27C2×#6292C2211yescharacteristic
28C2×#6291C2211yescharacteristic
29C2×#6290C2211yescharacteristic
30C2×#6290C2211yescharacteristic
31C2×#6290C2211yescharacteristic, complemented
32C2×#6289C2211yescharacteristic
33C2×Dic3×C3⋊D3C2211yescharacteristic
34C2×D3×C3⋊Dic3C2211yescharacteristic
35C4×D3×C3⋊D3—24no—
36#89020—24no—
37C33×C42C2211yescharacteristic, complemented
38#88859C2211yescharacteristic
39#88859C2211yescharacteristic
40#88857C2211yescharacteristic, complemented
41#88857C2211yescharacteristic, complemented
42C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43C3×#3752C2211yescharacteristic
44C3×#3752C2211yescharacteristic, complemented
45C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic
47C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C32×C4⋊Dic3C2211yescharacteristic, complemented
49#88806C2211yescharacteristic, complemented
50#88806C2211yescharacteristic, complemented
51#88803C2211yescharacteristic
52#88803C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55C2×#3828—31no—
56C22×C4×C3⋊D3—31no—
57C2×C4×D32—34no—
58C2×#3798—34no—
59C32×C4×D4—31no—
60#64148—31no—
61#64146—31no—
62C4×#638—31no—
63C4×#638—31no—
64#64105—31no—
65#64103—31no—
66#64093—31no—
67#64092—31no—
68#64091—31no—
69#64087—31no—
70C4×C4⋊(C3⋊D3)D311yescharacteristic, complemented
71#64081—31no—
72#64081—34no—
73#64081—64no—
74C3×C4×D12—34no—
75C3×C4×D12D314yescomplemented
76#63922—34no—
77#63922—34no—
78C4×#625—34no—
79C4×#625—34no—
80#63899—34no—
81#63899—34no—
82#63885—34no—
83#63885—34no—
84#63854—34no—
85#63854—34no—
86C22×C3⋊(C3⋊D3)C2311yescharacteristic
87C22×C3×C3⋊D3C2311yescharacteristic
88C22×C3×C3⋊D3C2311yescharacteristic
89C22×C32×D3C2311yescharacteristic
90C22×C32×D3C2311yescharacteristic
91C2×D3×C3⋊D3—22no—
92C2×D3×C3⋊D3—22no—
93C2×D3×C3⋊D3—22no—
94C2×C33×C4C2311yescharacteristic
95C2×C33×C4C2311yescharacteristic
96C2×C33×C4C2311yescharacteristic
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
100C4×C3⋊(C3⋊D3)D414yescomplemented
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C3×C4⋊(C3⋊D3)—22no—
104C3×C4×C3⋊D3—22no—
105C3×C4×C3⋊D3—22no—
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108C32×D12—22no—
109C32×C4×D3—22no—
110C32×C4×D3—22no—
111#6293—22no—
112#6292—22no—
113#6291—22no—
114#6290—22no—
115#6290—22no—
116#6290—22no—
117#6289—22no—
118Dic3×C3⋊D3—22no—
119D3×C3⋊Dic3—22no—
120#5547—94no—
121#5547—91no—
122C23×C3⋊D3—31no—
123C22×D32—34no—
124C2×C32×D4—31no—
125C22×C32×C4—31no—
126C22×C32×C4—31no—
127C2×#638—31no—
128C2×#638—31no—
129C2×#638—31no—
130C2×#638—31no—
131C22×C3⋊Dic3—31no—
132#3828—64no—
133C2×C4⋊(C3⋊D3)—31no—
134C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
135C2×C4×C3⋊D3—31no—
136C2×C4×C3⋊D3—34no—
137C2×C4×C3⋊D3—31no—
138C2×C4×C3⋊D3—31no—
139C2×C4×C3⋊D3—64no—
140C2×C4×C3⋊D3—64no—
141C2×C4×C3⋊D3C2×D311yescharacteristic
142C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
143C2×#634—31no—
144C2×C3×D12—34no—
145C2×C3×D12C2×D314yes—
146C2×C3×C4×D3—34no—
147C2×C3×C4×D3—34no—
148C2×C3×C4×D3C2×D314yes—
149C2×C3×C4×D3C2×D314yescomplemented
150C2×#627—34no—
151C2×#626—34no—
152C2×#626—34no—
153C2×#625—34no—
154C2×#625—34no—
155C2×#625—34no—
156C2×#624—34no—
157C2×D3×Dic3—34no—
158C2×D3×Dic3—34no—
159C4×D32—616no—
160#3798—616no—
161C32×C4⋊C4—31no—
162C32×C22⋊C4—31no—
163C32×C22⋊C4—31no—
164C32×C42—24no—
165C32×C42C2×D314yescomplemented
166C32×C42C2×D311yescharacteristic, complemented
167#3757—31no—
168#3757—31no—
169#3752—31no—
170#3752—31no—
171#3752—31no—
172#3752—31no—
173#3752—34no—
174#3752—34no—
175#3752—64no—
176#3752—64no—
177#3752C2×D311yescharacteristic
178#3752C2×D311yescharacteristic, complemented
179C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
180#3750—31no—
181#3750—31no—
182#3750—34no—
183#3750—34no—
184#3750—31no—
185#3750—31no—
186#3750—64no—
187#3750—64no—
188C4×C3⋊Dic3—31no—
189C4×C3⋊Dic3—34no—
190C4×C3⋊Dic3—64no—
191C3×(C2×D3)⋊C4—34no—
192C3×(C2×D3)⋊C4—34no—
193C3×(C2×D3)⋊C4C2×D314yes—
194C3×(C2×D3)⋊C4C2×D314yescomplemented
195C3×C4⋊Dic3—34no—
196C3×C4⋊Dic3C2×D314yescomplemented
197#3724—34no—
198#3724—34no—
199(C2×D3)⋊Dic3—34no—
200(C2×D3)⋊Dic3—34no—
201(C2×D3)⋊Dic3—34no—
202(C2×D3)⋊Dic3—34no—
203C22×C33C2411yescharacteristic
204C2×C3⋊(C3⋊D3)—21no—
205C2×C3⋊(C3⋊D3)—21no—
206C2×C3⋊(C3⋊D3)C2×D412yes—
207C2×C3×C3⋊D3—21no—
208C2×C3×C3⋊D3—21no—
209C2×C3×C3⋊D3—21no—
210C2×C3×C3⋊D3—21no—
211C2×C3×C3⋊D3—21no—
212C2×C3×C3⋊D3#4112yescomplemented
213C2×C32×D3—21no—
214C2×C32×D3—21no—
215C2×C32×D3—21no—
216C2×C32×D3—21no—
217C2×C32×D3—21no—
218C2×C32×D3#4112yescomplemented
219D3×C3⋊D3—28no—
220C33×C4—21no—
221C33×C4—21no—
222C33×C4C2×D412yes—
223C3⋊(C3⋊Dic3)—21no—
224C3⋊(C3⋊Dic3)—21no—
225C3⋊(C3⋊Dic3)C2×D412yes—
226C3×C3⋊Dic3—21no—
227C3×C3⋊Dic3—21no—
228C32×Dic3—21no—
229C32×Dic3—21no—
230C2×#235—94no—
231C2×#235—91no—
232C22×C4×D3—94no—
233C22×C4×D3—91no—
234C3×C4×D4—34no—
235C3×C4×D4—91no—
236#939—94no—
237#939—91no—
238#937—94no—
239#937—91no—
240C4×#67—94no—
241C4×#67—94no—
242C4×#67—91no—
243C4×#67—91no—
244#896—94no—
245#896—91no—
246#894—94no—
247#894—91no—
248#884—94no—
249#884—91no—
250#883—94no—
251#883—91no—
252#882—94no—
253#882—91no—
254#878—94no—
255#878—91no—
256C4×D12—34no—
257C4×D12C3⋊D311yescharacteristic, complemented
258#872—94no—
259#872—91no—
260#872—184no—
261C23×C32—31no—
262C23×C32—31no—
263C22×C3⋊D3—31no—
264C22×C3⋊D3—34no—
265C22×C3⋊D3—64no—
266C22×C3⋊D3—62no—
267C22×C3⋊D3—62no—
268C22×C3⋊D3—62no—
269C22×C3⋊D3C22×D311yescharacteristic
270C22×C3⋊D3C22×D311yescharacteristic
271C22×C3×D3—34no—
272C22×C3×D3—34no—
273C22×C3×D3C22×D314yes—
274C22×C3×D3C22×D314yes—
275C2×D32—68no—
276C2×D32—68no—
277C2×D32—68no—
278C32×D4—62no—
279C2×C32×C4—24no—
280C2×C32×C4—24no—
281C2×C32×C4—24no—
282C2×C32×C4—31no—
283C2×C32×C4—31no—
284C2×C32×C4—62no—
285C2×C32×C4—62no—
286C2×C32×C4C22×D314yes—
287C2×C32×C4C22×D314yes—
288C2×C32×C4C22×D314yes—
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291C2×C32×C4C22×D311yescharacteristic
292#638—62no—
293#638—62no—
294#638—62no—
295#638—62no—
296C2×C3⋊Dic3—31no—
297C2×C3⋊Dic3—31no—
298C2×C3⋊Dic3—31no—
299C2×C3⋊Dic3—34no—
300C2×C3⋊Dic3—34no—
301C2×C3⋊Dic3—34no—
302C2×C3⋊Dic3—64no—
303C2×C3⋊Dic3—64no—
304C2×C3⋊Dic3—64no—
305C2×C3⋊Dic3—62no—
306C2×C3⋊Dic3C22×D311yescharacteristic
307C2×C3⋊Dic3C22×D311yescharacteristic
308C4⋊(C3⋊D3)—22no—
309C4⋊(C3⋊D3)—62no—
310C4×C3⋊D3—22no—
311C4×C3⋊D3—22no—
312C4×C3⋊D3—34no—
313C4×C3⋊D3—316no—
314C4×C3⋊D3—616no—
315C4×C3⋊D3—62no—
316C4×C3⋊D3—62no—
317#634—62no—
318C2×C3×Dic3—34no—
319C2×C3×Dic3—34no—
320C2×C3×Dic3C22×D314yes—
321C2×C3×Dic3C22×D314yes—
322C3×D12—28no—
323C3×D12—68no—
324C3×C4×D3—28no—
325C3×C4×D3—28no—
326C3×C4×D3—68no—
327C3×C4×D3—68no—
328#627—68no—
329#626—68no—
330#626—68no—
331#625—68no—
332#625—68no—
333#625—68no—
334#624—68no—
335D3×Dic3—68no—
336D3×Dic3—68no—
337#525—271noSylow
338C2×C33C22×D411yescharacteristic
339C2×C33C2×#4111yescharacteristic
340C2×C33C2×#4111yescharacteristic
341C3⋊(C3⋊D3)—22no—
342C3×C3⋊D3—22no—
343C3×C3⋊D3—41no—
344C32×D3—22no—
345C32×D3—41no—
346C23×D3—94no—
347C23×D3—91no—
348C2×C3×D4—34no—
349C2×C3×D4—91no—
350C22×C3×C4—34no—
351C22×C3×C4—34no—
352C22×C3×C4—91no—
353C22×C3×C4—91no—
354C2×#67—94no—
355C2×#67—94no—
356C2×#67—94no—
357C2×#67—94no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—91no—
362C22×Dic3—94no—
363C22×Dic3—91no—
364#235—184no—
365#235—1816no—
366C2×D12—34no—
367C2×D12—94no—
368C2×D12—91no—
369C2×D12C2×C3⋊D311yescharacteristic
370C2×C4×D3—34no—
371C2×C4×D3—34no—
372C2×C4×D3—94no—
373C2×C4×D3—91no—
374C2×C4×D3—94no—
375C2×C4×D3—94no—
376C2×C4×D3—91no—
377C2×C4×D3—91no—
378C2×C4×D3—184no—
379C2×C4×D3—184no—
380C2×C4×D3—1816no—
381C2×C4×D3C2×C3⋊D311yescharacteristic
382C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
383C2×Dic6—94no—
384C2×Dic6—91no—
385C3×C4⋊C4—34no—
386C3×C4⋊C4—91no—
387C3×C22⋊C4—34no—
388C3×C22⋊C4—34no—
389C3×C22⋊C4—91no—
390C3×C22⋊C4—91no—
391C3×C42—24no—
392C3×C42D3214yescomplemented
393C3×C42C2×C3⋊D311yescharacteristic, complemented
394#217—94no—
395#217—94no—
396#217—91no—
397#217—91no—
398(C2×D3)⋊C4—34no—
399(C2×D3)⋊C4—34no—
400(C2×D3)⋊C4—94no—
401(C2×D3)⋊C4—94no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—94no—
405(C2×D3)⋊C4—94no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—184no—
409(C2×D3)⋊C4—184no—
410(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
411(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
412C4⋊Dic3—34no—
413C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
414Dic3⋊C4—94no—
415Dic3⋊C4—94no—
416Dic3⋊C4—94no—
417Dic3⋊C4—94no—
418Dic3⋊C4—91no—
419Dic3⋊C4—91no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—184no—
423Dic3⋊C4—184no—
424C4×Dic3—94no—
425C4×Dic3—91no—
426C4×Dic3—184no—
427C22×C32—24no—
428C22×C32—32no—
429C22×C32—61no—
430C22×C32—61no—
431C22×C32—61no—
432C22×C32—61no—
433C22×C32—61no—
434C22×C32C23×D314yes—
435C22×C32C23×D311yescharacteristic
436C2×C3⋊D3—21no—
437C2×C3⋊D3—21no—
438C2×C3⋊D3—21no—
439C2×C3⋊D3—21no—
440C2×C3⋊D3—21no—
441C2×C3⋊D3—32no—
442C2×C3⋊D3—38no—
443C2×C3⋊D3—68no—
444C2×C3⋊D3—68no—
445C2×C3⋊D3—61no—
446C2×C3⋊D3—61no—
447C2×C3⋊D3—64no—
448C2×C3⋊D3—64no—
449C2×C3⋊D3—124no—
450C2×C3⋊D3—124no—
451C2×C3⋊D3#23512yescomplemented
452C2×C3×D3—24no—
453C2×C3×D3—24no—
454C2×C3×D3—24no—
455C2×C3×D3—24no—
456C2×C3×D3—24no—
457C2×C3×D3—38no—
458C2×C3×D3—64no—
459C2×C3×D3—64no—
460C2×C3×D3—64no—
461C2×C3×D3—64no—
462C2×C3×D3—64no—
463C2×C3×D3#23518yescomplemented
464D32—632no—
465C32×C4—21no—
466C32×C4—21no—
467C32×C4—28no—
468C32×C4—24no—
469C32×C4—24no—
470C32×C4—44no—
471C32×C4—44no—
472C32×C4—61no—
473C32×C4—61no—
474C32×C4D3×D418yes—
475C32×C4D3×D412yes—
476C3⋊Dic3—21no—
477C3⋊Dic3—21no—
478C3⋊Dic3—32no—
479C3⋊Dic3—38no—
480C3⋊Dic3—68no—
481C3⋊Dic3—61no—
482C3⋊Dic3—61no—
483C3⋊Dic3—64no—
484C3⋊Dic3—64no—
485C3⋊Dic3—124no—
486C3⋊Dic3—124no—
487C3×Dic3—24no—
488C3×Dic3—24no—
489C3×Dic3—64no—
490C3×Dic3—64no—
491C2×#41—271no—
492C23×C4—271no—
493#123—271no—
494#123—271no—
495C22⋊Q8—271no—
496C22⋊Q8—271no—
497#121—271no—
498#121—271no—
499#120—271no—
500#120—271no—
501C4×D4—31no—
502C4×D4—91no—
503C4×D4—271no—
504C4×D4—271no—
505#117—271no—
506C33#52511yescharacteristic, complemented, Sylow
507C23×C3—34no—
508C23×C3—34no—
509C23×C3—91no—
510C23×C3—91no—
511C22×D3—34no—
512C22×D3—34no—
513C22×D3—94no—
514C22×D3—91no—
515C22×D3—184no—
516C22×D3—182no—
517C22×D3—182no—
518C22×D3—188no—
519C22×D3—188no—
520C22×D3—188no—
521C22×D3—182no—
522C22×D3C22×C3⋊D311yescharacteristic
523C22×D3C22×C3⋊D311yescharacteristic
524C3×D4—68no—
525C3×D4—182no—
526C2×C3×C4—24no—
527C2×C3×C4—24no—
528C2×C3×C4—24no—
529C2×C3×C4—34no—
530C2×C3×C4—34no—
531C2×C3×C4—68no—
532C2×C3×C4—68no—
533C2×C3×C4—91no—
534C2×C3×C4—91no—
535C2×C3×C4—182no—
536C2×C3×C4—182no—
537C2×C3×C4C2×D3214yes—
538C2×C3×C4C2×D3214yes—
539C2×C3×C4C2×D3214yes—
540C2×C3×C4C22×C3⋊D311yescharacteristic
541C2×C3×C4C22×C3⋊D311yescharacteristic
542C2×C3×C4C22×C3⋊D311yescharacteristic
543#67—182no—
544#67—188no—
545#67—182no—
546#67—188no—
547#67—182no—
548#67—188no—
549#67—188no—
550#67—182no—
551C2×Dic3—34no—
552C2×Dic3—34no—
553C2×Dic3—94no—
554C2×Dic3—91no—
555C2×Dic3—94no—
556C2×Dic3—94no—
557C2×Dic3—91no—
558C2×Dic3—91no—
559C2×Dic3—184no—
560C2×Dic3—184no—
561C2×Dic3—184no—
562C2×Dic3—182no—
563C2×Dic3—188no—
564C2×Dic3C22×C3⋊D311yescharacteristic
565C2×Dic3C22×C3⋊D311yescharacteristic
566D12—22no—
567D12—68no—
568D12—188no—
569D12—182no—
570C4×D3—22no—
571C4×D3—22no—
572C4×D3—68no—
573C4×D3—68no—
574C4×D3—916no—
575C4×D3—94no—
576C4×D3—1816no—
577C4×D3—182no—
578C4×D3—188no—
579C4×D3—188no—
580C4×D3—182no—
581Dic6—182no—
582Dic6—188no—
583C2×C32—24no—
584C2×C32—24no—
585C2×C32—24no—
586C2×C32—62no—
587C2×C32—121no—
588C2×C32C2×#23514yes—
589C2×C32C2×#23511yescharacteristic
590C2×C32C2×D3×D414yes—
591C2×C32C2×D3×D411yescharacteristic
592C2×C32D3×#4114yes—
593C2×C32D3×#4111yescharacteristic
594C3⋊D3—22no—
595C3⋊D3—41no—
596C3⋊D3—62no—
597C3⋊D3—68no—
598C3⋊D3—128no—
599C3×D3—28no—
600C3×D3—44no—
601C3×D3—68no—
602C3×D3—124no—
603C24—271no—
604#41—544no—
605C2×Q8—271no—
606C2×D4—31no—
607C2×D4—91no—
608C2×D4—271no—
609C2×D4—271no—
610C2×D4—271no—
611C2×D4—271no—
612C2×D4—271no—
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—91no—
616C22×C4—91no—
617C22×C4—271no—
618C22×C4—271no—
619C22×C4—271no—
620C22×C4—271no—
621C22×C4—544no—
622C4⋊C4—31no—
623C4⋊C4—91no—
624C4⋊C4—271no—
625C4⋊C4—271no—
626C4⋊C4—271no—
627C4⋊C4—271no—
628C22⋊C4—31no—
629C22⋊C4—31no—
630C22⋊C4—91no—
631C22⋊C4—91no—
632C22⋊C4—271no—
633C22⋊C4—271no—
634C22⋊C4—271no—
635C22⋊C4—271no—
636C22⋊C4—271no—
637C22⋊C4—271no—
638C42—271no—
639C42D3×C3⋊D311yescharacteristic, complemented
640C22×C3—24no—
641C22×C3—38no—
642C22×C3—64no—
643C22×C3—64no—
644C22×C3—64no—
645C22×C3—64no—
646C22×C3—64no—
647C22×C3—92no—
648C22×C3—181no—
649C22×C3—181no—
650C22×C3—181no—
651C22×C3—181no—
652C22×C3—181no—
653C22×C3C22×D3214yes—
654C22×C3C23×C3⋊D311yescharacteristic
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—38no—
661C2×D3—64no—
662C2×D3—64no—
663C2×D3—64no—
664C2×D3—64no—
665C2×D3—64no—
666C2×D3—98no—
667C2×D3—92no—
668C2×D3—188no—
669C2×D3—188no—
670C2×D3—1832no—
671C2×D3—184no—
672C2×D3—184no—
673C2×D3—181no—
674C2×D3—181no—
675C2×D3—364no—
676C2×D3—364no—
677C2×D3#382812yescomplemented
678C3×C4—24no—
679C3×C4—24no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—28no—
683C3×C4—44no—
684C3×C4—44no—
685C3×C4—64no—
686C3×C4—64no—
687C3×C4—181no—
688C3×C4—181no—
689C3×C4#380218yes—
690C3×C4D4×C3⋊D312yes—
691Dic3—21no—
692Dic3—21no—
693Dic3—64no—
694Dic3—64no—
695Dic3—98no—
696Dic3—92no—
697Dic3—188no—
698Dic3—184no—
699Dic3—184no—
700Dic3—181no—
701Dic3—181no—
702Dic3—364no—
703Dic3—364no—
704C32—24no—
705C32#554714yescomplemented
706C32#554711yescharacteristic, complemented
707C23—31no—
708C23—31no—
709C23—91no—
710C23—91no—
711C23—271no—
712C23—542no—
713C23—542no—
714C23—542no—
715Q8—542no—
716D4—62no—
717D4—182no—
718D4—542no—
719D4—542no—
720D4—542no—
721D4—542no—
722D4—542no—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—91no—
728C2×C4—91no—
729C2×C4—182no—
730C2×C4—182no—
731C2×C4—271no—
732C2×C4—274no—
733C2×C4—271no—
734C2×C4—271no—
735C2×C4—542no—
736C2×C4—542no—
737C2×C4—542no—
738C2×C4C2×D3×C3⋊D311yescharacteristic
739C2×C4C2×D3×C3⋊D311yescharacteristic
740C2×C4C2×D3×C3⋊D311yescharacteristic
741C2×C3—24no—
742C2×C3—24no—
743C2×C3—24no—
744C2×C3—68no—
745C2×C3—124no—
746C2×C3—182no—
747C2×C3—361no—
748C2×C3C2×#380214yes—
749C2×C3D3×#23514yes—
750C2×C3D3×#23514yes—
751C2×C3C2×#382811yescharacteristic
752C2×C3C2×D4×C3⋊D311yescharacteristic
753C2×C3#41×C3⋊D311yescharacteristic
754D3—22no—
755D3—41no—
756D3—68no—
757D3—124no—
758D3—182no—
759D3—188no—
760D3—368no—
761C22—32no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—61no—
766C22—61no—
767C22—92no—
768C22—181no—
769C22—181no—
770C22—181no—
771C22—181no—
772C22—181no—
773C22—272no—
774C22—548no—
775C22—541no—
776C22—541no—
777C22C22×D3×C3⋊D311yescharacteristic
778C4—21no—
779C4—21no—
780C4—61no—
781C4—61no—
782C4—181no—
783C4—181no—
784C4—272no—
785C4—541no—
786C4—541no—
787C4#8902612yes—
788C3—24no—
789C3#1059400614yescomplemented
790C3#1059601811yescharacteristic, complemented
791C2—62no—
792C2—121no—
793C2—182no—
794C2—361no—
795C2—542no—
796C2C2×#8902611yescharacteristic
797C2D3×#382811yescharacteristic
798C2C3⋊D3×#23511yescharacteristic
subgroupG/H
centerC2×C4C2×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FrattiniC22C22×D3×C3⋊D3
FittingC33×C42C22
hypercenterC42D3×C3⋊D3
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×D3×C3⋊D3C2semidirect
2. C2×#89020C2semidirect
3. #11723913C2semidirect
4. C3×C4×C4⋊(C3⋊D3)C2semidirect
5. C32×C4×D12C2semidirect
6. #11723541C2semidirect
7. #11723540C2semidirect
8. #11723519C2semidirect
9. C4×#6290C2semidirect
10. C4×#6290C2semidirect
11. #11723504C2semidirect
12. #11723502C2semidirect
13. #11723500C2semidirect
14. #11723474C2semidirect
15. #11723422C2semidirect
22. C2×C3×C4×C3⋊D3C22semidirect
25. C2×C32×C4×D3C22semidirect
26. C2×#6293C22semidirect
31. C2×#6290C22semidirect
37. C33×C42C22semidirect
40. #88857C22semidirect
41. #88857C22semidirect
42. C4×C3⋊(C3⋊Dic3)C22semidirect
44. C3×#3752C22semidirect
45. C3×C4⋊(C3⋊Dic3)C22semidirect
47. C32×(C2×D3)⋊C4C22semidirect
48. C32×C4⋊Dic3C22semidirect
49. #88806C22semidirect
50. #88806C22semidirect
52. #88803C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
70. C4×C4⋊(C3⋊D3)D3semidirect
75. C3×C4×D12D3semidirect
100. C4×C3⋊(C3⋊D3)D4semidirect
142. C2×C4×C3⋊D3C2×D3semidirect
149. C2×C3×C4×D3C2×D3semidirect
165. C32×C42C2×D3semidirect
166. C32×C42C2×D3semidirect
178. #3752C2×D3semidirect
179. C4⋊(C3⋊Dic3)C2×D3semidirect
194. C3×(C2×D3)⋊C4C2×D3semidirect
196. C3×C4⋊Dic3C2×D3semidirect
212. C2×C3×C3⋊D3#41semidirect
218. C2×C32×D3#41semidirect
257. C4×D12C3⋊D3semidirect
382. C2×C4×D3C2×C3⋊D3semidirect
392. C3×C42D32semidirect
393. C3×C42C2×C3⋊D3semidirect
411. (C2×D3)⋊C4C2×C3⋊D3semidirect
413. C4⋊Dic3C2×C3⋊D3semidirect
451. C2×C3⋊D3#235semidirect
463. C2×C3×D3#235semidirect
506. C33#525semidirect
639. C42D3×C3⋊D3semidirect
677. C2×D3#3828semidirect
705. C32#5547semidirect
706. C32#5547semidirect
789. C3#10594006semidirect
790. C3#10596018semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×C3⋊D32
C2×#890202
#117239132
C3×C4×C4⋊(C3⋊D3)2
C32×C4×D122
#117235412
#117235402
#117235192
C4×#62902
#117235042
#117235022
#117235002
#117234742
#117234222
#105960183
#105940063