Finite Group Databasebeta

← #13177316

Subgroups — #13177316

Order 1728.

2356 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#235C211yesmaximal, characteristic, complemented
2C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
3C4×#6312C211yesmaximal, characteristic, complemented
4C3×C4×#638C211yesmaximal, characteristic, complemented
5#11723643C211yesmaximal, characteristic, complemented
6#11723631C211yesmaximal, characteristic, complemented
7#11723614C211yesmaximal, characteristic, complemented
8#11723599C211yesmaximal, characteristic, complemented
9#11723540C211yesmaximal, characteristic, complemented
10C4×#6291C211yesmaximal, characteristic, complemented
11C4×#6290C211yesmaximal, characteristic, complemented
12#11723477C211yesmaximal, characteristic, complemented
13#11723476C211yesmaximal, characteristic, complemented
14#11723473C211yesmaximal, characteristic, complemented
15#11723423C211yesmaximal, characteristic, complemented
16#10596299—31nomaximal
17#10595060—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C22×C33×C4C2211yescharacteristic, complemented
20C2×#6312C2211yescharacteristic
21C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×C4×C3⋊D3C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic, complemented
26C32×#235—24no—
27C2×C32×D12C2211yescharacteristic
28C2×C32×C4×D3C2211yescharacteristic
29C2×C32×C4×D3C2211yescharacteristic, complemented
30C2×C32×Dic6C2211yescharacteristic, complemented
31C2×#6291C2211yescharacteristic
32C2×#6290C2211yescharacteristic
33C2×#6289C2211yescharacteristic
34C2×Dic3×C3⋊D3C2211yescharacteristic
35C2×D3×C3⋊Dic3C2211yescharacteristic
36C4×D3×C3⋊D3—24no—
37#88864C2211yescharacteristic, complemented
38#88859C2211yescharacteristic
39#88857C2211yescharacteristic, complemented
40C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41C3×#3757C2211yescharacteristic, complemented
42C3×#3752C2211yescharacteristic
43C3×#3750C2211yescharacteristic, complemented
44C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
45#88807C2211yescharacteristic, complemented
46#88806C2211yescharacteristic, complemented
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88804C2211yescharacteristic
50#88803C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55C2×C32×#41—31no—
56C22×C4×C3⋊D3—31no—
57C2×C3×#235D314yescomplemented
58C2×C4×D32—34no—
59#64155—31no—
60#64155—31no—
61#64147—31no—
62#64147—31no—
63#64146—31no—
64#64146—31no—
65#64144—31no—
66#64144—31no—
67C4×#638—31no—
68C4×#638—31no—
69C4×#638—31no—
70C4×#638—34no—
71C4×#638—64no—
72C4×#638D311yescharacteristic, complemented
73#64135—31no—
74C3×C4×#67—34no—
75#63983—34no—
76#63970—34no—
77#63969—34no—
78#63958—34no—
79#63922—34no—
80C4×#626—34no—
81C4×#625—34no—
82#63888—34no—
83#63887—34no—
84#63884—34no—
85#63855—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
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×C4—22no—
95C2×C33×C4C2311yescharacteristic
96C2×C33×C4C2311yescharacteristic
97#6312—22no—
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
100C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
101C4×C3⋊(C3⋊D3)—22no—
102C3×#638—22no—
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C2×C3×C3⋊Dic3C2311yescharacteristic
105C2×C3×C3⋊Dic3C2311yescharacteristic
106C3×C4×C3⋊D3—22no—
107C32×#67—22no—
108C32×#67—22no—
109C2×C32×Dic3C2311yescharacteristic
110C2×C32×Dic3C2311yescharacteristic
111C32×D12—22no—
112C32×C4×D3—22no—
113C32×C4×D3D414yescomplemented
114C32×Dic6—22no—
115#6291—22no—
116#6290—22no—
117#6289—22no—
118Dic3×C3⋊D3—22no—
119D3×C3⋊Dic3—22no—
120#5828—94no—
121#5547—91no—
122C23×C3⋊D3—31no—
123C22×D32—34no—
124C32×#41—64no—
125C2×C32×Q8—31no—
126C2×C32×D4—31no—
127C2×C32×D4—31no—
128C2×C32×D4—31no—
129C22×C32×C4—24no—
130C22×C32×C4—31no—
131C22×C32×C4—31no—
132C22×C32×C4C2×D314yescomplemented
133C22×C32×C4C2×D311yescharacteristic, complemented
134C2×#638—31no—
135C2×#638—34no—
136C2×#638—31no—
137C2×#638—31no—
138C2×#638—64no—
139C2×#638C2×D311yescharacteristic
140C22×C3⋊Dic3—31no—
141C2×C4×C3⋊D3—31no—
142C2×C4×C3⋊D3—31no—
143C2×C4×C3⋊D3—34no—
144C2×C4×C3⋊D3—31no—
145C2×C4×C3⋊D3—64no—
146C2×C4×C3⋊D3—64no—
147C2×C4×C3⋊D3C2×D311yescharacteristic
148C2×C3×#67—34no—
149C2×C3×#67C2×D314yes—
150C2×C3×#67C2×D314yescomplemented
151C3×#235—216no—
152C2×C3×D12C2×D314yes—
153C2×C3×C4×D3—34no—
154C2×C3×C4×D3C2×D314yes—
155C2×C3×C4×D3C2×D314yescomplemented
156C2×C3×Dic6C2×D314yescomplemented
157C2×#626—34no—
158C2×#625—34no—
159C2×#624—34no—
160C2×D3×Dic3—34no—
161C2×D3×Dic3—34no—
162C4×D32—616no—
163#3757—31no—
164#3757—34no—
165#3757—31no—
166#3757—31no—
167#3757—31no—
168#3757—31no—
169#3757—64no—
170#3757C2×D311yescharacteristic, complemented
171#3752—31no—
172#3752—31no—
173#3752—34no—
174#3752—31no—
175#3752—64no—
176#3752C2×D311yescharacteristic
177C4⋊(C3⋊Dic3)—31no—
178C4⋊(C3⋊Dic3)—31no—
179#3750—31no—
180#3750—34no—
181#3750—31no—
182#3750—31no—
183#3750—64no—
184#3750C2×D311yescharacteristic, complemented
185C4×C3⋊Dic3—31no—
186C4×C3⋊Dic3—34no—
187C4×C3⋊Dic3—64no—
188C4×C3⋊Dic3C2×D311yescharacteristic, complemented
189C3×#217—34no—
190C3×(C2×D3)⋊C4—34no—
191C3×Dic3⋊C4—34no—
192C3×C4×Dic3—34no—
193#3724—34no—
194Dic3⋊Dic3—34no—
195Dic3⋊Dic3—34no—
196Dic3⋊Dic3—34no—
197#3722—34no—
198(C2×D3)⋊Dic3—34no—
199(C2×D3)⋊Dic3—34no—
200(C2×D3)⋊Dic3—34no—
201(C2×D3)⋊Dic3—34no—
202(C2×D3)⋊Dic3—34no—
203C22×C33—21no—
204C22×C33—21no—
205C22×C33—21no—
206C22×C33C2411yescharacteristic
207C2×C3⋊(C3⋊D3)—21no—
208C2×C3⋊(C3⋊D3)—21no—
209C2×C3⋊(C3⋊D3)#4112yescomplemented
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×D3C2×D412yes—
219D3×C3⋊D3—28no—
220C33×C4—21no—
221C33×C4C2×D412yes—
222C3⋊(C3⋊Dic3)—21no—
223C3⋊(C3⋊Dic3)—21no—
224C3⋊(C3⋊Dic3)—21no—
225C3×C3⋊Dic3—21no—
226C3×C3⋊Dic3—21no—
227C3×C3⋊Dic3—21no—
228C32×Dic3—21no—
229C32×Dic3C2×D412yes—
230C2×C3×#41—34no—
231C2×#235C3⋊D311yescharacteristic, complemented
232C22×C4×D3—94no—
233C22×C4×D3—91no—
234C3×C4×D4—91no—
235#946—94no—
236#946—94no—
237#939—91no—
238#938—94no—
239#938—94no—
240#937—94no—
241#937—94no—
242#937—91no—
243#935—94no—
244#935—94no—
245C4×#67—34no—
246C4×#67—94no—
247C4×#67—94no—
248C4×#67—94no—
249C4×#67—91no—
250C4×#67—91no—
251C4×#67—184no—
252#926—94no—
253#896—91no—
254#894—91no—
255#884—91no—
256#883—91no—
257#882—91no—
258#878—91no—
259C4×D12—91no—
260#872—91no—
261C23×C32—24no—
262C23×C32—31no—
263C23×C32—31no—
264C23×C32C22×D314yes—
265C23×C32C22×D311yescharacteristic
266C22×C3⋊D3—31no—
267C22×C3⋊D3—34no—
268C22×C3⋊D3—64no—
269C22×C3⋊D3—62no—
270C22×C3⋊D3—62no—
271C22×C3⋊D3—62no—
272C22×C3⋊D3C22×D311yescharacteristic
273C22×C3×D3—34no—
274C22×C3×D3C22×D314yes—
275C22×C3×D3C22×D314yes—
276C2×D32—68no—
277C2×D32—68no—
278C2×D32—68no—
279C32×Q8—62no—
280C32×D4—62no—
281C32×D4—62no—
282C32×D4—62no—
283C2×C32×C4—22no—
284C2×C32×C4—24no—
285C2×C32×C4—24no—
286C2×C32×C4—28no—
287C2×C32×C4—31no—
288C2×C32×C4—34no—
289C2×C32×C4—31no—
290C2×C32×C4—48no—
291C2×C32×C4—62no—
292C2×C32×C4C22×D314yes—
293C2×C32×C4C22×D314yes—
294C2×C32×C4C22×D311yescharacteristic
295C2×C32×C4C22×D311yescharacteristic
296#638—22no—
297#638—62no—
298#638—62no—
299#638—68no—
300#638—616no—
301#638—62no—
302C2×C3⋊Dic3—31no—
303C2×C3⋊Dic3—31no—
304C2×C3⋊Dic3—31no—
305C2×C3⋊Dic3—34no—
306C2×C3⋊Dic3—34no—
307C2×C3⋊Dic3—34no—
308C2×C3⋊Dic3—64no—
309C2×C3⋊Dic3—64no—
310C2×C3⋊Dic3—64no—
311C2×C3⋊Dic3—62no—
312C2×C3⋊Dic3C22×D311yescharacteristic
313C2×C3⋊Dic3C22×D311yescharacteristic
314C2×C3⋊Dic3C22×D311yescharacteristic
315C4×C3⋊D3—22no—
316C4×C3⋊D3—62no—
317C4×C3⋊D3—62no—
318C4×C3⋊D3—62no—
319C4×C3⋊D3—68no—
320C4×C3⋊D3—128no—
321C3×#67—28no—
322C3×#67—28no—
323C3×#67—68no—
324C2×C3×Dic3—34no—
325C2×C3×Dic3—34no—
326C2×C3×Dic3—34no—
327C2×C3×Dic3C22×D314yes—
328C2×C3×Dic3C22×D314yes—
329C3×D12—28no—
330C3×C4×D3—28no—
331C3×C4×D3—68no—
332C3×C4×D3#67116yescomplemented
333C3×Dic6—28no—
334#626—68no—
335#625—68no—
336#624—68no—
337D3×Dic3—68no—
338D3×Dic3—68no—
339#525—271noSylow
340C2×C33—41no—
341C2×C33C22×D411yescharacteristic
342C2×C33C2×#4111yescharacteristic
343C2×C33C2×#4111yescharacteristic
344C3⋊(C3⋊D3)—22no—
345C3×C3⋊D3—22no—
346C32×D3—22no—
347C32×D3—41no—
348C23×D3—94no—
349C23×D3—91no—
350C3×#41—616no—
351C2×C3×Q8—34no—
352C2×C3×D4—34no—
353C2×C3×D4—34no—
354C2×C3×D4—34no—
355C2×C3×D4—91no—
356C22×C3×C4—24no—
357C22×C3×C4—34no—
358C22×C3×C4—34no—
359C22×C3×C4—91no—
360C22×C3×C4D3214yescomplemented
361C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
362C2×#67—34no—
363C2×#67—94no—
364C2×#67—94no—
365C2×#67—94no—
366C2×#67—91no—
367C2×#67—91no—
368C2×#67—184no—
369C2×#67C2×C3⋊D311yescharacteristic
370C2×#67C2×C3⋊D311yescharacteristic, complemented
371C22×Dic3—94no—
372C22×Dic3—91no—
373#235—24no—
374C2×D12—91no—
375C2×D12C2×C3⋊D311yescharacteristic
376C2×C4×D3—34no—
377C2×C4×D3—94no—
378C2×C4×D3—94no—
379C2×C4×D3—91no—
380C2×C4×D3—94no—
381C2×C4×D3—91no—
382C2×C4×D3—91no—
383C2×C4×D3—184no—
384C2×C4×D3—1816no—
385C2×C4×D3—184no—
386C2×C4×D3C2×C3⋊D311yescharacteristic
387C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
388C2×Dic6C2×C3⋊D311yescharacteristic, complemented
389C3×C4⋊C4—91no—
390C3×C22⋊C4—91no—
391C3×C22⋊C4—91no—
392C3×C42—91no—
393#217—34no—
394#217—94no—
395#217—94no—
396#217—94no—
397#217—94no—
398#217—94no—
399#217—91no—
400#217—91no—
401#217—184no—
402(C2×D3)⋊C4—34no—
403(C2×D3)⋊C4—94no—
404(C2×D3)⋊C4—94no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—94no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—91no—
412(C2×D3)⋊C4—184no—
413C4⋊Dic3—94no—
414C4⋊Dic3—94no—
415C4⋊Dic3—91no—
416Dic3⋊C4—34no—
417Dic3⋊C4—94no—
418Dic3⋊C4—94no—
419Dic3⋊C4—94no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—91no—
423Dic3⋊C4—91no—
424Dic3⋊C4—184no—
425C4×Dic3—34no—
426C4×Dic3—94no—
427C4×Dic3—91no—
428C4×Dic3—184no—
429C22×C32—28no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—24no—
433C22×C32—21no—
434C22×C32—24no—
435C22×C32—24no—
436C22×C32—24no—
437C22×C32—32no—
438C22×C32—44no—
439C22×C32—44no—
440C22×C32—61no—
441C22×C32—61no—
442C22×C32—61no—
443C22×C32—61no—
444C22×C32—61no—
445C22×C32C23×D314yes—
446C22×C32C23×D311yescharacteristic
447C2×C3⋊D3—21no—
448C2×C3⋊D3—21no—
449C2×C3⋊D3—32no—
450C2×C3⋊D3—38no—
451C2×C3⋊D3—68no—
452C2×C3⋊D3—68no—
453C2×C3⋊D3—61no—
454C2×C3⋊D3—61no—
455C2×C3⋊D3—64no—
456C2×C3⋊D3—64no—
457C2×C3⋊D3—124no—
458C2×C3⋊D3—124no—
459C2×C3⋊D3#23512yescomplemented
460C2×C3×D3—24no—
461C2×C3×D3—24no—
462C2×C3×D3—24no—
463C2×C3×D3—24no—
464C2×C3×D3—24no—
465C2×C3×D3—38no—
466C2×C3×D3—64no—
467C2×C3×D3—64no—
468C2×C3×D3C2×#6718yes—
469D32—632no—
470C32×C4—21no—
471C32×C4—28no—
472C32×C4—24no—
473C32×C4—32no—
474C32×C4—44no—
475C32×C4—61no—
476C32×C4D3×D412yes—
477C32×C4C2×#6718yes—
478C3⋊Dic3—21no—
479C3⋊Dic3—21no—
480C3⋊Dic3—21no—
481C3⋊Dic3—68no—
482C3⋊Dic3—61no—
483C3⋊Dic3—61no—
484C3⋊Dic3—64no—
485C3⋊Dic3—61no—
486C3⋊Dic3—64no—
487C3⋊Dic3—64no—
488C3⋊Dic3—124no—
489C3⋊Dic3—124no—
490C3×Dic3—24no—
491C3×Dic3—64no—
492C3×Dic3—64no—
493C3×Dic3—64no—
494C3×Dic3C2×#6718yes—
495C2×#41—31no—
496C23×C4—271no—
497#123—271no—
498#123—271no—
499C22⋊Q8—271no—
500C22⋊Q8—271no—
501#121—271no—
502#121—271no—
503#120—271no—
504#120—271no—
505C4×D4—91no—
506C4×D4—271no—
507C4×D4—271no—
508C4×D4—271no—
509#117—271no—
510C33#52511yescharacteristic, complemented, Sylow
511C23×C3—24no—
512C23×C3—34no—
513C23×C3—34no—
514C23×C3—91no—
515C23×C3C2×D3214yes—
516C23×C3C22×C3⋊D311yescharacteristic
517C22×D3—34no—
518C22×D3—94no—
519C22×D3—91no—
520C22×D3—184no—
521C22×D3—182no—
522C22×D3—182no—
523C22×D3—188no—
524C22×D3—188no—
525C22×D3—188no—
526C22×D3—182no—
527C22×D3C22×C3⋊D311yescharacteristic
528C22×D3C22×C3⋊D311yescharacteristic
529C3×Q8—68no—
530C3×D4—68no—
531C3×D4—68no—
532C3×D4—68no—
533C3×D4—182no—
534C2×C3×C4—28no—
535C2×C3×C4—22no—
536C2×C3×C4—24no—
537C2×C3×C4—24no—
538C2×C3×C4—34no—
539C2×C3×C4—316no—
540C2×C3×C4—34no—
541C2×C3×C4—48no—
542C2×C3×C4—68no—
543C2×C3×C4—91no—
544C2×C3×C4—91no—
545C2×C3×C4—91no—
546C2×C3×C4—182no—
547C2×C3×C4C2×D3214yes—
548C2×C3×C4C2×D3214yes—
549C2×C3×C4C22×C3⋊D311yescharacteristic
550C2×C3×C4C22×C3⋊D311yescharacteristic
551#67—22no—
552#67—22no—
553#67—68no—
554#67—188no—
555#67—182no—
556#67—188no—
557#67—188no—
558#67—182no—
559#67—1816no—
560C2×Dic3—34no—
561C2×Dic3—34no—
562C2×Dic3—34no—
563C2×Dic3—94no—
564C2×Dic3—94no—
565C2×Dic3—94no—
566C2×Dic3—91no—
567C2×Dic3—91no—
568C2×Dic3—91no—
569C2×Dic3—184no—
570C2×Dic3—184no—
571C2×Dic3—184no—
572C2×Dic3—188no—
573C2×Dic3—182no—
574C2×Dic3C22×C3⋊D311yescharacteristic
575C2×Dic3C22×C3⋊D311yescharacteristic
576D12—22no—
577D12—182no—
578C4×D3—22no—
579C4×D3—68no—
580C4×D3—188no—
581C4×D3—188no—
582C4×D3—182no—
583C4×D3—188no—
584C4×D3—182no—
585C4×D3—182no—
586C4×D3—368no—
587C4×D3#63814yescomplemented
588Dic6—22no—
589C2×C32—24no—
590C2×C32—24no—
591C2×C32—24no—
592C2×C32—48no—
593C2×C32—41no—
594C2×C32—44no—
595C2×C32—62no—
596C2×C32—121no—
597C2×C32C2×#23511yescharacteristic
598C2×C32C2×D3×D411yescharacteristic
599C2×C32D3×#4114yes—
600C2×C32D3×#4114yes—
601C2×C32D3×#4111yescharacteristic
602C2×C32C22×#6714yes—
603C3⋊D3—22no—
604C3⋊D3—62no—
605C3⋊D3—68no—
606C3⋊D3—128no—
607C3×D3—28no—
608C3×D3—44no—
609C3×D3—68no—
610C24—271no—
611#41—64no—
612C2×Q8—31no—
613C2×D4—31no—
614C2×D4—31no—
615C2×D4—31no—
616C2×D4—91no—
617C2×D4—271no—
618C2×D4—271no—
619C2×D4—271no—
620C22×C4—31no—
621C22×C4—31no—
622C22×C4—91no—
623C22×C4—271no—
624C22×C4—271no—
625C22×C4—271no—
626C22×C4—271no—
627C22×C4—544no—
628C22×C4D3×C3⋊D311yescharacteristic, complemented
629C4⋊C4—91no—
630C4⋊C4—271no—
631C4⋊C4—271no—
632C4⋊C4—271no—
633C4⋊C4—271no—
634C4⋊C4—271no—
635C22⋊C4—91no—
636C22⋊C4—91no—
637C22⋊C4—271no—
638C22⋊C4—271no—
639C22⋊C4—271no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C42—91no—
646C42—271no—
647C22×C3—28no—
648C22×C3—24no—
649C22×C3—24no—
650C22×C3—24no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—24no—
655C22×C3—38no—
656C22×C3—44no—
657C22×C3—44no—
658C22×C3—64no—
659C22×C3—64no—
660C22×C3—64no—
661C22×C3—64no—
662C22×C3—64no—
663C22×C3—92no—
664C22×C3—181no—
665C22×C3—181no—
666C22×C3C22×D3214yes—
667C22×C3C23×C3⋊D311yescharacteristic
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—38no—
674C2×D3—64no—
675C2×D3—64no—
676C2×D3—98no—
677C2×D3—92no—
678C2×D3—188no—
679C2×D3—188no—
680C2×D3—1832no—
681C2×D3—184no—
682C2×D3—184no—
683C2×D3—181no—
684C2×D3—181no—
685C2×D3—364no—
686C2×D3—364no—
687C2×D3C2×#63812yes—
688C3×C4—24no—
689C3×C4—21no—
690C3×C4—28no—
691C3×C4—38no—
692C3×C4—44no—
693C3×C4—64no—
694C3×C4—181no—
695C3×C4—181no—
696C3×C4—181no—
697C3×C4D3×#6718yes—
698C3×C4C2×#63812yes—
699Dic3—21no—
700Dic3—64no—
701Dic3—64no—
702Dic3—64no—
703Dic3—188no—
704Dic3—184no—
705Dic3—184no—
706Dic3—184no—
707Dic3—181no—
708Dic3—181no—
709Dic3—181no—
710Dic3—364no—
711Dic3—364no—
712Dic3C2×#63812yes—
713C32—24no—
714C32#554711yescharacteristic, complemented
715C32#582814yescomplemented
716C23—31no—
717C23—31no—
718C23—91no—
719C23—271no—
720C23—542no—
721C23—542no—
722C23—542no—
723C23C2×D3×C3⋊D311yescharacteristic
724Q8—62no—
725D4—62no—
726D4—62no—
727D4—62no—
728D4—182no—
729D4—542no—
730D4—542no—
731D4—542no—
732C2×C4—22no—
733C2×C4—31no—
734C2×C4—34no—
735C2×C4—31no—
736C2×C4—62no—
737C2×C4—91no—
738C2×C4—91no—
739C2×C4—91no—
740C2×C4—182no—
741C2×C4—271no—
742C2×C4—271no—
743C2×C4—271no—
744C2×C4—542no—
745C2×C4—542no—
746C2×C4—542no—
747C2×C4—542no—
748C2×C4C2×D3×C3⋊D311yescharacteristic
749C2×C4C2×D3×C3⋊D311yescharacteristic
750C2×C3—24no—
751C2×C3—24no—
752C2×C3—24no—
753C2×C3—48no—
754C2×C3—41no—
755C2×C3—44no—
756C2×C3—68no—
757C2×C3—124no—
758C2×C3—182no—
759C2×C3D3×#23514yes—
760C2×C3#6430614yes—
761C2×C3C2×D3×#6714yes—
762C2×C3#41×C3⋊D311yescharacteristic
763C2×C3#41×C3⋊D311yescharacteristic
764C2×C3C22×#63811yescharacteristic
765D3—22no—
766D3—41no—
767D3—68no—
768D3—182no—
769D3—188no—
770D3—368no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—32no—
775C22—61no—
776C22—61no—
777C22—61no—
778C22—61no—
779C22—61no—
780C22—92no—
781C22—181no—
782C22—181no—
783C22—272no—
784C22—548no—
785C22—541no—
786C22—541no—
787C22C22×D3×C3⋊D311yescharacteristic
788C4—21no—
789C4—32no—
790C4—61no—
791C4—181no—
792C4—181no—
793C4—181no—
794C4—541no—
795C4—541no—
796C4—541no—
797C4D3×#63812yes—
798C3—24no—
799C3#1059506014yescomplemented
800C3#1059629911yescharacteristic, complemented
801C2—41no—
802C2—62no—
803C2—121no—
804C2—182no—
805C2—542no—
806C2C3⋊D3×#23511yescharacteristic
807C2#1172457811yescharacteristic
808C2C2×D3×#63811yescharacteristic
subgroupG/H
centerC2×C4C2×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FrattiniC22C22×D3×C3⋊D3
FittingC22×C33×C4C22
hypercenterC22×C4D3×C3⋊D3
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×C32×#235C2semidirect
2. C2×C4×D3×C3⋊D3C2semidirect
3. C4×#6312C2semidirect
4. C3×C4×#638C2semidirect
5. #11723643C2semidirect
6. #11723631C2semidirect
7. #11723614C2semidirect
8. #11723599C2semidirect
9. #11723540C2semidirect
10. C4×#6291C2semidirect
11. C4×#6290C2semidirect
12. #11723477C2semidirect
13. #11723476C2semidirect
14. #11723473C2semidirect
15. #11723423C2semidirect
19. C22×C33×C4C22semidirect
25. C2×C32×#67C22semidirect
29. C2×C32×C4×D3C22semidirect
30. C2×C32×Dic6C22semidirect
37. #88864C22semidirect
39. #88857C22semidirect
40. C4×C3⋊(C3⋊Dic3)C22semidirect
41. C3×#3757C22semidirect
43. C3×#3750C22semidirect
44. C3×C4×C3⋊Dic3C22semidirect
45. #88807C22semidirect
46. #88806C22semidirect
47. Dic3⋊(C3⋊Dic3)C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
57. C2×C3×#235D3semidirect
72. C4×#638D3semidirect
113. C32×C4×D3D4semidirect
132. C22×C32×C4C2×D3semidirect
133. C22×C32×C4C2×D3semidirect
150. C2×C3×#67C2×D3semidirect
155. C2×C3×C4×D3C2×D3semidirect
156. C2×C3×Dic6C2×D3semidirect
170. #3757C2×D3semidirect
184. #3750C2×D3semidirect
188. C4×C3⋊Dic3C2×D3semidirect
209. C2×C3⋊(C3⋊D3)#41semidirect
212. C2×C3×C3⋊D3#41semidirect
231. C2×#235C3⋊D3semidirect
332. C3×C4×D3#67semidirect
360. C22×C3×C4D32semidirect
361. C22×C3×C4C2×C3⋊D3semidirect
370. C2×#67C2×C3⋊D3semidirect
387. C2×C4×D3C2×C3⋊D3semidirect
388. C2×Dic6C2×C3⋊D3semidirect
459. C2×C3⋊D3#235semidirect
510. C33#525semidirect
587. C4×D3#638semidirect
628. C22×C4D3×C3⋊D3semidirect
714. C32#5547semidirect
715. C32#5828semidirect
799. C3#10595060semidirect
800. C3#10596299semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2352
C2×C4×D3×C3⋊D32
C4×#63122
C3×C4×#6382
#117236432
#117236312
#117236142
#117235992
#117235402
C4×#62912
C4×#62902
#117234772
#117234762
#117234732
#117234232
#105962993
#105950603