Finite Group Databasebeta

← #13177303

Subgroups — #13177303

Order 1728.

2316 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3828C211yesmaximal, characteristic, complemented
2C2×D3×#638C211yesmaximal, characteristic, complemented
3#11723970C211yesmaximal, characteristic, complemented
4C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5#11723632C211yesmaximal, characteristic, complemented
6#11723629C211yesmaximal, characteristic, complemented
7Dic3×#638C211yesmaximal, characteristic, complemented
8#11723541C211yesmaximal, characteristic, complemented
9C3⋊D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11723521C211yesmaximal, characteristic, complemented
11#11723520C211yesmaximal, characteristic, complemented
12#11723519C211yesmaximal, characteristic, complemented
13#11723518C211yesmaximal, characteristic, complemented
14#11723507C211yesmaximal, characteristic, complemented
15#11723487C211yesmaximal, characteristic, complemented
16#10595961—31nomaximal
17#10595065—34nomaximal
18C23×C32×D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C3×#3828—24no—
25C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
26C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
27C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
28C2×C3×#634C2211yescharacteristic, complemented
29C22×C32×Dic3C2211yescharacteristic, complemented
30D3×#638—24no—
31C2×#6292C2211yescharacteristic, complemented
32C2×#6291C2211yescharacteristic
33C2×#6290C2211yescharacteristic
34C2×#6290C2211yescharacteristic
35C2×#6290C2211yescharacteristic, complemented
36C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
37C2×D3×C3⋊Dic3C2211yescharacteristic
38#88864C2211yescharacteristic, complemented
39#88859C2211yescharacteristic, complemented
40#88859C2211yescharacteristic, complemented
41#88857C2211yescharacteristic, complemented
42#88857C2211yescharacteristic, complemented
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×(C2×D3)⋊C4C2211yescharacteristic
45C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
47#88807C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50#88803C2211yescharacteristic, complemented
51#88803C2211yescharacteristic, complemented
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C22×#638—31no—
56C2×#3828D311yescharacteristic, complemented
57C2×C3×#235—34no—
58C2×D3×#67—34no—
59C2×C32×C22⋊C4—31no—
60#64162—31no—
61#64139—31no—
62#64138—31no—
63#64138—34no—
64#64138—64no—
65C4×#638—31no—
66#64094—31no—
67#64093—31no—
68#64093—31no—
69#64092—31no—
70#64091—31no—
71#64090—31no—
72C22⋊C4×C3⋊D3—31no—
73#64087—31no—
74C2×C3×(C2×D3)⋊C4D314yescomplemented
75#63978—34no—
76#63976—34no—
77Dic3×#67—34no—
78#63922—34no—
79D3×(C2×D3)⋊C4—34no—
80#63907—34no—
81#63906—34no—
82#63905—34no—
83#63887—34no—
84#63885—34no—
85#63879—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3×C3⋊D3C2311yescharacteristic
89C22×C3×C3⋊D3C2311yescharacteristic
90C22×C32×D3—22no—
91C22×C32×D3—22no—
92C22×C32×D3—41no—
93C22×C32×D3C2311yescharacteristic
94C22×C32×D3C2311yescharacteristic
95C2×D3×C3⋊D3—22no—
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3—41no—
98C2×C33×C4—22no—
99C2×C33×C4C2311yescharacteristic
100C2×C33×C4C2311yescharacteristic
101#6312—22no—
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C3×#638—22no—
106C3×#638D414yescomplemented
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C3×C4⋊(C3⋊D3)—22no—
110C3×C4×C3⋊D3—22no—
111C3×C4×C3⋊D3—22no—
112C3×#634—22no—
113C2×C32×Dic3—41no—
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116#6292—41no—
117#6291—22no—
118#6290—22no—
119#6290—22no—
120#6290—41no—
121Dic3×C3⋊D3—41no—
122D3×C3⋊Dic3—22no—
123#5829—91no—
124#5490—94no—
125C24×C32—31no—
126C23×C3⋊D3—31no—
127C23×C3×D3C2×D314yes—
128C22×D32—34no—
129C22×C32×C4—24no—
130C22×C32×C4—31no—
131C22×C32×C4C2×D314yescomplemented
132C22×C32×C4C2×D311yescharacteristic, complemented
133C2×#638—31no—
134C2×#638—34no—
135C2×#638—31no—
136C2×#638—31no—
137C2×#638—31no—
138C2×#638—31no—
139C2×#638—64no—
140C2×#638—64no—
141C2×#638C2×D311yescharacteristic
142C2×#638C2×D311yescharacteristic, complemented
143C22×C3⋊Dic3—31no—
144#3828—24no—
145C2×C4⋊(C3⋊D3)—31no—
146C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
147C2×C4×C3⋊D3—31no—
148C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
149C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
150C2×#634C2×D311yescharacteristic, complemented
151C2×C3×#67—34no—
152C2×C3×#67—34no—
153C22×C3×Dic3C2×D314yescomplemented
154C3×#235—616no—
155C2×C3×D12—34no—
156C2×C3×C4×D3—34no—
157C2×C3×C4×D3—34no—
158C2×C3×Dic6—34no—
159D3×#67—616no—
160C2×#626—34no—
161C2×#626—34no—
162C2×#625—34no—
163C2×#625—34no—
164C2×#625—34no—
165C2×D3×Dic3—34no—
166C2×D3×Dic3—34no—
167C32×C22⋊C4—31no—
168C32×C22⋊C4—31no—
169C32×C22⋊C4—31no—
170C32×C22⋊C4—31no—
171#3757—31no—
172#3757—34no—
173#3757—31no—
174#3757—31no—
175#3757—64no—
176#3752—31no—
177#3752—31no—
178#3752—31no—
179#3752—31no—
180#3752—34no—
181#3752—34no—
182#3752—31no—
183#3752—64no—
184#3752—64no—
185C4⋊(C3⋊Dic3)—31no—
186#3750—31no—
187#3750—31no—
188#3750—34no—
189#3750—34no—
190#3750—31no—
191#3750—64no—
192#3750—64no—
193C4×C3⋊Dic3—31no—
194C3×(C2×D3)⋊C4C2×D314yes—
195C3×(C2×D3)⋊C4C2×D314yes—
196C3×(C2×D3)⋊C4C2×D314yescomplemented
197C3×(C2×D3)⋊C4C2×D314yescomplemented
198Dic3⋊Dic3—34no—
199Dic3⋊Dic3—34no—
200#3722—34no—
201(C2×D3)⋊Dic3—34no—
202(C2×D3)⋊Dic3—34no—
203(C2×D3)⋊Dic3—34no—
204(C2×D3)⋊Dic3—34no—
205Dic32—34no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33C2×D412yes—
209C22×C33C2411yescharacteristic
210C2×C3⋊(C3⋊D3)—21no—
211C2×C3⋊(C3⋊D3)—21no—
212C2×C3⋊(C3⋊D3)—21no—
213C2×C3×C3⋊D3—21no—
214C2×C3×C3⋊D3—21no—
215C2×C3×C3⋊D3—21no—
216C2×C3×C3⋊D3—21no—
217C2×C3×C3⋊D3—21no—
218C2×C3×C3⋊D3C2×D412yes—
219C2×C32×D3—21no—
220C2×C32×D3—21no—
221C2×C32×D3—21no—
222C2×C32×D3—21no—
223C2×C32×D3—21no—
224C2×C32×D3—44no—
225C2×C32×D3#4112yescomplemented
226D3×C3⋊D3—44no—
227C33×C4—21no—
228C33×C4—21no—
229C3⋊(C3⋊Dic3)—21no—
230C3⋊(C3⋊Dic3)—21no—
231C3⋊(C3⋊Dic3)—21no—
232C3×C3⋊Dic3—21no—
233C3×C3⋊Dic3C2×D412yes—
234C32×Dic3—21no—
235C32×Dic3—21no—
236C2×C3×#41—91no—
237C22×#67—94no—
238C2×D3×D4—91no—
239C2×#235—34no—
240C2×C3×C22⋊C4—34no—
241#953—94no—
242#947—91no—
243#946—91no—
244#939—91no—
245#939—91no—
246#937—91no—
247#937—91no—
248D4×Dic3—91no—
249#930—94no—
250#930—91no—
251#929—94no—
252#929—91no—
253#929—91no—
254#929—184no—
255C4×#67—94no—
256C4×#67—91no—
257C2×(C2×D3)⋊C4—91no—
258C2×(C2×D3)⋊C4C3⋊D311yescharacteristic, complemented
259#885—94no—
260#884—94no—
261#884—94no—
262#883—94no—
263#882—94no—
264#67⋊C4—94no—
265D3×C22⋊C4—94no—
266#878—94no—
267C23×C32—24no—
268C23×C32—31no—
269C23×C32—31no—
270C23×C32—62no—
271C23×C32—62no—
272C23×C32—121no—
273C23×C32C22×D314yes—
274C23×C32C22×D311yescharacteristic
275C22×C3⋊D3—31no—
276C22×C3⋊D3—34no—
277C22×C3⋊D3—64no—
278C22×C3⋊D3—62no—
279C22×C3⋊D3—62no—
280C22×C3⋊D3—121no—
281C22×C3⋊D3C22×D311yescharacteristic
282C22×C3⋊D3C22×D311yescharacteristic
283C22×C3×D3—28no—
284C22×C3×D3—28no—
285C22×C3×D3—34no—
286C22×C3×D3—34no—
287C22×C3×D3—44no—
288C22×C3×D3C22×D314yes—
289C22×C3×D3C22×D314yes—
290C2×D32—68no—
291C2×D32—68no—
292C2×D32—124no—
293C2×C32×C4—22no—
294C2×C32×C4—24no—
295C2×C32×C4—24no—
296C2×C32×C4—28no—
297C2×C32×C4—31no—
298C2×C32×C4—31no—
299C2×C32×C4—48no—
300C2×C32×C4—121no—
301C2×C32×C4C22×D314yes—
302C2×C32×C4C22×D314yes—
303C2×C32×C4C22×D311yescharacteristic
304C2×C32×C4C22×D311yescharacteristic
305#638—22no—
306#638—62no—
307#638—62no—
308#638—62no—
309#638—62no—
310#638—68no—
311#638—128no—
312#638—121no—
313#638#6714yescomplemented
314C2×C3⋊Dic3—31no—
315C2×C3⋊Dic3—31no—
316C2×C3⋊Dic3—31no—
317C2×C3⋊Dic3—34no—
318C2×C3⋊Dic3—34no—
319C2×C3⋊Dic3—34no—
320C2×C3⋊Dic3—64no—
321C2×C3⋊Dic3—64no—
322C2×C3⋊Dic3—64no—
323C2×C3⋊Dic3—62no—
324C2×C3⋊Dic3C22×D311yescharacteristic
325C2×C3⋊Dic3C22×D311yescharacteristic
326C4⋊(C3⋊D3)—22no—
327C4⋊(C3⋊D3)—121no—
328C4×C3⋊D3—22no—
329C4×C3⋊D3—22no—
330C4×C3⋊D3—121no—
331#634—22no—
332C3×#67—316no—
333C3×#67—68no—
334C2×C3×Dic3—34no—
335C2×C3×Dic3—34no—
336C2×C3×Dic3—44no—
337C2×C3×Dic3C22×D314yes—
338C2×C3×Dic3C22×D314yes—
339C3×D12—68no—
340C3×C4×D3—68no—
341C3×C4×D3—68no—
342C3×Dic6—68no—
343#626—68no—
344#626—124no—
345#625—68no—
346#625—68no—
347#625—124no—
348D3×Dic3—68no—
349D3×Dic3—124no—
350#546—271noSylow
351C2×C33—22no—
352C2×C33C22×D411yescharacteristic
353C2×C33C2×#4111yescharacteristic
354C2×C33H(5,𝔽2)11yescharacteristic
355C3⋊(C3⋊D3)—41no—
356C3×C3⋊D3—22no—
357C3×C3⋊D3—41no—
358C32×D3—22no—
359C32×D3—41no—
360C24×C3—34no—
361C23×D3—94no—
362C23×D3—91no—
363C23×D3C2×C3⋊D311yescharacteristic
364C3×#41—184no—
365C2×C3×Q8—91no—
366C2×C3×D4—91no—
367C2×C3×D4—91no—
368C2×C3×D4—91no—
369C22×C3×C4—24no—
370C22×C3×C4—34no—
371C22×C3×C4—91no—
372C22×C3×C4—91no—
373C22×C3×C4D3214yescomplemented
374C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
375C2×#67—34no—
376C2×#67—34no—
377C2×#67—94no—
378C2×#67—94no—
379C2×#67—94no—
380C2×#67—94no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—91no—
384C2×#67—94no—
385C2×#67—91no—
386C2×#67—91no—
387C2×#67—184no—
388C2×#67—1816no—
389C22×Dic3—94no—
390C22×Dic3—91no—
391C22×Dic3C2×C3⋊D311yescharacteristic, complemented
392D3×D4—184no—
393#235—616no—
394C2×D12—34no—
395C2×D12—91no—
396C2×D12—94no—
397C2×C4×D3—34no—
398C2×C4×D3—34no—
399C2×C4×D3—91no—
400C2×C4×D3—94no—
401C2×Dic6—34no—
402C3×C22⋊C4—34no—
403C3×C22⋊C4—34no—
404C3×C22⋊C4—34no—
405C3×C22⋊C4—34no—
406#217—94no—
407#217—94no—
408#217—94no—
409#217—91no—
410#217—91no—
411#217—91no—
412#217—184no—
413(C2×D3)⋊C4—94no—
414(C2×D3)⋊C4—94no—
415(C2×D3)⋊C4—94no—
416(C2×D3)⋊C4—91no—
417(C2×D3)⋊C4—91no—
418(C2×D3)⋊C4—94no—
419(C2×D3)⋊C4—94no—
420(C2×D3)⋊C4—91no—
421(C2×D3)⋊C4—91no—
422(C2×D3)⋊C4—91no—
423(C2×D3)⋊C4—184no—
424(C2×D3)⋊C4—184no—
425(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
426(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
427(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
428(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
429C4⋊Dic3—94no—
430C4⋊Dic3—91no—
431Dic3⋊C4—94no—
432Dic3⋊C4—94no—
433Dic3⋊C4—94no—
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—184no—
438Dic3⋊C4—184no—
439C4×Dic3—94no—
440C4×Dic3—91no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—24no—
444C22×C32—28no—
445C22×C32—24no—
446C22×C32—24no—
447C22×C32—32no—
448C22×C32—44no—
449C22×C32—44no—
450C22×C32—61no—
451C22×C32—61no—
452C22×C32—61no—
453C22×C32—61no—
454C22×C32—61no—
455C22×C32—124no—
456C22×C32D3×D418yes—
457C22×C32C2×#6712yes—
458C22×C32C23×D314yes—
459C22×C32C23×D311yescharacteristic
460C2×C3⋊D3—21no—
461C2×C3⋊D3—21no—
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—21no—
465C2×C3⋊D3—61no—
466C2×C3⋊D3—61no—
467C2×C3⋊D3—61no—
468C2×C3⋊D3—64no—
469C2×C3⋊D3—64no—
470C2×C3⋊D3—64no—
471C2×C3⋊D3—124no—
472C2×C3⋊D3—124no—
473C2×C3⋊D3—124no—
474C2×C3⋊D3—124no—
475C2×C3⋊D3C2×#6712yes—
476C2×C3×D3—24no—
477C2×C3×D3—24no—
478C2×C3×D3—24no—
479C2×C3×D3—24no—
480C2×C3×D3—24no—
481C2×C3×D3—38no—
482C2×C3×D3—416no—
483C2×C3×D3—64no—
484C2×C3×D3—64no—
485C2×C3×D3—64no—
486C2×C3×D3—64no—
487C2×C3×D3—64no—
488C2×C3×D3#23518yescomplemented
489D32—1216no—
490C32×C4—21no—
491C32×C4—21no—
492C32×C4—24no—
493C32×C4—24no—
494C32×C4—44no—
495C32×C4—44no—
496C32×C4—61no—
497C32×C4—61no—
498C3⋊Dic3—21no—
499C3⋊Dic3—61no—
500C3⋊Dic3—61no—
501C3⋊Dic3—61no—
502C3⋊Dic3—64no—
503C3⋊Dic3—64no—
504C3⋊Dic3—64no—
505C3⋊Dic3—124no—
506C3⋊Dic3—124no—
507C3⋊Dic3—124no—
508C3⋊Dic3C2×#6712yes—
509C3×Dic3—24no—
510C3×Dic3—24no—
511C3×Dic3—38no—
512C3×Dic3—64no—
513C2×#41—91no—
514C22×D4—271no—
515#124—271no—
516#123—271no—
517#123—271no—
518C22⋊Q8—271no—
519#121—271no—
520#121—271no—
521#121—271no—
522#120—271no—
523#120—271no—
524C4×D4—271no—
525C4×D4—271no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—271no—
528C33#54611yescharacteristic, complemented, Sylow
529C23×C3—24no—
530C23×C3—34no—
531C23×C3—34no—
532C23×C3—68no—
533C23×C3—68no—
534C23×C3—91no—
535C23×C3—91no—
536C23×C3—124no—
537C23×C3C2×D3214yes—
538C23×C3C22×C3⋊D311yescharacteristic
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—34no—
542C22×D3—34no—
543C22×D3—41no—
544C22×D3—94no—
545C22×D3—91no—
546C22×D3—184no—
547C22×D3—182no—
548C22×D3—188no—
549C22×D3—188no—
550C22×D3—182no—
551C22×D3—361no—
552C22×D3—364no—
553C22×D3C22×C3⋊D311yescharacteristic
554C22×D3C22×C3⋊D311yescharacteristic
555C3×Q8—182no—
556C3×D4—94no—
557C3×D4—182no—
558C3×D4—182no—
559C2×C3×C4—28no—
560C2×C3×C4—22no—
561C2×C3×C4—24no—
562C2×C3×C4—24no—
563C2×C3×C4—34no—
564C2×C3×C4—34no—
565C2×C3×C4—48no—
566C2×C3×C4—91no—
567C2×C3×C4—91no—
568C2×C3×C4—124no—
569C2×C3×C4—182no—
570C2×C3×C4—182no—
571C2×C3×C4C2×D3214yes—
572C2×C3×C4C2×D3214yes—
573C2×C3×C4C22×C3⋊D311yescharacteristic
574C2×C3×C4C22×C3⋊D311yescharacteristic
575#67—316no—
576#67—68no—
577#67—188no—
578#67—182no—
579#67—188no—
580#67—188no—
581#67—188no—
582#67—182no—
583#67—182no—
584#67—368no—
585#67—361no—
586#67—361no—
587#67—364no—
588C2×Dic3—34no—
589C2×Dic3—34no—
590C2×Dic3—41no—
591C2×Dic3—94no—
592C2×Dic3—94no—
593C2×Dic3—94no—
594C2×Dic3—91no—
595C2×Dic3—91no—
596C2×Dic3—91no—
597C2×Dic3—184no—
598C2×Dic3—184no—
599C2×Dic3—184no—
600C2×Dic3—188no—
601C2×Dic3—361no—
602C2×Dic3C22×C3⋊D311yescharacteristic
603C2×Dic3C22×C3⋊D311yescharacteristic
604D12—68no—
605D12—182no—
606D12—364no—
607C4×D3—68no—
608C4×D3—68no—
609C4×D3—182no—
610C4×D3—364no—
611Dic6—68no—
612C2×C32—22no—
613C2×C32—24no—
614C2×C32—24no—
615C2×C32—24no—
616C2×C32—28no—
617C2×C32—48no—
618C2×C32—62no—
619C2×C32—121no—
620C2×C32C2×#23514yes—
621C2×C32C2×D3×D414yes—
622C2×C32#100414yes—
623C2×C32D3×#4111yescharacteristic
624C2×C32#100911yescharacteristic
625C2×C32C22×#6711yescharacteristic
626C3⋊D3—22no—
627C3⋊D3—41no—
628C3⋊D3—121no—
629C3⋊D3—124no—
630C3⋊D3—244no—
631C3×D3—28no—
632C3×D3—44no—
633C3×D3—68no—
634C3×D3—124no—
635C24—31no—
636C24—271no—
637#41—184no—
638C2×Q8—91no—
639C2×D4—91no—
640C2×D4—91no—
641C2×D4—91no—
642C2×D4—271no—
643C2×D4—271no—
644C2×D4—271no—
645C2×D4—271no—
646C2×D4—271no—
647C2×D4—271no—
648C2×D4—544no—
649C22×C4—31no—
650C22×C4—91no—
651C22×C4—91no—
652C22×C4—271no—
653C22×C4—271no—
654C22×C4D3×C3⋊D311yescharacteristic, complemented
655C4⋊C4—271no—
656C4⋊C4—271no—
657C4⋊C4—271no—
658C4⋊C4—271no—
659C22⋊C4—31no—
660C22⋊C4—31no—
661C22⋊C4—31no—
662C22⋊C4—31no—
663C22⋊C4—271no—
664C22⋊C4—271no—
665C22⋊C4—271no—
666C22⋊C4—271no—
667C22⋊C4—271no—
668C22⋊C4—271no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C42—271no—
672C22×C3—24no—
673C22×C3—24no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—24no—
677C22×C3—28no—
678C22×C3—38no—
679C22×C3—44no—
680C22×C3—44no—
681C22×C3—64no—
682C22×C3—64no—
683C22×C3—64no—
684C22×C3—64no—
685C22×C3—64no—
686C22×C3—92no—
687C22×C3—1216no—
688C22×C3—181no—
689C22×C3—181no—
690C22×C3—181no—
691C22×C3—181no—
692C22×C3—181no—
693C22×C3D3×#6718yes—
694C22×C3D4×C3⋊D312yes—
695C22×C3C22×D3214yes—
696C22×C3C23×C3⋊D311yescharacteristic
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—38no—
703C2×D3—44no—
704C2×D3—64no—
705C2×D3—64no—
706C2×D3—64no—
707C2×D3—64no—
708C2×D3—64no—
709C2×D3—184no—
710C2×D3—184no—
711C2×D3—184no—
712C2×D3—181no—
713C2×D3—181no—
714C2×D3—181no—
715C2×D3—364no—
716C2×D3—364no—
717C2×D3—364no—
718C2×D3—364no—
719C2×D3—3616no—
720C2×D3#382812yescomplemented
721C3×C4—24no—
722C3×C4—24no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—44no—
726C3×C4—44no—
727C3×C4—64no—
728C3×C4—64no—
729C3×C4—92no—
730C3×C4—181no—
731Dic3—21no—
732Dic3—21no—
733Dic3—38no—
734Dic3—64no—
735Dic3—184no—
736Dic3—184no—
737Dic3—184no—
738Dic3—181no—
739Dic3—181no—
740Dic3—181no—
741Dic3—364no—
742Dic3—364no—
743Dic3—364no—
744C32—24no—
745C32#549014yescomplemented
746C32#582911yescharacteristic, complemented
747C23—31no—
748C23—31no—
749C23—62no—
750C23—62no—
751C23—91no—
752C23—91no—
753C23—121no—
754C23—271no—
755C23—542no—
756C23—542no—
757C23—1081no—
758C23C2×D3×C3⋊D311yescharacteristic
759Q8—182no—
760D4—94no—
761D4—182no—
762D4—182no—
763D4—542no—
764D4—542no—
765D4—542no—
766D4—542no—
767D4—1081no—
768D4—1081no—
769C2×C4—22no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—91no—
773C2×C4—91no—
774C2×C4—121no—
775C2×C4—182no—
776C2×C4—182no—
777C2×C4—271no—
778C2×C4—271no—
779C2×C4—271no—
780C2×C4—542no—
781C2×C4—1081no—
782C2×C4C2×D3×C3⋊D311yescharacteristic
783C2×C4C2×D3×C3⋊D311yescharacteristic
784C2×C3—22no—
785C2×C3—28no—
786C2×C3—24no—
787C2×C3—24no—
788C2×C3—24no—
789C2×C3—48no—
790C2×C3—68no—
791C2×C3—124no—
792C2×C3—182no—
793C2×C3—361no—
794C2×C3D3×#23514yes—
795C2×C3#6430714yes—
796C2×C3C2×D3×#6714yes—
797C2×C3C2×#382811yescharacteristic
798C2×C3C2×D4×C3⋊D311yescharacteristic
799C2×C3#6436111yescharacteristic
800D3—22no—
801D3—41no—
802D3—68no—
803D3—124no—
804D3—361no—
805D3—364no—
806D3—724no—
807C22—21no—
808C22—21no—
809C22—32no—
810C22—61no—
811C22—61no—
812C22—61no—
813C22—61no—
814C22—61no—
815C22—92no—
816C22—124no—
817C22—181no—
818C22—181no—
819C22—181no—
820C22—181no—
821C22—181no—
822C22—541no—
823C22—541no—
824C22—541no—
825C22—1084no—
826C22C3⋊D3×#6712yes—
827C22C22×D3×C3⋊D311yescharacteristic
828C4—21no—
829C4—21no—
830C4—61no—
831C4—61no—
832C4—92no—
833C4—181no—
834C4—541no—
835C4—541no—
836C4—541no—
837C3—24no—
838C3#1059506514yescomplemented
839C3#1059596111yescharacteristic, complemented
840C2—22no—
841C2—62no—
842C2—121no—
843C2—182no—
844C2—361no—
845C2—1081no—
846C2D3×#382811yescharacteristic
847C2#1172457911yescharacteristic
848C2C2×C3⋊D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×C4C22
hypercenterC22×C4D3×C3⋊D3
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3828C2semidirect
2. C2×D3×#638C2semidirect
3. #11723970C2semidirect
4. C2×C32×(C2×D3)⋊C4C2semidirect
5. #11723632C2semidirect
6. #11723629C2semidirect
7. Dic3×#638C2semidirect
8. #11723541C2semidirect
9. C3⋊D3×(C2×D3)⋊C4C2semidirect
10. #11723521C2semidirect
11. #11723520C2semidirect
12. #11723519C2semidirect
13. #11723518C2semidirect
14. #11723507C2semidirect
15. #11723487C2semidirect
20. C22×C33×C4C22semidirect
23. C2×C3×#638C22semidirect
25. C2×C3×C4⋊(C3⋊D3)C22semidirect
26. C2×C3×C4×C3⋊D3C22semidirect
27. C2×C3×C4×C3⋊D3C22semidirect
28. C2×C3×#634C22semidirect
29. C22×C32×Dic3C22semidirect
31. C2×#6292C22semidirect
35. C2×#6290C22semidirect
36. C2×Dic3×C3⋊D3C22semidirect
38. #88864C22semidirect
39. #88859C22semidirect
40. #88859C22semidirect
41. #88857C22semidirect
42. #88857C22semidirect
45. C32×(C2×D3)⋊C4C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. #88807C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
49. #88804C22semidirect
50. #88803C22semidirect
51. #88803C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
56. C2×#3828D3semidirect
74. C2×C3×(C2×D3)⋊C4D3semidirect
106. C3×#638D4semidirect
131. C22×C32×C4C2×D3semidirect
132. C22×C32×C4C2×D3semidirect
142. C2×#638C2×D3semidirect
146. C2×C4⋊(C3⋊D3)C2×D3semidirect
148. C2×C4×C3⋊D3C2×D3semidirect
149. C2×C4×C3⋊D3C2×D3semidirect
150. C2×#634C2×D3semidirect
153. C22×C3×Dic3C2×D3semidirect
196. C3×(C2×D3)⋊C4C2×D3semidirect
197. C3×(C2×D3)⋊C4C2×D3semidirect
225. C2×C32×D3#41semidirect
258. C2×(C2×D3)⋊C4C3⋊D3semidirect
313. #638#67semidirect
373. C22×C3×C4D32semidirect
374. C22×C3×C4C2×C3⋊D3semidirect
391. C22×Dic3C2×C3⋊D3semidirect
427. (C2×D3)⋊C4C2×C3⋊D3semidirect
428. (C2×D3)⋊C4C2×C3⋊D3semidirect
488. C2×C3×D3#235semidirect
528. C33#546semidirect
654. C22×C4D3×C3⋊D3semidirect
720. C2×D3#3828semidirect
745. C32#5490semidirect
746. C32#5829semidirect
838. C3#10595065semidirect
839. C3#10595961semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38282
C2×D3×#6382
#117239702
C2×C32×(C2×D3)⋊C42
#117236322
#117236292
Dic3×#6382
#117235412
C3⋊D3×(C2×D3)⋊C42
#117235212
#117235202
#117235192
#117235182
#117235072
#117234872
#105959613
#105950653