Finite Group Databasebeta

← #13175940

Subgroups — #13175940

Order 1728.

2380 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#638C211yesmaximal, characteristic, complemented
2C2×#89028C211yesmaximal, characteristic, complemented
3#11723922C211yesmaximal, characteristic, complemented
4C3×#64095C211yesmaximal, characteristic, complemented
5C32×#882C211yesmaximal, characteristic, complemented
6#11723637C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
8#11723540C211yesmaximal, characteristic, complemented
9#11723539C211yesmaximal, characteristic, complemented
10#11723531C211yesmaximal, characteristic, complemented
11#11723530C211yesmaximal, characteristic, complemented
12#11723500C211yesmaximal, characteristic, complemented
13#11723499C211yesmaximal, characteristic, complemented
14#11723474C211yesmaximal, characteristic, complemented
15#11723422C211yesmaximal, characteristic, complemented
16#10596062—31nomaximal
17#10594294—34nomaximal
18C23×C32×D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic
24C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic, complemented
26C2×C32×D12C2211yescharacteristic
27C2×C32×D12C2211yescharacteristic, complemented
28D3×#638—24no—
29C2×#6293C2211yescharacteristic, complemented
30C2×#6291C2211yescharacteristic
31C2×#6291C2211yescharacteristic, complemented
32C2×#6290C2211yescharacteristic
33C2×#6290C2211yescharacteristic, complemented
34C2×#6289C2211yescharacteristic, complemented
35#89028—24no—
36C2×D3×C3⋊Dic3C2211yescharacteristic
37C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
38C33×C22⋊C4C2211yescharacteristic, complemented
39#88859C2211yescharacteristic, complemented
40#88857C2211yescharacteristic, complemented
41C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
42C3×#3752C2211yescharacteristic, complemented
43C3×#3752C2211yescharacteristic, complemented
44C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic
47C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
48#88806C2211yescharacteristic, complemented
49#88803C2211yescharacteristic, complemented
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55C22×#638—31no—
56C2×#3830—31no—
57C2×D3×#67—34no—
58C2×#3804—34no—
59C32×#120—31no—
60C2×#3757—31no—
61#64148—31no—
62#64148—31no—
63#64147—31no—
64#64146—31no—
65D4×C3⋊Dic3—31no—
66#64095D311yescharacteristic, complemented
67#64094—31no—
68#64092—31no—
69#64090—31no—
70#64090—34no—
71#64090—64no—
72C22⋊C4×C3⋊D3—31no—
73#64087—31no—
74C3×#886—34no—
75C3×#882D314yescomplemented
76#63980—34no—
77C2×(C2×D3)⋊Dic3—34no—
78#63922—34no—
79#63921—34no—
80#63916—34no—
81#63915—34no—
82#63899—34no—
83#63898—34no—
84#63885—34no—
85#63854—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3×C3⋊D3C2311yescharacteristic
89C22×C32×D3—22no—
90C22×C32×D3—22no—
91C22×C32×D3—41no—
92C22×C32×D3C2311yescharacteristic
93C22×C32×D3C2311yescharacteristic
94C22×C32×D3C2311yescharacteristic
95C2×D3×C3⋊D3—22no—
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3—41no—
98C2×C33×C4C2311yescharacteristic
99C2×C33×C4C2311yescharacteristic
100#6312D414yescomplemented
101C2×C3⋊(C3⋊Dic3)—41no—
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C4×C3⋊(C3⋊D3)—41no—
106C3×#638—22no—
107C2×C3×C3⋊Dic3—22no—
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C32×#67—22no—
112C2×C32×Dic3C2311yescharacteristic
113C32×D12—22no—
114C32×D12—41no—
115#6293—22no—
116#6291—22no—
117#6291—22no—
118#6290—22no—
119#6290—41no—
120#6289—22no—
121D3×C3⋊Dic3—22no—
122D3×C3⋊Dic3—22no—
123#5654—91no—
124#5591—94no—
125C24×C32—31no—
126C23×C3⋊D3—31no—
127C23×C3×D3C2×D314yes—
128C22×D32—34no—
129C2×C32×D4—31no—
130C2×C32×D4—31no—
131C2×C32×D4—31no—
132C2×#638—31no—
133C2×#638—34no—
134C2×#638—31no—
135C2×#638—31no—
136C2×#638—31no—
137C2×#638—31no—
138C2×#638—64no—
139C2×#638—64no—
140C2×#638C2×D311yescharacteristic
141C22×C3⋊Dic3—31no—
142C22×C3⋊Dic3—34no—
143C22×C3⋊Dic3—31no—
144C22×C3⋊Dic3—31no—
145C22×C3⋊Dic3—64no—
146C22×C3⋊Dic3C2×D311yescharacteristic, complemented
147#3830—64no—
148C2×C4×C3⋊D3—31no—
149C2×C4×C3⋊D3—31no—
150C2×C4×C3⋊D3—34no—
151C2×C4×C3⋊D3—64no—
152C2×#634—31no—
153C2×C3×#67—34no—
154C2×C3×#67C2×D314yescomplemented
155C22×C3×Dic3—34no—
156C2×C3×D12C2×D314yes—
157C2×C3×D12C2×D314yescomplemented
158D3×#67—616no—
159C2×#627—34no—
160C2×#626—34no—
161C2×#626—34no—
162C2×#625—34no—
163C2×#625—34no—
164C2×#624—34no—
165#3804—616no—
166C2×D3×Dic3—34no—
167C2×D3×Dic3—34no—
168C32×C22⋊C4—24no—
169C32×C22⋊C4—31no—
170C32×C22⋊C4—31no—
171C32×C22⋊C4C2×D314yescomplemented
172C32×C22⋊C4C2×D311yescharacteristic, complemented
173#3757—31no—
174#3757—31no—
175#3757—31no—
176#3757—31no—
177#3757—31no—
178#3752—31no—
179#3752—31no—
180#3752—34no—
181#3752—64no—
182#3752C2×D311yescharacteristic, complemented
183#3752C2×D311yescharacteristic, complemented
184C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
185C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
186#3750—31no—
187#3750—34no—
188#3750—31no—
189#3750—64no—
190C4×C3⋊Dic3—31no—
191C4×C3⋊Dic3—34no—
192C4×C3⋊Dic3—64no—
193C3×(C2×D3)⋊C4—34no—
194C3×(C2×D3)⋊C4—34no—
195C3×(C2×D3)⋊C4C2×D314yes—
196C3×(C2×D3)⋊C4C2×D314yescomplemented
197C3×C4⋊Dic3—34no—
198C3×C4⋊Dic3—34no—
199#3724—34no—
200(C2×D3)⋊Dic3—34no—
201(C2×D3)⋊Dic3—34no—
202(C2×D3)⋊Dic3—34no—
203(C2×D3)⋊Dic3—34no—
204(C2×D3)⋊Dic3—34no—
205(C2×D3)⋊Dic3—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)C2×D412yes—
213C2×C3×C3⋊D3—21no—
214C2×C3×C3⋊D3—21no—
215C2×C3×C3⋊D3—21no—
216C2×C32×D3—21no—
217C2×C32×D3—21no—
218C2×C32×D3—21no—
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)C2×D412yes—
232C3×C3⋊Dic3—21no—
233C3×C3⋊Dic3—21no—
234C3×C3⋊Dic3—21no—
235C32×Dic3—21no—
236C22×#67—94no—
237C2×#237—94no—
238C2×D3×D4—91no—
239C2×#235—91no—
240C3×#123—91no—
241C3×#120—34no—
242C2×#217—94no—
243#939—94no—
244#939—94no—
245#939—91no—
246#938—94no—
247#937—94no—
248D4×Dic3—94no—
249C2×(C2×D3)⋊C4—91no—
250#896—91no—
251#895—91no—
252#894—91no—
253#893—91no—
254#886—34no—
255#885—94no—
256#885—91no—
257#884—91no—
258#883—94no—
259#882—91no—
260#882C3⋊D311yescharacteristic, complemented
261#67⋊C4—94no—
262#67⋊C4—91no—
263#67⋊C4—184no—
264D3×C22⋊C4—94no—
265D3×C22⋊C4—91no—
266#878—94no—
267C23×C32—24no—
268C23×C32—31no—
269C23×C32—31no—
270C23×C32—31no—
271C23×C32—62no—
272C23×C32—62no—
273C23×C32—121no—
274C23×C32C22×D314yes—
275C23×C32C22×D311yescharacteristic
276C22×C3⋊D3—31no—
277C22×C3⋊D3—34no—
278C22×C3⋊D3—64no—
279C22×C3⋊D3—62no—
280C22×C3⋊D3—62no—
281C22×C3⋊D3—121no—
282C22×C3⋊D3C22×D311yescharacteristic
283C22×C3×D3—28no—
284C22×C3×D3—28no—
285C22×C3×D3—34no—
286C22×C3×D3—44no—
287C22×C3×D3C22×D314yes—
288C22×C3×D3C22×D314yes—
289C22×C3×D3C22×D314yes—
290C2×D32—68no—
291C2×D32—68no—
292C2×D32—124no—
293C32×D4—62no—
294C32×D4—62no—
295C32×D4—121no—
296C2×C32×C4—24no—
297C2×C32×C4—24no—
298C2×C32×C4—31no—
299C2×C32×C4C22×D314yes—
300C2×C32×C4C22×D314yes—
301C2×C32×C4C22×D311yescharacteristic
302C2×C32×C4C22×D311yescharacteristic
303#638—22no—
304#638—34no—
305#638—316no—
306#638—616no—
307#638—62no—
308#638—62no—
309#638—62no—
310#638—121no—
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⋊Dic3—62no—
323C2×C3⋊Dic3—121no—
324C2×C3⋊Dic3—124no—
325C2×C3⋊Dic3—128no—
326C2×C3⋊Dic3C22×D311yescharacteristic
327C2×C3⋊Dic3C22×D311yescharacteristic
328C2×C3⋊Dic3C22×D311yescharacteristic
329C4×C3⋊D3—62no—
330C4×C3⋊D3—121no—
331C4×C3⋊D3—124no—
332C4×C3⋊D3—128no—
333#634—62no—
334C3×#67—28no—
335C3×#67—68no—
336C2×C3×Dic3—34no—
337C2×C3×Dic3—34no—
338C2×C3×Dic3—34no—
339C2×C3×Dic3—68no—
340C2×C3×Dic3C22×D314yes—
341C3×D12—28no—
342C3×D12—44no—
343#627—68no—
344#626—68no—
345#626—68no—
346#625—68no—
347#625—124no—
348#624—68no—
349D3×Dic3—68no—
350D3×Dic3—68no—
351#546—271noSylow
352C2×C33—22no—
353C2×C33C22×D411yescharacteristic
354C2×C33C2×#4111yescharacteristic
355C2×C33H(5,𝔽2)11yescharacteristic
356C3⋊(C3⋊D3)—22no—
357C3×C3⋊D3—41no—
358C32×D3—22no—
359C32×D3—41no—
360C32×D3—41no—
361C24×C3—34no—
362C23×D3—94no—
363C23×D3—91no—
364C23×D3C2×C3⋊D311yescharacteristic
365C2×C3×D4—34no—
366C2×C3×D4—34no—
367C2×C3×D4—34no—
368C2×C3×D4—91no—
369C22×C3×C4—91no—
370C2×#67—34no—
371C2×#67—94no—
372C2×#67—94no—
373C2×#67—94no—
374C2×#67—91no—
375C2×#67—94no—
376C2×#67—91no—
377C2×#67—94no—
378C2×#67—91no—
379C2×#67—184no—
380C2×#67—1816no—
381C2×#67C2×C3⋊D311yescharacteristic, complemented
382C22×Dic3—34no—
383C22×Dic3—94no—
384C22×Dic3—94no—
385C22×Dic3—94no—
386C22×Dic3—91no—
387C22×Dic3—184no—
388#237—1816no—
389D3×D4—184no—
390#235—184no—
391C2×D12—91no—
392C2×D12—91no—
393C2×D12C2×C3⋊D311yescharacteristic
394C2×D12C2×C3⋊D311yescharacteristic, complemented
395C2×C4×D3—94no—
396C2×C4×D3—91no—
397C2×C4×D3—91no—
398C2×C4×D3—91no—
399C2×C4×D3—94no—
400C2×C4×D3—91no—
401C2×C4×D3—184no—
402C2×Dic6—94no—
403C2×Dic6—91no—
404C3×C4⋊C4—91no—
405C3×C4⋊C4—91no—
406C3×C22⋊C4—24no—
407C3×C22⋊C4—34no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—91no—
410C3×C22⋊C4—91no—
411C3×C22⋊C4D3214yescomplemented
412C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
413#217—94no—
414#217—94no—
415#217—94no—
416#217—94no—
417#217—94no—
418#217—91no—
419(C2×D3)⋊C4—34no—
420(C2×D3)⋊C4—34no—
421(C2×D3)⋊C4—94no—
422(C2×D3)⋊C4—91no—
423(C2×D3)⋊C4—91no—
424(C2×D3)⋊C4—91no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—94no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—184no—
430(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
431(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
432C4⋊Dic3—34no—
433C4⋊Dic3—34no—
434Dic3⋊C4—94no—
435Dic3⋊C4—94no—
436Dic3⋊C4—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—184no—
439C4×Dic3—94no—
440C4×Dic3—91no—
441C4×Dic3—184no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32—24no—
445C22×C32—28no—
446C22×C32—24no—
447C22×C32—24no—
448C22×C32—32no—
449C22×C32—44no—
450C22×C32—44no—
451C22×C32—61no—
452C22×C32—61no—
453C22×C32—61no—
454C22×C32—61no—
455C22×C32—61no—
456C22×C32—61no—
457C22×C32—61no—
458C22×C32—61no—
459C22×C32—124no—
460C22×C32D3×D418yes—
461C22×C32D3×D412yes—
462C22×C32C23×D314yes—
463C22×C32C23×D311yescharacteristic
464C2×C3⋊D3—21no—
465C2×C3⋊D3—21no—
466C2×C3⋊D3—21no—
467C2×C3⋊D3—32no—
468C2×C3⋊D3—38no—
469C2×C3⋊D3—68no—
470C2×C3⋊D3—61no—
471C2×C3⋊D3—61no—
472C2×C3⋊D3—64no—
473C2×C3⋊D3—64no—
474C2×C3⋊D3—124no—
475C2×C3⋊D3—124no—
476C2×C3⋊D3—124no—
477C2×C3×D3—24no—
478C2×C3×D3—24no—
479C2×C3×D3—24no—
480C2×C3×D3—24no—
481C2×C3×D3—24no—
482C2×C3×D3—24no—
483C2×C3×D3—24no—
484C2×C3×D3—24no—
485C2×C3×D3—416no—
486C2×C3×D3—64no—
487C2×C3×D3—64no—
488C2×C3×D3—64no—
489C2×C3×D3#23718yescomplemented
490D32—1216no—
491C32×C4—21no—
492C32×C4—21no—
493C32×C4—24no—
494C32×C4—24no—
495C32×C4—44no—
496C32×C4—44no—
497C32×C4—61no—
498C3⋊Dic3—21no—
499C3⋊Dic3—21no—
500C3⋊Dic3—21no—
501C3⋊Dic3—32no—
502C3⋊Dic3—38no—
503C3⋊Dic3—68no—
504C3⋊Dic3—68no—
505C3⋊Dic3—64no—
506C3⋊Dic3—61no—
507C3⋊Dic3—61no—
508C3⋊Dic3—64no—
509C3⋊Dic3—124no—
510C3×Dic3—24no—
511C3×Dic3—64no—
512C3×Dic3—64no—
513C3×Dic3—64no—
514C2×#41—271no—
515C22×D4—271no—
516#124—271no—
517#123—91no—
518#123—271no—
519C22⋊Q8—271no—
520#121—271no—
521#121—271no—
522#121—271no—
523#120—31no—
524#120—271no—
525C4×D4—271no—
526C4×D4—271no—
527C2×C22⋊C4—271no—
528C2×C22⋊C4—271no—
529C33#54611yescharacteristic, complemented, Sylow
530C23×C3—24no—
531C23×C3—34no—
532C23×C3—34no—
533C23×C3—34no—
534C23×C3—68no—
535C23×C3—68no—
536C23×C3—91no—
537C23×C3—124no—
538C23×C3C2×D3214yes—
539C23×C3C22×C3⋊D311yescharacteristic
540C22×D3—22no—
541C22×D3—22no—
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
555C22×D3C22×C3⋊D311yescharacteristic
556C3×D4—68no—
557C3×D4—68no—
558C3×D4—124no—
559C3×D4—182no—
560C2×C3×C4—24no—
561C2×C3×C4—24no—
562C2×C3×C4—34no—
563C2×C3×C4—91no—
564C2×C3×C4—91no—
565C2×C3×C4—91no—
566C2×C3×C4—182no—
567C2×C3×C4C2×D3214yes—
568C2×C3×C4C2×D3214yes—
569C2×C3×C4C22×C3⋊D311yescharacteristic
570C2×C3×C4C22×C3⋊D311yescharacteristic
571#67—22no—
572#67—68no—
573#67—916no—
574#67—94no—
575#67—1816no—
576#67—188no—
577#67—188no—
578#67—182no—
579#67—188no—
580#67—361no—
581#67—364no—
582C2×Dic3—34no—
583C2×Dic3—34no—
584C2×Dic3—34no—
585C2×Dic3—68no—
586C2×Dic3—94no—
587C2×Dic3—91no—
588C2×Dic3—94no—
589C2×Dic3—94no—
590C2×Dic3—91no—
591C2×Dic3—91no—
592C2×Dic3—184no—
593C2×Dic3—184no—
594C2×Dic3—184no—
595C2×Dic3—188no—
596C2×Dic3—188no—
597C2×Dic3—364no—
598C2×Dic3—361no—
599C2×Dic3—368no—
600C2×Dic3C22×C3⋊D311yescharacteristic
601D12—22no—
602D12—41no—
603D12—182no—
604D12—182no—
605C4×D3—182no—
606C4×D3—188no—
607C4×D3—182no—
608C4×D3—182no—
609C4×D3—364no—
610C4×D3—361no—
611C4×D3—368no—
612Dic6—182no—
613Dic6—188no—
614C2×C32—22no—
615C2×C32—24no—
616C2×C32—24no—
617C2×C32—24no—
618C2×C32—28no—
619C2×C32—48no—
620C2×C32—62no—
621C2×C32—121no—
622C2×C32—121no—
623C2×C32C2×D3×D414yes—
624C2×C32C2×D3×D411yescharacteristic
625C2×C32C2×#23714yes—
626C2×C32#100414yes—
627C2×C32D3×#4111yescharacteristic
628C2×C32#100911yescharacteristic
629C3⋊D3—41no—
630C3⋊D3—62no—
631C3⋊D3—68no—
632C3⋊D3—128no—
633C3×D3—28no—
634C3×D3—44no—
635C3×D3—44no—
636C3×D3—124no—
637C24—31no—
638C24—271no—
639#41—544no—
640C2×Q8—271no—
641C2×D4—31no—
642C2×D4—31no—
643C2×D4—31no—
644C2×D4—91no—
645C2×D4—271no—
646C2×D4—271no—
647C2×D4—271no—
648C2×D4—271no—
649C2×D4—271no—
650C2×D4—544no—
651C22×C4—91no—
652C22×C4—271no—
653C22×C4—271no—
654C22×C4—271no—
655C22×C4—271no—
656C22×C4—271no—
657C4⋊C4—91no—
658C4⋊C4—91no—
659C4⋊C4—271no—
660C4⋊C4—271no—
661C22⋊C4—31no—
662C22⋊C4—31no—
663C22⋊C4—91no—
664C22⋊C4—91no—
665C22⋊C4—271no—
666C22⋊C4—271no—
667C22⋊C4—271no—
668C22⋊C4—271no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C22⋊C4—271no—
672C22⋊C4D3×C3⋊D311yescharacteristic, complemented
673C42—271no—
674C22×C3—24no—
675C22×C3—24no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—24no—
679C22×C3—28no—
680C22×C3—38no—
681C22×C3—44no—
682C22×C3—44no—
683C22×C3—64no—
684C22×C3—64no—
685C22×C3—64no—
686C22×C3—64no—
687C22×C3—64no—
688C22×C3—64no—
689C22×C3—64no—
690C22×C3—64no—
691C22×C3—1216no—
692C22×C3—181no—
693C22×C3—181no—
694C22×C3—181no—
695C22×C3#380218yes—
696C22×C3D4×C3⋊D312yes—
697C22×C3C22×D3214yes—
698C22×C3C23×C3⋊D311yescharacteristic
699C2×D3—21no—
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—44no—
708C2×D3—64no—
709C2×D3—64no—
710C2×D3—64no—
711C2×D3—98no—
712C2×D3—92no—
713C2×D3—188no—
714C2×D3—184no—
715C2×D3—184no—
716C2×D3—181no—
717C2×D3—181no—
718C2×D3—364no—
719C2×D3—364no—
720C2×D3—364no—
721C2×D3—3616no—
722C2×D3#383012yescomplemented
723C3×C4—24no—
724C3×C4—24no—
725C3×C4—21no—
726C3×C4—21no—
727C3×C4—44no—
728C3×C4—44no—
729C3×C4—64no—
730C3×C4—181no—
731C3×C4—181no—
732C3×C4—181no—
733Dic3—21no—
734Dic3—64no—
735Dic3—64no—
736Dic3—64no—
737Dic3—98no—
738Dic3—92no—
739Dic3—188no—
740Dic3—188no—
741Dic3—184no—
742Dic3—184no—
743Dic3—181no—
744Dic3—181no—
745Dic3—364no—
746C32—24no—
747C32#559114yescomplemented
748C32#565411yescharacteristic, complemented
749C23—31no—
750C23—31no—
751C23—31no—
752C23—62no—
753C23—62no—
754C23—91no—
755C23—121no—
756C23—271no—
757C23—542no—
758C23—542no—
759C23—1081no—
760C23C2×D3×C3⋊D311yescharacteristic
761Q8—542no—
762D4—62no—
763D4—62no—
764D4—121no—
765D4—182no—
766D4—274no—
767D4—542no—
768D4—542no—
769D4—542no—
770D4—1081no—
771C2×C4—31no—
772C2×C4—91no—
773C2×C4—91no—
774C2×C4—91no—
775C2×C4—182no—
776C2×C4—271no—
777C2×C4—271no—
778C2×C4—271no—
779C2×C4—542no—
780C2×C4—542no—
781C2×C4—542no—
782C2×C4—1081no—
783C2×C4—1081no—
784C2×C4C2×D3×C3⋊D311yescharacteristic
785C2×C4C2×D3×C3⋊D311yescharacteristic
786C2×C3—22no—
787C2×C3—28no—
788C2×C3—24no—
789C2×C3—24no—
790C2×C3—24no—
791C2×C3—48no—
792C2×C3—68no—
793C2×C3—124no—
794C2×C3—124no—
795C2×C3—361no—
796C2×C3C2×#380214yes—
797C2×C3D3×#23714yes—
798C2×C3#6431414yes—
799C2×C3C2×D4×C3⋊D311yescharacteristic
800C2×C3C2×#383011yescharacteristic
801C2×C3#6436111yescharacteristic
802D3—22no—
803D3—41no—
804D3—41no—
805D3—124no—
806D3—182no—
807D3—188no—
808D3—368no—
809C22—21no—
810C22—21no—
811C22—32no—
812C22—61no—
813C22—61no—
814C22—61no—
815C22—61no—
816C22—61no—
817C22—61no—
818C22—61no—
819C22—61no—
820C22—124no—
821C22—181no—
822C22—181no—
823C22—181no—
824C22—272no—
825C22—541no—
826C22—541no—
827C22—1084no—
828C22#8902612yes—
829C22C22×D3×C3⋊D311yescharacteristic
830C4—21no—
831C4—21no—
832C4—61no—
833C4—181no—
834C4—181no—
835C4—181no—
836C4—272no—
837C4—541no—
838C4—541no—
839C3—24no—
840C3#1059429414yescomplemented
841C3#1059606211yescharacteristic, complemented
842C2—22no—
843C2—62no—
844C2—121no—
845C2—121no—
846C2—361no—
847C2—542no—
848C2C2×#8902611yescharacteristic
849C2D3×#383011yescharacteristic
850C2#1172458811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊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×D3×#638C2semidirect
2. C2×#89028C2semidirect
3. #11723922C2semidirect
4. C3×#64095C2semidirect
5. C32×#882C2semidirect
6. #11723637C2semidirect
7. C2×(C2×D3)⋊(C3⋊Dic3)C2semidirect
8. #11723540C2semidirect
9. #11723539C2semidirect
10. #11723531C2semidirect
11. #11723530C2semidirect
12. #11723500C2semidirect
13. #11723499C2semidirect
14. #11723474C2semidirect
15. #11723422C2semidirect
21. C22×C3⋊(C3⋊Dic3)C22semidirect
22. C2×C4×C3⋊(C3⋊D3)C22semidirect
24. C22×C3×C3⋊Dic3C22semidirect
25. C2×C32×#67C22semidirect
27. C2×C32×D12C22semidirect
29. C2×#6293C22semidirect
31. C2×#6291C22semidirect
33. C2×#6290C22semidirect
34. C2×#6289C22semidirect
37. C2×D3×C3⋊Dic3C22semidirect
38. C33×C22⋊C4C22semidirect
39. #88859C22semidirect
40. #88857C22semidirect
41. C4×C3⋊(C3⋊Dic3)C22semidirect
42. C3×#3752C22semidirect
43. C3×#3752C22semidirect
44. C3×C4⋊(C3⋊Dic3)C22semidirect
45. C3×C4⋊(C3⋊Dic3)C22semidirect
47. C32×(C2×D3)⋊C4C22semidirect
48. #88806C22semidirect
49. #88803C22semidirect
52. (C2×D3)⋊(C3⋊Dic3)C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
66. #64095D3semidirect
75. C3×#882D3semidirect
100. #6312D4semidirect
146. C22×C3⋊Dic3C2×D3semidirect
154. C2×C3×#67C2×D3semidirect
157. C2×C3×D12C2×D3semidirect
171. C32×C22⋊C4C2×D3semidirect
172. C32×C22⋊C4C2×D3semidirect
182. #3752C2×D3semidirect
183. #3752C2×D3semidirect
184. C4⋊(C3⋊Dic3)C2×D3semidirect
185. C4⋊(C3⋊Dic3)C2×D3semidirect
196. C3×(C2×D3)⋊C4C2×D3semidirect
225. C2×C32×D3#41semidirect
260. #882C3⋊D3semidirect
381. C2×#67C2×C3⋊D3semidirect
394. C2×D12C2×C3⋊D3semidirect
411. C3×C22⋊C4D32semidirect
412. C3×C22⋊C4C2×C3⋊D3semidirect
431. (C2×D3)⋊C4C2×C3⋊D3semidirect
489. C2×C3×D3#237semidirect
529. C33#546semidirect
672. C22⋊C4D3×C3⋊D3semidirect
722. C2×D3#3830semidirect
747. C32#5591semidirect
748. C32#5654semidirect
840. C3#10594294semidirect
841. C3#10596062semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6382
C2×#890282
#117239222
C3×#640952
C32×#8822
#117236372
C2×(C2×D3)⋊(C3⋊Dic3)2
#117235402
#117235392
#117235312
#117235302
#117235002
#117234992
#117234742
#117234222
#105960623
#105942943