Finite Group Databasebeta

← #13177507

Subgroups — #13177507

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
1C22×#6290C211yesmaximal, characteristic, complemented
2C2×#89029C211yesmaximal, characteristic, complemented
3D4×C3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
4C3×#64146C211yesmaximal, characteristic, complemented
5C32×#937C211yesmaximal, characteristic, complemented
6#11723642C211yesmaximal, characteristic, complemented
7#11723637C211yesmaximal, characteristic, complemented
8#11723631C211yesmaximal, characteristic, complemented
9C3⋊D3×#217C211yesmaximal, characteristic, complemented
10#11723615C211yesmaximal, characteristic, complemented
11D3×#3757C211yesmaximal, characteristic, complemented
12#11723530C211yesmaximal, characteristic, complemented
13#11723523C211yesmaximal, characteristic, complemented
14#11723508C211yesmaximal, characteristic, complemented
15#11723480C211yesmaximal, characteristic, complemented
16#10596062—31nomaximal
17#10595225—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic
19C23×C32×D3C2211yescharacteristic
20C2×C33×D4C2211yescharacteristic
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
22C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C3×#638C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic, complemented
26C2×C32×#67C2211yescharacteristic, complemented
27C2×#6293C2211yescharacteristic, complemented
28C2×#6290—24no—
29C2×#6290C2211yescharacteristic
30C2×#6290C2211yescharacteristic
31C2×#6290C2211yescharacteristic
32C2×#6290C2211yescharacteristic
33C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
34C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
35#89029—24no—
36C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
37C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
38#88864C2211yescharacteristic
39#88864C2211yescharacteristic, complemented
40C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
41C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
42C3×#3757C2211yescharacteristic
43C3×#3752C2211yescharacteristic, complemented
44C3×#3752C2211yescharacteristic, complemented
45C32×#217C2211yescharacteristic
46C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
48#88807C2211yescharacteristic, complemented
49#88806C2211yescharacteristic, complemented
50Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51#88803C2211yescharacteristic, complemented
52#88803C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55C22×#638—31no—
56C2×#3830—31no—
57C22×#625—34no—
58C2×#3805—34no—
59C32×#120—31no—
60C2×#3757—31no—
61#64148—31no—
62#64148—31no—
63#64147—31no—
64#64146D311yescharacteristic, complemented
65D4×C3⋊Dic3—31no—
66D4×C3⋊Dic3—34no—
67D4×C3⋊Dic3—64no—
68#64095—31no—
69#64094—31no—
70#64092—31no—
71#64090—31no—
72C22⋊C4×C3⋊D3—31no—
73#64087—31no—
74C3×#937—34no—
75C3×#937D314yescomplemented
76#63982—34no—
77#63980—34no—
78#63970—34no—
79#63970—34no—
80D3×#217—34no—
81D3×#217—34no—
82#63915—34no—
83#63902—34no—
84#63891—34no—
85#63891—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3×C3⋊D3—22no—
89C22×C3×C3⋊D3—22no—
90C22×C3×C3⋊D3—41no—
91C22×C3×C3⋊D3C2311yescharacteristic
92C22×C3×C3⋊D3C2311yescharacteristic
93C22×C32×D3—22no—
94C22×C32×D3—22no—
95C22×C32×D3—41no—
96C22×C32×D3C2311yescharacteristic
97C22×C32×D3C2311yescharacteristic
98C33×D4—22no—
99C2×C33×C4C2311yescharacteristic
100C2×C3⋊(C3⋊Dic3)—22no—
101C2×C3⋊(C3⋊Dic3)—22no—
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C3×#638—22no—
107C3×#638—41no—
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C32×#67—22no—
111C32×#67—41no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114#6293—22no—
115#6290—22no—
116#6290—22no—
117#6290—22no—
118#6290D414yescomplemented
119Dic3×C3⋊D3—22no—
120Dic3×C3⋊D3—41no—
121D3×C3⋊Dic3—22no—
122D3×C3⋊Dic3—41no—
123#5591—94no—
124#5591—91no—
125C24×C32—31no—
126C23×C3⋊D3C2×D311yescharacteristic
127C23×C3×D3—34no—
128C23×C3×D3C2×D314yes—
129C2×C32×D4—24no—
130C2×C32×D4—31no—
131C2×C32×D4—31no—
132C2×C32×D4C2×D314yes—
133C2×C32×D4C2×D311yescharacteristic
134C2×#638—31no—
135C2×#638—31no—
136C2×#638—31no—
137C2×#638—31no—
138C2×#638—64no—
139C2×#638C2×D311yescharacteristic, complemented
140C2×#638C2×D311yescharacteristic, complemented
141C22×C3⋊Dic3—31no—
142C22×C3⋊Dic3—31no—
143C22×C3⋊Dic3—34no—
144C22×C3⋊Dic3—34no—
145C22×C3⋊Dic3—31no—
146C22×C3⋊Dic3—31no—
147C22×C3⋊Dic3—64no—
148C22×C3⋊Dic3—64no—
149#3830—64no—
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3—31no—
152C2×#634—31no—
153C2×C3×#67—34no—
154C2×C3×#67—34no—
155C2×C3×#67C2×D314yescomplemented
156C2×C3×#67C2×D314yescomplemented
157C2×#627—34no—
158C2×#625—34no—
159C2×#625—34no—
160C2×#625—34no—
161C2×#625—34no—
162C2×#625—616no—
163#3805—616no—
164C2×D3×Dic3—34no—
165C2×D3×Dic3—34no—
166C2×D3×Dic3—34no—
167C2×D3×Dic3—34no—
168C32×C22⋊C4—31no—
169C32×C22⋊C4—31no—
170C32×C22⋊C4—31no—
171#3757—31no—
172#3757—31no—
173#3757—34no—
174#3757—34no—
175#3757—31no—
176#3757—31no—
177#3757—64no—
178#3757—64no—
179#3757C2×D311yescharacteristic
180#3752—31no—
181#3752—31no—
182#3752C2×D311yescharacteristic, complemented
183#3752C2×D311yescharacteristic, complemented
184C4⋊(C3⋊Dic3)—31no—
185C4⋊(C3⋊Dic3)—34no—
186C4⋊(C3⋊Dic3)—31no—
187C4⋊(C3⋊Dic3)—64no—
188#3750—31no—
189#3750—31no—
190C4×C3⋊Dic3—31no—
191C4×C3⋊Dic3—34no—
192C4×C3⋊Dic3—64no—
193C3×#217—34no—
194C3×#217C2×D314yes—
195C3×(C2×D3)⋊C4—34no—
196C3×(C2×D3)⋊C4—34no—
197C3×(C2×D3)⋊C4C2×D314yescomplemented
198C3×(C2×D3)⋊C4C2×D314yescomplemented
199#3724—34no—
200Dic3⋊Dic3—34no—
201Dic3⋊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×C33—21no—
209C22×C33—21no—
210C22×C33—21no—
211C22×C33#4112yescomplemented
212C22×C33C2411yescharacteristic
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⋊D3—44no—
219C2×C3×C3⋊D3C2×D412yes—
220C2×C32×D3—21no—
221C2×C32×D3—21no—
222C2×C32×D3—21no—
223C2×C32×D3—21no—
224C2×C32×D3—21no—
225C2×C32×D3—44no—
226C2×C32×D3C2×D412yes—
227C33×C4—21no—
228C3⋊(C3⋊Dic3)—21no—
229C3⋊(C3⋊Dic3)—21no—
230C3⋊(C3⋊Dic3)—21no—
231C3⋊(C3⋊Dic3)C2×D412yes—
232C3×C3⋊Dic3—21no—
233C3×C3⋊Dic3—21no—
234C32×Dic3—21no—
235C32×Dic3—21no—
236C22×#67—94no—
237C22×#67—91no—
238C2×#237—94no—
239C2×#237—91no—
240C3×#120—34no—
241C3×#120—91no—
242C2×#217—94no—
243C2×#217—91no—
244#939—94no—
245#939—94no—
246#939—91no—
247#939—91no—
248#938—94no—
249#938—91no—
250#937—34no—
251#937C3⋊D311yescharacteristic, complemented
252D4×Dic3—94no—
253D4×Dic3—91no—
254D4×Dic3—184no—
255#886—94no—
256#886—91no—
257#885—94no—
258#885—91no—
259#883—94no—
260#883—91no—
261#67⋊C4—94no—
262#67⋊C4—91no—
263D3×C22⋊C4—94no—
264D3×C22⋊C4—91no—
265#878—94no—
266#878—91no—
267C23×C32—24no—
268C23×C32—24no—
269C23×C32—31no—
270C23×C32—31no—
271C23×C32—62no—
272C23×C32—62no—
273C23×C32—121no—
274C23×C32C22×D314yes—
275C23×C32C22×D314yes—
276C23×C32C22×D311yescharacteristic
277C23×C32C22×D311yescharacteristic
278C22×C3⋊D3—22no—
279C22×C3⋊D3—22no—
280C22×C3⋊D3—41no—
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×D3—68no—
289C22×C3×D3—68no—
290C22×C3×D3—124no—
291C22×C3×D3C22×D314yes—
292C22×C3×D3C22×D314yes—
293C32×D4—216no—
294C32×D4—28no—
295C32×D4—22no—
296C32×D4—62no—
297C32×D4—121no—
298C2×C32×C4—24no—
299C2×C32×C4—31no—
300C2×C32×C4—31no—
301C2×C32×C4C22×D314yes—
302C2×C32×C4C22×D311yescharacteristic
303#638—22no—
304#638—34no—
305#638—41no—
306#638—62no—
307#638—62no—
308#638—62no—
309C2×C3⋊Dic3—31no—
310C2×C3⋊Dic3—31no—
311C2×C3⋊Dic3—31no—
312C2×C3⋊Dic3—31no—
313C2×C3⋊Dic3—34no—
314C2×C3⋊Dic3—34no—
315C2×C3⋊Dic3—34no—
316C2×C3⋊Dic3—34no—
317C2×C3⋊Dic3—64no—
318C2×C3⋊Dic3—64no—
319C2×C3⋊Dic3—64no—
320C2×C3⋊Dic3—64no—
321C2×C3⋊Dic3—62no—
322C2×C3⋊Dic3—62no—
323C2×C3⋊Dic3—62no—
324C2×C3⋊Dic3—68no—
325C2×C3⋊Dic3—68no—
326C2×C3⋊Dic3—128no—
327C2×C3⋊Dic3—128no—
328C2×C3⋊Dic3—121no—
329C2×C3⋊Dic3C22×D311yescharacteristic
330C2×C3⋊Dic3C22×D311yescharacteristic
331C4×C3⋊D3—62no—
332C4×C3⋊D3—121no—
333#634—62no—
334C3×#67—28no—
335C3×#67—44no—
336C3×#67—68no—
337C3×#67—124no—
338C2×C3×Dic3—34no—
339C2×C3×Dic3—34no—
340C2×C3×Dic3C22×D314yes—
341C2×C3×Dic3C22×D314yes—
342#627—68no—
343#625—316no—
344#625—68no—
345#625—68no—
346#625—68no—
347D3×Dic3—68no—
348D3×Dic3—68no—
349D3×Dic3—124no—
350D3×Dic3—124no—
351#546—271noSylow
352C2×C33—22no—
353C2×C33—41no—
354C2×C33C22×D411yescharacteristic
355C2×C33C2×#4111yescharacteristic
356C2×C33H(5,𝔽2)11yescharacteristic
357C3×C3⋊D3—22no—
358C3×C3⋊D3—41no—
359C32×D3—22no—
360C32×D3—41no—
361C24×C3—34no—
362C24×C3—91no—
363C23×D3—34no—
364C23×D3C2×C3⋊D311yescharacteristic
365C2×C3×D4—24no—
366C2×C3×D4—34no—
367C2×C3×D4—34no—
368C2×C3×D4—91no—
369C2×C3×D4—91no—
370C2×C3×D4D3214yes—
371C2×C3×D4C2×C3⋊D311yescharacteristic
372C2×#67—34no—
373C2×#67—34no—
374C2×#67—94no—
375C2×#67—91no—
376C2×#67—94no—
377C2×#67—94no—
378C2×#67—94no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67—184no—
383C2×#67—1816no—
384C2×#67C2×C3⋊D311yescharacteristic, complemented
385C2×#67C2×C3⋊D311yescharacteristic, complemented
386C22×Dic3—94no—
387C22×Dic3—94no—
388C22×Dic3—94no—
389C22×Dic3—94no—
390C22×Dic3—91no—
391C22×Dic3—91no—
392C22×Dic3—91no—
393C22×Dic3—91no—
394C22×Dic3—184no—
395C22×Dic3—184no—
396#237—184no—
397#237—1816no—
398C2×C4×D3—94no—
399C2×C4×D3—91no—
400C2×C4×D3—94no—
401C2×C4×D3—91no—
402C2×Dic6—94no—
403C2×Dic6—91no—
404C3×C22⋊C4—34no—
405C3×C22⋊C4—34no—
406C3×C22⋊C4—34no—
407C3×C22⋊C4—91no—
408C3×C22⋊C4—91no—
409C3×C22⋊C4—91no—
410#217—34no—
411#217—94no—
412#217—94no—
413#217—94no—
414#217—94no—
415#217—91no—
416#217—91no—
417#217—91no—
418#217—91no—
419#217—184no—
420#217—184no—
421#217C2×C3⋊D311yescharacteristic
422(C2×D3)⋊C4—34no—
423(C2×D3)⋊C4—34no—
424(C2×D3)⋊C4—94no—
425(C2×D3)⋊C4—94no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—91no—
428(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
429(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
430C4⋊Dic3—94no—
431C4⋊Dic3—94no—
432C4⋊Dic3—91no—
433C4⋊Dic3—91no—
434C4⋊Dic3—184no—
435Dic3⋊C4—94no—
436Dic3⋊C4—94no—
437Dic3⋊C4—91no—
438Dic3⋊C4—91no—
439C4×Dic3—94no—
440C4×Dic3—91no—
441C4×Dic3—184no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32—28no—
445C22×C32—21no—
446C22×C32—24no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—24no—
450C22×C32—28no—
451C22×C32—24no—
452C22×C32—24no—
453C22×C32—24no—
454C22×C32—24no—
455C22×C32—32no—
456C22×C32—44no—
457C22×C32—44no—
458C22×C32—44no—
459C22×C32—44no—
460C22×C32—61no—
461C22×C32—61no—
462C22×C32—61no—
463C22×C32—61no—
464C22×C32—61no—
465C22×C32—124no—
466C22×C32#23718yescomplemented
467C22×C32#23712yescomplemented
468C22×C32C23×D314yes—
469C22×C32C23×D311yescharacteristic
470C2×C3⋊D3—21no—
471C2×C3⋊D3—21no—
472C2×C3⋊D3—21no—
473C2×C3⋊D3—21no—
474C2×C3⋊D3—21no—
475C2×C3⋊D3—44no—
476C2×C3⋊D3D3×D412yes—
477C2×C3×D3—24no—
478C2×C3×D3—24no—
479C2×C3×D3—24no—
480C2×C3×D3—24no—
481C2×C3×D3—24no—
482C2×C3×D3—38no—
483C2×C3×D3—416no—
484C2×C3×D3—64no—
485C2×C3×D3—64no—
486C2×C3×D3—64no—
487C2×C3×D3—64no—
488C2×C3×D3—64no—
489C2×C3×D3—1216no—
490C2×C3×D3D3×D418yes—
491C32×C4—28no—
492C32×C4—24no—
493C32×C4—21no—
494C32×C4—61no—
495C32×C4—61no—
496C3⋊Dic3—21no—
497C3⋊Dic3—21no—
498C3⋊Dic3—32no—
499C3⋊Dic3—38no—
500C3⋊Dic3—68no—
501C3⋊Dic3—61no—
502C3⋊Dic3—61no—
503C3⋊Dic3—61no—
504C3⋊Dic3—64no—
505C3⋊Dic3—64no—
506C3⋊Dic3—64no—
507C3⋊Dic3—124no—
508C3⋊Dic3—124no—
509C3⋊Dic3—124no—
510C3×Dic3—24no—
511C3×Dic3—24no—
512C3×Dic3—64no—
513C3×Dic3—64no—
514C2×#41—271no—
515C22×D4—271no—
516#124—271no—
517#123—271no—
518#123—271no—
519C22⋊Q8—271no—
520#121—271no—
521#121—271no—
522#121—271no—
523#120—31no—
524#120—91no—
525C4×D4—271no—
526C4×D4—271no—
527C2×C22⋊C4—271no—
528C2×C22⋊C4—271no—
529C33#54611yescharacteristic, complemented, Sylow
530C23×C3—24no—
531C23×C3—24no—
532C23×C3—34no—
533C23×C3—34no—
534C23×C3—68no—
535C23×C3—68no—
536C23×C3—91no—
537C23×C3—91no—
538C23×C3—124no—
539C23×C3—182no—
540C23×C3—182no—
541C23×C3—361no—
542C23×C3C2×D3214yes—
543C23×C3C2×D3214yes—
544C23×C3C22×C3⋊D311yescharacteristic
545C23×C3C22×C3⋊D311yescharacteristic
546C22×D3—22no—
547C22×D3—22no—
548C22×D3—34no—
549C22×D3—34no—
550C22×D3—41no—
551C22×D3—68no—
552C22×D3—68no—
553C22×D3—124no—
554C22×D3C22×C3⋊D311yescharacteristic
555C22×D3C22×C3⋊D311yescharacteristic
556C3×D4—216no—
557C3×D4—28no—
558C3×D4—22no—
559C3×D4—68no—
560C3×D4—124no—
561C3×D4—182no—
562C3×D4—361no—
563C2×C3×C4—24no—
564C2×C3×C4—34no—
565C2×C3×C4—34no—
566C2×C3×C4—91no—
567C2×C3×C4—91no—
568C2×C3×C4C2×D3214yes—
569C2×C3×C4C22×C3⋊D311yescharacteristic
570#67—22no—
571#67—41no—
572#67—68no—
573#67—916no—
574#67—94no—
575#67—124no—
576#67—182no—
577#67—188no—
578#67—182no—
579#67—188no—
580#67—188no—
581#67—182no—
582C2×Dic3—34no—
583C2×Dic3—34no—
584C2×Dic3—94no—
585C2×Dic3—91no—
586C2×Dic3—94no—
587C2×Dic3—94no—
588C2×Dic3—94no—
589C2×Dic3—91no—
590C2×Dic3—91no—
591C2×Dic3—91no—
592C2×Dic3—184no—
593C2×Dic3—184no—
594C2×Dic3—184no—
595C2×Dic3—184no—
596C2×Dic3—182no—
597C2×Dic3—188no—
598C2×Dic3—182no—
599C2×Dic3—182no—
600C2×Dic3—188no—
601C2×Dic3—188no—
602C2×Dic3—368no—
603C2×Dic3—368no—
604C2×Dic3—361no—
605C2×Dic3—364no—
606C2×Dic3C22×C3⋊D311yescharacteristic
607C2×Dic3C22×C3⋊D311yescharacteristic
608C4×D3—188no—
609C4×D3—182no—
610C4×D3—364no—
611C4×D3—361no—
612Dic6—182no—
613Dic6—188no—
614C2×C32—22no—
615C2×C32—24no—
616C2×C32—24no—
617C2×C32—24no—
618C2×C32—28no—
619C2×C32—48no—
620C2×C32—48no—
621C2×C32—44no—
622C2×C32—41no—
623C2×C32—62no—
624C2×C32—121no—
625C2×C32C2×D3×D414yes—
626C2×C32C2×D3×D411yescharacteristic
627C2×C32C2×#23714yes—
628C2×C32C2×#23711yescharacteristic
629C2×C32#100414yes—
630C2×C32#100411yescharacteristic
631C3⋊D3—22no—
632C3⋊D3—41no—
633C3×D3—28no—
634C3×D3—44no—
635C3×D3—68no—
636C3×D3—124no—
637C24—31no—
638C24—91no—
639#41—544no—
640C2×Q8—271no—
641C2×D4—31no—
642C2×D4—31no—
643C2×D4—91no—
644C2×D4—91no—
645C2×D4—271no—
646C2×D4—271no—
647C2×D4—271no—
648C2×D4—271no—
649C2×D4—544no—
650C2×D4D3×C3⋊D311yescharacteristic
651C22×C4—271no—
652C22×C4—271no—
653C22×C4—271no—
654C22×C4—271no—
655C22×C4—271no—
656C22×C4—271no—
657C4⋊C4—271no—
658C4⋊C4—271no—
659C4⋊C4—271no—
660C4⋊C4—271no—
661C22⋊C4—31no—
662C22⋊C4—31no—
663C22⋊C4—31no—
664C22⋊C4—91no—
665C22⋊C4—91no—
666C22⋊C4—91no—
667C22⋊C4—271no—
668C22⋊C4—271no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C22⋊C4—271no—
672C22⋊C4—271no—
673C42—271no—
674C22×C3—24no—
675C22×C3—24no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—28no—
679C22×C3—24no—
680C22×C3—24no—
681C22×C3—24no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—24no—
686C22×C3—28no—
687C22×C3—38no—
688C22×C3—44no—
689C22×C3—44no—
690C22×C3—44no—
691C22×C3—44no—
692C22×C3—64no—
693C22×C3—64no—
694C22×C3—64no—
695C22×C3—64no—
696C22×C3—64no—
697C22×C3—92no—
698C22×C3—1216no—
699C22×C3—181no—
700C22×C3—181no—
701C22×C3—181no—
702C22×C3—181no—
703C22×C3—181no—
704C22×C3—364no—
705C22×C3#380518yescomplemented
706C22×C3#383012yescomplemented
707C22×C3C22×D3214yes—
708C22×C3C23×C3⋊D311yescharacteristic
709C2×D3—21no—
710C2×D3—21no—
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—21no—
714C2×D3—38no—
715C2×D3—44no—
716C2×D3—64no—
717C2×D3—64no—
718C2×D3—64no—
719C2×D3—64no—
720C2×D3—64no—
721C2×D3—1216no—
722C2×D3D4×C3⋊D312yes—
723C3×C4—28no—
724C3×C4—24no—
725C3×C4—21no—
726C3×C4—64no—
727C3×C4—64no—
728C3×C4—181no—
729C3×C4—181no—
730Dic3—21no—
731Dic3—21no—
732Dic3—64no—
733Dic3—64no—
734Dic3—98no—
735Dic3—92no—
736Dic3—188no—
737Dic3—184no—
738Dic3—184no—
739Dic3—184no—
740Dic3—181no—
741Dic3—181no—
742Dic3—181no—
743Dic3—364no—
744Dic3—364no—
745Dic3—364no—
746C32—24no—
747C32#559114yescomplemented
748C32#559111yescharacteristic, complemented
749C23—31no—
750C23—31no—
751C23—62no—
752C23—62no—
753C23—91no—
754C23—91no—
755C23—121no—
756C23—182no—
757C23—182no—
758C23—361no—
759C23C2×D3×C3⋊D311yescharacteristic
760C23C2×D3×C3⋊D311yescharacteristic
761Q8—542no—
762D4—22no—
763D4—62no—
764D4—121no—
765D4—182no—
766D4—274no—
767D4—361no—
768D4—542no—
769D4—542no—
770D4—542no—
771C2×C4—31no—
772C2×C4—31no—
773C2×C4—91no—
774C2×C4—91no—
775C2×C4—271no—
776C2×C4—271no—
777C2×C4—271no—
778C2×C4—271no—
779C2×C4—542no—
780C2×C4—542no—
781C2×C4—542no—
782C2×C4—542no—
783C2×C4—1081no—
784C2×C4—1081no—
785C2×C4C2×D3×C3⋊D311yescharacteristic
786C2×C3—28no—
787C2×C3—22no—
788C2×C3—24no—
789C2×C3—24no—
790C2×C3—24no—
791C2×C3—48no—
792C2×C3—48no—
793C2×C3—44no—
794C2×C3—41no—
795C2×C3—68no—
796C2×C3—124no—
797C2×C3—182no—
798C2×C3—361no—
799C2×C3D32×D414yes—
800C2×C3#6431314yes—
801C2×C3C2×#380514yes—
802C2×C3C2×D4×C3⋊D311yescharacteristic
803C2×C3C2×#383011yescharacteristic
804C2×C3#6436111yescharacteristic
805D3—22no—
806D3—41no—
807D3—68no—
808D3—124no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—32no—
815C22—61no—
816C22—61no—
817C22—61no—
818C22—61no—
819C22—61no—
820C22—92no—
821C22—124no—
822C22—181no—
823C22—181no—
824C22—181no—
825C22—181no—
826C22—181no—
827C22—364no—
828C22#8902912yescomplemented
829C22C22×D3×C3⋊D311yescharacteristic
830C4—21no—
831C4—61no—
832C4—61no—
833C4—181no—
834C4—181no—
835C4—272no—
836C4—541no—
837C4—541no—
838C4—541no—
839C3—24no—
840C3#1059522514yescomplemented
841C3#1059606211yescharacteristic, complemented
842C2—22no—
843C2—41no—
844C2—62no—
845C2—121no—
846C2—182no—
847C2—361no—
848C2D3×D4×C3⋊D311yescharacteristic
849C2#1172458711yescharacteristic
850C2C2×#8902911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C22×#6290C2semidirect
2. C2×#89029C2semidirect
3. D4×C3⋊(C3⋊Dic3)C2semidirect
4. C3×#64146C2semidirect
5. C32×#937C2semidirect
6. #11723642C2semidirect
7. #11723637C2semidirect
8. #11723631C2semidirect
9. C3⋊D3×#217C2semidirect
10. #11723615C2semidirect
11. D3×#3757C2semidirect
12. #11723530C2semidirect
13. #11723523C2semidirect
14. #11723508C2semidirect
15. #11723480C2semidirect
22. C22×C3⋊(C3⋊Dic3)C22semidirect
23. C2×C3×#638C22semidirect
24. C2×C3×#638C22semidirect
25. C2×C32×#67C22semidirect
26. C2×C32×#67C22semidirect
27. C2×#6293C22semidirect
33. C2×Dic3×C3⋊D3C22semidirect
34. C2×Dic3×C3⋊D3C22semidirect
36. C2×D3×C3⋊Dic3C22semidirect
37. C2×D3×C3⋊Dic3C22semidirect
39. #88864C22semidirect
40. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
41. C4×C3⋊(C3⋊Dic3)C22semidirect
43. C3×#3752C22semidirect
44. C3×#3752C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. C32×(C2×D3)⋊C4C22semidirect
48. #88807C22semidirect
49. #88806C22semidirect
50. Dic3⋊(C3⋊Dic3)C22semidirect
51. #88803C22semidirect
52. #88803C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
64. #64146D3semidirect
75. C3×#937D3semidirect
118. #6290D4semidirect
139. C2×#638C2×D3semidirect
140. C2×#638C2×D3semidirect
155. C2×C3×#67C2×D3semidirect
156. C2×C3×#67C2×D3semidirect
182. #3752C2×D3semidirect
183. #3752C2×D3semidirect
197. C3×(C2×D3)⋊C4C2×D3semidirect
198. C3×(C2×D3)⋊C4C2×D3semidirect
211. C22×C33#41semidirect
251. #937C3⋊D3semidirect
384. C2×#67C2×C3⋊D3semidirect
385. C2×#67C2×C3⋊D3semidirect
428. (C2×D3)⋊C4C2×C3⋊D3semidirect
429. (C2×D3)⋊C4C2×C3⋊D3semidirect
466. C22×C32#237semidirect
467. C22×C32#237semidirect
529. C33#546semidirect
705. C22×C3#3805semidirect
706. C22×C3#3830semidirect
747. C32#5591semidirect
748. C32#5591semidirect
828. C22#89029semidirect
840. C3#10595225semidirect
841. C3#10596062semidirect

Maximal subgroups

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

subgroupindex
C22×#62902
C2×#890292
D4×C3⋊(C3⋊Dic3)2
C3×#641462
C32×#9372
#117236422
#117236372
#117236312
C3⋊D3×#2172
#117236152
D3×#37572
#117235302
#117235232
#117235082
#117234802
#105960623
#105952253