Finite Group Databasebeta

← #13178043

Subgroups — #13178043

Order 1728.

2532 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#638C211yesmaximal, characteristic, complemented
2C2×#89029C211yesmaximal, characteristic, complemented
3C2×#88864C211yesmaximal, characteristic, complemented
4C32×#953C211yesmaximal, characteristic, complemented
5#11723641C211yesmaximal, characteristic, complemented
6#11723637C211yesmaximal, characteristic, complemented
7#11723634C211yesmaximal, characteristic, complemented
8#11723631C211yesmaximal, characteristic, complemented
9#11723626C211yesmaximal, characteristic, complemented
10#11723621C211yesmaximal, characteristic, complemented
11C3⋊D3×#217C211yesmaximal, characteristic, complemented
12#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
13#11723615C211yesmaximal, characteristic, complemented
14#11723609C211yesmaximal, characteristic, complemented
15#11723591C211yesmaximal, characteristic, complemented
16#10596062—31nomaximal
17#10595494—34nomaximal
18C24×C33C2211yescharacteristic
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C2×C3×#638—24no—
23C2×C3×#638C2211yescharacteristic
24C2×C3×#638C2211yescharacteristic
25C2×C3×#638C2211yescharacteristic
26C2×C3×#638C2211yescharacteristic
27C22×C3×C3⋊Dic3C2211yescharacteristic
28C2×C32×#67C2211yescharacteristic
29C2×C32×#67C2211yescharacteristic, complemented
30C2×C32×#67C2211yescharacteristic, complemented
31C2×#6293C2211yescharacteristic, complemented
32C2×#6290C2211yescharacteristic, complemented
33C2×#6290C2211yescharacteristic, complemented
34C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
35C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
36#89029—24no—
37C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
38#88864C2211yescharacteristic
39#88864C2211yescharacteristic
40#88864C2211yescharacteristic, complemented
41#88864C2211yescharacteristic, complemented
42C32×#217C2211yescharacteristic
43C32×#217C2211yescharacteristic, complemented
44C32×#217C2211yescharacteristic, complemented
45#88807C2211yescharacteristic, complemented
46#88806C2211yescharacteristic, complemented
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88803C2211yescharacteristic, complemented
50#88803C2211yescharacteristic, complemented
51#88803C2211yescharacteristic, complemented
52#88803C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C22×#638D311yescharacteristic, complemented
56C2×#3830—31no—
57C22×C3×#67—34no—
58C2×#3805—34no—
59C32×#120—31no—
60C2×#3757—31no—
61C2×#3757—34no—
62C2×#3757—64no—
63#64148—31no—
64#64148—31no—
65#64147—31no—
66#64146—31no—
67D4×C3⋊Dic3—31no—
68#64095—31no—
69#64094—31no—
70#64092—31no—
71#64090—31no—
72C22⋊C4×C3⋊D3—31no—
73#64087—31no—
74C3×#953D314yescomplemented
75#63980—34no—
76#63976—34no—
77#67⋊Dic3—34no—
78Dic3×#67—34no—
79#63970—34no—
80#63970—34no—
81#63969—34no—
82D3×#217—34no—
83#63964—34no—
84#63962—34no—
85#63959—34no—
86C23×C33—22no—
87C23×C33—22no—
88C23×C33—41no—
89C23×C33C2311yescharacteristic
90C23×C33C2311yescharacteristic
91C23×C33C2311yescharacteristic
92C22×C3×C3⋊D3—22no—
93C22×C3×C3⋊D3—22no—
94C22×C3×C3⋊D3—41no—
95C22×C3×C3⋊D3C2311yescharacteristic
96C22×C3×C3⋊D3C2311yescharacteristic
97C22×C32×D3C2311yescharacteristic
98C2×C3⋊(C3⋊Dic3)—22no—
99C2×C3⋊(C3⋊Dic3)—41no—
100C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
101C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C3×#638—22no—
105C3×#638—22no—
106C3×#638—22no—
107C3×#638D414yescomplemented
108C2×C3×C3⋊Dic3—22no—
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C32×#67—22no—
112C32×#67—22no—
113C32×#67—41no—
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117#6293—22no—
118#6290—22no—
119#6290—41no—
120Dic3×C3⋊D3—22no—
121Dic3×C3⋊D3—41no—
122D3×C3⋊Dic3—22no—
123#5806—91no—
124#5591—94no—
125C24×C32—24no—
126C24×C32C2×D314yes—
127C24×C32C2×D311yescharacteristic
128C23×C3⋊D3C2×D311yescharacteristic
129C23×C3×D3—34no—
130C2×C32×D4—31no—
131C2×C32×D4—31no—
132C2×C32×D4—31no—
133C2×#638—24no—
134C2×#638—31no—
135C2×#638—31no—
136C2×#638C2×D311yescharacteristic
137C2×#638C2×D311yescharacteristic
138C2×#638C2×D311yescharacteristic
139C2×#638C2×D311yescharacteristic
140C22×C3⋊Dic3—31no—
141C22×C3⋊Dic3—34no—
142C22×C3⋊Dic3—31no—
143C22×C3⋊Dic3—34no—
144C22×C3⋊Dic3—31no—
145C22×C3⋊Dic3—64no—
146C22×C3⋊Dic3—64no—
147C22×C3⋊Dic3C2×D311yescharacteristic
148#3830—64no—
149C2×C4×C3⋊D3—31no—
150C2×C4×C3⋊D3—31no—
151C2×#634—31no—
152C2×C3×#67—34no—
153C2×C3×#67—34no—
154C2×C3×#67—34no—
155C2×C3×#67—34no—
156C2×C3×#67—616no—
157C2×C3×#67C2×D314yes—
158C2×C3×#67C2×D314yescomplemented
159C2×C3×#67C2×D314yescomplemented
160C22×C3×Dic3—34no—
161C2×#627—34no—
162C2×#625—34no—
163C2×#625—34no—
164#3805—616no—
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—31no—
174#3757—31no—
175#3757—34no—
176#3757—34no—
177#3757—34no—
178#3757—34no—
179#3757—31no—
180#3757—64no—
181#3757—64no—
182#3757—64no—
183#3757—64no—
184#3752—31no—
185#3752—31no—
186#3752—31no—
187#3752—31no—
188C4⋊(C3⋊Dic3)—31no—
189C4⋊(C3⋊Dic3)—31no—
190#3750—31no—
191#3750—31no—
192C4×C3⋊Dic3—31no—
193C3×#217C2×D314yes—
194C3×#217C2×D314yescomplemented
195C3×#217C2×D314yescomplemented
196#3724—34no—
197Dic3⋊Dic3—34no—
198Dic3⋊Dic3—34no—
199Dic3⋊Dic3—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—
205Dic32—34no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33—21no—
209C22×C33—21no—
210C22×C33—21no—
211C22×C33—21no—
212C22×C33—21no—
213C22×C33—44no—
214C22×C33C2×D412yes—
215C22×C33#4112yescomplemented
216C22×C33C2411yescharacteristic
217C2×C3×C3⋊D3—21no—
218C2×C3×C3⋊D3—21no—
219C2×C3×C3⋊D3—21no—
220C2×C3×C3⋊D3—21no—
221C2×C3×C3⋊D3—21no—
222C2×C3×C3⋊D3—44no—
223C2×C3×C3⋊D3C2×D412yes—
224C2×C32×D3—21no—
225C2×C32×D3—21no—
226C2×C32×D3—21no—
227C3⋊(C3⋊Dic3)—21no—
228C3⋊(C3⋊Dic3)—21no—
229C3⋊(C3⋊Dic3)—21no—
230C3⋊(C3⋊Dic3)—21no—
231C3×C3⋊Dic3—21no—
232C3×C3⋊Dic3C2×D412yes—
233C32×Dic3—21no—
234C32×Dic3—21no—
235C32×Dic3—21no—
236C22×C3×D4—91no—
237C22×#67—34no—
238C2×#237—94no—
239C2×#237—91no—
240C3×#120—34no—
241#953—91no—
242#953C3⋊D311yescharacteristic, complemented
243C2×#217—94no—
244C2×#217—91no—
245C2×#217—91no—
246C2×#217—184no—
247#939—94no—
248#939—94no—
249#939—91no—
250#939—91no—
251#938—94no—
252#938—91no—
253#937—94no—
254#936—91no—
255#935—91no—
256#935—91no—
257D4×Dic3—94no—
258D4×Dic3—91no—
259C4×#67—91no—
260#924—91no—
261#886—94no—
262#885—94no—
263#883—94no—
264#67⋊C4—94no—
265D3×C22⋊C4—94no—
266#878—94no—
267C23×C32—216no—
268C23×C32—28no—
269C23×C32—22no—
270C23×C32—22no—
271C23×C32—24no—
272C23×C32—24no—
273C23×C32—24no—
274C23×C32—28no—
275C23×C32—31no—
276C23×C32—48no—
277C23×C32—41no—
278C23×C32—44no—
279C23×C32—48no—
280C23×C32C22×D314yes—
281C23×C32C22×D314yes—
282C23×C32C22×D314yes—
283C23×C32C22×D311yescharacteristic
284C23×C32C22×D311yescharacteristic
285C23×C32C22×D311yescharacteristic
286C22×C3⋊D3—22no—
287C22×C3⋊D3—22no—
288C22×C3⋊D3—41no—
289C22×C3⋊D3C22×D311yescharacteristic
290C22×C3⋊D3C22×D311yescharacteristic
291C22×C3×D3—34no—
292C22×C3×D3—34no—
293C22×C3×D3—68no—
294C22×C3×D3—68no—
295C22×C3×D3—124no—
296C22×C3×D3C22×D314yes—
297C32×D4—62no—
298C32×D4—62no—
299C32×D4—121no—
300C2×C32×C4—31no—
301C2×C32×C4—31no—
302C2×C32×C4—31no—
303#638—22no—
304#638—22no—
305#638—22no—
306#638—62no—
307#638—121no—
308#638#6714yescomplemented
309C2×C3⋊Dic3—22no—
310C2×C3⋊Dic3—31no—
311C2×C3⋊Dic3—31no—
312C2×C3⋊Dic3—31no—
313C2×C3⋊Dic3—31no—
314C2×C3⋊Dic3—34no—
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—64no—
322C2×C3⋊Dic3—62no—
323C2×C3⋊Dic3—62no—
324C2×C3⋊Dic3—68no—
325C2×C3⋊Dic3—128no—
326C2×C3⋊Dic3—121no—
327C2×C3⋊Dic3—124no—
328C2×C3⋊Dic3—128no—
329C2×C3⋊Dic3C22×D311yescharacteristic
330C2×C3⋊Dic3C22×D311yescharacteristic
331C4×C3⋊D3—62no—
332C4×C3⋊D3—121no—
333#634—62no—
334C3×#67—28no—
335C3×#67—28no—
336C3×#67—316no—
337C3×#67—44no—
338C3×#67—68no—
339C3×#67—68no—
340C3×#67—68no—
341C2×C3×Dic3—34no—
342C2×C3×Dic3—34no—
343C2×C3×Dic3—68no—
344C2×C3×Dic3C22×D314yes—
345C2×C3×Dic3C22×D314yes—
346C2×C3×Dic3C22×D314yes—
347#627—68no—
348#625—68no—
349#625—124no—
350D3×Dic3—68no—
351D3×Dic3—68no—
352D3×Dic3—124no—
353#546—271noSylow
354C2×C33—22no—
355C2×C33—22no—
356C2×C33—41no—
357C2×C33C22×D411yescharacteristic
358C2×C33C2×#4111yescharacteristic
359C2×C33H(5,𝔽2)11yescharacteristic
360C3×C3⋊D3—22no—
361C3×C3⋊D3—41no—
362C32×D3—41no—
363C24×C3—24no—
364C24×C3—91no—
365C24×C3D3214yes—
366C24×C3C2×C3⋊D311yescharacteristic
367C23×D3—34no—
368C2×C3×D4—34no—
369C2×C3×D4—34no—
370C2×C3×D4—34no—
371C2×C3×D4—91no—
372C2×C3×D4—91no—
373C2×C3×D4—91no—
374C2×C3×D4—91no—
375C2×C3×D4—184no—
376C22×C3×C4—91no—
377C2×#67—34no—
378C2×#67—34no—
379C2×#67—34no—
380C2×#67—34no—
381C2×#67—616no—
382C2×#67—94no—
383C2×#67—91no—
384C2×#67—94no—
385C2×#67—91no—
386C2×#67C2×C3⋊D311yescharacteristic
387C2×#67C2×C3⋊D311yescharacteristic, complemented
388C2×#67C2×C3⋊D311yescharacteristic, complemented
389C22×Dic3—34no—
390C22×Dic3—94no—
391C22×Dic3—94no—
392C22×Dic3—91no—
393C22×Dic3—94no—
394C22×Dic3—91no—
395C22×Dic3—91no—
396C22×Dic3—91no—
397C22×Dic3—184no—
398C22×Dic3—184no—
399#237—184no—
400#237—1816no—
401C2×C4×D3—94no—
402C2×C4×D3—91no—
403C2×C4×D3—94no—
404C2×Dic6—94no—
405C2×Dic6—91no—
406C3×C22⋊C4—34no—
407C3×C22⋊C4—34no—
408C3×C22⋊C4—34no—
409#217—94no—
410#217—94no—
411#217—94no—
412#217—94no—
413#217—94no—
414#217—91no—
415#217—91no—
416#217—91no—
417#217—91no—
418#217—91no—
419#217—91no—
420#217—91no—
421#217—91no—
422#217—184no—
423#217—184no—
424#217—184no—
425#217—184no—
426#217C2×C3⋊D311yescharacteristic
427#217C2×C3⋊D311yescharacteristic, complemented
428#217C2×C3⋊D311yescharacteristic, complemented
429(C2×D3)⋊C4—94no—
430(C2×D3)⋊C4—94no—
431(C2×D3)⋊C4—94no—
432(C2×D3)⋊C4—94no—
433(C2×D3)⋊C4—91no—
434C4⋊Dic3—94no—
435C4⋊Dic3—94no—
436C4⋊Dic3—91no—
437Dic3⋊C4—94no—
438Dic3⋊C4—94no—
439Dic3⋊C4—91no—
440Dic3⋊C4—91no—
441Dic3⋊C4—91no—
442C4×Dic3—94no—
443C4×Dic3—91no—
444C22×C32—28no—
445C22×C32—28no—
446C22×C32—24no—
447C22×C32—21no—
448C22×C32—24no—
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—28no—
453C22×C32—24no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—24no—
458C22×C32—28no—
459C22×C32—28no—
460C22×C32—24no—
461C22×C32—24no—
462C22×C32—24no—
463C22×C32—24no—
464C22×C32—44no—
465C22×C32—44no—
466C22×C32—44no—
467C22×C32—44no—
468C22×C32—44no—
469C22×C32—416no—
470C22×C32—432no—
471C22×C32—61no—
472C22×C32—61no—
473C22×C32—61no—
474C22×C32D3×D418yes—
475C22×C32#23718yescomplemented
476C22×C32#23712yescomplemented
477C22×C32C2×#6712yes—
478C22×C32C23×D314yes—
479C22×C32C23×D311yescharacteristic
480C2×C3⋊D3—21no—
481C2×C3⋊D3—21no—
482C2×C3⋊D3—21no—
483C2×C3⋊D3—21no—
484C2×C3⋊D3—21no—
485C2×C3⋊D3—44no—
486C2×C3⋊D3C2×#6712yes—
487C2×C3×D3—24no—
488C2×C3×D3—24no—
489C2×C3×D3—24no—
490C2×C3×D3—38no—
491C2×C3×D3—64no—
492C2×C3×D3—64no—
493C2×C3×D3—64no—
494C2×C3×D3—64no—
495C2×C3×D3—64no—
496C2×C3×D3—1216no—
497C32×C4—61no—
498C32×C4—61no—
499C32×C4—61no—
500C3⋊Dic3—21no—
501C3⋊Dic3—61no—
502C3⋊Dic3—61no—
503C3⋊Dic3—61no—
504C3⋊Dic3—61no—
505C3⋊Dic3—64no—
506C3⋊Dic3—64no—
507C3⋊Dic3—64no—
508C3⋊Dic3—64no—
509C3⋊Dic3—124no—
510C3⋊Dic3—124no—
511C3⋊Dic3—124no—
512C3⋊Dic3—124no—
513C3⋊Dic3C2×#6712yes—
514C3×Dic3—24no—
515C3×Dic3—24no—
516C3×Dic3—24no—
517C3×Dic3—38no—
518C3×Dic3—64no—
519C2×#41—271no—
520C22×D4—91no—
521#124—271no—
522#123—271no—
523#123—271no—
524C22⋊Q8—271no—
525#121—271no—
526#121—271no—
527#121—271no—
528#120—31no—
529#120—271no—
530C4×D4—271no—
531C4×D4—271no—
532C2×C22⋊C4—271no—
533C2×C22⋊C4—271no—
534C33#54611yescharacteristic, complemented, Sylow
535C23×C3—216no—
536C23×C3—28no—
537C23×C3—28no—
538C23×C3—22no—
539C23×C3—22no—
540C23×C3—24no—
541C23×C3—24no—
542C23×C3—24no—
543C23×C3—34no—
544C23×C3—48no—
545C23×C3—44no—
546C23×C3—41no—
547C23×C3—48no—
548C23×C3—91no—
549C23×C3—91no—
550C23×C3—182no—
551C23×C3—182no—
552C23×C3—361no—
553C23×C3C2×D3214yes—
554C23×C3C2×D3214yes—
555C23×C3C2×D3214yes—
556C23×C3C22×C3⋊D311yescharacteristic
557C23×C3C22×C3⋊D311yescharacteristic
558C23×C3C22×C3⋊D311yescharacteristic
559C22×D3—34no—
560C22×D3—34no—
561C22×D3—68no—
562C22×D3—68no—
563C22×D3—124no—
564C22×D3C22×C3⋊D311yescharacteristic
565C3×D4—68no—
566C3×D4—68no—
567C3×D4—94no—
568C3×D4—124no—
569C3×D4—182no—
570C3×D4—182no—
571C3×D4—182no—
572C2×C3×C4—34no—
573C2×C3×C4—34no—
574C2×C3×C4—34no—
575C2×C3×C4—91no—
576C2×C3×C4—91no—
577C2×C3×C4—182no—
578#67—22no—
579#67—22no—
580#67—316no—
581#67—41no—
582#67—68no—
583#67—68no—
584#67—68no—
585#67—182no—
586#67—188no—
587#67—361no—
588#67—364no—
589C2×Dic3—34no—
590C2×Dic3—34no—
591C2×Dic3—68no—
592C2×Dic3—94no—
593C2×Dic3—94no—
594C2×Dic3—94no—
595C2×Dic3—94no—
596C2×Dic3—91no—
597C2×Dic3—91no—
598C2×Dic3—91no—
599C2×Dic3—91no—
600C2×Dic3—184no—
601C2×Dic3—184no—
602C2×Dic3—184no—
603C2×Dic3—184no—
604C2×Dic3—182no—
605C2×Dic3—188no—
606C2×Dic3—188no—
607C2×Dic3—182no—
608C2×Dic3—368no—
609C2×Dic3—361no—
610C2×Dic3—364no—
611C2×Dic3—361no—
612C2×Dic3—368no—
613C2×Dic3C22×C3⋊D311yescharacteristic
614C2×Dic3C22×C3⋊D311yescharacteristic
615C2×Dic3C22×C3⋊D311yescharacteristic
616C4×D3—188no—
617C4×D3—182no—
618C4×D3—364no—
619Dic6—182no—
620Dic6—188no—
621C2×C32—216no—
622C2×C32—22no—
623C2×C32—22no—
624C2×C32—28no—
625C2×C32—24no—
626C2×C32—24no—
627C2×C32—24no—
628C2×C32—28no—
629C2×C32—48no—
630C2×C32—48no—
631C2×C32—41no—
632C2×C32—44no—
633C2×C32—121no—
634C2×C32C2×D3×D414yes—
635C2×C32C2×#23714yes—
636C2×C32C2×#23711yescharacteristic
637C2×C32#100414yes—
638C2×C32#100411yescharacteristic
639C2×C32C22×#6711yescharacteristic
640C3⋊D3—22no—
641C3⋊D3—41no—
642C3×D3—44no—
643C3×D3—68no—
644C3×D3—124no—
645C24—91no—
646C24D3×C3⋊D311yescharacteristic
647#41—544no—
648C2×Q8—271no—
649C2×D4—31no—
650C2×D4—31no—
651C2×D4—31no—
652C2×D4—91no—
653C2×D4—91no—
654C2×D4—91no—
655C2×D4—91no—
656C2×D4—184no—
657C2×D4—271no—
658C2×D4—271no—
659C22×C4—91no—
660C22×C4—271no—
661C22×C4—271no—
662C22×C4—271no—
663C22×C4—271no—
664C22×C4—271no—
665C4⋊C4—271no—
666C4⋊C4—271no—
667C4⋊C4—271no—
668C4⋊C4—271no—
669C22⋊C4—31no—
670C22⋊C4—31no—
671C22⋊C4—31no—
672C22⋊C4—271no—
673C22⋊C4—271no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—271no—
677C22⋊C4—271no—
678C22⋊C4—271no—
679C22⋊C4—271no—
680C22⋊C4—271no—
681C42—271no—
682C22×C3—28no—
683C22×C3—28no—
684C22×C3—24no—
685C22×C3—24no—
686C22×C3—24no—
687C22×C3—24no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—28no—
693C22×C3—24no—
694C22×C3—24no—
695C22×C3—24no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—24no—
700C22×C3—28no—
701C22×C3—28no—
702C22×C3—44no—
703C22×C3—44no—
704C22×C3—44no—
705C22×C3—44no—
706C22×C3—416no—
707C22×C3—44no—
708C22×C3—432no—
709C22×C3—64no—
710C22×C3—64no—
711C22×C3—64no—
712C22×C3—92no—
713C22×C3—181no—
714C22×C3—181no—
715C22×C3—181no—
716C22×C3—181no—
717C22×C3—181no—
718C22×C3—364no—
719C22×C3#380518yescomplemented
720C22×C3D3×#6718yes—
721C22×C3D4×C3⋊D312yes—
722C22×C3#383012yescomplemented
723C22×C3C22×D3214yes—
724C22×C3C23×C3⋊D311yescharacteristic
725C2×D3—21no—
726C2×D3—21no—
727C2×D3—21no—
728C2×D3—38no—
729C2×D3—64no—
730C2×D3—64no—
731C2×D3—64no—
732C2×D3—64no—
733C2×D3—64no—
734C2×D3—1216no—
735C3×C4—64no—
736C3×C4—64no—
737C3×C4—64no—
738C3×C4—92no—
739C3×C4—181no—
740Dic3—21no—
741Dic3—21no—
742Dic3—21no—
743Dic3—38no—
744Dic3—64no—
745Dic3—184no—
746Dic3—184no—
747Dic3—184no—
748Dic3—184no—
749Dic3—181no—
750Dic3—181no—
751Dic3—181no—
752Dic3—181no—
753Dic3—364no—
754Dic3—364no—
755Dic3—364no—
756Dic3—364no—
757C32—24no—
758C32#559114yescomplemented
759C32#580611yescharacteristic, complemented
760C23—22no—
761C23—22no—
762C23—31no—
763C23—41no—
764C23—91no—
765C23—91no—
766C23—182no—
767C23—182no—
768C23—361no—
769C23C2×D3×C3⋊D311yescharacteristic
770C23C2×D3×C3⋊D311yescharacteristic
771C23C2×D3×C3⋊D311yescharacteristic
772Q8—542no—
773D4—62no—
774D4—62no—
775D4—94no—
776D4—121no—
777D4—182no—
778D4—182no—
779D4—182no—
780D4—542no—
781D4—1081no—
782C2×C4—31no—
783C2×C4—31no—
784C2×C4—31no—
785C2×C4—91no—
786C2×C4—91no—
787C2×C4—182no—
788C2×C4—271no—
789C2×C4—271no—
790C2×C4—271no—
791C2×C4—271no—
792C2×C4—542no—
793C2×C4—542no—
794C2×C4—542no—
795C2×C4—1081no—
796C2×C4—1081no—
797C2×C3—216no—
798C2×C3—28no—
799C2×C3—28no—
800C2×C3—22no—
801C2×C3—22no—
802C2×C3—24no—
803C2×C3—24no—
804C2×C3—24no—
805C2×C3—48no—
806C2×C3—48no—
807C2×C3—44no—
808C2×C3—41no—
809C2×C3—124no—
810C2×C3—182no—
811C2×C3—361no—
812C2×C3C2×#380514yes—
813C2×C3C2×D3×#6714yes—
814C2×C3#6433014yes—
815C2×C3C2×D4×C3⋊D311yescharacteristic
816C2×C3C2×#383011yescharacteristic
817C2×C3#6436111yescharacteristic
818D3—41no—
819D3—68no—
820D3—124no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—44no—
829C22—61no—
830C22—61no—
831C22—61no—
832C22—92no—
833C22—181no—
834C22—181no—
835C22—181no—
836C22—181no—
837C22—181no—
838C22—364no—
839C22#8902912yescomplemented
840C22C3⋊D3×#6712yes—
841C22C22×D3×C3⋊D311yescharacteristic
842C4—61no—
843C4—61no—
844C4—61no—
845C4—92no—
846C4—181no—
847C4—541no—
848C4—541no—
849C4—541no—
850C4—541no—
851C3—24no—
852C3#1059549414yescomplemented
853C3#1059606211yescharacteristic, complemented
854C2—22no—
855C2—22no—
856C2—41no—
857C2—121no—
858C2—182no—
859C2—361no—
860C2C2×#8902911yescharacteristic
861C2C2×C3⋊D3×#6711yescharacteristic
862C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC24×C33C22
hypercenterC24D3×C3⋊D3
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C22×C3×#638C2semidirect
2. C2×#89029C2semidirect
3. C2×#88864C2semidirect
4. C32×#953C2semidirect
5. #11723641C2semidirect
6. #11723637C2semidirect
7. #11723634C2semidirect
8. #11723631C2semidirect
9. #11723626C2semidirect
10. #11723621C2semidirect
11. C3⋊D3×#217C2semidirect
12. #67×C3⋊Dic3C2semidirect
13. #11723615C2semidirect
14. #11723609C2semidirect
15. #11723591C2semidirect
20. C22×C3⋊(C3⋊Dic3)C22semidirect
21. C22×C3⋊(C3⋊Dic3)C22semidirect
29. C2×C32×#67C22semidirect
30. C2×C32×#67C22semidirect
31. C2×#6293C22semidirect
32. C2×#6290C22semidirect
33. C2×#6290C22semidirect
34. C2×Dic3×C3⋊D3C22semidirect
35. C2×Dic3×C3⋊D3C22semidirect
37. C2×D3×C3⋊Dic3C22semidirect
40. #88864C22semidirect
41. #88864C22semidirect
43. C32×#217C22semidirect
44. C32×#217C22semidirect
45. #88807C22semidirect
46. #88806C22semidirect
47. Dic3⋊(C3⋊Dic3)C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
49. #88803C22semidirect
50. #88803C22semidirect
51. #88803C22semidirect
52. #88803C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
55. C22×#638D3semidirect
74. C3×#953D3semidirect
107. C3×#638D4semidirect
158. C2×C3×#67C2×D3semidirect
159. C2×C3×#67C2×D3semidirect
194. C3×#217C2×D3semidirect
195. C3×#217C2×D3semidirect
215. C22×C33#41semidirect
242. #953C3⋊D3semidirect
308. #638#67semidirect
387. C2×#67C2×C3⋊D3semidirect
388. C2×#67C2×C3⋊D3semidirect
427. #217C2×C3⋊D3semidirect
428. #217C2×C3⋊D3semidirect
475. C22×C32#237semidirect
476. C22×C32#237semidirect
534. C33#546semidirect
719. C22×C3#3805semidirect
722. C22×C3#3830semidirect
758. C32#5591semidirect
759. C32#5806semidirect
839. C22#89029semidirect
852. C3#10595494semidirect
853. C3#10596062semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6382
C2×#890292
C2×#888642
C32×#9532
#117236412
#117236372
#117236342
#117236312
#117236262
#117236212
C3⋊D3×#2172
#67×C3⋊Dic32
#117236152
#117236092
#117235912
#105960623
#105954943