Finite Group Databasebeta

← #13177631

Subgroups — #13177631

Order 1728.

2032 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723978C211yesmaximal, characteristic, complemented
2C3×#64148C211yesmaximal, characteristic, complemented
3C32×#938C211yesmaximal, characteristic, complemented
4#11723639C211yesmaximal, characteristic, complemented
5#11723638C211yesmaximal, characteristic, complemented
6#11723635C211yesmaximal, characteristic, complemented
7#11723633C211yesmaximal, characteristic, complemented
8#11723631C211yesmaximal, characteristic, complemented
9#11723624C211yesmaximal, characteristic, complemented
10#11723608C211yesmaximal, characteristic, complemented
11#11723596C211yesmaximal, characteristic, complemented
12#11723514C211yesmaximal, characteristic, complemented
13#11723493C211yesmaximal, characteristic, complemented
14#11723414C211yesmaximal, characteristic, complemented
15#11723411C211yesmaximal, characteristic, complemented
16#10596091—31nomaximal
17#10595264—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic
26C2×C32×#67C2211yescharacteristic, complemented
27C2×C32×C4×D3C2211yescharacteristic, complemented
28C2×#6292C2211yescharacteristic
29C2×#6292C2211yescharacteristic
30C2×#6291C2211yescharacteristic
31C2×#6291C2211yescharacteristic
32C2×#6290C2211yescharacteristic, complemented
33C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
34#88864C2211yescharacteristic
35#88859C2211yescharacteristic
36#88859C2211yescharacteristic
37C3×#3757C2211yescharacteristic
38C3×#3752C2211yescharacteristic, complemented
39C3×#3750C2211yescharacteristic, complemented
40C32×#217C2211yescharacteristic
41C32×#217C2211yescharacteristic, complemented
42C32×C4⋊Dic3C2211yescharacteristic, complemented
43#88807C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#121—31no—
54#64149—31no—
55#64148—31no—
56#64148D311yescharacteristic, complemented
57#64147—31no—
58#64146—31no—
59#64146—31no—
60#64146—34no—
61#64146—64no—
62#64139—31no—
63#64138—31no—
64#64107—31no—
65#64103—31no—
66#64095—31no—
67#64093—31no—
68#64091—31no—
69#64088—31no—
70C3×#939—34no—
71C3×#938D314yescomplemented
72#63981—34no—
73#63981—34no—
74#63979—34no—
75#63978—34no—
76#63971—34no—
77#63970—34no—
78#63966—34no—
79#63956—34no—
80#63906—34no—
81#63890—34no—
82#63850—34no—
83#63848—34no—
84C23×C33C2311yescharacteristic
85C23×C33C2311yescharacteristic
86C22×C3⋊(C3⋊D3)—41no—
87C22×C3⋊(C3⋊D3)—41no—
88C22×C3⋊(C3⋊D3)—41no—
89C22×C3⋊(C3⋊D3)C2311yescharacteristic
90C22×C3⋊(C3⋊D3)C2311yescharacteristic
91C22×C3×C3⋊D3C2311yescharacteristic
92C22×C32×D3C2311yescharacteristic
93C33×D4—41no—
94C2×C33×C4C2311yescharacteristic
95#6312—41no—
96#6312—41no—
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C3×#638—41no—
100C3×#638—41no—
101C2×C3×C3⋊Dic3—41no—
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C2×C3×C3⋊Dic3C2311yescharacteristic
105C32×#67—41no—
106C32×#67—41no—
107C2×C32×Dic3C2311yescharacteristic
108C2×C32×Dic3C2311yescharacteristic
109C2×C32×Dic3C2311yescharacteristic
110C32×C4×D3—41no—
111#6292—41no—
112#6292—41no—
113#6291—41no—
114#6291—41no—
115#6290—41no—
116Dic3×C3⋊D3—41no—
117#5620—94no—
118#5620—91no—
119C23×C3⋊D3—31no—
120C23×C3⋊D3—34no—
121C23×C3⋊D3—64no—
122C2×C32×D4—24no—
123C2×C32×D4—31no—
124C2×C32×D4—31no—
125C2×C32×D4C2×D314yes—
126C2×C32×D4C2×D311yescharacteristic
127C22×C32×C4—31no—
128C2×#638—31no—
129C2×#638—31no—
130C2×#638—34no—
131C2×#638—34no—
132C2×#638—31no—
133C2×#638—31no—
134C2×#638—31no—
135C2×#638—64no—
136C2×#638—64no—
137C2×#638C2×D311yescharacteristic
138C2×#638C2×D311yescharacteristic, complemented
139C22×C3⋊Dic3C2×D311yescharacteristic, complemented
140C2×C4⋊(C3⋊D3)—31no—
141C2×C4⋊(C3⋊D3)—31no—
142C2×C4×C3⋊D3—31no—
143C2×C3×#67—34no—
144C2×C3×#67—34no—
145C2×C3×#67C2×D314yes—
146C2×C3×#67C2×D314yescomplemented
147C22×C3×Dic3—34no—
148C2×C3×C4×D3C2×D314yescomplemented
149C2×#626—34no—
150C2×#626—34no—
151C2×#626—34no—
152C2×#626—34no—
153C2×#625—34no—
154C2×D3×Dic3—34no—
155C32×C4⋊C4—31no—
156C32×C22⋊C4—31no—
157C32×C22⋊C4—31no—
158#3757—31no—
159#3757—34no—
160#3757—31no—
161#3757—64no—
162#3757C2×D311yescharacteristic
163#3752—31no—
164#3752—31no—
165#3752—34no—
166#3752—34no—
167#3752—31no—
168#3752—31no—
169#3752—31no—
170#3752—31no—
171#3752—64no—
172#3752—64no—
173#3752C2×D311yescharacteristic, complemented
174C4⋊(C3⋊Dic3)—31no—
175C4⋊(C3⋊Dic3)—31no—
176#3750—31no—
177#3750—31no—
178#3750C2×D311yescharacteristic, complemented
179C4×C3⋊Dic3—31no—
180C3×#217—34no—
181C3×#217C2×D314yes—
182C3×#217C2×D314yescomplemented
183C3×(C2×D3)⋊C4—34no—
184C3×C4⋊Dic3C2×D314yescomplemented
185C3×Dic3⋊C4—34no—
186#3724—34no—
187Dic3⋊Dic3—34no—
188Dic3⋊Dic3—34no—
189Dic3⋊Dic3—34no—
190#3722—34no—
191#3722—34no—
192#3722—34no—
193#3722—34no—
194(C2×D3)⋊Dic3—34no—
195Dic32—34no—
196C22×C33—21no—
197C22×C33—21no—
198C22×C33—21no—
199C22×C33—21no—
200C22×C33—21no—
201C22×C33—21no—
202C22×C33C2411yescharacteristic
203C2×C3⋊(C3⋊D3)—21no—
204C2×C3⋊(C3⋊D3)—21no—
205C2×C3⋊(C3⋊D3)—21no—
206C2×C3⋊(C3⋊D3)—21no—
207C2×C3⋊(C3⋊D3)—21no—
208C2×C3⋊(C3⋊D3)—21no—
209C2×C3⋊(C3⋊D3)—44no—
210C2×C3×C3⋊D3—21no—
211C2×C3×C3⋊D3—21no—
212C2×C3×C3⋊D3—21no—
213C2×C32×D3—21no—
214C2×C32×D3—21no—
215C2×C32×D3—21no—
216C33×C4—21no—
217C3⋊(C3⋊Dic3)—21no—
218C3⋊(C3⋊Dic3)—21no—
219C3×C3⋊Dic3—21no—
220C3×C3⋊Dic3—21no—
221C3×C3⋊Dic3—21no—
222C32×Dic3—21no—
223C32×Dic3—21no—
224C32×Dic3—21no—
225C3×#121—34no—
226C3×#121—91no—
227#940—94no—
228#940—91no—
229#939—34no—
230#939—94no—
231#939—91no—
232#939—91no—
233#938—94no—
234#938C3⋊D311yescharacteristic, complemented
235#937—94no—
236#937—94no—
237#937—91no—
238#937—91no—
239#937—184no—
240#930—94no—
241#930—91no—
242#929—94no—
243#929—91no—
244#898—94no—
245#898—91no—
246#894—94no—
247#894—91no—
248#886—94no—
249#886—91no—
250#884—94no—
251#884—91no—
252#882—94no—
253#882—91no—
254#879—94no—
255#879—91no—
256C23×C32—24no—
257C23×C32—24no—
258C23×C32—31no—
259C23×C32C22×D314yes—
260C23×C32C22×D314yes—
261C23×C32C22×D311yescharacteristic
262C23×C32C22×D311yescharacteristic
263C22×C3⋊D3—31no—
264C22×C3⋊D3—31no—
265C22×C3⋊D3—34no—
266C22×C3⋊D3—34no—
267C22×C3⋊D3—64no—
268C22×C3⋊D3—64no—
269C22×C3⋊D3—121no—
270C22×C3⋊D3—121no—
271C22×C3⋊D3—121no—
272C22×C3⋊D3—124no—
273C22×C3⋊D3—124no—
274C22×C3⋊D3—124no—
275C22×C3⋊D3—128no—
276C22×C3⋊D3—128no—
277C22×C3⋊D3—128no—
278C22×C3⋊D3C22×D311yescharacteristic
279C22×C3×D3—34no—
280C22×C3×D3C22×D314yes—
281C32×D4—41no—
282C32×D4—44no—
283C32×D4—48no—
284C32×D4—121no—
285C32×D4—121no—
286C2×C32×C4—24no—
287C2×C32×C4—31no—
288C2×C32×C4—31no—
289C2×C32×C4—31no—
290C2×C32×C4—121no—
291C2×C32×C4C22×D314yes—
292C2×C32×C4C22×D311yescharacteristic
293#638—41no—
294#638—41no—
295#638—121no—
296#638—121no—
297#638—121no—
298#638—121no—
299#638—121no—
300#638—124no—
301#638—124no—
302#638—128no—
303#638—128no—
304C2×C3⋊Dic3—31no—
305C2×C3⋊Dic3—31no—
306C2×C3⋊Dic3—34no—
307C2×C3⋊Dic3—34no—
308C2×C3⋊Dic3—41no—
309C2×C3⋊Dic3—64no—
310C2×C3⋊Dic3—64no—
311C2×C3⋊Dic3C22×D311yescharacteristic
312C2×C3⋊Dic3C22×D311yescharacteristic
313C2×C3⋊Dic3C22×D311yescharacteristic
314C4⋊(C3⋊D3)—121no—
315C4⋊(C3⋊D3)—121no—
316C4×C3⋊D3—121no—
317C3×#67—44no—
318C3×#67—44no—
319C3×#67—124no—
320C3×#67—124no—
321C2×C3×Dic3—34no—
322C2×C3×Dic3—34no—
323C2×C3×Dic3—34no—
324C2×C3×Dic3—124no—
325C2×C3×Dic3C22×D314yes—
326C2×C3×Dic3C22×D314yes—
327C2×C3×Dic3C22×D314yes—
328C3×C4×D3—44no—
329#626—124no—
330#626—124no—
331#626—124no—
332#626—124no—
333#625—124no—
334D3×Dic3—124no—
335#560—271noSylow
336C2×C33—41no—
337C2×C33—41no—
338C2×C33H(5,𝔽2)11yescharacteristic
339C2×C33H(5,𝔽2)11yescharacteristic
340C2×C33H(5,𝔽2)11yescharacteristic
341C3⋊(C3⋊D3)—41no—
342C3⋊(C3⋊D3)—41no—
343C3×C3⋊D3—41no—
344C32×D3—41no—
345C23×D3—94no—
346C23×D3—91no—
347C23×D3—184no—
348C2×C3×D4—24no—
349C2×C3×D4—34no—
350C2×C3×D4—34no—
351C2×C3×D4—91no—
352C2×C3×D4—91no—
353C2×C3×D4D3214yes—
354C2×C3×D4C2×C3⋊D311yescharacteristic
355C22×C3×C4—34no—
356C22×C3×C4—91no—
357C2×#67—34no—
358C2×#67—34no—
359C2×#67—94no—
360C2×#67—94no—
361C2×#67—94no—
362C2×#67—94no—
363C2×#67—94no—
364C2×#67—91no—
365C2×#67—91no—
366C2×#67—91no—
367C2×#67—91no—
368C2×#67—91no—
369C2×#67—184no—
370C2×#67—184no—
371C2×#67C2×C3⋊D311yescharacteristic
372C2×#67C2×C3⋊D311yescharacteristic, complemented
373C22×Dic3—34no—
374C22×Dic3—91no—
375C2×D12—94no—
376C2×D12—94no—
377C2×D12—91no—
378C2×D12—91no—
379C2×C4×D3—94no—
380C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
381C3×C4⋊C4—34no—
382C3×C4⋊C4—91no—
383C3×C22⋊C4—34no—
384C3×C22⋊C4—34no—
385C3×C22⋊C4—91no—
386C3×C22⋊C4—91no—
387#217—34no—
388#217—94no—
389#217—94no—
390#217—91no—
391#217—184no—
392#217C2×C3⋊D311yescharacteristic
393#217C2×C3⋊D311yescharacteristic, complemented
394(C2×D3)⋊C4—34no—
395(C2×D3)⋊C4—94no—
396(C2×D3)⋊C4—94no—
397(C2×D3)⋊C4—94no—
398(C2×D3)⋊C4—94no—
399(C2×D3)⋊C4—91no—
400(C2×D3)⋊C4—94no—
401(C2×D3)⋊C4—94no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—184no—
409(C2×D3)⋊C4—184no—
410C4⋊Dic3—94no—
411C4⋊Dic3—94no—
412C4⋊Dic3—91no—
413C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
414Dic3⋊C4—34no—
415Dic3⋊C4—94no—
416Dic3⋊C4—94no—
417Dic3⋊C4—91no—
418Dic3⋊C4—91no—
419Dic3⋊C4—91no—
420C4×Dic3—94no—
421C4×Dic3—91no—
422C22×C32—28no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—24no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—24no—
431C22×C32—24no—
432C22×C32—24no—
433C22×C32—24no—
434C22×C32—24no—
435C22×C32—24no—
436C22×C32—44no—
437C22×C32—44no—
438C22×C32—44no—
439C22×C32—44no—
440C22×C32—44no—
441C22×C32—61no—
442C22×C32—61no—
443C22×C32—61no—
444C22×C32C23×D314yes—
445C22×C32C23×D311yescharacteristic
446C2×C3⋊D3—21no—
447C2×C3⋊D3—21no—
448C2×C3⋊D3—21no—
449C2×C3⋊D3—68no—
450C2×C3⋊D3—68no—
451C2×C3⋊D3—61no—
452C2×C3⋊D3—64no—
453C2×C3⋊D3—61no—
454C2×C3⋊D3—61no—
455C2×C3⋊D3—61no—
456C2×C3⋊D3—61no—
457C2×C3⋊D3—64no—
458C2×C3⋊D3—61no—
459C2×C3⋊D3—64no—
460C2×C3⋊D3—64no—
461C2×C3⋊D3—64no—
462C2×C3⋊D3—64no—
463C2×C3⋊D3—124no—
464C2×C3⋊D3—124no—
465C2×C3⋊D3—124no—
466C2×C3⋊D3—124no—
467C2×C3⋊D3—1232no—
468C2×C3⋊D3—1216no—
469C2×C3⋊D3—124no—
470C2×C3×D3—24no—
471C2×C3×D3—24no—
472C2×C3×D3—24no—
473C2×C3×D3—64no—
474C2×C3×D3—64no—
475C2×C3×D3—64no—
476C32×C4—21no—
477C32×C4—24no—
478C32×C4—44no—
479C32×C4—61no—
480C32×C4—61no—
481C32×C4—61no—
482C3⋊Dic3—21no—
483C3⋊Dic3—21no—
484C3⋊Dic3—21no—
485C3⋊Dic3—61no—
486C3⋊Dic3—61no—
487C3⋊Dic3—64no—
488C3⋊Dic3—64no—
489C3⋊Dic3—124no—
490C3⋊Dic3—124no—
491C3×Dic3—24no—
492C3×Dic3—24no—
493C3×Dic3—24no—
494C3×Dic3—64no—
495C3×Dic3—64no—
496C3×Dic3—64no—
497#127—271no—
498#126—271no—
499#126—271no—
500#123—271no—
501#123—271no—
502#123—271no—
503#121—31no—
504#121—91no—
505#121—271no—
506#121—271no—
507#121—271no—
508#121—271no—
509#120—271no—
510#120—271no—
511#120—271no—
512C33#56011yescharacteristic, complemented, Sylow
513C23×C3—24no—
514C23×C3—24no—
515C23×C3—34no—
516C23×C3—91no—
517C23×C3C2×D3214yes—
518C23×C3C2×D3214yes—
519C23×C3C22×C3⋊D311yescharacteristic
520C23×C3C22×C3⋊D311yescharacteristic
521C22×D3—34no—
522C22×D3—94no—
523C22×D3—94no—
524C22×D3—91no—
525C22×D3—91no—
526C22×D3—184no—
527C22×D3—184no—
528C22×D3—364no—
529C22×D3—364no—
530C22×D3—364no—
531C22×D3—361no—
532C22×D3—361no—
533C22×D3—361no—
534C22×D3—368no—
535C22×D3—368no—
536C22×D3—368no—
537C22×D3C22×C3⋊D311yescharacteristic
538C3×D4—44no—
539C3×D4—41no—
540C3×D4—48no—
541C3×D4—124no—
542C3×D4—124no—
543C3×D4—361no—
544C3×D4—361no—
545C2×C3×C4—24no—
546C2×C3×C4—34no—
547C2×C3×C4—34no—
548C2×C3×C4—34no—
549C2×C3×C4—91no—
550C2×C3×C4—91no—
551C2×C3×C4—91no—
552C2×C3×C4—124no—
553C2×C3×C4—361no—
554C2×C3×C4C2×D3214yes—
555C2×C3×C4C22×C3⋊D311yescharacteristic
556#67—41no—
557#67—41no—
558#67—124no—
559#67—124no—
560#67—361no—
561#67—361no—
562#67—364no—
563#67—364no—
564#67—361no—
565#67—364no—
566#67—364no—
567#67—364no—
568#67—361no—
569#67—361no—
570#67—368no—
571#67—368no—
572C2×Dic3—34no—
573C2×Dic3—34no—
574C2×Dic3—34no—
575C2×Dic3—94no—
576C2×Dic3—94no—
577C2×Dic3—91no—
578C2×Dic3—91no—
579C2×Dic3—124no—
580C2×Dic3—184no—
581C2×Dic3—184no—
582C2×Dic3—361no—
583C2×Dic3C22×C3⋊D311yescharacteristic
584C2×Dic3C22×C3⋊D311yescharacteristic
585C2×Dic3C22×C3⋊D311yescharacteristic
586D12—364no—
587D12—364no—
588D12—361no—
589D12—361no—
590C4×D3—41no—
591C4×D3—364no—
592C2×C32—24no—
593C2×C32—24no—
594C2×C32—24no—
595C2×C32—48no—
596C2×C32—44no—
597C2×C32—41no—
598C2×C32—41no—
599C2×C32—44no—
600C2×C32—84no—
601C2×C32—121no—
602C2×C32#100414yes—
603C2×C32#100414yes—
604C2×C32#100411yescharacteristic
605C2×C32#100411yescharacteristic
606C2×C32#100914yes—
607C2×C32#100911yescharacteristic
608C3⋊D3—41no—
609C3⋊D3—128no—
610C3⋊D3—128no—
611C3⋊D3—124no—
612C3⋊D3—124no—
613C3⋊D3—121no—
614C3⋊D3—121no—
615C3×D3—44no—
616C3×D3—124no—
617C24—271no—
618C2×D4—31no—
619C2×D4—31no—
620C2×D4—91no—
621C2×D4—91no—
622C2×D4—271no—
623C2×D4—271no—
624C2×D4—271no—
625C2×D4—271no—
626C2×D4—271no—
627C2×D4—271no—
628C2×D4—271no—
629C2×D4D3×C3⋊D311yescharacteristic
630C22×C4—31no—
631C22×C4—91no—
632C22×C4—271no—
633C4⋊C4—31no—
634C4⋊C4—91no—
635C4⋊C4—271no—
636C4⋊C4—271no—
637C4⋊C4—271no—
638C4⋊C4—271no—
639C22⋊C4—31no—
640C22⋊C4—31no—
641C22⋊C4—91no—
642C22⋊C4—91no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C22⋊C4—271no—
646C22⋊C4—271no—
647C22⋊C4—271no—
648C22⋊C4—271no—
649C22⋊C4—271no—
650C22⋊C4—271no—
651C42—271no—
652C22×C3—28no—
653C22×C3—24no—
654C22×C3—24no—
655C22×C3—24no—
656C22×C3—24no—
657C22×C3—24no—
658C22×C3—24no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—24no—
666C22×C3—44no—
667C22×C3—44no—
668C22×C3—44no—
669C22×C3—44no—
670C22×C3—44no—
671C22×C3—64no—
672C22×C3—64no—
673C22×C3—64no—
674C22×C3—181no—
675C22×C3—181no—
676C22×C3—181no—
677C22×C3C22×D3214yes—
678C22×C3C23×C3⋊D311yescharacteristic
679C2×D3—21no—
680C2×D3—21no—
681C2×D3—21no—
682C2×D3—64no—
683C2×D3—64no—
684C2×D3—64no—
685C2×D3—188no—
686C2×D3—188no—
687C2×D3—184no—
688C2×D3—184no—
689C2×D3—184no—
690C2×D3—184no—
691C2×D3—184no—
692C2×D3—184no—
693C2×D3—181no—
694C2×D3—181no—
695C2×D3—181no—
696C2×D3—181no—
697C2×D3—181no—
698C2×D3—181no—
699C2×D3—364no—
700C2×D3—364no—
701C2×D3—364no—
702C2×D3—364no—
703C2×D3—3632no—
704C2×D3—3616no—
705C2×D3—364no—
706C3×C4—24no—
707C3×C4—21no—
708C3×C4—44no—
709C3×C4—64no—
710C3×C4—64no—
711C3×C4—64no—
712C3×C4—181no—
713C3×C4—181no—
714C3×C4—181no—
715Dic3—21no—
716Dic3—21no—
717Dic3—21no—
718Dic3—64no—
719Dic3—64no—
720Dic3—64no—
721Dic3—184no—
722Dic3—184no—
723Dic3—181no—
724Dic3—181no—
725Dic3—364no—
726Dic3—364no—
727C32—24no—
728C32#562014yescomplemented
729C32#562011yescharacteristic, complemented
730C23—31no—
731C23—91no—
732C23—271no—
733C23—271no—
734C23—1081no—
735C23—1081no—
736C23—1081no—
737C23C2×D3×C3⋊D311yescharacteristic
738C23C2×D3×C3⋊D311yescharacteristic
739D4—41no—
740D4—121no—
741D4—121no—
742D4—361no—
743D4—361no—
744D4—1081no—
745D4—1081no—
746D4—1081no—
747D4—1081no—
748D4—1081no—
749D4—1081no—
750D4—1081no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—31no—
754C2×C4—91no—
755C2×C4—91no—
756C2×C4—91no—
757C2×C4—121no—
758C2×C4—271no—
759C2×C4—271no—
760C2×C4—361no—
761C2×C4—1081no—
762C2×C4C2×D3×C3⋊D311yescharacteristic
763C2×C3—24no—
764C2×C3—24no—
765C2×C3—24no—
766C2×C3—48no—
767C2×C3—44no—
768C2×C3—44no—
769C2×C3—41no—
770C2×C3—41no—
771C2×C3—84no—
772C2×C3—124no—
773C2×C3—361no—
774C2×C3#6431414yes—
775C2×C3#6431414yes—
776C2×C3#6433014yes—
777C2×C3#6436111yescharacteristic
778C2×C3#6436111yescharacteristic
779C2×C3#6436611yescharacteristic
780D3—41no—
781D3—124no—
782D3—368no—
783D3—368no—
784D3—364no—
785D3—364no—
786D3—361no—
787D3—361no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—61no—
795C22—61no—
796C22—61no—
797C22—181no—
798C22—181no—
799C22—181no—
800C22—541no—
801C22—541no—
802C22—541no—
803C22—541no—
804C22—541no—
805C22—541no—
806C22—1084no—
807C22C22×D3×C3⋊D311yescharacteristic
808C4—21no—
809C4—61no—
810C4—61no—
811C4—61no—
812C4—181no—
813C4—181no—
814C4—181no—
815C4—541no—
816C4—541no—
817C3—24no—
818C3#1059526414yescomplemented
819C3#1059609111yescharacteristic, complemented
820C2—41no—
821C2—41no—
822C2—121no—
823C2—361no—
824C2—1081no—
825C2—1081no—
826C2#1172458811yescharacteristic
827C2#1172458911yescharacteristic
828C2#1172461111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#560
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #11723978C2semidirect
2. C3×#64148C2semidirect
3. C32×#938C2semidirect
4. #11723639C2semidirect
5. #11723638C2semidirect
6. #11723635C2semidirect
7. #11723633C2semidirect
8. #11723631C2semidirect
9. #11723624C2semidirect
10. #11723608C2semidirect
11. #11723596C2semidirect
12. #11723514C2semidirect
13. #11723493C2semidirect
14. #11723414C2semidirect
15. #11723411C2semidirect
23. C2×C3×#638C22semidirect
24. C22×C3×C3⋊Dic3C22semidirect
26. C2×C32×#67C22semidirect
27. C2×C32×C4×D3C22semidirect
32. C2×#6290C22semidirect
33. C2×Dic3×C3⋊D3C22semidirect
38. C3×#3752C22semidirect
39. C3×#3750C22semidirect
41. C32×#217C22semidirect
42. C32×C4⋊Dic3C22semidirect
43. #88807C22semidirect
44. #88806C22semidirect
45. Dic3⋊(C3⋊Dic3)C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
51. (C2×D3)⋊(C3⋊Dic3)C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
56. #64148D3semidirect
71. C3×#938D3semidirect
138. C2×#638C2×D3semidirect
139. C22×C3⋊Dic3C2×D3semidirect
146. C2×C3×#67C2×D3semidirect
148. C2×C3×C4×D3C2×D3semidirect
173. #3752C2×D3semidirect
178. #3750C2×D3semidirect
182. C3×#217C2×D3semidirect
184. C3×C4⋊Dic3C2×D3semidirect
234. #938C3⋊D3semidirect
372. C2×#67C2×C3⋊D3semidirect
380. C2×C4×D3C2×C3⋊D3semidirect
393. #217C2×C3⋊D3semidirect
413. C4⋊Dic3C2×C3⋊D3semidirect
512. C33#560semidirect
728. C32#5620semidirect
729. C32#5620semidirect
818. C3#10595264semidirect
819. C3#10596091semidirect

Maximal subgroups

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

subgroupindex
#117239782
C3×#641482
C32×#9382
#117236392
#117236382
#117236352
#117236332
#117236312
#117236242
#117236082
#117235962
#117235142
#117234932
#117234142
#117234112
#105960913
#105952643