Finite Group Databasebeta

← #13178650

Subgroups — #13178650

Order 1728.

1310 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64149C211yesmaximal, characteristic, complemented
2C3×#64147C211yesmaximal, characteristic, complemented
3C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#11723725C212yesmaximal, complemented
5#11723724C212yesmaximal, complemented
6#11723720C212yesmaximal, complemented
7#11723717C212yesmaximal, complemented
8#11723696C211yesmaximal, characteristic, complemented
9#11723691C211yesmaximal, characteristic, complemented
10#11723680C211yesmaximal, characteristic, complemented
11#11723673C211yesmaximal, characteristic, complemented
12#10595218—31nomaximal
13#10595217—31nomaximal
14#10595125—31nomaximal
15C2×C33×D4C2211yescharacteristic
16C2×C3×#638C2212yes—
17C2×C3×#638C2212yes—
18C2×C3×#638C2212yes—
19C22×C3×C3⋊Dic3C2212yes—
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×#6295C2212yes—
23C2×#6294C2212yes—
24C3×#3757C2212yes—
25C3×#3757C2212yes—
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C3×C4×C3⋊Dic3C2211yescharacteristic
29C3×C4×C3⋊Dic3C2211yescharacteristic
30#88815C2211yescharacteristic
31#88815C2211yescharacteristic
32#88815C2212yes—
33#88815C2212yes—
34#88814C2211yescharacteristic
35#88814C2211yescharacteristic
36#88814C2212yes—
37#88814C2212yes—
38#64149D311yescharacteristic, complemented
39#64147D311yescharacteristic, complemented
40D4×C3⋊Dic3D311yescharacteristic, complemented
41C3×#940—31no—
42C3×#940—31no—
43C3×#940—61no—
44C3×#938—31no—
45C3×#938—31no—
46C3×#938—61no—
47C3×D4×Dic3—31no—
48C3×D4×Dic3—31no—
49C3×D4×Dic3—61no—
50#63980—32no—
51#63978—32no—
52#63978—32no—
53#63975—32no—
54#63971—32no—
55#63970—32no—
56#63969—32no—
57#63969—32no—
58#63966—32no—
59#63962—32no—
60#63961—32no—
61#63958—32no—
62#63916—31no—
63#63909—31no—
64#63908—31no—
65#63898—31no—
66#63894—31no—
67Dic3×D12—31no—
68#63874—31no—
69#63872—31no—
70#63869—31no—
71#63869—31no—
72#63855—31no—
73#63855—31no—
74C23×C33C2312yes—
75C22×C3×C3⋊D3C2312yes—
76C22×C3×C3⋊D3C2311yescharacteristic
77C33×D4—22no—
78C2×C33×C4C2311yescharacteristic
79C3×#638—42no—
80C3×#638—42no—
81C3×#638—42no—
82C2×C3×C3⋊Dic3—42no—
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C2×C3×C3⋊Dic3C2311yescharacteristic
87C2×C3×C3⋊Dic3C2312yes—
88C2×C3×C3⋊Dic3C2312yes—
89C2×C3×C3⋊Dic3C2311yescharacteristic
90C3×C4⋊(C3⋊D3)—22no—
91C3×C4×C3⋊D3—22no—
92#6295—42no—
93#6294—42no—
94#5719—91no—
95#5619—91no—
96#5562—91no—
97C2×C32×D4—21no—
98C2×C32×D4—21no—
99C2×C32×D4—21no—
100C2×C32×D4—41no—
101C2×C32×D4C2×D311yescharacteristic
102C2×C32×D4C2×D311yescharacteristic
103C2×C32×D4C2×D311yescharacteristic
104C2×#638C2×D312yes—
105C2×#638C2×D312yes—
106C2×#638C2×D312yes—
107C22×C3⋊Dic3C2×D312yes—
108C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
109C2×C4×C3⋊D3C2×D311yescharacteristic
110C2×C3×#67—32no—
111C2×C3×#67—32no—
112C2×C3×#67—32no—
113C2×C3×#67—32no—
114C2×C3×#67—32no—
115C2×C3×#67—32no—
116C2×C3×#67—62no—
117C2×C3×#67—62no—
118C2×C3×#67—62no—
119C22×C3×Dic3—32no—
120C22×C3×Dic3—32no—
121C22×C3×Dic3—62no—
122C2×C3×D12—31no—
123C2×C3×D12—31no—
124C2×C3×D12—61no—
125C2×C3×C4×D3—31no—
126C2×C3×C4×D3—31no—
127C2×C3×C4×D3—61no—
128C2×#626—32no—
129C2×#626—32no—
130C2×#625—32no—
131C2×#624—32no—
132C2×D3×Dic3—32no—
133C2×D3×Dic3—32no—
134#3757C2×D312yes—
135#3757C2×D312yes—
136C4⋊(C3⋊Dic3)C2×D311yescharacteristic
137C4⋊(C3⋊Dic3)C2×D311yescharacteristic
138C4×C3⋊Dic3C2×D311yescharacteristic
139C4×C3⋊Dic3C2×D311yescharacteristic
140C3×#217—32no—
141C3×#217—32no—
142C3×#217—32no—
143C3×#217—32no—
144C3×#217—62no—
145C3×#217—62no—
146C3×C4⋊Dic3—31no—
147C3×C4⋊Dic3—31no—
148C3×C4⋊Dic3—31no—
149C3×C4⋊Dic3—31no—
150C3×C4⋊Dic3—61no—
151C3×C4⋊Dic3—61no—
152C3×C4×Dic3—31no—
153C3×C4×Dic3—31no—
154C3×C4×Dic3—31no—
155C3×C4×Dic3—31no—
156C3×C4×Dic3—61no—
157C3×C4×Dic3—61no—
158#3724—32no—
159#3724—32no—
160#3724—31no—
161#3724—31no—
162Dic3⋊Dic3—31no—
163Dic3⋊Dic3—31no—
164Dic3⋊Dic3—31no—
165Dic3⋊Dic3—31no—
166Dic3⋊Dic3—32no—
167Dic3⋊Dic3—32no—
168Dic3⋊Dic3—32no—
169Dic3⋊Dic3—32no—
170#3722—31no—
171#3722—31no—
172#3722—32no—
173#3722—32no—
174(C2×D3)⋊Dic3—31no—
175(C2×D3)⋊Dic3—31no—
176(C2×D3)⋊Dic3—31no—
177(C2×D3)⋊Dic3—31no—
178(C2×D3)⋊Dic3—32no—
179(C2×D3)⋊Dic3—32no—
180(C2×D3)⋊Dic3—32no—
181(C2×D3)⋊Dic3—32no—
182C22×C33—22no—
183C22×C33—22no—
184C22×C33—22no—
185C22×C33C2411yescharacteristic
186C2×C3×C3⋊D3—21no—
187C2×C3×C3⋊D3—22no—
188C2×C3×C3⋊D3—21no—
189C2×C3×C3⋊D3—22no—
190C2×C3×C3⋊D3—21no—
191C2×C3×C3⋊D3—22no—
192C33×C4#4112yes—
193C3×C3⋊Dic3—21no—
194C3×C3⋊Dic3—21no—
195C3×C3⋊Dic3—21no—
196C3×C3⋊Dic3—21no—
197C3×C3⋊Dic3—21no—
198C3×C3⋊Dic3—22no—
199C3×C3⋊Dic3—22no—
200C3×#127—91no—
201C3×#121—91no—
202C3×C4×D4—91no—
203#940—31no—
204#940—31no—
205#940—61no—
206#939—92no—
207#939—92no—
208#939—92no—
209#938—31no—
210#938—31no—
211#938—61no—
212#938—91no—
213#938—92no—
214#935—92no—
215#935—92no—
216D4×Dic3—31no—
217D4×Dic3—31no—
218D4×Dic3—61no—
219D4×Dic3—91no—
220#930—91no—
221#930—92no—
222#929—92no—
223#926—91no—
224#895—91no—
225#893—91no—
226#890—91no—
227#890—91no—
228#886—92no—
229#884—92no—
230#883—92no—
231#883—92no—
232C4×D12—91no—
233#872—91no—
234#872—91no—
235#870—91no—
236C23×C32—22no—
237C23×C32—22no—
238C23×C32—22no—
239C23×C32—42no—
240C23×C32C22×D312yes—
241C23×C32C22×D312yes—
242C23×C32C22×D312yes—
243C22×C3⋊D3C22×D312yes—
244C22×C3⋊D3C22×D311yescharacteristic
245C22×C3×D3—32no—
246C22×C3×D3—32no—
247C22×C3×D3—31no—
248C22×C3×D3—31no—
249C22×C3×D3—61no—
250C22×C3×D3—62no—
251C32×D4—22no—
252C32×D4—24no—
253C32×D4—22no—
254C32×D4—22no—
255C32×D4—42no—
256C32×D4—42no—
257C32×D4—44no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—41no—
262C2×C32×C4C22×D311yescharacteristic
263C2×C32×C4C22×D311yescharacteristic
264C2×C32×C4C22×D311yescharacteristic
265#638—42no—
266#638—42no—
267#638—42no—
268C2×C3⋊Dic3—42no—
269C2×C3⋊Dic3C22×D311yescharacteristic
270C2×C3⋊Dic3C22×D311yescharacteristic
271C2×C3⋊Dic3C22×D311yescharacteristic
272C2×C3⋊Dic3C22×D311yescharacteristic
273C2×C3⋊Dic3C22×D312yes—
274C2×C3⋊Dic3C22×D312yes—
275C2×C3⋊Dic3C22×D311yescharacteristic
276C4⋊(C3⋊D3)—22no—
277C4×C3⋊D3—22no—
278C3×#67—122no—
279C3×#67—122no—
280C3×#67—122no—
281C3×#67—122no—
282C3×#67—122no—
283C3×#67—122no—
284C3×#67—124no—
285C3×#67—124no—
286C3×#67—124no—
287C2×C3×Dic3—31no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—32no—
293C2×C3×Dic3—32no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—32no—
298C2×C3×Dic3—32no—
299C2×C3×Dic3—31no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3—61no—
302C2×C3×Dic3—61no—
303C2×C3×Dic3—61no—
304C2×C3×Dic3—61no—
305C2×C3×Dic3—62no—
306C2×C3×Dic3—62no—
307C2×C3×Dic3—61no—
308C2×C3×Dic3—122no—
309C2×C3×Dic3—122no—
310C2×C3×Dic3—124no—
311C3×D12—62no—
312C3×D12—62no—
313C3×D12—122no—
314C3×C4×D3—62no—
315C3×C4×D3—62no—
316C3×C4×D3—122no—
317#626—122no—
318#626—122no—
319#625—122no—
320#624—122no—
321D3×Dic3—122no—
322D3×Dic3—122no—
323#540—271noSylow
324C2×C33—42no—
325C2×C33C2×#4111yescharacteristic
326C2×C33H(5,𝔽2)11yescharacteristic
327C2×C33H(5,𝔽2)11yescharacteristic
328C3×C3⋊D3—41no—
329C3×C3⋊D3—42no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—41no—
334C2×C3×D4—92no—
335C2×C3×D4—92no—
336C2×C3×D4—92no—
337C2×C3×D4—91no—
338C2×C3×D4D3211yescharacteristic
339C2×C3×D4D3211yescharacteristic
340C2×C3×D4D3211yescharacteristic
341C22×C3×C4—92no—
342C22×C3×C4—91no—
343C2×#67—32no—
344C2×#67—32no—
345C2×#67—32no—
346C2×#67—32no—
347C2×#67—32no—
348C2×#67—32no—
349C2×#67—62no—
350C2×#67—62no—
351C2×#67—62no—
352C2×#67—92no—
353C2×#67—92no—
354C22×Dic3—32no—
355C22×Dic3—32no—
356C22×Dic3—62no—
357C22×Dic3—92no—
358C2×D12—31no—
359C2×D12—31no—
360C2×D12—61no—
361C2×D12—92no—
362C2×C4×D3—31no—
363C2×C4×D3—31no—
364C2×C4×D3—61no—
365C2×C4×D3—92no—
366C2×C4×D3—92no—
367C3×C4⋊C4—91no—
368C3×C4⋊C4—91no—
369C3×C22⋊C4—92no—
370C3×C22⋊C4—92no—
371C3×C42—91no—
372C3×C42—91no—
373#217—32no—
374#217—32no—
375#217—32no—
376#217—32no—
377#217—62no—
378#217—62no—
379#217—91no—
380#217—91no—
381#217—92no—
382#217—92no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—92no—
388(C2×D3)⋊C4—92no—
389(C2×D3)⋊C4—92no—
390(C2×D3)⋊C4—92no—
391C4⋊Dic3—31no—
392C4⋊Dic3—31no—
393C4⋊Dic3—31no—
394C4⋊Dic3—31no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3—91no—
398C4⋊Dic3—92no—
399C4⋊Dic3—91no—
400C4⋊Dic3—92no—
401Dic3⋊C4—92no—
402Dic3⋊C4—92no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406Dic3⋊C4—91no—
407Dic3⋊C4—92no—
408Dic3⋊C4—92no—
409C4×Dic3—31no—
410C4×Dic3—31no—
411C4×Dic3—31no—
412C4×Dic3—31no—
413C4×Dic3—61no—
414C4×Dic3—61no—
415C22×C32—22no—
416C22×C32—24no—
417C22×C32—22no—
418C22×C32—22no—
419C22×C32—22no—
420C22×C32—22no—
421C22×C32—22no—
422C22×C32—22no—
423C22×C32—22no—
424C22×C32—22no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—41no—
429C22×C32—42no—
430C22×C32—42no—
431C22×C32—44no—
432C22×C32—42no—
433C22×C32—42no—
434C22×C32—42no—
435C22×C32—42no—
436C22×C32—42no—
437C22×C32—42no—
438C22×C32—82no—
439C22×C32—82no—
440C22×C32C23×D311yescharacteristic
441C22×C32C23×D311yescharacteristic
442C22×C32C23×D311yescharacteristic
443C2×C3⋊D3—21no—
444C2×C3⋊D3—21no—
445C2×C3⋊D3—22no—
446C2×C3⋊D3—22no—
447C2×C3⋊D3—22no—
448C2×C3⋊D3—21no—
449C2×C3×D3—62no—
450C2×C3×D3—61no—
451C2×C3×D3—62no—
452C2×C3×D3—61no—
453C2×C3×D3—62no—
454C2×C3×D3—62no—
455C2×C3×D3—61no—
456C2×C3×D3—62no—
457C2×C3×D3—61no—
458C2×C3×D3—61no—
459C2×C3×D3—62no—
460C2×C3×D3—62no—
461C2×C3×D3—61no—
462C2×C3×D3—121no—
463C2×C3×D3—121no—
464C2×C3×D3—122no—
465C2×C3×D3—122no—
466C2×C3×D3—122no—
467C32×C4—22no—
468C32×C4—22no—
469C32×C4—22no—
470C32×C4—42no—
471C32×C4#23512yes—
472C32×C4#23712yes—
473C32×C4#23712yes—
474C3⋊Dic3—21no—
475C3⋊Dic3—21no—
476C3⋊Dic3—21no—
477C3⋊Dic3—21no—
478C3⋊Dic3—22no—
479C3⋊Dic3—22no—
480C3⋊Dic3—21no—
481C3×Dic3—62no—
482C3×Dic3—62no—
483C3×Dic3—62no—
484C3×Dic3—61no—
485C3×Dic3—61no—
486C3×Dic3—61no—
487C3×Dic3—61no—
488C3×Dic3—62no—
489C3×Dic3—62no—
490C3×Dic3—61no—
491C3×Dic3—61no—
492C3×Dic3—61no—
493C3×Dic3—62no—
494C3×Dic3—62no—
495C3×Dic3—61no—
496C3×Dic3—61no—
497C3×Dic3—61no—
498C3×Dic3—121no—
499C3×Dic3—121no—
500C3×Dic3—122no—
501C3×Dic3—122no—
502#127—91no—
503#125—271no—
504#123—272no—
505#123—272no—
506#121—91no—
507#121—272no—
508#121—271no—
509#121—272no—
510C4×D4—91no—
511C4×D4—271no—
512#117—271no—
513C33#54011yescharacteristic, complemented, Sylow
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—22no—
517C23×C3—42no—
518C23×C3—92no—
519C23×C3—91no—
520C23×C3C2×D3212yes—
521C23×C3C2×D3212yes—
522C23×C3C2×D3212yes—
523C22×D3—31no—
524C22×D3—31no—
525C22×D3—32no—
526C22×D3—32no—
527C22×D3—61no—
528C22×D3—62no—
529C3×D4—24no—
530C3×D4—22no—
531C3×D4—22no—
532C3×D4—22no—
533C3×D4—42no—
534C3×D4—42no—
535C3×D4—44no—
536C3×D4—182no—
537C3×D4—362no—
538C3×D4—362no—
539C3×D4—362no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—41no—
544C2×C3×C4—91no—
545C2×C3×C4—91no—
546C2×C3×C4—92no—
547C2×C3×C4—92no—
548C2×C3×C4—91no—
549C2×C3×C4—91no—
550C2×C3×C4—91no—
551C2×C3×C4—182no—
552C2×C3×C4—362no—
553C2×C3×C4C2×D3211yescharacteristic
554C2×C3×C4C2×D3211yescharacteristic
555C2×C3×C4C2×D3211yescharacteristic
556#67—122no—
557#67—122no—
558#67—122no—
559#67—122no—
560#67—122no—
561#67—122no—
562#67—124no—
563#67—124no—
564#67—124no—
565#67—362no—
566#67—362no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—31no—
575C2×Dic3—32no—
576C2×Dic3—32no—
577C2×Dic3—31no—
578C2×Dic3—31no—
579C2×Dic3—32no—
580C2×Dic3—32no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—62no—
586C2×Dic3—62no—
587C2×Dic3—61no—
588C2×Dic3—122no—
589C2×Dic3—122no—
590C2×Dic3—124no—
591C2×Dic3—362no—
592D12—62no—
593D12—62no—
594D12—122no—
595D12—362no—
596C4×D3—62no—
597C4×D3—62no—
598C4×D3—122no—
599C4×D3—362no—
600C4×D3—362no—
601C2×C32—21no—
602C2×C32—21no—
603C2×C32—21no—
604C2×C32—21no—
605C2×C32—21no—
606C2×C32—21no—
607C2×C32—21no—
608C2×C32—21no—
609C2×C32—21no—
610C2×C32—41no—
611C2×C32—41no—
612C2×C32—41no—
613C2×C32—42no—
614C2×C32—44no—
615C2×C32—42no—
616C2×C32—42no—
617C2×C32—82no—
618C2×C32—82no—
619C2×C32—84no—
620C2×C32C2×#23511yescharacteristic
621C2×C32C2×#23711yescharacteristic
622C2×C32C2×#23711yescharacteristic
623C2×C32#100411yescharacteristic
624C2×C32#100411yescharacteristic
625C2×C32#100411yescharacteristic
626C2×C32#100411yescharacteristic
627C2×C32#100911yescharacteristic
628C2×C32#100911yescharacteristic
629C3⋊D3—41no—
630C3⋊D3—42no—
631C3×D3—122no—
632C3×D3—121no—
633C3×D3—121no—
634C3×D3—122no—
635C3×D3—122no—
636C3×D3—242no—
637C2×D4—92no—
638C2×D4—92no—
639C2×D4—92no—
640C2×D4—91no—
641C2×D4—272no—
642C2×D4#111311yescharacteristic
643C22×C4—92no—
644C22×C4—91no—
645C22×C4—272no—
646C4⋊C4—91no—
647C4⋊C4—91no—
648C4⋊C4—271no—
649C4⋊C4—271no—
650C4⋊C4—272no—
651C4⋊C4—272no—
652C22⋊C4—92no—
653C22⋊C4—92no—
654C22⋊C4—271no—
655C22⋊C4—271no—
656C22⋊C4—272no—
657C22⋊C4—272no—
658C42—91no—
659C42—91no—
660C22×C3—24no—
661C22×C3—22no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—22no—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3—42no—
676C22×C3—42no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3—44no—
682C22×C3—41no—
683C22×C3—82no—
684C22×C3—82no—
685C22×C3—181no—
686C22×C3—182no—
687C22×C3—182no—
688C22×C3—181no—
689C22×C3—181no—
690C22×C3—182no—
691C22×C3C22×D3211yescharacteristic
692C22×C3C22×D3211yescharacteristic
693C22×C3C22×D3211yescharacteristic
694C2×D3—62no—
695C2×D3—62no—
696C2×D3—61no—
697C2×D3—62no—
698C2×D3—62no—
699C2×D3—61no—
700C2×D3—62no—
701C2×D3—61no—
702C2×D3—61no—
703C2×D3—61no—
704C2×D3—62no—
705C2×D3—61no—
706C2×D3—62no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—122no—
710C2×D3—122no—
711C2×D3—122no—
712C3×C4—22no—
713C3×C4—22no—
714C3×C4—22no—
715C3×C4—42no—
716C3×C4—181no—
717C3×C4—182no—
718C3×C4—182no—
719C3×C4—181no—
720C3×C4—181no—
721C3×C4—181no—
722C3×C4—181no—
723C3×C4#380412yes—
724C3×C4#380412yes—
725C3×C4#380512yes—
726Dic3—62no—
727Dic3—62no—
728Dic3—62no—
729Dic3—62no—
730Dic3—61no—
731Dic3—62no—
732Dic3—61no—
733Dic3—61no—
734Dic3—61no—
735Dic3—61no—
736Dic3—62no—
737Dic3—61no—
738Dic3—62no—
739Dic3—61no—
740Dic3—61no—
741Dic3—61no—
742Dic3—61no—
743Dic3—121no—
744Dic3—122no—
745Dic3—122no—
746Dic3—121no—
747C32—21no—
748C32—21no—
749C32—21no—
750C32—41no—
751C32#556211yescharacteristic, complemented
752C32#561911yescharacteristic, complemented
753C32#571911yescharacteristic, complemented
754C23—91no—
755C23—92no—
756C23C2×#111312yes—
757D4—22no—
758D4—182no—
759D4—362no—
760D4—362no—
761D4—362no—
762D4—1082no—
763C2×C4—91no—
764C2×C4—91no—
765C2×C4—91no—
766C2×C4—91no—
767C2×C4—91no—
768C2×C4—92no—
769C2×C4—92no—
770C2×C4—182no—
771C2×C4—362no—
772C2×C4—1082no—
773C2×C4C2×#111311yescharacteristic
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—44no—
784C2×C3—42no—
785C2×C3—42no—
786C2×C3—42no—
787C2×C3—41no—
788C2×C3—41no—
789C2×C3—41no—
790C2×C3—82no—
791C2×C3—82no—
792C2×C3—84no—
793C2×C3—362no—
794C2×C3—361no—
795C2×C3#6431311yescharacteristic
796C2×C3#6431311yescharacteristic
797C2×C3#6431411yescharacteristic
798C2×C3#6431411yescharacteristic
799C2×C3#6431411yescharacteristic
800C2×C3#6431411yescharacteristic
801C2×C3C2×#380411yescharacteristic
802C2×C3C2×#380411yescharacteristic
803C2×C3C2×#380511yescharacteristic
804D3—122no—
805D3—121no—
806D3—121no—
807D3—122no—
808D3—122no—
809D3—242no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—182no—
814C22—181no—
815C22—182no—
816C22—181no—
817C22—181no—
818C22—182no—
819C22C22×#111311yescharacteristic
820C4—181no—
821C4—182no—
822C4—181no—
823C4—182no—
824C4—181no—
825C4—181no—
826C4—181no—
827C4#8904612yes—
828C3—21no—
829C3—21no—
830C3—21no—
831C3—41no—
832C3#1059512511yescharacteristic, complemented
833C3#1059521711yescharacteristic, complemented
834C3#1059521811yescharacteristic, complemented
835C2—42no—
836C2—361no—
837C2—362no—
838C2#1172462311yescharacteristic
839C2#1172462311yescharacteristic
840C2C2×#8904611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33#540
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C3×#64149C2semidirect
2. C3×#64147C2semidirect
3. C3×D4×C3⋊Dic3C2semidirect
4. #11723725C2semidirect
5. #11723724C2semidirect
6. #11723720C2semidirect
7. #11723717C2semidirect
8. #11723696C2semidirect
9. #11723691C2semidirect
10. #11723680C2semidirect
11. #11723673C2semidirect
38. #64149D3semidirect
39. #64147D3semidirect
40. D4×C3⋊Dic3D3semidirect
513. C33#540semidirect
751. C32#5562semidirect
752. C32#5619semidirect
753. C32#5719semidirect
832. C3#10595125semidirect
833. C3#10595217semidirect
834. C3#10595218semidirect

Maximal subgroups

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

subgroupindex
C3×#641492
C3×#641472
C3×D4×C3⋊Dic32
#117237252
#117237242
#117237202
#117237172
#117236962
#117236912
#117236802
#117236732
#105952183
#105952173
#105951253