Finite Group Databasebeta

← #13178637

Subgroups — #13178637

Order 1728.

1668 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3830C211yesmaximal, characteristic, complemented
2C2×#89041C211yesmaximal, characteristic, complemented
3C3×#64149C211yesmaximal, characteristic, complemented
4C3×#64147C211yesmaximal, characteristic, complemented
5#11723728C212yesmaximal, complemented
6#11723726C212yesmaximal, complemented
7#11723725C212yesmaximal, complemented
8#11723717C212yesmaximal, complemented
9#11723696C211yesmaximal, characteristic, complemented
10C4×#6295C211yesmaximal, characteristic, complemented
11#11723668C211yesmaximal, characteristic, complemented
12#10595236—31nomaximal
13#10595164—31nomaximal
14#10595158—31nomaximal
15C2×C33×D4C2211yescharacteristic
16C2×C3×#638C2212yes—
17C2×C3×#638C2212yes—
18C2×C3×#638C2212yes—
19C2×C3×#638C2212yes—
20C22×C3×C3⋊Dic3C2212yes—
21C3×#3830—24no—
22C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
23C2×C3×C4×C3⋊D3C2211yescharacteristic
24C2×C3×C4×C3⋊D3C2211yescharacteristic
25C2×C3×#634C2211yescharacteristic
26C2×#6295C2212yes—
27C2×#6295C2211yescharacteristic
28C2×#6295C2212yes—
29C2×#6294C2212yes—
30#89041—24no—
31C3×#3757C2212yes—
32C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
33C3×C4×C3⋊Dic3C2211yescharacteristic
34#88815C2212yes—
35#88815C2211yescharacteristic
36#88814C2211yescharacteristic
37#88814C2211yescharacteristic
38#88814C2212yes—
39#88813C2212yes—
40C2×#3830D311yescharacteristic, complemented
41C2×C3×#237—31no—
42C2×C3×#237—31no—
43C2×C3×#237—61no—
44C2×#3799—31no—
45C2×#3796—31no—
46C2×#3795—31no—
47#64149D311yescharacteristic, complemented
48#64147D311yescharacteristic, complemented
49C3×#940—31no—
50C3×#940—31no—
51C3×#940—61no—
52C3×#938—31no—
53C3×#938—31no—
54C3×#938—61no—
55#63980—32no—
56#63979—32no—
57#63979—32no—
58#63979—32no—
59#63978—32no—
60#63978—32no—
61#67⋊Dic3—32no—
62Dic3×#67—32no—
63#63971—32no—
64#63970—32no—
65#63958—32no—
66#63952—32no—
67#63916—31no—
68#63909—31no—
69#63908—31no—
70C4×#626—31no—
71C4×#626—31no—
72C4×#625—31no—
73#63844—31no—
74#63843—31no—
75Dic3×Dic6—31no—
76C23×C33C2312yes—
77C22×C3×C3⋊D3C2312yes—
78C22×C3×C3⋊D3C2311yescharacteristic
79C22×C3×C3⋊D3C2311yescharacteristic
80C33×D4—22no—
81C2×C33×C4C2311yescharacteristic
82C3×#638—24no—
83C3×#638—24no—
84C3×#638—42no—
85C3×#638—42no—
86C2×C3×C3⋊Dic3—24no—
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C2×C3×C3⋊Dic3C2312yes—
89C2×C3×C3⋊Dic3C2311yescharacteristic
90C2×C3×C3⋊Dic3C2311yescharacteristic
91C2×C3×C3⋊Dic3C2312yes—
92C2×C3×C3⋊Dic3C2311yescharacteristic
93C3×C4⋊(C3⋊D3)—22no—
94C3×C4×C3⋊D3—22no—
95C3×C4×C3⋊D3—22no—
96C3×#634D414yescomplemented
97#6295—24no—
98#6295—22no—
99#6295—42no—
100#6294—24no—
101#5834—91no—
102#5718—91no—
103#5599—91no—
104C2×C32×D4—21no—
105C2×C32×D4—21no—
106C2×C32×D4—21no—
107C2×C32×D4—41no—
108C2×C32×D4C2×D311yescharacteristic
109C2×C32×D4C2×D311yescharacteristic
110C2×C32×D4C2×D311yescharacteristic
111C2×#638C2×D312yes—
112C2×#638C2×D312yes—
113C2×#638C2×D312yes—
114C2×#638C2×D312yes—
115C22×C3⋊Dic3C2×D312yes—
116#3830—24no—
117C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
118C2×C4×C3⋊D3C2×D311yescharacteristic
119C2×C4×C3⋊D3C2×D311yescharacteristic
120C2×#634C2×D311yescharacteristic
121C2×C3×#67—32no—
122C2×C3×#67—32no—
123C2×C3×#67—32no—
124C2×C3×#67—32no—
125C2×C3×#67—32no—
126C2×C3×#67—32no—
127C2×C3×#67—32no—
128C2×C3×#67—32no—
129C2×C3×#67—62no—
130C2×C3×#67—62no—
131C2×C3×#67—62no—
132C2×C3×#67—62no—
133C22×C3×Dic3—32no—
134C22×C3×Dic3—32no—
135C22×C3×Dic3—62no—
136C3×#237—64no—
137C3×#237—64no—
138C3×#237—68no—
139C2×C3×D12—31no—
140C2×C3×D12—31no—
141C2×C3×D12—61no—
142C2×C3×C4×D3—31no—
143C2×C3×C4×D3—31no—
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3—61no—
147C2×C3×C4×D3—61no—
148C2×C3×Dic6—31no—
149C2×C3×Dic6—31no—
150C2×C3×Dic6—61no—
151C2×#626—32no—
152C2×#626—32no—
153C2×#626—31no—
154C2×#626—31no—
155C2×#626—32no—
156C2×#626—32no—
157C2×#625—32no—
158C2×#625—31no—
159C2×#625—32no—
160C2×#624—32no—
161C2×D3×Dic3—32no—
162C2×D3×Dic3—32no—
163#3799—64no—
164#3796—64no—
165#3795—64no—
166#3757C2×D312yes—
167C4⋊(C3⋊Dic3)C2×D311yescharacteristic
168C4×C3⋊Dic3C2×D311yescharacteristic
169C3×#217—32no—
170C3×#217—32no—
171C3×#217—62no—
172C3×C4⋊Dic3—31no—
173C3×C4⋊Dic3—31no—
174C3×C4⋊Dic3—61no—
175C3×C4×Dic3—31no—
176C3×C4×Dic3—31no—
177C3×C4×Dic3—61no—
178#3724—32no—
179#3724—31no—
180Dic3⋊Dic3—32no—
181Dic3⋊Dic3—32no—
182Dic3⋊Dic3—31no—
183Dic3⋊Dic3—31no—
184#3722—31no—
185#3722—31no—
186#3722—32no—
187(C2×D3)⋊Dic3—31no—
188(C2×D3)⋊Dic3—31no—
189(C2×D3)⋊Dic3—31no—
190(C2×D3)⋊Dic3—31no—
191(C2×D3)⋊Dic3—32no—
192(C2×D3)⋊Dic3—32no—
193Dic32—32no—
194Dic32—32no—
195Dic32—32no—
196C22×C33—22no—
197C22×C33—22no—
198C22×C33—22no—
199C22×C33C2411yescharacteristic
200C2×C3×C3⋊D3—21no—
201C2×C3×C3⋊D3—22no—
202C2×C3×C3⋊D3—21no—
203C2×C3×C3⋊D3—21no—
204C2×C3×C3⋊D3—21no—
205C2×C3×C3⋊D3—22no—
206C2×C3×C3⋊D3—21no—
207C2×C3×C3⋊D3—21no—
208C2×C3×C3⋊D3—22no—
209C33×C4C2×D412yes—
210C3×C3⋊Dic3—21no—
211C3×C3⋊Dic3—21no—
212C3×C3⋊Dic3—21no—
213C3×C3⋊Dic3—22no—
214C3×C3⋊Dic3C2×D414yes—
215C3×C3⋊Dic3#4112yescomplemented
216C2×C3×#41—91no—
217C2×#239—91no—
218C2×#237—31no—
219C2×#237—31no—
220C2×#237—61no—
221C2×#237—91no—
222C2×#235—91no—
223C3×#127—91no—
224C3×#121—91no—
225Q8×Dic3—91no—
226#940—31no—
227#940—31no—
228#940—61no—
229#940—92no—
230#940—92no—
231#940—92no—
232#939—92no—
233#939—92no—
234#939—92no—
235#938—31no—
236#938—31no—
237#938—61no—
238#938—91no—
239#938—92no—
240D4×Dic3—92no—
241#930—91no—
242#930—92no—
243C4×#67—91no—
244C4×#67—91no—
245C4×#67—92no—
246#895—91no—
247#887—91no—
248#884—92no—
249#67⋊C4—92no—
250C4×D12—91no—
251C4×Dic6—91no—
252C23×C32—22no—
253C23×C32—22no—
254C23×C32—22no—
255C23×C32—42no—
256C23×C32C22×D312yes—
257C23×C32C22×D312yes—
258C23×C32C22×D312yes—
259C22×C3⋊D3C22×D312yes—
260C22×C3⋊D3C22×D311yescharacteristic
261C22×C3⋊D3C22×D311yescharacteristic
262C22×C3×D3—32no—
263C22×C3×D3—32no—
264C22×C3×D3—31no—
265C22×C3×D3—31no—
266C22×C3×D3—31no—
267C22×C3×D3—31no—
268C22×C3×D3—61no—
269C22×C3×D3—61no—
270C22×C3×D3—62no—
271C32×D4—22no—
272C32×D4—24no—
273C32×D4—22no—
274C32×D4—22no—
275C32×D4—42no—
276C32×D4—42no—
277C32×D4—44no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C32×C4—41no—
282C2×C32×C4C22×D311yescharacteristic
283C2×C32×C4C22×D311yescharacteristic
284C2×C32×C4C22×D311yescharacteristic
285#638—24no—
286#638—24no—
287#638—42no—
288#638—42no—
289C2×C3⋊Dic3—24no—
290C2×C3⋊Dic3C22×D312yes—
291C2×C3⋊Dic3C22×D311yescharacteristic
292C2×C3⋊Dic3C22×D311yescharacteristic
293C2×C3⋊Dic3C22×D311yescharacteristic
294C2×C3⋊Dic3C22×D311yescharacteristic
295C2×C3⋊Dic3C22×D312yes—
296C4⋊(C3⋊D3)—22no—
297C4×C3⋊D3—22no—
298C4×C3⋊D3—22no—
299#634#6714yescomplemented
300C3×#67—64no—
301C3×#67—64no—
302C3×#67—64no—
303C3×#67—64no—
304C3×#67—68no—
305C3×#67—124no—
306C3×#67—122no—
307C3×#67—122no—
308C3×#67—122no—
309C3×#67—122no—
310C3×#67—124no—
311C3×#67—124no—
312C2×C3×Dic3—31no—
313C2×C3×Dic3—31no—
314C2×C3×Dic3—32no—
315C2×C3×Dic3—32no—
316C2×C3×Dic3—32no—
317C2×C3×Dic3—32no—
318C2×C3×Dic3—31no—
319C2×C3×Dic3—31no—
320C2×C3×Dic3—31no—
321C2×C3×Dic3—31no—
322C2×C3×Dic3—31no—
323C2×C3×Dic3—31no—
324C2×C3×Dic3—61no—
325C2×C3×Dic3—61no—
326C2×C3×Dic3—62no—
327C2×C3×Dic3—61no—
328C2×C3×Dic3—62no—
329C2×C3×Dic3—61no—
330C2×C3×Dic3—64no—
331C2×C3×Dic3—64no—
332C2×C3×Dic3—68no—
333C3×D12—62no—
334C3×D12—62no—
335C3×D12—122no—
336C3×C4×D3—64no—
337C3×C4×D3—62no—
338C3×C4×D3—62no—
339C3×C4×D3—62no—
340C3×C4×D3—62no—
341C3×C4×D3—122no—
342C3×Dic6—34no—
343C3×Dic6—34no—
344C3×Dic6—64no—
345#626—64no—
346#626—64no—
347#626—62no—
348#626—62no—
349#626—122no—
350#626—122no—
351#625—62no—
352#625—64no—
353#625—122no—
354#624—64no—
355D3×Dic3—64no—
356D3×Dic3—64no—
357#550—271noSylow
358C2×C33—42no—
359C2×C33C22×D411yescharacteristic
360C2×C33C2×#4111yescharacteristic
361C2×C33H(5,𝔽2)11yescharacteristic
362C3×C3⋊D3—41no—
363C3×C3⋊D3—41no—
364C3×C3⋊D3—42no—
365C3×#41—184no—
366C2×C3×Q8—91no—
367C2×C3×D4—21no—
368C2×C3×D4—21no—
369C2×C3×D4—21no—
370C2×C3×D4—41no—
371C2×C3×D4—92no—
372C2×C3×D4—92no—
373C2×C3×D4—92no—
374C2×C3×D4—92no—
375C2×C3×D4—91no—
376C2×C3×D4D3211yescharacteristic
377C2×C3×D4D3211yescharacteristic
378C2×C3×D4D3211yescharacteristic
379C22×C3×C4—92no—
380C22×C3×C4—91no—
381C22×C3×C4—91no—
382C2×#67—32no—
383C2×#67—32no—
384C2×#67—32no—
385C2×#67—32no—
386C2×#67—32no—
387C2×#67—32no—
388C2×#67—32no—
389C2×#67—32no—
390C2×#67—62no—
391C2×#67—62no—
392C2×#67—62no—
393C2×#67—62no—
394C2×#67—91no—
395C2×#67—91no—
396C2×#67—92no—
397C2×#67—92no—
398C2×#67—92no—
399C2×#67—92no—
400C22×Dic3—32no—
401C22×Dic3—32no—
402C22×Dic3—62no—
403C22×Dic3—92no—
404#239—184no—
405#237—64no—
406#237—64no—
407#237—68no—
408#237—184no—
409#235—184no—
410C2×D12—31no—
411C2×D12—31no—
412C2×D12—61no—
413C2×D12—91no—
414C2×D12—92no—
415C2×D12—92no—
416C2×C4×D3—31no—
417C2×C4×D3—31no—
418C2×C4×D3—31no—
419C2×C4×D3—31no—
420C2×C4×D3—61no—
421C2×C4×D3—61no—
422C2×C4×D3—92no—
423C2×C4×D3—92no—
424C2×Dic6—31no—
425C2×Dic6—31no—
426C2×Dic6—61no—
427C3×C4⋊C4—91no—
428C3×C22⋊C4—92no—
429C3×C42—91no—
430#217—32no—
431#217—32no—
432#217—62no—
433#217—91no—
434#217—91no—
435#217—92no—
436(C2×D3)⋊C4—91no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4—92no—
439(C2×D3)⋊C4—91no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—92no—
442C4⋊Dic3—31no—
443C4⋊Dic3—31no—
444C4⋊Dic3—61no—
445C4⋊Dic3—91no—
446C4⋊Dic3—92no—
447Dic3⋊C4—92no—
448Dic3⋊C4—91no—
449Dic3⋊C4—92no—
450Dic3⋊C4—91no—
451C4×Dic3—31no—
452C4×Dic3—31no—
453C4×Dic3—61no—
454C4×Dic3—92no—
455C4×Dic3—92no—
456C4×Dic3—92no—
457C22×C32—22no—
458C22×C32—24no—
459C22×C32—22no—
460C22×C32—22no—
461C22×C32—22no—
462C22×C32—22no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—22no—
467C22×C32—21no—
468C22×C32—21no—
469C22×C32—21no—
470C22×C32—41no—
471C22×C32—42no—
472C22×C32—42no—
473C22×C32—44no—
474C22×C32—42no—
475C22×C32—42no—
476C22×C32—42no—
477C22×C32—42no—
478C22×C32—42no—
479C22×C32—42no—
480C22×C32—82no—
481C22×C32—82no—
482C22×C32C23×D311yescharacteristic
483C22×C32C23×D311yescharacteristic
484C22×C32C23×D311yescharacteristic
485C2×C3⋊D3—21no—
486C2×C3⋊D3—21no—
487C2×C3⋊D3—22no—
488C2×C3⋊D3—21no—
489C2×C3⋊D3—22no—
490C2×C3⋊D3—22no—
491C2×C3⋊D3—21no—
492C2×C3⋊D3—21no—
493C2×C3⋊D3—21no—
494C2×C3×D3—62no—
495C2×C3×D3—62no—
496C2×C3×D3—62no—
497C2×C3×D3—61no—
498C2×C3×D3—61no—
499C2×C3×D3—61no—
500C2×C3×D3—61no—
501C2×C3×D3—61no—
502C2×C3×D3—61no—
503C2×C3×D3—62no—
504C2×C3×D3—61no—
505C2×C3×D3—61no—
506C2×C3×D3—61no—
507C2×C3×D3—61no—
508C2×C3×D3—62no—
509C2×C3×D3—62no—
510C2×C3×D3—62no—
511C2×C3×D3—61no—
512C2×C3×D3—62no—
513C2×C3×D3—61no—
514C2×C3×D3—121no—
515C2×C3×D3—121no—
516C2×C3×D3—121no—
517C2×C3×D3—121no—
518C2×C3×D3—122no—
519C2×C3×D3—122no—
520C2×C3×D3—122no—
521C32×C4—22no—
522C32×C4—22no—
523C32×C4—22no—
524C32×C4—42no—
525C32×C4D3×D412yes—
526C32×C4D3×D412yes—
527C32×C4C2×#6712yes—
528C3⋊Dic3—21no—
529C3⋊Dic3—21no—
530C3⋊Dic3—21no—
531C3⋊Dic3—22no—
532C3⋊Dic3#23712yescomplemented
533C3⋊Dic3C2×#6714yes—
534C3×Dic3—34no—
535C3×Dic3—34no—
536C3×Dic3—32no—
537C3×Dic3—32no—
538C3×Dic3—64no—
539C3×Dic3—62no—
540C3×Dic3—62no—
541C3×Dic3—62no—
542C3×Dic3—61no—
543C3×Dic3—61no—
544C3×Dic3—61no—
545C3×Dic3—62no—
546C3×Dic3—61no—
547C3×Dic3—62no—
548C3×Dic3—61no—
549C3×Dic3—61no—
550C3×Dic3—121no—
551C3×Dic3—122no—
552C2×#41—91no—
553C2×#41—271no—
554#127—91no—
555#127—272no—
556#121—91no—
557#121—272no—
558#121—271no—
559#121—272no—
560C4×Q8—271no—
561C4×D4—271no—
562C4×D4—272no—
563C33#55011yescharacteristic, complemented, Sylow
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—42no—
568C23×C3—92no—
569C23×C3—91no—
570C23×C3—91no—
571C23×C3C2×D3212yes—
572C23×C3C2×D3212yes—
573C23×C3C2×D3212yes—
574C22×D3—31no—
575C22×D3—31no—
576C22×D3—31no—
577C22×D3—31no—
578C22×D3—32no—
579C22×D3—32no—
580C22×D3—61no—
581C22×D3—61no—
582C22×D3—62no—
583C3×Q8—94no—
584C3×D4—24no—
585C3×D4—22no—
586C3×D4—22no—
587C3×D4—22no—
588C3×D4—42no—
589C3×D4—42no—
590C3×D4—44no—
591C3×D4—184no—
592C3×D4—184no—
593C3×D4—182no—
594C3×D4—362no—
595C3×D4—362no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—41no—
600C2×C3×C4—91no—
601C2×C3×C4—92no—
602C2×C3×C4—92no—
603C2×C3×C4—91no—
604C2×C3×C4—91no—
605C2×C3×C4—91no—
606C2×C3×C4—184no—
607C2×C3×C4—182no—
608C2×C3×C4—182no—
609C2×C3×C4C2×D3211yescharacteristic
610C2×C3×C4C2×D3211yescharacteristic
611C2×C3×C4C2×D3211yescharacteristic
612#67—64no—
613#67—64no—
614#67—64no—
615#67—64no—
616#67—68no—
617#67—124no—
618#67—122no—
619#67—122no—
620#67—122no—
621#67—122no—
622#67—124no—
623#67—124no—
624#67—184no—
625#67—184no—
626#67—182no—
627#67—182no—
628#67—362no—
629#67—362no—
630C2×Dic3—31no—
631C2×Dic3—31no—
632C2×Dic3—32no—
633C2×Dic3—32no—
634C2×Dic3—31no—
635C2×Dic3—31no—
636C2×Dic3—32no—
637C2×Dic3—32no—
638C2×Dic3—31no—
639C2×Dic3—31no—
640C2×Dic3—31no—
641C2×Dic3—31no—
642C2×Dic3—61no—
643C2×Dic3—61no—
644C2×Dic3—62no—
645C2×Dic3—61no—
646C2×Dic3—62no—
647C2×Dic3—61no—
648C2×Dic3—64no—
649C2×Dic3—64no—
650C2×Dic3—68no—
651C2×Dic3—184no—
652D12—62no—
653D12—62no—
654D12—122no—
655D12—182no—
656D12—184no—
657D12—362no—
658C4×D3—64no—
659C4×D3—62no—
660C4×D3—62no—
661C4×D3—62no—
662C4×D3—62no—
663C4×D3—122no—
664C4×D3—184no—
665C4×D3—184no—
666Dic6—34no—
667Dic6—34no—
668Dic6—64no—
669C2×C32—21no—
670C2×C32—21no—
671C2×C32—21no—
672C2×C32—21no—
673C2×C32—21no—
674C2×C32—21no—
675C2×C32—21no—
676C2×C32—21no—
677C2×C32—21no—
678C2×C32—41no—
679C2×C32—41no—
680C2×C32—41no—
681C2×C32—42no—
682C2×C32—44no—
683C2×C32—42no—
684C2×C32—42no—
685C2×C32—82no—
686C2×C32—82no—
687C2×C32—84no—
688C2×C32C2×D3×D411yescharacteristic
689C2×C32C2×D3×D411yescharacteristic
690C2×C32C2×#23711yescharacteristic
691C2×C32#100411yescharacteristic
692C2×C32#100411yescharacteristic
693C2×C32D3×#4111yescharacteristic
694C2×C32D3×#4111yescharacteristic
695C2×C32#100911yescharacteristic
696C2×C32C22×#6711yescharacteristic
697C3⋊D3—41no—
698C3⋊D3—41no—
699C3⋊D3—42no—
700C3×D3—122no—
701C3×D3—122no—
702C3×D3—121no—
703C3×D3—121no—
704C3×D3—122no—
705C3×D3—121no—
706C3×D3—122no—
707C3×D3—121no—
708C3×D3—242no—
709#41—184no—
710#41—544no—
711C2×Q8—91no—
712C2×D4—92no—
713C2×D4—92no—
714C2×D4—92no—
715C2×D4—92no—
716C2×D4—91no—
717C2×D4—271no—
718C2×D4—272no—
719C2×D4—272no—
720C2×D4#111311yescharacteristic
721C22×C4—92no—
722C22×C4—91no—
723C22×C4—91no—
724C22×C4—272no—
725C4⋊C4—91no—
726C4⋊C4—271no—
727C4⋊C4—272no—
728C22⋊C4—92no—
729C22⋊C4—271no—
730C22⋊C4—271no—
731C22⋊C4—272no—
732C42—91no—
733C42—272no—
734C22×C3—24no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—42no—
748C22×C3—42no—
749C22×C3—42no—
750C22×C3—42no—
751C22×C3—42no—
752C22×C3—42no—
753C22×C3—42no—
754C22×C3—42no—
755C22×C3—44no—
756C22×C3—41no—
757C22×C3—82no—
758C22×C3—82no—
759C22×C3—181no—
760C22×C3—181no—
761C22×C3—182no—
762C22×C3—181no—
763C22×C3—182no—
764C22×C3—181no—
765C22×C3—182no—
766C22×C3—181no—
767C22×C3—181no—
768C22×C3C22×D3211yescharacteristic
769C22×C3C22×D3211yescharacteristic
770C22×C3C22×D3211yescharacteristic
771C2×D3—62no—
772C2×D3—62no—
773C2×D3—62no—
774C2×D3—62no—
775C2×D3—61no—
776C2×D3—61no—
777C2×D3—61no—
778C2×D3—61no—
779C2×D3—61no—
780C2×D3—62no—
781C2×D3—61no—
782C2×D3—62no—
783C2×D3—61no—
784C2×D3—61no—
785C2×D3—61no—
786C2×D3—61no—
787C2×D3—61no—
788C2×D3—62no—
789C2×D3—61no—
790C2×D3—62no—
791C2×D3—121no—
792C2×D3—121no—
793C2×D3—121no—
794C2×D3—121no—
795C2×D3—122no—
796C2×D3—122no—
797C2×D3—122no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—22no—
801C3×C4—42no—
802C3×C4—92no—
803C3×C4—94no—
804C3×C4—182no—
805C3×C4—181no—
806C3×C4—181no—
807C3×C4—181no—
808C3×C4D3×#6712yes—
809C3×C4D3×#6712yes—
810C3×C4#381112yes—
811Dic3—32no—
812Dic3—32no—
813Dic3—34no—
814Dic3—34no—
815Dic3—64no—
816Dic3—62no—
817Dic3—62no—
818Dic3—62no—
819Dic3—61no—
820Dic3—62no—
821Dic3—61no—
822Dic3—62no—
823Dic3—61no—
824Dic3—61no—
825Dic3—61no—
826Dic3—61no—
827Dic3—121no—
828Dic3—122no—
829C32—21no—
830C32—21no—
831C32—21no—
832C32—41no—
833C32#559911yescharacteristic, complemented
834C32#571811yescharacteristic, complemented
835C32#583411yescharacteristic, complemented
836C23—91no—
837C23—91no—
838C23—92no—
839C23C2×#111312yes—
840Q8—94no—
841D4—22no—
842D4—184no—
843D4—184no—
844D4—182no—
845D4—362no—
846D4—362no—
847D4—544no—
848D4—542no—
849D4—1082no—
850C2×C4—91no—
851C2×C4—92no—
852C2×C4—91no—
853C2×C4—92no—
854C2×C4—91no—
855C2×C4—91no—
856C2×C4—184no—
857C2×C4—182no—
858C2×C4—182no—
859C2×C4—544no—
860C2×C4C2×#111311yescharacteristic
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—21no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—44no—
871C2×C3—42no—
872C2×C3—42no—
873C2×C3—42no—
874C2×C3—41no—
875C2×C3—41no—
876C2×C3—41no—
877C2×C3—82no—
878C2×C3—82no—
879C2×C3—84no—
880C2×C3—361no—
881C2×C3—361no—
882C2×C3—362no—
883C2×C3D3×#23711yescharacteristic
884C2×C3D3×#23711yescharacteristic
885C2×C3#6431211yescharacteristic
886C2×C3#6431311yescharacteristic
887C2×C3#6431411yescharacteristic
888C2×C3#6431411yescharacteristic
889C2×C3C2×D3×#6711yescharacteristic
890C2×C3C2×D3×#6711yescharacteristic
891C2×C3C2×#381111yescharacteristic
892D3—122no—
893D3—122no—
894D3—121no—
895D3—122no—
896D3—121no—
897D3—122no—
898D3—121no—
899D3—121no—
900D3—242no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—182no—
905C22—181no—
906C22—181no—
907C22—181no—
908C22—182no—
909C22—181no—
910C22—181no—
911C22—181no—
912C22—182no—
913C22C22×#111311yescharacteristic
914C4—92no—
915C4—94no—
916C4—181no—
917C4—182no—
918C4—181no—
919C4—181no—
920C4#8904912yes—
921C3—21no—
922C3—21no—
923C3—21no—
924C3—41no—
925C3#1059515811yescharacteristic, complemented
926C3#1059516411yescharacteristic, complemented
927C3#1059523611yescharacteristic, complemented
928C2—42no—
929C2—361no—
930C2—361no—
931C2—362no—
932C2#1172462211yescharacteristic
933C2#1172462311yescharacteristic
934C2C2×#8904911yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33#550
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3830C2semidirect
2. C2×#89041C2semidirect
3. C3×#64149C2semidirect
4. C3×#64147C2semidirect
5. #11723728C2semidirect
6. #11723726C2semidirect
7. #11723725C2semidirect
8. #11723717C2semidirect
9. #11723696C2semidirect
10. C4×#6295C2semidirect
11. #11723668C2semidirect
40. C2×#3830D3semidirect
47. #64149D3semidirect
48. #64147D3semidirect
96. C3×#634D4semidirect
215. C3×C3⋊Dic3#41semidirect
299. #634#67semidirect
532. C3⋊Dic3#237semidirect
563. C33#550semidirect
833. C32#5599semidirect
834. C32#5718semidirect
835. C32#5834semidirect
925. C3#10595158semidirect
926. C3#10595164semidirect
927. C3#10595236semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38302
C2×#890412
C3×#641492
C3×#641472
#117237282
#117237262
#117237252
#117237172
#117236962
C4×#62952
#117236682
#105952363
#105951643
#105951583