Finite Group Databasebeta

← #13178235

Subgroups — #13178235

Order 1728.

2100 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89049C212yesmaximal, complemented
2C22×#6295C211yesmaximal, characteristic, complemented
3C2×C4⋊#1113C211yesmaximal, characteristic, complemented
4C3×#64091C212yesmaximal, complemented
5C3×#64090C211yesmaximal, characteristic, complemented
6#11723717C211yesmaximal, characteristic, complemented
7#11723701C212yesmaximal, complemented
8#11723697C211yesmaximal, characteristic, complemented
9#11723695C211yesmaximal, characteristic, complemented
10#11723687C212yesmaximal, complemented
11#11723685C211yesmaximal, characteristic, complemented
12#10594277—32nomaximal
13#10594271—31nomaximal
14C23×C3×C3⋊D3C2212yescomplemented
15C22×#1113C2212yescomplemented
16C2×C3×#638C2211yescharacteristic
17C2×C3×#638C2212yescomplemented
18C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
19C2×C3×C4⋊(C3⋊D3)C2212yescomplemented
20C2×C3×C4⋊(C3⋊D3)C2212yescomplemented
21C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
22#89049—28no—
23C2×#6295—24no—
24C2×#6295C2211yescharacteristic
25C2×#6295C2211yescharacteristic, complemented
26C2×#6295C2212yescomplemented
27C2×#6295C2211yescharacteristic, complemented
28C2×#6295C2212yescomplemented
29C2×#6295C2212yescomplemented
30C2×#6294C2212yescomplemented
31C4⋊#1113—24no—
32C33×C22⋊C4C2211yescharacteristic, complemented
33C3×#3752C2211yescharacteristic, complemented
34C3×#3752C2212yescomplemented
35C3×#3752C2212yescomplemented
36C3×#3750C2211yescharacteristic, complemented
37C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
38#88815C2211yescharacteristic, complemented
39#88814C2212yescomplemented
40C2×#3811—32no—
41C2×D3×#67—32no—
42C2×D3×#67—32no—
43C22×#626—32no—
44C22×#625—31no—
45C2×#3802—31no—
46C2×D3×D12—32no—
47#64091D312yescomplemented
48#64090D311yescharacteristic, complemented
49C3×#882—32no—
50C3×#882—32no—
51C3×#882—62no—
52C3×#67⋊C4—32no—
53C3×#67⋊C4—61no—
54#63980—31no—
55#63978—32no—
56#63923—32no—
57#63922—32no—
58#63922—32no—
59#63914—31no—
60#63912—31no—
61#63911—32no—
62#63910—32no—
63#63906—32no—
64#63902—31no—
65#63886—32no—
66#63885—32no—
67#63880—32no—
68C23×C33C2311yescharacteristic
69C22×C3×C3⋊D3—24no—
70C22×C3×C3⋊D3—24no—
71C22×C3×C3⋊D3—42no—
72C22×C3×C3⋊D3C2312yes—
73C22×C3×C3⋊D3C2312yes—
74C22×C3×C3⋊D3C2311yescharacteristic
75C22×C3×C3⋊D3C2312yes—
76C2×#1113—24no—
77C2×#1113—24no—
78C2×#1113—42no—
79C2×C33×C4C2311yescharacteristic
80C2×C33×C4C2311yescharacteristic
81C3×#638—24no—
82C3×#638D414yescomplemented
83C2×C3×C3⋊Dic3—22no—
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2312yes—
86C2×C3×C3⋊Dic3C2311yescharacteristic
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C3×C4⋊(C3⋊D3)—24no—
89C3×C4⋊(C3⋊D3)—42no—
90C3×C4×C3⋊D3—22no—
91#6295—24no—
92#6295—24no—
93#6295—22no—
94#6295—22no—
95#6295—24no—
96#6295D414yescomplemented
97#6294—24no—
98#5590—92no—
99D4×D12—91no—
100C23×C3⋊D3C2×D312yescomplemented
101C23×C3×D3—32no—
102C23×C3×D3—32no—
103C23×C3×D3—62no—
104C22×D32—32no—
105C22×D32—32no—
106C22×D32—32no—
107C2×#638C2×D311yescharacteristic
108C2×#638C2×D312yescomplemented
109C22×C3⋊Dic3C2×D311yescharacteristic, complemented
110C2×C4⋊(C3⋊D3)C2×D312yescomplemented
111C2×C4⋊(C3⋊D3)C2×D312yescomplemented
112C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
113C2×C3×#67—32no—
114C2×C3×#67—32no—
115C2×C3×#67—32no—
116C2×C3×#67—61no—
117C2×C3×#67—62no—
118C22×C3×Dic3—32no—
119C22×C3×Dic3—61no—
120C2×C3×D12—32no—
121C2×C3×D12—32no—
122C2×C3×D12—32no—
123C2×C3×D12—32no—
124C2×C3×D12—62no—
125C2×C3×D12—62no—
126C2×C3×C4×D3—32no—
127C2×C3×C4×D3—61no—
128#3811—68no—
129D3×#67—68no—
130D3×#67—68no—
131C2×#626—32no—
132C2×#626—32no—
133C2×#626—32no—
134C2×#626—32no—
135C2×#626—32no—
136C2×#626—32no—
137C2×#626—32no—
138C2×#626—32no—
139C2×#626—32no—
140C2×#626—68no—
141C2×#625—31no—
142C2×#625—31no—
143C2×#625—32no—
144C2×#625—31no—
145C2×#625—32no—
146C2×#625—32no—
147C2×#625—64no—
148C2×#624—32no—
149C2×D3×Dic3—32no—
150C2×D3×Dic3—32no—
151#3802—64no—
152D3×D12—68no—
153C32×C22⋊C4—21no—
154C32×C22⋊C4—22no—
155C32×C22⋊C4—41no—
156C32×C22⋊C4C2×D312yescomplemented
157C32×C22⋊C4C2×D311yescharacteristic, complemented
158#3752C2×D311yescharacteristic, complemented
159#3752C2×D312yescomplemented
160#3752C2×D312yescomplemented
161#3750C2×D311yescharacteristic, complemented
162C4×C3⋊Dic3C2×D311yescharacteristic, complemented
163C3×(C2×D3)⋊C4—32no—
164C3×(C2×D3)⋊C4—32no—
165C3×(C2×D3)⋊C4—32no—
166C3×(C2×D3)⋊C4—32no—
167C3×(C2×D3)⋊C4—32no—
168C3×(C2×D3)⋊C4—61no—
169C3×(C2×D3)⋊C4—62no—
170C3×(C2×D3)⋊C4—62no—
171C3×Dic3⋊C4—32no—
172C3×Dic3⋊C4—61no—
173C3×C4×Dic3—32no—
174C3×C4×Dic3—61no—
175#3724—31no—
176Dic3⋊Dic3—32no—
177#3722—32no—
178(C2×D3)⋊Dic3—32no—
179(C2×D3)⋊Dic3—32no—
180C22×C33—21no—
181C22×C33—21no—
182C22×C33C2×D412yescomplemented
183C22×C33C2411yescharacteristic
184C2×C3×C3⋊D3—22no—
185C2×C3×C3⋊D3—21no—
186C2×C3×C3⋊D3—21no—
187C2×C3×C3⋊D3—22no—
188C2×C3×C3⋊D3—22no—
189C2×C3×C3⋊D3—22no—
190C2×C3×C3⋊D3—22no—
191C2×C3×C3⋊D3—22no—
192C2×C3×C3⋊D3—22no—
193C2×C3×C3⋊D3—22no—
194C2×C3×C3⋊D3—48no—
195C2×C3×C3⋊D3C2×D412yescomplemented
196C2×C3×C3⋊D3C2×D414yescomplemented
197#1113—48no—
198C33×C4—21no—
199C33×C4—21no—
200C3×C3⋊Dic3—22no—
201C3×C3⋊Dic3—21no—
202C3×C3⋊Dic3C2×D412yescomplemented
203C3×C3⋊Dic3C2×D412yescomplemented
204C22×#67—92no—
205C22×#67—92no—
206C2×D3×D4—92no—
207C2×D3×D4—92no—
208C2×D3×D4—92no—
209C22×D12—91no—
210C22×D12—91no—
211C3×#120—92no—
212C3×C4×D4—91no—
213#940—92no—
214#939—92no—
215#939—92no—
216#937—92no—
217#930—91no—
218#930—91no—
219#895—92no—
220#884—92no—
221#884—92no—
222#882—32no—
223#882—32no—
224#882—62no—
225#882—92no—
226#882—92no—
227#67⋊C4—32no—
228#67⋊C4—61no—
229#67⋊C4—92no—
230#874—91no—
231C4×D12—91no—
232C23×C32—22no—
233C23×C32—21no—
234C23×C32—41no—
235C23×C32C22×D311yescharacteristic
236C23×C32C22×D312yes—
237C22×C3⋊D3—24no—
238C22×C3⋊D3—24no—
239C22×C3⋊D3—42no—
240C22×C3⋊D3C22×D312yes—
241C22×C3⋊D3C22×D312yes—
242C22×C3⋊D3C22×D311yescharacteristic
243C22×C3⋊D3C22×D312yes—
244C22×C3×D3—32no—
245C22×C3×D3—32no—
246C22×C3×D3—32no—
247C22×C3×D3—32no—
248C22×C3×D3—32no—
249C22×C3×D3—32no—
250C22×C3×D3—32no—
251C22×C3×D3—62no—
252C22×C3×D3—62no—
253C22×C3×D3—61no—
254C22×C3×D3—62no—
255C22×C3×D3—64no—
256C22×C3×D3—64no—
257C22×C3×D3—64no—
258C22×C3×D3—64no—
259C22×C3×D3—124no—
260C22×C3×D3—124no—
261C22×C3×D3—122no—
262C22×C3×D3—122no—
263C22×C3×D3—124no—
264C2×D32—64no—
265C2×D32—64no—
266C2×D32—64no—
267C2×D32—64no—
268C2×D32—64no—
269C2×D32—64no—
270C2×D32—122no—
271C2×D32—122no—
272C2×D32—122no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—22no—
276C2×C32×C4—22no—
277C2×C32×C4—41no—
278C2×C32×C4—41no—
279C2×C32×C4C22×D312yes—
280C2×C32×C4C22×D312yes—
281C2×C32×C4C22×D311yescharacteristic
282C2×C32×C4C22×D311yescharacteristic
283#638—24no—
284#638D1214yescomplemented
285C2×C3⋊Dic3—22no—
286C2×C3⋊Dic3C22×D311yescharacteristic
287C2×C3⋊Dic3C22×D312yes—
288C2×C3⋊Dic3C22×D311yescharacteristic
289C2×C3⋊Dic3C22×D311yescharacteristic
290C4⋊(C3⋊D3)—24no—
291C4⋊(C3⋊D3)—42no—
292C4×C3⋊D3—22no—
293C3×#67—38no—
294C3×#67—64no—
295C3×#67—64no—
296C3×#67—64no—
297C3×#67—124no—
298C2×C3×Dic3—32no—
299C2×C3×Dic3—32no—
300C2×C3×Dic3—32no—
301C2×C3×Dic3—32no—
302C2×C3×Dic3—32no—
303C2×C3×Dic3—61no—
304C2×C3×Dic3—61no—
305C2×C3×Dic3—61no—
306C2×C3×Dic3—62no—
307C2×C3×Dic3—64no—
308C2×C3×Dic3—122no—
309C3×D12—64no—
310C3×D12—64no—
311C3×D12—124no—
312C3×D12—122no—
313C3×D12—122no—
314C3×D12—124no—
315C3×C4×D3—64no—
316C3×C4×D3—122no—
317#626—38no—
318#626—64no—
319#626—64no—
320#626—64no—
321#626—64no—
322#626—64no—
323#626—64no—
324#626—64no—
325#626—64no—
326#625—34no—
327#625—64no—
328#625—64no—
329#625—64no—
330#625—62no—
331#625—62no—
332#624—64no—
333D3×Dic3—64no—
334D3×Dic3—64no—
335D42—271noSylow
336C2×C33—22no—
337C2×C33C22×D411yescharacteristic
338C2×C33C22×D411yescharacteristic
339C2×C33H(5,𝔽2)11yescharacteristic
340C3×C3⋊D3—22no—
341C3×C3⋊D3—24no—
342C3×C3⋊D3—42no—
343C3×C3⋊D3—42no—
344C24×C3—92no—
345C23×D3—32no—
346C23×D3—32no—
347C23×D3—62no—
348C23×D3—92no—
349C23×D3—92no—
350C23×D3—92no—
351C2×C3×D4—91no—
352C2×C3×D4—92no—
353C2×C3×D4—92no—
354C2×C3×D4—92no—
355C22×C3×C4—91no—
356C22×C3×C4—91no—
357C2×#67—32no—
358C2×#67—32no—
359C2×#67—32no—
360C2×#67—61no—
361C2×#67—62no—
362C2×#67—92no—
363C2×#67—92no—
364C2×#67—92no—
365C2×#67—92no—
366C2×#67—92no—
367C2×#67—92no—
368C2×#67—92no—
369C2×#67—92no—
370C2×#67—92no—
371C2×#67—188no—
372C2×#67—188no—
373C22×Dic3—32no—
374C22×Dic3—61no—
375C22×Dic3—92no—
376D3×D4—188no—
377D3×D4—188no—
378D3×D4—188no—
379C2×D12—32no—
380C2×D12—32no—
381C2×D12—32no—
382C2×D12—32no—
383C2×D12—62no—
384C2×D12—62no—
385C2×D12—91no—
386C2×D12—92no—
387C2×D12—91no—
388C2×D12—91no—
389C2×D12—92no—
390C2×D12—92no—
391C2×D12—184no—
392C2×D12—184no—
393C2×C4×D3—32no—
394C2×C4×D3—61no—
395C2×C4×D3—92no—
396C2×C4×D3—92no—
397C3×C4⋊C4—91no—
398C3×C22⋊C4—21no—
399C3×C22⋊C4—22no—
400C3×C22⋊C4—41no—
401C3×C22⋊C4—92no—
402C3×C22⋊C4—91no—
403C3×C22⋊C4—92no—
404C3×C22⋊C4D3212yescomplemented
405C3×C22⋊C4D3211yescharacteristic, complemented
406C3×C42—91no—
407#217—92no—
408(C2×D3)⋊C4—32no—
409(C2×D3)⋊C4—32no—
410(C2×D3)⋊C4—32no—
411(C2×D3)⋊C4—32no—
412(C2×D3)⋊C4—32no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—62no—
415(C2×D3)⋊C4—62no—
416(C2×D3)⋊C4—92no—
417(C2×D3)⋊C4—92no—
418C4⋊Dic3—91no—
419Dic3⋊C4—32no—
420Dic3⋊C4—61no—
421Dic3⋊C4—92no—
422C4×Dic3—32no—
423C4×Dic3—61no—
424C22×C32—22no—
425C22×C32—21no—
426C22×C32—22no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—22no—
430C22×C32—24no—
431C22×C32—22no—
432C22×C32—41no—
433C22×C32—42no—
434C22×C32—41no—
435C22×C32—42no—
436C22×C32—42no—
437C22×C32—41no—
438C22×C32—81no—
439C22×C32—81no—
440C22×C32C2×D1212yescomplemented
441C22×C32D3×D414yescomplemented
442C22×C32C23×D311yescharacteristic
443C22×C32C23×D312yes—
444C2×C3⋊D3—22no—
445C2×C3⋊D3—22no—
446C2×C3⋊D3—21no—
447C2×C3⋊D3—22no—
448C2×C3⋊D3—21no—
449C2×C3⋊D3—22no—
450C2×C3⋊D3—22no—
451C2×C3⋊D3—22no—
452C2×C3⋊D3—22no—
453C2×C3⋊D3—22no—
454C2×C3⋊D3—48no—
455C2×C3⋊D3C2×D1212yescomplemented
456C2×C3⋊D3D3×D414yescomplemented
457C2×C3×D3—34no—
458C2×C3×D3—34no—
459C2×C3×D3—34no—
460C2×C3×D3—64no—
461C2×C3×D3—62no—
462C2×C3×D3—62no—
463C2×C3×D3—62no—
464C2×C3×D3—62no—
465C2×C3×D3—62no—
466C2×C3×D3—62no—
467C2×C3×D3—62no—
468C2×C3×D3—64no—
469C2×C3×D3—62no—
470C2×C3×D3—62no—
471C2×C3×D3—62no—
472C2×C3×D3—62no—
473C2×C3×D3—62no—
474C2×C3×D3—62no—
475C2×C3×D3—62no—
476C2×C3×D3—62no—
477C2×C3×D3—62no—
478C2×C3×D3—62no—
479C2×C3×D3—62no—
480C2×C3×D3—62no—
481C2×C3×D3—121no—
482C2×C3×D3—121no—
483C2×C3×D3—122no—
484C2×C3×D3—122no—
485C2×C3×D3—122no—
486C2×C3×D3—122no—
487C2×C3×D3—122no—
488C2×C3×D3—122no—
489C2×C3×D3—122no—
490C2×C3×D3—128no—
491C2×C3×D3—128no—
492C2×C3×D3—1216no—
493D32—128no—
494D32—128no—
495D32—128no—
496C32×C4—22no—
497C32×C4—21no—
498C32×C4—22no—
499C32×C4—21no—
500C32×C4—41no—
501C32×C4—42no—
502C32×C4—42no—
503C32×C4—41no—
504C32×C4—81no—
505C32×C4—81no—
506C3⋊Dic3—22no—
507C3⋊Dic3—21no—
508C3⋊Dic3C2×D1212yescomplemented
509C3⋊Dic3D3×D412yescomplemented
510C3×Dic3—34no—
511C3×Dic3—34no—
512C3×Dic3—62no—
513C3×Dic3—62no—
514C3×Dic3—62no—
515C3×Dic3—62no—
516C3×Dic3—62no—
517C3×Dic3—121no—
518C3×Dic3—122no—
519C22×D4—271no—
520C22×D4—271no—
521C22×D4—272no—
522#127—271no—
523#121—271no—
524#121—272no—
525#121—271no—
526#120—92no—
527#120—272no—
528C4×D4—91no—
529C4×D4—271no—
530C33D4211yescharacteristic, complemented, Sylow
531C23×C3—21no—
532C23×C3—22no—
533C23×C3—41no—
534C23×C3—92no—
535C23×C3—91no—
536C23×C3—92no—
537C23×C3—92no—
538C23×C3—184no—
539C23×C3—184no—
540C23×C3—362no—
541C23×C3C2×D3212yes—
542C23×C3C2×D3211yescharacteristic
543C22×D3—32no—
544C22×D3—32no—
545C22×D3—32no—
546C22×D3—32no—
547C22×D3—32no—
548C22×D3—32no—
549C22×D3—32no—
550C22×D3—61no—
551C22×D3—62no—
552C22×D3—62no—
553C22×D3—62no—
554C22×D3—64no—
555C22×D3—64no—
556C22×D3—64no—
557C22×D3—64no—
558C22×D3—124no—
559C22×D3—124no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—124no—
563C22×D3—184no—
564C22×D3—184no—
565C22×D3—184no—
566C22×D3—184no—
567C22×D3—184no—
568C22×D3—184no—
569C22×D3—362no—
570C22×D3—362no—
571C22×D3—362no—
572C3×D4—94no—
573C3×D4—184no—
574C3×D4—184no—
575C3×D4—362no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—41no—
581C2×C3×C4—41no—
582C2×C3×C4—91no—
583C2×C3×C4—91no—
584C2×C3×C4—92no—
585C2×C3×C4—91no—
586C2×C3×C4—182no—
587C2×C3×C4—182no—
588C2×C3×C4C2×D3212yes—
589C2×C3×C4C2×D3212yes—
590C2×C3×C4C2×D3211yescharacteristic
591C2×C3×C4C2×D3211yescharacteristic
592#67—38no—
593#67—64no—
594#67—64no—
595#67—64no—
596#67—98no—
597#67—124no—
598#67—184no—
599#67—184no—
600#67—184no—
601#67—184no—
602#67—184no—
603#67—184no—
604#67—184no—
605#67—184no—
606C2×Dic3—32no—
607C2×Dic3—32no—
608C2×Dic3—32no—
609C2×Dic3—32no—
610C2×Dic3—32no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—62no—
615C2×Dic3—64no—
616C2×Dic3—122no—
617C2×Dic3—184no—
618D12—64no—
619D12—64no—
620D12—94no—
621D12—124no—
622D12—122no—
623D12—122no—
624D12—124no—
625D12—182no—
626D12—182no—
627D12—184no—
628D12—184no—
629D12—184no—
630C4×D3—64no—
631C4×D3—122no—
632C4×D3—184no—
633C4×D3—184no—
634C2×C32—22no—
635C2×C32—24no—
636C2×C32—22no—
637C2×C32—21no—
638C2×C32—21no—
639C2×C32—22no—
640C2×C32—21no—
641C2×C32—22no—
642C2×C32—41no—
643C2×C32—41no—
644C2×C32—41no—
645C2×C32—44no—
646C2×C32—42no—
647C2×C32—82no—
648C2×C32C22×D1211yescharacteristic
649C2×C32C2×D3×D412yes—
650C2×C32C2×D3×D411yescharacteristic
651C2×C32C2×D3×D412yes—
652C2×C32#100412yes—
653C2×C32#100911yescharacteristic
654C3⋊D3—22no—
655C3⋊D3—24no—
656C3⋊D3—42no—
657C3⋊D3—42no—
658C3×D3—64no—
659C3×D3—64no—
660C3×D3—64no—
661C3×D3—122no—
662C3×D3—124no—
663C3×D3—124no—
664C3×D3—122no—
665C3×D3—122no—
666C3×D3—122no—
667C3×D3—122no—
668C3×D3—242no—
669C24—92no—
670C24—272no—
671C2×D4—91no—
672C2×D4—92no—
673C2×D4—92no—
674C2×D4—92no—
675C2×D4—271no—
676C2×D4—272no—
677C2×D4—272no—
678C2×D4—272no—
679C2×D4—271no—
680C2×D4—271no—
681C2×D4—544no—
682C2×D4—544no—
683C2×D4—548no—
684C22×C4—91no—
685C22×C4—91no—
686C22×C4—272no—
687C4⋊C4—91no—
688C4⋊C4—271no—
689C22⋊C4—91no—
690C22⋊C4—92no—
691C22⋊C4—92no—
692C22⋊C4—272no—
693C22⋊C4#111311yescharacteristic, complemented
694C42—91no—
695C22×C3—22no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—22no—
699C22×C3—21no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—24no—
703C22×C3—41no—
704C22×C3—42no—
705C22×C3—42no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—42no—
709C22×C3—81no—
710C22×C3—81no—
711C22×C3—92no—
712C22×C3—94no—
713C22×C3—182no—
714C22×C3—181no—
715C22×C3—181no—
716C22×C3—182no—
717C22×C3—182no—
718C22×C3—182no—
719C22×C3—182no—
720C22×C3—182no—
721C22×C3—182no—
722C22×C3—182no—
723C22×C3—368no—
724C22×C3D3×D1214yescomplemented
725C22×C3#380212yescomplemented
726C22×C3C22×D3212yes—
727C22×C3C22×D3211yescharacteristic
728C2×D3—34no—
729C2×D3—34no—
730C2×D3—34no—
731C2×D3—64no—
732C2×D3—62no—
733C2×D3—62no—
734C2×D3—62no—
735C2×D3—62no—
736C2×D3—62no—
737C2×D3—62no—
738C2×D3—62no—
739C2×D3—64no—
740C2×D3—62no—
741C2×D3—62no—
742C2×D3—62no—
743C2×D3—62no—
744C2×D3—62no—
745C2×D3—62no—
746C2×D3—62no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—62no—
750C2×D3—62no—
751C2×D3—62no—
752C2×D3—121no—
753C2×D3—122no—
754C2×D3—122no—
755C2×D3—122no—
756C2×D3—122no—
757C2×D3—121no—
758C2×D3—122no—
759C2×D3—122no—
760C2×D3—122no—
761C2×D3—128no—
762C2×D3—128no—
763C2×D3—1216no—
764C2×D3—368no—
765C2×D3—368no—
766C2×D3—368no—
767C3×C4—22no—
768C3×C4—21no—
769C3×C4—21no—
770C3×C4—22no—
771C3×C4—41no—
772C3×C4—42no—
773C3×C4—42no—
774C3×C4—41no—
775C3×C4—81no—
776C3×C4—81no—
777C3×C4—92no—
778C3×C4—92no—
779C3×C4—182no—
780C3×C4—181no—
781Dic3—34no—
782Dic3—34no—
783Dic3—62no—
784Dic3—62no—
785Dic3—62no—
786Dic3—62no—
787Dic3—62no—
788Dic3—121no—
789Dic3—122no—
790C32—21no—
791C32—22no—
792C32—41no—
793C32D4×D1211yescharacteristic, complemented
794C32#559012yescomplemented
795C23—91no—
796C23—92no—
797C23—92no—
798C23—92no—
799C23—184no—
800C23—184no—
801C23—362no—
802C23—544no—
803C23—544no—
804C23—1082no—
805C23C2×#111311yescharacteristic
806D4—94no—
807D4—184no—
808D4—184no—
809D4—274no—
810D4—362no—
811D4—544no—
812D4—542no—
813D4—542no—
814D4—544no—
815D4—544no—
816C2×C4—91no—
817C2×C4—91no—
818C2×C4—92no—
819C2×C4—91no—
820C2×C4—182no—
821C2×C4—182no—
822C2×C4—544no—
823C2×C4C2×#111311yescharacteristic
824C2×C4C2×#111311yescharacteristic
825C2×C3—22no—
826C2×C3—24no—
827C2×C3—21no—
828C2×C3—22no—
829C2×C3—21no—
830C2×C3—22no—
831C2×C3—22no—
832C2×C3—21no—
833C2×C3—44no—
834C2×C3—42no—
835C2×C3—41no—
836C2×C3—41no—
837C2×C3—41no—
838C2×C3—82no—
839C2×C3—182no—
840C2×C3—184no—
841C2×C3—362no—
842C2×C3—362no—
843C2×C3C2×D3×D1212yes—
844C2×C3C2×#380211yescharacteristic
845C2×C3D32×D411yescharacteristic
846C2×C3D32×D412yes—
847C2×C3#6431311yescharacteristic
848C2×C3#6431412yes—
849D3—64no—
850D3—64no—
851D3—64no—
852D3—124no—
853D3—122no—
854D3—124no—
855D3—122no—
856D3—122no—
857D3—122no—
858D3—122no—
859D3—242no—
860C22—21no—
861C22—21no—
862C22—92no—
863C22—94no—
864C22—182no—
865C22—181no—
866C22—182no—
867C22—181no—
868C22—182no—
869C22—182no—
870C22—182no—
871C22—182no—
872C22—182no—
873C22—182no—
874C22—368no—
875C22—1088no—
876C22C4⋊#111312yescomplemented
877C22C22×#111311yescharacteristic
878C4—21no—
879C4—21no—
880C4—92no—
881C4—92no—
882C4—182no—
883C4—181no—
884C3—22no—
885C3—21no—
886C3—41no—
887C3#1059427111yescharacteristic, complemented
888C3#1059427712yescomplemented
889C2—22no—
890C2—184no—
891C2—182no—
892C2—362no—
893C2—362no—
894C2C2×C4⋊#111311yescharacteristic
895C2D4×#111311yescharacteristic
896C2#1172462311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4#1113
hypocenterC33D42
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#89049C2semidirect
2. C22×#6295C2semidirect
3. C2×C4⋊#1113C2semidirect
4. C3×#64091C2semidirect
5. C3×#64090C2semidirect
6. #11723717C2semidirect
7. #11723701C2semidirect
8. #11723697C2semidirect
9. #11723695C2semidirect
10. #11723687C2semidirect
11. #11723685C2semidirect
14. C23×C3×C3⋊D3C22semidirect
15. C22×#1113C22semidirect
17. C2×C3×#638C22semidirect
18. C22×C3×C3⋊Dic3C22semidirect
19. C2×C3×C4⋊(C3⋊D3)C22semidirect
20. C2×C3×C4⋊(C3⋊D3)C22semidirect
21. C2×C3×C4×C3⋊D3C22semidirect
25. C2×#6295C22semidirect
26. C2×#6295C22semidirect
27. C2×#6295C22semidirect
28. C2×#6295C22semidirect
29. C2×#6295C22semidirect
30. C2×#6294C22semidirect
32. C33×C22⋊C4C22semidirect
33. C3×#3752C22semidirect
34. C3×#3752C22semidirect
35. C3×#3752C22semidirect
36. C3×#3750C22semidirect
37. C3×C4×C3⋊Dic3C22semidirect
38. #88815C22semidirect
39. #88814C22semidirect
47. #64091D3semidirect
48. #64090D3semidirect
82. C3×#638D4semidirect
96. #6295D4semidirect
100. C23×C3⋊D3C2×D3semidirect
108. C2×#638C2×D3semidirect
109. C22×C3⋊Dic3C2×D3semidirect
110. C2×C4⋊(C3⋊D3)C2×D3semidirect
111. C2×C4⋊(C3⋊D3)C2×D3semidirect
112. C2×C4×C3⋊D3C2×D3semidirect
156. C32×C22⋊C4C2×D3semidirect
157. C32×C22⋊C4C2×D3semidirect
158. #3752C2×D3semidirect
159. #3752C2×D3semidirect
160. #3752C2×D3semidirect
161. #3750C2×D3semidirect
162. C4×C3⋊Dic3C2×D3semidirect
182. C22×C33C2×D4semidirect
195. C2×C3×C3⋊D3C2×D4semidirect
196. C2×C3×C3⋊D3C2×D4semidirect
202. C3×C3⋊Dic3C2×D4semidirect
203. C3×C3⋊Dic3C2×D4semidirect
284. #638D12semidirect
404. C3×C22⋊C4D32semidirect
405. C3×C22⋊C4D32semidirect
440. C22×C32C2×D12semidirect
441. C22×C32D3×D4semidirect
455. C2×C3⋊D3C2×D12semidirect
456. C2×C3⋊D3D3×D4semidirect
508. C3⋊Dic3C2×D12semidirect
509. C3⋊Dic3D3×D4semidirect
530. C33D42semidirect
693. C22⋊C4#1113semidirect
724. C22×C3D3×D12semidirect
725. C22×C3#3802semidirect
793. C32D4×D12semidirect
794. C32#5590semidirect
876. C22C4⋊#1113semidirect
887. C3#10594271semidirect
888. C3#10594277semidirect

Maximal subgroups

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

subgroupindex
C2×#890492
C22×#62952
C2×C4⋊#11132
C3×#640912
C3×#640902
#117237172
#117237012
#117236972
#117236952
#117236872
#117236852
#105942773
#105942713