Finite Group Databasebeta

← #13178285

Subgroups — #13178285

Order 1728.

2058 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89049C211yesmaximal, characteristic, complemented
2C2×#89049C211yesmaximal, characteristic, complemented
3C2×C4⋊#1113C211yesmaximal, characteristic, complemented
4C2×C4×#1113C211yesmaximal, characteristic, complemented
5C3×#64093C212yesmaximal, complemented
6C3×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
7#11723725C212yesmaximal, complemented
8#11723700C211yesmaximal, characteristic, complemented
9#11723695C212yesmaximal, complemented
10#11723687C212yesmaximal, complemented
11#11723682C211yesmaximal, characteristic, complemented
12#10594265—31nomaximal
13D3×#884—32nomaximal
14C23×C3×C3⋊D3C2211yescharacteristic
15C22×#1113C2211yescharacteristic
16C22×#1113C2211yescharacteristic
17C2×C3×#638C2212yescomplemented
18C2×C3×#638C2212yescomplemented
19C2×C3×C4⋊(C3⋊D3)C2212yescomplemented
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2212yescomplemented
23#89049—24no—
24#89049—24no—
25C2×#6295C2212yescomplemented
26C2×#6295C2212yescomplemented
27C2×#6295C2212yescomplemented
28C2×#6294C2211yescharacteristic
29C2×#6294C2211yescharacteristic
30C2×#6294C2212yescomplemented
31C4⋊#1113—24no—
32C4×#1113—24no—
33C33×C22⋊C4C2211yescharacteristic, complemented
34C3×#3757C2211yescharacteristic, complemented
35C3×#3752C2211yescharacteristic, complemented
36C3×#3752C2211yescharacteristic, complemented
37C3×#3752C2212yescomplemented
38C3×#3750C2212yescomplemented
39#88815C2212yescomplemented
40#88814C2212yescomplemented
41C2×#3811—31no—
42C2×#3811—31no—
43C2×D3×#67—32no—
44C2×D3×#67—32no—
45C2×#3802—31no—
46C2×D3×D12—32no—
47C2×C4×D32—31no—
48C2×C4×D32—32no—
49#64093D312yescomplemented
50C22⋊C4×C3⋊D3D311yescharacteristic, complemented
51C3×#884—32no—
52C3×#884—32no—
53C3×#884—62no—
54C3×D3×C22⋊C4—32no—
55C3×D3×C22⋊C4—61no—
56#63971—32no—
57#63970—32no—
58#63958—32no—
59#63921—31no—
60D3×(C2×D3)⋊C4—32no—
61#63912—32no—
62#63910—32no—
63#63906—32no—
64#63906—32no—
65#63886—32no—
66#63885—32no—
67#63883—31no—
68D3×Dic3⋊C4—32no—
69C23×C33C2311yescharacteristic
70C22×C3×C3⋊D3—22no—
71C22×C3×C3⋊D3—22no—
72C22×C3×C3⋊D3—22no—
73C22×C3×C3⋊D3C2311yescharacteristic
74C22×C3×C3⋊D3C2312yes—
75C22×C3×C3⋊D3C2312yes—
76C22×C3×C3⋊D3C2311yescharacteristic
77C2×#1113—22no—
78C2×#1113—22no—
79C2×#1113—22no—
80C2×#1113—22no—
81C2×#1113—22no—
82C2×#1113D414yescomplemented
83C2×C33×C4C2311yescharacteristic
84C2×C33×C4C2311yescharacteristic
85C3×#638—24no—
86C3×#638—24no—
87C2×C3×C3⋊Dic3C2312yes—
88C2×C3×C3⋊Dic3C2311yescharacteristic
89C2×C3×C3⋊Dic3C2311yescharacteristic
90C2×C3×C3⋊Dic3C2312yes—
91C3×C4⋊(C3⋊D3)—24no—
92C3×C4×C3⋊D3—22no—
93C3×C4×C3⋊D3—22no—
94C3×C4×C3⋊D3—24no—
95#6295—24no—
96#6295—24no—
97#6295—24no—
98#6294—22no—
99#6294—24no—
100#6294D414yescomplemented
101D3×#121—92no—
102C2×#884—91no—
103C23×C3⋊D3C2×D311yescharacteristic
104C23×C3×D3—32no—
105C23×C3×D3—61no—
106C22×D32—32no—
107C22×D32—31no—
108C22×D32—32no—
109C22×D32—31no—
110C2×#638C2×D312yescomplemented
111C2×#638C2×D312yescomplemented
112C2×C4⋊(C3⋊D3)C2×D312yescomplemented
113C2×C4×C3⋊D3C2×D311yescharacteristic
114C2×C4×C3⋊D3C2×D311yescharacteristic
115C2×C4×C3⋊D3C2×D312yescomplemented
116C2×C3×#67—32no—
117C2×C3×#67—32no—
118C2×C3×#67—32no—
119C2×C3×#67—32no—
120C2×C3×#67—62no—
121C2×C3×#67—62no—
122C2×C3×D12—32no—
123C2×C3×D12—32no—
124C2×C3×D12—62no—
125C2×C3×C4×D3—32no—
126C2×C3×C4×D3—32no—
127C2×C3×C4×D3—32no—
128C2×C3×C4×D3—32no—
129C2×C3×C4×D3—61no—
130C2×C3×C4×D3—61no—
131C2×C3×C4×D3—62no—
132#3811—64no—
133#3811—64no—
134D3×#67—68no—
135D3×#67—68no—
136C2×#626—32no—
137C2×#626—32no—
138C2×#626—32no—
139C2×#626—32no—
140C2×#626—32no—
141C2×#626—32no—
142C2×#625—32no—
143C2×#625—32no—
144C2×#625—32no—
145C2×#624—31no—
146C2×#624—32no—
147C2×#624—31no—
148C2×D3×Dic3—32no—
149C2×D3×Dic3—32no—
150C2×D3×Dic3—32no—
151C2×D3×Dic3—32no—
152#3802—64no—
153D3×D12—68no—
154C4×D32—68no—
155C4×D32—64no—
156C32×C22⋊C4—21no—
157C32×C22⋊C4—22no—
158C32×C22⋊C4—41no—
159C32×C22⋊C4C2×D312yescomplemented
160C32×C22⋊C4C2×D311yescharacteristic, complemented
161#3757C2×D311yescharacteristic, complemented
162#3752C2×D311yescharacteristic, complemented
163#3752C2×D311yescharacteristic, complemented
164#3752C2×D312yescomplemented
165#3750C2×D312yescomplemented
166C3×#217—32no—
167C3×#217—61no—
168C3×(C2×D3)⋊C4—32no—
169C3×(C2×D3)⋊C4—32no—
170C3×(C2×D3)⋊C4—32no—
171C3×(C2×D3)⋊C4—32no—
172C3×(C2×D3)⋊C4—61no—
173C3×(C2×D3)⋊C4—61no—
174C3×(C2×D3)⋊C4—62no—
175C3×Dic3⋊C4—32no—
176C3×Dic3⋊C4—32no—
177C3×Dic3⋊C4—62no—
178#3724—32no—
179Dic3⋊Dic3—32no—
180Dic3⋊Dic3—32no—
181#3722—32no—
182(C2×D3)⋊Dic3—32no—
183(C2×D3)⋊Dic3—32no—
184C22×C33—21no—
185C22×C33—21no—
186C22×C33—21no—
187C22×C33C2411yescharacteristic
188C2×C3×C3⋊D3—22no—
189C2×C3×C3⋊D3—22no—
190C2×C3×C3⋊D3—21no—
191C2×C3×C3⋊D3—21no—
192C2×C3×C3⋊D3—22no—
193C2×C3×C3⋊D3—22no—
194C2×C3×C3⋊D3—21no—
195C2×C3×C3⋊D3—22no—
196C2×C3×C3⋊D3—44no—
197C2×C3×C3⋊D3C2×D412yes—
198C2×C3×C3⋊D3C2×D412yes—
199C2×C3×C3⋊D3C2×D414yescomplemented
200C2×C3×C3⋊D3#4112yes—
201#1113—28no—
202#1113—44no—
203C33×C4—21no—
204C33×C4—21no—
205C3×C3⋊Dic3—21no—
206C3×C3⋊Dic3—22no—
207C3×C3⋊Dic3—21no—
208C3×C3⋊Dic3C2×D414yescomplemented
209C22×#67—91no—
210C22×#67—91no—
211C2×D3×D4—92no—
212C2×D3×D4—92no—
213C2×D3×D4—92no—
214C22×D12—91no—
215C22×C4×D3—91no—
216C22×C4×D3—92no—
217C3×#121—92no—
218C2×C3×C22⋊C4—91no—
219#939—92no—
220#939—92no—
221#938—92no—
222#930—92no—
223C2×(C2×D3)⋊C4—91no—
224C2×Dic3⋊C4—91no—
225#895—92no—
226D3×C4⋊C4—92no—
227#884—32no—
228#884—32no—
229#884—62no—
230#884—92no—
231#884—92no—
232#884—92no—
233#884—92no—
234D3×C22⋊C4—32no—
235D3×C22⋊C4—61no—
236D3×C22⋊C4—92no—
237C23×C32—21no—
238C23×C32—22no—
239C23×C32—41no—
240C23×C32C22×D312yes—
241C23×C32C22×D311yescharacteristic
242C22×C3⋊D3—22no—
243C22×C3⋊D3—22no—
244C22×C3⋊D3—22no—
245C22×C3⋊D3C22×D312yes—
246C22×C3⋊D3C22×D311yescharacteristic
247C22×C3⋊D3C22×D312yes—
248C22×C3⋊D3C22×D311yescharacteristic
249C22×C3×D3—32no—
250C22×C3×D3—32no—
251C22×C3×D3—32no—
252C22×C3×D3—32no—
253C22×C3×D3—32no—
254C22×C3×D3—32no—
255C22×C3×D3—61no—
256C22×C3×D3—61no—
257C22×C3×D3—62no—
258C22×C3×D3—62no—
259C22×C3×D3—64no—
260C22×C3×D3—64no—
261C22×C3×D3—64no—
262C22×C3×D3—64no—
263C22×C3×D3—122no—
264C22×C3×D3—122no—
265C2×D32—34no—
266C2×D32—38no—
267C2×D32—64no—
268C2×D32—64no—
269C2×D32—62no—
270C2×D32—62no—
271C2×D32—64no—
272C2×D32—64no—
273C2×D32—64no—
274C2×D32—62no—
275C2×D32—62no—
276C2×D32—62no—
277C2×C32×C4—22no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4—22no—
281C2×C32×C4—41no—
282C2×C32×C4—41no—
283C2×C32×C4C22×D311yescharacteristic
284C2×C32×C4C22×D312yes—
285C2×C32×C4C22×D311yescharacteristic
286C2×C32×C4C22×D312yes—
287#638—24no—
288#638—24no—
289C2×C3⋊Dic3C22×D311yescharacteristic
290C2×C3⋊Dic3C22×D312yes—
291C2×C3⋊Dic3C22×D311yescharacteristic
292C2×C3⋊Dic3C22×D312yes—
293C4⋊(C3⋊D3)—24no—
294C4×C3⋊D3—22no—
295C4×C3⋊D3—22no—
296C4×C3⋊D3—24no—
297C3×#67—64no—
298C3×#67—64no—
299C3×#67—64no—
300C3×#67—64no—
301C3×#67—124no—
302C3×#67—124no—
303C2×C3×Dic3—32no—
304C2×C3×Dic3—32no—
305C2×C3×Dic3—32no—
306C2×C3×Dic3—32no—
307C2×C3×Dic3—32no—
308C2×C3×Dic3—32no—
309C2×C3×Dic3—62no—
310C2×C3×Dic3—62no—
311C2×C3×Dic3—61no—
312C2×C3×Dic3—61no—
313C3×D12—64no—
314C3×D12—64no—
315C3×D12—124no—
316C3×C4×D3—64no—
317C3×C4×D3—64no—
318C3×C4×D3—64no—
319C3×C4×D3—64no—
320C3×C4×D3—124no—
321C3×C4×D3—122no—
322C3×C4×D3—122no—
323#626—64no—
324#626—64no—
325#626—64no—
326#626—64no—
327#626—64no—
328#626—64no—
329#625—64no—
330#625—64no—
331#625—64no—
332#624—34no—
333#624—64no—
334#624—62no—
335D3×Dic3—38no—
336D3×Dic3—64no—
337D3×Dic3—64no—
338D3×Dic3—64no—
339C2×#121—271noSylow
340C2×C33—41no—
341C2×C33C22×D411yescharacteristic
342C2×C33C22×D411yescharacteristic
343C2×C33C2×#4111yescharacteristic
344C3×C3⋊D3—24no—
345C3×C3⋊D3—41no—
346C3×C3⋊D3—42no—
347C3×C3⋊D3#12114yescomplemented
348C24×C3—91no—
349C23×D3—32no—
350C23×D3—61no—
351C23×D3—91no—
352C23×D3—92no—
353C23×D3—92no—
354C23×D3—91no—
355C2×C3×D4—92no—
356C2×C3×D4—92no—
357C2×C3×D4—92no—
358C22×C3×C4—91no—
359C22×C3×C4—91no—
360C22×C3×C4—92no—
361C2×#67—32no—
362C2×#67—32no—
363C2×#67—32no—
364C2×#67—32no—
365C2×#67—62no—
366C2×#67—62no—
367C2×#67—92no—
368C2×#67—92no—
369C2×#67—92no—
370C2×#67—92no—
371C2×#67—92no—
372C2×#67—92no—
373C2×#67—184no—
374C2×#67—184no—
375C22×Dic3—91no—
376C22×Dic3—91no—
377C22×Dic3—92no—
378D3×D4—188no—
379D3×D4—188no—
380D3×D4—188no—
381C2×D12—32no—
382C2×D12—32no—
383C2×D12—62no—
384C2×D12—92no—
385C2×D12—92no—
386C2×D12—92no—
387C2×D12—184no—
388C2×C4×D3—32no—
389C2×C4×D3—32no—
390C2×C4×D3—32no—
391C2×C4×D3—32no—
392C2×C4×D3—61no—
393C2×C4×D3—61no—
394C2×C4×D3—62no—
395C2×C4×D3—92no—
396C2×C4×D3—92no—
397C2×C4×D3—92no—
398C2×C4×D3—92no—
399C2×C4×D3—188no—
400C2×C4×D3—184no—
401C3×C4⋊C4—92no—
402C3×C22⋊C4—21no—
403C3×C22⋊C4—22no—
404C3×C22⋊C4—41no—
405C3×C22⋊C4—91no—
406C3×C22⋊C4—92no—
407C3×C22⋊C4—91no—
408C3×C22⋊C4—91no—
409C3×C22⋊C4D3212yescomplemented
410C3×C22⋊C4D3211yescharacteristic, complemented
411#217—32no—
412#217—61no—
413#217—92no—
414(C2×D3)⋊C4—32no—
415(C2×D3)⋊C4—32no—
416(C2×D3)⋊C4—32no—
417(C2×D3)⋊C4—32no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—62no—
421(C2×D3)⋊C4—92no—
422(C2×D3)⋊C4—92no—
423C4⋊Dic3—92no—
424Dic3⋊C4—32no—
425Dic3⋊C4—32no—
426Dic3⋊C4—62no—
427Dic3⋊C4—92no—
428Dic3⋊C4—92no—
429C22×C32—21no—
430C22×C32—22no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—22no—
434C22×C32—22no—
435C22×C32—22no—
436C22×C32—22no—
437C22×C32—21no—
438C22×C32—41no—
439C22×C32—42no—
440C22×C32—42no—
441C22×C32—41no—
442C22×C32—41no—
443C22×C32—42no—
444C22×C32—42no—
445C22×C32—81no—
446C22×C32—81no—
447C22×C32C23×D311yescharacteristic
448C22×C32C23×D312yes—
449C2×C3⋊D3—21no—
450C2×C3⋊D3—22no—
451C2×C3⋊D3—22no—
452C2×C3⋊D3—21no—
453C2×C3⋊D3—21no—
454C2×C3⋊D3—22no—
455C2×C3⋊D3—22no—
456C2×C3⋊D3—22no—
457C2×C3⋊D3—44no—
458C2×C3⋊D3#23512yes—
459C2×C3⋊D3D3×D412yes—
460C2×C3⋊D3D3×D412yes—
461C2×C3⋊D3D3×D414yescomplemented
462C2×C3×D3—34no—
463C2×C3×D3—34no—
464C2×C3×D3—34no—
465C2×C3×D3—34no—
466C2×C3×D3—34no—
467C2×C3×D3—62no—
468C2×C3×D3—62no—
469C2×C3×D3—62no—
470C2×C3×D3—64no—
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—62no—
482C2×C3×D3—62no—
483C2×C3×D3—62no—
484C2×C3×D3—62no—
485C2×C3×D3—122no—
486C2×C3×D3—122no—
487C2×C3×D3—121no—
488C2×C3×D3—121no—
489C2×C3×D3—122no—
490C2×C3×D3—122no—
491C2×C3×D3—122no—
492C2×C3×D3—128no—
493C2×C3×D3—128no—
494D32—616no—
495D32—68no—
496D32—128no—
497D32—124no—
498C32×C4—21no—
499C32×C4—22no—
500C32×C4—22no—
501C32×C4—21no—
502C32×C4—42no—
503C32×C4—41no—
504C32×C4—41no—
505C32×C4—42no—
506C32×C4—81no—
507C32×C4—81no—
508C3⋊Dic3—21no—
509C3⋊Dic3—22no—
510C3⋊Dic3—21no—
511C3⋊Dic3D3×D414yescomplemented
512C3×Dic3—34no—
513C3×Dic3—34no—
514C3×Dic3—64no—
515C3×Dic3—62no—
516C3×Dic3—62no—
517C3×Dic3—62no—
518C3×Dic3—62no—
519C3×Dic3—121no—
520C3×Dic3—121no—
521C3×Dic3—122no—
522C22×D4—271no—
523C22×D4—271no—
524C22×D4—271no—
525C23×C4—271no—
526#121—92no—
527#121—272no—
528#121—272no—
529#121—272no—
530C2×C4⋊C4—271no—
531C2×C22⋊C4—91no—
532C2×C22⋊C4—271no—
533C33C2×#12111yescharacteristic, complemented, Sylow
534C23×C3—21no—
535C23×C3—22no—
536C23×C3—41no—
537C23×C3—91no—
538C23×C3—92no—
539C23×C3—92no—
540C23×C3—91no—
541C23×C3—182no—
542C23×C3—182no—
543C23×C3—182no—
544C23×C3C2×D3212yes—
545C23×C3C2×D3211yescharacteristic
546C22×D3—32no—
547C22×D3—32no—
548C22×D3—32no—
549C22×D3—32no—
550C22×D3—32no—
551C22×D3—32no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—62no—
555C22×D3—62no—
556C22×D3—64no—
557C22×D3—64no—
558C22×D3—64no—
559C22×D3—64no—
560C22×D3—94no—
561C22×D3—98no—
562C22×D3—122no—
563C22×D3—122no—
564C22×D3—184no—
565C22×D3—184no—
566C22×D3—184no—
567C22×D3—184no—
568C22×D3—184no—
569C22×D3—182no—
570C22×D3—182no—
571C22×D3—182no—
572C22×D3—182no—
573C22×D3—182no—
574C3×D4—184no—
575C3×D4—184no—
576C3×D4—184no—
577C2×C3×C4—22no—
578C2×C3×C4—21no—
579C2×C3×C4—22no—
580C2×C3×C4—21no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—92no—
584C2×C3×C4—91no—
585C2×C3×C4—92no—
586C2×C3×C4—91no—
587C2×C3×C4—184no—
588C2×C3×C4—182no—
589C2×C3×C4—182no—
590C2×C3×C4C2×D3211yescharacteristic
591C2×C3×C4C2×D3212yes—
592C2×C3×C4C2×D3212yes—
593C2×C3×C4C2×D3211yescharacteristic
594#67—64no—
595#67—64no—
596#67—64no—
597#67—64no—
598#67—124no—
599#67—124no—
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—32no—
612C2×Dic3—62no—
613C2×Dic3—62no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—94no—
617C2×Dic3—184no—
618C2×Dic3—182no—
619D12—64no—
620D12—64no—
621D12—124no—
622D12—184no—
623D12—184no—
624D12—184no—
625C4×D3—64no—
626C4×D3—64no—
627C4×D3—64no—
628C4×D3—64no—
629C4×D3—98no—
630C4×D3—124no—
631C4×D3—122no—
632C4×D3—122no—
633C4×D3—184no—
634C4×D3—184no—
635C4×D3—184no—
636C2×C32—22no—
637C2×C32—21no—
638C2×C32—22no—
639C2×C32—22no—
640C2×C32—21no—
641C2×C32—21no—
642C2×C32—41no—
643C2×C32—41no—
644C2×C32—41no—
645C2×C32—41no—
646C2×C32—42no—
647C2×C32—42no—
648C2×C32—82no—
649C2×C32—82no—
650C2×C32C2×#23511yescharacteristic
651C2×C32C2×D3×D411yescharacteristic
652C2×C32C2×D3×D411yescharacteristic
653C2×C32C2×D3×D412yes—
654C2×C32C2×D3×D412yes—
655C2×C32D3×#4112yes—
656C3⋊D3—24no—
657C3⋊D3—41no—
658C3⋊D3—42no—
659C3⋊D3#88414yescomplemented
660C3×D3—38no—
661C3×D3—64no—
662C3×D3—64no—
663C3×D3—64no—
664C3×D3—124no—
665C3×D3—122no—
666C3×D3—122no—
667C3×D3—122no—
668C3×D3—122no—
669C3×D3—242no—
670C24—91no—
671C24—271no—
672C24—271no—
673C2×D4—92no—
674C2×D4—92no—
675C2×D4—92no—
676C2×D4—272no—
677C2×D4—272no—
678C2×D4—272no—
679C2×D4—544no—
680C2×D4—544no—
681C2×D4—544no—
682C22×C4—91no—
683C22×C4—91no—
684C22×C4—92no—
685C22×C4—271no—
686C22×C4—271no—
687C22×C4—272no—
688C22×C4—544no—
689C4⋊C4—92no—
690C4⋊C4—272no—
691C22⋊C4—91no—
692C22⋊C4—91no—
693C22⋊C4—91no—
694C22⋊C4—92no—
695C22⋊C4—272no—
696C22⋊C4#111311yescharacteristic, complemented
697C22×C3—22no—
698C22×C3—22no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—22no—
703C22×C3—22no—
704C22×C3—21no—
705C22×C3—22no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—41no—
713C22×C3—81no—
714C22×C3—81no—
715C22×C3—92no—
716C22×C3—92no—
717C22×C3—92no—
718C22×C3—94no—
719C22×C3—182no—
720C22×C3—182no—
721C22×C3—182no—
722C22×C3—181no—
723C22×C3—181no—
724C22×C3—181no—
725C22×C3—182no—
726C22×C3—182no—
727C22×C3—364no—
728C22×C3C22×D3212yes—
729C22×C3C22×D3211yescharacteristic
730C2×D3—34no—
731C2×D3—34no—
732C2×D3—34no—
733C2×D3—34no—
734C2×D3—34no—
735C2×D3—62no—
736C2×D3—62no—
737C2×D3—62no—
738C2×D3—64no—
739C2×D3—62no—
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—62no—
753C2×D3—122no—
754C2×D3—121no—
755C2×D3—121no—
756C2×D3—122no—
757C2×D3—122no—
758C2×D3—122no—
759C2×D3—122no—
760C2×D3—128no—
761C2×D3—128no—
762C2×D3—1816no—
763C2×D3—188no—
764C2×D3—368no—
765C2×D3—364no—
766C3×C4—22no—
767C3×C4—21no—
768C3×C4—22no—
769C3×C4—21no—
770C3×C4—42no—
771C3×C4—41no—
772C3×C4—41no—
773C3×C4—42no—
774C3×C4—81no—
775C3×C4—81no—
776C3×C4—94no—
777C3×C4—181no—
778C3×C4—182no—
779C3×C4—181no—
780Dic3—34no—
781Dic3—34no—
782Dic3—64no—
783Dic3—62no—
784Dic3—62no—
785Dic3—62no—
786Dic3—62no—
787Dic3—121no—
788Dic3—121no—
789Dic3—122no—
790C32—22no—
791C32—21no—
792C32—41no—
793C32C2×#88411yescharacteristic, complemented
794C32D3×#12112yescomplemented
795C23—91no—
796C23—92no—
797C23—91no—
798C23—92no—
799C23—182no—
800C23—182no—
801C23—182no—
802C23—274no—
803C23—542no—
804C23—542no—
805C23—542no—
806C23—542no—
807C23—542no—
808C23C2×#111311yescharacteristic
809D4—184no—
810D4—184no—
811D4—184no—
812D4—544no—
813D4—544no—
814D4—544no—
815C2×C4—92no—
816C2×C4—91no—
817C2×C4—91no—
818C2×C4—92no—
819C2×C4—184no—
820C2×C4—182no—
821C2×C4—182no—
822C2×C4—274no—
823C2×C4—544no—
824C2×C4—542no—
825C2×C4C2×#111311yescharacteristic
826C2×C4C2×#111311yescharacteristic
827C2×C3—21no—
828C2×C3—22no—
829C2×C3—22no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—22no—
833C2×C3—42no—
834C2×C3—42no—
835C2×C3—41no—
836C2×C3—41no—
837C2×C3—41no—
838C2×C3—41no—
839C2×C3—82no—
840C2×C3—82no—
841C2×C3—94no—
842C2×C3—184no—
843C2×C3—362no—
844C2×C3—361no—
845C2×C3D3×#23512yes—
846C2×C3#6430611yescharacteristic
847C2×C3D32×D412yes—
848C2×C3D32×D412yes—
849C2×C3D32×D411yescharacteristic
850C2×C3D32×D411yescharacteristic
851D3—38no—
852D3—64no—
853D3—64no—
854D3—64no—
855D3—124no—
856D3—122no—
857D3—122no—
858D3—122no—
859D3—122no—
860D3—242no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—92no—
865C22—92no—
866C22—92no—
867C22—94no—
868C22—182no—
869C22—182no—
870C22—181no—
871C22—182no—
872C22—182no—
873C22—182no—
874C22—181no—
875C22—181no—
876C22—364no—
877C22—548no—
878C22—1084no—
879C22C22×#111311yescharacteristic
880C4—21no—
881C4—21no—
882C4—94no—
883C4—181no—
884C4—181no—
885C4—182no—
886C3—21no—
887C3—22no—
888C3—41no—
889C3D3×#88412yescomplemented
890C3#1059426511yescharacteristic, complemented
891C2—41no—
892C2—94no—
893C2—184no—
894C2—361no—
895C2—362no—
896C2#1172461811yescharacteristic
897C2D4×#111311yescharacteristic
898C2D4×#111311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4#1113
hypocenterC33C2×#121
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. C2×#89049C2semidirect
3. C2×C4⋊#1113C2semidirect
4. C2×C4×#1113C2semidirect
5. C3×#64093C2semidirect
6. C3×C22⋊C4×C3⋊D3C2semidirect
7. #11723725C2semidirect
8. #11723700C2semidirect
9. #11723695C2semidirect
10. #11723687C2semidirect
11. #11723682C2semidirect
17. C2×C3×#638C22semidirect
18. C2×C3×#638C22semidirect
19. C2×C3×C4⋊(C3⋊D3)C22semidirect
22. C2×C3×C4×C3⋊D3C22semidirect
25. C2×#6295C22semidirect
26. C2×#6295C22semidirect
27. C2×#6295C22semidirect
30. C2×#6294C22semidirect
33. C33×C22⋊C4C22semidirect
34. C3×#3757C22semidirect
35. C3×#3752C22semidirect
36. C3×#3752C22semidirect
37. C3×#3752C22semidirect
38. C3×#3750C22semidirect
39. #88815C22semidirect
40. #88814C22semidirect
49. #64093D3semidirect
50. C22⋊C4×C3⋊D3D3semidirect
82. C2×#1113D4semidirect
100. #6294D4semidirect
110. C2×#638C2×D3semidirect
111. C2×#638C2×D3semidirect
112. C2×C4⋊(C3⋊D3)C2×D3semidirect
115. C2×C4×C3⋊D3C2×D3semidirect
159. C32×C22⋊C4C2×D3semidirect
160. C32×C22⋊C4C2×D3semidirect
161. #3757C2×D3semidirect
162. #3752C2×D3semidirect
163. #3752C2×D3semidirect
164. #3752C2×D3semidirect
165. #3750C2×D3semidirect
199. C2×C3×C3⋊D3C2×D4semidirect
208. C3×C3⋊Dic3C2×D4semidirect
347. C3×C3⋊D3#121semidirect
409. C3×C22⋊C4D32semidirect
410. C3×C22⋊C4D32semidirect
461. C2×C3⋊D3D3×D4semidirect
511. C3⋊Dic3D3×D4semidirect
533. C33C2×#121semidirect
659. C3⋊D3#884semidirect
696. C22⋊C4#1113semidirect
793. C32C2×#884semidirect
794. C32D3×#121semidirect
889. C3D3×#884semidirect
890. C3#10594265semidirect

Maximal subgroups

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

subgroupindex
C2×#890492
C2×C4⋊#11132
C2×C4×#11132
C3×#640932
C3×C22⋊C4×C3⋊D32
#117237252
#117237002
#117236952
#117236872
#117236822
#105942653
D3×#8843