Finite Group Databasebeta

← D3×#4991 #11808154

Subgroups — D3×#4991 #11808154

Order 1152.

2623 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D12C211yesmaximal, characteristic
2C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×D3×(C2×D3)⋊C4C212yesmaximal, complemented
4C2×D3×(C2×D3)⋊C4C212yesmaximal, complemented
5#10592690C211yesmaximal, characteristic, complemented
6C3×#4991C211yesmaximal, characteristic, complemented
7#10591392C212yesmaximal, complemented
8D3×C3⋊#95C211yesmaximal, characteristic, complemented
9#10591321C211yesmaximal, characteristic, complemented
10#10591300C211yesmaximal, characteristic, complemented
11#10591291C212yesmaximal, complemented
12C2×#4991—31nomaximal
13D3×#394—31nomaximal
14C23×D32C2212yes—
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C3×D12C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×#626C2212yes—
21C22×D3×Dic3C2212yes—
22C2×D3×D12—24no—
23C2×D3×D12—28no—
24C2×C32×C4⋊C4C2211yescharacteristic, complemented
25C2×#3752C2212yescomplemented
26C2×#3752C2212yescomplemented
27C2×C3×(C2×D3)⋊C4C2212yescomplemented
28C2×C3×(C2×D3)⋊C4C2212yescomplemented
29C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
30C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
31C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
32C3×D3×C4⋊C4—24no—
33C2×#3722C2212yescomplemented
34C2×#3722C2212yescomplemented
35C2×(C2×D3)⋊Dic3C2212yescomplemented
36C2×(C2×D3)⋊Dic3C2212yescomplemented
37D3×(C2×D3)⋊C4—28no—
38D3×(C2×D3)⋊C4—28no—
39#63658C2211yescharacteristic, complemented
40C3×C3⋊#95C2211yescharacteristic, complemented
41#63579C2212yescomplemented
42C22×D3×D4—31no—
43C23×D12—31no—
44C22×C3×C4⋊C4—31no—
45C22×(C2×D3)⋊C4—32no—
46C22×(C2×D3)⋊C4—32no—
47C2×D3×C4⋊C4D311yescharacteristic, complemented
48C2×D3×C22⋊C4—32no—
49C2×D3×C22⋊C4—32no—
50C3×#394—31no—
51#5222—31no—
52C2×C3⋊#95—31no—
53#4991—31no—
54#4991—31no—
55#4991—31no—
56#4991—32no—
57#4991—32no—
58#4991—31no—
59#4991—61no—
60#4991D311yescharacteristic, direct product factor
61#4961—32no—
62#4959—32no—
63#4672—31no—
64D3×#95—31no—
65C23×C3⋊D3C2312yes—
66C23×C3×D3C2312yes—
67C23×C3×D3C2311yescharacteristic
68C22×D32—24no—
69C22×D32—24no—
70C22×D32—24no—
71C22×D32—24no—
72C22×D32—24no—
73C22×D32—24no—
74C22×D32D418yes—
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2312yes—
79C2×C4⋊(C3⋊D3)—24no—
80C2×C4⋊(C3⋊D3)—22no—
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2311yescharacteristic
85C2×C3×D12—24no—
86C2×C3×D12—22no—
87C2×C3×C4×D3—22no—
88C2×C3×C4×D3—24no—
89C2×C3×C4×D3—22no—
90C2×C3×C4×D3—22no—
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3D414yes—
93C2×C3×C4×D3D414yescomplemented
94C2×#626—24no—
95C2×#626—24no—
96C2×#626—24no—
97C2×D3×Dic3—24no—
98C2×D3×Dic3—24no—
99C2×D3×Dic3—24no—
100D3×D12—232no—
101C32×C4⋊C4—22no—
102#3752—24no—
103#3752—24no—
104C3×(C2×D3)⋊C4—24no—
105C3×(C2×D3)⋊C4—24no—
106C3×C4⋊Dic3—22no—
107C3×Dic3⋊C4—22no—
108C3×Dic3⋊C4—22no—
109#3722—24no—
110#3722—24no—
111(C2×D3)⋊Dic3—24no—
112(C2×D3)⋊Dic3—24no—
113C2×#394—91noSylow
114C24×D3—32no—
115C24×D3—32no—
116C22×C3×D4—31no—
117C23×C3×C4—31no—
118C23×C3×C4—31no—
119C23×C3×C4—31no—
120C22×#67—32no—
121C23×Dic3—32no—
122C2×D3×D4—68no—
123C2×D3×D4—64no—
124C22×D12—32no—
125C22×D12—31no—
126C22×D12—31no—
127C22×D12—61no—
128C22×D12—64no—
129C22×D12—68no—
130C22×D12C2×D311yescharacteristic
131C22×C4×D3—32no—
132C22×C4×D3C2×D311yescharacteristic
133C22×C4×D3C2×D311yescharacteristic
134C22×C4×D3C2×D311yescharacteristic
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—64no—
140C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
141C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
142C2×C3×C22⋊C4—32no—
143C2×C3×C22⋊C4—32no—
144C2×#217—32no—
145C2×#217—32no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4—32no—
148C2×(C2×D3)⋊C4—32no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4—32no—
154C2×(C2×D3)⋊C4—32no—
155C2×(C2×D3)⋊C4—32no—
156C2×(C2×D3)⋊C4—62no—
157C2×(C2×D3)⋊C4—62no—
158C2×(C2×D3)⋊C4—68no—
159C2×(C2×D3)⋊C4—68no—
160C2×(C2×D3)⋊C4C2×D312yescomplemented
161C2×(C2×D3)⋊C4C2×D312yescomplemented
162C2×C4⋊Dic3C2×D311yescharacteristic, complemented
163C2×Dic3⋊C4C2×D311yescharacteristic, complemented
164C2×Dic3⋊C4C2×D311yescharacteristic, complemented
165D3×C4⋊C4—24no—
166D3×C22⋊C4—68no—
167D3×C22⋊C4—68no—
168C3×#95—31no—
169C3⋊#95—31no—
170C3⋊#95—31no—
171C3⋊#95—32no—
172C3⋊#95—32no—
173C3⋊#95—61no—
174C3⋊#95C2×D311yescharacteristic, complemented
175C23×C32C2411yescharacteristic
176C22×C3⋊D3—22no—
177C22×C3⋊D3—22no—
178C22×C3⋊D3—22no—
179C22×C3⋊D3—22no—
180C22×C3⋊D3—22no—
181C22×C3⋊D3—22no—
182C22×C3⋊D3C2×D414yes—
183C22×C3×D3—22no—
184C22×C3×D3—22no—
185C22×C3×D3—22no—
186C22×C3×D3—22no—
187C22×C3×D3—22no—
188C22×C3×D3—22no—
189C22×C3×D3C2×D412yes—
190C22×C3×D3C2×D414yes—
191C22×C3×D3C2×D414yes—
192C22×C3×D3C2×D412yes—
193C22×C3×D3#4112yes—
194C22×C3×D3#4114yes—
195C2×D32—216no—
196C2×D32—216no—
197C2×D32—216no—
198C2×D32—48no—
199C2×D32—48no—
200C2×D32—48no—
201C2×D32—48no—
202C2×C32×C4—21no—
203C2×C32×C4—22no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—22no—
207C2×C32×C4C2×D412yes—
208C2×C32×C4C2×D412yescomplemented
209C2×C3⋊Dic3—22no—
210C2×C3⋊Dic3—22no—
211C2×C3⋊Dic3—22no—
212C4⋊(C3⋊D3)—28no—
213C2×C3×Dic3—21no—
214C2×C3×Dic3—22no—
215C2×C3×Dic3—21no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—22no—
219C2×C3×Dic3—21no—
220C2×C3×Dic3—22no—
221C2×C3×Dic3C2×D412yes—
222C2×C3×Dic3C2×D412yescomplemented
223C3×D12—28no—
224C3×C4×D3—28no—
225C3×C4×D3—28no—
226C3×C4×D3—44no—
227#626—216no—
228D3×Dic3—48no—
229C23×D4—91no—
230C22×C4⋊C4—31no—
231C22×C22⋊C4—92no—
232C22×C22⋊C4—92no—
233#394—31no—
234#394—91no—
235#394—92no—
236#394—92no—
237#394—91no—
238#394—91no—
239C2×#95—91no—
240C24×C3—31no—
241C24×C3—32no—
242C23×D3—32no—
243C23×D3—32no—
244C23×D3—38no—
245C23×D3—38no—
246C23×D3—62no—
247C23×D3—64no—
248C23×D3—64no—
249C23×D3—64no—
250C23×D3—64no—
251C23×D3—64no—
252C23×D3—64no—
253C23×D3—64no—
254C23×D3—64no—
255C23×D3—64no—
256C23×D3—64no—
257C23×D3—64no—
258C23×D3—64no—
259C23×D3C22×D312yes—
260C23×D3C22×D311yescharacteristic
261C2×C3×D4—64no—
262C2×C3×D4—62no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—31no—
267C22×C3×C4—31no—
268C22×C3×C4—34no—
269C22×C3×C4—34no—
270C22×C3×C4—32no—
271C22×C3×C4—31no—
272C22×C3×C4—62no—
273C22×C3×C4—64no—
274C22×C3×C4—62no—
275C22×C3×C4—64no—
276C22×C3×C4—62no—
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C22×D311yescharacteristic
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C22×C3×C4C22×D311yescharacteristic
283C2×#67—64no—
284C2×#67—64no—
285C2×#67—64no—
286C22×Dic3—32no—
287C22×Dic3—32no—
288C22×Dic3—62no—
289C22×Dic3—64no—
290C22×Dic3—64no—
291C22×Dic3—64no—
292C22×Dic3C22×D312yes—
293C22×Dic3C22×D311yescharacteristic
294C22×Dic3C22×D311yescharacteristic
295C22×Dic3C22×D311yescharacteristic
296D3×D4—632no—
297C2×D12—24no—
298C2×D12—22no—
299C2×D12—632no—
300C2×D12—64no—
301C2×D12—64no—
302C2×D12—64no—
303C2×D12—64no—
304C2×D12—64no—
305C2×D12—62no—
306C2×D12—62no—
307C2×D12—122no—
308C2×D12—124no—
309C2×C4×D3—22no—
310C2×C4×D3—24no—
311C2×C4×D3—22no—
312C2×C4×D3—24no—
313C2×C4×D3—22no—
314C2×C4×D3—64no—
315C2×C4×D3—64no—
316C2×C4×D3—64no—
317C2×C4×D3D1214yescomplemented
318C2×C4×D3#6714yes—
319C3×C4⋊C4—22no—
320C3×C4⋊C4—22no—
321C3×C4⋊C4—42no—
322C3×C4⋊C4—62no—
323C3×C4⋊C4—62no—
324C3×C4⋊C4—62no—
325C3×C22⋊C4—64no—
326C3×C22⋊C4—64no—
327#217—64no—
328#217—64no—
329(C2×D3)⋊C4—24no—
330(C2×D3)⋊C4—24no—
331(C2×D3)⋊C4—64no—
332(C2×D3)⋊C4—64no—
333(C2×D3)⋊C4—64no—
334(C2×D3)⋊C4—64no—
335(C2×D3)⋊C4—64no—
336(C2×D3)⋊C4—64no—
337(C2×D3)⋊C4—64no—
338(C2×D3)⋊C4—64no—
339(C2×D3)⋊C4—64no—
340(C2×D3)⋊C4—64no—
341(C2×D3)⋊C4—124no—
342(C2×D3)⋊C4—124no—
343C4⋊Dic3—22no—
344Dic3⋊C4—22no—
345Dic3⋊C4—22no—
346C22×C32C22×D411yescharacteristic
347C22×C32C22×D412yes—
348C22×C32C22×D411yescharacteristic
349C22×C32C2×#4111yescharacteristic
350C22×C32C2×#4112yes—
351C2×C3⋊D3—24no—
352C2×C3⋊D3—24no—
353C2×C3⋊D3—24no—
354C2×C3⋊D3—42no—
355C2×C3⋊D3—42no—
356C2×C3⋊D3—42no—
357C2×C3⋊D3—42no—
358C2×C3×D3—24no—
359C2×C3×D3—24no—
360C2×C3×D3—24no—
361C2×C3×D3—42no—
362C2×C3×D3—42no—
363C2×C3×D3—42no—
364C2×C3×D3—42no—
365C2×C3×D3#12014yes—
366C2×C3×D3#12118yes—
367C2×C3×D3#12114yes—
368C2×C3×D3#12318yes—
369C2×C3×D3#12414yes—
370D32—432no—
371C32×C4—22no—
372C32×C4—22no—
373C32×C4—41no—
374C3⋊Dic3—42no—
375C3×Dic3—22no—
376C3×Dic3—22no—
377C3×Dic3—41no—
378C3×Dic3—42no—
379C25—92no—
380C22×D4—31no—
381C22×D4—92no—
382C22×D4—91no—
383C22×D4—184no—
384C22×D4—188no—
385C23×C4—31no—
386C23×C4—31no—
387C23×C4—31no—
388C23×C4—92no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—64no—
393C2×C4⋊C4D3211yescharacteristic, complemented
394C2×C22⋊C4—32no—
395C2×C22⋊C4—32no—
396C2×C22⋊C4—92no—
397C2×C22⋊C4—92no—
398C2×C22⋊C4—92no—
399C2×C22⋊C4—92no—
400C2×C22⋊C4—92no—
401C2×C22⋊C4—92no—
402C2×C22⋊C4—188no—
403C2×C22⋊C4—188no—
404#95—31no—
405#95—92no—
406#95—91no—
407C23×C3—21no—
408C23×C3—32no—
409C23×C3—34no—
410C23×C3—32no—
411C23×C3—34no—
412C23×C3—32no—
413C23×C3—34no—
414C23×C3—62no—
415C23×C3—62no—
416C23×C3—62no—
417C23×C3—62no—
418C23×C3—62no—
419C23×C3—62no—
420C23×C3C23×D311yescharacteristic
421C23×C3C23×D311yescharacteristic
422C22×D3—22no—
423C22×D3—22no—
424C22×D3—22no—
425C22×D3—22no—
426C22×D3—22no—
427C22×D3—22no—
428C22×D3—34no—
429C22×D3—34no—
430C22×D3—64no—
431C22×D3—616no—
432C22×D3—616no—
433C22×D3—616no—
434C22×D3—62no—
435C22×D3—62no—
436C22×D3—62no—
437C22×D3—62no—
438C22×D3—62no—
439C22×D3—62no—
440C22×D3—62no—
441C22×D3—62no—
442C22×D3—62no—
443C22×D3—62no—
444C22×D3—62no—
445C22×D3—62no—
446C22×D3—616no—
447C22×D3—616no—
448C22×D3—616no—
449C22×D3—122no—
450C22×D3—122no—
451C22×D3—122no—
452C22×D3—122no—
453C22×D3—122no—
454C22×D3—122no—
455C22×D3—128no—
456C22×D3—128no—
457C22×D3—128no—
458C22×D3—128no—
459C22×D3—128no—
460C22×D3—128no—
461C22×D3—128no—
462C22×D3—128no—
463C22×D3C2×D1212yes—
464C22×D3#23512yes—
465C22×D3D3×D414yes—
466C22×D3D3×D414yes—
467C22×D3#23914yes—
468C22×D3C2×#6712yes—
469C3×D4—68no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—32no—
483C2×C3×C4—32no—
484C2×C3×C4—41no—
485C2×C3×C4—42no—
486C2×C3×C4—41no—
487C2×C3×C4—42no—
488C2×C3×C4—41no—
489C2×C3×C4—68no—
490C2×C3×C4—68no—
491C2×C3×C4—61no—
492C2×C3×C4—62no—
493C2×C3×C4—61no—
494C2×C3×C4—62no—
495C2×C3×C4—62no—
496C2×C3×C4—62no—
497C2×C3×C4—61no—
498C2×C3×C4—62no—
499C2×C3×C4—124no—
500C2×C3×C4C2×D1212yescomplemented
501C2×C3×C4D3×D412yes—
502C2×C3×C4D3×D412yescomplemented
503C2×C3×C4C2×#6712yes—
504#67—616no—
505C2×Dic3—21no—
506C2×Dic3—22no—
507C2×Dic3—21no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—21no—
513C2×Dic3—62no—
514C2×Dic3—62no—
515C2×Dic3—62no—
516C2×Dic3—62no—
517C2×Dic3—62no—
518C2×Dic3—62no—
519C2×Dic3—122no—
520C2×Dic3—122no—
521C2×Dic3—122no—
522C2×Dic3—128no—
523C2×Dic3C2×D1212yescomplemented
524C2×Dic3C2×#6712yes—
525D12—28no—
526D12—68no—
527D12—68no—
528D12—616no—
529D12—128no—
530C4×D3—28no—
531C4×D3—28no—
532C4×D3—44no—
533C4×D3—128no—
534C2×C32C2×#12011yescharacteristic
535C2×C32C2×#12112yes—
536C2×C32C2×#12111yescharacteristic
537C2×C32C2×#12312yes—
538C2×C32C2×#12411yescharacteristic
539C3⋊D3—44no—
540C3×D3—44no—
541C3×D3#39418yescomplemented
542C24—31no—
543C24—32no—
544C24—98no—
545C24—92no—
546C24—184no—
547C24—184no—
548C24—184no—
549C24—184no—
550C24—184no—
551C24—184no—
552C2×D4—64no—
553C2×D4—62no—
554C2×D4—184no—
555C2×D4—184no—
556C2×D4—1832no—
557C2×D4—184no—
558C2×D4—184no—
559C2×D4—182no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—34no—
563C22×C4—34no—
564C22×C4—32no—
565C22×C4—31no—
566C22×C4—62no—
567C22×C4—64no—
568C22×C4—62no—
569C22×C4—64no—
570C22×C4—62no—
571C22×C4—92no—
572C22×C4—184no—
573C22×C4—184no—
574C22×C4—184no—
575C22×C4C2×D3211yescharacteristic
576C22×C4C2×D3211yescharacteristic
577C22×C4C2×D3211yescharacteristic
578C4⋊C4—22no—
579C4⋊C4—62no—
580C4⋊C4—62no—
581C4⋊C4—62no—
582C22⋊C4—64no—
583C22⋊C4—64no—
584C22⋊C4—184no—
585C22⋊C4—184no—
586C22⋊C4—184no—
587C22⋊C4—184no—
588C22⋊C4—184no—
589C22⋊C4—184no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—21no—
595C22×C3—38no—
596C22×C3—34no—
597C22×C3—34no—
598C22×C3—38no—
599C22×C3—34no—
600C22×C3—64no—
601C22×C3—64no—
602C22×C3—64no—
603C22×C3—122no—
604C22×C3—122no—
605C22×C3—122no—
606C22×C3—122no—
607C22×C3C22×D1211yescharacteristic
608C22×C3C2×#23511yescharacteristic
609C22×C3C2×D3×D411yescharacteristic
610C22×C3C2×D3×D412yes—
611C22×C3C2×D3×D412yes—
612C22×C3C2×D3×D411yescharacteristic
613C22×C3C2×#23912yes—
614C22×C3D3×#4111yescharacteristic
615C22×C3D3×#4112yes—
616C22×C3C22×#6711yescharacteristic
617C2×D3—24no—
618C2×D3—24no—
619C2×D3—24no—
620C2×D3—42no—
621C2×D3—42no—
622C2×D3—42no—
623C2×D3—42no—
624C2×D3—64no—
625C2×D3—64no—
626C2×D3—64no—
627C2×D3—64no—
628C2×D3—64no—
629C2×D3—64no—
630C2×D3—124no—
631C2×D3—124no—
632C2×D3—124no—
633C2×D3—1232no—
634C2×D3—122no—
635C2×D3—122no—
636C2×D3—122no—
637C2×D3—122no—
638C2×D3—122no—
639C2×D3—122no—
640C2×D3—122no—
641C2×D3—122no—
642C2×D3—1232no—
643C2×D3—242no—
644C2×D3—242no—
645C2×D3—242no—
646C2×D3—242no—
647C2×D3#89418yes—
648C2×D3#89518yes—
649C2×D3#93014yes—
650C2×D3#93714yes—
651C2×D3#94714yes—
652C3×C4—22no—
653C3×C4—22no—
654C3×C4—22no—
655C3×C4—22no—
656C3×C4—42no—
657C3×C4—42no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—62no—
661C3×C4—62no—
662C3×C4—81no—
663C3×C4—122no—
664C3×C4—121no—
665Dic3—22no—
666Dic3—22no—
667Dic3—41no—
668Dic3—42no—
669Dic3—122no—
670Dic3—122no—
671Dic3—242no—
672C32C2×#39411yescharacteristic, complemented, Sylow
673C23—32no—
674C23—32no—
675C23—34no—
676C23—34no—
677C23—32no—
678C23—34no—
679C23—62no—
680C23—62no—
681C23—62no—
682C23—62no—
683C23—62no—
684C23—62no—
685C23—94no—
686C23—1816no—
687C23—1816no—
688C23—1816no—
689C23—182no—
690C23—182no—
691C23—182no—
692C23—182no—
693C23—182no—
694C23—182no—
695C23—368no—
696C23—368no—
697C23—368no—
698C23—368no—
699C23C22×D3211yescharacteristic
700D4—68no—
701D4—188no—
702D4—1816no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—32no—
709C2×C4—32no—
710C2×C4—68no—
711C2×C4—68no—
712C2×C4—61no—
713C2×C4—62no—
714C2×C4—61no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—61no—
720C2×C4—124no—
721C2×C4—182no—
722C2×C4—182no—
723C2×C4—182no—
724C2×C4—368no—
725C2×C4D3×D1212yescomplemented
726C2×C4D3×#6712yes—
727C2×C3—22no—
728C2×C3—22no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—38no—
733C2×C3—124no—
734C2×C3C2×#89412yes—
735C2×C3C2×#89512yes—
736C2×C3D3×#12011yescharacteristic
737C2×C3D3×#12112yes—
738C2×C3D3×#12111yescharacteristic
739C2×C3D3×#12312yes—
740C2×C3D3×#12411yescharacteristic
741C2×C3C2×#93011yescharacteristic
742C2×C3C2×#93711yescharacteristic
743C2×C3C2×#94711yescharacteristic
744D3—44no—
745D3—124no—
746D3—124no—
747D3—244no—
748D3#499118yesdirect product factor
749C22—38no—
750C22—38no—
751C22—34no—
752C22—34no—
753C22—34no—
754C22—64no—
755C22—64no—
756C22—64no—
757C22—122no—
758C22—122no—
759C22—122no—
760C22—122no—
761C22—184no—
762C22—184no—
763C22—184no—
764C22—3632no—
765C22—362no—
766C22—362no—
767C22—362no—
768C22—362no—
769C22C2×D3×D1211yescharacteristic
770C22D3×#23511yescharacteristic
771C22D32×D412yes—
772C22D3×#23912yes—
773C22C2×D3×#6711yescharacteristic
774C4—22no—
775C4—22no—
776C4—41no—
777C4—62no—
778C4—62no—
779C4—122no—
780C4—121no—
781C4—362no—
782C3—21no—
783C3D3×#39411yescharacteristic, complemented
784C3C2×#499111yescharacteristic, complemented
785C2—38no—
786C2—124no—
787C2—364no—
788C2D3×#89412yes—
789C2D3×#89512yes—
790C2D3×#93011yescharacteristic
791C2D3×#93711yescharacteristic
792C2D3×#94711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC22×D3×D12C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#394
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×C4⋊C4C2semidirect
3. C2×D3×(C2×D3)⋊C4C2semidirect
4. C2×D3×(C2×D3)⋊C4C2semidirect
5. #10592690C2semidirect
6. C3×#4991C2semidirect
7. #10591392C2semidirect
8. D3×C3⋊#95C2semidirect
9. #10591321C2semidirect
10. #10591300C2semidirect
11. #10591291C2semidirect
24. C2×C32×C4⋊C4C22semidirect
25. C2×#3752C22semidirect
26. C2×#3752C22semidirect
27. C2×C3×(C2×D3)⋊C4C22semidirect
28. C2×C3×(C2×D3)⋊C4C22semidirect
29. C2×C3×C4⋊Dic3C22semidirect
30. C2×C3×Dic3⋊C4C22semidirect
31. C2×C3×Dic3⋊C4C22semidirect
33. C2×#3722C22semidirect
34. C2×#3722C22semidirect
35. C2×(C2×D3)⋊Dic3C22semidirect
36. C2×(C2×D3)⋊Dic3C22semidirect
39. #63658C22semidirect
40. C3×C3⋊#95C22semidirect
41. #63579C22semidirect
47. C2×D3×C4⋊C4D3semidirect
60. #4991D3direct (N × H)
93. C2×C3×C4×D3D4semidirect
140. C2×C3×C4⋊C4C2×D3semidirect
141. C2×C3×C4⋊C4C2×D3semidirect
160. C2×(C2×D3)⋊C4C2×D3semidirect
161. C2×(C2×D3)⋊C4C2×D3semidirect
162. C2×C4⋊Dic3C2×D3semidirect
163. C2×Dic3⋊C4C2×D3semidirect
164. C2×Dic3⋊C4C2×D3semidirect
174. C3⋊#95C2×D3semidirect
208. C2×C32×C4C2×D4semidirect
222. C2×C3×Dic3C2×D4semidirect
317. C2×C4×D3D12semidirect
393. C2×C4⋊C4D32semidirect
500. C2×C3×C4C2×D12semidirect
502. C2×C3×C4D3×D4semidirect
523. C2×Dic3C2×D12semidirect
541. C3×D3#394semidirect
672. C32C2×#394semidirect
725. C2×C4D3×D12semidirect
748. D3#4991direct (N × H)
783. C3D3×#394semidirect
784. C3C2×#4991semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D122
C2×C3×D3×C4⋊C42
C2×D3×(C2×D3)⋊C42
#105926902
C3×#49912
#105913922
D3×C3⋊#952
#105913212
#105913002
#105912912
C2×#49913
D3×#3943