Finite Group Databasebeta

← D3×#5521 #11900013

Subgroups — D3×#5521 #11900013

Order 1152.

4009 conjugacy classes of subgroups.

The subgroup lattice has 807 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D12C211yesmaximal, characteristic
2#10595992C211yesmaximal, characteristic, complemented
3C3×#5521C211yesmaximal, characteristic, complemented
4C3×D3×#117C211yesmaximal, characteristic, complemented
5#10594996C211yesmaximal, characteristic, complemented
6#10594982C211yesmaximal, characteristic, complemented
7D3×#926C211yesmaximal, characteristic, complemented
8#10594604C214yesmaximal, complemented
9D3×#893C214yesmaximal, complemented
10D32×C22⋊C4C214yesmaximal, complemented
11#10594182C214yesmaximal, complemented
12#10593994C214yesmaximal, complemented
13C4×D3×D12C214yesmaximal, complemented
14D3×#518—31nomaximal
15C2×#5521—31nomaximal
16C23×D32C2212yes—
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×#626C2212yes—
21C2×D3×D12C4116yescomplemented
22C2×D3×D12C2212yes—
23C2×D3×D12C2212yes—
24C2×D3×D12C2212yes—
25C2×D3×D12C2212yes—
26C2×C4×D32C2218yescomplemented
27C32×#117C2211yescharacteristic, complemented
28#64135C2211yescharacteristic, complemented
29#64102C2214yescomplemented
30C22⋊C4×C3⋊D3C2214yescomplemented
31C4×C4⋊(C3⋊D3)C2214yescomplemented
32C3×#926C2211yescharacteristic, complemented
33C3×#926C2211yescharacteristic, complemented
34C3×#893C2214yescomplemented
35C3×#892C2212yescomplemented
36C3×D3×C4⋊C4C2212yescomplemented
37C3×D3×C22⋊C4C2212yes—
38C3×D3×C22⋊C4C2214yescomplemented
39C3×#877C2212yescomplemented
40C3×C4×D12C2214yescomplemented
41C3×#872C2212yescomplemented
42C3×C42×D3C2212yescomplemented
43#63974C2214yescomplemented
44D3×#217C2212yes—
45D3×#217C2214yescomplemented
46#63955C2212yescomplemented
47#63921C2218yescomplemented
48D3×(C2×D3)⋊C4C2218yescomplemented
49D3×(C2×D3)⋊C4C2218yescomplemented
50#63904C2218yescomplemented
51C4×#626C2218yescomplemented
52#63898C2214yescomplemented
53#63894C2214yescomplemented
54#63894C2214yescomplemented
55Dic3×D12C2214yescomplemented
56D3×C4⋊Dic3C2212yescomplemented
57#63881C2218yescomplemented
58#63880C2218yescomplemented
59C4×D3×Dic3C2212yescomplemented
60#63855C2212yescomplemented
61#63841C2212yescomplemented
62C22×D3×D4—31no—
63C23×D12—31no—
64C3×#518—31no—
65C2×C3×#117—31no—
66#5798—31no—
67C2×#926—31no—
68#5545—34no—
69#5545—34no—
70C4×D3×D4—34no—
71C4×D3×D4—34no—
72#5521—31no—
73#5521—31no—
74#5521—31no—
75#5521—31no—
76#5521—31no—
77#5521—34no—
78#5521—34no—
79#5521—34no—
80#5521—61no—
81#5521D311yescharacteristic, direct product factor
82D3×#117—31no—
83D3×#117D311yescharacteristic, complemented
84C2×#893—34no—
85#5486—34no—
86C2×D3×C22⋊C4—34no—
87C2×D3×C22⋊C4—34no—
88C2×C4×D12—34no—
89C23×C3⋊D3C2312yes—
90C23×C3×D3C2311yescharacteristic
91C23×C3×D3C2312yes—
92C22×D32—48no—
93C22×D32C2×C4116yescomplemented
94C22×D32C2314yes—
95C22×D32C2314yes—
96C22×C32×C4C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2×C418yescomplemented
98C2×C4⋊(C3⋊D3)C2312yes—
99C2×C4⋊(C3⋊D3)C2312yes—
100C2×C4×C3⋊D3C2318yescomplemented
101C22×C3×Dic3C2311yescharacteristic
102C2×C3×D12C2×C418yescomplemented
103C2×C3×D12C2312yes—
104C2×C3×D12C2312yes—
105C2×C3×C4×D3C2×C418yescomplemented
106C2×C3×C4×D3C2314yes—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2318yescomplemented
112C2×#626C2×C4116yescomplemented
113C2×#626C2314yes—
114C2×#626C2314yes—
115C2×#624C2318yescomplemented
116C2×D3×Dic3C2314yes—
117C2×D3×Dic3C2318yescomplemented
118D3×D12C2×C4116yescomplemented
119D3×D12C2×C4116yescomplemented
120D3×D12C2×C4116yescomplemented
121D3×D12C2×C4116yescomplemented
122C4×D32—416no—
123C32×C4⋊C4C2312yescomplemented
124C32×C22⋊C4C2312yes—
125C32×C42C2312yescomplemented
126#3757C2312yes—
127#3752C2318yescomplemented
128C4⋊(C3⋊Dic3)C2312yescomplemented
129C4×C3⋊Dic3C2312yescomplemented
130C3×#217C2312yes—
131C3×#217C2312yes—
132C3×(C2×D3)⋊C4C2314yes—
133C3×(C2×D3)⋊C4C2318yescomplemented
134C3×C4⋊Dic3C2312yescomplemented
135C3×C4⋊Dic3C2312yescomplemented
136C3×Dic3⋊C4C2314yescomplemented
137C3×C4×Dic3C2314yescomplemented
138C3×C4×Dic3C2312yescomplemented
139C3×C4×Dic3C2312yescomplemented
140Dic3⋊Dic3C2314yescomplemented
141#3722C2318yescomplemented
142(C2×D3)⋊Dic3C2314yes—
143(C2×D3)⋊Dic3C2318yescomplemented
144Dic32C2314yescomplemented
145C2×#518—91noSylow
146C24×D3—32no—
147C24×D3—32no—
148C22×C3×D4—31no—
149C23×C3×C4—31no—
150C22×#67—32no—
151C2×D3×D4—316no—
152C2×D3×D4—32no—
153C2×D3×D4—32no—
154C2×D3×D4—32no—
155C2×D3×D4—32no—
156C22×D12—32no—
157C22×D12—31no—
158C22×D12—31no—
159C22×D12—316no—
160C22×D12—32no—
161C22×D12—32no—
162C22×D12—32no—
163C22×D12—32no—
164C22×D12—61no—
165C22×D12C2×D311yescharacteristic
166C22×C4×D3—38no—
167C22×C4×D3—38no—
168C22×C4×D3C2×D311yescharacteristic
169C3×C4×D4—34no—
170C3×C4×D4—34no—
171C3×#117—21no—
172C3×#117—31no—
173C3×#117—31no—
174C3×#117—32no—
175C3×#117—32no—
176C3×#117—32no—
177C3×#117C2×D311yescharacteristic, complemented
178C3×#117C2×D311yescharacteristic, complemented
179C2×C3×C4⋊C4—32no—
180C2×C3×C22⋊C4—32no—
181C2×C3×C22⋊C4—34no—
182C2×C3×C42—32no—
183C2×#217—32no—
184C2×#217—34no—
185D4×Dic3—34no—
186D4×Dic3—34no—
187C4×#67—38no—
188C4×#67—38no—
189C2×(C2×D3)⋊C4—38no—
190C2×(C2×D3)⋊C4—38no—
191#926—31no—
192#926—31no—
193#926—32no—
194#926—32no—
195#926—32no—
196#926—61no—
197#926C2×D311yescharacteristic, complemented
198#926C2×D311yescharacteristic, complemented
199C2×C4⋊Dic3—32no—
200C2×C4×Dic3—32no—
201#893—34no—
202#893—38no—
203#893—34no—
204#893—34no—
205#893—38no—
206#893—34no—
207#893—34no—
208#893—64no—
209#893C2×D314yescomplemented
210#892—32no—
211#892C2×D312yescomplemented
212D3×C4⋊C4—32no—
213D3×C4⋊C4C2×D312yescomplemented
214#67⋊C4—38no—
215#67⋊C4—38no—
216D3×C22⋊C4—32no—
217D3×C22⋊C4—34no—
218D3×C22⋊C4—38no—
219D3×C22⋊C4—38no—
220D3×C22⋊C4—34no—
221D3×C22⋊C4—34no—
222D3×C22⋊C4—34no—
223D3×C22⋊C4—34no—
224D3×C22⋊C4—38no—
225D3×C22⋊C4—38no—
226D3×C22⋊C4—64no—
227D3×C22⋊C4C2×D312yes—
228D3×C22⋊C4C2×D314yescomplemented
229#877—32no—
230#877C2×D312yescomplemented
231C4×D12—34no—
232C4×D12—38no—
233C4×D12—34no—
234C4×D12—34no—
235C4×D12—38no—
236C4×D12—34no—
237C4×D12—34no—
238C4×D12—64no—
239C4×D12C2×D314yescomplemented
240#872—32no—
241#872C2×D312yescomplemented
242C42×D3—32no—
243C42×D3C2×D312yescomplemented
244C23×C32C2411yescharacteristic
245C22×C3⋊D3—44no—
246C22×C3⋊D3C22×C418yescomplemented
247C22×C3⋊D3C2414yes—
248C22×C3×D3—24no—
249C22×C3×D3—44no—
250C22×C3×D3C22×C414yes—
251C22×C3×D3C22×C418yescomplemented
252C22×C3×D3C2411yescharacteristic
253C22×C3×D3C2414yes—
254C22×C3×D3C2411yescharacteristic
255C2×D32—216no—
256C2×D32—432no—
257C2×D32—48no—
258C2×D32C22×C4116yes—
259C2×D32C22×C4116yescomplemented
260C2×C32×C4C22×C414yescomplemented
261C2×C32×C4C2414yes—
262C2×C32×C4C2411yescharacteristic
263C2×C32×C4C2411yescharacteristic
264C2×C3⋊Dic3C2414yes—
265C4⋊(C3⋊D3)C22×C418yescomplemented
266C4⋊(C3⋊D3)C22×C418yescomplemented
267C4×C3⋊D3—48no—
268C2×C3×Dic3C22×C414yescomplemented
269C2×C3×Dic3C2414yes—
270C2×C3×Dic3C2414yes—
271C2×C3×Dic3C2411yescharacteristic
272C2×C3×Dic3C2411yescharacteristic
273C3×D12C22×C418yescomplemented
274C3×D12C22×C418yescomplemented
275C3×C4×D3—28no—
276C3×C4×D3—48no—
277C3×C4×D3C22×C414yes—
278C3×C4×D3C22×C414yes—
279C3×C4×D3C22×C414yescomplemented
280C3×C4×D3C22×C414yescomplemented
281#626C22×C4116yescomplemented
282#626C22×C4116yescomplemented
283#624—48no—
284D3×Dic3—28no—
285D3×Dic3—48no—
286C23×D4—91no—
287#518—31no—
288#518—94no—
289#518—91no—
290#518—94no—
291#518—94no—
292#518—91no—
293#518—91no—
294C2×C4×D4—94no—
295C2×C4×D4—94no—
296C2×#117—31no—
297C2×#117—91no—
298C22×C22⋊C4—94no—
299C24×C3—31no—
300C24×C3—32no—
301C23×D3—32no—
302C23×D3—32no—
303C23×D3—34no—
304C23×D3—34no—
305C23×D3—316no—
306C23×D3—316no—
307C23×D3—34no—
308C23×D3—34no—
309C23×D3—62no—
310C23×D3—128no—
311C23×D3—128no—
312C23×D3C22×D311yescharacteristic
313C23×D3C22×D312yes—
314C2×C3×D4—38no—
315C2×C3×D4—32no—
316C2×C3×D4—32no—
317C22×C3×C4—21no—
318C22×C3×C4—31no—
319C22×C3×C4—38no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—34no—
325C22×C3×C4—38no—
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C2×#67—316no—
329C2×#67—34no—
330C2×#67—34no—
331C22×Dic3—34no—
332C22×Dic3—38no—
333C22×Dic3C22×D311yescharacteristic
334D3×D4—316no—
335D3×D4—316no—
336D3×D4—316no—
337D3×D4—316no—
338C2×D12—316no—
339C2×D12—34no—
340C2×D12—34no—
341C2×D12—38no—
342C2×D12—38no—
343C2×D12—32no—
344C2×D12—32no—
345C2×D12—32no—
346C2×D12—32no—
347C2×D12—316no—
348C2×D12—316no—
349C2×D12—316no—
350C2×D12—316no—
351C2×D12—62no—
352C2×D12—62no—
353C2×D12—68no—
354C2×D12C4×D318yescomplemented
355C2×D12C22×D312yes—
356C2×D12C22×D312yes—
357C2×C4×D3—34no—
358C2×C4×D3—38no—
359C2×C4×D3—38no—
360C2×C4×D3—38no—
361C2×C4×D3—38no—
362C2×C4×D3—38no—
363C2×C4×D3—68no—
364C2×C4×D3—1216no—
365C2×C4×D3—1216no—
366C2×C4×D3C4×D318yescomplemented
367C2×C4×D3C22×D314yes—
368C2×C4×D3C22×D311yescharacteristic
369C2×C4×D3C22×D311yescharacteristic
370C2×C4×D3C22×D311yescharacteristic
371C2×C4×D3C22×D311yescharacteristic
372C2×C4×D3C22×D318yescomplemented
373C3×C4⋊C4—22no—
374C3×C4⋊C4—32no—
375C3×C4⋊C4—34no—
376C3×C4⋊C4—32no—
377C3×C4⋊C4C22×D312yescomplemented
378C3×C4⋊C4C22×D312yescomplemented
379C3×C22⋊C4—22no—
380C3×C22⋊C4—32no—
381C3×C22⋊C4—32no—
382C3×C22⋊C4—34no—
383C3×C22⋊C4—38no—
384C3×C22⋊C4C22×D312yes—
385C3×C22⋊C4C22×D312yes—
386C3×C42—22no—
387C3×C42—32no—
388C3×C42—34no—
389C3×C42—32no—
390C3×C42C22×D312yescomplemented
391C3×C42C22×D312yescomplemented
392#217—32no—
393#217—32no—
394#217—34no—
395#217—38no—
396#217—62no—
397#217C22×D312yes—
398#217C22×D312yes—
399(C2×D3)⋊C4—34no—
400(C2×D3)⋊C4—38no—
401(C2×D3)⋊C4—38no—
402(C2×D3)⋊C4—38no—
403(C2×D3)⋊C4—38no—
404(C2×D3)⋊C4—38no—
405(C2×D3)⋊C4—68no—
406(C2×D3)⋊C4C22×D314yes—
407(C2×D3)⋊C4C22×D318yescomplemented
408C4⋊Dic3—32no—
409C4⋊Dic3—32no—
410C4⋊Dic3—34no—
411C4⋊Dic3—62no—
412C4⋊Dic3C22×D312yescomplemented
413C4⋊Dic3C22×D312yescomplemented
414Dic3⋊C4—34no—
415Dic3⋊C4C22×D314yescomplemented
416C4×Dic3—32no—
417C4×Dic3—32no—
418C4×Dic3—34no—
419C4×Dic3—34no—
420C4×Dic3—62no—
421C4×Dic3C22×D312yescomplemented
422C4×Dic3C22×D314yescomplemented
423C4×Dic3C22×D312yescomplemented
424C22×C32—22no—
425C22×C32C23×C412yes—
426C22×C32C2511yescharacteristic
427C2×C3⋊D3—28no—
428C2×C3⋊D3—48no—
429C2×C3⋊D3C23×C418yes—
430C2×C3×D3—28no—
431C2×C3×D3—22no—
432C2×C3×D3—28no—
433C2×C3×D3—48no—
434C2×C3×D3C23×C418yes—
435C2×C3×D3C23×C412yes—
436C2×C3×D3C23×C412yes—
437C2×C3×D3H(5,𝔽2)14yes—
438D32—232no—
439D32—416no—
440C32×C4—24no—
441C32×C4C23×C412yes—
442C32×C4C23×C412yes—
443C3⋊Dic3—24no—
444C3×Dic3—24no—
445C3×Dic3—24no—
446C3×Dic3C23×C412yes—
447C3×Dic3C23×C412yes—
448C25—92no—
449C22×D4—31no—
450C22×D4—92no—
451C22×D4—92no—
452C22×D4—92no—
453C22×D4—92no—
454C22×D4—916no—
455C22×D4—92no—
456C22×D4—91no—
457C23×C4—31no—
458C23×C4—98no—
459C4×D4—34no—
460C4×D4—34no—
461C4×D4—98no—
462C4×D4—94no—
463C4×D4—94no—
464C4×D4—98no—
465C4×D4—94no—
466C4×D4—98no—
467C4×D4—98no—
468C4×D4—94no—
469C4×D4—94no—
470C4×D4—94no—
471#117—31no—
472#117—31no—
473#117—32no—
474#117—32no—
475#117—32no—
476#117—92no—
477#117—92no—
478#117—92no—
479#117—91no—
480#117D3211yescharacteristic, complemented
481C2×C4⋊C4—32no—
482C2×C4⋊C4—92no—
483C2×C22⋊C4—32no—
484C2×C22⋊C4—34no—
485C2×C22⋊C4—94no—
486C2×C22⋊C4—98no—
487C2×C22⋊C4—98no—
488C2×C22⋊C4—98no—
489C2×C22⋊C4—92no—
490C2×C22⋊C4—94no—
491C2×C22⋊C4—94no—
492C2×C42—32no—
493C2×C42—92no—
494C23×C3—21no—
495C23×C3—31no—
496C23×C3—34no—
497C23×C3—31no—
498C23×C3—34no—
499C23×C3—38no—
500C23×C3—64no—
501C23×C3—124no—
502C23×C3C23×D311yescharacteristic
503C23×C3C23×D311yescharacteristic
504C22×D3—24no—
505C22×D3—34no—
506C22×D3—34no—
507C22×D3—38no—
508C22×D3—38no—
509C22×D3—316no—
510C22×D3—316no—
511C22×D3—316no—
512C22×D3—316no—
513C22×D3—44no—
514C22×D3—64no—
515C22×D3—68no—
516C22×D3—616no—
517C22×D3—616no—
518C22×D3—1232no—
519C22×D3—128no—
520C22×D3—128no—
521C22×D3—1232no—
522C22×D3—124no—
523C22×D3—124no—
524C22×D3—244no—
525C22×D3C2×C4×D314yes—
526C22×D3C2×C4×D318yescomplemented
527C22×D3C23×D311yescharacteristic
528C22×D3C23×D314yes—
529C22×D3C23×D311yescharacteristic
530C3×D4—38no—
531C3×D4—38no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—24no—
535C2×C3×C4—24no—
536C2×C3×C4—34no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—34no—
540C2×C3×C4—34no—
541C2×C3×C4—34no—
542C2×C3×C4—34no—
543C2×C3×C4—34no—
544C2×C3×C4—34no—
545C2×C3×C4—68no—
546C2×C3×C4—128no—
547C2×C3×C4C2×C4×D314yescomplemented
548C2×C3×C4C2×C4×D314yescomplemented
549C2×C3×C4C23×D314yes—
550C2×C3×C4C23×D314yes—
551C2×C3×C4C23×D311yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555#67—316no—
556#67—316no—
557C2×Dic3—34no—
558C2×Dic3—34no—
559C2×Dic3—64no—
560C2×Dic3—68no—
561C2×Dic3—128no—
562C2×Dic3C2×C4×D314yescomplemented
563C2×Dic3C23×D314yes—
564C2×Dic3C23×D314yes—
565C2×Dic3C23×D311yescharacteristic
566C2×Dic3C23×D311yescharacteristic
567D12—316no—
568D12—316no—
569D12—38no—
570D12—38no—
571D12—38no—
572D12—38no—
573D12—68no—
574D12—68no—
575D12C2×C4×D318yescomplemented
576D12C2×C4×D318yescomplemented
577C4×D3—28no—
578C4×D3—48no—
579C4×D3—68no—
580C4×D3—128no—
581C4×D3—128no—
582C4×D3—128no—
583C4×D3—128no—
584C4×D3—128no—
585C4×D3—248no—
586C4×D3C2×C4×D314yes—
587C4×D3C2×C4×D314yes—
588C4×D3C2×C4×D314yescomplemented
589C4×D3C2×C4×D314yescomplemented
590C2×C32—22no—
591C2×C32C24×C411yescharacteristic
592C2×C32C2×H(5,𝔽2)12yes—
593C3⋊D3—28no—
594C3×D3—28no—
595C3×D3—22no—
596C3×D3#51814yescomplemented
597C24—31no—
598C24—32no—
599C24—94no—
600C24—94no—
601C24—916no—
602C24—92no—
603C24—368no—
604C2×D4—32no—
605C2×D4—32no—
606C2×D4—38no—
607C2×D4—916no—
608C2×D4—916no—
609C2×D4—916no—
610C2×D4—916no—
611C2×D4—94no—
612C2×D4—94no—
613C2×D4—916no—
614C2×D4—92no—
615C2×D4—92no—
616C2×D4—98no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—31no—
622C22×C4—38no—
623C22×C4—34no—
624C22×C4—38no—
625C22×C4—98no—
626C22×C4—94no—
627C22×C4—98no—
628C22×C4—98no—
629C22×C4—3616no—
630C22×C4C2×D3211yescharacteristic
631C4⋊C4—34no—
632C4⋊C4—32no—
633C4⋊C4—32no—
634C4⋊C4—94no—
635C4⋊C4—92no—
636C4⋊C4C2×D3212yescomplemented
637C22⋊C4—32no—
638C22⋊C4—32no—
639C22⋊C4—34no—
640C22⋊C4—38no—
641C22⋊C4—98no—
642C22⋊C4—94no—
643C22⋊C4—98no—
644C22⋊C4—92no—
645C22⋊C4—98no—
646C22⋊C4C2×D3212yes—
647C42—34no—
648C42—32no—
649C42—32no—
650C42—94no—
651C42—92no—
652C42C2×D3212yescomplemented
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—21no—
657C22×C3—32no—
658C22×C3—34no—
659C22×C3—38no—
660C22×C3—32no—
661C22×C3—42no—
662C22×C3—68no—
663C22×C3—68no—
664C22×C3—62no—
665C22×C3—128no—
666C22×C3C22×C4×D312yes—
667C22×C3C22×C4×D312yes—
668C22×C3C24×D311yescharacteristic
669C22×C3C24×D311yescharacteristic
670C2×D3—22no—
671C2×D3—28no—
672C2×D3—28no—
673C2×D3—38no—
674C2×D3—38no—
675C2×D3—48no—
676C2×D3—68no—
677C2×D3—632no—
678C2×D3—68no—
679C2×D3—68no—
680C2×D3—632no—
681C2×D3—128no—
682C2×D3—1216no—
683C2×D3—1216no—
684C2×D3—128no—
685C2×D3—128no—
686C2×D3—248no—
687C2×D3C22×C4×D312yes—
688C2×D3C22×C4×D318yes—
689C2×D3C22×C4×D312yes—
690C2×D3#100914yes—
691C3×C4—24no—
692C3×C4—24no—
693C3×C4—22no—
694C3×C4—22no—
695C3×C4—32no—
696C3×C4—32no—
697C3×C4—44no—
698C3×C4—64no—
699C3×C4—64no—
700C3×C4C22×C4×D312yes—
701C3×C4C22×C4×D312yes—
702C3×C4C22×C4×D312yes—
703C3×C4C22×C4×D312yes—
704Dic3—24no—
705Dic3—24no—
706Dic3—64no—
707Dic3—64no—
708Dic3—124no—
709Dic3C22×C4×D312yes—
710Dic3C22×C4×D312yes—
711C32C2×#51811yescharacteristic, complemented, Sylow
712C23—31no—
713C23—34no—
714C23—31no—
715C23—34no—
716C23—38no—
717C23—64no—
718C23—916no—
719C23—916no—
720C23—94no—
721C23—98no—
722C23—124no—
723C23—1816no—
724C23—364no—
725C23—368no—
726C23—3632no—
727C23C22×D3211yescharacteristic
728D4—38no—
729D4—38no—
730D4—916no—
731D4—916no—
732D4—98no—
733D4—98no—
734C2×C4—34no—
735C2×C4—31no—
736C2×C4—31no—
737C2×C4—34no—
738C2×C4—34no—
739C2×C4—34no—
740C2×C4—34no—
741C2×C4—34no—
742C2×C4—34no—
743C2×C4—68no—
744C2×C4—94no—
745C2×C4—128no—
746C2×C4—188no—
747C2×C4—368no—
748C2×C4—368no—
749C2×C4—368no—
750C2×C4C4×D3214yescomplemented
751C2×C4C22×D3214yes—
752C2×C4C22×D3211yescharacteristic
753C2×C4C22×D3211yescharacteristic
754C2×C3—22no—
755C2×C3—22no—
756C2×C3—21no—
757C2×C3—22no—
758C2×C3—34no—
759C2×C3—42no—
760C2×C3—62no—
761C2×C3—68no—
762C2×C3C23×C4×D311yescharacteristic
763C2×C3C23×C4×D311yescharacteristic
764C2×C3C2×#100912yes—
765C2×C3D3×H(5,𝔽2)12yes—
766D3—28no—
767D3—22no—
768D3—68no—
769D3—68no—
770D3—128no—
771D3#552114yesdirect product factor
772C22—22no—
773C22—32no—
774C22—34no—
775C22—32no—
776C22—38no—
777C22—68no—
778C22—68no—
779C22—62no—
780C22—98no—
781C22—128no—
782C22—1832no—
783C22—188no—
784C22—368no—
785C22—3616no—
786C22C2×C4×D3212yes—
787C22C23×D3211yescharacteristic
788C4—24no—
789C4—32no—
790C4—32no—
791C4—64no—
792C4—64no—
793C4—184no—
794C4C2×C4×D3212yes—
795C4C2×C4×D3212yes—
796C3—21no—
797C3C2×#552111yescharacteristic, complemented
798C3D3×#51811yescharacteristic, complemented
799C2—22no—
800C2—34no—
801C2—62no—
802C2—68no—
803C2—188no—
804C2C22×C4×D3211yescharacteristic
805C2D3×#100912yes—
subgroupG/H
center, FrattiniC22C23×D32
commutatorC2×C32C24×C4
FittingC32×#117C22
socle, cosocleC22×C32C25
prime radicalC22×D3×D12C2
hypercenter#117D32
hypocenterC32C2×#518
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10595992C2semidirect
3. C3×#5521C2semidirect
4. C3×D3×#117C2semidirect
5. #10594996C2semidirect
6. #10594982C2semidirect
7. D3×#926C2semidirect
8. #10594604C2semidirect
9. D3×#893C2semidirect
10. D32×C22⋊C4C2semidirect
11. #10594182C2semidirect
12. #10593994C2semidirect
13. C4×D3×D12C2semidirect
21. C2×D3×D12C4semidirect
26. C2×C4×D32C22semidirect
27. C32×#117C22semidirect
28. #64135C22semidirect
29. #64102C22semidirect
30. C22⋊C4×C3⋊D3C22semidirect
31. C4×C4⋊(C3⋊D3)C22semidirect
32. C3×#926C22semidirect
33. C3×#926C22semidirect
34. C3×#893C22semidirect
35. C3×#892C22semidirect
36. C3×D3×C4⋊C4C22semidirect
38. C3×D3×C22⋊C4C22semidirect
39. C3×#877C22semidirect
40. C3×C4×D12C22semidirect
41. C3×#872C22semidirect
42. C3×C42×D3C22semidirect
43. #63974C22semidirect
45. D3×#217C22semidirect
46. #63955C22semidirect
47. #63921C22semidirect
48. D3×(C2×D3)⋊C4C22semidirect
49. D3×(C2×D3)⋊C4C22semidirect
50. #63904C22semidirect
51. C4×#626C22semidirect
52. #63898C22semidirect
53. #63894C22semidirect
54. #63894C22semidirect
55. Dic3×D12C22semidirect
56. D3×C4⋊Dic3C22semidirect
57. #63881C22semidirect
58. #63880C22semidirect
59. C4×D3×Dic3C22semidirect
60. #63855C22semidirect
61. #63841C22semidirect
81. #5521D3direct (N × H)
83. D3×#117D3semidirect
93. C22×D32C2×C4semidirect
97. C2×C4⋊(C3⋊D3)C2×C4semidirect
100. C2×C4×C3⋊D3C23semidirect
102. C2×C3×D12C2×C4semidirect
105. C2×C3×C4×D3C2×C4semidirect
111. C2×C3×C4×D3C23semidirect
112. C2×#626C2×C4semidirect
115. C2×#624C23semidirect
117. C2×D3×Dic3C23semidirect
118. D3×D12C2×C4semidirect
119. D3×D12C2×C4semidirect
120. D3×D12C2×C4semidirect
121. D3×D12C2×C4semidirect
123. C32×C4⋊C4C23semidirect
125. C32×C42C23semidirect
127. #3752C23semidirect
128. C4⋊(C3⋊Dic3)C23semidirect
129. C4×C3⋊Dic3C23semidirect
133. C3×(C2×D3)⋊C4C23semidirect
134. C3×C4⋊Dic3C23semidirect
135. C3×C4⋊Dic3C23semidirect
136. C3×Dic3⋊C4C23semidirect
137. C3×C4×Dic3C23semidirect
138. C3×C4×Dic3C23semidirect
139. C3×C4×Dic3C23semidirect
140. Dic3⋊Dic3C23semidirect
141. #3722C23semidirect
143. (C2×D3)⋊Dic3C23semidirect
144. Dic32C23semidirect
177. C3×#117C2×D3semidirect
178. C3×#117C2×D3semidirect
197. #926C2×D3semidirect
198. #926C2×D3semidirect
209. #893C2×D3semidirect
211. #892C2×D3semidirect
213. D3×C4⋊C4C2×D3semidirect
228. D3×C22⋊C4C2×D3semidirect
230. #877C2×D3semidirect
239. C4×D12C2×D3semidirect
241. #872C2×D3semidirect
243. C42×D3C2×D3semidirect
246. C22×C3⋊D3C22×C4semidirect
251. C22×C3×D3C22×C4semidirect
259. C2×D32C22×C4semidirect
260. C2×C32×C4C22×C4semidirect
265. C4⋊(C3⋊D3)C22×C4semidirect
266. C4⋊(C3⋊D3)C22×C4semidirect
268. C2×C3×Dic3C22×C4semidirect
273. C3×D12C22×C4semidirect
274. C3×D12C22×C4semidirect
279. C3×C4×D3C22×C4semidirect
280. C3×C4×D3C22×C4semidirect
281. #626C22×C4semidirect
282. #626C22×C4semidirect
354. C2×D12C4×D3semidirect
366. C2×C4×D3C4×D3semidirect
372. C2×C4×D3C22×D3semidirect
377. C3×C4⋊C4C22×D3semidirect
378. C3×C4⋊C4C22×D3semidirect
390. C3×C42C22×D3semidirect
391. C3×C42C22×D3semidirect
407. (C2×D3)⋊C4C22×D3semidirect
412. C4⋊Dic3C22×D3semidirect
413. C4⋊Dic3C22×D3semidirect
415. Dic3⋊C4C22×D3semidirect
421. C4×Dic3C22×D3semidirect
422. C4×Dic3C22×D3semidirect
423. C4×Dic3C22×D3semidirect
480. #117D32semidirect
526. C22×D3C2×C4×D3semidirect
547. C2×C3×C4C2×C4×D3semidirect
548. C2×C3×C4C2×C4×D3semidirect
562. C2×Dic3C2×C4×D3semidirect
575. D12C2×C4×D3semidirect
576. D12C2×C4×D3semidirect
588. C4×D3C2×C4×D3semidirect
589. C4×D3C2×C4×D3semidirect
596. C3×D3#518semidirect
636. C4⋊C4C2×D32semidirect
652. C42C2×D32semidirect
711. C32C2×#518semidirect
750. C2×C4C4×D32semidirect
771. D3#5521direct (N × H)
797. C3C2×#5521semidirect
798. C3D3×#518semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D122
#105959922
C3×#55212
C3×D3×#1172
#105949962
#105949822
D3×#9262
#105946042
D3×#8932
D32×C22⋊C42
#105941822
#105939942
C4×D3×D122
D3×#5183
C2×#55213