Finite Group Databasebeta

← C2×D32×D12 #13181256

Subgroups — C2×D32×D12 #13181256

Order 1728.

6210 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D33C212yesmaximal, complemented
2C2×C4⋊#1113C211yesmaximal, characteristic, complemented
3C2×C3⋊D3×D12C211yesmaximal, characteristic, complemented
4C2×D3×C4⋊(C3⋊D3)C212yesmaximal, complemented
5C2×C3×D3×D12C212yesmaximal, complemented
6C2×C3×C4×D32C211yesmaximal, characteristic, complemented
7C2×#88955C212yesmaximal, complemented
8C2×D3×#626C214yesmaximal, complemented
9D32×D12C2116yesmaximal, direct product factor
10C2×D32×D4—31nomaximal
11C22×D3×D12—32nomaximal
12C22×#1113C2212yescomplemented
13C22×D3×C3⋊D3C2214yescomplemented
14C22×D3×C3⋊D3C2212yescomplemented
15C22×C3×D32C2211yescharacteristic
16C22×C3×D32C2214yescomplemented
17C2×D33—216no—
18C2×D33C22116yescomplemented
19C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
20C2×C3×C4⋊(C3⋊D3)C2212yescomplemented
21C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
22C2×C32×D12C2211yescharacteristic, complemented
23C2×C32×C4×D3C2212yescomplemented
24C2×#6295C2212yescomplemented
25C4⋊#1113C2218yescomplemented
26C2×#6292C2214yescomplemented
27C2×#6291C2212yescomplemented
28C3⋊D3×D12C2218yescomplemented
29D3×C4⋊(C3⋊D3)C22116yescomplemented
30C2×C3×#626C2214yescomplemented
31C2×C3×#624C2211yescharacteristic, complemented
32C2×C3×D3×Dic3C2212yescomplemented
33C3×D3×D12C22116yescomplemented
34C3×C4×D32C2218yescomplemented
35#88955C22116yescomplemented
36D3×#626C22132yescomplemented
37C23×D32—32no—
38C23×D32—34no—
39C2×D4×C3⋊D3—31no—
40C22×C4⋊(C3⋊D3)—32no—
41C2×C3×D3×D4—32no—
42C22×C3×D12—32no—
43C22×C3×C4×D3—32no—
44C2×#3811—32no—
45C2×D3×#67—34no—
46C22×#626—34no—
47D32×D4—316no—
48C2×#3802—31no—
49C2×D3×D12—32no—
50C2×D3×D12—32no—
51C2×D3×D12—32no—
52C2×D3×D12—32no—
53C2×D3×D12—34no—
54C2×D3×D12—332no—
55C2×D3×D12—34no—
56C2×D3×D12—61no—
57C2×D3×D12—62no—
58C2×D3×D12D312yesdirect product factor
59C2×C4×D32D311yescharacteristic, complemented
60C22×C3⋊(C3⋊D3)C2312yescomplemented
61C22×C3×C3⋊D3C2311yescharacteristic
62C22×C3×C3⋊D3C2314yescomplemented
63C22×C32×D3C2312yes—
64C22×C32×D3C2312yescomplemented
65C2×#1113—28no—
66C2×#1113C2318yescomplemented
67C2×D3×C3⋊D3—28no—
68C2×D3×C3⋊D3—216no—
69C2×D3×C3⋊D3C23116yescomplemented
70C2×D3×C3⋊D3C2318yescomplemented
71C2×C3×D32—216no—
72C2×C3×D32D418yescomplemented
73C2×C3×D32C2314yes—
74C2×C3×D32C23116yescomplemented
75D33—264no—
76C2×C33×C4C2311yescharacteristic, complemented
77C4⋊(C3⋊(C3⋊D3))C2314yescomplemented
78C2×C3×C3⋊Dic3C2311yescharacteristic, complemented
79C3×C4⋊(C3⋊D3)C2318yescomplemented
80C3×C4×C3⋊D3C2314yescomplemented
81C2×C32×Dic3C2312yescomplemented
82C32×D12C2314yescomplemented
83C32×C4×D3C2318yescomplemented
84#6295C2318yescomplemented
85#6292C23116yescomplemented
86#6291C2318yescomplemented
87C3×#626C23116yescomplemented
88C3×#624C2314yescomplemented
89C3×D3×Dic3C2318yescomplemented
90C22×D3×D4—92no—
91C23×D12—91no—
92C23×C3⋊D3—32no—
93C23×C3⋊D3—34no—
94C23×C3×D3—32no—
95C23×C3×D3—34no—
96C23×C3×D3—34no—
97C22×D32—32no—
98C22×D32—34no—
99C22×D32—34no—
100C22×D32—34no—
101C22×D32—34no—
102C22×D32—316no—
103C22×D32—332no—
104C22×D32—632no—
105C22×D32—616no—
106C22×D32—64no—
107C22×D32—62no—
108C22×D32C2×D311yescharacteristic
109C22×D32C2×D314yescomplemented
110C2×C32×D4—31no—
111C22×C32×C4—32no—
112C2×#638—32no—
113D4×C3⋊D3—38no—
114C2×C4⋊(C3⋊D3)—34no—
115C2×C4⋊(C3⋊D3)—32no—
116C2×C4⋊(C3⋊D3)—31no—
117C2×C4⋊(C3⋊D3)—316no—
118C2×C4⋊(C3⋊D3)—62no—
119C2×C4⋊(C3⋊D3)—61no—
120C2×C4⋊(C3⋊D3)—121no—
121C2×C4⋊(C3⋊D3)C2×D312yescomplemented
122C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
123C2×C3×#67—34no—
124C22×C3×Dic3—32no—
125C3×D3×D4—316no—
126C2×C3×D12—21no—
127C2×C3×D12—34no—
128C2×C3×D12—32no—
129C2×C3×D12—32no—
130C2×C3×D12—316no—
131C2×C3×D12—62no—
132C2×C3×D12C2×D312yescomplemented
133C2×C3×C4×D3—22no—
134C2×C3×C4×D3—32no—
135C2×C3×C4×D3—32no—
136C2×C3×C4×D3—32no—
137C2×C3×C4×D3—316no—
138C2×C3×C4×D3—61no—
139C2×C3×C4×D3C2×D312yescomplemented
140C2×C3×C4×D3C2×D312yescomplemented
141#3811—316no—
142D3×#67—332no—
143C2×#626—34no—
144C2×#626—34no—
145C2×#626—34no—
146C2×#626—34no—
147C2×#626—332no—
148C2×#626—64no—
149C2×#626—62no—
150C2×#626C2×D314yescomplemented
151C2×#625—32no—
152C2×#624C2×D311yescharacteristic, complemented
153C2×D3×Dic3C2×D312yescomplemented
154#3802—38no—
155D3×D12—332no—
156D3×D12—316no—
157D3×D12—316no—
158D3×D12—316no—
159D3×D12—316no—
160D3×D12—332no—
161D3×D12—616no—
162D3×D12—68no—
163D3×D12C2×D3116yesdirect product factor
164C4×D32C2×D318yescomplemented
165C22×C33C2411yescharacteristic
166C2×C3⋊(C3⋊D3)—24no—
167C2×C3⋊(C3⋊D3)C2414yescomplemented
168C2×C3×C3⋊D3—28no—
169C2×C3×C3⋊D3C2×D414yescomplemented
170C2×C3×C3⋊D3C2412yes—
171C2×C3×C3⋊D3C2418yescomplemented
172C2×C32×D3—24no—
173C2×C32×D3C2×D418yescomplemented
174C2×C32×D3C2414yes—
175C2×C32×D3C2414yescomplemented
176#1113—216no—
177D3×C3⋊D3—216no—
178D3×C3⋊D3—232no—
179C3×D32—232no—
180C3×D32C2×D4116yescomplemented
181C33×C4C2412yescomplemented
182C3×C3⋊Dic3C2412yescomplemented
183C32×Dic3C2414yescomplemented
184C24×D3—92no—
185C24×D3—94no—
186C22×C3×D4—92no—
187C23×C3×C4—91no—
188C22×#67—94no—
189C2×D3×D4—32no—
190C2×D3×D4—92no—
191C2×D3×D4—932no—
192C2×D3×D4—94no—
193C2×D3×D4—92no—
194C2×D3×D4—94no—
195C2×D3×D4—92no—
196C2×D3×D4—181no—
197C22×D12—32no—
198C22×D12—92no—
199C22×D12—91no—
200C22×D12—916no—
201C22×D12—92no—
202C22×D12—92no—
203C22×D12—94no—
204C22×D12—91no—
205C22×D12—182no—
206C22×C4×D3—32no—
207C23×C32—32no—
208C23×C32—32no—
209C22×C3⋊D3—34no—
210C22×C3⋊D3—32no—
211C22×C3⋊D3—38no—
212C22×C3⋊D3—316no—
213C22×C3⋊D3—62no—
214C22×C3⋊D3—64no—
215C22×C3⋊D3—616no—
216C22×C3⋊D3—68no—
217C22×C3⋊D3—122no—
218C22×C3⋊D3C22×D311yescharacteristic
219C22×C3⋊D3C22×D314yescomplemented
220C22×C3×D3—22no—
221C22×C3×D3—22no—
222C22×C3×D3—32no—
223C22×C3×D3—316no—
224C22×C3×D3—38no—
225C22×C3×D3—34no—
226C22×C3×D3—34no—
227C22×C3×D3—316no—
228C22×C3×D3—316no—
229C22×C3×D3—61no—
230C22×C3×D3—64no—
231C22×C3×D3—616no—
232C22×C3×D3—616no—
233C22×C3×D3C22×D312yes—
234C22×C3×D3C22×D312yes—
235C22×C3×D3C22×D314yescomplemented
236C2×D32—216no—
237C2×D32—38no—
238C2×D32—316no—
239C2×D32—316no—
240C2×D32—316no—
241C2×D32—316no—
242C2×D32—616no—
243C2×D32—68no—
244C2×D32—6128no—
245C2×D32—616no—
246C2×D32—616no—
247C2×D32—68no—
248C2×D32—616no—
249C2×D32—616no—
250C2×D32—664no—
251C2×D32—1216no—
252C2×D32—128no—
253C2×D32D1218yesdirect product factor
254C2×D32C22×D314yes—
255C2×D32C22×D3116yescomplemented
256C32×D4—34no—
257C2×C32×C4—22no—
258C2×C32×C4—21no—
259C2×C32×C4—32no—
260C2×C32×C4—38no—
261C2×C32×C4—41no—
262C2×C32×C4C22×D312yescomplemented
263C2×C32×C4C22×D311yescharacteristic, complemented
264#638—38no—
265C2×C3⋊Dic3C22×D311yescharacteristic, complemented
266C4⋊(C3⋊D3)—316no—
267C4⋊(C3⋊D3)—38no—
268C4⋊(C3⋊D3)—34no—
269C4⋊(C3⋊D3)—64no—
270C4⋊(C3⋊D3)—68no—
271C4⋊(C3⋊D3)—124no—
272C4⋊(C3⋊D3)C22×D318yescomplemented
273C4×C3⋊D3C22×D314yescomplemented
274C3×#67—316no—
275C2×C3×Dic3—22no—
276C2×C3×Dic3—32no—
277C2×C3×Dic3—38no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3C22×D312yescomplemented
280C2×C3×Dic3C22×D312yescomplemented
281C3×D12—24no—
282C3×D12—316no—
283C3×D12—38no—
284C3×D12—38no—
285C3×D12—68no—
286C3×D12C22×D318yescomplemented
287C3×C4×D3—28no—
288C3×C4×D3—38no—
289C3×C4×D3—38no—
290C3×C4×D3—38no—
291C3×C4×D3—64no—
292C3×C4×D3C22×D318yescomplemented
293C3×C4×D3C22×D318yescomplemented
294#626—316no—
295#626—316no—
296#626—316no—
297#626—316no—
298#626—68no—
299#626—616no—
300#626C22×D3116yescomplemented
301#625—38no—
302#624C22×D314yescomplemented
303D3×Dic3C22×D318yescomplemented
304C23×D4—271noSylow
305C2×C33C22×D412yescomplemented
306C2×C33C2511yescharacteristic
307C3⋊(C3⋊D3)—24no—
308C3×C3⋊D3—28no—
309C3×C3⋊D3C22×D414yescomplemented
310C32×D3—24no—
311C32×D3C22×D418yescomplemented
312C24×C3—91no—
313C24×C3—94no—
314C23×D3—32no—
315C23×D3—34no—
316C23×D3—34no—
317C23×D3—92no—
318C23×D3—916no—
319C23×D3—94no—
320C23×D3—932no—
321C23×D3—94no—
322C23×D3—94no—
323C23×D3—94no—
324C23×D3—94no—
325C23×D3—92no—
326C23×D3—184no—
327C23×D3—182no—
328C23×D3—1832no—
329C23×D3—1816no—
330C2×C3×D4—32no—
331C2×C3×D4—61no—
332C2×C3×D4—916no—
333C2×C3×D4—94no—
334C2×C3×D4—92no—
335C22×C3×C4—32no—
336C22×C3×C4—32no—
337C22×C3×C4—62no—
338C22×C3×C4—91no—
339C22×C3×C4—98no—
340C22×C3×C4—92no—
341C22×C3×C4—91no—
342C2×#67—34no—
343C2×#67—932no—
344C2×#67—94no—
345C2×#67—94no—
346C2×#67—94no—
347C2×#67—182no—
348C22×Dic3—32no—
349D3×D4—316no—
350D3×D4—916no—
351D3×D4—932no—
352D3×D4—916no—
353D3×D4—932no—
354D3×D4—916no—
355D3×D4—188no—
356C2×D12—34no—
357C2×D12—32no—
358C2×D12—32no—
359C2×D12—316no—
360C2×D12—62no—
361C2×D12—916no—
362C2×D12—98no—
363C2×D12—916no—
364C2×D12—916no—
365C2×D12—932no—
366C2×D12—94no—
367C2×D12—94no—
368C2×D12—92no—
369C2×D12—92no—
370C2×D12—91no—
371C2×D12—92no—
372C2×D12—98no—
373C2×D12—1816no—
374C2×D12—182no—
375C2×D12—181no—
376C2×D12—184no—
377C2×D12—361no—
378C2×D12D3211yescharacteristic, direct product factor
379C2×C4×D3—32no—
380C2×C4×D3—32no—
381C2×C4×D3—32no—
382C2×C4×D3—316no—
383C2×C4×D3—61no—
384C2×C4×D3D3212yescomplemented
385C22×C32—22no—
386C22×C32—21no—
387C22×C32—38no—
388C22×C32—34no—
389C22×C32—34no—
390C22×C32—41no—
391C22×C32—64no—
392C22×C32C23×D311yescharacteristic
393C22×C32C23×D312yes—
394C2×C3⋊D3—28no—
395C2×C3⋊D3—38no—
396C2×C3⋊D3—34no—
397C2×C3⋊D3—64no—
398C2×C3⋊D3—68no—
399C2×C3⋊D3—632no—
400C2×C3⋊D3—64no—
401C2×C3⋊D3—68no—
402C2×C3⋊D3—616no—
403C2×C3⋊D3—124no—
404C2×C3⋊D3—128no—
405C2×C3⋊D3—124no—
406C2×C3⋊D3—244no—
407C2×C3⋊D3C2×D1214yescomplemented
408C2×C3⋊D3C23×D312yes—
409C2×C3⋊D3C23×D318yescomplemented
410C2×C3×D3—28no—
411C2×C3×D3—24no—
412C2×C3×D3—24no—
413C2×C3×D3—28no—
414C2×C3×D3—38no—
415C2×C3×D3—34no—
416C2×C3×D3—332no—
417C2×C3×D3—38no—
418C2×C3×D3—38no—
419C2×C3×D3—44no—
420C2×C3×D3—64no—
421C2×C3×D3—62no—
422C2×C3×D3—68no—
423C2×C3×D3—632no—
424C2×C3×D3—68no—
425C2×C3×D3—68no—
426C2×C3×D3—632no—
427C2×C3×D3—128no—
428C2×C3×D3C2×D1218yescomplemented
429C2×C3×D3D3×D418yescomplemented
430C2×C3×D3C23×D314yes—
431C2×C3×D3C23×D314yes—
432C2×C3×D3C23×D318yescomplemented
433D32—232no—
434D32—632no—
435D32—632no—
436D32—616no—
437D32—632no—
438D32—632no—
439D32—1232no—
440D32—1216no—
441D32C2×D12116yesdirect product factor
442C32×C4—24no—
443C32×C4—22no—
444C32×C4—34no—
445C32×C4—42no—
446C32×C4C23×D314yescomplemented
447C32×C4C23×D312yescomplemented
448C3⋊Dic3C23×D312yescomplemented
449C3×Dic3—24no—
450C3×Dic3—34no—
451C3×Dic3—62no—
452C3×Dic3C23×D314yescomplemented
453C3×Dic3C23×D314yescomplemented
454C25—272no—
455C22×D4—92no—
456C22×D4—272no—
457C22×D4—271no—
458C22×D4—2716no—
459C22×D4—272no—
460C22×D4—271no—
461C22×D4—274no—
462C23×C4—91no—
463C33C23×D411yescharacteristic, complemented, Sylow
464C23×C3—32no—
465C23×C3—32no—
466C23×C3—34no—
467C23×C3—62no—
468C23×C3—62no—
469C23×C3—94no—
470C23×C3—98no—
471C23×C3—916no—
472C23×C3—91no—
473C23×C3—94no—
474C23×C3—1816no—
475C22×D3—32no—
476C22×D3—38no—
477C22×D3—316no—
478C22×D3—34no—
479C22×D3—34no—
480C22×D3—316no—
481C22×D3—316no—
482C22×D3—61no—
483C22×D3—64no—
484C22×D3—616no—
485C22×D3—616no—
486C22×D3—98no—
487C22×D3—916no—
488C22×D3—916no—
489C22×D3—916no—
490C22×D3—916no—
491C22×D3—92no—
492C22×D3—94no—
493C22×D3—916no—
494C22×D3—98no—
495C22×D3—1816no—
496C22×D3—188no—
497C22×D3—184no—
498C22×D3—182no—
499C22×D3—188no—
500C22×D3—1816no—
501C22×D3—18128no—
502C22×D3—1816no—
503C22×D3—1864no—
504C22×D3—188no—
505C22×D3—1816no—
506C22×D3—1816no—
507C22×D3—1816no—
508C22×D3—362no—
509C22×D3—368no—
510C22×D3—3616no—
511C22×D3C2×D3212yes—
512C22×D3C2×D3212yescomplemented
513C3×D4—38no—
514C3×D4—64no—
515C3×D4—916no—
516C3×D4—98no—
517C2×C3×C4—21no—
518C2×C3×C4—22no—
519C2×C3×C4—32no—
520C2×C3×C4—32no—
521C2×C3×C4—38no—
522C2×C3×C4—38no—
523C2×C3×C4—41no—
524C2×C3×C4—68no—
525C2×C3×C4—62no—
526C2×C3×C4—94no—
527C2×C3×C4—98no—
528C2×C3×C4—91no—
529C2×C3×C4—94no—
530C2×C3×C4C2×D3212yescomplemented
531C2×C3×C4C2×D3211yescharacteristic, complemented
532#67—316no—
533#67—916no—
534#67—916no—
535#67—916no—
536#67—188no—
537C2×Dic3—32no—
538C2×Dic3—38no—
539C2×Dic3—61no—
540C2×Dic3C2×D3212yescomplemented
541D12—316no—
542D12—38no—
543D12—38no—
544D12—68no—
545D12—916no—
546D12—916no—
547D12—98no—
548D12—98no—
549D12—94no—
550D12—98no—
551D12—188no—
552D12—184no—
553D12—1816no—
554D12—364no—
555D12C2×D3214yesdirect product factor
556C4×D3—38no—
557C4×D3—38no—
558C4×D3—38no—
559C4×D3—64no—
560C4×D3C2×D3218yescomplemented
561C2×C32—24no—
562C2×C32—22no—
563C2×C32—22no—
564C2×C32—21no—
565C2×C32—38no—
566C2×C32—42no—
567C2×C32—41no—
568C2×C32—64no—
569C2×C32C22×D1212yescomplemented
570C2×C32C2×D3×D414yescomplemented
571C2×C32C24×D311yescharacteristic
572C2×C32C24×D312yes—
573C3⋊D3—28no—
574C3⋊D3—64no—
575C3⋊D3—68no—
576C3⋊D3—128no—
577C3⋊D3—124no—
578C3⋊D3—244no—
579C3⋊D3C22×D1214yescomplemented
580C3×D3—28no—
581C3×D3—28no—
582C3×D3—38no—
583C3×D3—44no—
584C3×D3—64no—
585C3×D3—68no—
586C3×D3—68no—
587C3×D3—128no—
588C3×D3C22×D1218yescomplemented
589C3×D3C2×D3×D418yescomplemented
590C24—91no—
591C24—94no—
592C24—274no—
593C24—272no—
594C24—2716no—
595C24—272no—
596C24—5416no—
597C2×D4—31no—
598C2×D4—916no—
599C2×D4—94no—
600C2×D4—92no—
601C2×D4—2716no—
602C2×D4—274no—
603C2×D4—278no—
604C2×D4—2716no—
605C2×D4—278no—
606C2×D4—2732no—
607C2×D4—272no—
608C2×D4—272no—
609C2×D4—271no—
610C22×C4—32no—
611C22×C4—91no—
612C22×C4—98no—
613C22×C4—92no—
614C22×C4—91no—
615C22×C3—21no—
616C22×C3—22no—
617C22×C3—38no—
618C22×C3—38no—
619C22×C3—34no—
620C22×C3—34no—
621C22×C3—38no—
622C22×C3—41no—
623C22×C3—64no—
624C22×C3—68no—
625C22×C3—64no—
626C22×C3—68no—
627C22×C3—916no—
628C22×C3—94no—
629C22×C3—92no—
630C22×C3—98no—
631C22×C3—124no—
632C22×C3—1832no—
633C22×C3—188no—
634C22×C3C22×D3212yes—
635C22×C3C22×D3211yescharacteristic
636C2×D3—24no—
637C2×D3—38no—
638C2×D3—34no—
639C2×D3—332no—
640C2×D3—38no—
641C2×D3—38no—
642C2×D3—62no—
643C2×D3—64no—
644C2×D3—68no—
645C2×D3—632no—
646C2×D3—68no—
647C2×D3—68no—
648C2×D3—632no—
649C2×D3—94no—
650C2×D3—98no—
651C2×D3—128no—
652C2×D3—188no—
653C2×D3—184no—
654C2×D3—1816no—
655C2×D3—1832no—
656C2×D3—1832no—
657C2×D3—1816no—
658C2×D3—1832no—
659C2×D3—1832no—
660C2×D3—188no—
661C2×D3—184no—
662C2×D3—1832no—
663C2×D3—364no—
664C2×D3—3616no—
665C2×D3—3632no—
666C2×D3—364no—
667C2×D3—368no—
668C2×D3—724no—
669C2×D3D3×D1218yesdirect product factor
670C2×D3C22×D3214yes—
671C2×D3C22×D3214yescomplemented
672C3×C4—22no—
673C3×C4—24no—
674C3×C4—34no—
675C3×C4—34no—
676C3×C4—42no—
677C3×C4—64no—
678C3×C4—92no—
679C3×C4C22×D3214yescomplemented
680C3×C4C22×D3212yescomplemented
681Dic3—34no—
682Dic3—62no—
683Dic3C22×D3214yescomplemented
684C32—22no—
685C32—21no—
686C32—41no—
687C32C23×D1211yescharacteristic, complemented
688C32C22×D3×D412yescomplemented
689C23—32no—
690C23—32no—
691C23—94no—
692C23—98no—
693C23—916no—
694C23—91no—
695C23—94no—
696C23—1816no—
697C23—2716no—
698C23—278no—
699C23—278no—
700C23—272no—
701C23—5416no—
702C23—548no—
703C23—5464no—
704C23—548no—
705D4—34no—
706D4—916no—
707D4—98no—
708D4—2716no—
709D4—278no—
710D4—278no—
711D4—274no—
712C2×C4—32no—
713C2×C4—38no—
714C2×C4—94no—
715C2×C4—98no—
716C2×C4—91no—
717C2×C4—94no—
718C2×C4D3311yescharacteristic, complemented
719C2×C3—22no—
720C2×C3—24no—
721C2×C3—21no—
722C2×C3—22no—
723C2×C3—38no—
724C2×C3—38no—
725C2×C3—42no—
726C2×C3—41no—
727C2×C3—68no—
728C2×C3—68no—
729C2×C3—94no—
730C2×C3—124no—
731C2×C3—188no—
732C2×C3C2×D3×D1214yescomplemented
733C2×C3D32×D412yescomplemented
734C2×C3C23×D3212yes—
735C2×C3C23×D3211yescharacteristic
736D3—24no—
737D3—38no—
738D3—64no—
739D3—68no—
740D3—68no—
741D3—128no—
742D3—188no—
743D3—184no—
744D3—364no—
745D3—368no—
746D3—724no—
747D3C2×D3×D1218yesdirect product factor
748C22—38no—
749C22—34no—
750C22—34no—
751C22—64no—
752C22—916no—
753C22—94no—
754C22—92no—
755C22—98no—
756C22—1832no—
757C22—188no—
758C22—274no—
759C22—5432no—
760C22—5416no—
761C22—5416no—
762C22—544no—
763C22C2×D3311yescharacteristic
764C4—34no—
765C4—92no—
766C4C2×D3312yescomplemented
767C3—21no—
768C3—22no—
769C3—41no—
770C3C22×D3×D1212yescomplemented
771C3C2×D32×D411yescharacteristic, complemented
772C2—38no—
773C2—64no—
774C2—94no—
775C2—188no—
776C2—544no—
777C2D32×D1212yesdirect product factor
778C2C22×D3311yescharacteristic
subgroupG/H
centerC22C2×D33
commutator, cosocleC2×C33C25
FrattiniC2C22×D33
FittingC2×C33×C4C23
socleC22×C33C24
hypercenterC2×C4D33
hypocenterC33C23×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C22×D33C2semidirect
2. C2×C4⋊#1113C2semidirect
3. C2×C3⋊D3×D12C2semidirect
4. C2×D3×C4⋊(C3⋊D3)C2semidirect
5. C2×C3×D3×D12C2semidirect
6. C2×C3×C4×D32C2semidirect
7. C2×#88955C2semidirect
8. C2×D3×#626C2semidirect
9. D32×D12C2direct (N × H)
12. C22×#1113C22semidirect
13. C22×D3×C3⋊D3C22semidirect
14. C22×D3×C3⋊D3C22semidirect
16. C22×C3×D32C22semidirect
18. C2×D33C22semidirect
19. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
20. C2×C3×C4⋊(C3⋊D3)C22semidirect
21. C2×C3×C4×C3⋊D3C22semidirect
22. C2×C32×D12C22semidirect
23. C2×C32×C4×D3C22semidirect
24. C2×#6295C22semidirect
25. C4⋊#1113C22semidirect
26. C2×#6292C22semidirect
27. C2×#6291C22semidirect
28. C3⋊D3×D12C22semidirect
29. D3×C4⋊(C3⋊D3)C22semidirect
30. C2×C3×#626C22semidirect
31. C2×C3×#624C22semidirect
32. C2×C3×D3×Dic3C22semidirect
33. C3×D3×D12C22semidirect
34. C3×C4×D32C22semidirect
35. #88955C22semidirect
36. D3×#626C22semidirect
58. C2×D3×D12D3direct (N × H)
59. C2×C4×D32D3semidirect
60. C22×C3⋊(C3⋊D3)C23semidirect
62. C22×C3×C3⋊D3C23semidirect
64. C22×C32×D3C23semidirect
66. C2×#1113C23semidirect
69. C2×D3×C3⋊D3C23semidirect
70. C2×D3×C3⋊D3C23semidirect
72. C2×C3×D32D4semidirect
74. C2×C3×D32C23semidirect
76. C2×C33×C4C23semidirect
77. C4⋊(C3⋊(C3⋊D3))C23semidirect
78. C2×C3×C3⋊Dic3C23semidirect
79. C3×C4⋊(C3⋊D3)C23semidirect
80. C3×C4×C3⋊D3C23semidirect
81. C2×C32×Dic3C23semidirect
82. C32×D12C23semidirect
83. C32×C4×D3C23semidirect
84. #6295C23semidirect
85. #6292C23semidirect
86. #6291C23semidirect
87. C3×#626C23semidirect
88. C3×#624C23semidirect
89. C3×D3×Dic3C23semidirect
109. C22×D32C2×D3semidirect
121. C2×C4⋊(C3⋊D3)C2×D3semidirect
122. C2×C4×C3⋊D3C2×D3semidirect
132. C2×C3×D12C2×D3semidirect
139. C2×C3×C4×D3C2×D3semidirect
140. C2×C3×C4×D3C2×D3semidirect
150. C2×#626C2×D3semidirect
152. C2×#624C2×D3semidirect
153. C2×D3×Dic3C2×D3semidirect
163. D3×D12C2×D3direct (N × H)
164. C4×D32C2×D3semidirect
167. C2×C3⋊(C3⋊D3)C24semidirect
169. C2×C3×C3⋊D3C2×D4semidirect
171. C2×C3×C3⋊D3C24semidirect
173. C2×C32×D3C2×D4semidirect
175. C2×C32×D3C24semidirect
180. C3×D32C2×D4semidirect
181. C33×C4C24semidirect
182. C3×C3⋊Dic3C24semidirect
183. C32×Dic3C24semidirect
219. C22×C3⋊D3C22×D3semidirect
235. C22×C3×D3C22×D3semidirect
253. C2×D32D12direct (N × H)
255. C2×D32C22×D3semidirect
262. C2×C32×C4C22×D3semidirect
263. C2×C32×C4C22×D3semidirect
265. C2×C3⋊Dic3C22×D3semidirect
272. C4⋊(C3⋊D3)C22×D3semidirect
273. C4×C3⋊D3C22×D3semidirect
279. C2×C3×Dic3C22×D3semidirect
280. C2×C3×Dic3C22×D3semidirect
286. C3×D12C22×D3semidirect
292. C3×C4×D3C22×D3semidirect
293. C3×C4×D3C22×D3semidirect
300. #626C22×D3semidirect
302. #624C22×D3semidirect
303. D3×Dic3C22×D3semidirect
305. C2×C33C22×D4semidirect
309. C3×C3⋊D3C22×D4semidirect
311. C32×D3C22×D4semidirect
378. C2×D12D32direct (N × H)
384. C2×C4×D3D32semidirect
407. C2×C3⋊D3C2×D12semidirect
409. C2×C3⋊D3C23×D3semidirect
428. C2×C3×D3C2×D12semidirect
429. C2×C3×D3D3×D4semidirect
432. C2×C3×D3C23×D3semidirect
441. D32C2×D12direct (N × H)
446. C32×C4C23×D3semidirect
447. C32×C4C23×D3semidirect
448. C3⋊Dic3C23×D3semidirect
452. C3×Dic3C23×D3semidirect
453. C3×Dic3C23×D3semidirect
463. C33C23×D4semidirect
512. C22×D3C2×D32semidirect
530. C2×C3×C4C2×D32semidirect
531. C2×C3×C4C2×D32semidirect
540. C2×Dic3C2×D32semidirect
555. D12C2×D32direct (N × H)
560. C4×D3C2×D32semidirect
569. C2×C32C22×D12semidirect
570. C2×C32C2×D3×D4semidirect
579. C3⋊D3C22×D12semidirect
588. C3×D3C22×D12semidirect
589. C3×D3C2×D3×D4semidirect
669. C2×D3D3×D12direct (N × H)
671. C2×D3C22×D32semidirect
679. C3×C4C22×D32semidirect
680. C3×C4C22×D32semidirect
683. Dic3C22×D32semidirect
687. C32C23×D12semidirect
688. C32C22×D3×D4semidirect
718. C2×C4D33semidirect
732. C2×C3C2×D3×D12semidirect
733. C2×C3D32×D4semidirect
747. D3C2×D3×D12direct (N × H)
766. C4C2×D33semidirect
770. C3C22×D3×D12semidirect
771. C3C2×D32×D4semidirect
777. C2D32×D12direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D332
C2×C4⋊#11132
C2×C3⋊D3×D122
C2×D3×C4⋊(C3⋊D3)2
C2×C3×D3×D122
C2×C3×C4×D322
C2×#889552
C2×D3×#6262
D32×D122
C2×D32×D43
C22×D3×D123