Finite Group Databasebeta

← C2×D3×#3805 #13181310

Subgroups — C2×D3×#3805 #13181310

Order 1728.

4178 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89046C211yesmaximal, characteristic, complemented
2C2×#89029C212yesmaximal, complemented
3C22×D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C2×C3×D3×#67C212yesmaximal, complemented
5C2×C3×#3805C211yesmaximal, characteristic, complemented
6C2×#88964C211yesmaximal, characteristic, complemented
7C2×#88963C211yesmaximal, characteristic, complemented
8C2×#88961C212yesmaximal, complemented
9C2×D3×#627C211yesmaximal, characteristic, complemented
10C2×D3×#625C211yesmaximal, characteristic, complemented
11D3×#3805C2116yesmaximal, direct product factor
12C2×D32×Dic3C212yesmaximal, complemented
13C22×#3805—31nomaximal
14C2×D3×#237—32nomaximal
15C23×C32×D3C2211yescharacteristic
16C22×C3×D32C2212yes—
17C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
18C2×C3×#638C2212yescomplemented
19C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
20C2×C32×#67C2212yescomplemented
21C2×#6296C2211yescharacteristic, complemented
22C2×#6295C2211yescharacteristic, complemented
23#89046C2218yescomplemented
24C2×#6294C2212yescomplemented
25C2×#6293C2212yescomplemented
26C2×#6290C2212yescomplemented
27C2×Dic3×C3⋊D3C2212yescomplemented
28#89029C22116yescomplemented
29C2×D3×C3⋊Dic3C2211yescharacteristic
30C2×D3×C3⋊Dic3C2211yescharacteristic
31C2×D3×C3⋊Dic3C2218yescomplemented
32C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
33C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
34C2×D3×C3⋊Dic3C2212yescomplemented
35C3×D3×#67C22116yescomplemented
36C2×C3×#627C2211yescharacteristic, complemented
37C2×C3×#626C2212yescomplemented
38C2×C3×#625C2211yescharacteristic, complemented
39C2×C3×#625C2212yescomplemented
40C3×#3805C2218yescomplemented
41C2×C3×D3×Dic3C2212yes—
42C2×C3×D3×Dic3C2212yescomplemented
43#88964C2218yescomplemented
44#88963C2218yescomplemented
45#88961C22116yescomplemented
46D3×#627C2218yescomplemented
47D3×#625C2218yescomplemented
48D32×Dic3C22116yescomplemented
49C23×C3⋊Dic3—31no—
50C2×#3830—32no—
51C22×C3×#67—32no—
52C2×C3×#237—32no—
53C2×C3×D3×D4—32no—
54C2×D3×#67—32no—
55C2×D3×#67D312yescomplemented
56C22×#627—31no—
57C22×#625—31no—
58C2×#3805—31no—
59C2×#3805—32no—
60C2×#3805—32no—
61C2×#3805—31no—
62C2×#3805—32no—
63C2×#3805—31no—
64C2×#3805—316no—
65C2×#3805—32no—
66C2×#3805—62no—
67C2×#3805D311yescharacteristic, direct product factor
68C2×#3804—32no—
69C2×#3804—32no—
70C22×D3×Dic3—32no—
71C22×D3×Dic3—32no—
72C22×D3×Dic3—32no—
73C22×D3×Dic3—61no—
74D3×#237—332no—
75C2×C4×D32—32no—
76C2×#3796—32no—
77C2×#3795—32no—
78C2×D3×Dic6—32no—
79C23×C33C2311yescharacteristic
80C22×C3×C3⋊D3C2312yes—
81C22×C32×D3—24no—
82C22×C32×D3C2312yes—
83C22×C32×D3C2311yescharacteristic
84C22×C32×D3C2314yes—
85C22×C32×D3C2311yescharacteristic
86C2×C3×D32—28no—
87C2×C3×D32C2318yes—
88C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
89C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
90C2×C3⋊(C3⋊Dic3)C2314yescomplemented
91C3×#638C2318yescomplemented
92C2×C3×C3⋊Dic3C2312yes—
93C2×C3×C3⋊Dic3C2311yescharacteristic
94C2×C3×C3⋊Dic3C2311yescharacteristic
95C2×C3×C3⋊Dic3C2314yescomplemented
96C32×#67C2318yescomplemented
97C2×C32×Dic3C2312yes—
98#6296C2314yescomplemented
99#6295C2314yescomplemented
100#6294C2318yescomplemented
101#6293C2318yescomplemented
102#6290C2318yescomplemented
103Dic3×C3⋊D3C2318yescomplemented
104D3×C3⋊Dic3C2314yes—
105D3×C3⋊Dic3C2314yes—
106D3×C3⋊Dic3C2318yescomplemented
107D3×C3⋊Dic3C2314yescomplemented
108D3×C3⋊Dic3C2314yescomplemented
109C3×#627C2314yescomplemented
110C3×#626C2318yescomplemented
111C3×#625C2314yescomplemented
112C3×#625C2318yescomplemented
113C3×D3×Dic3C2318yes—
114C3×D3×Dic3C2318yescomplemented
115C2×D3×#41—91no—
116C22×#237—92no—
117C24×C32—31no—
118C23×C3×D3—21no—
119C23×C3×D3—32no—
120C23×C3×D3—32no—
121C23×C3×D3C2×D312yes—
122C22×D32C2×D312yes—
123C2×C32×D4—32no—
124C2×#638—32no—
125C2×#638C2×D312yescomplemented
126C22×C3⋊Dic3—32no—
127C22×C3⋊Dic3—31no—
128C22×C3⋊Dic3—31no—
129C22×C3⋊Dic3—32no—
130C22×C3⋊Dic3—31no—
131C22×C3⋊Dic3—31no—
132C22×C3⋊Dic3—31no—
133C22×C3⋊Dic3—38no—
134C22×C3⋊Dic3—61no—
135C22×C3⋊Dic3—62no—
136C22×C3⋊Dic3—121no—
137C22×C3⋊Dic3C2×D311yescharacteristic, complemented
138#3830—316no—
139C2×C4×C3⋊D3—32no—
140C2×#634—32no—
141C2×C3×#67—22no—
142C2×C3×#67—32no—
143C2×C3×#67—32no—
144C2×C3×#67—32no—
145C2×C3×#67—32no—
146C2×C3×#67—32no—
147C2×C3×#67—316no—
148C2×C3×#67—32no—
149C2×C3×#67—62no—
150C2×C3×#67C2×D312yescomplemented
151C2×C3×#67C2×D312yescomplemented
152C22×C3×Dic3—32no—
153C22×C3×Dic3—32no—
154C22×C3×Dic3—32no—
155C22×C3×Dic3—61no—
156C3×#237—316no—
157C3×D3×D4—316no—
158C2×C3×D12—32no—
159C2×C3×C4×D3—32no—
160C2×C3×C4×D3—32no—
161C2×C3×Dic6—32no—
162D3×#67—316no—
163D3×#67C2×D3116yescomplemented
164C2×#627—32no—
165C2×#627—31no—
166C2×#627—32no—
167C2×#627—32no—
168C2×#627—38no—
169C2×#627—62no—
170C2×#627C2×D311yescharacteristic, complemented
171C2×#626—32no—
172C2×#626C2×D312yescomplemented
173C2×#625—32no—
174C2×#625—32no—
175C2×#625—31no—
176C2×#625—38no—
177C2×#625—62no—
178C2×#625C2×D312yescomplemented
179C2×#625C2×D311yescharacteristic, complemented
180C2×#624—32no—
181#3805—38no—
182#3805—316no—
183#3805—316no—
184#3805—38no—
185#3805—316no—
186#3805—38no—
187#3805—316no—
188#3805—616no—
189#3805C2×D318yesdirect product factor
190#3804—316no—
191#3804—316no—
192C2×D3×Dic3—32no—
193C2×D3×Dic3—32no—
194C2×D3×Dic3—32no—
195C2×D3×Dic3—32no—
196C2×D3×Dic3—32no—
197C2×D3×Dic3—316no—
198C2×D3×Dic3—32no—
199C2×D3×Dic3—32no—
200C2×D3×Dic3—32no—
201C2×D3×Dic3—32no—
202C2×D3×Dic3—32no—
203C2×D3×Dic3—316no—
204C2×D3×Dic3—316no—
205C2×D3×Dic3—62no—
206C2×D3×Dic3—61no—
207C2×D3×Dic3—61no—
208C2×D3×Dic3—68no—
209C2×D3×Dic3—61no—
210C2×D3×Dic3—61no—
211C2×D3×Dic3—62no—
212C2×D3×Dic3C2×D312yes—
213C2×D3×Dic3C2×D312yescomplemented
214C4×D32—316no—
215#3796—316no—
216#3795—316no—
217D3×Dic6—316no—
218C22×C33—22no—
219C22×C33C2412yes—
220C22×C33C2411yescharacteristic
221C2×C3×C3⋊D3—24no—
222C2×C3×C3⋊D3C2414yes—
223C2×C32×D3—22no—
224C2×C32×D3—24no—
225C2×C32×D3—28no—
226C2×C32×D3#4114yescomplemented
227C2×C32×D3C2414yes—
228C2×C32×D3C2412yes—
229C2×C32×D3C2412yes—
230C3×D32—216no—
231C3⋊(C3⋊Dic3)C2412yes—
232C3⋊(C3⋊Dic3)C2412yes—
233C3×C3⋊Dic3C2414yes—
234C3×C3⋊Dic3C2412yes—
235C3×C3⋊Dic3C2412yes—
236C32×Dic3C2414yes—
237C2×C3×#41—91no—
238C22×C3×D4—92no—
239C22×#67—32no—
240C22×#67—92no—
241C23×Dic3—92no—
242C23×Dic3—92no—
243C23×Dic3—181no—
244D3×#41—916no—
245C2×#239—91no—
246C2×D3×Q8—91no—
247C2×#237—32no—
248C2×#237—92no—
249C2×#237—92no—
250C2×#237—932no—
251C2×#237—92no—
252C2×#237—92no—
253C2×#237—92no—
254C2×#237—91no—
255C2×#237—92no—
256C2×#237—92no—
257C2×#237—92no—
258C2×#237—182no—
259C2×D3×D4—32no—
260C2×D3×D4—91no—
261C2×#235—92no—
262C2×#235—91no—
263C22×C4×D3—92no—
264C22×C4×D3—92no—
265C22×C4×D3—91no—
266C22×Dic6—92no—
267C23×C32—21no—
268C23×C32—22no—
269C23×C32—31no—
270C23×C32—32no—
271C23×C32—34no—
272C23×C32—31no—
273C23×C32—41no—
274C23×C32—64no—
275C23×C32C22×D312yes—
276C23×C32C22×D311yescharacteristic
277C22×C3⋊D3C22×D312yes—
278C22×C3×D3—28no—
279C22×C3×D3—28no—
280C22×C3×D3—21no—
281C22×C3×D3—24no—
282C22×C3×D3—21no—
283C22×C3×D3—22no—
284C22×C3×D3—32no—
285C22×C3×D3—32no—
286C22×C3×D3—38no—
287C22×C3×D3—38no—
288C22×C3×D3—62no—
289C22×C3×D3—68no—
290C22×C3×D3—68no—
291C22×C3×D3C22×D312yes—
292C22×C3×D3C22×D312yes—
293C22×C3×D3C22×D312yes—
294C22×C3×D3C22×D318yes—
295C22×C3×D3C22×D312yes—
296C2×D32—28no—
297C2×D32C22×D318yes—
298C32×D4—38no—
299C2×C32×C4—32no—
300#638—38no—
301#638C22×D318yescomplemented
302C2×C3⋊Dic3—32no—
303C2×C3⋊Dic3—31no—
304C2×C3⋊Dic3—32no—
305C2×C3⋊Dic3—31no—
306C2×C3⋊Dic3—38no—
307C2×C3⋊Dic3—34no—
308C2×C3⋊Dic3—34no—
309C2×C3⋊Dic3—34no—
310C2×C3⋊Dic3—38no—
311C2×C3⋊Dic3—34no—
312C2×C3⋊Dic3—34no—
313C2×C3⋊Dic3—61no—
314C2×C3⋊Dic3—61no—
315C2×C3⋊Dic3—62no—
316C2×C3⋊Dic3—62no—
317C2×C3⋊Dic3—64no—
318C2×C3⋊Dic3—68no—
319C2×C3⋊Dic3—121no—
320C2×C3⋊Dic3—121no—
321C2×C3⋊Dic3—124no—
322C2×C3⋊Dic3C22×D311yescharacteristic
323C2×C3⋊Dic3C22×D312yes—
324C2×C3⋊Dic3C22×D311yescharacteristic
325C2×C3⋊Dic3C22×D314yescomplemented
326C4×C3⋊D3—38no—
327#634—38no—
328C3×#67—28no—
329C3×#67—38no—
330C3×#67—38no—
331C3×#67—38no—
332C3×#67—38no—
333C3×#67—38no—
334C3×#67—38no—
335C3×#67—68no—
336C3×#67C22×D318yescomplemented
337C3×#67C22×D318yescomplemented
338C2×C3×Dic3—22no—
339C2×C3×Dic3—32no—
340C2×C3×Dic3—32no—
341C2×C3×Dic3—32no—
342C2×C3×Dic3—32no—
343C2×C3×Dic3—38no—
344C2×C3×Dic3—38no—
345C2×C3×Dic3—38no—
346C2×C3×Dic3—61no—
347C2×C3×Dic3—61no—
348C2×C3×Dic3—62no—
349C2×C3×Dic3—64no—
350C2×C3×Dic3C22×D312yes—
351C2×C3×Dic3C22×D312yes—
352C3×D12—38no—
353C3×C4×D3—38no—
354C3×C4×D3—38no—
355C3×Dic6—38no—
356#627—38no—
357#627—34no—
358#627—38no—
359#627—38no—
360#627—68no—
361#627C22×D314yescomplemented
362#626—38no—
363#626C22×D318yescomplemented
364#625—38no—
365#625—38no—
366#625—34no—
367#625—68no—
368#625C22×D318yescomplemented
369#625C22×D314yescomplemented
370#624—38no—
371D3×Dic3—38no—
372D3×Dic3—38no—
373D3×Dic3—38no—
374D3×Dic3—38no—
375D3×Dic3—38no—
376D3×Dic3—38no—
377D3×Dic3—38no—
378D3×Dic3—38no—
379D3×Dic3—38no—
380D3×Dic3—38no—
381D3×Dic3—64no—
382D3×Dic3—64no—
383D3×Dic3—64no—
384D3×Dic3—64no—
385D3×Dic3—68no—
386D3×Dic3—68no—
387D3×Dic3C22×D318yes—
388D3×Dic3C22×D318yescomplemented
389C22×#41—271noSylow
390C2×C33—22no—
391C2×C33C2×#4112yescomplemented
392C2×C33C2511yescharacteristic
393C3×C3⋊D3—24no—
394C32×D3—22no—
395C32×D3—24no—
396C32×D3C2×#4114yescomplemented
397C24×C3—32no—
398C24×C3—61no—
399C24×C3—92no—
400C23×D3—32no—
401C23×D3—32no—
402C23×D3D3211yescharacteristic
403C3×#41—98no—
404C2×C3×Q8—91no—
405C2×C3×D4—32no—
406C2×C3×D4—32no—
407C2×C3×D4—62no—
408C2×C3×D4—92no—
409C2×C3×D4—916no—
410C2×C3×D4—91no—
411C2×C3×D4—92no—
412C2×C3×D4—92no—
413C22×C3×C4—92no—
414C22×C3×C4—92no—
415C22×C3×C4—91no—
416C2×#67—32no—
417C2×#67—32no—
418C2×#67—32no—
419C2×#67—32no—
420C2×#67—32no—
421C2×#67—316no—
422C2×#67—32no—
423C2×#67—62no—
424C2×#67—92no—
425C2×#67—916no—
426C2×#67—92no—
427C2×#67—92no—
428C2×#67—92no—
429C2×#67—182no—
430C2×#67D3212yescomplemented
431C22×Dic3—32no—
432C22×Dic3—32no—
433C22×Dic3—32no—
434C22×Dic3—61no—
435C22×Dic3—92no—
436C22×Dic3—916no—
437C22×Dic3—92no—
438C22×Dic3—92no—
439C22×Dic3—92no—
440C22×Dic3—92no—
441C22×Dic3—92no—
442C22×Dic3—92no—
443C22×Dic3—916no—
444C22×Dic3—91no—
445C22×Dic3—92no—
446C22×Dic3—92no—
447C22×Dic3—182no—
448C22×Dic3—181no—
449C22×Dic3—181no—
450C22×Dic3—181no—
451C22×Dic3—181no—
452C22×Dic3—188no—
453C22×Dic3—182no—
454C22×Dic3—181no—
455C22×Dic3—361no—
456#239—98no—
457D3×Q8—98no—
458#237—316no—
459#237—916no—
460#237—916no—
461#237—916no—
462#237—916no—
463#237—916no—
464#237—98no—
465#237—916no—
466#237—916no—
467#237—916no—
468#237—1816no—
469D3×D4—316no—
470D3×D4—98no—
471#235—916no—
472#235—98no—
473C2×D12—32no—
474C2×D12—91no—
475C2×C4×D3—32no—
476C2×C4×D3—32no—
477C2×C4×D3—916no—
478C2×C4×D3—916no—
479C2×C4×D3—92no—
480C2×C4×D3—92no—
481C2×C4×D3—92no—
482C2×C4×D3—92no—
483C2×C4×D3—91no—
484C2×C4×D3—91no—
485C2×C4×D3—91no—
486C2×C4×D3—92no—
487C2×C4×D3—91no—
488C2×C4×D3—98no—
489C2×C4×D3—182no—
490C2×Dic6—32no—
491C2×Dic6—916no—
492C2×Dic6—92no—
493C2×Dic6—91no—
494C2×Dic6—92no—
495C2×Dic6—92no—
496C2×Dic6—92no—
497C2×Dic6—182no—
498C22×C32—22no—
499C22×C32—24no—
500C22×C32—24no—
501C22×C32—22no—
502C22×C32—22no—
503C22×C32—21no—
504C22×C32—24no—
505C22×C32—34no—
506C22×C32—32no—
507C22×C32—34no—
508C22×C32—32no—
509C22×C32—42no—
510C22×C32—41no—
511C22×C32—44no—
512C22×C32—44no—
513C22×C32—68no—
514C22×C32—62no—
515C22×C32—64no—
516C22×C32C23×D314yes—
517C22×C32C23×D312yes—
518C22×C32C23×D312yes—
519C22×C32C23×D311yescharacteristic
520C2×C3⋊D3—24no—
521C2×C3⋊D3C23×D314yes—
522C2×C3×D3—24no—
523C2×C3×D3—216no—
524C2×C3×D3—24no—
525C2×C3×D3—24no—
526C2×C3×D3—24no—
527C2×C3×D3—216no—
528C2×C3×D3—22no—
529C2×C3×D3—22no—
530C2×C3×D3—24no—
531C2×C3×D3—24no—
532C2×C3×D3—34no—
533C2×C3×D3—34no—
534C2×C3×D3—44no—
535C2×C3×D3—64no—
536C2×C3×D3—616no—
537C2×C3×D3—64no—
538C2×C3×D3—64no—
539C2×C3×D3—616no—
540C2×C3×D3—124no—
541C2×C3×D3#23718yescomplemented
542C2×C3×D3C23×D314yes—
543C2×C3×D3C23×D314yes—
544C2×C3×D3C23×D314yes—
545C2×C3×D3C23×D314yes—
546D32—216no—
547C32×C4—34no—
548C3⋊Dic3—34no—
549C3⋊Dic3—32no—
550C3⋊Dic3—34no—
551C3⋊Dic3—32no—
552C3⋊Dic3—62no—
553C3⋊Dic3—62no—
554C3⋊Dic3—64no—
555C3⋊Dic3—64no—
556C3⋊Dic3—122no—
557C3⋊Dic3—122no—
558C3⋊Dic3C23×D312yes—
559C3⋊Dic3C23×D314yes—
560C3⋊Dic3C23×D312yes—
561C3×Dic3—24no—
562C3×Dic3—34no—
563C3×Dic3—34no—
564C3×Dic3—34no—
565C3×Dic3—34no—
566C3×Dic3—62no—
567C3×Dic3—62no—
568C3×Dic3—64no—
569C3×Dic3C23×D314yes—
570C3×Dic3C23×D314yes—
571C2×#41—91no—
572C2×#41—272no—
573C2×#41—271no—
574C2×#41—272no—
575C2×#41—271no—
576C2×#41—271no—
577C2×#41—2716no—
578C22×Q8—271no—
579C22×D4—92no—
580C22×D4—271no—
581C23×C4—272no—
582C23×C4—271no—
583C33C22×#4111yescharacteristic, complemented, Sylow
584C23×C3—21no—
585C23×C3—22no—
586C23×C3—32no—
587C23×C3—32no—
588C23×C3—38no—
589C23×C3—32no—
590C23×C3—32no—
591C23×C3—41no—
592C23×C3—61no—
593C23×C3—64no—
594C23×C3—61no—
595C23×C3—62no—
596C23×C3—68no—
597C23×C3—68no—
598C23×C3—98no—
599C23×C3—92no—
600C23×C3—188no—
601C23×C3C2×D3212yes—
602C23×C3C2×D3211yescharacteristic
603C22×D3—24no—
604C22×D3—32no—
605C22×D3—32no—
606C22×D3—38no—
607C22×D3—38no—
608C22×D3—62no—
609C22×D3—68no—
610C22×D3—68no—
611C22×D3C2×D3212yes—
612C22×D3C2×D3211yescharacteristic
613C22×D3C2×D3214yes—
614C22×D3C2×D3211yescharacteristic
615C3×Q8—94no—
616C3×D4—38no—
617C3×D4—38no—
618C3×D4—68no—
619C3×D4—98no—
620C3×D4—94no—
621C3×D4—98no—
622C3×D4—98no—
623C2×C3×C4—32no—
624C2×C3×C4—32no—
625C2×C3×C4—62no—
626C2×C3×C4—98no—
627C2×C3×C4—98no—
628C2×C3×C4—92no—
629C2×C3×C4—91no—
630C2×C3×C4—91no—
631C2×C3×C4—94no—
632#67—38no—
633#67—38no—
634#67—38no—
635#67—38no—
636#67—38no—
637#67—38no—
638#67—68no—
639#67—98no—
640#67—98no—
641#67—98no—
642#67—98no—
643#67—188no—
644#67C2×D3218yescomplemented
645C2×Dic3—32no—
646C2×Dic3—32no—
647C2×Dic3—32no—
648C2×Dic3—32no—
649C2×Dic3—38no—
650C2×Dic3—38no—
651C2×Dic3—38no—
652C2×Dic3—62no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3—64no—
656C2×Dic3—98no—
657C2×Dic3—98no—
658C2×Dic3—98no—
659C2×Dic3—98no—
660C2×Dic3—98no—
661C2×Dic3—98no—
662C2×Dic3—98no—
663C2×Dic3—91no—
664C2×Dic3—92no—
665C2×Dic3—91no—
666C2×Dic3—94no—
667C2×Dic3—92no—
668C2×Dic3—98no—
669C2×Dic3—98no—
670C2×Dic3—188no—
671C2×Dic3—184no—
672C2×Dic3—184no—
673C2×Dic3—184no—
674C2×Dic3—184no—
675C2×Dic3—182no—
676C2×Dic3—182no—
677C2×Dic3—188no—
678C2×Dic3—184no—
679C2×Dic3—181no—
680C2×Dic3—181no—
681C2×Dic3—364no—
682C2×Dic3—361no—
683C2×Dic3—361no—
684C2×Dic3C2×D3212yes—
685D12—38no—
686D12—94no—
687C4×D3—38no—
688C4×D3—38no—
689C4×D3—98no—
690C4×D3—98no—
691C4×D3—98no—
692C4×D3—98no—
693C4×D3—94no—
694C4×D3—94no—
695C4×D3—94no—
696C4×D3—98no—
697C4×D3—94no—
698C4×D3—188no—
699Dic6—38no—
700Dic6—98no—
701Dic6—94no—
702Dic6—98no—
703Dic6—98no—
704Dic6—98no—
705Dic6—188no—
706C2×C32—22no—
707C2×C32—24no—
708C2×C32—24no—
709C2×C32—24no—
710C2×C32—22no—
711C2×C32—22no—
712C2×C32—21no—
713C2×C32—34no—
714C2×C32—42no—
715C2×C32—41no—
716C2×C32—44no—
717C2×C32—44no—
718C2×C32—62no—
719C2×C32—64no—
720C2×C32C2×#23714yescomplemented
721C2×C32D3×#4112yescomplemented
722C2×C32C24×D312yes—
723C2×C32C24×D311yescharacteristic
724C3⋊D3—24no—
725C3×D3—24no—
726C3×D3—24no—
727C3×D3—24no—
728C3×D3—24no—
729C3×D3—24no—
730C3×D3—44no—
731C3×D3—64no—
732C3×D3—64no—
733C3×D3—124no—
734C3×D3C2×#23718yescomplemented
735C24—31no—
736C24—92no—
737#41—98no—
738#41—2716no—
739#41—278no—
740#41—2716no—
741#41—278no—
742#41—278no—
743C2×Q8—91no—
744C2×Q8—272no—
745C2×Q8—271no—
746C2×Q8—278no—
747C2×D4—32no—
748C2×D4—92no—
749C2×D4—916no—
750C2×D4—92no—
751C2×D4—91no—
752C2×D4—92no—
753C2×D4—271no—
754C2×D4—278no—
755C2×D4—272no—
756C22×C4—92no—
757C22×C4—92no—
758C22×C4—91no—
759C22×C4—272no—
760C22×C4—2716no—
761C22×C4—272no—
762C22×C4—271no—
763C22×C4—271no—
764C22×C4—278no—
765C22×C4—271no—
766C22×C4—272no—
767C22×C4—271no—
768C22×C4—271no—
769C22×C3—24no—
770C22×C3—24no—
771C22×C3—22no—
772C22×C3—22no—
773C22×C3—24no—
774C22×C3—21no—
775C22×C3—22no—
776C22×C3—38no—
777C22×C3—34no—
778C22×C3—34no—
779C22×C3—34no—
780C22×C3—34no—
781C22×C3—44no—
782C22×C3—44no—
783C22×C3—42no—
784C22×C3—41no—
785C22×C3—62no—
786C22×C3—62no—
787C22×C3—64no—
788C22×C3—64no—
789C22×C3—616no—
790C22×C3—616no—
791C22×C3—64no—
792C22×C3—64no—
793C22×C3—64no—
794C22×C3—64no—
795C22×C3—94no—
796C22×C3—124no—
797C22×C3—1816no—
798C22×C3—184no—
799C22×C3C22×D3214yes—
800C22×C3C22×D3212yes—
801C22×C3C22×D3212yes—
802C22×C3C22×D3211yescharacteristic
803C2×D3—24no—
804C2×D3—22no—
805C2×D3—28no—
806C2×D3—34no—
807C2×D3—34no—
808C2×D3—64no—
809C2×D3—616no—
810C2×D3—64no—
811C2×D3—64no—
812C2×D3—616no—
813C2×D3—124no—
814C2×D3#380514yesdirect product factor
815C2×D3C22×D3214yes—
816C2×D3C22×D3212yes—
817C2×D3C22×D3212yes—
818C3×C4—34no—
819C3×C4—34no—
820C3×C4—64no—
821C3×C4—94no—
822C3×C4—92no—
823C3×C4—92no—
824Dic3—34no—
825Dic3—34no—
826Dic3—34no—
827Dic3—34no—
828Dic3—64no—
829Dic3—62no—
830Dic3—62no—
831Dic3—92no—
832Dic3—94no—
833Dic3—92no—
834Dic3—94no—
835Dic3—184no—
836Dic3—184no—
837Dic3—182no—
838Dic3—182no—
839Dic3—362no—
840Dic3—362no—
841Dic3C22×D3214yes—
842C32—22no—
843C32—21no—
844C32—41no—
845C32C22×#23712yescomplemented
846C32C2×D3×#4111yescharacteristic, complemented
847C23—31no—
848C23—34no—
849C23—32no—
850C23—31no—
851C23—64no—
852C23—98no—
853C23—92no—
854C23—188no—
855C23D3311yescharacteristic
856Q8—94no—
857Q8—278no—
858Q8—274no—
859D4—38no—
860D4—98no—
861D4—98no—
862D4—94no—
863D4—98no—
864D4—274no—
865D4—278no—
866C2×C4—32no—
867C2×C4—98no—
868C2×C4—98no—
869C2×C4—94no—
870C2×C4—91no—
871C2×C4—92no—
872C2×C4—91no—
873C2×C4—278no—
874C2×C4—278no—
875C2×C4—274no—
876C2×C4—274no—
877C2×C4—274no—
878C2×C4—278no—
879C2×C4—274no—
880C2×C4—274no—
881C2×C4—271no—
882C2×C4—271no—
883C2×C3—24no—
884C2×C3—24no—
885C2×C3—22no—
886C2×C3—24no—
887C2×C3—22no—
888C2×C3—21no—
889C2×C3—22no—
890C2×C3—38no—
891C2×C3—44no—
892C2×C3—44no—
893C2×C3—42no—
894C2×C3—41no—
895C2×C3—64no—
896C2×C3—64no—
897C2×C3—64no—
898C2×C3—64no—
899C2×C3—64no—
900C2×C3—124no—
901C2×C3—184no—
902C2×C3D3×#23714yescomplemented
903C2×C3C2×#380512yescomplemented
904C2×C3C23×D3212yes—
905C2×C3C23×D3211yescharacteristic
906D3—24no—
907D3—22no—
908D3—64no—
909D3—64no—
910D3—124no—
911D3C2×#380514yesdirect product factor
912C22—22no—
913C22—34no—
914C22—32no—
915C22—34no—
916C22—32no—
917C22—68no—
918C22—62no—
919C22—64no—
920C22—94no—
921C22—1816no—
922C22—184no—
923C22C2×D3312yes—
924C22C2×D3311yescharacteristic
925C4—34no—
926C4—92no—
927C4—94no—
928C4—92no—
929C4—272no—
930C4—272no—
931C3—22no—
932C3—21no—
933C3—41no—
934C3C2×D3×#23712yescomplemented
935C3C22×#380511yescharacteristic, complemented
936C2—22no—
937C2—34no—
938C2—62no—
939C2—64no—
940C2—184no—
941C2D3×#380512yesdirect product factor
942C2C22×D3311yescharacteristic
subgroupG/H
centerC22C2×D33
commutator, cosocleC2×C33C25
FrattiniC2C22×D33
FittingC23×C33C23
socleC22×C33C24
hypercenterC23D33
hypocenterC33C22×#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#89046C2semidirect
2. C2×#89029C2semidirect
3. C22×D3×C3⋊Dic3C2semidirect
4. C2×C3×D3×#67C2semidirect
5. C2×C3×#3805C2semidirect
6. C2×#88964C2semidirect
7. C2×#88963C2semidirect
8. C2×#88961C2semidirect
9. C2×D3×#627C2semidirect
10. C2×D3×#625C2semidirect
11. D3×#3805C2direct (N × H)
12. C2×D32×Dic3C2semidirect
17. C22×C3⋊(C3⋊Dic3)C22semidirect
18. C2×C3×#638C22semidirect
19. C22×C3×C3⋊Dic3C22semidirect
20. C2×C32×#67C22semidirect
21. C2×#6296C22semidirect
22. C2×#6295C22semidirect
23. #89046C22semidirect
24. C2×#6294C22semidirect
25. C2×#6293C22semidirect
26. C2×#6290C22semidirect
27. C2×Dic3×C3⋊D3C22semidirect
28. #89029C22semidirect
31. C2×D3×C3⋊Dic3C22semidirect
32. C2×D3×C3⋊Dic3C22semidirect
33. C2×D3×C3⋊Dic3C22semidirect
34. C2×D3×C3⋊Dic3C22semidirect
35. C3×D3×#67C22semidirect
36. C2×C3×#627C22semidirect
37. C2×C3×#626C22semidirect
38. C2×C3×#625C22semidirect
39. C2×C3×#625C22semidirect
40. C3×#3805C22semidirect
42. C2×C3×D3×Dic3C22semidirect
43. #88964C22semidirect
44. #88963C22semidirect
45. #88961C22semidirect
46. D3×#627C22semidirect
47. D3×#625C22semidirect
48. D32×Dic3C22semidirect
55. C2×D3×#67D3semidirect
67. C2×#3805D3direct (N × H)
90. C2×C3⋊(C3⋊Dic3)C23semidirect
91. C3×#638C23semidirect
95. C2×C3×C3⋊Dic3C23semidirect
96. C32×#67C23semidirect
98. #6296C23semidirect
99. #6295C23semidirect
100. #6294C23semidirect
101. #6293C23semidirect
102. #6290C23semidirect
103. Dic3×C3⋊D3C23semidirect
106. D3×C3⋊Dic3C23semidirect
107. D3×C3⋊Dic3C23semidirect
108. D3×C3⋊Dic3C23semidirect
109. C3×#627C23semidirect
110. C3×#626C23semidirect
111. C3×#625C23semidirect
112. C3×#625C23semidirect
114. C3×D3×Dic3C23semidirect
125. C2×#638C2×D3semidirect
137. C22×C3⋊Dic3C2×D3semidirect
150. C2×C3×#67C2×D3semidirect
151. C2×C3×#67C2×D3semidirect
163. D3×#67C2×D3semidirect
170. C2×#627C2×D3semidirect
172. C2×#626C2×D3semidirect
178. C2×#625C2×D3semidirect
179. C2×#625C2×D3semidirect
189. #3805C2×D3direct (N × H)
213. C2×D3×Dic3C2×D3semidirect
226. C2×C32×D3#41semidirect
301. #638C22×D3semidirect
325. C2×C3⋊Dic3C22×D3semidirect
336. C3×#67C22×D3semidirect
337. C3×#67C22×D3semidirect
361. #627C22×D3semidirect
363. #626C22×D3semidirect
368. #625C22×D3semidirect
369. #625C22×D3semidirect
388. D3×Dic3C22×D3semidirect
391. C2×C33C2×#41semidirect
396. C32×D3C2×#41semidirect
430. C2×#67D32semidirect
541. C2×C3×D3#237semidirect
583. C33C22×#41semidirect
644. #67C2×D32semidirect
720. C2×C32C2×#237semidirect
721. C2×C32D3×#41semidirect
734. C3×D3C2×#237semidirect
814. C2×D3#3805direct (N × H)
845. C32C22×#237semidirect
846. C32C2×D3×#41semidirect
902. C2×C3D3×#237semidirect
903. C2×C3C2×#3805semidirect
911. D3C2×#3805direct (N × H)
934. C3C2×D3×#237semidirect
935. C3C22×#3805semidirect
941. C2D3×#3805direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#890462
C2×#890292
C22×D3×C3⋊Dic32
C2×C3×D3×#672
C2×C3×#38052
C2×#889642
C2×#889632
C2×#889612
C2×D3×#6272
C2×D3×#6252
D3×#38052
C2×D32×Dic32
C22×#38053
C2×D3×#2373