Finite Group Databasebeta

← C2×#11724415 #13181322

Subgroups — C2×#11724415 #13181322

Order 1728.

4210 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89049C211yesmaximal, characteristic, complemented
2C22×#6290C211yesmaximal, characteristic, complemented
3C2×#89029C212yesmaximal, complemented
4C2×C3×#3811C211yesmaximal, characteristic, complemented
5C2×C3×D3×#67C212yesmaximal, complemented
6C2×#88961C212yesmaximal, complemented
7C2×#88960C212yesmaximal, complemented
8C2×#88953C212yesmaximal, complemented
9#11724415C2116yesmaximal, direct product factor
10C2×D3×#625C212yesmaximal, complemented
11C2×#64330—31nomaximal
12C2×#64313—32nomaximal
13C23×C3×C3⋊D3C2211yescharacteristic, complemented
14C23×C32×D3C2211yescharacteristic, complemented
15C22×#1113C2211yescharacteristic, complemented
16C22×C3×D32C2212yescomplemented
17C22×C3×D32C2211yescharacteristic, complemented
18C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
19C2×C3×#638C2212yescomplemented
20C2×C32×#67C2212yescomplemented
21#89049C2218yescomplemented
22C2×#6295C2212yescomplemented
23C2×#6294C2211yescharacteristic, complemented
24C2×#6293C2212yescomplemented
25C2×#6290C2212yescomplemented
26C2×#6290C2212yescomplemented
27C2×#6290C2212yescomplemented
28C2×#6290C2218yescomplemented
29C2×Dic3×C3⋊D3C2212yescomplemented
30#89029C22116yescomplemented
31C2×D3×C3⋊Dic3C2212yescomplemented
32C3×#3811C2218yescomplemented
33C3×D3×#67C22116yescomplemented
34C2×C3×#626C2212yescomplemented
35C2×C3×#626C2212yescomplemented
36C2×C3×#625C2212yescomplemented
37C2×C3×#624C2211yescharacteristic, complemented
38C2×C3×D3×Dic3C2212yescomplemented
39#88961C22116yescomplemented
40#88960C22116yescomplemented
41#88953C22116yescomplemented
42D3×#625C22116yescomplemented
43C22×#638—31no—
44C2×#3830—32no—
45C22×C3×#67—32no—
46C2×C3×D3×D4—32no—
47C2×C3×D3×D4—32no—
48#64330—316no—
49C2×#3811—31no—
50C2×#3811D311yescharacteristic, complemented
51C2×D3×#67—32no—
52C2×D3×#67—32no—
53C2×D3×#67—32no—
54C2×D3×#67—32no—
55C2×D3×#67—32no—
56C2×D3×#67D312yescomplemented
57C22×#625—32no—
58C22×#625—32no—
59C22×#625—61no—
60C2×#3805—32no—
61C2×#3805—32no—
62C2×#3805—32no—
63C2×#3805—62no—
64C2×#3804—32no—
65C2×#3804—32no—
66#64313—332no—
67C2×#3802—32no—
68C2×#3798—32no—
69C2×#3795—32no—
70C2×#3795—32no—
71C23×C33C2311yescharacteristic
72C22×C3×C3⋊D3—42no—
73C22×C3×C3⋊D3C2312yes—
74C22×C3×C3⋊D3C2311yescharacteristic
75C22×C3×C3⋊D3C2311yescharacteristic
76C22×C3×C3⋊D3C2314yescomplemented
77C22×C32×D3—42no—
78C22×C32×D3C2312yes—
79C22×C32×D3C2312yes—
80C22×C32×D3C2314yescomplemented
81C2×#1113—42no—
82C2×#1113C2314yescomplemented
83C2×C3×D32—42no—
84C2×C3×D32—44no—
85C2×C3×D32C2314yescomplemented
86C2×C3×D32C2318yescomplemented
87C2×C3⋊(C3⋊Dic3)C2312yes—
88C2×C3⋊(C3⋊Dic3)C2314yescomplemented
89C3×#638C2318yescomplemented
90C2×C3×C3⋊Dic3C2312yes—
91C32×#67C2318yescomplemented
92C2×C32×Dic3C2312yes—
93#6295C2318yescomplemented
94#6294C2314yescomplemented
95#6293C2318yescomplemented
96#6290C2318yescomplemented
97#6290C2318yescomplemented
98#6290C2318yescomplemented
99Dic3×C3⋊D3C2318yescomplemented
100D3×C3⋊Dic3C2318yescomplemented
101C3×#626C2318yescomplemented
102C3×#626C2318yescomplemented
103C3×#625C2318yescomplemented
104C3×#624C2314yescomplemented
105C3×D3×Dic3C2318yescomplemented
106C2×#1004—91no—
107C2×#1004—92no—
108C24×C32—31no—
109C23×C3⋊D3C2×D311yescharacteristic, complemented
110C23×C3×D3—21no—
111C23×C3×D3—32no—
112C23×C3×D3—32no—
113C23×C3×D3—32no—
114C23×C3×D3—32no—
115C23×C3×D3—61no—
116C23×C3×D3C2×D312yescomplemented
117C22×D32—32no—
118C22×D32—31no—
119C22×D32C2×D312yescomplemented
120C22×D32C2×D311yescharacteristic, complemented
121C2×C32×D4—32no—
122C2×#638—32no—
123C2×#638—32no—
124C2×#638—32no—
125C2×#638—38no—
126C2×#638C2×D312yescomplemented
127C22×C3⋊Dic3—31no—
128C22×C3⋊Dic3—32no—
129C22×C3⋊Dic3—32no—
130C22×C3⋊Dic3—62no—
131C22×C3⋊Dic3—61no—
132C22×C3⋊Dic3—121no—
133#3830—316no—
134C2×C4×C3⋊D3—32no—
135C2×#634—32no—
136C2×C3×#67—22no—
137C2×C3×#67—32no—
138C2×C3×#67—32no—
139C2×C3×#67—32no—
140C2×C3×#67—32no—
141C2×C3×#67—316no—
142C2×C3×#67—32no—
143C2×C3×#67—32no—
144C2×C3×#67—62no—
145C2×C3×#67C2×D312yescomplemented
146C2×C3×#67C2×D312yescomplemented
147C22×C3×Dic3—32no—
148C3×D3×D4—316no—
149C3×D3×D4—316no—
150C2×C3×D12—32no—
151C2×C3×D12—32no—
152C2×C3×C4×D3—32no—
153C2×C3×C4×D3—32no—
154#3811—38no—
155#3811C2×D318yescomplemented
156D3×#67—316no—
157D3×#67—316no—
158D3×#67—316no—
159D3×#67—316no—
160D3×#67—316no—
161D3×#67C2×D3116yescomplemented
162C2×#627—32no—
163C2×#627—32no—
164C2×#627—62no—
165C2×#626—32no—
166C2×#626—32no—
167C2×#626C2×D312yescomplemented
168C2×#626C2×D312yescomplemented
169C2×#625—32no—
170C2×#625—32no—
171C2×#625—32no—
172C2×#625—32no—
173C2×#625—32no—
174C2×#625—32no—
175C2×#625—316no—
176C2×#625—32no—
177C2×#625—316no—
178C2×#625—62no—
179C2×#625—62no—
180C2×#625—62no—
181C2×#625—68no—
182C2×#625C2×D312yescomplemented
183C2×#624—31no—
184C2×#624C2×D311yescharacteristic, complemented
185#3805—316no—
186#3805—316no—
187#3805—316no—
188#3805—616no—
189#3804—316no—
190#3804—316no—
191C2×D3×Dic3—32no—
192C2×D3×Dic3—32no—
193C2×D3×Dic3—32no—
194C2×D3×Dic3—32no—
195C2×D3×Dic3—32no—
196C2×D3×Dic3—62no—
197C2×D3×Dic3—62no—
198C2×D3×Dic3C2×D312yescomplemented
199#3802—316no—
200#3798—316no—
201#3795—316no—
202#3795—316no—
203C22×C33—22no—
204C22×C33C2412yes—
205C22×C33C2411yescharacteristic
206C2×C3×C3⋊D3—24no—
207C2×C3×C3⋊D3—22no—
208C2×C3×C3⋊D3—22no—
209C2×C3×C3⋊D3—44no—
210C2×C3×C3⋊D3C2412yes—
211C2×C3×C3⋊D3C2412yes—
212C2×C3×C3⋊D3C2414yes—
213C2×C32×D3—24no—
214C2×C32×D3—24no—
215C2×C32×D3—44no—
216C2×C32×D3C2414yes—
217C2×C32×D3C2414yes—
218#1113—44no—
219C3×D32—44no—
220C3×D32—48no—
221C3⋊(C3⋊Dic3)C2414yes—
222C3×C3⋊Dic3C2414yes—
223C32×Dic3C2414yes—
224C22×C3×D4—91no—
225C22×C3×D4—92no—
226C22×#67—32no—
227C22×#67—91no—
228C22×#67—92no—
229C22×#67—92no—
230C22×#67—92no—
231C22×#67—92no—
232C22×#67—91no—
233C22×#67—181no—
234#1004—916no—
235#1004—932no—
236C2×#237—92no—
237C2×#237—92no—
238C2×#237—92no—
239C2×#237—92no—
240C2×#237—92no—
241C2×#237—92no—
242C2×#237—182no—
243C2×D3×D4—32no—
244C2×D3×D4—32no—
245C2×D3×D4—92no—
246C2×D3×D4—92no—
247C2×D3×D4—92no—
248C2×D3×D4—92no—
249C2×#235—92no—
250C2×#235—92no—
251C2×#235—92no—
252C23×C32—21no—
253C23×C32—22no—
254C23×C32—32no—
255C23×C32—32no—
256C23×C32—34no—
257C23×C32—41no—
258C23×C32—122no—
259C23×C32C22×D312yes—
260C23×C32C22×D311yescharacteristic
261C22×C3⋊D3—42no—
262C22×C3⋊D3C22×D312yes—
263C22×C3⋊D3C22×D311yescharacteristic
264C22×C3⋊D3C22×D311yescharacteristic
265C22×C3⋊D3C22×D314yescomplemented
266C22×C3×D3—22no—
267C22×C3×D3—22no—
268C22×C3×D3—24no—
269C22×C3×D3—32no—
270C22×C3×D3—32no—
271C22×C3×D3—32no—
272C22×C3×D3—32no—
273C22×C3×D3—38no—
274C22×C3×D3—38no—
275C22×C3×D3—38no—
276C22×C3×D3—38no—
277C22×C3×D3—44no—
278C22×C3×D3—44no—
279C22×C3×D3—61no—
280C22×C3×D3—61no—
281C22×C3×D3—64no—
282C22×C3×D3—62no—
283C22×C3×D3—124no—
284C22×C3×D3—124no—
285C22×C3×D3—124no—
286C22×C3×D3—124no—
287C22×C3×D3—124no—
288C22×C3×D3C22×D312yes—
289C22×C3×D3C22×D312yes—
290C22×C3×D3C22×D312yes—
291C22×C3×D3C22×D312yes—
292C22×C3×D3C22×D318yescomplemented
293C2×D32—38no—
294C2×D32—34no—
295C2×D32—44no—
296C2×D32—42no—
297C2×D32—124no—
298C2×D32—122no—
299C2×D32C22×D318yescomplemented
300C2×D32C22×D314yescomplemented
301C32×D4—38no—
302C2×C32×C4—32no—
303#638—38no—
304#638—38no—
305#638—38no—
306#638C22×D318yescomplemented
307C2×C3⋊Dic3—32no—
308C2×C3⋊Dic3—32no—
309C2×C3⋊Dic3—32no—
310C2×C3⋊Dic3—34no—
311C2×C3⋊Dic3—38no—
312C2×C3⋊Dic3—38no—
313C2×C3⋊Dic3—62no—
314C2×C3⋊Dic3—62no—
315C2×C3⋊Dic3—62no—
316C2×C3⋊Dic3—68no—
317C2×C3⋊Dic3—64no—
318C2×C3⋊Dic3—122no—
319C2×C3⋊Dic3—124no—
320C2×C3⋊Dic3C22×D312yes—
321C4×C3⋊D3—38no—
322#634—38no—
323C3×#67—28no—
324C3×#67—38no—
325C3×#67—38no—
326C3×#67—38no—
327C3×#67—38no—
328C3×#67—38no—
329C3×#67—38no—
330C3×#67—68no—
331C3×#67C22×D318yescomplemented
332C3×#67C22×D318yescomplemented
333C2×C3×Dic3—22no—
334C2×C3×Dic3—32no—
335C2×C3×Dic3—32no—
336C2×C3×Dic3—38no—
337C2×C3×Dic3—62no—
338C2×C3×Dic3C22×D312yes—
339C2×C3×Dic3C22×D312yes—
340C3×D12—38no—
341C3×D12—38no—
342C3×C4×D3—38no—
343C3×C4×D3—38no—
344#627—38no—
345#627—38no—
346#627—68no—
347#626—38no—
348#626—38no—
349#626C22×D318yescomplemented
350#626C22×D318yescomplemented
351#625—38no—
352#625—38no—
353#625—38no—
354#625—38no—
355#625—38no—
356#625—38no—
357#625—38no—
358#625—68no—
359#625—68no—
360#625—68no—
361#625C22×D318yescomplemented
362#624—34no—
363#624C22×D314yescomplemented
364D3×Dic3—38no—
365D3×Dic3—38no—
366D3×Dic3—38no—
367D3×Dic3—38no—
368D3×Dic3—38no—
369D3×Dic3—68no—
370D3×Dic3—68no—
371D3×Dic3C22×D318yescomplemented
372C2×H(5,𝔽2)—271noSylow
373C2×C33—22no—
374C2×C33H(5,𝔽2)12yescomplemented
375C2×C33C2511yescharacteristic
376C3×C3⋊D3—24no—
377C3×C3⋊D3—22no—
378C3×C3⋊D3—22no—
379C32×D3—24no—
380C32×D3—24no—
381C24×C3—32no—
382C24×C3—61no—
383C24×C3—91no—
384C24×C3—92no—
385C24×C3—91no—
386C23×D3—32no—
387C23×D3—32no—
388C23×D3—32no—
389C23×D3—32no—
390C23×D3—61no—
391C23×D3—91no—
392C23×D3—92no—
393C23×D3D3211yescharacteristic, complemented
394C2×C3×D4—32no—
395C2×C3×D4—32no—
396C2×C3×D4—62no—
397C2×C3×D4—92no—
398C2×C3×D4—92no—
399C2×C3×D4—98no—
400C2×C3×D4—916no—
401C2×C3×D4—92no—
402C2×C3×D4—92no—
403C22×C3×C4—91no—
404C22×C3×C4—92no—
405C2×#67—32no—
406C2×#67—32no—
407C2×#67—32no—
408C2×#67—32no—
409C2×#67—316no—
410C2×#67—32no—
411C2×#67—32no—
412C2×#67—62no—
413C2×#67—92no—
414C2×#67—92no—
415C2×#67—98no—
416C2×#67—916no—
417C2×#67—916no—
418C2×#67—916no—
419C2×#67—92no—
420C2×#67—92no—
421C2×#67—92no—
422C2×#67—92no—
423C2×#67—92no—
424C2×#67—92no—
425C2×#67—916no—
426C2×#67—92no—
427C2×#67—92no—
428C2×#67—92no—
429C2×#67—98no—
430C2×#67—182no—
431C2×#67—182no—
432C2×#67—182no—
433C2×#67—188no—
434C2×#67D3212yescomplemented
435C22×Dic3—32no—
436C22×Dic3—91no—
437C22×Dic3—92no—
438C22×Dic3—92no—
439C22×Dic3—91no—
440C22×Dic3—92no—
441C22×Dic3—92no—
442C22×Dic3—182no—
443C22×Dic3—182no—
444C22×Dic3—181no—
445C22×Dic3—361no—
446#237—916no—
447#237—916no—
448#237—916no—
449#237—916no—
450#237—916no—
451#237—916no—
452#237—1816no—
453D3×D4—316no—
454D3×D4—316no—
455D3×D4—916no—
456D3×D4—916no—
457D3×D4—916no—
458D3×D4—916no—
459#235—916no—
460#235—916no—
461#235—916no—
462C2×D12—32no—
463C2×D12—32no—
464C2×D12—92no—
465C2×C4×D3—32no—
466C2×C4×D3—32no—
467C2×C4×D3—92no—
468C2×C4×D3—92no—
469C2×C4×D3—92no—
470C2×C4×D3—92no—
471C2×C4×D3—182no—
472C2×Dic6—92no—
473C2×Dic6—92no—
474C2×Dic6—92no—
475C2×Dic6—182no—
476C22×C32—22no—
477C22×C32—24no—
478C22×C32—24no—
479C22×C32—22no—
480C22×C32—22no—
481C22×C32—21no—
482C22×C32—24no—
483C22×C32—34no—
484C22×C32—34no—
485C22×C32—42no—
486C22×C32—41no—
487C22×C32—44no—
488C22×C32—44no—
489C22×C32—64no—
490C22×C32—64no—
491C22×C32—124no—
492C22×C32C23×D312yes—
493C22×C32C23×D314yes—
494C22×C32C23×D311yescharacteristic
495C22×C32C23×D312yes—
496C2×C3⋊D3—24no—
497C2×C3⋊D3—22no—
498C2×C3⋊D3—22no—
499C2×C3⋊D3—44no—
500C2×C3⋊D3C23×D312yes—
501C2×C3⋊D3C23×D312yes—
502C2×C3⋊D3C23×D314yes—
503C2×C3×D3—24no—
504C2×C3×D3—24no—
505C2×C3×D3—24no—
506C2×C3×D3—24no—
507C2×C3×D3—24no—
508C2×C3×D3—24no—
509C2×C3×D3—34no—
510C2×C3×D3—34no—
511C2×C3×D3—34no—
512C2×C3×D3—34no—
513C2×C3×D3—44no—
514C2×C3×D3—44no—
515C2×C3×D3—48no—
516C2×C3×D3—48no—
517C2×C3×D3—64no—
518C2×C3×D3—62no—
519C2×C3×D3—62no—
520C2×C3×D3—64no—
521C2×C3×D3—64no—
522C2×C3×D3—64no—
523C2×C3×D3—64no—
524C2×C3×D3—124no—
525C2×C3×D3—122no—
526C2×C3×D3—122no—
527C2×C3×D3—128no—
528C2×C3×D3—128no—
529C2×C3×D3—128no—
530C2×C3×D3—128no—
531C2×C3×D3—128no—
532C2×C3×D3C23×D314yes—
533C2×C3×D3C23×D314yes—
534C2×C3×D3C23×D314yes—
535C2×C3×D3C23×D314yes—
536D32—48no—
537D32—44no—
538D32—128no—
539D32—124no—
540C32×C4—34no—
541C3⋊Dic3—34no—
542C3⋊Dic3—34no—
543C3⋊Dic3—34no—
544C3⋊Dic3—64no—
545C3⋊Dic3—64no—
546C3⋊Dic3—64no—
547C3⋊Dic3—124no—
548C3⋊Dic3C23×D314yes—
549C3×Dic3—24no—
550C3×Dic3—34no—
551C3×Dic3—34no—
552C3×Dic3—64no—
553C3×Dic3C23×D314yes—
554C3×Dic3C23×D314yes—
555H(5,𝔽2)—2716no—
556C2×#41—272no—
557C2×#41—272no—
558C2×#41—272no—
559C22×D4—91no—
560C22×D4—92no—
561C22×D4—272no—
562C22×D4—271no—
563C22×D4—272no—
564C22×D4—271no—
565C33C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
566C23×C3—21no—
567C23×C3—22no—
568C23×C3—32no—
569C23×C3—32no—
570C23×C3—32no—
571C23×C3—32no—
572C23×C3—38no—
573C23×C3—41no—
574C23×C3—62no—
575C23×C3—62no—
576C23×C3—64no—
577C23×C3—94no—
578C23×C3—98no—
579C23×C3—92no—
580C23×C3—91no—
581C23×C3—91no—
582C23×C3—94no—
583C23×C3—124no—
584C23×C3—124no—
585C23×C3—362no—
586C23×C3—364no—
587C23×C3—362no—
588C23×C3C2×D3211yescharacteristic
589C23×C3C2×D3212yes—
590C22×D3—32no—
591C22×D3—32no—
592C22×D3—32no—
593C22×D3—32no—
594C22×D3—38no—
595C22×D3—38no—
596C22×D3—38no—
597C22×D3—38no—
598C22×D3—42no—
599C22×D3—62no—
600C22×D3—61no—
601C22×D3—61no—
602C22×D3—64no—
603C22×D3—94no—
604C22×D3—98no—
605C22×D3—124no—
606C22×D3—124no—
607C22×D3—124no—
608C22×D3—124no—
609C22×D3—124no—
610C22×D3—364no—
611C22×D3—362no—
612C22×D3C2×D3212yes—
613C22×D3C2×D3212yes—
614C22×D3C2×D3214yescomplemented
615C3×D4—38no—
616C3×D4—38no—
617C3×D4—68no—
618C3×D4—98no—
619C3×D4—98no—
620C3×D4—98no—
621C3×D4—98no—
622C2×C3×C4—32no—
623C2×C3×C4—32no—
624C2×C3×C4—62no—
625C2×C3×C4—94no—
626C2×C3×C4—98no—
627C2×C3×C4—92no—
628#67—38no—
629#67—38no—
630#67—38no—
631#67—38no—
632#67—38no—
633#67—38no—
634#67—68no—
635#67—98no—
636#67—98no—
637#67—98no—
638#67—98no—
639#67—98no—
640#67—98no—
641#67—98no—
642#67—98no—
643#67—98no—
644#67—98no—
645#67—98no—
646#67—188no—
647#67—188no—
648#67—188no—
649#67C2×D3218yescomplemented
650C2×Dic3—32no—
651C2×Dic3—32no—
652C2×Dic3—38no—
653C2×Dic3—62no—
654C2×Dic3—94no—
655C2×Dic3—98no—
656C2×Dic3—98no—
657C2×Dic3—92no—
658C2×Dic3—92no—
659C2×Dic3—92no—
660C2×Dic3—94no—
661C2×Dic3—98no—
662C2×Dic3—98no—
663C2×Dic3—188no—
664C2×Dic3—182no—
665C2×Dic3—182no—
666C2×Dic3—188no—
667C2×Dic3—184no—
668C2×Dic3—182no—
669C2×Dic3—364no—
670C2×Dic3—362no—
671C2×Dic3C2×D3212yes—
672D12—38no—
673D12—38no—
674D12—98no—
675C4×D3—38no—
676C4×D3—38no—
677C4×D3—98no—
678C4×D3—98no—
679C4×D3—98no—
680C4×D3—98no—
681C4×D3—188no—
682Dic6—98no—
683Dic6—98no—
684Dic6—98no—
685Dic6—188no—
686C2×C32—22no—
687C2×C32—24no—
688C2×C32—24no—
689C2×C32—24no—
690C2×C32—22no—
691C2×C32—22no—
692C2×C32—21no—
693C2×C32—42no—
694C2×C32—41no—
695C2×C32—44no—
696C2×C32—44no—
697C2×C32—64no—
698C2×C32—64no—
699C2×C32#100412yescomplemented
700C2×C32#100414yescomplemented
701C2×C32C24×D311yescharacteristic
702C2×C32C24×D312yes—
703C3⋊D3—24no—
704C3⋊D3—22no—
705C3⋊D3—22no—
706C3×D3—24no—
707C3×D3—24no—
708C3×D3—24no—
709C3×D3—24no—
710C3×D3—44no—
711C3×D3—44no—
712C3×D3—64no—
713C3×D3—64no—
714C3×D3—64no—
715C3×D3—64no—
716C3×D3—124no—
717C3×D3—122no—
718C3×D3—122no—
719C24—31no—
720C24—92no—
721C24—91no—
722C24—91no—
723C24—271no—
724#41—2716no—
725#41—2716no—
726#41—2716no—
727C2×Q8—272no—
728C2×D4—32no—
729C2×D4—92no—
730C2×D4—92no—
731C2×D4—98no—
732C2×D4—916no—
733C2×D4—92no—
734C2×D4—92no—
735C2×D4—272no—
736C2×D4—2716no—
737C2×D4—278no—
738C2×D4—2716no—
739C2×D4—272no—
740C2×D4—272no—
741C2×D4—272no—
742C2×D4—278no—
743C22×C4—91no—
744C22×C4—92no—
745C22×C4—272no—
746C22×C4—271no—
747C22×C4—272no—
748C22×C4—271no—
749C22×C3—24no—
750C22×C3—24no—
751C22×C3—22no—
752C22×C3—22no—
753C22×C3—24no—
754C22×C3—22no—
755C22×C3—21no—
756C22×C3—34no—
757C22×C3—34no—
758C22×C3—34no—
759C22×C3—34no—
760C22×C3—44no—
761C22×C3—44no—
762C22×C3—42no—
763C22×C3—41no—
764C22×C3—64no—
765C22×C3—64no—
766C22×C3—64no—
767C22×C3—64no—
768C22×C3—64no—
769C22×C3—64no—
770C22×C3—94no—
771C22×C3—92no—
772C22×C3—92no—
773C22×C3—124no—
774C22×C3—124no—
775C22×C3—128no—
776C22×C3—128no—
777C22×C3—184no—
778C22×C3—182no—
779C22×C3—182no—
780C22×C3—364no—
781C22×C3—368no—
782C22×C3—364no—
783C22×C3C22×D3212yes—
784C22×C3C22×D3214yes—
785C22×C3C22×D3212yes—
786C22×C3C22×D3211yescharacteristic
787C2×D3—24no—
788C2×D3—24no—
789C2×D3—34no—
790C2×D3—34no—
791C2×D3—34no—
792C2×D3—34no—
793C2×D3—44no—
794C2×D3—64no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—64no—
798C2×D3—64no—
799C2×D3—64no—
800C2×D3—64no—
801C2×D3—122no—
802C2×D3—122no—
803C2×D3—124no—
804C2×D3—128no—
805C2×D3—128no—
806C2×D3—128no—
807C2×D3—128no—
808C2×D3—128no—
809C2×D3—368no—
810C2×D3—364no—
811C2×D3C22×D3214yes—
812C2×D3C22×D3214yes—
813C3×C4—34no—
814C3×C4—34no—
815C3×C4—64no—
816C3×C4—94no—
817Dic3—34no—
818Dic3—34no—
819Dic3—64no—
820Dic3—94no—
821Dic3—94no—
822Dic3—94no—
823Dic3—184no—
824Dic3—184no—
825Dic3—184no—
826Dic3—364no—
827Dic3C22×D3214yes—
828C32—22no—
829C32—21no—
830C32—41no—
831C32C2×#100411yescharacteristic, complemented
832C32C2×#100412yescomplemented
833C23—32no—
834C23—32no—
835C23—34no—
836C23—98no—
837C23—94no—
838C23—91no—
839C23—92no—
840C23—91no—
841C23—94no—
842C23—122no—
843C23—274no—
844C23—362no—
845C23—364no—
846C23—362no—
847C23—1082no—
848C23D3311yescharacteristic
849Q8—278no—
850D4—38no—
851D4—98no—
852D4—98no—
853D4—98no—
854D4—98no—
855D4—278no—
856D4—278no—
857D4—278no—
858D4—278no—
859C2×C4—32no—
860C2×C4—94no—
861C2×C4—98no—
862C2×C4—92no—
863C2×C4—278no—
864C2×C4—274no—
865C2×C4—278no—
866C2×C4—274no—
867C2×C4—272no—
868C2×C3—24no—
869C2×C3—24no—
870C2×C3—22no—
871C2×C3—22no—
872C2×C3—24no—
873C2×C3—22no—
874C2×C3—21no—
875C2×C3—44no—
876C2×C3—44no—
877C2×C3—42no—
878C2×C3—41no—
879C2×C3—64no—
880C2×C3—64no—
881C2×C3—64no—
882C2×C3—64no—
883C2×C3—124no—
884C2×C3—124no—
885C2×C3—184no—
886C2×C3—182no—
887C2×C3—182no—
888C2×C3#6431314yescomplemented
889C2×C3#6433012yescomplemented
890C2×C3C23×D3212yes—
891C2×C3C23×D3211yescharacteristic
892D3—24no—
893D3—24no—
894D3—64no—
895D3—64no—
896D3—64no—
897D3—64no—
898D3—122no—
899D3—122no—
900D3—124no—
901C22—22no—
902C22—34no—
903C22—34no—
904C22—64no—
905C22—64no—
906C22—92no—
907C22—94no—
908C22—92no—
909C22—124no—
910C22—182no—
911C22—182no—
912C22—184no—
913C22—364no—
914C22—368no—
915C22—364no—
916C22—1084no—
917C22C2×D3312yes—
918C22C2×D3311yescharacteristic
919C4—34no—
920C4—94no—
921C4—274no—
922C3—21no—
923C3—22no—
924C3—41no—
925C3C2×#6431312yescomplemented
926C3C2×#6433011yescharacteristic, complemented
927C2—22no—
928C2—64no—
929C2—64no—
930C2—182no—
931C2—182no—
932C2—184no—
933C2#1172441512yesdirect product factor
934C2C22×D3311yescharacteristic
subgroupG/H
centerC22C2×D33
commutator, cosocleC2×C33C25
FrattiniC2C22×D33
FittingC23×C33C23
socleC22×C33C24
hypercenterC23D33
hypocenterC33C2×H(5,𝔽2)
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#89049C2semidirect
2. C22×#6290C2semidirect
3. C2×#89029C2semidirect
4. C2×C3×#3811C2semidirect
5. C2×C3×D3×#67C2semidirect
6. C2×#88961C2semidirect
7. C2×#88960C2semidirect
8. C2×#88953C2semidirect
9. #11724415C2direct (N × H)
10. C2×D3×#625C2semidirect
13. C23×C3×C3⋊D3C22semidirect
14. C23×C32×D3C22semidirect
15. C22×#1113C22semidirect
16. C22×C3×D32C22semidirect
17. C22×C3×D32C22semidirect
18. C22×C3⋊(C3⋊Dic3)C22semidirect
19. C2×C3×#638C22semidirect
20. C2×C32×#67C22semidirect
21. #89049C22semidirect
22. C2×#6295C22semidirect
23. C2×#6294C22semidirect
24. C2×#6293C22semidirect
25. C2×#6290C22semidirect
26. C2×#6290C22semidirect
27. C2×#6290C22semidirect
28. C2×#6290C22semidirect
29. C2×Dic3×C3⋊D3C22semidirect
30. #89029C22semidirect
31. C2×D3×C3⋊Dic3C22semidirect
32. C3×#3811C22semidirect
33. C3×D3×#67C22semidirect
34. C2×C3×#626C22semidirect
35. C2×C3×#626C22semidirect
36. C2×C3×#625C22semidirect
37. C2×C3×#624C22semidirect
38. C2×C3×D3×Dic3C22semidirect
39. #88961C22semidirect
40. #88960C22semidirect
41. #88953C22semidirect
42. D3×#625C22semidirect
50. C2×#3811D3semidirect
56. C2×D3×#67D3semidirect
76. C22×C3×C3⋊D3C23semidirect
80. C22×C32×D3C23semidirect
82. C2×#1113C23semidirect
85. C2×C3×D32C23semidirect
86. C2×C3×D32C23semidirect
88. C2×C3⋊(C3⋊Dic3)C23semidirect
89. C3×#638C23semidirect
91. C32×#67C23semidirect
93. #6295C23semidirect
94. #6294C23semidirect
95. #6293C23semidirect
96. #6290C23semidirect
97. #6290C23semidirect
98. #6290C23semidirect
99. Dic3×C3⋊D3C23semidirect
100. D3×C3⋊Dic3C23semidirect
101. C3×#626C23semidirect
102. C3×#626C23semidirect
103. C3×#625C23semidirect
104. C3×#624C23semidirect
105. C3×D3×Dic3C23semidirect
109. C23×C3⋊D3C2×D3semidirect
116. C23×C3×D3C2×D3semidirect
119. C22×D32C2×D3semidirect
120. C22×D32C2×D3semidirect
126. C2×#638C2×D3semidirect
145. C2×C3×#67C2×D3semidirect
146. C2×C3×#67C2×D3semidirect
155. #3811C2×D3semidirect
161. D3×#67C2×D3semidirect
167. C2×#626C2×D3semidirect
168. C2×#626C2×D3semidirect
182. C2×#625C2×D3semidirect
184. C2×#624C2×D3semidirect
198. C2×D3×Dic3C2×D3semidirect
265. C22×C3⋊D3C22×D3semidirect
292. C22×C3×D3C22×D3semidirect
299. C2×D32C22×D3semidirect
300. C2×D32C22×D3semidirect
306. #638C22×D3semidirect
331. C3×#67C22×D3semidirect
332. C3×#67C22×D3semidirect
349. #626C22×D3semidirect
350. #626C22×D3semidirect
361. #625C22×D3semidirect
363. #624C22×D3semidirect
371. D3×Dic3C22×D3semidirect
374. C2×C33H(5,𝔽2)semidirect
393. C23×D3D32semidirect
434. C2×#67D32semidirect
565. C33C2×H(5,𝔽2)semidirect
614. C22×D3C2×D32semidirect
649. #67C2×D32semidirect
699. C2×C32#1004semidirect
700. C2×C32#1004semidirect
831. C32C2×#1004semidirect
832. C32C2×#1004semidirect
888. C2×C3#64313semidirect
889. C2×C3#64330semidirect
925. C3C2×#64313semidirect
926. C3C2×#64330semidirect
933. C2#11724415direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#890492
C22×#62902
C2×#890292
C2×C3×#38112
C2×C3×D3×#672
C2×#889612
C2×#889602
C2×#889532
#117244152
C2×D3×#6252
C2×#643303
C2×#643133