Finite Group Databasebeta

← C2×#11722885 #13170682

Subgroups — C2×#11722885 #13170682

Order 1728.

1386 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89022C211yesmaximal, characteristic
2C2×C3×D3×Dic6C211yesmaximal, characteristic, complemented
3C2×#88812C211yesmaximal, characteristic, complemented
4C2×#88797C211yesmaximal, characteristic, complemented
5C2×#88795C211yesmaximal, characteristic, complemented
6C2×C3×#3719C211yesmaximal, characteristic, complemented
7C2×C3×#3711C211yesmaximal, characteristic, complemented
8#11722885C218yesmaximal, direct product factor
9C2×#63948—31nomaximal
10C2×#63833—31nomaximal
11C2×#63801—31nomaximal
12C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
13C2×C3×#634C2211yescharacteristic
14C2×C3×#634C2211yescharacteristic
15C2×C32×C4×D3C2211yescharacteristic
16C2×C32×Dic6C2211yescharacteristic
17C2×#6291—21no—
18C2×#6289—21no—
19#89022—22no—
20#89022C2214yes—
21C2×C3×#627—21no—
22C2×C3×D3×Dic3—21no—
23C3×D3×Dic6—22no—
24C3×D3×Dic6C2214yescomplemented
25C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
26C2×C32×C3⋊C8C2211yescharacteristic
27#88812C2214yescomplemented
28#88797C2214yescomplemented
29#88795C2214yescomplemented
30C3×#3719C2214yescomplemented
31C3×#3711C2214yescomplemented
32C2×#3828—31no—
33C2×C3×D3×Q8—31no—
34C22×C3×Dic6—31no—
35C2×#3799—31no—
36C2×#3799—31no—
37C2×#3799—61no—
38C2×D3×Dic6D311yescharacteristic, complemented
39C2×#3755—31no—
40C2×#3744—31no—
41C2×C3×#216—31no—
42C2×C3×#208—31no—
43C2×C3×Dic12—31no—
44C2×C3×ΓL(1,𝔽25)—31no—
45#63948—38no—
46C2×#3719—31no—
47C2×#3719—31no—
48C2×#3719D311yescharacteristic, complemented
49C2×#3718—31no—
50#63833—38no—
51C2×#3717—31no—
52C2×#3717—31no—
53C2×#3717—31no—
54C2×#3717—31no—
55C2×#3717—61no—
56C2×#3717—61no—
57C2×#3711D311yescharacteristic, complemented
58#63801—38no—
59C22×C3⋊(C3⋊D3)—21no—
60C22×C32×D3D411yescharacteristic
61C2×C33×C4C2311yescharacteristic
62C4⋊(C3⋊(C3⋊D3))—21no—
63C4⋊(C3⋊(C3⋊D3))C2312yes—
64C2×C3×C3⋊Dic3—21no—
65C2×C3×C3⋊Dic3—21no—
66C3×#634—21no—
67C3×#634—21no—
68C3×#634C2312yes—
69C3×#634C2312yes—
70C2×C32×Dic3—21no—
71C2×C32×Dic3D411yescharacteristic
72C32×C4×D3D412yes—
73C32×C4×D3C2312yes—
74C32×Dic6—21no—
75C32×Dic6C2312yes—
76#6291—24no—
77#6289—24no—
78C3×#627—24no—
79C3×D3×Dic3—24no—
80C3×C3⋊(C3⋊C8)C2312yes—
81C32×C3⋊C8C2312yes—
82C2×#942—91no—
83C2×#918—91no—
84C2×#909—91no—
85C2×C32×Q8—31no—
86C22×C32×C4—31no—
87C2×#638—61no—
88#3828—34no—
89#3828—62no—
90C2×C4⋊(C3⋊D3)—31no—
91C2×C4⋊(C3⋊D3)—31no—
92C2×C4⋊(C3⋊D3)—31no—
93C2×C4⋊(C3⋊D3)—61no—
94C2×C4⋊(C3⋊D3)—61no—
95C2×C4⋊(C3⋊D3)—61no—
96C2×C4⋊(C3⋊D3)—121no—
97C2×C4×C3⋊D3—61no—
98C2×#634C2×D311yescharacteristic
99C2×#634C2×D311yescharacteristic
100C22×C3×Dic3—61no—
101C3×D3×Q8—34no—
102C3×D3×Q8—62no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—61no—
105C2×C3×C4×D3C2×D311yescharacteristic
106C2×C3×C4×D3C2×D311yescharacteristic
107C2×C3×Dic6—21no—
108C2×C3×Dic6—31no—
109C2×C3×Dic6—31no—
110C2×C3×Dic6—31no—
111C2×C3×Dic6—31no—
112C2×C3×Dic6—34no—
113C2×C3×Dic6—62no—
114C2×C3×Dic6—61no—
115C2×C3×Dic6—61no—
116C2×C3×Dic6—61no—
117C2×C3×Dic6—61no—
118C2×C3×Dic6C2×D311yescharacteristic
119C2×C3×Dic6C2×D311yescharacteristic
120C2×#627—21no—
121C2×#626—62no—
122C2×#626—61no—
123C2×#626—61no—
124C2×#624—62no—
125C2×#624—61no—
126C2×#624—61no—
127C2×D3×Dic3—21no—
128#3799—34no—
129#3799—34no—
130#3799—64no—
131#3799—64no—
132#3799—62no—
133#3799—62no—
134D3×Dic6—22no—
135D3×Dic6C2×D314yescomplemented
136C2×C32×C8—31no—
137#3755—34no—
138C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
139#3744—34no—
140C3×#216—34no—
141C3×#208—34no—
142C2×C3×C3⋊C8—21no—
143C2×C3×C3⋊C8—31no—
144C2×C3×C3⋊C8—31no—
145C2×C3×C3⋊C8—61no—
146C2×C3×C3⋊C8C2×D311yescharacteristic
147C2×C3×C3⋊C8C2×D311yescharacteristic
148C3×Dic12—34no—
149C3×ΓL(1,𝔽25)—34no—
150#3719—34no—
151#3719—34no—
152#3719C2×D314yescomplemented
153#3718—34no—
154#3717—34no—
155#3717—34no—
156#3717—34no—
157#3717—34no—
158#3717—64no—
159#3717—64no—
160#3711C2×D314yescomplemented
161C22×C33C2×D411yescharacteristic
162C2×C3⋊(C3⋊D3)—22no—
163C2×C3⋊(C3⋊D3)—42no—
164C2×C32×D3—22no—
165C2×C32×D3C2×D412yes—
166C33×C4C2×D411yescharacteristic
167C33×C4C2411yescharacteristic
168C3×C3⋊Dic3—22no—
169C3×C3⋊Dic3—22no—
170C32×Dic3—22no—
171C32×Dic3C2×D412yes—
172C22×C3×Q8—91no—
173C2×#239—91no—
174C2×D3×Q8—31no—
175C2×#235—91no—
176C2×#235—91no—
177C2×#235—181no—
178C22×Dic6—31no—
179C2×C3×Q16—91no—
180C2×C3×M16—91no—
181C2×#216—31no—
182C2×#216—91no—
183C2×#216—91no—
184#942—98no—
185C2×#215—91no—
186C2×#215—91no—
187C2×#215—91no—
188C2×#215—181no—
189C2×#208—31no—
190#918—98no—
191#909—98no—
192C2×Dic12—31no—
193C2×Dic12—91no—
194C2×#204—91no—
195C2×#204—91no—
196C2×#204—91no—
197C2×#204—181no—
198C2×ΓL(1,𝔽25)—31no—
199C23×C32—31no—
200C22×C3⋊D3—61no—
201C22×C3⋊D3—62no—
202C22×C3⋊D3—61no—
203C22×C3⋊D3—61no—
204C22×C3⋊D3—121no—
205C22×C3⋊D3—121no—
206C22×C3⋊D3—122no—
207C22×C3×D3—21no—
208C22×C3×D3D1211yescharacteristic
209C22×C3×D3#6711yescharacteristic
210C32×Q8—32no—
211C32×Q8—61no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—31no—
216C2×C32×C4—32no—
217C2×C32×C4—32no—
218C2×C32×C4—41no—
219C2×C32×C4—61no—
220C2×C32×C4C22×D311yescharacteristic
221C2×C32×C4C22×D311yescharacteristic
222C2×C32×C4C22×D311yescharacteristic
223#638—64no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C4⋊(C3⋊D3)—32no—
227C4⋊(C3⋊D3)—32no—
228C4⋊(C3⋊D3)—32no—
229C4⋊(C3⋊D3)—62no—
230C4⋊(C3⋊D3)—62no—
231C4⋊(C3⋊D3)—62no—
232C4⋊(C3⋊D3)—61no—
233C4⋊(C3⋊D3)—62no—
234C4⋊(C3⋊D3)—61no—
235C4⋊(C3⋊D3)—61no—
236C4⋊(C3⋊D3)—122no—
237C4⋊(C3⋊D3)—121no—
238C4⋊(C3⋊D3)—121no—
239C4⋊(C3⋊D3)—122no—
240C4×C3⋊D3—64no—
241#634—21no—
242#634—21no—
243#634C22×D312yes—
244#634C22×D312yes—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—41no—
249C2×C3×Dic3—64no—
250C2×C3×Dic3—62no—
251C2×C3×Dic3—61no—
252C2×C3×Dic3—61no—
253C2×C3×Dic3—61no—
254C2×C3×Dic3—61no—
255C2×C3×Dic3—121no—
256C2×C3×Dic3D1211yescharacteristic
257C2×C3×Dic3#6711yescharacteristic
258C3×C4×D3—22no—
259C3×C4×D3—22no—
260C3×C4×D3—64no—
261C3×C4×D3D1212yes—
262C3×C4×D3#6712yes—
263C3×C4×D3C22×D312yes—
264C3×C4×D3C22×D312yes—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—22no—
268C3×Dic6—32no—
269C3×Dic6—32no—
270C3×Dic6—32no—
271C3×Dic6—32no—
272C3×Dic6—41no—
273C3×Dic6—62no—
274C3×Dic6—62no—
275C3×Dic6—64no—
276C3×Dic6—62no—
277C3×Dic6—61no—
278C3×Dic6—61no—
279C3×Dic6—61no—
280C3×Dic6—61no—
281C3×Dic6—64no—
282C3×Dic6—121no—
283C3×Dic6C22×D312yes—
284C3×Dic6C22×D312yes—
285#627—24no—
286#626—68no—
287#626—64no—
288#626—64no—
289#624—68no—
290#624—64no—
291#624—64no—
292D3×Dic3—24no—
293C32×C8—32no—
294C3⋊(C3⋊C8)C22×D312yes—
295C3×C3⋊C8—22no—
296C3×C3⋊C8—32no—
297C3×C3⋊C8—32no—
298C3×C3⋊C8—62no—
299C3×C3⋊C8C22×D312yes—
300C3×C3⋊C8C22×D312yes—
301C2×#137—271noSylow
302C2×C33#13712yescomplemented
303C2×C33C22×D411yescharacteristic
304C3⋊(C3⋊D3)—42no—
305C32×D3—22no—
306C2×C3×Q8—31no—
307C2×C3×Q8—31no—
308C2×C3×Q8—61no—
309C2×C3×Q8—94no—
310C2×C3×Q8—91no—
311C2×C3×Q8—91no—
312C2×C3×Q8—181no—
313C2×C3×Q8—182no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—61no—
317C22×C3×C4—181no—
318C2×#67—181no—
319C2×#67—181no—
320C2×#67—182no—
321C22×Dic3—61no—
322#239—94no—
323#239—182no—
324D3×Q8—34no—
325D3×Q8—62no—
326#235—94no—
327#235—94no—
328#235—184no—
329#235—182no—
330#235—182no—
331#235—184no—
332C2×D12—91no—
333C2×D12—91no—
334C2×D12—91no—
335C2×D12—181no—
336C2×D12—181no—
337C2×D12—181no—
338C2×D12—181no—
339C2×D12—361no—
340C2×C4×D3—61no—
341C2×C4×D3—181no—
342C2×C4×D3—181no—
343C2×C4×D3—182no—
344C2×C4×D3—181no—
345C2×C4×D3D3211yescharacteristic
346C2×Dic6—31no—
347C2×Dic6—31no—
348C2×Dic6—31no—
349C2×Dic6—31no—
350C2×Dic6—34no—
351C2×Dic6—61no—
352C2×Dic6—61no—
353C2×Dic6—62no—
354C2×Dic6—61no—
355C2×Dic6—61no—
356C2×Dic6D3211yescharacteristic
357C3×Q16—94no—
358C3×M16—94no—
359C2×C3×C8—31no—
360C2×C3×C8—31no—
361C2×C3×C8—61no—
362C2×C3×C8—91no—
363#216—34no—
364#216—94no—
365#216—94no—
366#215—94no—
367#215—94no—
368#215—94no—
369#215—184no—
370#208—34no—
371C2×C3⋊C8—31no—
372C2×C3⋊C8—31no—
373C2×C3⋊C8—61no—
374C2×C3⋊C8D3211yescharacteristic
375Dic12—34no—
376Dic12—94no—
377#204—94no—
378#204—94no—
379#204—94no—
380#204—184no—
381ΓL(1,𝔽25)—34no—
382C22×C32—21no—
383C22×C32—21no—
384C22×C32—21no—
385C22×C32—32no—
386C22×C32—41no—
387C22×C32—62no—
388C22×C32C2×D1211yescharacteristic
389C22×C32D3×D411yescharacteristic
390C22×C32C2×#6711yescharacteristic
391C2×C3⋊D3—62no—
392C2×C3⋊D3—64no—
393C2×C3⋊D3—62no—
394C2×C3⋊D3—62no—
395C2×C3⋊D3—122no—
396C2×C3⋊D3—122no—
397C2×C3⋊D3—124no—
398C2×C3⋊D3—122no—
399C2×C3⋊D3—124no—
400C2×C3⋊D3—122no—
401C2×C3⋊D3—122no—
402C2×C3⋊D3—242no—
403C2×C3⋊D3—242no—
404C2×C3⋊D3—244no—
405C2×C3×D3—22no—
406C2×C3×D3—22no—
407C2×C3×D3—22no—
408C2×C3×D3—42no—
409C2×C3×D3C2×D1212yes—
410C2×C3×D3C2×#6712yes—
411C32×C4—21no—
412C32×C4—21no—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4—21no—
417C32×C4—32no—
418C32×C4—41no—
419C32×C4—41no—
420C32×C4—62no—
421C32×C4C2×D1211yescharacteristic
422C32×C4D3×D411yescharacteristic
423C32×C4C2×#6711yescharacteristic
424C32×C4C23×D311yescharacteristic
425C32×C4C23×D311yescharacteristic
426C32×C4C23×D311yescharacteristic
427C3⋊Dic3—22no—
428C3⋊Dic3—22no—
429C3×Dic3—22no—
430C3×Dic3—22no—
431C3×Dic3—22no—
432C3×Dic3—42no—
433C3×Dic3—64no—
434C3×Dic3—62no—
435C3×Dic3—62no—
436C3×Dic3—62no—
437C3×Dic3—62no—
438C3×Dic3—122no—
439C3×Dic3C2×D1212yes—
440C3×Dic3C2×#6712yes—
441C2×#41—271no—
442C22×Q8—91no—
443#137—278no—
444C2×Q16—91no—
445C2×Q16—271no—
446C2×SD16—271no—
447C2×SD16—271no—
448C2×M16—91no—
449C33C2×#13711yescharacteristic, complemented, Sylow
450C23×C3—31no—
451C23×C3—31no—
452C23×C3—61no—
453C22×D3—182no—
454C22×D3—181no—
455C22×D3—181no—
456C22×D3—181no—
457C22×D3—361no—
458C22×D3—361no—
459C22×D3—362no—
460C22×D3#62611yescharacteristic
461C3×Q8—32no—
462C3×Q8—32no—
463C3×Q8—62no—
464C3×Q8—61no—
465C3×Q8—61no—
466C3×Q8—92no—
467C3×Q8—92no—
468C3×Q8—121no—
469C3×Q8—184no—
470C3×Q8—181no—
471C3×Q8—181no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—31no—
476C2×C3×C4—31no—
477C2×C3×C4—32no—
478C2×C3×C4—32no—
479C2×C3×C4—32no—
480C2×C3×C4—32no—
481C2×C3×C4—41no—
482C2×C3×C4—62no—
483C2×C3×C4—62no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—121no—
488C2×C3×C4—184no—
489C2×C3×C4—181no—
490C2×C3×C4—181no—
491C2×C3×C4C2×D3211yescharacteristic
492C2×C3×C4C2×D3211yescharacteristic
493C2×C3×C4C2×D3211yescharacteristic
494#67—184no—
495#67—184no—
496#67—188no—
497C2×Dic3—21no—
498C2×Dic3—64no—
499C2×Dic3—62no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—121no—
505C2×Dic3#62611yescharacteristic
506D12—92no—
507D12—92no—
508D12—92no—
509D12—182no—
510D12—182no—
511D12—182no—
512D12—182no—
513D12—184no—
514D12—181no—
515D12—181no—
516D12—181no—
517D12—362no—
518D12—361no—
519D12—361no—
520D12—362no—
521C4×D3—64no—
522C4×D3—184no—
523C4×D3—184no—
524C4×D3—188no—
525C4×D3—184no—
526C4×D3#62612yes—
527C4×D3C2×D3212yes—
528Dic6—21no—
529Dic6—32no—
530Dic6—32no—
531Dic6—32no—
532Dic6—32no—
533Dic6—62no—
534Dic6—62no—
535Dic6—64no—
536Dic6—62no—
537Dic6—61no—
538Dic6—61no—
539Dic6—61no—
540Dic6—61no—
541Dic6—64no—
542Dic6—121no—
543Dic6C2×D3212yes—
544C3×C8—32no—
545C3×C8—32no—
546C3×C8—62no—
547C3×C8—92no—
548C3⋊C8—32no—
549C3⋊C8—32no—
550C3⋊C8—62no—
551C3⋊C8C2×D3212yes—
552C2×C32—21no—
553C2×C32—22no—
554C2×C32—21no—
555C2×C32—21no—
556C2×C32—22no—
557C2×C32—22no—
558C2×C32—42no—
559C2×C32—41no—
560C2×C32—62no—
561C2×C32#90912yescomplemented
562C2×C32#91812yescomplemented
563C2×C32#94212yescomplemented
564C2×C32C22×D1211yescharacteristic
565C2×C32C2×D3×D411yescharacteristic
566C2×C32C22×#6711yescharacteristic
567C3⋊D3—122no—
568C3⋊D3—124no—
569C3⋊D3—122no—
570C3⋊D3—122no—
571C3⋊D3—242no—
572C3⋊D3—242no—
573C3⋊D3—244no—
574C3×D3—22no—
575C3×D3—22no—
576C3×D3—42no—
577#41—274no—
578#41—542no—
579C2×Q8—31no—
580C2×Q8—94no—
581C2×Q8—91no—
582C2×Q8—91no—
583C2×Q8—181no—
584C2×Q8—182no—
585C2×D4—271no—
586C2×D4—541no—
587C22×C4—31no—
588C22×C4—181no—
589C22×C4—541no—
590Q16—94no—
591Q16—274no—
592SD16—274no—
593SD16—274no—
594M16—94no—
595C2×C8—31no—
596C2×C8—91no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—32no—
601C22×C3—32no—
602C22×C3—41no—
603C22×C3—62no—
604C22×C3—62no—
605C22×C3—62no—
606C22×C3—122no—
607C22×C3D3×D1211yescharacteristic
608C22×C3C2×#62611yescharacteristic
609C22×C3D3×#6711yescharacteristic
610C2×D3—22no—
611C2×D3—184no—
612C2×D3—182no—
613C2×D3—182no—
614C2×D3—182no—
615C2×D3—362no—
616C2×D3—362no—
617C2×D3—364no—
618C2×D3—364no—
619C2×D3—362no—
620C2×D3—362no—
621C2×D3—362no—
622C2×D3—722no—
623C2×D3—722no—
624C2×D3—724no—
625C2×D3C2×#62612yes—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—32no—
633C3×C4—32no—
634C3×C4—41no—
635C3×C4—41no—
636C3×C4—62no—
637C3×C4—62no—
638C3×C4—62no—
639C3×C4—122no—
640C3×C4—182no—
641C3×C4—182no—
642C3×C4D3×D1211yescharacteristic
643C3×C4C2×#62611yescharacteristic
644C3×C4D3×#6711yescharacteristic
645C3×C4C22×D3211yescharacteristic
646C3×C4C22×D3211yescharacteristic
647C3×C4C22×D3211yescharacteristic
648Dic3—22no—
649Dic3—64no—
650Dic3—62no—
651Dic3—62no—
652Dic3—62no—
653Dic3—62no—
654Dic3—122no—
655Dic3C2×#62612yes—
656C32—21no—
657C32—21no—
658C32—21no—
659C32—41no—
660C32C2×#90911yescharacteristic, complemented
661C32C2×#91811yescharacteristic, complemented
662C32C2×#94211yescharacteristic, complemented
663C23—31no—
664C23—541no—
665Q8—32no—
666Q8—61no—
667Q8—92no—
668Q8—92no—
669Q8—184no—
670Q8—181no—
671Q8—181no—
672D4—272no—
673D4—544no—
674D4—541no—
675C2×C4—31no—
676C2×C4—32no—
677C2×C4—32no—
678C2×C4—61no—
679C2×C4—184no—
680C2×C4—181no—
681C2×C4—181no—
682C2×C4—544no—
683C2×C4D3311yescharacteristic
684C8—32no—
685C8—92no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—22no—
690C2×C3—22no—
691C2×C3—22no—
692C2×C3—41no—
693C2×C3—42no—
694C2×C3—62no—
695C2×C3—62no—
696C2×C3—122no—
697C2×C3#6380112yescomplemented
698C2×C3#6383312yescomplemented
699C2×C3#6394812yescomplemented
700C2×C3C2×D3×D1211yescharacteristic
701C2×C3C22×#62611yescharacteristic
702C2×C3C2×D3×#6711yescharacteristic
703D3—22no—
704D3—364no—
705D3—362no—
706D3—362no—
707D3—362no—
708D3—722no—
709D3—722no—
710D3—724no—
711C22—32no—
712C22—62no—
713C22—542no—
714C22—1082no—
715C22D3×#62611yescharacteristic
716C4—32no—
717C4—62no—
718C4—182no—
719C4—182no—
720C4D3×#62611yescharacteristic
721C4C2×D3311yescharacteristic
722C3—21no—
723C3—21no—
724C3—21no—
725C3—41no—
726C3C2×#6380111yescharacteristic, complemented
727C3C2×#6383311yescharacteristic, complemented
728C3C2×#6394811yescharacteristic, complemented
729C2—62no—
730C2—1082no—
731C2#1172288512yesdirect product factor
732C2C2×D3×#62611yescharacteristic
subgroupG/H
centerC22D3×#626
commutator, cosocleC33×C4C24
FrattiniC4C2×D33
FittingC2×C33×C4C23
socleC22×C33C2×D4
prime radicalC2×#89022C2
hypercenterC2×C4D33
hypocenterC33C2×#137
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×Dic6C2semidirect
3. C2×#88812C2semidirect
4. C2×#88797C2semidirect
5. C2×#88795C2semidirect
6. C2×C3×#3719C2semidirect
7. C2×C3×#3711C2semidirect
8. #11722885C2direct (N × H)
24. C3×D3×Dic6C22semidirect
27. #88812C22semidirect
28. #88797C22semidirect
29. #88795C22semidirect
30. C3×#3719C22semidirect
31. C3×#3711C22semidirect
38. C2×D3×Dic6D3semidirect
48. C2×#3719D3semidirect
57. C2×#3711D3semidirect
135. D3×Dic6C2×D3semidirect
152. #3719C2×D3semidirect
160. #3711C2×D3semidirect
302. C2×C33#137semidirect
449. C33C2×#137semidirect
561. C2×C32#909semidirect
562. C2×C32#918semidirect
563. C2×C32#942semidirect
660. C32C2×#909semidirect
661. C32C2×#918semidirect
662. C32C2×#942semidirect
697. C2×C3#63801semidirect
698. C2×C3#63833semidirect
699. C2×C3#63948semidirect
726. C3C2×#63801semidirect
727. C3C2×#63833semidirect
728. C3C2×#63948semidirect
731. C2#11722885direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#890222
C2×C3×D3×Dic62
C2×#888122
C2×#887972
C2×#887952
C2×C3×#37192
C2×C3×#37112
#117228852
C2×#639483
C2×#638333
C2×#638013