Finite Group Databasebeta

← C2×#11722865 #13170640

Subgroups — C2×#11722865 #13170640

Order 1728.

1426 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89041C211yesmaximal, characteristic, complemented
2C2×#89018C211yesmaximal, characteristic, complemented
3C2×#88797C211yesmaximal, characteristic, complemented
4C2×#88791C211yesmaximal, characteristic, complemented
5C2×C3×#3719C211yesmaximal, characteristic, complemented
6C2×C3×#3717C211yesmaximal, characteristic, complemented
7C2×C3×#3710C211yesmaximal, characteristic, complemented
8#11722865C218yesmaximal, direct product factor
9C2×#63950—31nomaximal
10C2×#63808—31nomaximal
11C2×#63806—31nomaximal
12C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
13C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×C4×C3⋊D3C2211yescharacteristic
15C2×C3×#634C2211yescharacteristic
16C2×C32×Dic6C2211yescharacteristic
17C2×#6295—21no—
18C2×#6294—21no—
19#89041—22no—
20#89041C2214yescomplemented
21C2×#6292—21no—
22C2×#6289—21no—
23#89018—22no—
24#89018C2214yescomplemented
25C2×C32×C3⋊C8C2211yescharacteristic
26C2×C32×C3⋊C8C2211yescharacteristic
27#88797C2214yescomplemented
28#88791C2214yescomplemented
29C3×#3719C2214yescomplemented
30C3×#3717C2214yescomplemented
31C3×#3710C2214yescomplemented
32C2×#3832—31no—
33C2×#3799—31no—
34C2×#3799—31no—
35C2×#3799—31no—
36C2×#3799—61no—
37C2×#3796—31no—
38C2×#3795—31no—
39C2×#3745—31no—
40C2×#3744—31no—
41C2×C3×#216—31no—
42C2×C3×#215—31no—
43C2×C3×Dic12—31no—
44C2×C3×#204—31no—
45C2×C3×D3×C8—31no—
46C2×C3×D3×C8—31no—
47#63950—38no—
48C2×#3719D311yescharacteristic, complemented
49C2×#3717—31no—
50C2×#3717—31no—
51C2×#3717—61no—
52C2×#3717D311yescharacteristic, complemented
53C2×#3714—31no—
54C2×#3714—31no—
55C2×#3714—61no—
56C2×#3710D311yescharacteristic, complemented
57#63808—38no—
58#63806—38no—
59C22×C3⋊(C3⋊D3)—21no—
60C22×C3×C3⋊D3—21no—
61C22×C3×C3⋊D3D411yescharacteristic
62C2×C33×C4C2311yescharacteristic
63C4⋊(C3⋊(C3⋊D3))—21no—
64C4⋊(C3⋊(C3⋊D3))C2312yes—
65C2×C3×C3⋊Dic3—21no—
66C2×C3×C3⋊Dic3D411yescharacteristic
67C3×C4⋊(C3⋊D3)—21no—
68C3×C4⋊(C3⋊D3)C2312yes—
69C3×C4×C3⋊D3D412yes—
70C3×C4×C3⋊D3C2312yes—
71C3×#634—21no—
72C3×#634C2312yes—
73C2×C32×Dic3—21no—
74C32×Dic6—21no—
75C32×Dic6C2312yes—
76#6295—24no—
77#6294—24no—
78#6292—24no—
79#6289—24no—
80C32×C3⋊C8C2312yes—
81C32×C3⋊C8C2312yes—
82C2×#919—91no—
83C2×#916—91no—
84C2×#904—91no—
85C2×C32×Q8—31no—
86#3832—34no—
87#3832—62no—
88C2×C4⋊(C3⋊D3)—31no—
89C2×C4⋊(C3⋊D3)—31no—
90C2×C4⋊(C3⋊D3)—31no—
91C2×C4⋊(C3⋊D3)—61no—
92C2×C4⋊(C3⋊D3)—61no—
93C2×C4⋊(C3⋊D3)—61no—
94C2×C4⋊(C3⋊D3)—61no—
95C2×C4⋊(C3⋊D3)—121no—
96C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
97C2×C4×C3⋊D3—61no—
98C2×C4×C3⋊D3C2×D311yescharacteristic
99C2×#634C2×D311yescharacteristic
100C2×C3×D12—31no—
101C2×C3×D12—31no—
102C2×C3×D12—61no—
103C2×C3×C4×D3—31no—
104C2×C3×C4×D3—31no—
105C2×C3×C4×D3—61no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6—31no—
108C2×C3×Dic6—31no—
109C2×C3×Dic6—61no—
110C2×C3×Dic6C2×D311yescharacteristic
111C2×C3×Dic6C2×D311yescharacteristic
112C2×#626—61no—
113C2×#626—61no—
114C2×#626—62no—
115C2×#626—61no—
116C2×#626—61no—
117C2×#625—61no—
118C2×#624—61no—
119C2×#624—61no—
120C2×#624—62no—
121C2×#624—61no—
122C2×D3×Dic3—61no—
123C2×D3×Dic3—61no—
124#3799—34no—
125#3799—34no—
126#3799—34no—
127#3799—62no—
128#3799—62no—
129#3799—64no—
130#3799—64no—
131#3799—62no—
132#3796—34no—
133#3796—62no—
134#3795—34no—
135#3795—62no—
136C2×C32×C8—31no—
137C2×C32×C8—31no—
138#3745—34no—
139#3744—34no—
140C3×#216—34no—
141C3×#215—34no—
142C2×C3×C3⋊C8—21no—
143C2×C3×C3⋊C8—21no—
144C2×C3×C3⋊C8C2×D311yescharacteristic
145C2×C3×C3⋊C8C2×D311yescharacteristic
146C2×C3×C3⋊C8C2×D311yescharacteristic
147C2×C3×C3⋊C8C2×D311yescharacteristic
148C3×Dic12—34no—
149C3×#204—34no—
150C3×D3×C8—34no—
151C3×D3×C8—34no—
152#3719C2×D314yescomplemented
153#3717—34no—
154#3717—34no—
155#3717—64no—
156#3717C2×D314yescomplemented
157#3714—34no—
158#3714—34no—
159#3714—64no—
160#3710C2×D314yescomplemented
161C22×C33C2×D411yescharacteristic
162C2×C3⋊(C3⋊D3)—22no—
163C2×C3⋊(C3⋊D3)—42no—
164C2×C3×C3⋊D3—22no—
165C2×C3×C3⋊D3—22no—
166C2×C3×C3⋊D3—42no—
167C2×C3×C3⋊D3C2×D412yes—
168C33×C4C2×D411yescharacteristic
169C33×C4C2411yescharacteristic
170C3×C3⋊Dic3—22no—
171C3×C3⋊Dic3C2×D412yes—
172C32×Dic3—22no—
173C2×#239—91no—
174C2×#239—91no—
175C2×#239—91no—
176C2×#239—181no—
177C2×#237—91no—
178C2×#235—91no—
179C2×#235—91no—
180C2×C3×Q16—91no—
181C2×C3×SD16—91no—
182C22×C3×C8—91no—
183C2×#216—31no—
184C2×#215—31no—
185C2×#215—91no—
186C2×#213—91no—
187#919—98no—
188#916—98no—
189C2×Dic12—31no—
190#904—98no—
191C2×D24—91no—
192C2×D24—91no—
193C2×D24—181no—
194C2×#204—31no—
195C2×#204—91no—
196C2×#204—91no—
197C2×#204—181no—
198C2×D3×C8—31no—
199C2×D3×C8—31no—
200C22×C3⋊D3—21no—
201C22×C3⋊D3—61no—
202C22×C3⋊D3—62no—
203C22×C3⋊D3—61no—
204C22×C3⋊D3—61no—
205C22×C3⋊D3—121no—
206C22×C3⋊D3—121no—
207C22×C3⋊D3—122no—
208C22×C3⋊D3D1211yescharacteristic
209C22×C3×D3—31no—
210C22×C3×D3—31no—
211C22×C3×D3—61no—
212C22×C3×D3—61no—
213C22×C3×D3—61no—
214C22×C3×D3—121no—
215C32×Q8—32no—
216C32×Q8—61no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—41no—
221C2×C32×C4—61no—
222C2×C32×C4C22×D311yescharacteristic
223C2×C32×C4C22×D311yescharacteristic
224C2×C32×C4C22×D311yescharacteristic
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3D1211yescharacteristic
227C4⋊(C3⋊D3)—21no—
228C4⋊(C3⋊D3)—32no—
229C4⋊(C3⋊D3)—32no—
230C4⋊(C3⋊D3)—32no—
231C4⋊(C3⋊D3)—62no—
232C4⋊(C3⋊D3)—62no—
233C4⋊(C3⋊D3)—62no—
234C4⋊(C3⋊D3)—64no—
235C4⋊(C3⋊D3)—61no—
236C4⋊(C3⋊D3)—62no—
237C4⋊(C3⋊D3)—61no—
238C4⋊(C3⋊D3)—61no—
239C4⋊(C3⋊D3)—122no—
240C4⋊(C3⋊D3)—121no—
241C4⋊(C3⋊D3)—121no—
242C4⋊(C3⋊D3)—122no—
243C4⋊(C3⋊D3)C22×D312yes—
244C4×C3⋊D3—64no—
245C4×C3⋊D3D1212yes—
246C4×C3⋊D3C22×D312yes—
247#634—21no—
248#634C22×D312yes—
249C2×C3×Dic3—22no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—31no—
253C2×C3×Dic3—31no—
254C2×C3×Dic3—61no—
255C2×C3×Dic3—61no—
256C2×C3×Dic3—61no—
257C2×C3×Dic3—121no—
258C3×D12—32no—
259C3×D12—32no—
260C3×D12—62no—
261C3×D12—61no—
262C3×D12—61no—
263C3×D12—121no—
264C3×C4×D3—32no—
265C3×C4×D3—32no—
266C3×C4×D3—32no—
267C3×C4×D3—32no—
268C3×C4×D3—62no—
269C3×C4×D3—62no—
270C3×Dic6—22no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—22no—
274C3×Dic6—32no—
275C3×Dic6—32no—
276C3×Dic6—62no—
277C3×Dic6—61no—
278C3×Dic6—61no—
279C3×Dic6—121no—
280C3×Dic6C22×D312yes—
281C3×Dic6C22×D312yes—
282#626—64no—
283#626—64no—
284#626—68no—
285#626—64no—
286#626—64no—
287#625—64no—
288#624—64no—
289#624—64no—
290#624—68no—
291#624—64no—
292D3×Dic3—64no—
293D3×Dic3—64no—
294C32×C8—32no—
295C32×C8—32no—
296C3×C3⋊C8—22no—
297C3×C3⋊C8—22no—
298C3×C3⋊C8C22×D312yes—
299C3×C3⋊C8C22×D312yes—
300C3×C3⋊C8C22×D312yes—
301C3×C3⋊C8C22×D312yes—
302C2×#135—271noSylow
303C2×C33#13512yescomplemented
304C2×C33C22×D411yescharacteristic
305C3⋊(C3⋊D3)—42no—
306C3×C3⋊D3—22no—
307C3×C3⋊D3—42no—
308C2×C3×Q8—31no—
309C2×C3×Q8—31no—
310C2×C3×Q8—61no—
311C2×C3×Q8—91no—
312C2×C3×D4—91no—
313C22×C3×C4—91no—
314C2×#67—181no—
315C2×#67—181no—
316C2×#67—181no—
317C22×Dic3—181no—
318#239—94no—
319#239—94no—
320#239—94no—
321#239—184no—
322#239—182no—
323#239—182no—
324#239—182no—
325#239—184no—
326#237—94no—
327#237—182no—
328#235—94no—
329#235—94no—
330#235—182no—
331#235—182no—
332C2×D12—31no—
333C2×D12—31no—
334C2×D12—61no—
335C2×D12—91no—
336C2×D12—91no—
337C2×D12—91no—
338C2×D12—181no—
339C2×D12—181no—
340C2×D12—181no—
341C2×D12—181no—
342C2×D12—181no—
343C2×D12—182no—
344C2×D12—181no—
345C2×D12—361no—
346C2×C4×D3—31no—
347C2×C4×D3—31no—
348C2×C4×D3—61no—
349C2×C4×D3—181no—
350C2×C4×D3—181no—
351C2×C4×D3—181no—
352C2×C4×D3—181no—
353C2×C4×D3—182no—
354C2×C4×D3—181no—
355C2×Dic6—31no—
356C2×Dic6—31no—
357C2×Dic6—61no—
358C2×Dic6D3211yescharacteristic
359C3×Q16—94no—
360C3×SD16—94no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8—31no—
364C2×C3×C8—31no—
365C2×C3×C8—61no—
366C2×C3×C8—61no—
367C2×C3×C8—94no—
368#216—34no—
369#215—34no—
370#215—94no—
371#213—94no—
372C2×C3⋊C8D3211yescharacteristic
373C2×C3⋊C8D3211yescharacteristic
374Dic12—34no—
375D24—94no—
376D24—94no—
377D24—184no—
378#204—34no—
379#204—94no—
380#204—94no—
381#204—184no—
382D3×C8—34no—
383D3×C8—34no—
384C22×C32—21no—
385C22×C32—21no—
386C22×C32—21no—
387C22×C32—41no—
388C22×C32C2×D1211yescharacteristic
389C22×C32D3×D411yescharacteristic
390C22×C32D3×D411yescharacteristic
391C2×C3⋊D3—22no—
392C2×C3⋊D3—22no—
393C2×C3⋊D3—42no—
394C2×C3⋊D3—62no—
395C2×C3⋊D3—64no—
396C2×C3⋊D3—62no—
397C2×C3⋊D3—62no—
398C2×C3⋊D3—122no—
399C2×C3⋊D3—122no—
400C2×C3⋊D3—124no—
401C2×C3⋊D3—122no—
402C2×C3⋊D3—124no—
403C2×C3⋊D3—122no—
404C2×C3⋊D3—122no—
405C2×C3⋊D3—242no—
406C2×C3⋊D3—242no—
407C2×C3⋊D3—244no—
408C2×C3⋊D3C2×D1212yes—
409C2×C3×D3—32no—
410C2×C3×D3—32no—
411C2×C3×D3—62no—
412C2×C3×D3—62no—
413C2×C3×D3—62no—
414C2×C3×D3—62no—
415C2×C3×D3—62no—
416C2×C3×D3—122no—
417C2×C3×D3—122no—
418C2×C3×D3—122no—
419C2×C3×D3—122no—
420C2×C3×D3—242no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—41no—
428C32×C4—41no—
429C32×C4—62no—
430C32×C4C2×D1211yescharacteristic
431C32×C4D3×D411yescharacteristic
432C32×C4D3×D411yescharacteristic
433C32×C4C23×D311yescharacteristic
434C32×C4C23×D311yescharacteristic
435C32×C4C23×D311yescharacteristic
436C3⋊Dic3—22no—
437C3⋊Dic3C2×D1212yes—
438C3×Dic3—24no—
439C3×Dic3—22no—
440C3×Dic3—22no—
441C3×Dic3—32no—
442C3×Dic3—32no—
443C3×Dic3—62no—
444C3×Dic3—62no—
445C3×Dic3—62no—
446C3×Dic3—122no—
447C2×#41—271no—
448C2×#41—271no—
449#135—278no—
450C2×Q16—91no—
451C2×SD16—91no—
452C2×SD16—271no—
453C2×D8—271no—
454C22×C8—91no—
455C33C2×#13511yescharacteristic, complemented, Sylow
456C23×C3—91no—
457C23×C3—181no—
458C22×D3—31no—
459C22×D3—31no—
460C22×D3—61no—
461C22×D3—61no—
462C22×D3—61no—
463C22×D3—121no—
464C22×D3—182no—
465C22×D3—181no—
466C22×D3—181no—
467C22×D3—181no—
468C22×D3—361no—
469C22×D3—361no—
470C22×D3—362no—
471C3×Q8—32no—
472C3×Q8—32no—
473C3×Q8—62no—
474C3×Q8—62no—
475C3×Q8—61no—
476C3×Q8—61no—
477C3×Q8—92no—
478C3×Q8—181no—
479C3×D4—92no—
480C3×D4—181no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—41no—
485C2×C3×C4—62no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—91no—
489C2×C3×C4—92no—
490C2×C3×C4—92no—
491C2×C3×C4—181no—
492C2×C3×C4C2×D3211yescharacteristic
493C2×C3×C4C2×D3211yescharacteristic
494C2×C3×C4C2×D3211yescharacteristic
495#67—184no—
496#67—184no—
497#67—184no—
498C2×Dic3—21no—
499C2×Dic3—31no—
500C2×Dic3—31no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—121no—
505C2×Dic3—184no—
506D12—32no—
507D12—32no—
508D12—62no—
509D12—61no—
510D12—61no—
511D12—92no—
512D12—92no—
513D12—92no—
514D12—121no—
515D12—182no—
516D12—182no—
517D12—182no—
518D12—182no—
519D12—184no—
520D12—184no—
521D12—188no—
522D12—184no—
523D12—181no—
524D12—181no—
525D12—181no—
526D12—362no—
527D12—361no—
528D12—361no—
529D12—362no—
530C4×D3—32no—
531C4×D3—32no—
532C4×D3—32no—
533C4×D3—32no—
534C4×D3—62no—
535C4×D3—62no—
536C4×D3—184no—
537C4×D3—184no—
538C4×D3—184no—
539C4×D3—184no—
540C4×D3—188no—
541C4×D3—184no—
542Dic6—21no—
543Dic6—32no—
544Dic6—32no—
545Dic6—62no—
546Dic6—61no—
547Dic6—61no—
548Dic6—121no—
549Dic6C2×D3212yes—
550C3×C8—32no—
551C3×C8—32no—
552C3×C8—32no—
553C3×C8—32no—
554C3×C8—62no—
555C3×C8—62no—
556C3⋊C8C2×D3212yes—
557C3⋊C8C2×D3212yes—
558C2×C32—21no—
559C2×C32—21no—
560C2×C32—22no—
561C2×C32—22no—
562C2×C32—21no—
563C2×C32—22no—
564C2×C32—42no—
565C2×C32—41no—
566C2×C32#90412yescomplemented
567C2×C32#91612yescomplemented
568C2×C32#91912yescomplemented
569C2×C32C22×D1211yescharacteristic
570C2×C32C2×D3×D411yescharacteristic
571C2×C32C2×D3×D411yescharacteristic
572C3⋊D3—22no—
573C3⋊D3—42no—
574C3⋊D3—122no—
575C3⋊D3—124no—
576C3⋊D3—122no—
577C3⋊D3—122no—
578C3⋊D3—242no—
579C3⋊D3—242no—
580C3⋊D3—244no—
581C3×D3—62no—
582C3×D3—62no—
583C3×D3—122no—
584C3×D3—122no—
585C3×D3—122no—
586C3×D3—242no—
587#41—274no—
588#41—274no—
589#41—542no—
590#41—542no—
591C2×Q8—31no—
592C2×Q8—91no—
593C2×D4—91no—
594C2×D4—271no—
595C2×D4—541no—
596C2×D4—541no—
597C22×C4—91no—
598C22×C4—541no—
599C22×C4—541no—
600Q16—94no—
601SD16—94no—
602SD16—274no—
603D8—274no—
604C2×C8—31no—
605C2×C8—31no—
606C2×C8—94no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—41no—
611C22×C3—92no—
612C22×C3—182no—
613C22×C3—182no—
614C22×C3—362no—
615C22×C3D3×D1211yescharacteristic
616C22×C3D3×D1211yescharacteristic
617C22×C3#381111yescharacteristic
618C2×D3—32no—
619C2×D3—32no—
620C2×D3—62no—
621C2×D3—62no—
622C2×D3—62no—
623C2×D3—62no—
624C2×D3—62no—
625C2×D3—122no—
626C2×D3—122no—
627C2×D3—122no—
628C2×D3—122no—
629C2×D3—184no—
630C2×D3—182no—
631C2×D3—182no—
632C2×D3—182no—
633C2×D3—242no—
634C2×D3—362no—
635C2×D3—362no—
636C2×D3—364no—
637C2×D3—364no—
638C2×D3—362no—
639C2×D3—362no—
640C2×D3—362no—
641C2×D3—722no—
642C2×D3—722no—
643C2×D3—724no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—64no—
653C3×C4—62no—
654C3×C4—62no—
655C3×C4—92no—
656C3×C4—182no—
657C3×C4D3×D1211yescharacteristic
658C3×C4D3×D1211yescharacteristic
659C3×C4#381111yescharacteristic
660C3×C4C22×D3211yescharacteristic
661C3×C4C22×D3211yescharacteristic
662C3×C4C22×D3211yescharacteristic
663Dic3—22no—
664Dic3—32no—
665Dic3—32no—
666Dic3—62no—
667Dic3—62no—
668Dic3—62no—
669Dic3—122no—
670C32—21no—
671C32—21no—
672C32—21no—
673C32—41no—
674C32C2×#90411yescharacteristic, complemented
675C32C2×#91611yescharacteristic, complemented
676C32C2×#91911yescharacteristic, complemented
677C23—91no—
678C23—181no—
679C23—541no—
680Q8—32no—
681Q8—61no—
682Q8—92no—
683Q8—181no—
684D4—92no—
685D4—181no—
686D4—272no—
687D4—544no—
688D4—544no—
689D4—541no—
690C2×C4—61no—
691C2×C4—91no—
692C2×C4—92no—
693C2×C4—92no—
694C2×C4—181no—
695C2×C4—544no—
696C2×C4—544no—
697C2×C4D3311yescharacteristic
698C8—32no—
699C8—32no—
700C2×C3—22no—
701C2×C3—22no—
702C2×C3—22no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—42no—
707C2×C3—41no—
708C2×C3—182no—
709C2×C3—362no—
710C2×C3#6380612yescomplemented
711C2×C3#6380812yescomplemented
712C2×C3#6395012yescomplemented
713C2×C3C2×D3×D1211yescharacteristic
714C2×C3C2×D3×D1211yescharacteristic
715C2×C3C2×#381111yescharacteristic
716D3—62no—
717D3—62no—
718D3—122no—
719D3—122no—
720D3—122no—
721D3—242no—
722D3—364no—
723D3—362no—
724D3—362no—
725D3—362no—
726D3—722no—
727D3—722no—
728D3—724no—
729C22—92no—
730C22—182no—
731C22—182no—
732C22—362no—
733C22—542no—
734C22—1082no—
735C22#8895511yescharacteristic
736C4—62no—
737C4—92no—
738C4—182no—
739C4#8895511yescharacteristic
740C4C2×D3311yescharacteristic
741C3—21no—
742C3—21no—
743C3—21no—
744C3—41no—
745C3C2×#6380611yescharacteristic, complemented
746C3C2×#6380811yescharacteristic, complemented
747C3C2×#6395011yescharacteristic, complemented
748C2—182no—
749C2—362no—
750C2—1082no—
751C2#1172286512yesdirect product factor
752C2C2×#8895511yescharacteristic
subgroupG/H
centerC22#88955
commutator, cosocleC33×C4C24
FrattiniC4C2×D33
FittingC2×C33×C4C23
socleC22×C33C2×D4
hypercenterC2×C4D33
hypocenterC33C2×#135
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#89041C2semidirect
2. C2×#89018C2semidirect
3. C2×#88797C2semidirect
4. C2×#88791C2semidirect
5. C2×C3×#3719C2semidirect
6. C2×C3×#3717C2semidirect
7. C2×C3×#3710C2semidirect
8. #11722865C2direct (N × H)
20. #89041C22semidirect
24. #89018C22semidirect
27. #88797C22semidirect
28. #88791C22semidirect
29. C3×#3719C22semidirect
30. C3×#3717C22semidirect
31. C3×#3710C22semidirect
48. C2×#3719D3semidirect
52. C2×#3717D3semidirect
56. C2×#3710D3semidirect
152. #3719C2×D3semidirect
156. #3717C2×D3semidirect
160. #3710C2×D3semidirect
303. C2×C33#135semidirect
455. C33C2×#135semidirect
566. C2×C32#904semidirect
567. C2×C32#916semidirect
568. C2×C32#919semidirect
674. C32C2×#904semidirect
675. C32C2×#916semidirect
676. C32C2×#919semidirect
710. C2×C3#63806semidirect
711. C2×C3#63808semidirect
712. C2×C3#63950semidirect
745. C3C2×#63806semidirect
746. C3C2×#63808semidirect
747. C3C2×#63950semidirect
751. C2#11722865direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#890412
C2×#890182
C2×#887972
C2×#887912
C2×C3×#37192
C2×C3×#37172
C2×C3×#37102
#117228652
C2×#639503
C2×#638083
C2×#638063