Finite Group Databasebeta

← C2×#11722856 #13170614

Subgroups — C2×#11722856 #13170614

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×#89022C211yesmaximal, characteristic, complemented
2C2×C3×#3799C211yesmaximal, characteristic, complemented
3C2×#88811C211yesmaximal, characteristic, complemented
4C2×#88795C211yesmaximal, characteristic, complemented
5C2×#88791C211yesmaximal, characteristic, complemented
6C2×C3×#3719C211yesmaximal, characteristic, complemented
7C2×C3×D3×C3⋊C8C211yesmaximal, characteristic, complemented
8#11722856C218yesmaximal, direct product factor
9C2×#63949—31nomaximal
10C2×#63829—31nomaximal
11C2×#63808—31nomaximal
12C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
13C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×#634C2211yescharacteristic
15C2×C32×C4×D3C2211yescharacteristic
16C2×C32×Dic6C2211yescharacteristic
17C2×#6291—21no—
18C2×#6289—21no—
19#89022—22no—
20#89022C2214yescomplemented
21C2×C3×#626—21no—
22C2×C3×#624—21no—
23C3×#3799—22no—
24C3×#3799C2214yescomplemented
25C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
26C2×C32×C3⋊C8C2211yescharacteristic
27#88811C2214yescomplemented
28#88795C2214yescomplemented
29#88791C2214yescomplemented
30C3×#3719C2214yescomplemented
31C3×D3×C3⋊C8C2214yescomplemented
32C2×#3828—31no—
33C2×C3×#239—31no—
34C2×C3×#235—31no—
35C2×#3799—31no—
36C2×#3799—31no—
37C2×#3799—61no—
38C2×#3799D311yescharacteristic, complemented
39C2×#3755—31no—
40C2×#3745—31no—
41C2×C3×#216—31no—
42C22×C3×C3⋊C8—31no—
43C2×C3×Dic12—31no—
44C2×C3×D3×C8—31no—
45#63949—38no—
46C2×#3719D311yescharacteristic, complemented
47C2×#3717—31no—
48C2×#3717—31no—
49C2×#3717—31no—
50C2×#3717—61no—
51#63829—38no—
52C2×#3716—31no—
53C2×#3715—31no—
54C2×#3714—31no—
55C2×#3714—31no—
56C2×#3714—61no—
57C2×D3×C3⋊C8D311yescharacteristic, complemented
58#63808—38no—
59C22×C3⋊(C3⋊D3)—21no—
60C22×C3×C3⋊D3—21no—
61C22×C32×D3D411yescharacteristic
62C2×C33×C4C2311yescharacteristic
63C4⋊(C3⋊(C3⋊D3))—21no—
64C4⋊(C3⋊(C3⋊D3))C2312yes—
65C2×C3×C3⋊Dic3—21no—
66C3×C4⋊(C3⋊D3)—21no—
67C3×C4⋊(C3⋊D3)C2312yes—
68C3×#634—21no—
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×#626—24no—
79C3×#624—24no—
80C3×C3⋊(C3⋊C8)C2312yes—
81C32×C3⋊C8C2312yes—
82C2×#950—91no—
83C2×#919—91no—
84C2×#904—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)C2×D311yescharacteristic
98C2×C4×C3⋊D3—61no—
99C2×#634C2×D311yescharacteristic
100C2×C3×#67—61no—
101C3×#239—34no—
102C3×#239—62no—
103C3×#235—34no—
104C3×#235—62no—
105C2×C3×D12—31no—
106C2×C3×D12—31no—
107C2×C3×D12—61no—
108C2×C3×D12—61no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—61no—
111C2×C3×C4×D3—61no—
112C2×C3×C4×D3C2×D311yescharacteristic
113C2×C3×C4×D3C2×D311yescharacteristic
114C2×C3×Dic6—21no—
115C2×C3×Dic6—31no—
116C2×C3×Dic6—31no—
117C2×C3×Dic6—61no—
118C2×C3×Dic6C2×D311yescharacteristic
119C2×C3×Dic6C2×D311yescharacteristic
120C2×#626—21no—
121C2×#626—62no—
122C2×#626—61no—
123C2×#626—61no—
124C2×#624—21no—
125C2×#624—62no—
126C2×#624—61no—
127C2×#624—61no—
128#3799—22no—
129#3799—34no—
130#3799—34no—
131#3799—64no—
132#3799—64no—
133#3799—62no—
134#3799—62no—
135#3799C2×D314yescomplemented
136C2×C32×C8—31no—
137#3755—34no—
138C2×C3⋊(C3⋊C8)C2×D311yescharacteristic
139#3745—34no—
140C3×#216—34no—
141C2×C3×C3⋊C8—21no—
142C2×C3×C3⋊C8—31no—
143C2×C3×C3⋊C8—31no—
144C2×C3×C3⋊C8—34no—
145C2×C3×C3⋊C8—61no—
146C2×C3×C3⋊C8C2×D311yescharacteristic
147C2×C3×C3⋊C8C2×D311yescharacteristic
148C3×Dic12—34no—
149C3×D3×C8—34no—
150#3719C2×D314yescomplemented
151#3717—34no—
152#3717—34no—
153#3717—34no—
154#3717—64no—
155#3716—34no—
156#3715—34no—
157#3714—34no—
158#3714—34no—
159#3714—64no—
160D3×C3⋊C8C2×D314yescomplemented
161C22×C33C2×D411yescharacteristic
162C2×C3⋊(C3⋊D3)—22no—
163C2×C3⋊(C3⋊D3)—42no—
164C2×C3×C3⋊D3—22no—
165C2×C3×C3⋊D3—42no—
166C2×C32×D3—22no—
167C2×C32×D3C2×D412yes—
168C33×C4C2×D411yescharacteristic
169C33×C4C2411yescharacteristic
170C3×C3⋊Dic3—22no—
171C32×Dic3—22no—
172C32×Dic3C2×D412yes—
173C2×C3×#41—91no—
174C2×#239—31no—
175C2×#239—91no—
176C2×#235—31no—
177C2×#235—91no—
178C2×#235—91no—
179C2×#235—181no—
180C2×C3×Q16—91no—
181C22×C3×C8—91no—
182#950—98no—
183C2×#216—31no—
184C2×#215—91no—
185C2×#215—91no—
186C2×#215—91no—
187C2×#215—181no—
188C2×#214—91no—
189C2×#213—91no—
190C22×C3⋊C8—31no—
191#919—98no—
192C2×Dic12—31no—
193#904—98no—
194C2×D24—91no—
195C2×D24—91no—
196C2×D24—181no—
197C2×#204—91no—
198C2×#204—91no—
199C2×D3×C8—31no—
200C23×C32—31no—
201C22×C3⋊D3—21no—
202C22×C3⋊D3—61no—
203C22×C3⋊D3—62no—
204C22×C3⋊D3—61no—
205C22×C3⋊D3—61no—
206C22×C3⋊D3—121no—
207C22×C3⋊D3—121no—
208C22×C3⋊D3—122no—
209C22×C3×D3—21no—
210C22×C3×D3—61no—
211C22×C3×D3—61no—
212C22×C3×D3—121no—
213C22×C3×D3D1211yescharacteristic
214C22×C3×D3#6711yescharacteristic
215C32×Q8—32no—
216C32×Q8—61no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—31no—
221C2×C32×C4—32no—
222C2×C32×C4—32no—
223C2×C32×C4—41no—
224C2×C32×C4—61no—
225C2×C32×C4C22×D311yescharacteristic
226C2×C32×C4C22×D311yescharacteristic
227C2×C32×C4C22×D311yescharacteristic
228#638—64no—
229C2×C3⋊Dic3—21no—
230C4⋊(C3⋊D3)—21no—
231C4⋊(C3⋊D3)—32no—
232C4⋊(C3⋊D3)—32no—
233C4⋊(C3⋊D3)—32no—
234C4⋊(C3⋊D3)—62no—
235C4⋊(C3⋊D3)—62no—
236C4⋊(C3⋊D3)—62no—
237C4⋊(C3⋊D3)—61no—
238C4⋊(C3⋊D3)—62no—
239C4⋊(C3⋊D3)—61no—
240C4⋊(C3⋊D3)—61no—
241C4⋊(C3⋊D3)—122no—
242C4⋊(C3⋊D3)—121no—
243C4⋊(C3⋊D3)—121no—
244C4⋊(C3⋊D3)—122no—
245C4⋊(C3⋊D3)C22×D312yes—
246C4×C3⋊D3—64no—
247#634—21no—
248#634C22×D312yes—
249C3×#67—64no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—41no—
254C2×C3×Dic3—62no—
255C2×C3×Dic3—61no—
256C2×C3×Dic3—61no—
257C2×C3×Dic3D1211yescharacteristic
258C2×C3×Dic3#6711yescharacteristic
259C3×D12—32no—
260C3×D12—32no—
261C3×D12—62no—
262C3×D12—64no—
263C3×D12—61no—
264C3×D12—61no—
265C3×D12—121no—
266C3×C4×D3—22no—
267C3×C4×D3—22no—
268C3×C4×D3—64no—
269C3×C4×D3—64no—
270C3×C4×D3D1212yes—
271C3×C4×D3#6712yes—
272C3×C4×D3C22×D312yes—
273C3×C4×D3C22×D312yes—
274C3×Dic6—21no—
275C3×Dic6—21no—
276C3×Dic6—22no—
277C3×Dic6—32no—
278C3×Dic6—32no—
279C3×Dic6—41no—
280C3×Dic6—62no—
281C3×Dic6—62no—
282C3×Dic6—61no—
283C3×Dic6—61no—
284C3×Dic6C22×D312yes—
285C3×Dic6C22×D312yes—
286#626—24no—
287#626—68no—
288#626—64no—
289#626—64no—
290#624—24no—
291#624—68no—
292#624—64no—
293#624—64no—
294C32×C8—32no—
295C3⋊(C3⋊C8)C22×D312yes—
296C3×C3⋊C8—22no—
297C3×C3⋊C8—32no—
298C3×C3⋊C8—32no—
299C3×C3⋊C8—62no—
300C3×C3⋊C8C22×D312yes—
301C3×C3⋊C8C22×D312yes—
302C2×#135—271noSylow
303C2×C33#13512yescomplemented
304C2×C33C22×D411yescharacteristic
305C3⋊(C3⋊D3)—42no—
306C3×C3⋊D3—42no—
307C32×D3—22no—
308C3×#41—94no—
309C3×#41—182no—
310C2×C3×Q8—31no—
311C2×C3×Q8—31no—
312C2×C3×Q8—61no—
313C2×C3×Q8—91no—
314C2×C3×D4—91no—
315C2×C3×D4—181no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—61no—
319C22×C3×C4—181no—
320C2×#67—61no—
321C2×#67—181no—
322C2×#67—181no—
323C2×#67—182no—
324#239—34no—
325#239—62no—
326#239—94no—
327#239—182no—
328#235—34no—
329#235—62no—
330#235—94no—
331#235—94no—
332#235—184no—
333#235—182no—
334#235—182no—
335#235—184no—
336C2×D12—31no—
337C2×D12—31no—
338C2×D12—61no—
339C2×D12—61no—
340C2×D12—91no—
341C2×D12—91no—
342C2×D12—91no—
343C2×D12—181no—
344C2×D12—181no—
345C2×D12—181no—
346C2×D12—181no—
347C2×D12—361no—
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×C4×D3—181no—
351C2×C4×D3—181no—
352C2×C4×D3—182no—
353C2×C4×D3—181no—
354C2×C4×D3D3211yescharacteristic
355C2×Dic6—31no—
356C2×Dic6—31no—
357C2×Dic6—61no—
358C2×Dic6D3211yescharacteristic
359C3×Q16—94no—
360C2×C3×C8—31no—
361C2×C3×C8—31no—
362C2×C3×C8—61no—
363C2×C3×C8—94no—
364C2×C3×C8—91no—
365#216—34no—
366#215—94no—
367#215—94no—
368#215—94no—
369#215—184no—
370#214—94no—
371#213—94no—
372C2×C3⋊C8—31no—
373C2×C3⋊C8—31no—
374C2×C3⋊C8—34no—
375C2×C3⋊C8—61no—
376C2×C3⋊C8D3211yescharacteristic
377Dic12—34no—
378D24—94no—
379D24—94no—
380D24—184no—
381#204—94no—
382#204—94no—
383D3×C8—34no—
384C22×C32—21no—
385C22×C32—21no—
386C22×C32—21no—
387C22×C32—32no—
388C22×C32—41no—
389C22×C32—62no—
390C22×C32C2×D1211yescharacteristic
391C22×C32D3×D411yescharacteristic
392C22×C32C2×#6711yescharacteristic
393C2×C3⋊D3—22no—
394C2×C3⋊D3—42no—
395C2×C3⋊D3—62no—
396C2×C3⋊D3—64no—
397C2×C3⋊D3—62no—
398C2×C3⋊D3—62no—
399C2×C3⋊D3—122no—
400C2×C3⋊D3—122no—
401C2×C3⋊D3—124no—
402C2×C3⋊D3—122no—
403C2×C3⋊D3—124no—
404C2×C3⋊D3—122no—
405C2×C3⋊D3—122no—
406C2×C3⋊D3—242no—
407C2×C3⋊D3—242no—
408C2×C3⋊D3—244no—
409C2×C3×D3—22no—
410C2×C3×D3—22no—
411C2×C3×D3—22no—
412C2×C3×D3—42no—
413C2×C3×D3—62no—
414C2×C3×D3—62no—
415C2×C3×D3—122no—
416C2×C3×D3—122no—
417C2×C3×D3—122no—
418C2×C3×D3—242no—
419C2×C3×D3C2×D1212yes—
420C2×C3×D3C2×#6712yes—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—32no—
428C32×C4—41no—
429C32×C4—41no—
430C32×C4—62no—
431C32×C4C2×D1211yescharacteristic
432C32×C4D3×D411yescharacteristic
433C32×C4C2×#6711yescharacteristic
434C32×C4C23×D311yescharacteristic
435C32×C4C23×D311yescharacteristic
436C32×C4C23×D311yescharacteristic
437C3⋊Dic3—22no—
438C3×Dic3—22no—
439C3×Dic3—22no—
440C3×Dic3—22no—
441C3×Dic3—42no—
442C3×Dic3—64no—
443C3×Dic3—62no—
444C3×Dic3—62no—
445C3×Dic3C2×D1212yes—
446C3×Dic3C2×#6712yes—
447C2×#41—91no—
448C2×#41—271no—
449#135—278no—
450C2×Q16—91no—
451C2×SD16—271no—
452C2×SD16—271no—
453C2×D8—271no—
454C22×C8—91no—
455C33C2×#13511yescharacteristic, complemented, Sylow
456C23×C3—31no—
457C23×C3—31no—
458C23×C3—61no—
459C23×C3—181no—
460C22×D3—61no—
461C22×D3—61no—
462C22×D3—121no—
463C22×D3—182no—
464C22×D3—181no—
465C22×D3—181no—
466C22×D3—181no—
467C22×D3—361no—
468C22×D3—361no—
469C22×D3—362no—
470C22×D3#62611yescharacteristic
471C3×Q8—32no—
472C3×Q8—32no—
473C3×Q8—62no—
474C3×Q8—61no—
475C3×Q8—61no—
476C3×Q8—92no—
477C3×Q8—121no—
478C3×Q8—181no—
479C3×D4—92no—
480C3×D4—184no—
481C3×D4—181no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—32no—
488C2×C3×C4—32no—
489C2×C3×C4—32no—
490C2×C3×C4—32no—
491C2×C3×C4—41no—
492C2×C3×C4—62no—
493C2×C3×C4—62no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—121no—
498C2×C3×C4—184no—
499C2×C3×C4—181no—
500C2×C3×C4C2×D3211yescharacteristic
501C2×C3×C4C2×D3211yescharacteristic
502C2×C3×C4C2×D3211yescharacteristic
503#67—64no—
504#67—184no—
505#67—184no—
506#67—188no—
507C2×Dic3—21no—
508C2×Dic3—62no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3#62611yescharacteristic
512D12—32no—
513D12—32no—
514D12—62no—
515D12—64no—
516D12—61no—
517D12—61no—
518D12—92no—
519D12—92no—
520D12—92no—
521D12—121no—
522D12—182no—
523D12—182no—
524D12—182no—
525D12—182no—
526D12—184no—
527D12—181no—
528D12—181no—
529D12—181no—
530D12—362no—
531D12—361no—
532D12—361no—
533D12—362no—
534C4×D3—64no—
535C4×D3—64no—
536C4×D3—184no—
537C4×D3—184no—
538C4×D3—188no—
539C4×D3—184no—
540C4×D3#62612yes—
541C4×D3C2×D3212yes—
542Dic6—21no—
543Dic6—32no—
544Dic6—32no—
545Dic6—62no—
546Dic6—62no—
547Dic6—61no—
548Dic6—61no—
549Dic6C2×D3212yes—
550C3×C8—32no—
551C3×C8—32no—
552C3×C8—62no—
553C3×C8—92no—
554C3⋊C8—32no—
555C3⋊C8—32no—
556C3⋊C8—62no—
557C3⋊C8C2×D3212yes—
558C2×C32—21no—
559C2×C32—22no—
560C2×C32—21no—
561C2×C32—21no—
562C2×C32—22no—
563C2×C32—22no—
564C2×C32—42no—
565C2×C32—41no—
566C2×C32—62no—
567C2×C32#90412yescomplemented
568C2×C32#91912yescomplemented
569C2×C32#95012yescomplemented
570C2×C32C22×D1211yescharacteristic
571C2×C32C2×D3×D411yescharacteristic
572C2×C32C22×#6711yescharacteristic
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—22no—
582C3×D3—22no—
583C3×D3—42no—
584C3×D3—122no—
585C3×D3—122no—
586C3×D3—242no—
587#41—94no—
588#41—182no—
589#41—274no—
590#41—542no—
591C2×Q8—31no—
592C2×Q8—91no—
593C2×D4—91no—
594C2×D4—181no—
595C2×D4—271no—
596C2×D4—541no—
597C22×C4—31no—
598C22×C4—181no—
599C22×C4—541no—
600Q16—94no—
601SD16—274no—
602SD16—274no—
603D8—274no—
604C2×C8—31no—
605C2×C8—94no—
606C2×C8—91no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—32no—
611C22×C3—32no—
612C22×C3—41no—
613C22×C3—62no—
614C22×C3—62no—
615C22×C3—62no—
616C22×C3—122no—
617C22×C3—182no—
618C22×C3—362no—
619C22×C3D3×D1211yescharacteristic
620C22×C3C2×#62611yescharacteristic
621C22×C3D3×#6711yescharacteristic
622C2×D3—22no—
623C2×D3—62no—
624C2×D3—62no—
625C2×D3—122no—
626C2×D3—122no—
627C2×D3—122no—
628C2×D3—184no—
629C2×D3—182no—
630C2×D3—182no—
631C2×D3—182no—
632C2×D3—242no—
633C2×D3—362no—
634C2×D3—362no—
635C2×D3—364no—
636C2×D3—364no—
637C2×D3—362no—
638C2×D3—362no—
639C2×D3—362no—
640C2×D3—722no—
641C2×D3—722no—
642C2×D3—724no—
643C2×D3C2×#62612yes—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—32no—
651C3×C4—32no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—62no—
655C3×C4—62no—
656C3×C4—62no—
657C3×C4—122no—
658C3×C4—182no—
659C3×C4D3×D1211yescharacteristic
660C3×C4C2×#62611yescharacteristic
661C3×C4D3×#6711yescharacteristic
662C3×C4C22×D3211yescharacteristic
663C3×C4C22×D3211yescharacteristic
664C3×C4C22×D3211yescharacteristic
665Dic3—22no—
666Dic3—64no—
667Dic3—62no—
668Dic3—62no—
669Dic3C2×#62612yes—
670C32—21no—
671C32—21no—
672C32—21no—
673C32—41no—
674C32C2×#90411yescharacteristic, complemented
675C32C2×#91911yescharacteristic, complemented
676C32C2×#95011yescharacteristic, complemented
677C23—31no—
678C23—181no—
679C23—541no—
680Q8—32no—
681Q8—61no—
682Q8—92no—
683Q8—181no—
684D4—92no—
685D4—184no—
686D4—181no—
687D4—272no—
688D4—544no—
689D4—541no—
690C2×C4—31no—
691C2×C4—32no—
692C2×C4—32no—
693C2×C4—61no—
694C2×C4—184no—
695C2×C4—181no—
696C2×C4—544no—
697C2×C4D3311yescharacteristic
698C8—32no—
699C8—92no—
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—62no—
709C2×C3—62no—
710C2×C3—122no—
711C2×C3—362no—
712C2×C3#6380812yescomplemented
713C2×C3#6382912yescomplemented
714C2×C3#6394912yescomplemented
715C2×C3C2×D3×D1211yescharacteristic
716C2×C3C22×#62611yescharacteristic
717C2×C3C2×D3×#6711yescharacteristic
718D3—22no—
719D3—122no—
720D3—122no—
721D3—242no—
722D3—364no—
723D3—362no—
724D3—362no—
725D3—362no—
726D3—722no—
727D3—722no—
728D3—724no—
729C22—32no—
730C22—62no—
731C22—182no—
732C22—362no—
733C22—542no—
734C22—1082no—
735C22D3×#62611yescharacteristic
736C4—32no—
737C4—62no—
738C4—182no—
739C4D3×#62611yescharacteristic
740C4C2×D3311yescharacteristic
741C3—21no—
742C3—21no—
743C3—21no—
744C3—41no—
745C3C2×#6380811yescharacteristic, complemented
746C3C2×#6382911yescharacteristic, complemented
747C3C2×#6394911yescharacteristic, complemented
748C2—62no—
749C2—362no—
750C2—1082no—
751C2#1172285612yesdirect product factor
752C2C2×D3×#62611yescharacteristic
subgroupG/H
centerC22D3×#626
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×#89022C2semidirect
2. C2×C3×#3799C2semidirect
3. C2×#88811C2semidirect
4. C2×#88795C2semidirect
5. C2×#88791C2semidirect
6. C2×C3×#3719C2semidirect
7. C2×C3×D3×C3⋊C8C2semidirect
8. #11722856C2direct (N × H)
20. #89022C22semidirect
24. C3×#3799C22semidirect
27. #88811C22semidirect
28. #88795C22semidirect
29. #88791C22semidirect
30. C3×#3719C22semidirect
31. C3×D3×C3⋊C8C22semidirect
38. C2×#3799D3semidirect
46. C2×#3719D3semidirect
57. C2×D3×C3⋊C8D3semidirect
135. #3799C2×D3semidirect
150. #3719C2×D3semidirect
160. D3×C3⋊C8C2×D3semidirect
303. C2×C33#135semidirect
455. C33C2×#135semidirect
567. C2×C32#904semidirect
568. C2×C32#919semidirect
569. C2×C32#950semidirect
674. C32C2×#904semidirect
675. C32C2×#919semidirect
676. C32C2×#950semidirect
712. C2×C3#63808semidirect
713. C2×C3#63829semidirect
714. C2×C3#63949semidirect
745. C3C2×#63808semidirect
746. C3C2×#63829semidirect
747. C3C2×#63949semidirect
751. C2#11722856direct (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×#37992
C2×#888112
C2×#887952
C2×#887912
C2×C3×#37192
C2×C3×D3×C3⋊C82
#117228562
C2×#639493
C2×#638293
C2×#638083