Finite Group Databasebeta

← C2×#11722869 #13170650

Subgroups — C2×#11722869 #13170650

Order 1728.

1530 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89021C211yesmaximal, characteristic, complemented
2C2×C3×D3×D12C211yesmaximal, characteristic, complemented
3C2×#88810C211yesmaximal, characteristic, complemented
4C2×#88796C211yesmaximal, characteristic, complemented
5C2×#88794C211yesmaximal, characteristic, complemented
6C2×C3×#3714C211yesmaximal, characteristic, complemented
7C2×C3×#3711C211yesmaximal, characteristic, complemented
8#11722869C218yesmaximal, direct product factor
9C2×#63932—31nomaximal
10C2×#63830—31nomaximal
11C2×#63795—31nomaximal
12C22×C3×D32—21no—
13C2×#6308C2211yescharacteristic, complemented
14C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
15C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
16C2×C32×D12C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×#6290—21no—
19C2×Dic3×C3⋊D3—21no—
20#89021—22no—
21#89021C2214yescomplemented
22C2×C3×#626—21no—
23C3×D3×D12—22no—
24C3×D3×D12C2214yescomplemented
25C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
26C2×C32×C3⋊C8C2211yescharacteristic, complemented
27#88810C2214yescomplemented
28#88796C2214yescomplemented
29#88794C2214yescomplemented
30C3×#3714C2214yescomplemented
31C3×#3711C2214yescomplemented
32C2×#3828—31no—
33C2×C3×D3×D4—31no—
34C22×C3×D12—31no—
35C2×D3×D12D311yescharacteristic, complemented
36C2×#3795—31no—
37C2×#3795—31no—
38C2×#3795—61no—
39C2×#3754—31no—
40C2×#3744—31no—
41C2×C3×#213—31no—
42C2×C3×#208—31no—
43C2×C3×D24—31no—
44C2×C3×ΓL(1,𝔽25)—31no—
45#63932—38no—
46#63830—38no—
47C2×#3716—31no—
48C2×#3716—31no—
49C2×#3716—31no—
50C2×#3716—31no—
51C2×#3716—61no—
52C2×#3716—61no—
53C2×#3714—31no—
54C2×#3714—31no—
55C2×#3714D311yescharacteristic, complemented
56C2×#3713—31no—
57C2×#3711D311yescharacteristic, complemented
58#63795—38no—
59C22×C3×C3⋊D3—21no—
60C22×C3×C3⋊D3—21no—
61C22×C32×D3—21no—
62C22×C32×D3D411yescharacteristic
63C2×C3×D32—24no—
64C2×C3×D32—44no—
65C2×C33×C4C2311yescharacteristic
66C2×C3⋊(C3⋊Dic3)—21no—
67#6308—21no—
68#6308C2312yescomplemented
69C3×C4⋊(C3⋊D3)—21no—
70C3×C4⋊(C3⋊D3)—21no—
71C3×C4⋊(C3⋊D3)C2312yes—
72C3×C4⋊(C3⋊D3)C2312yescomplemented
73C2×C32×Dic3D411yescharacteristic
74C32×D12—21no—
75C32×D12C2312yes—
76C32×C4×D3D412yes—
77C32×C4×D3C2312yes—
78#6290—24no—
79Dic3×C3⋊D3—24no—
80C3×#626—24no—
81C3×C3⋊(C3⋊C8)C2312yescomplemented
82C32×C3⋊C8C2312yescomplemented
83C2×#932—91no—
84C2×#911—91no—
85C2×#908—91no—
86C23×C3×D3—61no—
87C23×C3×D3—61no—
88C22×D32—21no—
89C2×C32×D4—31no—
90C22×C32×C4—31no—
91C2×#638—61no—
92#3828—34no—
93#3828—62no—
94C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
95C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
96C2×C4×C3⋊D3—61no—
97C2×#634—31no—
98C2×#634—31no—
99C2×#634—31no—
100C2×#634—61no—
101C2×#634—61no—
102C2×#634—61no—
103C2×#634—121no—
104C2×C3×#67—61no—
105C3×D3×D4—34no—
106C3×D3×D4—62no—
107C2×C3×D12—21no—
108C2×C3×D12—31no—
109C2×C3×D12—31no—
110C2×C3×D12—31no—
111C2×C3×D12—31no—
112C2×C3×D12—34no—
113C2×C3×D12—62no—
114C2×C3×D12—61no—
115C2×C3×D12—61no—
116C2×C3×D12—61no—
117C2×C3×D12C2×D311yescharacteristic
118C2×C3×D12C2×D311yescharacteristic
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3C2×D311yescharacteristic
121C2×C3×C4×D3C2×D311yescharacteristic
122C2×#626—21no—
123C2×#625—62no—
124C2×#625—61no—
125C2×#625—61no—
126C2×D3×Dic3—62no—
127C2×D3×Dic3—61no—
128C2×D3×Dic3—61no—
129D3×D12—22no—
130D3×D12C2×D314yescomplemented
131#3795—34no—
132#3795—34no—
133#3795—64no—
134#3795—64no—
135#3795—62no—
136#3795—62no—
137C2×C32×C8—31no—
138#3754—34no—
139C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
140#3744—34no—
141C3×#213—34no—
142C3×#208—34no—
143C2×C3×C3⋊C8—21no—
144C2×C3×C3⋊C8—31no—
145C2×C3×C3⋊C8—31no—
146C2×C3×C3⋊C8—61no—
147C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
148C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
149C3×D24—34no—
150C3×ΓL(1,𝔽25)—34no—
151#3716—34no—
152#3716—34no—
153#3716—34no—
154#3716—34no—
155#3716—64no—
156#3716—64no—
157#3714—34no—
158#3714—34no—
159#3714C2×D314yescomplemented
160#3713—34no—
161#3711C2×D314yescomplemented
162C22×C33C2×D411yescharacteristic
163C2×C3×C3⋊D3—22no—
164C2×C3×C3⋊D3—22no—
165C2×C3×C3⋊D3—42no—
166C2×C3×C3⋊D3—42no—
167C2×C32×D3—22no—
168C2×C32×D3—22no—
169C2×C32×D3—42no—
170C2×C32×D3C2×D412yes—
171C3×D32—48no—
172C33×C4C2×D411yescharacteristic
173C33×C4C2411yescharacteristic
174C3⋊(C3⋊Dic3)—22no—
175C32×Dic3C2×D412yes—
176C22×C3×D4—91no—
177C2×#237—91no—
178C2×D3×D4—31no—
179C2×#235—91no—
180C2×#235—91no—
181C2×#235—181no—
182C22×D12—31no—
183C2×C3×D8—91no—
184C2×C3×M16—91no—
185C2×#214—91no—
186C2×#214—91no—
187C2×#214—91no—
188C2×#214—181no—
189#932—98no—
190C2×#213—31no—
191C2×#213—91no—
192C2×#213—91no—
193C2×#208—31no—
194#911—98no—
195#908—98no—
196C2×D24—31no—
197C2×D24—91no—
198C2×#204—91no—
199C2×#204—91no—
200C2×#204—91no—
201C2×#204—181no—
202C2×ΓL(1,𝔽25)—31no—
203C23×C32—31no—
204C23×C32—61no—
205C22×C3⋊D3—21no—
206C22×C3⋊D3—21no—
207C22×C3×D3—21no—
208C22×C3×D3—21no—
209C22×C3×D3—21no—
210C22×C3×D3—41no—
211C22×C3×D3—64no—
212C22×C3×D3—62no—
213C22×C3×D3—61no—
214C22×C3×D3—61no—
215C22×C3×D3—61no—
216C22×C3×D3—61no—
217C22×C3×D3—64no—
218C22×C3×D3—121no—
219C22×C3×D3—124no—
220C22×C3×D3—124no—
221C22×C3×D3D1211yescharacteristic
222C22×C3×D3#6711yescharacteristic
223C2×D32—24no—
224C2×D32—44no—
225C32×D4—32no—
226C32×D4—61no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—31no—
231C2×C32×C4—32no—
232C2×C32×C4—32no—
233C2×C32×C4—41no—
234C2×C32×C4C22×D311yescharacteristic
235C2×C32×C4C22×D311yescharacteristic
236C2×C32×C4C22×D311yescharacteristic
237#638—64no—
238C2×C3⋊Dic3—61no—
239C2×C3⋊Dic3—62no—
240C2×C3⋊Dic3—61no—
241C2×C3⋊Dic3—61no—
242C2×C3⋊Dic3—121no—
243C2×C3⋊Dic3—121no—
244C2×C3⋊Dic3—122no—
245C4⋊(C3⋊D3)—21no—
246C4⋊(C3⋊D3)—21no—
247C4⋊(C3⋊D3)C22×D312yes—
248C4⋊(C3⋊D3)C22×D312yescomplemented
249C4×C3⋊D3—64no—
250#634—32no—
251#634—32no—
252#634—32no—
253#634—62no—
254#634—62no—
255#634—62no—
256#634—61no—
257#634—62no—
258#634—61no—
259#634—61no—
260#634—122no—
261#634—121no—
262#634—121no—
263#634—122no—
264C3×#67—64no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3D1211yescharacteristic
267C2×C3×Dic3#6711yescharacteristic
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—22no—
271C3×D12—32no—
272C3×D12—32no—
273C3×D12—32no—
274C3×D12—32no—
275C3×D12—41no—
276C3×D12—62no—
277C3×D12—62no—
278C3×D12—62no—
279C3×D12—64no—
280C3×D12—61no—
281C3×D12—61no—
282C3×D12—61no—
283C3×D12—61no—
284C3×D12—121no—
285C3×D12C22×D312yes—
286C3×D12C22×D312yes—
287C3×C4×D3—22no—
288C3×C4×D3—22no—
289C3×C4×D3D1212yes—
290C3×C4×D3#6712yes—
291C3×C4×D3C22×D312yes—
292C3×C4×D3C22×D312yes—
293#626—24no—
294#625—68no—
295#625—64no—
296#625—64no—
297D3×Dic3—68no—
298D3×Dic3—64no—
299D3×Dic3—64no—
300C32×C8—32no—
301C3⋊(C3⋊C8)C22×D312yescomplemented
302C3×C3⋊C8—22no—
303C3×C3⋊C8—32no—
304C3×C3⋊C8—32no—
305C3×C3⋊C8—62no—
306C3×C3⋊C8C22×D312yescomplemented
307C3×C3⋊C8C22×D312yescomplemented
308C2×AGL(1,ℤ/8)—271noSylow
309C2×C33AGL(1,ℤ/8)12yescomplemented
310C2×C33C22×D411yescharacteristic
311C3×C3⋊D3—42no—
312C3×C3⋊D3—42no—
313C32×D3—22no—
314C32×D3—42no—
315C24×C3—181no—
316C23×D3—61no—
317C23×D3—61no—
318C2×C3×D4—31no—
319C2×C3×D4—31no—
320C2×C3×D4—61no—
321C2×C3×D4—94no—
322C2×C3×D4—91no—
323C2×C3×D4—91no—
324C2×C3×D4—182no—
325C2×C3×D4—181no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—61no—
329C2×#67—61no—
330C2×#67—181no—
331C2×#67—181no—
332C2×#67—182no—
333C2×#67—181no—
334C22×Dic3—181no—
335#237—94no—
336#237—182no—
337D3×D4—34no—
338D3×D4—62no—
339#235—94no—
340#235—94no—
341#235—184no—
342#235—182no—
343#235—182no—
344#235—184no—
345C2×D12—31no—
346C2×D12—31no—
347C2×D12—31no—
348C2×D12—31no—
349C2×D12—34no—
350C2×D12—61no—
351C2×D12—61no—
352C2×D12—62no—
353C2×D12—61no—
354C2×D12D3211yescharacteristic
355C2×C4×D3—181no—
356C2×C4×D3—181no—
357C2×C4×D3—182no—
358C2×C4×D3D3211yescharacteristic
359C2×Dic6—91no—
360C2×Dic6—91no—
361C2×Dic6—91no—
362C2×Dic6—181no—
363C2×Dic6—181no—
364C2×Dic6—181no—
365C2×Dic6—361no—
366C3×D8—94no—
367C3×M16—94no—
368C2×C3×C8—31no—
369C2×C3×C8—31no—
370C2×C3×C8—61no—
371C2×C3×C8—91no—
372#214—94no—
373#214—94no—
374#214—94no—
375#214—184no—
376#213—34no—
377#213—94no—
378#213—94no—
379#208—34no—
380C2×C3⋊C8—31no—
381C2×C3⋊C8—31no—
382C2×C3⋊C8—61no—
383C2×C3⋊C8D3211yescharacteristic, complemented
384D24—34no—
385D24—94no—
386#204—94no—
387#204—94no—
388#204—94no—
389#204—184no—
390ΓL(1,𝔽25)—34no—
391C22×C32—21no—
392C22×C32—21no—
393C22×C32—21no—
394C22×C32—32no—
395C22×C32—41no—
396C22×C32—62no—
397C22×C32—62no—
398C22×C32—122no—
399C22×C32C2×D1211yescharacteristic
400C22×C32D3×D411yescharacteristic
401C22×C32C2×#6711yescharacteristic
402C2×C3⋊D3—22no—
403C2×C3⋊D3—22no—
404C2×C3⋊D3—42no—
405C2×C3⋊D3—42no—
406C2×C3×D3—22no—
407C2×C3×D3—22no—
408C2×C3×D3—22no—
409C2×C3×D3—22no—
410C2×C3×D3—22no—
411C2×C3×D3—42no—
412C2×C3×D3—42no—
413C2×C3×D3—42no—
414C2×C3×D3—42no—
415C2×C3×D3—64no—
416C2×C3×D3—62no—
417C2×C3×D3—62no—
418C2×C3×D3—62no—
419C2×C3×D3—62no—
420C2×C3×D3—82no—
421C2×C3×D3—122no—
422C2×C3×D3—128no—
423C2×C3×D3—128no—
424C2×C3×D3—124no—
425C2×C3×D3—122no—
426C2×C3×D3—122no—
427C2×C3×D3—122no—
428C2×C3×D3—122no—
429C2×C3×D3—242no—
430C2×C3×D3C2×D1212yes—
431C2×C3×D3C2×#6712yes—
432D32—48no—
433C32×C4—21no—
434C32×C4—21no—
435C32×C4—21no—
436C32×C4—21no—
437C32×C4—21no—
438C32×C4—21no—
439C32×C4—32no—
440C32×C4—41no—
441C32×C4—41no—
442C32×C4C2×D1211yescharacteristic
443C32×C4D3×D411yescharacteristic
444C32×C4C2×#6711yescharacteristic
445C32×C4C23×D311yescharacteristic
446C32×C4C23×D311yescharacteristic
447C32×C4C23×D311yescharacteristic
448C3⋊Dic3—62no—
449C3⋊Dic3—64no—
450C3⋊Dic3—62no—
451C3⋊Dic3—62no—
452C3⋊Dic3—122no—
453C3⋊Dic3—122no—
454C3⋊Dic3—124no—
455C3×Dic3—22no—
456C3×Dic3C2×D1212yes—
457C3×Dic3C2×#6712yes—
458C2×#41—271no—
459C22×D4—91no—
460AGL(1,ℤ/8)—278no—
461C2×SD16—271no—
462C2×SD16—271no—
463C2×D8—91no—
464C2×D8—271no—
465C2×M16—91no—
466C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
467C23×C3—31no—
468C23×C3—31no—
469C23×C3—61no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3—121no—
473C23×C3—184no—
474C23×C3—181no—
475C23×C3—181no—
476C23×C3—364no—
477C22×D3—21no—
478C22×D3—64no—
479C22×D3—62no—
480C22×D3—61no—
481C22×D3—61no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—64no—
485C22×D3—121no—
486C22×D3—124no—
487C22×D3—124no—
488C22×D3#62611yescharacteristic
489C3×D4—32no—
490C3×D4—32no—
491C3×D4—62no—
492C3×D4—61no—
493C3×D4—61no—
494C3×D4—92no—
495C3×D4—92no—
496C3×D4—121no—
497C3×D4—184no—
498C3×D4—181no—
499C3×D4—181no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—32no—
506C2×C3×C4—32no—
507C2×C3×C4—32no—
508C2×C3×C4—32no—
509C2×C3×C4—41no—
510C2×C3×C4—62no—
511C2×C3×C4—62no—
512C2×C3×C4—61no—
513C2×C3×C4C2×D3211yescharacteristic
514C2×C3×C4C2×D3211yescharacteristic
515C2×C3×C4C2×D3211yescharacteristic
516#67—64no—
517#67—184no—
518#67—184no—
519#67—188no—
520#67—184no—
521C2×Dic3—182no—
522C2×Dic3—181no—
523C2×Dic3—181no—
524C2×Dic3—181no—
525C2×Dic3—184no—
526C2×Dic3—361no—
527C2×Dic3—361no—
528C2×Dic3—362no—
529C2×Dic3#62611yescharacteristic
530D12—21no—
531D12—32no—
532D12—32no—
533D12—32no—
534D12—32no—
535D12—62no—
536D12—62no—
537D12—62no—
538D12—64no—
539D12—61no—
540D12—61no—
541D12—61no—
542D12—61no—
543D12—121no—
544D12C2×D3212yes—
545C4×D3—184no—
546C4×D3—184no—
547C4×D3—188no—
548C4×D3#62612yes—
549C4×D3C2×D3212yes—
550Dic6—92no—
551Dic6—92no—
552Dic6—92no—
553Dic6—182no—
554Dic6—182no—
555Dic6—182no—
556Dic6—182no—
557Dic6—181no—
558Dic6—181no—
559Dic6—181no—
560Dic6—362no—
561Dic6—361no—
562Dic6—361no—
563Dic6—362no—
564C3×C8—32no—
565C3×C8—32no—
566C3×C8—62no—
567C3×C8—92no—
568C3⋊C8—32no—
569C3⋊C8—32no—
570C3⋊C8—62no—
571C3⋊C8C2×D3212yescomplemented
572C2×C32—21no—
573C2×C32—22no—
574C2×C32—21no—
575C2×C32—21no—
576C2×C32—22no—
577C2×C32—22no—
578C2×C32—42no—
579C2×C32—41no—
580C2×C32—62no—
581C2×C32—122no—
582C2×C32#90812yescomplemented
583C2×C32#91112yescomplemented
584C2×C32#93212yescomplemented
585C2×C32C22×D1211yescharacteristic
586C2×C32C2×D3×D411yescharacteristic
587C2×C32C22×#6711yescharacteristic
588C3⋊D3—42no—
589C3⋊D3—42no—
590C3×D3—22no—
591C3×D3—22no—
592C3×D3—42no—
593C3×D3—42no—
594C3×D3—42no—
595C3×D3—82no—
596C3×D3—124no—
597C3×D3—122no—
598C3×D3—122no—
599C3×D3—122no—
600C3×D3—122no—
601C3×D3—242no—
602C24—181no—
603#41—274no—
604#41—542no—
605C2×Q8—271no—
606C2×D4—31no—
607C2×D4—94no—
608C2×D4—91no—
609C2×D4—91no—
610C2×D4—182no—
611C2×D4—181no—
612C2×D4—541no—
613C22×C4—31no—
614C22×C4—541no—
615SD16—274no—
616SD16—274no—
617D8—94no—
618D8—274no—
619M16—94no—
620C2×C8—31no—
621C2×C8—91no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—32no—
626C22×C3—32no—
627C22×C3—41no—
628C22×C3—62no—
629C22×C3—62no—
630C22×C3—62no—
631C22×C3—62no—
632C22×C3—62no—
633C22×C3—122no—
634C22×C3—122no—
635C22×C3—122no—
636C22×C3—122no—
637C22×C3—182no—
638C22×C3—182no—
639C22×C3—242no—
640C22×C3—368no—
641C22×C3—362no—
642C22×C3—362no—
643C22×C3D3×D1211yescharacteristic
644C22×C3C2×#62611yescharacteristic
645C22×C3D3×#6711yescharacteristic
646C2×D3—22no—
647C2×D3—22no—
648C2×D3—42no—
649C2×D3—64no—
650C2×D3—62no—
651C2×D3—62no—
652C2×D3—62no—
653C2×D3—62no—
654C2×D3—122no—
655C2×D3—128no—
656C2×D3—128no—
657C2×D3—124no—
658C2×D3—122no—
659C2×D3—122no—
660C2×D3—122no—
661C2×D3—122no—
662C2×D3—242no—
663C2×D3C2×#62612yes—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—32no—
671C3×C4—32no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—62no—
675C3×C4D3×D1211yescharacteristic
676C3×C4C2×#62611yescharacteristic
677C3×C4D3×#6711yescharacteristic
678C3×C4C22×D3211yescharacteristic
679C3×C4C22×D3211yescharacteristic
680C3×C4C22×D3211yescharacteristic
681Dic3—184no—
682Dic3—182no—
683Dic3—182no—
684Dic3—182no—
685Dic3—362no—
686Dic3—362no—
687Dic3—364no—
688Dic3C2×#62612yes—
689C32—21no—
690C32—21no—
691C32—21no—
692C32—41no—
693C32C2×#90811yescharacteristic, complemented
694C32C2×#91111yescharacteristic, complemented
695C32C2×#93211yescharacteristic, complemented
696C23—31no—
697C23—61no—
698C23—184no—
699C23—181no—
700C23—181no—
701C23—364no—
702Q8—272no—
703Q8—541no—
704D4—32no—
705D4—61no—
706D4—92no—
707D4—92no—
708D4—184no—
709D4—181no—
710D4—181no—
711D4—544no—
712C2×C4—31no—
713C2×C4—32no—
714C2×C4—32no—
715C2×C4—544no—
716C2×C4—541no—
717C2×C4D3311yescharacteristic
718C8—32no—
719C8—92no—
720C2×C3—22no—
721C2×C3—22no—
722C2×C3—22no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—42no—
727C2×C3—41no—
728C2×C3—62no—
729C2×C3—62no—
730C2×C3—122no—
731C2×C3—122no—
732C2×C3—122no—
733C2×C3—242no—
734C2×C3—362no—
735C2×C3—362no—
736C2×C3#6379512yescomplemented
737C2×C3#6383012yescomplemented
738C2×C3#6393212yescomplemented
739C2×C3C2×D3×D1211yescharacteristic
740C2×C3C22×#62611yescharacteristic
741C2×C3C2×D3×#6711yescharacteristic
742D3—22no—
743D3—42no—
744D3—124no—
745D3—122no—
746D3—122no—
747D3—122no—
748D3—122no—
749D3—242no—
750C22—32no—
751C22—62no—
752C22—62no—
753C22—122no—
754C22—182no—
755C22—182no—
756C22—368no—
757C22—362no—
758C22—362no—
759C22D3×#62611yescharacteristic
760C4—32no—
761C4—542no—
762C4D3×#62611yescharacteristic
763C4C2×D3311yescharacteristic
764C3—21no—
765C3—21no—
766C3—21no—
767C3—41no—
768C3C2×#6379511yescharacteristic, complemented
769C3C2×#6383011yescharacteristic, complemented
770C3C2×#6393211yescharacteristic, complemented
771C2—62no—
772C2—122no—
773C2—362no—
774C2—362no—
775C2#1172286912yesdirect product factor
776C2C2×D3×#62611yescharacteristic
subgroupG/H
centerC22D3×#626
commutator, cosocleC33×C4C24
FrattiniC4C2×D33
FittingC2×C33×C4C23
socleC22×C33C2×D4
hypercenterC2×C4D33
hypocenterC33C2×AGL(1,ℤ/8)
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×#89021C2semidirect
2. C2×C3×D3×D12C2semidirect
3. C2×#88810C2semidirect
4. C2×#88796C2semidirect
5. C2×#88794C2semidirect
6. C2×C3×#3714C2semidirect
7. C2×C3×#3711C2semidirect
8. #11722869C2direct (N × H)
13. C2×#6308C22semidirect
15. C2×C3×C4⋊(C3⋊D3)C22semidirect
21. #89021C22semidirect
24. C3×D3×D12C22semidirect
25. C2×C3×C3⋊(C3⋊C8)C22semidirect
26. C2×C32×C3⋊C8C22semidirect
27. #88810C22semidirect
28. #88796C22semidirect
29. #88794C22semidirect
30. C3×#3714C22semidirect
31. C3×#3711C22semidirect
35. C2×D3×D12D3semidirect
55. C2×#3714D3semidirect
57. C2×#3711D3semidirect
68. #6308C23semidirect
72. C3×C4⋊(C3⋊D3)C23semidirect
81. C3×C3⋊(C3⋊C8)C23semidirect
82. C32×C3⋊C8C23semidirect
95. C2×C4⋊(C3⋊D3)C2×D3semidirect
130. D3×D12C2×D3semidirect
139. C2×C3⋊(C3⋊C8)C2×D3semidirect
147. C2×C3×C3⋊C8C2×D3semidirect
148. C2×C3×C3⋊C8C2×D3semidirect
159. #3714C2×D3semidirect
161. #3711C2×D3semidirect
248. C4⋊(C3⋊D3)C22×D3semidirect
301. C3⋊(C3⋊C8)C22×D3semidirect
306. C3×C3⋊C8C22×D3semidirect
307. C3×C3⋊C8C22×D3semidirect
309. C2×C33AGL(1,ℤ/8)semidirect
383. C2×C3⋊C8D32semidirect
466. C33C2×AGL(1,ℤ/8)semidirect
571. C3⋊C8C2×D32semidirect
582. C2×C32#908semidirect
583. C2×C32#911semidirect
584. C2×C32#932semidirect
693. C32C2×#908semidirect
694. C32C2×#911semidirect
695. C32C2×#932semidirect
736. C2×C3#63795semidirect
737. C2×C3#63830semidirect
738. C2×C3#63932semidirect
768. C3C2×#63795semidirect
769. C3C2×#63830semidirect
770. C3C2×#63932semidirect
775. C2#11722869direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#890212
C2×C3×D3×D122
C2×#888102
C2×#887962
C2×#887942
C2×C3×#37142
C2×C3×#37112
#117228692
C2×#639323
C2×#638303
C2×#637953