Finite Group Databasebeta

← C2×#11722879 #13170674

Subgroups — C2×#11722879 #13170674

Order 1728.

1626 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89041C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×D12C211yesmaximal, characteristic, complemented
3C2×#88797C211yesmaximal, characteristic, complemented
4C2×#88791C211yesmaximal, characteristic, complemented
5C2×C3×#3716C211yesmaximal, characteristic, complemented
6C2×C3×#3714C211yesmaximal, characteristic, complemented
7C2×C3×#3712C211yesmaximal, characteristic, complemented
8#11722879C218yesmaximal, direct product factor
9C2×#63937—31nomaximal
10C2×#63795—31nomaximal
11C2×#63794—31nomaximal
12C22×D3×C3⋊D3—21no—
13C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
14C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic, complemented
17C2×C32×D12C2211yescharacteristic
18C2×#6295—21no—
19C2×#6294—21no—
20#89041—22no—
21#89041C2214yescomplemented
22C2×#6291—21no—
23C3⋊D3×D12—22no—
24C3⋊D3×D12C2214yescomplemented
25C2×C32×C3⋊C8C2211yescharacteristic, complemented
26C2×C32×C3⋊C8C2211yescharacteristic, complemented
27#88797C2214yescomplemented
28#88791C2214yescomplemented
29C3×#3716C2214yescomplemented
30C3×#3714C2214yescomplemented
31C3×#3712C2214yescomplemented
32C2×D4×C3⋊D3—31no—
33C2×D3×D12—31no—
34C2×D3×D12—31no—
35C2×D3×D12—61no—
36C2×#3799—31no—
37C2×#3796—31no—
38C2×#3795—31no—
39C2×#3745—31no—
40C2×#3744—31no—
41C2×C3×#214—31no—
42C2×C3×#213—31no—
43C2×C3×D24—31no—
44C2×C3×#204—31no—
45C2×C3×ΓL(1,𝔽25)—31no—
46C2×C3×ΓL(1,𝔽25)—31no—
47#63937—38no—
48C2×#3717—31no—
49C2×#3717—31no—
50C2×#3717—61no—
51C2×#3716D311yescharacteristic, complemented
52C2×#3714—31no—
53C2×#3714—31no—
54C2×#3714—61no—
55C2×#3714D311yescharacteristic, complemented
56C2×#3712D311yescharacteristic, complemented
57#63795—38no—
58#63794—38no—
59C22×C3⋊(C3⋊D3)—21no—
60C22×C3×C3⋊D3—21no—
61C22×C3×C3⋊D3D411yescharacteristic
62C22×C32×D3—21no—
63C2×D3×C3⋊D3—24no—
64C2×D3×C3⋊D3—44no—
65C2×C33×C4C2311yescharacteristic
66C4⋊(C3⋊(C3⋊D3))—21no—
67C4⋊(C3⋊(C3⋊D3))C2312yes—
68C2×C3×C3⋊Dic3—21no—
69C2×C3×C3⋊Dic3D411yescharacteristic
70C3×C4⋊(C3⋊D3)—21no—
71C3×C4⋊(C3⋊D3)C2312yescomplemented
72C3×C4×C3⋊D3D412yes—
73C3×C4×C3⋊D3C2312yes—
74C3×#634—21no—
75C3×#634C2312yescomplemented
76C32×D12—21no—
77C32×D12C2312yes—
78#6295—24no—
79#6294—24no—
80#6291—24no—
81C32×C3⋊C8C2312yescomplemented
82C32×C3⋊C8C2312yescomplemented
83C2×#914—91no—
84C2×#911—91no—
85C2×#908—91no—
86C23×C3⋊D3—61no—
87C22×D32—61no—
88C22×D32—61no—
89C22×D32—62no—
90C2×C32×D4—31no—
91C2×#638—61no—
92D4×C3⋊D3—34no—
93D4×C3⋊D3—62no—
94C2×C4⋊(C3⋊D3)—31no—
95C2×C4⋊(C3⋊D3)—31no—
96C2×C4⋊(C3⋊D3)—31no—
97C2×C4⋊(C3⋊D3)—61no—
98C2×C4⋊(C3⋊D3)—61no—
99C2×C4⋊(C3⋊D3)—61no—
100C2×C4⋊(C3⋊D3)—121no—
101C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
102C2×C4×C3⋊D3C2×D311yescharacteristic
103C2×#634C2×D311yescharacteristic, complemented
104C2×C3×D12—21no—
105C2×C3×D12—31no—
106C2×C3×D12—31no—
107C2×C3×D12—61no—
108C2×C3×D12C2×D311yescharacteristic
109C2×C3×D12C2×D311yescharacteristic
110C2×C3×C4×D3—31no—
111C2×C3×C4×D3—31no—
112C2×C3×C4×D3—61no—
113C2×C3×Dic6—31no—
114C2×C3×Dic6—31no—
115C2×C3×Dic6—61no—
116C2×#626—61no—
117C2×#626—61no—
118C2×#626—62no—
119C2×#626—61no—
120C2×#626—61no—
121C2×#625—61no—
122C2×#624—61no—
123C2×D3×Dic3—61no—
124C2×D3×Dic3—61no—
125D3×D12—34no—
126D3×D12—34no—
127D3×D12—62no—
128D3×D12—62no—
129D3×D12—64no—
130D3×D12—64no—
131#3799—34no—
132#3799—62no—
133#3796—34no—
134#3796—62no—
135#3795—34no—
136#3795—62no—
137C2×C32×C8—31no—
138C2×C32×C8—31no—
139#3745—34no—
140#3744—34no—
141C3×#214—34no—
142C3×#213—34no—
143C2×C3×C3⋊C8—21no—
144C2×C3×C3⋊C8—21no—
145C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
146C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
147C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
148C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
149C3×D24—34no—
150C3×#204—34no—
151C3×ΓL(1,𝔽25)—34no—
152C3×ΓL(1,𝔽25)—34no—
153#3717—34no—
154#3717—34no—
155#3717—64no—
156#3716C2×D314yescomplemented
157#3714—34no—
158#3714—34no—
159#3714—64no—
160#3714C2×D314yescomplemented
161#3712C2×D314yescomplemented
162C22×C33C2×D411yescharacteristic
163C2×C3⋊(C3⋊D3)—22no—
164C2×C3⋊(C3⋊D3)—42no—
165C2×C3×C3⋊D3—22no—
166C2×C3×C3⋊D3—22no—
167C2×C3×C3⋊D3—42no—
168C2×C3×C3⋊D3C2×D412yes—
169C2×C32×D3—22no—
170C2×C32×D3—42no—
171D3×C3⋊D3—48no—
172C33×C4C2×D411yescharacteristic
173C33×C4C2411yescharacteristic
174C3×C3⋊Dic3—22no—
175C3×C3⋊Dic3C2×D412yes—
176C2×#239—91no—
177C2×#237—91no—
178C2×D3×D4—91no—
179C2×D3×D4—91no—
180C2×D3×D4—181no—
181C2×#235—91no—
182C22×D12—91no—
183C2×C3×SD16—91no—
184C2×C3×D8—91no—
185C2×C3×M16—91no—
186C2×#215—91no—
187C2×#214—31no—
188C2×#213—31no—
189C2×#213—91no—
190#914—98no—
191#911—98no—
192#908—98no—
193C2×D24—31no—
194C2×D24—91no—
195C2×D24—91no—
196C2×D24—181no—
197C2×#204—31no—
198C2×#204—91no—
199C2×#204—91no—
200C2×#204—181no—
201C2×ΓL(1,𝔽25)—31no—
202C2×ΓL(1,𝔽25)—31no—
203C23×C32—61no—
204C22×C3⋊D3—21no—
205C22×C3⋊D3—61no—
206C22×C3⋊D3—64no—
207C22×C3⋊D3—62no—
208C22×C3⋊D3—61no—
209C22×C3⋊D3—61no—
210C22×C3⋊D3—121no—
211C22×C3⋊D3—121no—
212C22×C3⋊D3—122no—
213C22×C3⋊D3—124no—
214C22×C3⋊D3D1211yescharacteristic
215C22×C3×D3—22no—
216C22×C3×D3—21no—
217C22×C3×D3—21no—
218C22×C3×D3—31no—
219C22×C3×D3—31no—
220C22×C3×D3—61no—
221C22×C3×D3—61no—
222C22×C3×D3—61no—
223C22×C3×D3—121no—
224C2×D32—64no—
225C2×D32—64no—
226C2×D32—68no—
227C2×D32—128no—
228C2×D32—124no—
229C2×D32—124no—
230C32×D4—32no—
231C32×D4—61no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—41no—
236C2×C32×C4C22×D311yescharacteristic
237C2×C32×C4C22×D311yescharacteristic
238C2×C32×C4C22×D311yescharacteristic
239#638—64no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3D1211yescharacteristic
242C4⋊(C3⋊D3)—21no—
243C4⋊(C3⋊D3)—32no—
244C4⋊(C3⋊D3)—32no—
245C4⋊(C3⋊D3)—32no—
246C4⋊(C3⋊D3)—62no—
247C4⋊(C3⋊D3)—62no—
248C4⋊(C3⋊D3)—62no—
249C4⋊(C3⋊D3)—61no—
250C4⋊(C3⋊D3)—62no—
251C4⋊(C3⋊D3)—61no—
252C4⋊(C3⋊D3)—61no—
253C4⋊(C3⋊D3)—122no—
254C4⋊(C3⋊D3)—121no—
255C4⋊(C3⋊D3)—121no—
256C4⋊(C3⋊D3)—122no—
257C4⋊(C3⋊D3)C22×D312yescomplemented
258C4×C3⋊D3D1212yes—
259C4×C3⋊D3C22×D312yes—
260#634—21no—
261#634C22×D312yescomplemented
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—61no—
265C2×C3×Dic3—61no—
266C2×C3×Dic3—61no—
267C2×C3×Dic3—121no—
268C3×D12—22no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—22no—
272C3×D12—32no—
273C3×D12—32no—
274C3×D12—62no—
275C3×D12—61no—
276C3×D12—61no—
277C3×D12—121no—
278C3×D12C22×D312yes—
279C3×D12C22×D312yes—
280C3×C4×D3—32no—
281C3×C4×D3—32no—
282C3×C4×D3—32no—
283C3×C4×D3—32no—
284C3×C4×D3—62no—
285C3×C4×D3—62no—
286C3×Dic6—32no—
287C3×Dic6—32no—
288C3×Dic6—62no—
289C3×Dic6—61no—
290C3×Dic6—61no—
291C3×Dic6—121no—
292#626—64no—
293#626—64no—
294#626—68no—
295#626—64no—
296#626—64no—
297#625—64no—
298#624—64no—
299D3×Dic3—64no—
300D3×Dic3—64no—
301C32×C8—32no—
302C32×C8—32no—
303C3×C3⋊C8—22no—
304C3×C3⋊C8—22no—
305C3×C3⋊C8C22×D312yescomplemented
306C3×C3⋊C8C22×D312yescomplemented
307C3×C3⋊C8C22×D312yescomplemented
308C3×C3⋊C8C22×D312yescomplemented
309C2×AGL(1,ℤ/8)—271noSylow
310C2×C33AGL(1,ℤ/8)12yescomplemented
311C2×C33C22×D411yescharacteristic
312C3⋊(C3⋊D3)—42no—
313C3×C3⋊D3—22no—
314C3×C3⋊D3—42no—
315C32×D3—42no—
316C23×D3—181no—
317C23×D3—181no—
318C23×D3—181no—
319C23×D3—182no—
320C2×C3×Q8—91no—
321C2×C3×D4—31no—
322C2×C3×D4—31no—
323C2×C3×D4—61no—
324C2×C3×D4—91no—
325C22×C3×C4—91no—
326C2×#67—181no—
327C2×#67—181no—
328C2×#67—181no—
329C2×#67—181no—
330C2×#67—182no—
331C22×Dic3—181no—
332#239—94no—
333#239—182no—
334#237—94no—
335#237—182no—
336D3×D4—94no—
337D3×D4—94no—
338D3×D4—184no—
339D3×D4—182no—
340D3×D4—182no—
341D3×D4—184no—
342#235—94no—
343#235—182no—
344C2×D12—31no—
345C2×D12—31no—
346C2×D12—61no—
347C2×D12—91no—
348C2×D12—91no—
349C2×D12—91no—
350C2×D12—94no—
351C2×D12—181no—
352C2×D12—181no—
353C2×D12—181no—
354C2×D12—182no—
355C2×D12—181no—
356C2×D12—181no—
357C2×D12—361no—
358C2×D12D3211yescharacteristic
359C2×C4×D3—31no—
360C2×C4×D3—31no—
361C2×C4×D3—61no—
362C2×C4×D3—181no—
363C2×C4×D3—181no—
364C2×Dic6—31no—
365C2×Dic6—31no—
366C2×Dic6—61no—
367C3×SD16—94no—
368C3×D8—94no—
369C3×M16—94no—
370C2×C3×C8—31no—
371C2×C3×C8—31no—
372C2×C3×C8—31no—
373C2×C3×C8—31no—
374C2×C3×C8—61no—
375C2×C3×C8—61no—
376#215—94no—
377#214—34no—
378#213—34no—
379#213—94no—
380C2×C3⋊C8D3211yescharacteristic, complemented
381C2×C3⋊C8D3211yescharacteristic, complemented
382D24—34no—
383D24—94no—
384D24—94no—
385D24—184no—
386#204—34no—
387#204—94no—
388#204—94no—
389#204—184no—
390ΓL(1,𝔽25)—34no—
391ΓL(1,𝔽25)—34no—
392C22×C32—21no—
393C22×C32—21no—
394C22×C32—21no—
395C22×C32—41no—
396C22×C32—62no—
397C22×C32—122no—
398C22×C32C2×D1211yescharacteristic
399C22×C32D3×D411yescharacteristic
400C22×C32D3×D411yescharacteristic
401C2×C3⋊D3—22no—
402C2×C3⋊D3—22no—
403C2×C3⋊D3—42no—
404C2×C3⋊D3—62no—
405C2×C3⋊D3—64no—
406C2×C3⋊D3—62no—
407C2×C3⋊D3—62no—
408C2×C3⋊D3—122no—
409C2×C3⋊D3—122no—
410C2×C3⋊D3—124no—
411C2×C3⋊D3—128no—
412C2×C3⋊D3—122no—
413C2×C3⋊D3—124no—
414C2×C3⋊D3—122no—
415C2×C3⋊D3—122no—
416C2×C3⋊D3—242no—
417C2×C3⋊D3—242no—
418C2×C3⋊D3—244no—
419C2×C3⋊D3C2×D1212yes—
420C2×C3×D3—24no—
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—32no—
424C2×C3×D3—32no—
425C2×C3×D3—44no—
426C2×C3×D3—42no—
427C2×C3×D3—42no—
428C2×C3×D3—62no—
429C2×C3×D3—64no—
430C2×C3×D3—62no—
431C2×C3×D3—62no—
432C2×C3×D3—62no—
433C2×C3×D3—62no—
434C2×C3×D3—122no—
435C2×C3×D3—122no—
436C2×C3×D3—122no—
437C2×C3×D3—242no—
438D32—1216no—
439D32—128no—
440D32—128no—
441C32×C4—21no—
442C32×C4—21no—
443C32×C4—21no—
444C32×C4—21no—
445C32×C4—21no—
446C32×C4—21no—
447C32×C4—41no—
448C32×C4—41no—
449C32×C4C2×D1211yescharacteristic
450C32×C4D3×D411yescharacteristic
451C32×C4D3×D411yescharacteristic
452C32×C4C23×D311yescharacteristic
453C32×C4C23×D311yescharacteristic
454C32×C4C23×D311yescharacteristic
455C3⋊Dic3—22no—
456C3⋊Dic3C2×D1212yes—
457C3×Dic3—32no—
458C3×Dic3—32no—
459C3×Dic3—62no—
460C3×Dic3—62no—
461C3×Dic3—62no—
462C3×Dic3—122no—
463C2×#41—271no—
464C22×D4—271no—
465AGL(1,ℤ/8)—278no—
466C2×SD16—91no—
467C2×SD16—271no—
468C2×D8—91no—
469C2×D8—271no—
470C2×M16—91no—
471C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
472C23×C3—62no—
473C23×C3—61no—
474C23×C3—61no—
475C23×C3—91no—
476C23×C3—181no—
477C22×D3—21no—
478C22×D3—31no—
479C22×D3—31no—
480C22×D3—61no—
481C22×D3—61no—
482C22×D3—61no—
483C22×D3—121no—
484C22×D3—184no—
485C22×D3—184no—
486C22×D3—184no—
487C22×D3—188no—
488C22×D3—182no—
489C22×D3—181no—
490C22×D3—181no—
491C22×D3—181no—
492C22×D3—361no—
493C22×D3—361no—
494C22×D3—362no—
495C22×D3—364no—
496C22×D3—368no—
497C22×D3—364no—
498C22×D3—364no—
499C3×Q8—92no—
500C3×Q8—181no—
501C3×D4—32no—
502C3×D4—32no—
503C3×D4—62no—
504C3×D4—62no—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—92no—
508C3×D4—181no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—41no—
513C2×C3×C4—91no—
514C2×C3×C4—92no—
515C2×C3×C4—92no—
516C2×C3×C4—181no—
517C2×C3×C4C2×D3211yescharacteristic
518C2×C3×C4C2×D3211yescharacteristic
519C2×C3×C4C2×D3211yescharacteristic
520#67—184no—
521#67—184no—
522#67—184no—
523#67—184no—
524#67—188no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—121no—
531C2×Dic3—184no—
532D12—21no—
533D12—32no—
534D12—32no—
535D12—62no—
536D12—61no—
537D12—61no—
538D12—92no—
539D12—92no—
540D12—92no—
541D12—121no—
542D12—182no—
543D12—182no—
544D12—182no—
545D12—182no—
546D12—184no—
547D12—184no—
548D12—181no—
549D12—181no—
550D12—181no—
551D12—362no—
552D12—361no—
553D12—361no—
554D12—362no—
555D12C2×D3212yes—
556C4×D3—32no—
557C4×D3—32no—
558C4×D3—32no—
559C4×D3—32no—
560C4×D3—62no—
561C4×D3—62no—
562C4×D3—184no—
563C4×D3—184no—
564Dic6—32no—
565Dic6—32no—
566Dic6—62no—
567Dic6—61no—
568Dic6—61no—
569Dic6—121no—
570C3×C8—32no—
571C3×C8—32no—
572C3×C8—32no—
573C3×C8—32no—
574C3×C8—62no—
575C3×C8—62no—
576C3⋊C8C2×D3212yescomplemented
577C3⋊C8C2×D3212yescomplemented
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—22no—
581C2×C32—22no—
582C2×C32—21no—
583C2×C32—22no—
584C2×C32—42no—
585C2×C32—41no—
586C2×C32—122no—
587C2×C32#90812yescomplemented
588C2×C32#91112yescomplemented
589C2×C32#91412yescomplemented
590C2×C32C22×D1211yescharacteristic
591C2×C32C2×D3×D411yescharacteristic
592C2×C32C2×D3×D411yescharacteristic
593C3⋊D3—22no—
594C3⋊D3—42no—
595C3⋊D3—122no—
596C3⋊D3—124no—
597C3⋊D3—122no—
598C3⋊D3—122no—
599C3⋊D3—242no—
600C3⋊D3—242no—
601C3⋊D3—244no—
602C3×D3—44no—
603C3×D3—42no—
604C3×D3—42no—
605C3×D3—64no—
606C3×D3—62no—
607C3×D3—62no—
608C3×D3—122no—
609C3×D3—122no—
610C3×D3—242no—
611C24—541no—
612#41—274no—
613#41—542no—
614C2×Q8—91no—
615C2×D4—31no—
616C2×D4—91no—
617C2×D4—274no—
618C2×D4—271no—
619C2×D4—542no—
620C2×D4—541no—
621C2×D4—541no—
622C22×C4—91no—
623C22×C4—541no—
624SD16—94no—
625SD16—274no—
626D8—94no—
627D8—274no—
628M16—94no—
629C2×C8—31no—
630C2×C8—31no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—41no—
635C22×C3—64no—
636C22×C3—62no—
637C22×C3—62no—
638C22×C3—92no—
639C22×C3—124no—
640C22×C3—122no—
641C22×C3—122no—
642C22×C3—182no—
643C22×C3—182no—
644C22×C3—362no—
645C22×C3D3×D1211yescharacteristic
646C22×C3D3×D1211yescharacteristic
647C22×C3#381111yescharacteristic
648C2×D3—22no—
649C2×D3—32no—
650C2×D3—32no—
651C2×D3—42no—
652C2×D3—62no—
653C2×D3—64no—
654C2×D3—62no—
655C2×D3—62no—
656C2×D3—62no—
657C2×D3—62no—
658C2×D3—122no—
659C2×D3—122no—
660C2×D3—122no—
661C2×D3—184no—
662C2×D3—182no—
663C2×D3—182no—
664C2×D3—182no—
665C2×D3—242no—
666C2×D3—362no—
667C2×D3—362no—
668C2×D3—364no—
669C2×D3—368no—
670C2×D3—3616no—
671C2×D3—368no—
672C2×D3—368no—
673C2×D3—364no—
674C2×D3—362no—
675C2×D3—362no—
676C2×D3—362no—
677C2×D3—722no—
678C2×D3—722no—
679C2×D3—724no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—92no—
689C3×C4—182no—
690C3×C4D3×D1211yescharacteristic
691C3×C4D3×D1211yescharacteristic
692C3×C4#381111yescharacteristic
693C3×C4C22×D3211yescharacteristic
694C3×C4C22×D3211yescharacteristic
695C3×C4C22×D3211yescharacteristic
696Dic3—32no—
697Dic3—32no—
698Dic3—62no—
699Dic3—62no—
700Dic3—62no—
701Dic3—122no—
702C32—21no—
703C32—21no—
704C32—21no—
705C32—41no—
706C32C2×#90811yescharacteristic, complemented
707C32C2×#91111yescharacteristic, complemented
708C32C2×#91411yescharacteristic, complemented
709C23—61no—
710C23—91no—
711C23—181no—
712C23—544no—
713C23—541no—
714C23—1084no—
715Q8—92no—
716Q8—181no—
717D4—32no—
718D4—61no—
719D4—92no—
720D4—181no—
721D4—272no—
722D4—544no—
723D4—544no—
724D4—541no—
725C2×C4—91no—
726C2×C4—92no—
727C2×C4—92no—
728C2×C4—181no—
729C2×C4—544no—
730C2×C4D3311yescharacteristic
731C8—32no—
732C8—32no—
733C2×C3—22no—
734C2×C3—22no—
735C2×C3—22no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—42no—
740C2×C3—41no—
741C2×C3—124no—
742C2×C3—122no—
743C2×C3—122no—
744C2×C3—182no—
745C2×C3—362no—
746C2×C3#6379412yescomplemented
747C2×C3#6379512yescomplemented
748C2×C3#6393712yescomplemented
749C2×C3C2×D3×D1211yescharacteristic
750C2×C3C2×D3×D1211yescharacteristic
751C2×C3C2×#381111yescharacteristic
752D3—42no—
753D3—64no—
754D3—62no—
755D3—62no—
756D3—122no—
757D3—122no—
758D3—242no—
759D3—364no—
760D3—362no—
761D3—362no—
762D3—362no—
763D3—722no—
764D3—722no—
765D3—724no—
766C22—62no—
767C22—92no—
768C22—122no—
769C22—182no—
770C22—182no—
771C22—362no—
772C22—542no—
773C22—1088no—
774C22—1082no—
775C22#8895511yescharacteristic
776C4—92no—
777C4—182no—
778C4#8895511yescharacteristic
779C4C2×D3311yescharacteristic
780C3—21no—
781C3—21no—
782C3—21no—
783C3—41no—
784C3C2×#6379411yescharacteristic, complemented
785C3C2×#6379511yescharacteristic, complemented
786C3C2×#6393711yescharacteristic, complemented
787C2—122no—
788C2—182no—
789C2—362no—
790C2—1082no—
791C2#1172287912yesdirect product factor
792C2C2×#8895511yescharacteristic
subgroupG/H
centerC22#88955
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×#89041C2semidirect
2. C2×C3⋊D3×D12C2semidirect
3. C2×#88797C2semidirect
4. C2×#88791C2semidirect
5. C2×C3×#3716C2semidirect
6. C2×C3×#3714C2semidirect
7. C2×C3×#3712C2semidirect
8. #11722879C2direct (N × H)
14. C2×C3×C4⋊(C3⋊D3)C22semidirect
16. C2×C3×#634C22semidirect
21. #89041C22semidirect
24. C3⋊D3×D12C22semidirect
25. C2×C32×C3⋊C8C22semidirect
26. C2×C32×C3⋊C8C22semidirect
27. #88797C22semidirect
28. #88791C22semidirect
29. C3×#3716C22semidirect
30. C3×#3714C22semidirect
31. C3×#3712C22semidirect
51. C2×#3716D3semidirect
55. C2×#3714D3semidirect
56. C2×#3712D3semidirect
71. C3×C4⋊(C3⋊D3)C23semidirect
75. C3×#634C23semidirect
81. C32×C3⋊C8C23semidirect
82. C32×C3⋊C8C23semidirect
101. C2×C4⋊(C3⋊D3)C2×D3semidirect
103. C2×#634C2×D3semidirect
145. C2×C3×C3⋊C8C2×D3semidirect
146. C2×C3×C3⋊C8C2×D3semidirect
147. C2×C3×C3⋊C8C2×D3semidirect
148. C2×C3×C3⋊C8C2×D3semidirect
156. #3716C2×D3semidirect
160. #3714C2×D3semidirect
161. #3712C2×D3semidirect
257. C4⋊(C3⋊D3)C22×D3semidirect
261. #634C22×D3semidirect
305. C3×C3⋊C8C22×D3semidirect
306. C3×C3⋊C8C22×D3semidirect
307. C3×C3⋊C8C22×D3semidirect
308. C3×C3⋊C8C22×D3semidirect
310. C2×C33AGL(1,ℤ/8)semidirect
380. C2×C3⋊C8D32semidirect
381. C2×C3⋊C8D32semidirect
471. C33C2×AGL(1,ℤ/8)semidirect
576. C3⋊C8C2×D32semidirect
577. C3⋊C8C2×D32semidirect
587. C2×C32#908semidirect
588. C2×C32#911semidirect
589. C2×C32#914semidirect
706. C32C2×#908semidirect
707. C32C2×#911semidirect
708. C32C2×#914semidirect
746. C2×C3#63794semidirect
747. C2×C3#63795semidirect
748. C2×C3#63937semidirect
784. C3C2×#63794semidirect
785. C3C2×#63795semidirect
786. C3C2×#63937semidirect
791. C2#11722879direct (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×C3⋊D3×D122
C2×#887972
C2×#887912
C2×C3×#37162
C2×C3×#37142
C2×C3×#37122
#117228792
C2×#639373
C2×#637953
C2×#637943