Finite Group Databasebeta

← C2×#11722877 #13170667

Subgroups — C2×#11722877 #13170667

Order 1728.

1714 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89026C211yesmaximal, characteristic, complemented
2C2×#89015C211yesmaximal, characteristic, complemented
3C2×#88811C211yesmaximal, characteristic, complemented
4C2×#88788C211yesmaximal, characteristic, complemented
5C2×C3×#3716C211yesmaximal, characteristic, complemented
6C2×C3×#3714C211yesmaximal, characteristic, complemented
7C2×C3×#3713C211yesmaximal, characteristic, complemented
8#11722877C218yesmaximal, direct product factor
9C2×#63937—31nomaximal
10C2×#63927—31nomaximal
11C2×#63798—31nomaximal
12C22×D3×C3⋊D3—21no—
13C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
15C2×C3×#634C2211yescharacteristic, complemented
16C2×C32×D12C2211yescharacteristic
17C2×C32×D12C2211yescharacteristic, complemented
18C2×#6291—21no—
19C2×#6290—21no—
20C2×D3×C3⋊Dic3—21no—
21#89026—22no—
22#89026C2214yescomplemented
23#89015—22no—
24#89015C2214yescomplemented
25C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
26C2×C32×C3⋊C8C2211yescharacteristic, complemented
27#88811C2214yescomplemented
28#88788C2214yescomplemented
29C3×#3716C2214yescomplemented
30C3×#3714C2214yescomplemented
31C3×#3713C2214yescomplemented
32C2×#3830—31no—
33C2×D4×C3⋊D3—31no—
34C2×#3802—31no—
35C2×#3802—31no—
36C2×#3802—61no—
37C2×#3796—31no—
38C2×#3796—31no—
39C2×#3796—61no—
40C2×#3743—31no—
41C2×C3×#214—31no—
42C2×C3×#213—31no—
43C2×C3×#213—31no—
44C2×C3×#213—31no—
45C2×C3×D24—31no—
46C2×C3×#204—31no—
47#63937—38no—
48#63927—38no—
49C2×#3717—31no—
50C2×#3716—31no—
51C2×#3716D311yescharacteristic, complemented
52C2×#3715—31no—
53C2×#3714D311yescharacteristic, complemented
54C2×#3713D311yescharacteristic, complemented
55C2×#3712—31no—
56C2×#3712—31no—
57C2×#3712—61no—
58#63798—38no—
59C22×C3⋊(C3⋊D3)D411yescharacteristic
60C22×C3×C3⋊D3—21no—
61C22×C32×D3—21no—
62C22×C32×D3—21no—
63C2×D3×C3⋊D3—24no—
64C2×D3×C3⋊D3—44no—
65C2×C33×C4C2311yescharacteristic
66C2×C3⋊(C3⋊Dic3)D411yescharacteristic
67C4×C3⋊(C3⋊D3)D412yes—
68C4×C3⋊(C3⋊D3)C2312yes—
69C2×C3×C3⋊Dic3—21no—
70C3×C4⋊(C3⋊D3)—21no—
71C3×C4⋊(C3⋊D3)C2312yes—
72C3×#634—21no—
73C3×#634C2312yescomplemented
74C32×D12—21no—
75C32×D12—21no—
76C32×D12C2312yes—
77C32×D12C2312yescomplemented
78#6291—24no—
79#6290—24no—
80D3×C3⋊Dic3—24no—
81C3×C3⋊(C3⋊C8)C2312yescomplemented
82C32×C3⋊C8C2312yescomplemented
83C2×#914—91no—
84C2×#911—91no—
85C2×#911—91no—
86C23×C3⋊D3—61no—
87C22×D32—61no—
88C22×D32—61no—
89C22×D32—62no—
90C2×C32×D4—31no—
91C2×C32×D4—31no—
92C2×#638—61no—
93C2×#638—61no—
94C22×C3⋊Dic3—61no—
95#3830—34no—
96#3830—62no—
97D4×C3⋊D3—34no—
98D4×C3⋊D3—62no—
99C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
100C2×C4×C3⋊D3—31no—
101C2×C4×C3⋊D3—31no—
102C2×C4×C3⋊D3—31no—
103C2×C4×C3⋊D3—61no—
104C2×C4×C3⋊D3—61no—
105C2×C4×C3⋊D3—61no—
106C2×C4×C3⋊D3—121no—
107C2×#634C2×D311yescharacteristic, complemented
108C2×C3×D12—21no—
109C2×C3×D12—21no—
110C2×C3×D12—31no—
111C2×C3×D12—31no—
112C2×C3×D12—61no—
113C2×C3×D12C2×D311yescharacteristic
114C2×C3×D12C2×D311yescharacteristic
115C2×C3×D12C2×D311yescharacteristic, complemented
116C2×C3×D12C2×D311yescharacteristic, complemented
117C2×C3×Dic6—31no—
118C2×C3×Dic6—31no—
119C2×C3×Dic6—61no—
120C2×#626—61no—
121C2×#626—61no—
122C2×#626—62no—
123C2×#625—61no—
124C2×#625—61no—
125C2×#625—62no—
126C2×D3×Dic3—61no—
127C2×D3×Dic3—61no—
128C2×D3×Dic3—62no—
129#3802—34no—
130#3802—34no—
131#3802—62no—
132#3802—62no—
133#3802—64no—
134#3802—64no—
135#3796—34no—
136#3796—34no—
137#3796—62no—
138#3796—62no—
139#3796—64no—
140#3796—64no—
141C2×C32×C8—31no—
142C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
143#3743—34no—
144C3×#214—34no—
145C3×#213—34no—
146C3×#213—34no—
147C3×#213—34no—
148C2×C3×C3⋊C8—21no—
149C2×C3×C3⋊C8—31no—
150C2×C3×C3⋊C8—31no—
151C2×C3×C3⋊C8—61no—
152C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
153C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
154C3×D24—34no—
155C3×#204—34no—
156#3717—34no—
157#3716—34no—
158#3716C2×D314yescomplemented
159#3715—34no—
160#3714C2×D314yescomplemented
161#3713C2×D314yescomplemented
162#3712—34no—
163#3712—34no—
164#3712—64no—
165C22×C33C2×D411yescharacteristic
166C2×C3⋊(C3⋊D3)—22no—
167C2×C3⋊(C3⋊D3)C2×D412yes—
168C2×C3×C3⋊D3—22no—
169C2×C3×C3⋊D3—42no—
170C2×C32×D3—22no—
171C2×C32×D3—22no—
172C2×C32×D3—42no—
173C2×C32×D3—42no—
174D3×C3⋊D3—48no—
175C33×C4C2×D411yescharacteristic
176C33×C4C2411yescharacteristic
177C3⋊(C3⋊Dic3)C2×D412yes—
178C3×C3⋊Dic3—22no—
179C2×#239—91no—
180C2×#237—91no—
181C2×#237—91no—
182C2×#237—181no—
183C2×D3×D4—91no—
184C2×D3×D4—91no—
185C2×D3×D4—91no—
186C2×D3×D4—181no—
187C2×C3×SD16—91no—
188C2×C3×D8—91no—
189C2×C3×D8—91no—
190C2×#215—91no—
191C2×#214—31no—
192C2×#214—91no—
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—31no—
196#914—98no—
197#911—98no—
198#911—98no—
199C2×D24—31no—
200C2×#204—31no—
201C2×#204—91no—
202C2×ΓL(1,𝔽25)—91no—
203C2×ΓL(1,𝔽25)—91no—
204C2×ΓL(1,𝔽25)—91no—
205C2×ΓL(1,𝔽25)—181no—
206C23×C32—61no—
207C23×C32—61no—
208C22×C3⋊D3—21no—
209C22×C3⋊D3—31no—
210C22×C3⋊D3—31no—
211C22×C3⋊D3—31no—
212C22×C3⋊D3—61no—
213C22×C3⋊D3—61no—
214C22×C3⋊D3—61no—
215C22×C3⋊D3—64no—
216C22×C3⋊D3—121no—
217C22×C3⋊D3—124no—
218C22×C3×D3—22no—
219C22×C3×D3—22no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—62no—
225C22×C3×D3—61no—
226C22×C3×D3—61no—
227C2×D32—64no—
228C2×D32—64no—
229C2×D32—68no—
230C2×D32—128no—
231C2×D32—124no—
232C2×D32—124no—
233C32×D4—32no—
234C32×D4—32no—
235C32×D4—61no—
236C32×D4—61no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—41no—
241C2×C32×C4C22×D311yescharacteristic
242C2×C32×C4C22×D311yescharacteristic
243C2×C32×C4C22×D311yescharacteristic
244#638—64no—
245#638—64no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—31no—
248C2×C3⋊Dic3—31no—
249C2×C3⋊Dic3—31no—
250C2×C3⋊Dic3—61no—
251C2×C3⋊Dic3—61no—
252C2×C3⋊Dic3—61no—
253C2×C3⋊Dic3—64no—
254C2×C3⋊Dic3—121no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)C22×D312yes—
257C4×C3⋊D3—32no—
258C4×C3⋊D3—32no—
259C4×C3⋊D3—32no—
260C4×C3⋊D3—32no—
261C4×C3⋊D3—32no—
262C4×C3⋊D3—32no—
263C4×C3⋊D3—62no—
264C4×C3⋊D3—62no—
265C4×C3⋊D3—62no—
266C4×C3⋊D3—62no—
267C4×C3⋊D3—62no—
268C4×C3⋊D3—62no—
269C4×C3⋊D3—122no—
270C4×C3⋊D3—122no—
271#634—21no—
272#634C22×D312yescomplemented
273C2×C3×Dic3—62no—
274C2×C3×Dic3—61no—
275C2×C3×Dic3—61no—
276C3×D12—22no—
277C3×D12—22no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—22no—
283C3×D12—22no—
284C3×D12—32no—
285C3×D12—32no—
286C3×D12—62no—
287C3×D12—62no—
288C3×D12—61no—
289C3×D12—61no—
290C3×D12C22×D312yes—
291C3×D12C22×D312yes—
292C3×D12C22×D312yescomplemented
293C3×D12C22×D312yescomplemented
294C3×Dic6—32no—
295C3×Dic6—32no—
296C3×Dic6—62no—
297C3×Dic6—62no—
298C3×Dic6—61no—
299C3×Dic6—61no—
300#626—64no—
301#626—64no—
302#626—68no—
303#625—64no—
304#625—64no—
305#625—68no—
306D3×Dic3—64no—
307D3×Dic3—64no—
308D3×Dic3—68no—
309C32×C8—32no—
310C3⋊(C3⋊C8)C22×D312yescomplemented
311C3×C3⋊C8—22no—
312C3×C3⋊C8—32no—
313C3×C3⋊C8—32no—
314C3×C3⋊C8—62no—
315C3×C3⋊C8C22×D312yescomplemented
316C3×C3⋊C8C22×D312yescomplemented
317C2×AGL(1,ℤ/8)—271noSylow
318C2×C33AGL(1,ℤ/8)12yescomplemented
319C2×C33C22×D411yescharacteristic
320C3⋊(C3⋊D3)—22no—
321C3×C3⋊D3—42no—
322C32×D3—42no—
323C32×D3—42no—
324C23×D3—181no—
325C23×D3—181no—
326C23×D3—181no—
327C23×D3—182no—
328C2×C3×Q8—91no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4—91no—
336C2×#67—181no—
337C2×#67—181no—
338C2×#67—182no—
339C2×#67—181no—
340C2×#67—181no—
341C2×#67—181no—
342C2×#67—182no—
343C22×Dic3—181no—
344C22×Dic3—181no—
345C22×Dic3—182no—
346#239—94no—
347#239—182no—
348#237—94no—
349#237—94no—
350#237—184no—
351#237—182no—
352#237—182no—
353#237—184no—
354D3×D4—94no—
355D3×D4—94no—
356D3×D4—94no—
357D3×D4—184no—
358D3×D4—182no—
359D3×D4—182no—
360D3×D4—182no—
361D3×D4—184no—
362C2×D12—31no—
363C2×D12—31no—
364C2×D12—61no—
365C2×D12—181no—
366C2×D12D3211yescharacteristic
367C2×D12D3211yescharacteristic, complemented
368C2×C4×D3—91no—
369C2×C4×D3—91no—
370C2×C4×D3—91no—
371C2×C4×D3—181no—
372C2×C4×D3—181no—
373C2×C4×D3—181no—
374C2×C4×D3—181no—
375C2×C4×D3—361no—
376C2×Dic6—31no—
377C2×Dic6—31no—
378C2×Dic6—61no—
379C3×SD16—94no—
380C3×D8—94no—
381C3×D8—94no—
382C2×C3×C8—31no—
383C2×C3×C8—31no—
384C2×C3×C8—61no—
385C2×C3×C8—91no—
386#215—94no—
387#214—34no—
388#214—94no—
389#213—34no—
390#213—34no—
391#213—34no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—61no—
395C2×C3⋊C8D3211yescharacteristic, complemented
396D24—34no—
397#204—34no—
398#204—94no—
399ΓL(1,𝔽25)—94no—
400ΓL(1,𝔽25)—94no—
401ΓL(1,𝔽25)—94no—
402ΓL(1,𝔽25)—184no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—41no—
407C22×C32—62no—
408C22×C32—62no—
409C22×C32—122no—
410C22×C32—122no—
411C22×C32D3×D411yescharacteristic
412C22×C32D3×D411yescharacteristic
413C22×C32D3×D411yescharacteristic
414C2×C3⋊D3—22no—
415C2×C3⋊D3—32no—
416C2×C3⋊D3—32no—
417C2×C3⋊D3—32no—
418C2×C3⋊D3—42no—
419C2×C3⋊D3—62no—
420C2×C3⋊D3—62no—
421C2×C3⋊D3—62no—
422C2×C3⋊D3—62no—
423C2×C3⋊D3—64no—
424C2×C3⋊D3—62no—
425C2×C3⋊D3—62no—
426C2×C3⋊D3—122no—
427C2×C3⋊D3—122no—
428C2×C3⋊D3—122no—
429C2×C3⋊D3—124no—
430C2×C3⋊D3—128no—
431C2×C3×D3—24no—
432C2×C3×D3—24no—
433C2×C3×D3—22no—
434C2×C3×D3—22no—
435C2×C3×D3—22no—
436C2×C3×D3—22no—
437C2×C3×D3—44no—
438C2×C3×D3—44no—
439C2×C3×D3—42no—
440C2×C3×D3—42no—
441C2×C3×D3—42no—
442C2×C3×D3—42no—
443C2×C3×D3—64no—
444C2×C3×D3—62no—
445C2×C3×D3—62no—
446C2×C3×D3—124no—
447C2×C3×D3—122no—
448C2×C3×D3—122no—
449D32—1216no—
450D32—128no—
451D32—128no—
452C32×C4—21no—
453C32×C4—21no—
454C32×C4—21no—
455C32×C4—21no—
456C32×C4—21no—
457C32×C4—21no—
458C32×C4—41no—
459C32×C4—41no—
460C32×C4D3×D411yescharacteristic
461C32×C4D3×D411yescharacteristic
462C32×C4D3×D411yescharacteristic
463C32×C4C23×D311yescharacteristic
464C32×C4C23×D311yescharacteristic
465C32×C4C23×D311yescharacteristic
466C3⋊Dic3—22no—
467C3⋊Dic3—32no—
468C3⋊Dic3—32no—
469C3⋊Dic3—32no—
470C3⋊Dic3—62no—
471C3⋊Dic3—62no—
472C3⋊Dic3—62no—
473C3⋊Dic3—122no—
474C3×Dic3—64no—
475C3×Dic3—62no—
476C3×Dic3—62no—
477C2×#41—271no—
478C22×D4—271no—
479AGL(1,ℤ/8)—278no—
480C2×SD16—91no—
481C2×SD16—271no—
482C2×D8—91no—
483C2×D8—91no—
484C2×M16—271no—
485C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
486C23×C3—62no—
487C23×C3—62no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—61no—
491C23×C3—61no—
492C23×C3—181no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—62no—
496C22×D3—61no—
497C22×D3—61no—
498C22×D3—91no—
499C22×D3—91no—
500C22×D3—91no—
501C22×D3—181no—
502C22×D3—181no—
503C22×D3—181no—
504C22×D3—184no—
505C22×D3—184no—
506C22×D3—184no—
507C22×D3—188no—
508C22×D3—361no—
509C22×D3—364no—
510C22×D3—368no—
511C22×D3—364no—
512C22×D3—364no—
513C3×Q8—92no—
514C3×Q8—181no—
515C3×D4—32no—
516C3×D4—32no—
517C3×D4—32no—
518C3×D4—32no—
519C3×D4—62no—
520C3×D4—62no—
521C3×D4—62no—
522C3×D4—62no—
523C3×D4—61no—
524C3×D4—61no—
525C3×D4—61no—
526C3×D4—61no—
527C3×D4—92no—
528C3×D4—181no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—41no—
533C2×C3×C4—181no—
534C2×C3×C4C2×D3211yescharacteristic
535C2×C3×C4C2×D3211yescharacteristic
536C2×C3×C4C2×D3211yescharacteristic
537#67—184no—
538#67—184no—
539#67—188no—
540#67—184no—
541#67—184no—
542#67—184no—
543#67—188no—
544C2×Dic3—62no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—91no—
548C2×Dic3—91no—
549C2×Dic3—91no—
550C2×Dic3—181no—
551C2×Dic3—181no—
552C2×Dic3—181no—
553C2×Dic3—184no—
554C2×Dic3—184no—
555C2×Dic3—188no—
556C2×Dic3—361no—
557D12—21no—
558D12—21no—
559D12—32no—
560D12—32no—
561D12—62no—
562D12—62no—
563D12—61no—
564D12—61no—
565D12—184no—
566D12C2×D3212yes—
567D12C2×D3212yescomplemented
568C4×D3—92no—
569C4×D3—92no—
570C4×D3—92no—
571C4×D3—92no—
572C4×D3—92no—
573C4×D3—92no—
574C4×D3—182no—
575C4×D3—182no—
576C4×D3—182no—
577C4×D3—182no—
578C4×D3—182no—
579C4×D3—182no—
580C4×D3—184no—
581C4×D3—362no—
582C4×D3—362no—
583Dic6—32no—
584Dic6—32no—
585Dic6—62no—
586Dic6—62no—
587Dic6—61no—
588Dic6—61no—
589C3×C8—32no—
590C3×C8—32no—
591C3×C8—62no—
592C3×C8—92no—
593C3⋊C8—32no—
594C3⋊C8—32no—
595C3⋊C8—62no—
596C3⋊C8C2×D3212yescomplemented
597C2×C32—21no—
598C2×C32—22no—
599C2×C32—21no—
600C2×C32—21no—
601C2×C32—22no—
602C2×C32—22no—
603C2×C32—42no—
604C2×C32—41no—
605C2×C32—122no—
606C2×C32—122no—
607C2×C32#91112yescomplemented
608C2×C32#91112yescomplemented
609C2×C32#91412yescomplemented
610C2×C32C2×D3×D411yescharacteristic
611C2×C32C2×D3×D411yescharacteristic
612C2×C32C2×D3×D411yescharacteristic
613C3⋊D3—42no—
614C3⋊D3—62no—
615C3⋊D3—64no—
616C3⋊D3—62no—
617C3⋊D3—62no—
618C3⋊D3—122no—
619C3⋊D3—122no—
620C3⋊D3—124no—
621C3×D3—44no—
622C3×D3—44no—
623C3×D3—42no—
624C3×D3—42no—
625C3×D3—42no—
626C3×D3—42no—
627C3×D3—124no—
628C3×D3—122no—
629C3×D3—122no—
630C24—541no—
631#41—274no—
632#41—542no—
633C2×Q8—91no—
634C2×D4—31no—
635C2×D4—31no—
636C2×D4—91no—
637C2×D4—274no—
638C2×D4—541no—
639C2×D4—542no—
640C2×D4—541no—
641C22×C4—271no—
642C22×C4—541no—
643SD16—94no—
644SD16—274no—
645D8—94no—
646D8—94no—
647M16—274no—
648C2×C8—31no—
649C2×C8—91no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—41no—
654C22×C3—64no—
655C22×C3—64no—
656C22×C3—62no—
657C22×C3—62no—
658C22×C3—62no—
659C22×C3—62no—
660C22×C3—124no—
661C22×C3—124no—
662C22×C3—122no—
663C22×C3—122no—
664C22×C3—122no—
665C22×C3—122no—
666C22×C3—182no—
667C22×C3—362no—
668C22×C3#380211yescharacteristic
669C22×C3#381111yescharacteristic
670C22×C3#381111yescharacteristic
671C2×D3—22no—
672C2×D3—22no—
673C2×D3—42no—
674C2×D3—42no—
675C2×D3—64no—
676C2×D3—62no—
677C2×D3—62no—
678C2×D3—92no—
679C2×D3—92no—
680C2×D3—92no—
681C2×D3—124no—
682C2×D3—122no—
683C2×D3—122no—
684C2×D3—182no—
685C2×D3—182no—
686C2×D3—182no—
687C2×D3—184no—
688C2×D3—182no—
689C2×D3—182no—
690C2×D3—182no—
691C2×D3—362no—
692C2×D3—362no—
693C2×D3—362no—
694C2×D3—364no—
695C2×D3—368no—
696C2×D3—3616no—
697C2×D3—368no—
698C2×D3—368no—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—182no—
708C3×C4#380211yescharacteristic
709C3×C4#381111yescharacteristic
710C3×C4#381111yescharacteristic
711C3×C4C22×D3211yescharacteristic
712C3×C4C22×D3211yescharacteristic
713C3×C4C22×D3211yescharacteristic
714Dic3—64no—
715Dic3—62no—
716Dic3—62no—
717Dic3—92no—
718Dic3—92no—
719Dic3—92no—
720Dic3—182no—
721Dic3—182no—
722Dic3—182no—
723Dic3—362no—
724C32—21no—
725C32—21no—
726C32—21no—
727C32—41no—
728C32C2×#91111yescharacteristic, complemented
729C32C2×#91111yescharacteristic, complemented
730C32C2×#91411yescharacteristic, complemented
731C23—61no—
732C23—61no—
733C23—181no—
734C23—271no—
735C23—544no—
736C23—1084no—
737Q8—92no—
738Q8—181no—
739D4—32no—
740D4—32no—
741D4—61no—
742D4—61no—
743D4—92no—
744D4—181no—
745D4—544no—
746D4—544no—
747C2×C4—181no—
748C2×C4—271no—
749C2×C4—272no—
750C2×C4—272no—
751C2×C4—544no—
752C2×C4D3311yescharacteristic
753C8—32no—
754C8—92no—
755C2×C3—22no—
756C2×C3—22no—
757C2×C3—22no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—42no—
762C2×C3—41no—
763C2×C3—124no—
764C2×C3—124no—
765C2×C3—122no—
766C2×C3—122no—
767C2×C3—122no—
768C2×C3—122no—
769C2×C3—362no—
770C2×C3#6379812yescomplemented
771C2×C3#6392712yescomplemented
772C2×C3#6393712yescomplemented
773C2×C3C2×#380211yescharacteristic
774C2×C3C2×#381111yescharacteristic
775C2×C3C2×#381111yescharacteristic
776D3—42no—
777D3—42no—
778D3—124no—
779D3—122no—
780D3—122no—
781D3—184no—
782D3—182no—
783D3—182no—
784D3—182no—
785D3—362no—
786D3—362no—
787D3—364no—
788C22—62no—
789C22—62no—
790C22—122no—
791C22—122no—
792C22—182no—
793C22—272no—
794C22—362no—
795C22—542no—
796C22—1088no—
797C22#8895411yescharacteristic
798C4—182no—
799C4—272no—
800C4#8895411yescharacteristic
801C4C2×D3311yescharacteristic
802C3—21no—
803C3—21no—
804C3—21no—
805C3—41no—
806C3C2×#6379811yescharacteristic, complemented
807C3C2×#6392711yescharacteristic, complemented
808C3C2×#6393711yescharacteristic, complemented
809C2—122no—
810C2—122no—
811C2—362no—
812C2—542no—
813C2#1172287712yesdirect product factor
814C2C2×#8895411yescharacteristic
subgroupG/H
centerC22#88954
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×#89026C2semidirect
2. C2×#89015C2semidirect
3. C2×#88811C2semidirect
4. C2×#88788C2semidirect
5. C2×C3×#3716C2semidirect
6. C2×C3×#3714C2semidirect
7. C2×C3×#3713C2semidirect
8. #11722877C2direct (N × H)
15. C2×C3×#634C22semidirect
17. C2×C32×D12C22semidirect
22. #89026C22semidirect
24. #89015C22semidirect
25. C2×C3×C3⋊(C3⋊C8)C22semidirect
26. C2×C32×C3⋊C8C22semidirect
27. #88811C22semidirect
28. #88788C22semidirect
29. C3×#3716C22semidirect
30. C3×#3714C22semidirect
31. C3×#3713C22semidirect
51. C2×#3716D3semidirect
53. C2×#3714D3semidirect
54. C2×#3713D3semidirect
73. C3×#634C23semidirect
77. C32×D12C23semidirect
81. C3×C3⋊(C3⋊C8)C23semidirect
82. C32×C3⋊C8C23semidirect
107. C2×#634C2×D3semidirect
115. C2×C3×D12C2×D3semidirect
116. C2×C3×D12C2×D3semidirect
142. C2×C3⋊(C3⋊C8)C2×D3semidirect
152. C2×C3×C3⋊C8C2×D3semidirect
153. C2×C3×C3⋊C8C2×D3semidirect
158. #3716C2×D3semidirect
160. #3714C2×D3semidirect
161. #3713C2×D3semidirect
272. #634C22×D3semidirect
292. C3×D12C22×D3semidirect
293. C3×D12C22×D3semidirect
310. C3⋊(C3⋊C8)C22×D3semidirect
315. C3×C3⋊C8C22×D3semidirect
316. C3×C3⋊C8C22×D3semidirect
318. C2×C33AGL(1,ℤ/8)semidirect
367. C2×D12D32semidirect
395. C2×C3⋊C8D32semidirect
485. C33C2×AGL(1,ℤ/8)semidirect
567. D12C2×D32semidirect
596. C3⋊C8C2×D32semidirect
607. C2×C32#911semidirect
608. C2×C32#911semidirect
609. C2×C32#914semidirect
728. C32C2×#911semidirect
729. C32C2×#911semidirect
730. C32C2×#914semidirect
770. C2×C3#63798semidirect
771. C2×C3#63927semidirect
772. C2×C3#63937semidirect
806. C3C2×#63798semidirect
807. C3C2×#63927semidirect
808. C3C2×#63937semidirect
813. C2#11722877direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#890262
C2×#890152
C2×#888112
C2×#887882
C2×C3×#37162
C2×C3×#37142
C2×C3×#37132
#117228772
C2×#639373
C2×#639273
C2×#637983