Finite Group Databasebeta

← #10967590

Subgroups — #10967590

Order 768.

2630 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#237C211yesmaximal, characteristic
2C22×#887C211yesmaximal, characteristic, complemented
3C3×#2486C211yesmaximal, characteristic, complemented
4#82841C212yesmaximal
5Dic3×#123C212yesmaximal, complemented
6#82349C211yesmaximal, characteristic, complemented
7#82196C211yesmaximal, characteristic, complemented
8#77810C212yesmaximal, complemented
9#77740C212yesmaximal, complemented
10#77533C212yesmaximal, complemented
11#77460C212yesmaximal, complemented
12#76076C212yesmaximal, complemented
13#75965C212yesmaximal, complemented
14#74073C212yesmaximal, complemented
15#74052C212yesmaximal, complemented
16#74017C211yesmaximal, characteristic, complemented
17#73934C212yesmaximal, complemented
18#73866C212yesmaximal, complemented
19#73863C211yesmaximal, characteristic, complemented
20#34971—31nomaximal, Sylow
21C22×#237C2211yescharacteristic
22C23×Dic6C2211yescharacteristic
23C2×C3×#123C2212yes—
24C2×C3×C4×D4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C2×D4×Dic3C2211yescharacteristic
27C2×#929C2212yes—
28C2×C4×#67C2211yescharacteristic
29C2×C4×#67C2211yescharacteristic
30C2×#924C2212yes—
31C22×Dic3⋊C4C2212yes—
32C22×C4×Dic3C2212yes—
33C22×C4×Dic3C2211yescharacteristic
34C22×C4×Dic3C2211yescharacteristic
35C4×#237—28no—
36C2×#897C2212yes—
37C2×#892C2211yescharacteristic
38C2×#887—28no—
39C2×#887C2212yes—
40C2×#887C2212yes—
41C2×#887C2212yes—
42C2×#887C2211yescharacteristic
43C2×#887C2212yes—
44C2×#67⋊C4C2211yescharacteristic
45C2×#67⋊C4C2211yescharacteristic
46C2×#877C2211yescharacteristic
47C2×#877C2211yescharacteristic
48C2×C42×D3C2211yescharacteristic
49C2×C4×Dic6C2211yescharacteristic
50C3×#398C2212yes—
51C3×#397C2212yes—
52C3×#389C2212yes—
53C3×#381C2212yes—
54C3×#380C2211yescharacteristic
55C3×#380C2212yes—
56#5220C2212yes—
57#5212C2211yescharacteristic
58#5211C2212yes—
59#4992C2212yes—
60#4989C2214yes—
61#4987C2212yes—
62#4983C2212yes—
63#4980C2214yes—
64#4979C2214yes—
65#4979C2212yes—
66#4977C2212yes—
67Dic3×C4⋊C4C2212yes—
68Dic3×C4⋊C4C2214yes—
69#4973C2212yes—
70#4972C2212yes—
71#4959C2214yes—
72#4958C2212yes—
73#4951C2214yes—
74#4950C2212yes—
75#4947C2212yes—
76#4946C2212yes—
77#4946C2214yes—
78#4943C2212yes—
79Dic3×C22⋊C4C2212yes—
80Dic3×C22⋊C4C2214yes—
81#4929C2212yes—
82#4673C2212yes—
83#4669C2214yes—
84#4666C2214yes—
85#4658C2214yes—
86#4657C2214yes—
87#4656C2212yes—
88#4654C2214yes—
89#4652C2214yes—
90#4652C2214yes—
91#4651C2212yes—
92#4649C2214yes—
93#4648C2212yes—
94C2×C4×#41—31no—
95C22×C4×Q8—31no—
96#2599—32no—
97#2599—32no—
98#2581—32no—
99#2536—32no—
100#2486—31no—
101#2486D311yescharacteristic, complemented
102#2484—32no—
103#2409—31no—
104#2409—31no—
105#2406—32no—
106#2399—32no—
107#2398—32no—
108C4×C22⋊Q8—32no—
109C4×C22⋊Q8—32no—
110C4×#123—32no—
111C4×#123—32no—
112#2283—31no—
113C22×C3×D4C2311yescharacteristic
114C23×C3×C4C2312yes—
115C23×C3×C4C2311yescharacteristic
116C23×C3×C4C2311yescharacteristic
117C22×#67C2311yescharacteristic
118C22×#67C2311yescharacteristic
119C23×Dic3C2312yes—
120C23×Dic3C2311yescharacteristic
121C23×Dic3C2311yescharacteristic
122C23×Dic3C2311yescharacteristic
123C23×Dic3C2311yescharacteristic
124C2×#237—24no—
125C2×#237—24no—
126C2×#237—24no—
127C22×C4×D3C2311yescharacteristic
128C22×C4×D3C2311yescharacteristic
129C22×C4×D3C2311yescharacteristic
130C22×Dic6—24no—
131C22×Dic6—28no—
132C22×Dic6C2312yes—
133C22×Dic6C2311yescharacteristic
134C22×Dic6C2312yes—
135C3×#123—28no—
136C3×C4×D4—24no—
137C2×C3×C4⋊C4—24no—
138C2×C3×C4⋊C4C2312yes—
139C2×C3×C4⋊C4C2312yes—
140C2×C3×C4⋊C4C2314yes—
141C2×C3×C4⋊C4C2311yescharacteristic
142C2×C3×C4⋊C4C2312yes—
143C2×C3×C22⋊C4C2312yes—
144C2×C3×C22⋊C4C2314yes—
145C2×C3×C22⋊C4C2311yescharacteristic
146C2×C3×C22⋊C4C2311yescharacteristic
147C2×C3×C42C2311yescharacteristic
148C2×#217C2312yes—
149C2×#217C2314yes—
150C2×#217C2311yescharacteristic
151C2×#217C2311yescharacteristic
152D4×Dic3—24no—
153#929—28no—
154C4×#67—24no—
155C4×#67—24no—
156C2×(C2×D3)⋊C4C2314yes—
157C2×(C2×D3)⋊C4C2314yes—
158C2×(C2×D3)⋊C4C2311yescharacteristic
159C2×(C2×D3)⋊C4C2311yescharacteristic
160C2×C4⋊Dic3C2314yes—
161C2×C4⋊Dic3C2312yes—
162C2×C4⋊Dic3C2311yescharacteristic
163#924—28no—
164C2×Dic3⋊C4—28no—
165C2×Dic3⋊C4C2314yes—
166C2×Dic3⋊C4C2314yes—
167C2×Dic3⋊C4C2311yescharacteristic
168C2×Dic3⋊C4C2314yes—
169C2×Dic3⋊C4C2311yescharacteristic
170C2×Dic3⋊C4C2311yescharacteristic
171C2×Dic3⋊C4C2314yes—
172C2×Dic3⋊C4C2311yescharacteristic
173C2×C4×Dic3—28no—
174C2×C4×Dic3—24no—
175C2×C4×Dic3D418yes—
176C2×C4×Dic3C2314yes—
177C2×C4×Dic3C2311yescharacteristic
178C2×C4×Dic3C2314yes—
179C2×C4×Dic3C2311yescharacteristic
180C2×C4×Dic3C2314yes—
181C2×C4×Dic3C2311yescharacteristic
182C2×C4×Dic3C2311yescharacteristic
183C2×C4×Dic3C2311yescharacteristic
184C2×C4×Dic3C2311yescharacteristic
185C2×C4×Dic3C2311yescharacteristic
186C2×C4×Dic3C2311yescharacteristic
187C2×C4×Dic3C2311yescharacteristic
188#897—28no—
189#892—24no—
190#887—28no—
191#887—28no—
192#887—28no—
193#887—28no—
194#887—24no—
195#67⋊C4—24no—
196#67⋊C4—24no—
197#877—24no—
198#877—24no—
199C42×D3—24no—
200C4×Dic6—24no—
201C3×#95C2312yes—
202C3×#95C2314yes—
203C3×#95C2314yes—
204C3⋊#95C2312yes—
205C3⋊#95C2314yes—
206C3⋊#95C2314yes—
207C3⋊#95C2314yes—
208C3⋊#95C2314yes—
209C3⋊#95C2314yes—
210C3⋊#95C2314yes—
211C3⋊#95C2314yes—
212C3⋊#95C2314yes—
213C3⋊#95C2314yes—
214C22×#41—31no—
215C23×Q8—31no—
216C2×#123—32no—
217C2×#123C2×D312yes—
218C2×C22⋊Q8—32no—
219C2×C22⋊Q8—32no—
220C4×#41—68no—
221C2×C4×Q8—32no—
222C2×C4×Q8—32no—
223C2×C4×Q8—32no—
224C2×C4×Q8—31no—
225C2×C4×Q8—32no—
226C2×C4×Q8—31no—
227C2×C4×Q8—68no—
228C2×C4×D4—31no—
229C2×C4×D4—31no—
230C2×C4×D4—31no—
231C2×C4×D4—31no—
232C2×C4×D4—31no—
233C2×C4×D4C2×D311yescharacteristic
234C2×#117—31no—
235C2×#117—31no—
236C2×#117—31no—
237C22×C4⋊C4—32no—
238C22×C4⋊C4C2×D311yescharacteristic
239C22×C42—31no—
240C22×C42—32no—
241C22×C42—31no—
242C22×C42—31no—
243#400—34no—
244#398—32no—
245#398—34no—
246#398C2×D312yes—
247#397—32no—
248#397C2×D312yes—
249#395—34no—
250#395—32no—
251#395—32no—
252#394—34no—
253#393—32no—
254#393—32no—
255#391—32no—
256#391—32no—
257#389—32no—
258#389C2×D312yes—
259#388—34no—
260#388—34no—
261#387—34no—
262#387—34no—
263#387—34no—
264#387—34no—
265#386—32no—
266#386—32no—
267#385—34no—
268#385—34no—
269#385—32no—
270#385—32no—
271#383—32no—
272#382—32no—
273#381—32no—
274#381—32no—
275#381C2×D312yes—
276#380—31no—
277#380—32no—
278#380C2×D311yescharacteristic
279#380C2×D312yes—
280C4×C4⋊C4—34no—
281C4×C4⋊C4—32no—
282C4×C4⋊C4—34no—
283C4×C22⋊C4—34no—
284C4×C22⋊C4—32no—
285C4×C22⋊C4—34no—
286#376—32no—
287C24×C3C2411yescharacteristic
288C24×C3C2411yescharacteristic
289C23×D3C2411yescharacteristic
290C2×C3×D4—22no—
291C2×C3×D4—22no—
292C2×C3×D4#4114yes—
293C22×C3×C4—24no—
294C22×C3×C4—24no—
295C22×C3×C4—24no—
296C22×C3×C4—24no—
297C22×C3×C4—22no—
298C22×C3×C4—24no—
299C22×C3×C4C2×D414yes—
300C22×C3×C4C2414yes—
301C22×C3×C4C2411yescharacteristic
302C22×C3×C4C2414yes—
303C22×C3×C4C2411yescharacteristic
304C22×C3×C4C2411yescharacteristic
305C22×C3×C4C2411yescharacteristic
306C22×C3×C4C2411yescharacteristic
307C2×#67—22no—
308C2×#67—22no—
309C2×#67—22no—
310C2×#67—22no—
311C2×#67—22no—
312C2×#67#4114yes—
313C22×Dic3—24no—
314C22×Dic3—22no—
315C22×Dic3—22no—
316C22×Dic3—22no—
317C22×Dic3—22no—
318C22×Dic3—28no—
319C22×Dic3—22no—
320C22×Dic3—24no—
321C22×Dic3—22no—
322C22×Dic3—24no—
323C22×Dic3C2×D414yes—
324C22×Dic3C2×D414yes—
325C22×Dic3C2411yescharacteristic
326C22×Dic3C2414yes—
327C22×Dic3C2411yescharacteristic
328C22×Dic3C2411yescharacteristic
329C22×Dic3C2411yescharacteristic
330C22×Dic3C2411yescharacteristic
331C22×Dic3C2411yescharacteristic
332C22×Dic3C2414yes—
333C22×Dic3C2411yescharacteristic
334#237—232no—
335C2×C4×D3—22no—
336C2×C4×D3—22no—
337C2×C4×D3—22no—
338C2×C4×D3—22no—
339C2×C4×D3—24no—
340C2×C4×D3—22no—
341C2×C4×D3—24no—
342C2×Dic6—232no—
343C2×Dic6—24no—
344C2×Dic6—24no—
345C2×Dic6—24no—
346C2×Dic6—22no—
347C2×Dic6—22no—
348C2×Dic6—28no—
349C2×Dic6—22no—
350C2×Dic6#4118yescomplemented
351C3×C4⋊C4—24no—
352C3×C4⋊C4—24no—
353C3×C4⋊C4—22no—
354C3×C4⋊C4—24no—
355C3×C4⋊C4—28no—
356C3×C22⋊C4—22no—
357C3×C22⋊C4—24no—
358C3×C22⋊C4—28no—
359C3×C22⋊C4—22no—
360C3×C42—22no—
361#217—22no—
362#217—24no—
363#217—22no—
364#217—28no—
365(C2×D3)⋊C4—28no—
366(C2×D3)⋊C4—22no—
367(C2×D3)⋊C4—22no—
368(C2×D3)⋊C4—28no—
369C4⋊Dic3—24no—
370C4⋊Dic3—22no—
371C4⋊Dic3—28no—
372Dic3⋊C4—22no—
373Dic3⋊C4—22no—
374Dic3⋊C4—22no—
375Dic3⋊C4—22no—
376Dic3⋊C4—28no—
377Dic3⋊C4—28no—
378Dic3⋊C4—28no—
379Dic3⋊C4—28no—
380C4×Dic3—22no—
381C4×Dic3—22no—
382C4×Dic3—22no—
383C4×Dic3—22no—
384C4×Dic3—22no—
385C4×Dic3—28no—
386C4×Dic3—28no—
387C4×Dic3—28no—
388C4×Dic3C2×D414yes—
389C4×Dic3C2×D414yes—
390C4×Dic3C2×D414yes—
391C4×Dic3C2×D414yes—
392C2×#41—64no—
393C2×#41—64no—
394C2×#41—64no—
395C22×Q8—32no—
396C22×Q8—32no—
397C22×Q8—31no—
398C22×Q8—68no—
399C22×Q8—64no—
400C22×D4—31no—
401C22×D4—31no—
402C22×D4C22×D311yescharacteristic
403C23×C4—31no—
404C23×C4—31no—
405C23×C4—32no—
406C23×C4—31no—
407C23×C4—31no—
408C23×C4—31no—
409C23×C4—31no—
410C23×C4—31no—
411C23×C4C22×D312yes—
412C23×C4C22×D311yescharacteristic
413C23×C4C22×D311yescharacteristic
414#123—28no—
415#123—68no—
416C22⋊Q8—68no—
417C22⋊Q8—68no—
418C4×Q8—64no—
419C4×Q8—68no—
420C4×Q8—68no—
421C4×Q8—68no—
422C4×Q8—68no—
423C4×Q8—64no—
424C4×D4—24no—
425C4×D4—64no—
426C4×D4—64no—
427C4×D4—64no—
428C4×D4—64no—
429C4×D4—64no—
430#117—64no—
431#117—64no—
432#117—64no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—34no—
435C2×C4⋊C4—34no—
436C2×C4⋊C4—31no—
437C2×C4⋊C4—31no—
438C2×C4⋊C4—31no—
439C2×C4⋊C4—31no—
440C2×C4⋊C4—31no—
441C2×C4⋊C4—32no—
442C2×C4⋊C4—34no—
443C2×C4⋊C4—34no—
444C2×C4⋊C4—34no—
445C2×C4⋊C4—68no—
446C2×C4⋊C4C22×D312yes—
447C2×C4⋊C4C22×D312yes—
448C2×C4⋊C4C22×D311yescharacteristic
449C2×C4⋊C4C22×D312yes—
450C2×C4⋊C4C22×D314yes—
451C2×C22⋊C4—31no—
452C2×C22⋊C4—31no—
453C2×C22⋊C4—34no—
454C2×C22⋊C4—32no—
455C2×C22⋊C4—31no—
456C2×C22⋊C4—31no—
457C2×C22⋊C4—34no—
458C2×C22⋊C4—34no—
459C2×C22⋊C4C22×D311yescharacteristic
460C2×C22⋊C4C22×D311yescharacteristic
461C2×C22⋊C4C22×D312yes—
462C2×C22⋊C4C22×D314yes—
463C2×C42—38no—
464C2×C42—31no—
465C2×C42—31no—
466C2×C42—31no—
467C2×C42—31no—
468C2×C42—31no—
469C2×C42—31no—
470C2×C42—31no—
471C2×C42—31no—
472C2×C42—31no—
473C2×C42—34no—
474C2×C42—34no—
475C2×C42—34no—
476C2×C42—64no—
477C2×C42—64no—
478C2×C42—68no—
479C2×C42C22×D311yescharacteristic
480#95—32no—
481#95—34no—
482#95—34no—
483#95—34no—
484#95—34no—
485#95—34no—
486#95—34no—
487#95—34no—
488#95—34no—
489#95—34no—
490#95C22×D312yes—
491#95C22×D314yes—
492#95C22×D314yes—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—21no—
496C23×C3—22no—
497C23×C3—21no—
498C23×C3—22no—
499C23×C3C22×D412yes—
500C23×C3C2×#4112yes—
501C23×C3C2×#4112yes—
502C23×C3C2×#4112yes—
503C23×C3C2511yescharacteristic
504C22×D3—21no—
505C22×D3—22no—
506C22×D3—21no—
507C22×D3—22no—
508C22×D3C2×#4112yes—
509C3×D4—28no—
510C2×C3×C4—21no—
511C2×C3×C4—22no—
512C2×C3×C4—21no—
513C2×C3×C4—28no—
514C2×C3×C4—24no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—22no—
518C2×C3×C4—24no—
519C2×C3×C4—24no—
520C2×C3×C4—24no—
521C2×C3×C4—24no—
522C2×C3×C4—24no—
523C2×C3×C4—22no—
524C2×C3×C4—48no—
525C2×C3×C4—44no—
526C2×C3×C4C22×D412yes—
527C2×C3×C4C22×D412yes—
528C2×C3×C4C2×#4112yes—
529C2×C3×C4C2×#4114yes—
530#67—28no—
531#67—28no—
532C2×Dic3—216no—
533C2×Dic3—28no—
534C2×Dic3—28no—
535C2×Dic3—24no—
536C2×Dic3—21no—
537C2×Dic3—24no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—22no—
544C2×Dic3—28no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—24no—
548C2×Dic3—24no—
549C2×Dic3—22no—
550C2×Dic3—24no—
551C2×Dic3—22no—
552C2×Dic3—44no—
553C2×Dic3C22×D412yes—
554C2×Dic3C22×D412yes—
555C2×Dic3C22×D412yes—
556C2×Dic3C22×D412yes—
557C2×Dic3C2×#4112yes—
558C2×Dic3C2×#4118yes—
559C2×Dic32−1+414yes—
560C4×D3—28no—
561C4×D3—44no—
562C4×D3—44no—
563Dic6—216no—
564Dic6—28no—
565Dic6—216no—
566C24—31no—
567C24C23×D311yescharacteristic
568C24C23×D311yescharacteristic
569#41—632no—
570C2×Q8—38no—
571C2×Q8—62no—
572C2×Q8—68no—
573C2×Q8—62no—
574C2×Q8—632no—
575C2×Q8—64no—
576C2×Q8—64no—
577C2×Q8—62no—
578C2×Q8—64no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—34no—
582C2×D4—62no—
583C2×D4—62no—
584C2×D4—62no—
585C2×D4—62no—
586C2×D4—62no—
587C2×D4#23714yes—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—31no—
595C22×C4—34no—
596C22×C4—34no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—34no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—31no—
603C22×C4—34no—
604C22×C4—31no—
605C22×C4—62no—
606C22×C4—62no—
607C22×C4—64no—
608C22×C4—62no—
609C22×C4—62no—
610C22×C4—68no—
611C22×C4—62no—
612C22×C4—64no—
613C22×C4—62no—
614C22×C4—64no—
615C22×C4—64no—
616C22×C4—62no—
617C22×C4—62no—
618C22×C4—62no—
619C22×C4—62no—
620C22×C4—62no—
621C22×C4—64no—
622C22×C4D3×D414yes—
623C22×C4C23×D314yes—
624C22×C4C23×D311yescharacteristic
625C22×C4C23×D314yes—
626C22×C4C23×D311yescharacteristic
627C22×C4C23×D311yescharacteristic
628C22×C4C23×D311yescharacteristic
629C22×C4C23×D311yescharacteristic
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—22no—
633C4⋊C4—28no—
634C4⋊C4—24no—
635C4⋊C4—68no—
636C4⋊C4—68no—
637C4⋊C4—62no—
638C4⋊C4—62no—
639C4⋊C4—62no—
640C4⋊C4—62no—
641C4⋊C4—68no—
642C4⋊C4—68no—
643C4⋊C4—68no—
644C4⋊C4—62no—
645C4⋊C4—64no—
646C22⋊C4—22no—
647C22⋊C4—24no—
648C22⋊C4—28no—
649C22⋊C4—22no—
650C22⋊C4—62no—
651C22⋊C4—68no—
652C22⋊C4—68no—
653C22⋊C4—62no—
654C22⋊C4—68no—
655C22⋊C4—62no—
656C22⋊C4—64no—
657C22⋊C4—62no—
658C42—22no—
659C42—34no—
660C42—34no—
661C42—34no—
662C42—34no—
663C42—62no—
664C42—62no—
665C42—62no—
666C42—62no—
667C42—68no—
668C42—68no—
669C42—68no—
670C42—62no—
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—24no—
674C22×C3—24no—
675C22×C3—22no—
676C22×C3—24no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—42no—
680C22×C3#52514yes—
681C22×C3C23×D411yescharacteristic
682C22×C3C22×#4111yescharacteristic
683C22×C3C22×#4111yescharacteristic
684C22×C3C22×#4112yes—
685C22×C3C2×2−1+412yes—
686C2×D3—22no—
687C2×D3—24no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—42no—
691C3×C4—22no—
692C3×C4—22no—
693C3×C4—44no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—44no—
697C3×C4#52514yes—
698Dic3—28no—
699Dic3—22no—
700Dic3—22no—
701Dic3—22no—
702Dic3—22no—
703Dic3—41no—
704Dic3—41no—
705Dic3—44no—
706Dic3#53614yes—
707C23—22no—
708C23—22no—
709C23—21no—
710C23—22no—
711C23—21no—
712C23—22no—
713C23—32no—
714C23—61no—
715C23—61no—
716C23—62no—
717C23—62no—
718C23C2×D3×D412yes—
719C23C2×#23712yes—
720C23C2×#23712yes—
721C23D3×#4112yes—
722C23C24×D311yescharacteristic
723Q8—616no—
724Q8—68no—
725Q8—616no—
726D4—28no—
727D4—68no—
728D4—68no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—28no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—32no—
744C2×C4—34no—
745C2×C4—32no—
746C2×C4—32no—
747C2×C4—32no—
748C2×C4—38no—
749C2×C4—32no—
750C2×C4—48no—
751C2×C4—44no—
752C2×C4—68no—
753C2×C4—68no—
754C2×C4—616no—
755C2×C4—68no—
756C2×C4—61no—
757C2×C4—64no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—64no—
764C2×C4—62no—
765C2×C4—68no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—64no—
769C2×C4—64no—
770C2×C4—62no—
771C2×C4—64no—
772C2×C4—62no—
773C2×C4—124no—
774C2×C4—124no—
775C2×C4—124no—
776C2×C4C2×D3×D412yes—
777C2×C4C2×D3×D412yes—
778C2×C4C2×#23712yes—
779C2×C4D3×#4114yes—
780C2×C3—24no—
781C2×C3—42no—
782C2×C3C2×#52511yescharacteristic
783C2×C3C2×#52511yescharacteristic
784C2×C3C2×#53611yescharacteristic
785C2×C3#348212yes—
786C2×C3#348212yes—
787D3—42no—
788C22—24no—
789C22—22no—
790C22—24no—
791C22—22no—
792C22—24no—
793C22—22no—
794C22—42no—
795C22—41no—
796C22—41no—
797C22—64no—
798C22—62no—
799C22—121no—
800C22—122no—
801C22—121no—
802C22#560614yes—
803C22C22×D3×D411yescharacteristic
804C22C22×#23711yescharacteristic
805C22C2×D3×#4111yescharacteristic
806C22C2×D3×#4112yes—
807C22D3×2−1+412yes—
808C4—22no—
809C4—22no—
810C4—34no—
811C4—41no—
812C4—44no—
813C4—44no—
814C4—41no—
815C4—62no—
816C4—62no—
817C4—62no—
818C4—62no—
819C4—68no—
820C4—124no—
821C4—121no—
822C4—121no—
823C4#565614yes—
824C3#3497111yescharacteristic, complemented, Sylow
825C2—24no—
826C2—42no—
827C2—122no—
828C2C2×#560611yescharacteristic
829C2C2×#565611yescharacteristic
830C2D3×#53611yescharacteristic
831C2#8667612yes—
832C2#8682812yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2486C2
prime radicalC22×#237C22
hypercenter#2486D3
hypocenterC3#34971
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2486

Complements

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

NH ≅ G/Ntype
2. C22×#887C2semidirect
3. C3×#2486C2semidirect
5. Dic3×#123C2semidirect
6. #82349C2semidirect
7. #82196C2semidirect
8. #77810C2semidirect
9. #77740C2semidirect
10. #77533C2semidirect
11. #77460C2semidirect
12. #76076C2semidirect
13. #75965C2semidirect
14. #74073C2semidirect
15. #74052C2semidirect
16. #74017C2semidirect
17. #73934C2semidirect
18. #73866C2semidirect
19. #73863C2semidirect
101. #2486D3semidirect
350. C2×Dic6#41semidirect
824. C3#34971semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#2372
C22×#8872
C3×#24862
#828412
Dic3×#1232
#823492
#821962
#778102
#777402
#775332
#774602
#760762
#759652
#740732
#740522
#740172
#739342
#738662
#738632
#349713