Finite Group Databasebeta

← #11058562

Subgroups — #11058562

Order 768.

2778 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#924C211yesmaximal, characteristic, complemented
2C2×#5611C211yesmaximal, characteristic, complemented
3C3×#2847C211yesmaximal, characteristic, complemented
4C4×#953C211yesmaximal, characteristic, complemented
5#82668C212yesmaximal, complemented
6#82654C211yesmaximal, characteristic, complemented
7#82647C212yesmaximal, complemented
8#82583C212yesmaximal, complemented
9#82581C212yesmaximal, complemented
10#74808C214yesmaximal, complemented
11#74803C214yesmaximal, complemented
12#74782C212yesmaximal, complemented
13#74662C212yesmaximal, complemented
14#74017C211yesmaximal, characteristic, complemented
15#73916C212yesmaximal, complemented
16#73888C212yesmaximal, complemented
17#73878C211yesmaximal, characteristic, complemented
18#38905—31nomaximal, Sylow
19C24×C3×C4C2211yescharacteristic
20C22×#237C2212yes—
21C23×Dic6C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic
23C2×C3×#121C2212yes—
24C2×C3×#120C2212yes—
25C2×#953C2211yescharacteristic
26C22×#217C2212yes—
27C2×#938C2211yescharacteristic, complemented
28C2×#936C2212yescomplemented
29C2×#935C2212yes—
30C2×D4×Dic3C2211yescharacteristic, complemented
31C2×C4×#67C2211yescharacteristic
32C2×C4×#67C2212yes—
33C22×C4⋊Dic3C2211yescharacteristic
34C2×#924—28no—
35C2×#924C2214yes—
36C2×#924C2212yes—
37C2×#924C2212yes—
38C22×Dic3⋊C4C2212yes—
39#5611—28no—
40C2×#897C2212yescomplemented
41C2×D3×C4⋊C4C2211yescharacteristic, complemented
42C2×#888C2211yescharacteristic, complemented
43C2×#883C2212yescomplemented
44C2×#878C2212yescomplemented
45C2×#877C2212yes—
46C3×#386C2212yes—
47C3×#386C2214yes—
48C3×#380C2211yescharacteristic
49C3×#380C2212yes—
50#5247C2211yescharacteristic
51#5223C2214yes—
52#5222C2214yes—
53#5221C2214yes—
54#5220C2212yes—
55#5220C2214yes—
56#5220C2212yes—
57#5213C2212yes—
58#5213C2211yescharacteristic
59#5210C2211yescharacteristic
60#5210C2212yes—
61C4×#217C2211yescharacteristic
62C4×#217C2212yes—
63Dic3×C4⋊C4C2212yescomplemented
64#4973C2212yescomplemented
65#4973C2212yescomplemented
66#4972C2212yescomplemented
67#4958C2212yes—
68#4957C2214yescomplemented
69#4956C2214yes—
70#4952C2214yescomplemented
71#4950C2212yes—
72#4949C2214yescomplemented
73#4948C2214yes—
74#4947C2214yes—
75#4947C2214yescomplemented
76#4944C2214yes—
77#4943C2212yes—
78#4942C2214yescomplemented
79#4673C2212yescomplemented
80#4667C2214yescomplemented
81#4658C2214yescomplemented
82#4657C2214yescomplemented
83#4656C2212yescomplemented
84#4654C2214yescomplemented
85#4646C2214yescomplemented
86C2×#547—31no—
87C22×C22⋊Q8—31no—
88#2847D311yescharacteristic, complemented
89#2696—34no—
90#2692—34no—
91#2623—32no—
92#2540—32no—
93#2492—32no—
94#2436—31no—
95#2427—32no—
96#2417—32no—
97#2411—32no—
98#2409—31no—
99#2404—32no—
100#2344—31no—
101#2311—32no—
102C4×#120—31no—
103C25×C3C2311yescharacteristic
104C22×C3×D4C2312yes—
105C22×C3×D4C2311yescharacteristic
106C22×C3×D4C2314yes—
107C23×C3×C4—24no—
108C23×C3×C4—44no—
109C23×C3×C4C2312yes—
110C23×C3×C4C2311yescharacteristic
111C23×C3×C4C2311yescharacteristic
112C23×C3×C4C2312yes—
113C22×#67C2312yes—
114C22×#67C2312yes—
115C22×#67C2311yescharacteristic
116C23×Dic3C2312yes—
117C23×Dic3C2312yes—
118C23×Dic3C2312yes—
119C2×#237—28no—
120C2×#237—28no—
121C2×#237—44no—
122C22×C4×D3C2311yescharacteristic
123C22×C4×D3C2312yes—
124C22×Dic6—24no—
125C22×Dic6—44no—
126C22×Dic6C2312yes—
127C22×Dic6C2312yes—
128C22×Dic6C2312yes—
129C3×#121—24no—
130C3×#121—44no—
131C3×#120—44no—
132C2×C3×C4⋊C4C2312yes—
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C22⋊C4C2312yes—
135C2×C3×C22⋊C4C2312yes—
136C2×C3×C22⋊C4C2314yes—
137C2×C3×C22⋊C4C2314yes—
138#953—24no—
139C2×#217—28no—
140C2×#217C2311yescharacteristic
141C2×#217C2312yes—
142C2×#217C2314yes—
143C2×#217C2312yes—
144C2×#217C2314yes—
145C2×#217C2312yes—
146C2×#217C2311yescharacteristic
147C2×#217C2312yes—
148C2×#217C2311yescharacteristic
149C2×#217C2314yes—
150C2×#217C2314yes—
151C2×#217C2312yes—
152#938—24no—
153#936—44no—
154#935—28no—
155D4×Dic3—24no—
156C4×#67—24no—
157C4×#67—44no—
158C2×(C2×D3)⋊C4C2311yescharacteristic
159C2×(C2×D3)⋊C4C2312yes—
160C2×(C2×D3)⋊C4C2314yes—
161C2×C4⋊Dic3D418yescomplemented
162C2×C4⋊Dic3C2314yes—
163C2×C4⋊Dic3C2312yes—
164C2×C4⋊Dic3C2311yescharacteristic
165C2×C4⋊Dic3C2311yescharacteristic
166#924—216no—
167#924—28no—
168#924—28no—
169C2×Dic3⋊C4—28no—
170C2×Dic3⋊C4C2314yes—
171C2×Dic3⋊C4C2311yescharacteristic
172C2×Dic3⋊C4C2312yes—
173C2×Dic3⋊C4C2314yes—
174C2×Dic3⋊C4C2312yes—
175C2×Dic3⋊C4C2314yes—
176C2×Dic3⋊C4C2312yes—
177C2×C4×Dic3C2312yes—
178C2×C4×Dic3C2311yescharacteristic
179C2×C4×Dic3C2314yes—
180#897—44no—
181D3×C4⋊C4—24no—
182#888—24no—
183#883—28no—
184#878—28no—
185#877—44no—
186C3×#95C2314yes—
187C3×#95C2312yes—
188C3⋊#95C2312yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2312yes—
192C3⋊#95C2314yes—
193C3⋊#95C2314yes—
194C3⋊#95C2314yes—
195C3⋊#95C2312yes—
196C3⋊#95C2314yes—
197C22×#41—32no—
198C23×Q8—31no—
199C24×C4C2×D311yescharacteristic
200#547—68no—
201C2×C4⋊Q8—31no—
202C2×#124—32no—
203C2×#123—32no—
204C2×#123—32no—
205C2×C22⋊Q8—32no—
206C2×C22⋊Q8—34no—
207C2×C22⋊Q8—32no—
208C2×C22⋊Q8—32no—
209C2×C22⋊Q8—32no—
210C2×C22⋊Q8—68no—
211C2×#121—31no—
212C2×#121C2×D311yescharacteristic
213C2×#121C2×D312yes—
214C2×#120—31no—
215C2×#120C2×D312yes—
216C2×C4×D4—31no—
217C2×C4×D4—31no—
218C2×C4×D4—32no—
219C2×#117—32no—
220C22×C4⋊C4—31no—
221C22×C4⋊C4—32no—
222C22×C4⋊C4—31no—
223C22×C22⋊C4—32no—
224#400—34no—
225#399—34no—
226#398—34no—
227#397—34no—
228#396—34no—
229#395—32no—
230#394—34no—
231#393—34no—
232#393—34no—
233#393—32no—
234#392—34no—
235#391—32no—
236#391—32no—
237#391—34no—
238#390—34no—
239#390—34no—
240#389—32no—
241#388—34no—
242#387—34no—
243#386—32no—
244#386—32no—
245#386—34no—
246#386—31no—
247#386—32no—
248#386—32no—
249#386—34no—
250#386C2×D312yes—
251#386C2×D314yes—
252#385—31no—
253#385—32no—
254#385—32no—
255#381—32no—
256#380—34no—
257#380—34no—
258#380C2×D311yescharacteristic
259#380C2×D312yes—
260#379—31no—
261C4×C4⋊C4—32no—
262C4×C22⋊C4—31no—
263C4×C22⋊C4—32no—
264C24×C3—22no—
265C24×C3—24no—
266C24×C3—22no—
267C24×C3—22no—
268C24×C3—42no—
269C24×C3C2412yes—
270C24×C3C2412yes—
271C24×C3C2411yescharacteristic
272C23×D3C2411yescharacteristic
273C2×C3×D4—24no—
274C2×C3×D4—24no—
275C2×C3×D4—24no—
276C2×C3×D4—28no—
277C2×C3×D4—22no—
278C2×C3×D4—24no—
279C2×C3×D4—44no—
280C2×C3×D4—44no—
281C22×C3×C4—24no—
282C22×C3×C4—22no—
283C22×C3×C4—24no—
284C22×C3×C4—24no—
285C22×C3×C4—24no—
286C22×C3×C4—24no—
287C22×C3×C4—42no—
288C22×C3×C4—42no—
289C22×C3×C4—42no—
290C22×C3×C4—416no—
291C22×C3×C4C2×D414yes—
292C22×C3×C4C2414yes—
293C22×C3×C4C2412yes—
294C22×C3×C4C2412yes—
295C22×C3×C4C2411yescharacteristic
296C22×C3×C4C2411yescharacteristic
297C2×#67—22no—
298C2×#67—22no—
299C2×#67—24no—
300C2×#67—24no—
301C2×#67—24no—
302C2×#67—24no—
303C2×#67—42no—
304C2×#67—42no—
305C2×#67#4114yes—
306C22×Dic3—24no—
307C22×Dic3—24no—
308C22×Dic3—24no—
309C22×Dic3—24no—
310C22×Dic3—24no—
311C22×Dic3—44no—
312C22×Dic3—42no—
313C22×Dic3C2×D418yes—
314C22×Dic3C2412yes—
315C22×Dic3C2411yescharacteristic
316C22×Dic3C2412yes—
317C22×Dic3C2414yes—
318C22×Dic3C2411yescharacteristic
319C22×Dic3C2412yes—
320C22×Dic3C2412yes—
321C22×Dic3C2411yescharacteristic
322#237—432no—
323C2×C4×D3—24no—
324C2×C4×D3—22no—
325C2×C4×D3—24no—
326C2×C4×D3—24no—
327C2×C4×D3—42no—
328C2×Dic6—24no—
329C2×Dic6—24no—
330C2×Dic6—24no—
331C2×Dic6—24no—
332C2×Dic6—24no—
333C2×Dic6—24no—
334C2×Dic6—44no—
335C2×Dic6—42no—
336C2×Dic6—416no—
337C3×C4⋊C4—22no—
338C3×C4⋊C4—24no—
339C3×C22⋊C4—24no—
340C3×C22⋊C4—24no—
341C3×C22⋊C4—44no—
342C3×C22⋊C4—44no—
343#217—22no—
344#217—22no—
345#217—22no—
346#217—24no—
347#217—24no—
348#217—24no—
349#217—28no—
350#217—28no—
351#217—24no—
352#217—42no—
353#217—44no—
354#217—44no—
355(C2×D3)⋊C4—22no—
356(C2×D3)⋊C4—44no—
357(C2×D3)⋊C4—42no—
358C4⋊Dic3—44no—
359C4⋊Dic3C2×D418yes—
360C4⋊Dic3C2×D414yes—
361C4⋊Dic3C2×D414yes—
362Dic3⋊C4—22no—
363Dic3⋊C4—24no—
364Dic3⋊C4—24no—
365Dic3⋊C4—28no—
366Dic3⋊C4—28no—
367Dic3⋊C4—44no—
368Dic3⋊C4—42no—
369C4×Dic3—22no—
370C4×Dic3—24no—
371C4×Dic3—44no—
372C25C22×D311yescharacteristic
373C2×#41—68no—
374C2×#41—68no—
375C2×#41—124no—
376C22×Q8—32no—
377C22×Q8—32no—
378C22×Q8—32no—
379C22×Q8—64no—
380C22×Q8—124no—
381C22×D4—31no—
382C22×D4—32no—
383C22×D4—32no—
384C22×D4C22×D311yescharacteristic
385C22×D4C22×D312yes—
386C22×D4C22×D314yes—
387C23×C4—24no—
388C23×C4—32no—
389C23×C4—32no—
390C23×C4—32no—
391C23×C4—31no—
392C23×C4—32no—
393C23×C4—44no—
394C23×C4C22×D312yes—
395C23×C4C22×D311yescharacteristic
396C23×C4C22×D311yescharacteristic
397C23×C4C22×D312yes—
398C4⋊Q8—64no—
399#124—124no—
400#123—68no—
401#123—68no—
402C22⋊Q8—68no—
403C22⋊Q8—68no—
404C22⋊Q8—68no—
405C22⋊Q8—616no—
406C22⋊Q8—124no—
407#121—24no—
408#121—44no—
409#121—64no—
410#120—44no—
411#120—64no—
412C4×D4—64no—
413C4×D4—64no—
414C4×D4—124no—
415#117—124no—
416C2×C4⋊C4—38no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—32no—
420C2×C4⋊C4—34no—
421C2×C4⋊C4—34no—
422C2×C4⋊C4—32no—
423C2×C4⋊C4—31no—
424C2×C4⋊C4—32no—
425C2×C4⋊C4—34no—
426C2×C4⋊C4—32no—
427C2×C4⋊C4—34no—
428C2×C4⋊C4—64no—
429C2×C4⋊C4—68no—
430C2×C4⋊C4C22×D311yescharacteristic
431C2×C4⋊C4C22×D312yes—
432C2×C22⋊C4—34no—
433C2×C22⋊C4—34no—
434C2×C22⋊C4—31no—
435C2×C22⋊C4—31no—
436C2×C22⋊C4—32no—
437C2×C22⋊C4—31no—
438C2×C22⋊C4—32no—
439C2×C22⋊C4—32no—
440C2×C22⋊C4—32no—
441C2×C22⋊C4—31no—
442C2×C22⋊C4—32no—
443C2×C22⋊C4—34no—
444C2×C22⋊C4—34no—
445C2×C22⋊C4—32no—
446C2×C22⋊C4—34no—
447C2×C22⋊C4—68no—
448C2×C22⋊C4C22×D312yes—
449C2×C22⋊C4C22×D312yes—
450C2×C22⋊C4C22×D314yes—
451C2×C22⋊C4C22×D314yes—
452C2×C42—31no—
453C2×C42—32no—
454C2×C42—34no—
455#95—32no—
456#95—32no—
457#95—32no—
458#95—34no—
459#95—34no—
460#95—34no—
461#95—34no—
462#95—34no—
463#95—34no—
464#95C22×D314yes—
465#95C22×D312yes—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—28no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—24no—
478C23×C3—22no—
479C23×C3—24no—
480C23×C3—48no—
481C23×C3—48no—
482C23×C3—44no—
483C23×C3—44no—
484C23×C3C22×D412yes—
485C23×C3C2×#4112yes—
486C23×C3H(5,𝔽2)12yes—
487C23×C32−1+414yes—
488C23×C3C2511yescharacteristic
489C22×D3—21no—
490C22×D3—22no—
491C22×D3—21no—
492C22×D3—22no—
493C22×D3C2×#4112yes—
494C3×D4—48no—
495C3×D4—44no—
496C3×D4—88no—
497C2×C3×C4—22no—
498C2×C3×C4—28no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—24no—
503C2×C3×C4—22no—
504C2×C3×C4—24no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—24no—
508C2×C3×C4—48no—
509C2×C3×C4—44no—
510C2×C3×C4—48no—
511C2×C3×C4C22×D412yes—
512C2×C3×C4C22×D412yes—
513C2×C3×C4H(5,𝔽2)14yes—
514#67—28no—
515#67—48no—
516#67—48no—
517C2×Dic3—216no—
518C2×Dic3—21no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—24no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—24no—
533C2×Dic3—24no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—48no—
538C2×Dic3—48no—
539C2×Dic3C22×D414yes—
540C2×Dic3C22×D414yes—
541C2×Dic3C2×#4112yes—
542C4×D3—48no—
543C4×D3—44no—
544Dic6—48no—
545Dic6—48no—
546Dic6—48no—
547C24—22no—
548C24—24no—
549C24—22no—
550C24—22no—
551C24—31no—
552C24—42no—
553C24C23×D312yes—
554C24C23×D312yes—
555C24C23×D311yescharacteristic
556#41—1232no—
557C2×Q8—64no—
558C2×Q8—64no—
559C2×Q8—64no—
560C2×Q8—64no—
561C2×Q8—64no—
562C2×Q8—64no—
563C2×Q8—124no—
564C2×Q8—122no—
565C2×Q8—1216no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—24no—
569C2×D4—28no—
570C2×D4—22no—
571C2×D4—24no—
572C2×D4—34no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—64no—
576C2×D4—62no—
577C2×D4—62no—
578C2×D4—64no—
579C2×D4—64no—
580C2×D4—64no—
581C2×D4—122no—
582C2×D4—122no—
583C22×C4—24no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—38no—
590C22×C4—31no—
591C22×C4—32no—
592C22×C4—32no—
593C22×C4—32no—
594C22×C4—31no—
595C22×C4—32no—
596C22×C4—34no—
597C22×C4—31no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—416no—
602C22×C4—64no—
603C22×C4—64no—
604C22×C4—64no—
605C22×C4—64no—
606C22×C4—64no—
607C22×C4—64no—
608C22×C4—64no—
609C22×C4—62no—
610C22×C4—64no—
611C22×C4—122no—
612C22×C4—124no—
613C22×C4—122no—
614C22×C4D3×D414yes—
615C22×C4C23×D314yes—
616C22×C4C23×D312yes—
617C22×C4C23×D312yes—
618C22×C4C23×D311yescharacteristic
619C22×C4C23×D311yescharacteristic
620C4⋊C4—22no—
621C4⋊C4—24no—
622C4⋊C4—34no—
623C4⋊C4—34no—
624C4⋊C4—38no—
625C4⋊C4—68no—
626C4⋊C4—68no—
627C4⋊C4—64no—
628C4⋊C4—64no—
629C4⋊C4—62no—
630C4⋊C4—124no—
631C4⋊C4—122no—
632C4⋊C4—124no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C22⋊C4—68no—
638C22⋊C4—68no—
639C22⋊C4—64no—
640C22⋊C4—64no—
641C22⋊C4—64no—
642C22⋊C4—62no—
643C22⋊C4—62no—
644C22⋊C4—62no—
645C22⋊C4—64no—
646C22⋊C4—62no—
647C22⋊C4—122no—
648C22⋊C4—124no—
649C22⋊C4—122no—
650C22⋊C4—124no—
651C22⋊C4—124no—
652C42—62no—
653C42—64no—
654C42—124no—
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—24no—
658C22×C3—24no—
659C22×C3—24no—
660C22×C3—24no—
661C22×C3—24no—
662C22×C3—416no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—44no—
671C22×C3—44no—
672C22×C3#54614yes—
673C22×C3C23×D411yescharacteristic
674C22×C3C22×#4111yescharacteristic
675C22×C3C2×H(5,𝔽2)12yes—
676C22×C3C2×H(5,𝔽2)11yescharacteristic
677C22×C3C2×2−1+412yes—
678C2×D3—22no—
679C2×D3—24no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—42no—
683C3×C4—22no—
684C3×C4—42no—
685C3×C4—42no—
686C3×C4—44no—
687C3×C4#53514yes—
688Dic3—22no—
689Dic3—24no—
690Dic3—24no—
691Dic3—44no—
692Dic3—41no—
693Dic3—41no—
694Dic3—42no—
695Dic3—42no—
696C23—22no—
697C23—22no—
698C23—28no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—22no—
708C23—22no—
709C23—24no—
710C23—32no—
711C23—48no—
712C23—48no—
713C23—44no—
714C23—44no—
715C23—61no—
716C23—62no—
717C23—61no—
718C23—62no—
719C23C2×D3×D412yes—
720C23#100412yes—
721C23D3×#4112yes—
722C23#101014yes—
723C23C24×D311yescharacteristic
724Q8—128no—
725Q8—128no—
726Q8—128no—
727D4—48no—
728D4—44no—
729D4—68no—
730D4—88no—
731D4—128no—
732D4—128no—
733C2×C4—22no—
734C2×C4—28no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—34no—
745C2×C4—34no—
746C2×C4—32no—
747C2×C4—48no—
748C2×C4—44no—
749C2×C4—48no—
750C2×C4—61no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—61no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—616no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—64no—
760C2×C4—62no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—64no—
764C2×C4—62no—
765C2×C4—64no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—128no—
771C2×C4—128no—
772C2×C4—128no—
773C2×C4—124no—
774C2×C4C2×D3×D412yes—
775C2×C4C2×D3×D412yes—
776C2×C4#100414yes—
777C2×C3—24no—
778C2×C3—44no—
779C2×C3—82no—
780C2×C3C2×#53511yescharacteristic
781C2×C3C2×#54611yescharacteristic
782C2×C3#348611yescharacteristic
783C2×C3#352012yes—
784C2×C3#353612yes—
785D3—42no—
786C22—22no—
787C22—24no—
788C22—22no—
789C22—24no—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—416no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—44no—
800C22—42no—
801C22—42no—
802C22—44no—
803C22—64no—
804C22—62no—
805C22—121no—
806C22—121no—
807C22—122no—
808C22#561214yes—
809C22C22×D3×D411yescharacteristic
810C22C2×#100412yes—
811C22C2×#100411yescharacteristic
812C22C2×D3×#4111yescharacteristic
813C22C2×#101012yes—
814C4—22no—
815C4—42no—
816C4—42no—
817C4—44no—
818C4—64no—
819C4—64no—
820C4—62no—
821C4—121no—
822C4—122no—
823C4—124no—
824C4—121no—
825C4—122no—
826C4#559214yes—
827C3#3890511yescharacteristic, complemented, Sylow
828C2—24no—
829C2—44no—
830C2—82no—
831C2—122no—
832C2C2×#559211yescharacteristic
833C2C2×#561211yescharacteristic
834C2#8595512yes—
835C2#8602211yescharacteristic
836C2#8604712yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2847C2
hypercenter#2847D3
hypocenterC3#38905
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. C22×#924C2semidirect
2. C2×#5611C2semidirect
3. C3×#2847C2semidirect
4. C4×#953C2semidirect
5. #82668C2semidirect
6. #82654C2semidirect
7. #82647C2semidirect
8. #82583C2semidirect
9. #82581C2semidirect
10. #74808C2semidirect
11. #74803C2semidirect
12. #74782C2semidirect
13. #74662C2semidirect
14. #74017C2semidirect
15. #73916C2semidirect
16. #73888C2semidirect
17. #73878C2semidirect
27. C2×#938C22semidirect
28. C2×#936C22semidirect
30. C2×D4×Dic3C22semidirect
40. C2×#897C22semidirect
41. C2×D3×C4⋊C4C22semidirect
42. C2×#888C22semidirect
43. C2×#883C22semidirect
44. C2×#878C22semidirect
63. Dic3×C4⋊C4C22semidirect
64. #4973C22semidirect
65. #4973C22semidirect
66. #4972C22semidirect
68. #4957C22semidirect
70. #4952C22semidirect
72. #4949C22semidirect
75. #4947C22semidirect
78. #4942C22semidirect
79. #4673C22semidirect
80. #4667C22semidirect
81. #4658C22semidirect
82. #4657C22semidirect
83. #4656C22semidirect
84. #4654C22semidirect
85. #4646C22semidirect
88. #2847D3semidirect
161. C2×C4⋊Dic3D4semidirect
827. C3#38905semidirect

Maximal subgroups

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

subgroupindex
C22×#9242
C2×#56112
C3×#28472
C4×#9532
#826682
#826542
#826472
#825832
#825812
#748082
#748032
#747822
#746622
#740172
#739162
#738882
#738782
#389053