Finite Group Databasebeta

← #11058629

Subgroups — #11058629

Order 768.

2612 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×#5557C211yesmaximal, characteristic, complemented
2C2×#5553C211yesmaximal, characteristic, complemented
3C3×D4×C4⋊C4C211yesmaximal, characteristic, complemented
4#82409C212yesmaximal, complemented
5#82381C212yesmaximal, complemented
6#82193C212yesmaximal, complemented
7#82186C212yesmaximal, complemented
8#76219C212yesmaximal, complemented
9#76016C212yesmaximal, complemented
10#74635C214yesmaximal, complemented
11#74628C214yesmaximal, complemented
12#74375C211yesmaximal, characteristic, complemented
13#74343C211yesmaximal, characteristic, complemented
14#74033C212yesmaximal, complemented
15#74015C212yesmaximal, complemented
16C4×#897C211yesmaximal, characteristic, complemented
17#73712C211yesmaximal, characteristic, complemented
18#38909—31nomaximal, Sylow
19C22×#235C2212yes—
20C2×C3×C4×D4C2212yes—
21C2×C3×C4×D4C2211yescharacteristic
22C22×C3×C4⋊C4C2212yes—
23C2×#940C2212yes—
24C2×#938C2211yescharacteristic
25C2×#936C2211yescharacteristic
26C2×#930C2212yes—
27C2×#930C2214yes—
28C2×C4×#67C2212yes—
29C2×#926C2212yes—
30#5557—28no—
31#5553—28no—
32C2×#897C2211yescharacteristic
33C2×#897C2211yescharacteristic
34C2×#895C2212yes—
35C2×#895C2212yes—
36C2×#895C2212yes—
37C2×#893C2212yes—
38C2×#890C2211yescharacteristic
39C2×#884C2214yes—
40C2×#883C2212yes—
41C2×#879C2212yes—
42C2×#875C2212yes—
43C2×#874C2211yescharacteristic
44C2×C42×D3C2211yescharacteristic
45C2×C4×Dic6C2211yescharacteristic
46C2×C4×Dic6C2211yescharacteristic
47C3×#389C2212yes—
48C3×#385C2214yes—
49C3×#384C2211yescharacteristic
50C3×#380C2212yes—
51C3×C4×C4⋊C4C2211yescharacteristic
52#5213C2214yes—
53#5213C2214yes—
54#5213C2214yes—
55#4994C2214yes—
56#4991C2214yes—
57#4988C2212yes—
58#4988C2212yes—
59#4988C2212yes—
60#4988C2212yes—
61#4988C2212yes—
62#4987C2214yes—
63#4987C2214yes—
64#4987C2211yescharacteristic
65#4984C2212yes—
66#4984C2211yescharacteristic
67#4984C2212yes—
68#4981C2214yes—
69#4973C2211yescharacteristic
70#4973C2212yes—
71#4973C2212yes—
72#4961C2214yes—
73#4961C2214yes—
74#4961C2214yes—
75#4960C2214yes—
76#4939C2212yes—
77C4×(C2×D3)⋊C4C2212yes—
78C4×C4⋊Dic3C2212yes—
79#4677C2214yes—
80#4674C2214yes—
81#4672C2214yes—
82#4668C2212yes—
83#4668C2214yes—
84#4665C2214yes—
85#4653C2212yes—
86C2×#550—31no—
87C2×#529—31no—
88#2856—31no—
89#2691—34no—
90#2671—34no—
91#2624—32no—
92#2582—31no—
93#2548—31no—
94#2544—32no—
95#2454—32no—
96#2428—32no—
97#2427—32no—
98#2416—32no—
99#2407—32no—
100D4×C4⋊C4D311yescharacteristic, complemented
101#2311—32no—
102C4×C22⋊Q8—31no—
103C22×C3×D4C2311yescharacteristic
104C23×C3×C4C2312yes—
105C23×C3×C4C2314yes—
106C22×#67C2314yes—
107C22×#67C2312yes—
108C22×#67C2314yes—
109C2×#235—28no—
110C2×#235—28no—
111C2×#235—44no—
112C22×D12C2312yes—
113C22×D12C2312yes—
114C22×D12C2314yes—
115C22×D12C2312yes—
116C22×C4×D3C2311yescharacteristic
117C22×C4×D3C2311yescharacteristic
118C22×C4×D3C2314yes—
119C22×C4×D3C2311yescharacteristic
120C22×Dic6C2311yescharacteristic
121C22×Dic6C2311yescharacteristic
122C3×C4×D4—44no—
123C3×C4×D4D418yescomplemented
124C2×C3×C4⋊C4—44no—
125C2×C3×C4⋊C4C2312yes—
126C2×C3×C4⋊C4C2312yes—
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2312yes—
130C2×C3×C4⋊C4C2314yes—
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C22⋊C4C2314yes—
133C2×C3×C22⋊C4C2312yes—
134C2×C3×C42C2312yes—
135C2×C3×C42C2311yescharacteristic
136C2×#217C2312yes—
137C2×#217C2312yes—
138C2×#217C2312yes—
139#940—28no—
140#938—24no—
141#936—24no—
142#930—28no—
143#930—48no—
144C4×#67—28no—
145C2×(C2×D3)⋊C4C2312yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2312yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2314yes—
150C2×(C2×D3)⋊C4C2314yes—
151C2×(C2×D3)⋊C4C2314yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2314yes—
155C2×(C2×D3)⋊C4C2314yes—
156#926—28no—
157C2×C4⋊Dic3C2312yes—
158C2×C4⋊Dic3C2312yes—
159C2×C4⋊Dic3C2312yes—
160C2×C4⋊Dic3C2311yescharacteristic
161C2×C4⋊Dic3C2311yescharacteristic
162C2×C4⋊Dic3C2312yes—
163C2×C4⋊Dic3C2314yes—
164C2×Dic3⋊C4C2312yes—
165C2×Dic3⋊C4C2312yes—
166C2×Dic3⋊C4C2312yes—
167C2×C4×Dic3C2311yescharacteristic
168C2×C4×Dic3C2311yescharacteristic
169C2×C4×Dic3C2312yes—
170C2×C4×Dic3C2312yes—
171C2×C4×Dic3C2311yescharacteristic
172#897—24no—
173#897—24no—
174#895—44no—
175#895—44no—
176#895—44no—
177#893—28no—
178#890—24no—
179#884—216no—
180#883—28no—
181#879—28no—
182#875—44no—
183#874—24no—
184C42×D3—24no—
185C4×Dic6—24no—
186C4×Dic6—24no—
187C3×#95C2312yes—
188C3×#95C2314yes—
189C3⋊#95C2312yes—
190C3⋊#95C2312yes—
191C3⋊#95C2312yes—
192C3⋊#95C2314yes—
193C3⋊#95C2312yes—
194C3⋊#95C2314yes—
195C3⋊#95C2314yes—
196C22×#41—32no—
197#550—68no—
198C2×#127—32no—
199C2×#127—31no—
200#529—68no—
201C2×#126—32no—
202C2×#125—31no—
203C2×#124—31no—
204C2×#124—32no—
205C2×#123—32no—
206C2×C22⋊Q8—31no—
207C2×C22⋊Q8—31no—
208C2×#121—31no—
209C2×#121—32no—
210C2×#121—34no—
211C2×#121—32no—
212C2×#121—32no—
213C2×#121—32no—
214C2×#121—34no—
215C2×C4×Q8—31no—
216C2×C4×Q8—31no—
217C2×C4×D4—32no—
218C2×C4×D4—32no—
219C2×C4×D4C2×D312yes—
220C2×C4×D4C2×D311yescharacteristic
221C2×#117—32no—
222C22×C4⋊C4C2×D312yes—
223C22×C42—31no—
224#399—34no—
225#398—34no—
226#397—34no—
227#396—34no—
228#394—34no—
229#394—34no—
230#394—34no—
231#394—34no—
232#394—34no—
233#392—34no—
234#391—31no—
235#391—32no—
236#391—32no—
237#390—32no—
238#390—32no—
239#390—32no—
240#390—32no—
241#390—32no—
242#390—32no—
243#389—32no—
244#389—32no—
245#389—31no—
246#389C2×D312yes—
247#387—32no—
248#386—34no—
249#386—34no—
250#386—34no—
251#386—34no—
252#385—34no—
253#385—32no—
254#385C2×D314yes—
255#384C2×D311yescharacteristic
256#380—34no—
257#380—34no—
258#380—31no—
259#380C2×D312yes—
260C4×C4⋊C4—32no—
261C4×C4⋊C4C2×D311yescharacteristic
262C4×C22⋊C4—32no—
263C24×C3C2412yes—
264C23×D3C2414yes—
265C23×D3C2411yescharacteristic
266C2×C3×D4—22no—
267C2×C3×D4—22no—
268C2×C3×D4C2×D414yes—
269C22×C3×C4—24no—
270C22×C3×C4—24no—
271C22×C3×C4—44no—
272C22×C3×C4—44no—
273C22×C3×C4—44no—
274C22×C3×C4C2×D418yes—
275C22×C3×C4C2414yes—
276C22×C3×C4C2412yes—
277C22×C3×C4C2412yes—
278C22×C3×C4C2411yescharacteristic
279C22×C3×C4C2412yes—
280C22×C3×C4C2411yescharacteristic
281C22×C3×C4C2411yescharacteristic
282C2×#67—24no—
283C2×#67—28no—
284C2×#67—24no—
285C2×#67—28no—
286C2×#67—28no—
287C2×#67—44no—
288C2×#67—42no—
289C2×#67—44no—
290C2×#67—44no—
291C22×Dic3C2411yescharacteristic
292C22×Dic3C2412yes—
293C22×Dic3C2412yes—
294C22×Dic3C2411yescharacteristic
295C22×Dic3C2411yescharacteristic
296C22×Dic3C2412yes—
297C22×Dic3C2412yes—
298#235—432no—
299C2×D12—24no—
300C2×D12—24no—
301C2×D12—24no—
302C2×D12—24no—
303C2×D12—24no—
304C2×D12—24no—
305C2×D12—28no—
306C2×D12—24no—
307C2×D12—42no—
308C2×D12—44no—
309C2×D12—44no—
310C2×D12—42no—
311C2×C4×D3—22no—
312C2×C4×D3—22no—
313C2×C4×D3—22no—
314C2×C4×D3—22no—
315C2×C4×D3—28no—
316C2×C4×D3—22no—
317C2×C4×D3—22no—
318C2×C4×D3—22no—
319C2×C4×D3—22no—
320C2×C4×D3—28no—
321C2×C4×D3—41no—
322C2×C4×D3—44no—
323C2×Dic6—22no—
324C2×Dic6—22no—
325C2×Dic6—22no—
326C2×Dic6—22no—
327C2×Dic6—22no—
328C2×Dic6#4114yes—
329C3×C4⋊C4—22no—
330C3×C4⋊C4—24no—
331C3×C4⋊C4—24no—
332C3×C4⋊C4—22no—
333C3×C4⋊C4—42no—
334C3×C4⋊C4—44no—
335C3×C4⋊C4C2×D414yes—
336C3×C22⋊C4—44no—
337C3×C22⋊C4C2×D418yes—
338C3×C42—24no—
339C3×C42C2×D414yes—
340#217—24no—
341#217—24no—
342#217—24no—
343(C2×D3)⋊C4—24no—
344(C2×D3)⋊C4—24no—
345(C2×D3)⋊C4—28no—
346(C2×D3)⋊C4—24no—
347(C2×D3)⋊C4—44no—
348(C2×D3)⋊C4—44no—
349(C2×D3)⋊C4—44no—
350(C2×D3)⋊C4—44no—
351(C2×D3)⋊C4—44no—
352(C2×D3)⋊C4—44no—
353(C2×D3)⋊C4—44no—
354C4⋊Dic3—22no—
355C4⋊Dic3—22no—
356C4⋊Dic3—24no—
357C4⋊Dic3—24no—
358C4⋊Dic3—24no—
359C4⋊Dic3—42no—
360C4⋊Dic3—44no—
361Dic3⋊C4—24no—
362Dic3⋊C4—24no—
363Dic3⋊C4—24no—
364C4×Dic3—24no—
365C4×Dic3—24no—
366C4×Dic3—22no—
367C4×Dic3—22no—
368C4×Dic3—22no—
369C2×#41—68no—
370C2×#41—68no—
371C2×#41—124no—
372C22×Q8—31no—
373C22×Q8—31no—
374C22×D4—32no—
375C22×D4—34no—
376C22×D4—34no—
377C22×D4—32no—
378C22×D4—32no—
379C22×D4—34no—
380C22×D4—32no—
381C22×D4C22×D311yescharacteristic
382C23×C4—31no—
383C23×C4—31no—
384C23×C4—34no—
385C23×C4—31no—
386C23×C4C22×D312yes—
387C23×C4C22×D314yes—
388#127—68no—
389#127—64no—
390#126—68no—
391#125—64no—
392#124—64no—
393#124—124no—
394#123—68no—
395C22⋊Q8—64no—
396C22⋊Q8—64no—
397#121—64no—
398#121—68no—
399#121—616no—
400#121—128no—
401#121—124no—
402#121—124no—
403#121—124no—
404C4×Q8—64no—
405C4×Q8—64no—
406C4×D4—44no—
407C4×D4—68no—
408C4×D4—68no—
409C4×D4D1218yescomplemented
410#117—68no—
411C2×C4⋊C4—32no—
412C2×C4⋊C4—32no—
413C2×C4⋊C4—32no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—32no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—32no—
418C2×C4⋊C4—32no—
419C2×C4⋊C4—34no—
420C2×C4⋊C4—32no—
421C2×C4⋊C4—44no—
422C2×C4⋊C4C22×D311yescharacteristic
423C2×C4⋊C4C22×D312yes—
424C2×C4⋊C4C22×D312yes—
425C2×C4⋊C4C22×D311yescharacteristic
426C2×C4⋊C4C22×D314yes—
427C2×C4⋊C4C22×D312yes—
428C2×C4⋊C4C22×D311yescharacteristic
429C2×C22⋊C4—32no—
430C2×C22⋊C4—32no—
431C2×C22⋊C4—32no—
432C2×C22⋊C4—34no—
433C2×C22⋊C4—32no—
434C2×C22⋊C4—32no—
435C2×C22⋊C4—32no—
436C2×C22⋊C4—34no—
437C2×C22⋊C4—34no—
438C2×C22⋊C4—34no—
439C2×C22⋊C4—34no—
440C2×C22⋊C4—34no—
441C2×C22⋊C4—34no—
442C2×C22⋊C4—34no—
443C2×C22⋊C4C22×D314yes—
444C2×C22⋊C4C22×D312yes—
445C2×C42—31no—
446C2×C42—32no—
447C2×C42—32no—
448C2×C42—31no—
449C2×C42—31no—
450C2×C42—64no—
451C2×C42C22×D312yes—
452C2×C42C22×D311yescharacteristic
453#95—32no—
454#95—32no—
455#95—32no—
456#95—32no—
457#95—34no—
458#95—34no—
459#95—34no—
460#95C22×D312yes—
461#95C22×D314yes—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3C22×D414yes—
469C23×C3C2511yescharacteristic
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—24no—
477C22×D3—24no—
478C22×D3—24no—
479C22×D3—24no—
480C22×D3—24no—
481C22×D3—24no—
482C22×D3—24no—
483C22×D3H(5,𝔽2)12yes—
484C3×D4—28no—
485C2×C3×C4—22no—
486C2×C3×C4—21no—
487C2×C3×C4—22no—
488C2×C3×C4—21no—
489C2×C3×C4—216no—
490C2×C3×C4—22no—
491C2×C3×C4—24no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—24no—
496C2×C3×C4—24no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—88no—
500C2×C3×C4C22×D412yes—
501C2×C3×C4C22×D414yes—
502C2×C3×C4C22×D412yes—
503C2×C3×C4C22×D412yes—
504C2×C3×C4C2×#4112yes—
505C2×C3×C4H(5,𝔽2)12yes—
506C2×C3×C4H(5,𝔽2)12yes—
507C2×C3×C42−1+412yes—
508#67—416no—
509#67—48no—
510#67—88no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—22no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—21no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—22no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—22no—
530C2×Dic3—22no—
531C2×Dic3C2×#4114yes—
532D12—48no—
533D12—48no—
534D12—84no—
535D12—88no—
536C4×D3—416no—
537C4×D3—44no—
538C4×D3—44no—
539C4×D3—44no—
540Dic6—28no—
541Dic6—44no—
542C24—31no—
543C24—34no—
544C24C23×D312yes—
545#41—1232no—
546C2×Q8—34no—
547C2×Q8—62no—
548C2×Q8—62no—
549C2×Q8—62no—
550C2×Q8—62no—
551C2×Q8—62no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—68no—
555C2×D4—68no—
556C2×D4—64no—
557C2×D4—64no—
558C2×D4—68no—
559C2×D4—68no—
560C2×D4—64no—
561C2×D4—64no—
562C2×D4—64no—
563C2×D4—64no—
564C2×D4—64no—
565C2×D4—64no—
566C2×D4—64no—
567C2×D4—122no—
568C2×D4—124no—
569C2×D4—124no—
570C2×D4—122no—
571C2×D4—124no—
572C2×D4—122no—
573C2×D4—124no—
574C2×D4—124no—
575C2×D4C2×D1214yes—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—32no—
579C22×C4—31no—
580C22×C4—32no—
581C22×C4—32no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—32no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—68no—
589C22×C4—62no—
590C22×C4—62no—
591C22×C4—62no—
592C22×C4—62no—
593C22×C4—68no—
594C22×C4—62no—
595C22×C4—62no—
596C22×C4—62no—
597C22×C4—62no—
598C22×C4—124no—
599C22×C4—121no—
600C22×C4C2×D1218yes—
601C22×C4C23×D312yes—
602C22×C4C23×D314yes—
603C22×C4C23×D312yes—
604C22×C4C23×D311yescharacteristic
605C22×C4C23×D312yes—
606C22×C4C23×D311yescharacteristic
607C22×C4C23×D311yescharacteristic
608C4⋊C4—22no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—22no—
612C4⋊C4—44no—
613C4⋊C4—42no—
614C4⋊C4—64no—
615C4⋊C4—64no—
616C4⋊C4—64no—
617C4⋊C4—64no—
618C4⋊C4—64no—
619C4⋊C4—62no—
620C4⋊C4—62no—
621C4⋊C4—64no—
622C4⋊C4—124no—
623C4⋊C4—122no—
624C4⋊C4C2×D1214yes—
625C22⋊C4—44no—
626C22⋊C4—64no—
627C22⋊C4—64no—
628C22⋊C4—64no—
629C22⋊C4—64no—
630C22⋊C4—64no—
631C22⋊C4—68no—
632C22⋊C4—64no—
633C22⋊C4—124no—
634C22⋊C4—124no—
635C22⋊C4—124no—
636C22⋊C4—124no—
637C22⋊C4—124no—
638C22⋊C4—124no—
639C22⋊C4—124no—
640C22⋊C4C2×D1218yes—
641C42—24no—
642C42—62no—
643C42—62no—
644C42—62no—
645C42—64no—
646C42—64no—
647C42C2×D1214yes—
648C22×C3—24no—
649C22×C3—24no—
650C22×C3—24no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3C23×D411yescharacteristic
656C22×C3C22×#4111yescharacteristic
657C22×C3C2×H(5,𝔽2)11yescharacteristic
658C22×C3C2×H(5,𝔽2)11yescharacteristic
659C22×C3C2×H(5,𝔽2)11yescharacteristic
660C22×C3C2×2−1+411yescharacteristic
661C22×C3#58511yescharacteristic
662C2×D3—22no—
663C2×D3—22no—
664C2×D3—22no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—44no—
670C2×D3—44no—
671C2×D3—44no—
672C2×D3—44no—
673C2×D3—44no—
674C2×D3—44no—
675C2×D3—44no—
676C3×C4—24no—
677C3×C4—22no—
678C3×C4—42no—
679C3×C4—44no—
680C3×C4—42no—
681C3×C4#53714yes—
682C3×C4#54614yes—
683Dic3—24no—
684Dic3—42no—
685Dic3—41no—
686Dic3—41no—
687Dic3—41no—
688Dic3—42no—
689Dic3—42no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—32no—
697C23—61no—
698C23—61no—
699C23—61no—
700C23—61no—
701C23—61no—
702C23—61no—
703C23—64no—
704C23—64no—
705C23—64no—
706C23—64no—
707C23—64no—
708C23—64no—
709C23—64no—
710C23C22×D1214yes—
711C23C24×D311yescharacteristic
712Q8—68no—
713Q8—124no—
714D4—28no—
715D4—1216no—
716D4—128no—
717D4—128no—
718D4—128no—
719D4—244no—
720D4—248no—
721D4—248no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—216no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—34no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—62no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—62no—
748C2×C4—61no—
749C2×C4—62no—
750C2×C4—61no—
751C2×C4—62no—
752C2×C4—61no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—61no—
756C2×C4—62no—
757C2×C4—88no—
758C2×C4—1216no—
759C2×C4—124no—
760C2×C4—124no—
761C2×C4—124no—
762C2×C4C22×D1212yes—
763C2×C4C22×D1214yes—
764C2×C4C22×D1212yes—
765C2×C4C22×D1212yes—
766C2×C4#100412yes—
767C2×C4#100412yes—
768C2×C4#100712yes—
769C2×C4D3×#4112yes—
770C2×C3—44no—
771C2×C3C2×#53711yescharacteristic
772C2×C3C2×#54611yescharacteristic
773C2×C3#348811yescharacteristic
774C2×C3#351711yescharacteristic
775C2×C3#352211yescharacteristic
776C2×C3#354311yescharacteristic
777C2×C3#355411yescharacteristic
778D3—42no—
779D3—84no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—62no—
788C22—62no—
789C22—62no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—124no—
795C22—124no—
796C22—124no—
797C22—124no—
798C22—124no—
799C22—124no—
800C22—124no—
801C22C23×D1211yescharacteristic
802C22C2×#100411yescharacteristic
803C22C2×#100411yescharacteristic
804C22C2×#100711yescharacteristic
805C22C2×D3×#4111yescharacteristic
806C22D3×H(5,𝔽2)11yescharacteristic
807C22#596811yescharacteristic
808C4—24no—
809C4—22no—
810C4—42no—
811C4—44no—
812C4—42no—
813C4—64no—
814C4—121no—
815C4—121no—
816C4—122no—
817C4—122no—
818C4—121no—
819C4—122no—
820C4#551014yes—
821C4#555414yes—
822C3#3890911yescharacteristic, complemented, Sylow
823C2—44no—
824C2—122no—
825C2—244no—
826C2C2×#551011yescharacteristic
827C2C2×#555411yescharacteristic
828C2#8590011yescharacteristic
829C2#8662411yescharacteristic
830C2#8668411yescharacteristic
831C2#8676511yescharacteristic
832C2#8693611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×D4×C4⋊C4C2
hypercenterD4×C4⋊C4D3
hypocenterC3#38909
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#5557C2semidirect
2. C2×#5553C2semidirect
3. C3×D4×C4⋊C4C2semidirect
4. #82409C2semidirect
5. #82381C2semidirect
6. #82193C2semidirect
7. #82186C2semidirect
8. #76219C2semidirect
9. #76016C2semidirect
10. #74635C2semidirect
11. #74628C2semidirect
12. #74375C2semidirect
13. #74343C2semidirect
14. #74033C2semidirect
15. #74015C2semidirect
16. C4×#897C2semidirect
17. #73712C2semidirect
100. D4×C4⋊C4D3semidirect
123. C3×C4×D4D4semidirect
409. C4×D4D12semidirect
822. C3#38909semidirect

Maximal subgroups

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

subgroupindex
C2×#55572
C2×#55532
C3×D4×C4⋊C42
#824092
#823812
#821932
#821862
#762192
#760162
#746352
#746282
#743752
#743432
#740332
#740152
C4×#8972
#737122
#389093