Finite Group Databasebeta

← #10972983

Subgroups — #10972983

Order 768.

2534 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#537C211yesmaximal, characteristic
2C2×Dic3×#41C211yesmaximal, characteristic, complemented
3#84087C211yesmaximal, characteristic, complemented
4#84087C211yesmaximal, characteristic, complemented
5#84086C211yesmaximal, characteristic, complemented
6#82810C212yesmaximal, complemented
7#82787C212yesmaximal, complemented
8#82754C212yesmaximal, complemented
9#82753C212yesmaximal, complemented
10#82699C212yesmaximal, complemented
11#82678C212yesmaximal, complemented
12#82656C214yesmaximal, complemented
13#82655C214yesmaximal, complemented
14#82644C212yesmaximal, complemented
15#82643C212yesmaximal, complemented
16#82157C211yesmaximal, characteristic, complemented
17C2×#4972C211yesmaximal, characteristic, complemented
18#35255—31nomaximal, Sylow
19C22×C3×#41C2211yescharacteristic
20C22×C3×#41C2211yescharacteristic
21C3×#537—28no—
22C2×C3×C22⋊Q8C2212yes—
23C2×C3×C22⋊Q8C2212yes—
24C2×C3×#121C2212yes—
25C2×C3×#121C2212yes—
26C2×C3×#121C2214yes—
27C22×C3×C4⋊C4C2211yescharacteristic
28Dic3×#41—28no—
29C2×Q8×Dic3C2211yescharacteristic
30C2×Q8×Dic3C2211yescharacteristic
31C2×#935C2214yes—
32C2×D4×Dic3C2211yescharacteristic
33C2×D4×Dic3C2211yescharacteristic
34C2×D4×Dic3C2212yes—
35C2×D4×Dic3C2212yes—
36C2×#926C2212yes—
37C2×#926C2211yescharacteristic
38C2×#926C2211yescharacteristic
39C22×C4⋊Dic3C2211yescharacteristic
40C22×Dic3⋊C4C2212yes—
41C22×C4×Dic3C2212yes—
42C22×C4×Dic3C2211yescharacteristic
43#5229C2212yes—
44#5229C2211yescharacteristic
45#5229C2212yes—
46#5229C2211yescharacteristic
47#5222C2214yes—
48#5222C2214yes—
49#5221C2211yescharacteristic
50#5221C2212yes—
51#5221C2211yescharacteristic
52#5221C2212yes—
53#5220C2214yes—
54#5220C2212yes—
55#5220C2212yes—
56#5220C2214yes—
57#5220C2214yes—
58#5212C2212yes—
59#5212C2212yes—
60#5212C2212yes—
61#5212C2212yes—
62#5210C2214yes—
63C4×#217C2212yes—
64C4×#217C2212yes—
65C2×C3⋊#95C2212yes—
66#4986C2214yes—
67#4981C2214yes—
68#4978C2214yes—
69#4978C2214yes—
70#4977C2212yes—
71#4975C2212yes—
72#4972C2212yes—
73#4972C2212yes—
74#4972C2212yes—
75#4972C2212yes—
76#4972C2212yes—
77#4972C2212yes—
78#4953C2214yes—
79#4952C2214yes—
80#4952C2214yes—
81#4949C2214yes—
82#4946C2214yes—
83#4944C2214yes—
84#4944C2214yes—
85#4943C2214yes—
86C2×#537D311yescharacteristic
87C2×C4×#41—31no—
88#2855—32no—
89#2854—32no—
90#2625—32no—
91#2624—32no—
92#2444—34no—
93#2443—34no—
94#2423—32no—
95#2422—32no—
96#2421—32no—
97#2420—32no—
98#2317—31no—
99#2311—31no—
100#2311—31no—
101#2297—31no—
102C2×#389—31no—
103C2×C3×#41—24no—
104C2×C3×#41—24no—
105C2×C3×#41—24no—
106C2×C3×#41—24no—
107C2×C3×#41—24no—
108C2×C3×#41D418yes—
109C22×C3×Q8C2311yescharacteristic
110C22×C3×Q8C2311yescharacteristic
111C22×C3×D4C2312yes—
112C22×C3×D4C2311yescharacteristic
113C22×C3×D4C2312yes—
114C22×C3×D4C2311yescharacteristic
115C22×C3×D4C2314yes—
116C23×C3×C4C2312yes—
117C23×C3×C4C2312yes—
118C23×C3×C4C2312yes—
119C23×C3×C4C2311yescharacteristic
120C23×Dic3C2312yes—
121C23×Dic3C2312yes—
122C23×Dic3C2311yescharacteristic
123C23×Dic3C2311yescharacteristic
124C23×Dic3C2312yes—
125C3×C22⋊Q8—28no—
126C3×C22⋊Q8—28no—
127C3×#121—28no—
128C3×#121—216no—
129C3×#121—28no—
130C2×C3×C4⋊C4—24no—
131C2×C3×C4⋊C4C2312yes—
132C2×C3×C4⋊C4C2312yes—
133C2×C3×C4⋊C4C2314yes—
134C2×C3×C22⋊C4C2314yes—
135C2×C3×C22⋊C4C2314yes—
136C2×#217C2312yes—
137C2×#217C2312yes—
138C2×#217C2312yes—
139C2×#217C2312yes—
140C2×#217C2312yes—
141C2×#217C2312yes—
142C2×#217C2314yes—
143C2×#217C2314yes—
144C2×#217C2314yes—
145C2×#217C2312yes—
146C2×#217C2314yes—
147C2×#217C2312yes—
148Q8×Dic3—24no—
149Q8×Dic3—24no—
150#935—48no—
151D4×Dic3—24no—
152D4×Dic3—24no—
153D4×Dic3—28no—
154D4×Dic3—28no—
155#926—28no—
156#926—24no—
157#926—24no—
158C2×C4⋊Dic3—24no—
159C2×C4⋊Dic3C2312yes—
160C2×C4⋊Dic3C2312yes—
161C2×C4⋊Dic3C2312yes—
162C2×C4⋊Dic3C2312yes—
163C2×C4⋊Dic3C2311yescharacteristic
164C2×C4⋊Dic3C2311yescharacteristic
165C2×C4⋊Dic3C2311yescharacteristic
166C2×C4⋊Dic3C2311yescharacteristic
167C2×Dic3⋊C4—44no—
168C2×Dic3⋊C4C2314yes—
169C2×Dic3⋊C4C2314yes—
170C2×Dic3⋊C4C2314yes—
171C2×Dic3⋊C4C2314yes—
172C2×C4×Dic3—28no—
173C2×C4×Dic3—24no—
174C2×C4×Dic3C2312yes—
175C2×C4×Dic3C2312yes—
176C2×C4×Dic3C2312yes—
177C2×C4×Dic3C2311yescharacteristic
178C2×C4×Dic3C2311yescharacteristic
179C2×C4×Dic3C2311yescharacteristic
180C2×C4×Dic3C2312yes—
181C2×C4×Dic3C2311yescharacteristic
182C3⋊#95C2312yes—
183C3⋊#95C2314yes—
184C3⋊#95C2314yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2312yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2312yes—
192C3⋊#95C2312yes—
193C3⋊#95C2314yes—
194C22×#41C2×D311yescharacteristic
195C22×#41C2×D311yescharacteristic
196#537—28no—
197C2×#123—34no—
198C2×C22⋊Q8C2×D312yes—
199C2×C22⋊Q8C2×D312yes—
200C2×#121C2×D312yes—
201C2×#121C2×D312yes—
202C2×#121C2×D314yes—
203C4×#41—68no—
204C2×C4×Q8—31no—
205C2×C4×Q8—31no—
206C2×C4×D4—31no—
207C2×C4×D4—31no—
208C2×C4×D4—32no—
209C2×C4×D4—32no—
210C2×#117—31no—
211C2×#117—31no—
212C2×#117—32no—
213C22×C4⋊C4—31no—
214C22×C4⋊C4—32no—
215C22×C4⋊C4C2×D311yescharacteristic
216C22×C42—32no—
217C22×C42—31no—
218#400—34no—
219#399—34no—
220#398—34no—
221#397—34no—
222#397—34no—
223#397—34no—
224#394—34no—
225#394—34no—
226#391—32no—
227#391—32no—
228#391—31no—
229#391—31no—
230#390—32no—
231#390—32no—
232#390—31no—
233#390—31no—
234#389—32no—
235#389—32no—
236#389—32no—
237#389—32no—
238#389—32no—
239#389—32no—
240#388—34no—
241#388—34no—
242#387—34no—
243#387—34no—
244#386—34no—
245#386—34no—
246#386—34no—
247#386—32no—
248#386—32no—
249#385—34no—
250#385—34no—
251#384—32no—
252#382—32no—
253#381—34no—
254#380—32no—
255#380—32no—
256#380—32no—
257#380—32no—
258C4×C22⋊C4—32no—
259C4×C22⋊C4—32no—
260C2×#95—32no—
261C24×C3C2412yes—
262C24×C3C2412yes—
263C24×C3C2411yescharacteristic
264C3×#41—232no—
265C3×#41—416no—
266C2×C3×Q8—22no—
267C2×C3×Q8—22no—
268C2×C3×Q8—22no—
269C2×C3×Q8—22no—
270C2×C3×Q8—22no—
271C2×C3×Q8C2×D414yes—
272C2×C3×D4—24no—
273C2×C3×D4—24no—
274C2×C3×D4—24no—
275C2×C3×D4—24no—
276C2×C3×D4—24no—
277C2×C3×D4—28no—
278C2×C3×D4—22no—
279C2×C3×D4—22no—
280C2×C3×D4—22no—
281C2×C3×D4—22no—
282C2×C3×D4—22no—
283C2×C3×D4—44no—
284C2×C3×D4—44no—
285C2×C3×D4C2×D418yes—
286C2×C3×D4C2×D414yes—
287C22×C3×C4—24no—
288C22×C3×C4—24no—
289C22×C3×C4—24no—
290C22×C3×C4—24no—
291C22×C3×C4—24no—
292C22×C3×C4—24no—
293C22×C3×C4—42no—
294C22×C3×C4—42no—
295C22×C3×C4C2×D418yes—
296C22×C3×C4C2×D414yes—
297C22×C3×C4#4114yes—
298C22×C3×C4#4114yes—
299C22×C3×C4C2412yes—
300C22×C3×C4C2414yes—
301C22×C3×C4C2412yes—
302C22×C3×C4C2411yescharacteristic
303C22×C3×C4C2411yescharacteristic
304C22×Dic3—24no—
305C22×Dic3—24no—
306C22×Dic3—22no—
307C22×Dic3—22no—
308C22×Dic3—24no—
309C22×Dic3—22no—
310C22×Dic3—24no—
311C22×Dic3—22no—
312C22×Dic3—24no—
313C22×Dic3—42no—
314C22×Dic3—42no—
315C22×Dic3—41no—
316C22×Dic3—41no—
317C22×Dic3—42no—
318C22×Dic3—42no—
319C22×Dic3C2412yes—
320C22×Dic3C2411yescharacteristic
321C22×Dic3C2412yes—
322C22×Dic3C2412yes—
323C22×Dic3C2414yes—
324C22×Dic3C2411yescharacteristic
325C22×Dic3C2412yes—
326C22×Dic3C2411yescharacteristic
327C22×Dic3C2411yescharacteristic
328C3×C4⋊C4—24no—
329C3×C4⋊C4—24no—
330C3×C4⋊C4—28no—
331C3×C22⋊C4—28no—
332C3×C22⋊C4—28no—
333#217—24no—
334#217—24no—
335#217—24no—
336#217—24no—
337#217—24no—
338#217—24no—
339#217—44no—
340#217—44no—
341#217—42no—
342#217—44no—
343#217—42no—
344#217—44no—
345C4⋊Dic3—24no—
346C4⋊Dic3—24no—
347C4⋊Dic3—22no—
348C4⋊Dic3—22no—
349C4⋊Dic3—24no—
350C4⋊Dic3—24no—
351C4⋊Dic3—22no—
352C4⋊Dic3—22no—
353Dic3⋊C4—28no—
354Dic3⋊C4—44no—
355Dic3⋊C4—44no—
356Dic3⋊C4—44no—
357C4×Dic3—22no—
358C4×Dic3—24no—
359C4×Dic3—22no—
360C4×Dic3—24no—
361C4×Dic3—24no—
362C4×Dic3—22no—
363C4×Dic3—22no—
364C4×Dic3—24no—
365C2×#41—24no—
366C2×#41—24no—
367C2×#41—24no—
368C2×#41—24no—
369C2×#41—24no—
370C2×#41#6718yes—
371C22×Q8C22×D311yescharacteristic
372C22×Q8C22×D311yescharacteristic
373C22×D4C22×D312yes—
374C22×D4C22×D311yescharacteristic
375C22×D4C22×D312yes—
376C22×D4C22×D311yescharacteristic
377C22×D4C22×D314yes—
378C23×C4—31no—
379C23×C4—32no—
380C23×C4—31no—
381C23×C4—32no—
382C23×C4—32no—
383C23×C4C22×D312yes—
384C23×C4C22×D312yes—
385C23×C4C22×D312yes—
386C23×C4C22×D311yescharacteristic
387#123—128no—
388C22⋊Q8—28no—
389C22⋊Q8—28no—
390#121—28no—
391#121—216no—
392#121—28no—
393C4×Q8—64no—
394C4×Q8—64no—
395C4×D4—64no—
396C4×D4—64no—
397C4×D4—68no—
398C4×D4—68no—
399#117—64no—
400#117—68no—
401#117—64no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—34no—
404C2×C4⋊C4—32no—
405C2×C4⋊C4—32no—
406C2×C4⋊C4—31no—
407C2×C4⋊C4—31no—
408C2×C4⋊C4—32no—
409C2×C4⋊C4—32no—
410C2×C4⋊C4—31no—
411C2×C4⋊C4—31no—
412C2×C4⋊C4—34no—
413C2×C4⋊C4—34no—
414C2×C4⋊C4—34no—
415C2×C4⋊C4—64no—
416C2×C4⋊C4—124no—
417C2×C4⋊C4C22×D312yes—
418C2×C4⋊C4C22×D312yes—
419C2×C4⋊C4C22×D314yes—
420C2×C22⋊C4—32no—
421C2×C22⋊C4—32no—
422C2×C22⋊C4—32no—
423C2×C22⋊C4—32no—
424C2×C22⋊C4—32no—
425C2×C22⋊C4—32no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4—34no—
428C2×C22⋊C4—32no—
429C2×C22⋊C4—32no—
430C2×C22⋊C4—34no—
431C2×C22⋊C4—34no—
432C2×C22⋊C4C22×D314yes—
433C2×C22⋊C4C22×D314yes—
434C2×C42—32no—
435C2×C42—31no—
436C2×C42—32no—
437C2×C42—31no—
438C2×C42—31no—
439C2×C42—32no—
440C2×C42—32no—
441C2×C42—31no—
442C2×C42—68no—
443C2×C42—64no—
444#95—34no—
445#95—34no—
446#95—32no—
447#95—32no—
448#95—32no—
449#95—32no—
450#95—34no—
451#95—34no—
452#95—34no—
453#95—34no—
454#95—34no—
455#95—34no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3C22×D414yes—
474C23×C3C22×D412yes—
475C23×C3C2×#4112yes—
476C23×C3C2×#4112yes—
477C23×C3C2511yescharacteristic
478C3×Q8—28no—
479C3×Q8—44no—
480C3×D4—216no—
481C3×D4—28no—
482C3×D4—48no—
483C3×D4—44no—
484C3×D4—88no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—216no—
488C2×C3×C4—24no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—24no—
493C2×C3×C4—24no—
494C2×C3×C4—48no—
495C2×C3×C4—84no—
496C2×C3×C4#123116yescomplemented
497C2×C3×C4C22×D414yes—
498C2×C3×C4C22×D412yes—
499C2×C3×C4C22×D412yes—
500C2×C3×C4C2×#4112yes—
501C2×C3×C4C2×#4112yes—
502C2×C3×C4C2×#4112yes—
503C2×C3×C4C2×#4112yes—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—21no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—24no—
515C2×Dic3—24no—
516C2×Dic3—21no—
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—21no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—21no—
526C2×Dic3—24no—
527C2×Dic3—21no—
528C2×Dic3—22no—
529C2×Dic3—44no—
530C2×Dic3—48no—
531C2×Dic3—44no—
532C2×Dic3—48no—
533C2×Dic3—48no—
534C2×Dic3H(5,𝔽2)12yes—
535C2×Dic32−1+412yes—
536C24C23×D312yes—
537C24C23×D312yes—
538C24C23×D311yescharacteristic
539#41—232no—
540#41—416no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8C2×#6714yes—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—28no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—44no—
559C2×D4—44no—
560C2×D4C2×#6718yes—
561C2×D4C2×#6714yes—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—32no—
572C22×C4—32no—
573C22×C4—32no—
574C22×C4—34no—
575C22×C4—32no—
576C22×C4—31no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—62no—
580C22×C4—64no—
581C22×C4—62no—
582C22×C4—64no—
583C22×C4—64no—
584C22×C4—64no—
585C22×C4—64no—
586C22×C4—62no—
587C22×C4—62no—
588C22×C4—122no—
589C22×C4—121no—
590C22×C4—122no—
591C22×C4—121no—
592C22×C4—122no—
593C22×C4—122no—
594C22×C4#23714yes—
595C22×C4#23714yes—
596C22×C4C2×#6718yes—
597C22×C4C2×#6714yes—
598C22×C4C23×D312yes—
599C22×C4C23×D314yes—
600C22×C4C23×D312yes—
601C22×C4C23×D311yescharacteristic
602C22×C4C23×D311yescharacteristic
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—28no—
606C4⋊C4—68no—
607C4⋊C4—64no—
608C4⋊C4—64no—
609C4⋊C4—62no—
610C4⋊C4—62no—
611C4⋊C4—64no—
612C4⋊C4—64no—
613C4⋊C4—62no—
614C4⋊C4—62no—
615C4⋊C4—124no—
616C4⋊C4—124no—
617C4⋊C4—124no—
618C22⋊C4—28no—
619C22⋊C4—28no—
620C22⋊C4—64no—
621C22⋊C4—64no—
622C22⋊C4—64no—
623C22⋊C4—64no—
624C22⋊C4—64no—
625C22⋊C4—64no—
626C22⋊C4—124no—
627C22⋊C4—124no—
628C22⋊C4—122no—
629C22⋊C4—124no—
630C22⋊C4—122no—
631C22⋊C4—124no—
632C42—64no—
633C42—62no—
634C42—64no—
635C42—62no—
636C42—64no—
637C42—64no—
638C42—62no—
639C42—62no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—22no—
646C22×C3—24no—
647C22×C3—24no—
648C22×C3—24no—
649C22×C3—42no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—42no—
659C22×C3—42no—
660C22×C3C2×#12314yes—
661C22×C3C23×D411yescharacteristic
662C22×C3C22×#4111yescharacteristic
663C22×C3C22×#4111yescharacteristic
664C22×C3C2×H(5,𝔽2)11yescharacteristic
665C22×C3C2×2−1+411yescharacteristic
666C22×C3#58511yescharacteristic
667C22×C3#58511yescharacteristic
668C3×C4—24no—
669C3×C4—42no—
670C3×C4—44no—
671C3×C4C2×#12314yes—
672C3×C4C2×#12314yes—
673Dic3—22no—
674Dic3—22no—
675Dic3—44no—
676Dic3—41no—
677Dic3—42no—
678Dic3—41no—
679Dic3—42no—
680Dic3—42no—
681Dic3—42no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23C2×#23712yes—
700C23C2×#23712yes—
701C23C22×#6714yes—
702C23C22×#6712yes—
703C23C24×D311yescharacteristic
704Q8—28no—
705Q8—44no—
706D4—216no—
707D4—28no—
708D4—48no—
709D4—44no—
710D4—88no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—216no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—32no—
721C2×C4—32no—
722C2×C4—48no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—64no—
730C2×C4—62no—
731C2×C4—64no—
732C2×C4—62no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—62no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—61no—
739C2×C4—62no—
740C2×C4—62no—
741C2×C4—64no—
742C2×C4—61no—
743C2×C4—62no—
744C2×C4—62no—
745C2×C4—61no—
746C2×C4—62no—
747C2×C4—61no—
748C2×C4—84no—
749C2×C4—124no—
750C2×C4—128no—
751C2×C4—124no—
752C2×C4—128no—
753C2×C4—128no—
754C2×C4#935116yescomplemented
755C2×C4C2×#23712yes—
756C2×C4C2×#23712yes—
757C2×C4C2×#23712yes—
758C2×C4C2×#23712yes—
759C2×C4C22×#6714yes—
760C2×C4C22×#6712yes—
761C2×C4C22×#6712yes—
762C2×C3—24no—
763C2×C3—44no—
764C2×C3—82no—
765C2×C3C22×#12311yescharacteristic
766C2×C3#346011yescharacteristic
767C2×C3#346111yescharacteristic
768C2×C3#348811yescharacteristic
769C2×C3#348911yescharacteristic
770C2×C3#351111yescharacteristic
771C2×C3#351211yescharacteristic
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22C2×#93514yes—
793C22C22×#23711yescharacteristic
794C22C22×#23711yescharacteristic
795C22D3×H(5,𝔽2)11yescharacteristic
796C22#596611yescharacteristic
797C22D3×2−1+411yescharacteristic
798C22#596811yescharacteristic
799C22C23×#6711yescharacteristic
800C4—24no—
801C4—42no—
802C4—44no—
803C4—62no—
804C4—62no—
805C4—124no—
806C4—122no—
807C4—122no—
808C4—122no—
809C4—121no—
810C4—121no—
811C4—122no—
812C4C2×#93514yes—
813C4C2×#93514yes—
814C3#3525511yescharacteristic, complemented, Sylow
815C2—24no—
816C2—44no—
817C2—82no—
818C2#8636411yescharacteristic
819C2#8636511yescharacteristic
820C2#8636811yescharacteristic
821C2#8636911yescharacteristic
822C2C22×#93511yescharacteristic
823C2#8728511yescharacteristic
824C2#8729511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
Fitting, prime radicalC2×C3×#537C2
hypercenterC2×#537D3
hypocenterC3#35255
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×#41C2semidirect
3. #84087C2semidirect
4. #84087C2semidirect
5. #84086C2semidirect
6. #82810C2semidirect
7. #82787C2semidirect
8. #82754C2semidirect
9. #82753C2semidirect
10. #82699C2semidirect
11. #82678C2semidirect
12. #82656C2semidirect
13. #82655C2semidirect
14. #82644C2semidirect
15. #82643C2semidirect
16. #82157C2semidirect
17. C2×#4972C2semidirect
496. C2×C3×C4#123semidirect
754. C2×C4#935semidirect
814. C3#35255semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5372
C2×Dic3×#412
#840872
#840862
#828102
#827872
#827542
#827532
#826992
#826782
#826562
#826552
#826442
#826432
#821572
C2×#49722
#352553