Finite Group Databasebeta

← #11058602

Subgroups — #11058602

Order 768.

2468 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#547C211yesmaximal, characteristic, complemented
2C2×#5557C211yesmaximal, characteristic, complemented
3#84097C212yesmaximal, complemented
4#84087C212yesmaximal, complemented
5#83269C211yesmaximal, characteristic, complemented
6#83244C211yesmaximal, characteristic, complemented
7#82877C214yesmaximal, complemented
8#82875C214yesmaximal, complemented
9#82815C212yesmaximal, complemented
10#82787C212yesmaximal, complemented
11#82666C212yesmaximal, complemented
12#82647C212yesmaximal, complemented
13C4×#938C211yesmaximal, characteristic, complemented
14#82376C211yesmaximal, characteristic, complemented
15D4×C4⋊Dic3C211yesmaximal, characteristic, complemented
16#82194C212yesmaximal, complemented
17#82172C212yesmaximal, complemented
18#38908—31nomaximal, Sylow
19C22×C3×#41C2212yes—
20C3×#547—28no—
21C2×C3×C4⋊Q8C2211yescharacteristic
22C2×C3×#123C2214yes—
23C2×C3×C22⋊Q8C2212yes—
24C2×C3×#121C2212yes—
25C2×C3×C4×D4C2211yescharacteristic
26C2×C3×C4×D4C2211yescharacteristic
27C22×C3×C4⋊C4C2212yes—
28C2×#946C2212yes—
29C2×#938C2211yescharacteristic
30C2×#938C2211yescharacteristic
31C2×#936C2211yescharacteristic
32C2×D4×Dic3C2212yes—
33C2×C4×#67C2212yes—
34C2×C4×#67C2212yes—
35C2×#926C2212yes—
36C22×C4⋊Dic3C2212yes—
37C2×#924C2212yes—
38#5557—28no—
39C2×#897C2211yescharacteristic
40C2×#890C2211yescharacteristic
41C2×#883C2212yes—
42C2×#879C2212yes—
43C2×C42×D3C2211yescharacteristic
44C2×C4×Dic6C2211yescharacteristic
45#5229C2212yes—
46#5229C2212yes—
47#5229C2212yes—
48#5223C2214yes—
49#5222C2214yes—
50#5221C2211yescharacteristic
51#5221C2212yes—
52#5220C2214yes—
53#5220C2214yes—
54#5213C2214yes—
55#5212C2214yes—
56#5212C2212yes—
57#5212C2214yes—
58#5212C2212yes—
59#5210C2214yes—
60C4×#217C2212yes—
61#4994C2214yes—
62#4987C2212yes—
63#4987C2212yes—
64#4987C2211yescharacteristic
65#4986C2214yes—
66#4985C2214yes—
67#4984C2212yes—
68#4982C2214yes—
69#4981C2214yes—
70#4977C2212yes—
71#4973C2212yes—
72#4972C2212yes—
73#4972C2212yes—
74#4972C2211yescharacteristic
75#4972C2212yes—
76#4958C2214yes—
77#4956C2212yes—
78#4952C2214yes—
79#4952C2214yes—
80#4950C2214yes—
81#4948C2214yes—
82#4944C2212yes—
83#4942C2214yes—
84#4935C2211yescharacteristic
85C4×C4⋊Dic3C2211yescharacteristic
86C2×#547D311yescharacteristic, complemented
87C2×#529—31no—
88#2857—31no—
89#2695—34no—
90#2693—34no—
91#2625—32no—
92#2568—31no—
93#2538—31no—
94#2535—32no—
95#2442—32no—
96#2427—32no—
97#2417—32no—
98#2417—32no—
99#2407—32no—
100D4×C4⋊C4—31no—
101#2311—32no—
102C4×#121—31no—
103C2×C3×#41—28no—
104C2×C3×#41—28no—
105C2×C3×#41—44no—
106C22×C3×Q8C2312yes—
107C22×C3×D4C2314yes—
108C22×C3×D4C2311yescharacteristic
109C22×C3×D4C2311yescharacteristic
110C23×C3×C4C2312yes—
111C23×C3×C4C2314yes—
112C23×C3×C4C2312yes—
113C22×#67C2312yes—
114C22×#67C2312yes—
115C23×Dic3C2314yes—
116C22×C4×D3C2311yescharacteristic
117C22×C4×D3C2311yescharacteristic
118C22×C4×D3C2311yescharacteristic
119C22×Dic6C2311yescharacteristic
120C3×C4⋊Q8—24no—
121C3×#123—216no—
122C3×C22⋊Q8—28no—
123C3×#121—28no—
124C3×C4×D4—24no—
125C3×C4×D4D418yescomplemented
126C2×C3×C4⋊C4—28no—
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2312yes—
129C2×C3×C4⋊C4C2312yes—
130C2×C3×C4⋊C4C2314yes—
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C22⋊C4C2314yes—
133C2×C3×C22⋊C4C2312yes—
134C2×C3×C22⋊C4C2312yes—
135C2×C3×C42C2311yescharacteristic
136C2×#217C2312yes—
137C2×#217C2312yes—
138C2×#217C2312yes—
139C2×#217C2312yes—
140C2×#217C2312yes—
141C2×#217C2314yes—
142C2×#217C2314yes—
143C2×#217C2314yes—
144C2×#217C2312yes—
145#946—44no—
146#938—24no—
147#938—24no—
148#936—24no—
149D4×Dic3—44no—
150C4×#67—28no—
151C4×#67—44no—
152C2×(C2×D3)⋊C4C2312yes—
153C2×(C2×D3)⋊C4C2312yes—
154C2×(C2×D3)⋊C4C2314yes—
155#926—28no—
156C2×C4⋊Dic3—44no—
157C2×C4⋊Dic3C2311yescharacteristic
158C2×C4⋊Dic3C2311yescharacteristic
159C2×C4⋊Dic3C2312yes—
160C2×C4⋊Dic3C2312yes—
161C2×C4⋊Dic3C2311yescharacteristic
162C2×C4⋊Dic3C2312yes—
163C2×C4⋊Dic3C2312yes—
164C2×C4⋊Dic3C2312yes—
165C2×C4⋊Dic3C2314yes—
166#924—44no—
167C2×Dic3⋊C4C2312yes—
168C2×Dic3⋊C4C2312yes—
169C2×Dic3⋊C4C2314yes—
170C2×Dic3⋊C4C2314yes—
171C2×Dic3⋊C4C2312yes—
172C2×C4×Dic3C2312yes—
173C2×C4×Dic3C2311yescharacteristic
174C2×C4×Dic3C2311yescharacteristic
175C2×C4×Dic3C2312yes—
176C2×C4×Dic3C2311yescharacteristic
177#897—24no—
178#890—24no—
179#883—28no—
180#879—28no—
181C42×D3—24no—
182C4×Dic6—24no—
183C3⋊#95C2312yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2312yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2314yes—
192C3⋊#95C2314yes—
193C3⋊#95C2314yes—
194C22×#41C2×D312yes—
195#547—28no—
196C2×C4⋊Q8C2×D311yescharacteristic
197#529—68no—
198C2×#126—32no—
199C2×#125—31no—
200C2×#124—31no—
201C2×#123—32no—
202C2×#123C2×D314yes—
203C2×C22⋊Q8—32no—
204C2×C22⋊Q8—32no—
205C2×C22⋊Q8—31no—
206C2×C22⋊Q8C2×D312yes—
207C2×#121—31no—
208C2×#121—31no—
209C2×#121C2×D312yes—
210C2×C4×Q8—31no—
211C2×C4×D4—32no—
212C2×C4×D4—32no—
213C2×C4×D4—32no—
214C2×C4×D4C2×D311yescharacteristic
215C2×C4×D4C2×D311yescharacteristic
216C2×#117—32no—
217C22×C4⋊C4—32no—
218C22×C4⋊C4C2×D312yes—
219C22×C42—31no—
220#400—34no—
221#400—34no—
222#398—34no—
223#398—34no—
224#397—34no—
225#397—34no—
226#396—34no—
227#396—34no—
228#394—34no—
229#392—34no—
230#391—32no—
231#391—32no—
232#391—32no—
233#391—32no—
234#390—31no—
235#390—32no—
236#389—32no—
237#389—32no—
238#389—32no—
239#389—31no—
240#389—32no—
241#388—32no—
242#386—34no—
243#386—34no—
244#386—34no—
245#386—32no—
246#386—34no—
247#385—34no—
248#385—34no—
249#384—31no—
250#382—32no—
251#380—34no—
252#380—34no—
253#380—32no—
254#380—32no—
255#380—32no—
256#380—32no—
257#380—31no—
258#380—34no—
259C4×C4⋊C4—31no—
260C4×C22⋊C4—32no—
261C24×C3C2412yes—
262C24×C3C2412yes—
263C23×D3C2411yescharacteristic
264C3×#41—432no—
265C2×C3×Q8—24no—
266C2×C3×Q8—24no—
267C2×C3×Q8—24no—
268C2×C3×D4—28no—
269C2×C3×D4—28no—
270C2×C3×D4—22no—
271C2×C3×D4—22no—
272C2×C3×D4—22no—
273C2×C3×D4—22no—
274C2×C3×D4—44no—
275C2×C3×D4C2×D414yes—
276C2×C3×D4#4114yes—
277C22×C3×C4—24no—
278C22×C3×C4—24no—
279C22×C3×C4—28no—
280C22×C3×C4—24no—
281C22×C3×C4—28no—
282C22×C3×C4—24no—
283C22×C3×C4—24no—
284C22×C3×C4—44no—
285C22×C3×C4C2×D418yes—
286C22×C3×C4C2414yes—
287C22×C3×C4C2412yes—
288C22×C3×C4C2411yescharacteristic
289C22×C3×C4C2412yes—
290C22×C3×C4C2411yescharacteristic
291C22×C3×C4C2411yescharacteristic
292C2×#67—24no—
293C2×#67—24no—
294C2×#67—24no—
295C2×#67—24no—
296C2×#67—42no—
297C2×#67—42no—
298C22×Dic3—44no—
299C22×Dic3—44no—
300C22×Dic3—44no—
301C22×Dic3C2412yes—
302C22×Dic3C2411yescharacteristic
303C22×Dic3C2412yes—
304C22×Dic3C2412yes—
305C22×Dic3C2411yescharacteristic
306C22×Dic3C2412yes—
307C22×Dic3C2414yes—
308C22×Dic3C2411yescharacteristic
309C2×C4×D3—22no—
310C2×C4×D3—22no—
311C2×C4×D3—22no—
312C2×C4×D3—22no—
313C2×C4×D3—22no—
314C2×C4×D3—22no—
315C2×C4×D3—22no—
316C2×C4×D3—22no—
317C2×C4×D3—41no—
318C2×Dic6—22no—
319C2×Dic6—22no—
320C2×Dic6—22no—
321C3×C4⋊C4—24no—
322C3×C4⋊C4—28no—
323C3×C4⋊C4—22no—
324C3×C4⋊C4—24no—
325C3×C4⋊C4C2×D414yes—
326C3×C22⋊C4—28no—
327C3×C22⋊C4—24no—
328C3×C22⋊C4C2×D418yes—
329C3×C42C2×D414yes—
330#217—24no—
331#217—24no—
332#217—24no—
333#217—24no—
334#217—44no—
335#217—42no—
336#217—44no—
337#217—44no—
338#217—42no—
339(C2×D3)⋊C4—24no—
340(C2×D3)⋊C4—42no—
341(C2×D3)⋊C4—44no—
342C4⋊Dic3—22no—
343C4⋊Dic3—24no—
344C4⋊Dic3—24no—
345C4⋊Dic3—22no—
346C4⋊Dic3—24no—
347C4⋊Dic3—22no—
348C4⋊Dic3—24no—
349C4⋊Dic3—44no—
350C4⋊Dic3—42no—
351Dic3⋊C4—24no—
352Dic3⋊C4—24no—
353Dic3⋊C4—44no—
354Dic3⋊C4—42no—
355Dic3⋊C4—44no—
356C4×Dic3—24no—
357C4×Dic3—22no—
358C4×Dic3—22no—
359C4×Dic3—22no—
360C4×Dic3—24no—
361C2×#41—28no—
362C2×#41—28no—
363C2×#41—44no—
364C22×Q8—31no—
365C22×Q8C22×D312yes—
366C22×D4—32no—
367C22×D4—32no—
368C22×D4C22×D314yes—
369C22×D4C22×D311yescharacteristic
370C22×D4C22×D311yescharacteristic
371C23×C4—34no—
372C23×C4—31no—
373C23×C4—31no—
374C23×C4—31no—
375C23×C4C22×D312yes—
376C23×C4C22×D314yes—
377C23×C4C22×D312yes—
378C4⋊Q8—24no—
379#126—68no—
380#125—64no—
381#124—64no—
382#123—216no—
383#123—68no—
384C22⋊Q8—28no—
385C22⋊Q8—64no—
386C22⋊Q8—124no—
387C22⋊Q8—124no—
388#121—28no—
389#121—64no—
390#121—64no—
391C4×Q8—64no—
392C4×D4—24no—
393C4×D4—68no—
394C4×D4—124no—
395C4×D4—124no—
396C4×D4#6718yescomplemented
397#117—68no—
398C2×C4⋊C4—28no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—32no—
401C2×C4⋊C4—32no—
402C2×C4⋊C4—32no—
403C2×C4⋊C4—32no—
404C2×C4⋊C4—32no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—32no—
407C2×C4⋊C4—31no—
408C2×C4⋊C4—34no—
409C2×C4⋊C4—32no—
410C2×C4⋊C4—34no—
411C2×C4⋊C4—34no—
412C2×C4⋊C4—32no—
413C2×C4⋊C4—124no—
414C2×C4⋊C4C22×D312yes—
415C2×C4⋊C4C22×D314yes—
416C2×C4⋊C4C22×D311yescharacteristic
417C2×C4⋊C4C22×D312yes—
418C2×C4⋊C4C22×D311yescharacteristic
419C2×C22⋊C4—32no—
420C2×C22⋊C4—32no—
421C2×C22⋊C4—32no—
422C2×C22⋊C4—32no—
423C2×C22⋊C4—32no—
424C2×C22⋊C4—32no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4—32no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4—32no—
430C2×C22⋊C4—34no—
431C2×C22⋊C4C22×D312yes—
432C2×C22⋊C4C22×D314yes—
433C2×C22⋊C4C22×D312yes—
434C2×C42—31no—
435C2×C42—32no—
436C2×C42—32no—
437C2×C42—31no—
438C2×C42—31no—
439C2×C42—64no—
440C2×C42C22×D311yescharacteristic
441#95—32no—
442#95—32no—
443#95—32no—
444#95—34no—
445#95—34no—
446#95—34no—
447#95—34no—
448#95—34no—
449#95—34no—
450#95—34no—
451#95—34no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3C22×D414yes—
465C23×C3C2×#4114yes—
466C23×C3C2511yescharacteristic
467C22×D3—21no—
468C22×D3—21no—
469C22×D3—21no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D32−1+412yes—
474C3×Q8—48no—
475C3×D4—28no—
476C3×D4—28no—
477C3×D4—416no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—216no—
483C2×C3×C4—22no—
484C2×C3×C4—24no—
485C2×C3×C4—24no—
486C2×C3×C4—22no—
487C2×C3×C4—24no—
488C2×C3×C4—22no—
489C2×C3×C4—416no—
490C2×C3×C4—48no—
491C2×C3×C4C22×D412yes—
492C2×C3×C4C22×D414yes—
493C2×C3×C4C22×D412yes—
494C2×C3×C4C22×D412yes—
495C2×C3×C4C2×#4112yes—
496C2×C3×C4H(5,𝔽2)12yes—
497C2×C3×C4H(5,𝔽2)12yes—
498C2×C3×C42−1+412yes—
499#67—48no—
500#67—48no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—21no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—21no—
511C2×Dic3—22no—
512C2×Dic3—21no—
513C2×Dic3—24no—
514C2×Dic3—24no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—24no—
522C2×Dic3—21no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—88no—
526C4×D3—44no—
527C4×D3—44no—
528C4×D3—44no—
529Dic6—44no—
530C24—31no—
531C24C23×D312yes—
532C24C23×D312yes—
533#41—432no—
534C2×Q8—24no—
535C2×Q8—24no—
536C2×Q8—24no—
537C2×Q8—62no—
538C2×Q8—62no—
539C2×Q8—62no—
540C2×D4—28no—
541C2×D4—28no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—44no—
547C2×D4—64no—
548C2×D4—64no—
549C2×D4—64no—
550C2×D4—64no—
551C2×D4—122no—
552C2×D4—122no—
553C2×D4#23714yes—
554C2×D4C2×#6714yes—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—28no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—28no—
562C22×C4—32no—
563C22×C4—31no—
564C22×C4—32no—
565C22×C4—32no—
566C22×C4—31no—
567C22×C4—32no—
568C22×C4—34no—
569C22×C4—31no—
570C22×C4—44no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—62no—
574C22×C4—62no—
575C22×C4—62no—
576C22×C4—62no—
577C22×C4—62no—
578C22×C4—62no—
579C22×C4—121no—
580C22×C4—124no—
581C22×C4—124no—
582C22×C4—124no—
583C22×C4C2×#6718yes—
584C22×C4C23×D314yes—
585C22×C4C23×D312yes—
586C22×C4C23×D311yescharacteristic
587C22×C4C23×D312yes—
588C22×C4C23×D311yescharacteristic
589C22×C4C23×D311yescharacteristic
590C4⋊C4—24no—
591C4⋊C4—28no—
592C4⋊C4—22no—
593C4⋊C4—24no—
594C4⋊C4—62no—
595C4⋊C4—62no—
596C4⋊C4—64no—
597C4⋊C4—64no—
598C4⋊C4—64no—
599C4⋊C4—64no—
600C4⋊C4—64no—
601C4⋊C4—62no—
602C4⋊C4—64no—
603C4⋊C4—124no—
604C4⋊C4—122no—
605C4⋊C4—124no—
606C4⋊C4—124no—
607C4⋊C4—122no—
608C4⋊C4C2×#6714yes—
609C22⋊C4—28no—
610C22⋊C4—24no—
611C22⋊C4—64no—
612C22⋊C4—64no—
613C22⋊C4—64no—
614C22⋊C4—64no—
615C22⋊C4—64no—
616C22⋊C4—122no—
617C22⋊C4—124no—
618C22⋊C4—124no—
619C22⋊C4—122no—
620C22⋊C4—124no—
621C22⋊C4—122no—
622C22⋊C4—124no—
623C22⋊C4C2×#6718yes—
624C42—64no—
625C42—62no—
626C42—62no—
627C42—62no—
628C42—64no—
629C42C2×#6714yes—
630C22×C3—24no—
631C22×C3—24no—
632C22×C3—24no—
633C22×C3—24no—
634C22×C3—24no—
635C22×C3—24no—
636C22×C3—42no—
637C22×C3—42no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—42no—
641C22×C3—42no—
642C22×C3—42no—
643C22×C3—42no—
644C22×C3C23×D411yescharacteristic
645C22×C3C22×#4111yescharacteristic
646C22×C3C2×H(5,𝔽2)11yescharacteristic
647C22×C3C2×H(5,𝔽2)11yescharacteristic
648C22×C3C2×2−1+411yescharacteristic
649C22×C3C2×2−1+411yescharacteristic
650C22×C3#58511yescharacteristic
651C2×D3—22no—
652C2×D3—22no—
653C2×D3—22no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C3×C4—24no—
659C3×C4—22no—
660C3×C4—42no—
661C3×C4—44no—
662C3×C4#53714yes—
663C3×C4#54614yes—
664Dic3—42no—
665Dic3—41no—
666Dic3—41no—
667Dic3—41no—
668Dic3—42no—
669Dic3—42no—
670Dic3—44no—
671Dic3—42no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—32no—
685C23—61no—
686C23—61no—
687C23—61no—
688C23—61no—
689C23—61no—
690C23—61no—
691C23C2×#23714yes—
692C23C22×#6714yes—
693C23C24×D311yescharacteristic
694Q8—48no—
695Q8—124no—
696D4—28no—
697D4—28no—
698D4—416no—
699D4—128no—
700D4—128no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—216no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—416no—
713C2×C4—48no—
714C2×C4—61no—
715C2×C4—62no—
716C2×C4—64no—
717C2×C4—62no—
718C2×C4—61no—
719C2×C4—62no—
720C2×C4—62no—
721C2×C4—64no—
722C2×C4—61no—
723C2×C4—62no—
724C2×C4—61no—
725C2×C4—62no—
726C2×C4—61no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—61no—
730C2×C4—62no—
731C2×C4—64no—
732C2×C4—62no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—124no—
739C2×C4—124no—
740C2×C4—124no—
741C2×C4—248no—
742C2×C4C2×#23712yes—
743C2×C4#100412yes—
744C2×C4#100912yes—
745C2×C4#101012yes—
746C2×C4C22×#6712yes—
747C2×C4C22×#6714yes—
748C2×C4C22×#6712yes—
749C2×C4C22×#6712yes—
750C2×C3—44no—
751C2×C3—44no—
752C2×C3C2×#53711yescharacteristic
753C2×C3C2×#54611yescharacteristic
754C2×C3#348911yescharacteristic
755C2×C3#351511yescharacteristic
756C2×C3#352011yescharacteristic
757C2×C3#354611yescharacteristic
758C2×C3#355211yescharacteristic
759D3—42no—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—24no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—62no—
775C22—62no—
776C22—62no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22—121no—
781C22C22×#23711yescharacteristic
782C22C2×#100411yescharacteristic
783C22C2×#100911yescharacteristic
784C22C2×#101011yescharacteristic
785C22D3×2−1+411yescharacteristic
786C22#596811yescharacteristic
787C22C23×#6711yescharacteristic
788C4—24no—
789C4—22no—
790C4—44no—
791C4—42no—
792C4—122no—
793C4—122no—
794C4—124no—
795C4—121no—
796C4—121no—
797C4—122no—
798C4—121no—
799C4—122no—
800C4#580614yes—
801C4#583314yes—
802C3#3890811yescharacteristic, complemented, Sylow
803C2—44no—
804C2—44no—
805C2—122no—
806C2#8668311yescharacteristic
807C2#8668511yescharacteristic
808C2#8670711yescharacteristic
809C2#8670911yescharacteristic
810C2C2×#580611yescharacteristic
811C2C2×#583311yescharacteristic
812C2#8729511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#547C2
hypercenterC2×#547D3
hypocenterC3#38908
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×C3×#547C2semidirect
2. C2×#5557C2semidirect
3. #84097C2semidirect
4. #84087C2semidirect
5. #83269C2semidirect
6. #83244C2semidirect
7. #82877C2semidirect
8. #82875C2semidirect
9. #82815C2semidirect
10. #82787C2semidirect
11. #82666C2semidirect
12. #82647C2semidirect
13. C4×#938C2semidirect
14. #82376C2semidirect
15. D4×C4⋊Dic3C2semidirect
16. #82194C2semidirect
17. #82172C2semidirect
86. C2×#547D3semidirect
125. C3×C4×D4D4semidirect
396. C4×D4#67semidirect
802. C3#38908semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5472
C2×#55572
#840972
#840872
#832692
#832442
#828772
#828752
#828152
#827872
#826662
#826472
C4×#9382
#823762
D4×C4⋊Dic32
#821942
#821722
#389083