Finite Group Databasebeta

← #10972996

Subgroups — #10972996

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×#5833C211yesmaximal, characteristic
2C2×#5522C211yesmaximal, characteristic, complemented
3C3×#2311C211yesmaximal, characteristic, complemented
4#84086C211yesmaximal, characteristic, complemented
5#82234C211yesmaximal, characteristic, complemented
6#82186C211yesmaximal, characteristic, complemented
7C2×#4984C211yesmaximal, characteristic, complemented
8#76663C212yesmaximal, complemented
9#76642C212yesmaximal, complemented
10#76475C212yesmaximal, complemented
11#76458C212yesmaximal, complemented
12#74707C214yesmaximal, complemented
13#74704C214yesmaximal, complemented
14#73894C212yesmaximal, complemented
15#73893C212yesmaximal, complemented
16#73892C212yesmaximal, complemented
17#73891C212yesmaximal, complemented
18#35255—31nomaximal, Sylow
19C22×C3×#41C2211yescharacteristic
20C22×#235C2211yescharacteristic
21C2×C3×#117C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23#5833—28no—
24C2×#946C2212yes—
25C2×#939C2214yes—
26C2×#938C2212yes—
27C2×#930C2212yes—
28C2×#926C2211yescharacteristic
29C22×C4⋊Dic3C2211yescharacteristic
30C22×C4⋊Dic3C2212yes—
31C2×#924C2212yes—
32C22×C4×Dic3C2211yescharacteristic
33#5522—28no—
34C2×#893C2211yescharacteristic
35C2×#893C2211yescharacteristic
36C2×#887C2211yescharacteristic
37C2×#887C2211yescharacteristic
38C2×#883C2214yes—
39C2×#67⋊C4C2212yes—
40C2×#67⋊C4C2212yes—
41C2×#872C2212yes—
42C2×C42×D3C2212yes—
43C3×#391C2212yes—
44C3×#390C2212yes—
45C3×#386C2214yes—
46C3×#380C2212yes—
47C3×#380C2212yes—
48#5229C2211yescharacteristic
49#5229C2211yescharacteristic
50#5221C2211yescharacteristic
51#5221C2211yescharacteristic
52#5220C2212yes—
53#5220C2212yes—
54#5213C2214yes—
55C4×#217C2212yes—
56C4×#217C2212yes—
57C2×C3⋊#95C2212yes—
58#4988C2212yes—
59#4987C2212yes—
60#4987C2212yes—
61#4984C2212yes—
62#4984C2212yes—
63#4984C2212yes—
64#4984C2212yes—
65#4977C2212yes—
66#4975C2212yes—
67#4973C2212yes—
68#4961C2214yes—
69#4959C2214yes—
70#4956C2214yes—
71#4952C2214yes—
72#4951C2214yes—
73#4949C2214yes—
74#4946C2214yes—
75#4945C2214yes—
76#4928C2212yes—
77#4928C2212yes—
78#4675C2214yes—
79#4674C2214yes—
80#4668C2214yes—
81#4664C2214yes—
82#4658C2214yes—
83#4657C2214yes—
84#4654C2214yes—
85#4652C2214yes—
86C2×#537—31no—
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#2311D311yescharacteristic, complemented
101#2297—31no—
102C2×#389—31no—
103C2×C3×#41—24no—
104C2×C3×#41—24no—
105C2×C3×#41—24no—
106C22×C3×Q8C2311yescharacteristic
107C22×C3×D4C2312yes—
108C22×C3×D4C2311yescharacteristic
109C23×C3×C4C2312yes—
110C23×C3×C4C2312yes—
111C23×C3×C4C2311yescharacteristic
112C22×#67C2312yes—
113C22×#67C2314yes—
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2312yes—
117C2×#235—24no—
118C2×#235—24no—
119C2×#235D418yes—
120C22×D12C2311yescharacteristic
121C22×C4×D3C2312yes—
122C22×C4×D3C2312yes—
123C22×C4×D3C2312yes—
124C22×Dic6C2311yescharacteristic
125C3×#117—24no—
126C2×C3×C4⋊C4—24no—
127C2×C3×C4⋊C4C2312yes—
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2312yes—
131C2×C3×C22⋊C4C2312yes—
132C2×C3×C22⋊C4C2314yes—
133C2×C3×C22⋊C4C2314yes—
134C2×C3×C42C2312yes—
135C2×#217C2312yes—
136C2×#217C2314yes—
137C2×#217C2312yes—
138C2×#217C2312yes—
139C2×#217C2312yes—
140C2×#217C2312yes—
141#946—28no—
142#939—216no—
143#938—28no—
144#930—28no—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2312yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2314yes—
150#926—24no—
151C2×C4⋊Dic3—24no—
152C2×C4⋊Dic3—44no—
153C2×C4⋊Dic3C2314yes—
154C2×C4⋊Dic3C2311yescharacteristic
155C2×C4⋊Dic3C2311yescharacteristic
156C2×C4⋊Dic3C2312yes—
157C2×C4⋊Dic3C2312yes—
158C2×C4⋊Dic3C2314yes—
159#924—28no—
160C2×Dic3⋊C4C2314yes—
161C2×Dic3⋊C4C2312yes—
162C2×Dic3⋊C4C2312yes—
163C2×Dic3⋊C4C2314yes—
164C2×Dic3⋊C4C2314yes—
165C2×C4×Dic3—24no—
166C2×C4×Dic3C2312yes—
167C2×C4×Dic3C2312yes—
168C2×C4×Dic3C2312yes—
169C2×C4×Dic3C2311yescharacteristic
170C2×C4×Dic3C2311yescharacteristic
171C2×C4×Dic3C2311yescharacteristic
172C2×C4×Dic3C2311yescharacteristic
173#893—24no—
174#893—24no—
175#887—24no—
176#887—24no—
177#883—48no—
178#67⋊C4—28no—
179#67⋊C4—28no—
180#872—28no—
181C42×D3—28no—
182C3×#95C2314yes—
183C3×#95C2314yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2312yes—
188C3⋊#95C2314yes—
189C3⋊#95C2312yes—
190C3⋊#95C2314yes—
191C3⋊#95C2312yes—
192C3⋊#95C2314yes—
193C3⋊#95C2314yes—
194C22×#41—31no—
195C22×#41C2×D311yescharacteristic
196#537—68no—
197C2×#123—34no—
198C2×C22⋊Q8—32no—
199C2×C22⋊Q8—32no—
200C2×#121—32no—
201C2×#121—34no—
202C2×#121—32no—
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—32no—
212C2×#117C2×D311yescharacteristic
213C22×C4⋊C4—31no—
214C22×C4⋊C4—32no—
215C22×C4⋊C4C2×D311yescharacteristic
216C22×C42—31no—
217C22×C42—32no—
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—31no—
227#391—31no—
228#391—32no—
229#391C2×D312yes—
230#390—31no—
231#390—31no—
232#390—32no—
233#390C2×D312yes—
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—32no—
245#386—32no—
246#386—34no—
247#386—34no—
248#386C2×D314yes—
249#385—34no—
250#385—34no—
251#384—32no—
252#382—32no—
253#381—34no—
254#380—32no—
255#380—32no—
256#380C2×D312yes—
257#380C2×D312yes—
258C4×C22⋊C4—32no—
259C4×C22⋊C4—32no—
260C2×#95—32no—
261C24×C3C2412yes—
262C24×C3C2411yescharacteristic
263C23×D3C2412yes—
264C3×#41—416no—
265C2×C3×Q8—22no—
266C2×C3×Q8—22no—
267C2×C3×Q8—22no—
268C2×C3×D4—24no—
269C2×C3×D4—24no—
270C2×C3×D4—24no—
271C2×C3×D4—22no—
272C2×C3×D4—22no—
273C2×C3×D4—22no—
274C22×C3×C4—24no—
275C22×C3×C4—24no—
276C22×C3×C4—24no—
277C22×C3×C4—24no—
278C22×C3×C4—42no—
279C22×C3×C4—42no—
280C22×C3×C4C2×D414yes—
281C22×C3×C4#4114yes—
282C22×C3×C4#4114yes—
283C22×C3×C4C2412yes—
284C22×C3×C4C2412yes—
285C22×C3×C4C2414yes—
286C22×C3×C4C2412yes—
287C22×C3×C4C2411yescharacteristic
288C22×C3×C4C2411yescharacteristic
289C2×#67—24no—
290C2×#67—24no—
291C2×#67—28no—
292C2×#67—44no—
293C2×#67—44no—
294C2×#67C2×D418yes—
295C22×Dic3—22no—
296C22×Dic3—22no—
297C22×Dic3—24no—
298C22×Dic3—22no—
299C22×Dic3—22no—
300C22×Dic3—41no—
301C22×Dic3—41no—
302C22×Dic3—42no—
303C22×Dic3—42no—
304C22×Dic3C2411yescharacteristic
305C22×Dic3C2412yes—
306C22×Dic3C2412yes—
307C22×Dic3C2414yes—
308C22×Dic3C2411yescharacteristic
309C22×Dic3C2412yes—
310C22×Dic3C2411yescharacteristic
311C22×Dic3C2411yescharacteristic
312#235—232no—
313C2×D12—22no—
314C2×D12—22no—
315C2×D12C2×D414yes—
316C2×C4×D3—24no—
317C2×C4×D3—24no—
318C2×C4×D3—24no—
319C2×C4×D3—24no—
320C2×C4×D3—24no—
321C2×C4×D3—24no—
322C2×C4×D3—42no—
323C2×C4×D3—42no—
324C2×C4×D3C2×D418yes—
325C2×Dic6—22no—
326C2×Dic6—22no—
327C2×Dic6C2×D414yes—
328C3×C4⋊C4—22no—
329C3×C4⋊C4—22no—
330C3×C4⋊C4—24no—
331C3×C4⋊C4—24no—
332C3×C22⋊C4—24no—
333C3×C22⋊C4—44no—
334C3×C22⋊C4—44no—
335C3×C42—24no—
336#217—24no—
337#217—28no—
338#217—24no—
339#217—24no—
340#217—42no—
341#217—42no—
342(C2×D3)⋊C4—24no—
343(C2×D3)⋊C4—24no—
344(C2×D3)⋊C4—28no—
345(C2×D3)⋊C4—44no—
346(C2×D3)⋊C4—44no—
347C4⋊Dic3—24no—
348C4⋊Dic3—24no—
349C4⋊Dic3—22no—
350C4⋊Dic3—22no—
351C4⋊Dic3—28no—
352C4⋊Dic3—44no—
353Dic3⋊C4—24no—
354Dic3⋊C4—24no—
355Dic3⋊C4—28no—
356Dic3⋊C4—44no—
357Dic3⋊C4—44no—
358C4×Dic3—22no—
359C4×Dic3—22no—
360C4×Dic3—22no—
361C4×Dic3—22no—
362C4×Dic3—24no—
363C4×Dic3—24no—
364C4×Dic3—24no—
365C2×#41—24no—
366C2×#41—24no—
367C2×#41—24no—
368C2×#41—38no—
369C2×#41—64no—
370C2×#41—64no—
371C22×Q8—31no—
372C22×Q8C22×D311yescharacteristic
373C22×D4—32no—
374C22×D4—34no—
375C22×D4—31no—
376C22×D4C22×D312yes—
377C22×D4C22×D311yescharacteristic
378C23×C4—32no—
379C23×C4—31no—
380C23×C4—31no—
381C23×C4—32no—
382C23×C4—32no—
383C23×C4—32no—
384C23×C4C22×D312yes—
385C23×C4C22×D312yes—
386C23×C4C22×D311yescharacteristic
387#123—128no—
388C22⋊Q8—68no—
389C22⋊Q8—68no—
390#121—68no—
391#121—68no—
392#121—616no—
393C4×Q8—64no—
394C4×Q8—64no—
395C4×D4—68no—
396C4×D4—68no—
397C4×D4—64no—
398C4×D4—64no—
399#117—24no—
400#117—68no—
401#117—64no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—32no—
404C2×C4⋊C4—32no—
405C2×C4⋊C4—34no—
406C2×C4⋊C4—32no—
407C2×C4⋊C4—32no—
408C2×C4⋊C4—31no—
409C2×C4⋊C4—31no—
410C2×C4⋊C4—34no—
411C2×C4⋊C4—34no—
412C2×C4⋊C4—34no—
413C2×C4⋊C4—34no—
414C2×C4⋊C4—64no—
415C2×C4⋊C4—124no—
416C2×C4⋊C4C22×D312yes—
417C2×C4⋊C4C22×D312yes—
418C2×C4⋊C4C22×D311yescharacteristic
419C2×C4⋊C4C22×D311yescharacteristic
420C2×C22⋊C4—32no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—32no—
423C2×C22⋊C4—32no—
424C2×C22⋊C4—32no—
425C2×C22⋊C4—32no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4—32no—
428C2×C22⋊C4—32no—
429C2×C22⋊C4—34no—
430C2×C22⋊C4—34no—
431C2×C22⋊C4C22×D312yes—
432C2×C22⋊C4C22×D314yes—
433C2×C22⋊C4C22×D314yes—
434C2×C42—31no—
435C2×C42—32no—
436C2×C42—31no—
437C2×C42—31no—
438C2×C42—32no—
439C2×C42—32no—
440C2×C42—31no—
441C2×C42—68no—
442C2×C42—64no—
443C2×C42C22×D312yes—
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#95C22×D314yes—
455#95C22×D314yes—
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×C3C22×D412yes—
468C23×C3C2×#4112yes—
469C23×C3C2×#4112yes—
470C23×C3C2511yescharacteristic
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
477C22×D3C22×D414yes—
478C3×Q8—44no—
479C3×D4—48no—
480C3×D4—44no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—24no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—24no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—24no—
492C2×C3×C4—22no—
493C2×C3×C4—48no—
494C2×C3×C4—48no—
495C2×C3×C4#123116yescomplemented
496C2×C3×C4C22×D412yes—
497C2×C3×C4C22×D412yes—
498C2×C3×C4C2×#4112yes—
499C2×C3×C4C2×#4112yes—
500C2×C3×C4C2×#4112yes—
501C2×C3×C4C2×#4112yes—
502#67—216no—
503#67—88no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—24no—
513C2×Dic3—22no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—24no—
517C2×Dic3—21no—
518C2×Dic3—22no—
519C2×Dic3—21no—
520C2×Dic3—22no—
521C2×Dic3—24no—
522C2×Dic3—22no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—44no—
526C2×Dic3—44no—
527C2×Dic3—84no—
528C2×Dic3C22×D414yes—
529C2×Dic3H(5,𝔽2)12yes—
530C2×Dic32−1+412yes—
531D12—28no—
532C4×D3—216no—
533C4×D3—48no—
534C4×D3—48no—
535Dic6—28no—
536C24—32no—
537C24C23×D312yes—
538C24C23×D311yescharacteristic
539#41—416no—
540#41—632no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—34no—
545C2×Q8—62no—
546C2×Q8—62no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—38no—
554C2×D4—34no—
555C2×D4—64no—
556C2×D4—64no—
557C2×D4—68no—
558C2×D4—62no—
559C2×D4—62no—
560C2×D4—124no—
561C2×D4—124no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—31no—
567C22×C4—32no—
568C22×C4—31no—
569C22×C4—38no—
570C22×C4—31no—
571C22×C4—32no—
572C22×C4—32no—
573C22×C4—34no—
574C22×C4—31no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—64no—
578C22×C4—64no—
579C22×C4—64no—
580C22×C4—64no—
581C22×C4—62no—
582C22×C4—62no—
583C22×C4—64no—
584C22×C4—64no—
585C22×C4—62no—
586C22×C4—62no—
587C22×C4—64no—
588C22×C4—122no—
589C22×C4—122no—
590C22×C4—121no—
591C22×C4—121no—
592C22×C4—122no—
593C22×C4—122no—
594C22×C4#23514yes—
595C22×C4D3×D414yes—
596C22×C4#23714yes—
597C22×C4C23×D312yes—
598C22×C4C23×D312yes—
599C22×C4C23×D314yes—
600C22×C4C23×D312yes—
601C22×C4C23×D311yescharacteristic
602C22×C4C23×D311yescharacteristic
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—68no—
608C4⋊C4—64no—
609C4⋊C4—64no—
610C4⋊C4—68no—
611C4⋊C4—62no—
612C4⋊C4—62no—
613C4⋊C4—64no—
614C4⋊C4—64no—
615C4⋊C4—124no—
616C4⋊C4—124no—
617C4⋊C4—124no—
618C22⋊C4—24no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—64no—
622C22⋊C4—64no—
623C22⋊C4—68no—
624C22⋊C4—68no—
625C22⋊C4—64no—
626C22⋊C4—64no—
627C22⋊C4—64no—
628C22⋊C4—124no—
629C22⋊C4—124no—
630C22⋊C4—122no—
631C22⋊C4—122no—
632C42—24no—
633C42—64no—
634C42—64no—
635C42—64no—
636C42—62no—
637C42—62no—
638C42—62no—
639C42—62no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—22no—
646C22×C3—42no—
647C22×C3—42no—
648C22×C3—42no—
649C22×C3—42no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3C2×#12314yes—
654C22×C3C23×D411yescharacteristic
655C22×C3C22×#4111yescharacteristic
656C22×C3C22×#4111yescharacteristic
657C22×C3C2×H(5,𝔽2)11yescharacteristic
658C22×C3C2×2−1+411yescharacteristic
659C22×C3#58511yescharacteristic
660C22×C3#58511yescharacteristic
661C2×D3—24no—
662C2×D3—24no—
663C2×D3—24no—
664C2×D3—42no—
665C2×D3—42no—
666C2×D3—42no—
667C2×D3—42no—
668C3×C4—42no—
669C3×C4—44no—
670C3×C4—42no—
671C3×C4—42no—
672C3×C4C2×#12314yes—
673C3×C4C2×#12314yes—
674Dic3—24no—
675Dic3—22no—
676Dic3—22no—
677Dic3—41no—
678Dic3—44no—
679Dic3—41no—
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—34no—
694C23—62no—
695C23—62no—
696C23—62no—
697C23—62no—
698C23—62no—
699C23—62no—
700C23C2×#23512yes—
701C23C2×D3×D412yes—
702C23C2×#23712yes—
703C23C24×D311yescharacteristic
704Q8—44no—
705Q8—68no—
706D4—48no—
707D4—44no—
708D4—616no—
709D4—68no—
710D4—248no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—34no—
724C2×C4—32no—
725C2×C4—32no—
726C2×C4—48no—
727C2×C4—48no—
728C2×C4—62no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—62no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—616no—
735C2×C4—62no—
736C2×C4—62no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—64no—
740C2×C4—62no—
741C2×C4—64no—
742C2×C4—61no—
743C2×C4—62no—
744C2×C4—61no—
745C2×C4—62no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—62no—
749C2×C4—64no—
750C2×C4—128no—
751C2×C4—128no—
752C2×C4—124no—
753C2×C4—124no—
754C2×C4—244no—
755C2×C4#883116yescomplemented
756C2×C4C2×#23512yes—
757C2×C4C2×#23512yes—
758C2×C4C2×D3×D412yes—
759C2×C4C2×D3×D412yes—
760C2×C4C2×#23712yes—
761C2×C4C2×#23712yes—
762C2×C3—24no—
763C2×C3—82no—
764C2×C3C22×#12311yescharacteristic
765C2×C3#346011yescharacteristic
766C2×C3#346111yescharacteristic
767C2×C3#348811yescharacteristic
768C2×C3#348911yescharacteristic
769C2×C3#351111yescharacteristic
770C2×C3#351211yescharacteristic
771D3—44no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—64no—
786C22—64no—
787C22—64no—
788C22—122no—
789C22—122no—
790C22—122no—
791C22—122no—
792C22C2×#88314yes—
793C22C22×#23511yescharacteristic
794C22C22×D3×D411yescharacteristic
795C22C22×#23711yescharacteristic
796C22D3×H(5,𝔽2)11yescharacteristic
797C22#596611yescharacteristic
798C22D3×2−1+411yescharacteristic
799C22#596811yescharacteristic
800C4—44no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—62no—
805C4—62no—
806C4—64no—
807C4—121no—
808C4—124no—
809C4—121no—
810C4—122no—
811C4—122no—
812C4C2×#88314yes—
813C4C2×#88314yes—
814C3#3525511yescharacteristic, complemented, Sylow
815C2—24no—
816C2—82no—
817C2—124no—
818C2C22×#88311yescharacteristic
819C2#8589311yescharacteristic
820C2#8589411yescharacteristic
821C2#8631411yescharacteristic
822C2#8633911yescharacteristic
823C2#8637911yescharacteristic
824C2#8638011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2311C2
prime radicalC2×#5833C2
hypercenter#2311D3
hypocenterC3#35255
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C2×#5522C2semidirect
3. C3×#2311C2semidirect
4. #84086C2semidirect
5. #82234C2semidirect
6. #82186C2semidirect
7. C2×#4984C2semidirect
8. #76663C2semidirect
9. #76642C2semidirect
10. #76475C2semidirect
11. #76458C2semidirect
12. #74707C2semidirect
13. #74704C2semidirect
14. #73894C2semidirect
15. #73893C2semidirect
16. #73892C2semidirect
17. #73891C2semidirect
100. #2311D3semidirect
495. C2×C3×C4#123semidirect
755. C2×C4#883semidirect
814. C3#35255semidirect

Maximal subgroups

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

subgroupindex
C2×#58332
C2×#55222
C3×#23112
#840862
#822342
#821862
C2×#49842
#766632
#766422
#764752
#764582
#747072
#747042
#738942
#738932
#738922
#738912
#352553