Finite Group Databasebeta

← #11058551

Subgroups — #11058551

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
1C2×C3×#547C211yesmaximal, characteristic, complemented
2C22×#897C211yesmaximal, characteristic, complemented
3#84096C212yesmaximal, complemented
4#84087C212yesmaximal, complemented
5#83258C212yesmaximal, complemented
6#82894C212yesmaximal, complemented
7#82878C214yesmaximal, complemented
8#82866C212yesmaximal, complemented
9#82797C214yesmaximal, complemented
10#82723C211yesmaximal, characteristic, complemented
11#82668C212yesmaximal, complemented
12#82654C211yesmaximal, characteristic, complemented
13#82408C212yesmaximal, complemented
14C4×#937C211yesmaximal, characteristic, complemented
15#82349C211yesmaximal, characteristic, complemented
16#82194C212yesmaximal, complemented
17#82159C211yesmaximal, characteristic, complemented
18#38905—31nomaximal, Sylow
19C22×C3×#41C2212yes—
20C23×C4×D3C2211yescharacteristic
21C23×Dic6C2211yescharacteristic
22C3×#547—28no—
23C2×C3×C4⋊Q8C2211yescharacteristic, complemented
24C2×C3×#123C2212yes—
25C2×C3×#123C2212yescomplemented
26C2×C3×C22⋊Q8C2212yescomplemented
27C2×C3×#121C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic, complemented
29C2×C3×C4×D4C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic, complemented
31C22×C3×C4⋊C4C2211yescharacteristic
32C22×C3×C4⋊C4C2211yescharacteristic, complemented
33C2×#938C2212yes—
34C2×#937C2211yescharacteristic
35C2×#937C2212yes—
36C2×#936C2212yescomplemented
37C2×C4×#67C2212yes—
38C22×(C2×D3)⋊C4C2212yes—
39C2×#926C2212yes—
40C22×C4⋊Dic3C2212yes—
41C2×#924C2212yescomplemented
42C2×#897—28no—
43C2×#897C2212yes—
44C2×#897C2212yes—
45C2×#897C2214yes—
46#5231C2214yes—
47#5229C2214yescomplemented
48#5223C2214yes—
49#5221C2214yescomplemented
50#5220C2212yes—
51#5220C2211yescharacteristic
52#5220C2212yes—
53#5220C2212yes—
54#5220C2212yes—
55#5213C2214yes—
56#5213C2214yes—
57#5212C2211yescharacteristic
58#5212C2214yescomplemented
59#5212C2214yescomplemented
60#5211C2212yes—
61C4×#217C2211yescharacteristic
62#4994C2214yes—
63#4990C2214yes—
64#4989C2212yes—
65#4987C2212yes—
66#4986C2214yescomplemented
67#4984C2212yescomplemented
68#4981C2214yescomplemented
69#4980C2214yescomplemented
70#4979C2212yescomplemented
71Dic3×C4⋊C4C2212yescomplemented
72#4973C2212yescomplemented
73#4961C2214yes—
74#4957C2214yes—
75#4956C2214yes—
76#4956C2212yes—
77#4955C2211yescharacteristic
78#4953C2214yescomplemented
79#4949C2214yescomplemented
80#4947C2214yescomplemented
81#4947C2212yescomplemented
82#4946C2212yes—
83#4946C2211yescharacteristic
84C4×(C2×D3)⋊C4C2212yes—
85#4929C2212yescomplemented
86C2×#547D311yescharacteristic, complemented
87C22×C22⋊Q8—31no—
88#2847—31no—
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—
103C24×D3C2311yescharacteristic
104C2×C3×#41—28no—
105C2×C3×#41—28no—
106C2×C3×#41—44no—
107C22×C3×Q8C2312yes—
108C22×C3×D4C2312yes—
109C22×C3×D4C2311yescharacteristic
110C22×C3×D4C2312yes—
111C22×C3×D4C2311yescharacteristic
112C23×C3×C4C2311yescharacteristic
113C23×C3×C4C2312yes—
114C23×C3×C4C2312yes—
115C23×C3×C4C2311yescharacteristic
116C23×C3×C4C2312yes—
117C22×#67C2312yes—
118C22×#67C2314yes—
119C23×Dic3C2312yes—
120C23×Dic3C2311yescharacteristic
121C22×C4×D3—24no—
122C22×C4×D3—44no—
123C22×C4×D3C2312yes—
124C22×C4×D3C2312yes—
125C22×Dic6—24no—
126C22×Dic6—44no—
127C22×Dic6C2312yes—
128C22×Dic6C2312yes—
129C3×C4⋊Q8—24no—
130C3×#123—28no—
131C3×#123—28no—
132C3×C22⋊Q8—28no—
133C3×#121—24no—
134C3×#121—24no—
135C3×C4×D4—24no—
136C3×C4×D4—24no—
137C2×C3×C4⋊C4—24no—
138C2×C3×C4⋊C4D418yescomplemented
139C2×C3×C4⋊C4C2311yescharacteristic
140C2×C3×C4⋊C4C2311yescharacteristic
141C2×C3×C4⋊C4C2312yes—
142C2×C3×C4⋊C4C2312yes—
143C2×C3×C4⋊C4C2311yescharacteristic
144C2×C3×C4⋊C4C2312yes—
145C2×C3×C4⋊C4C2311yescharacteristic
146C2×C3×C22⋊C4C2311yescharacteristic
147C2×C3×C22⋊C4C2311yescharacteristic
148C2×C3×C22⋊C4C2312yes—
149C2×C3×C22⋊C4C2312yes—
150C2×C3×C22⋊C4C2312yes—
151C2×C3×C42C2311yescharacteristic
152C2×#217C2311yescharacteristic
153C2×#217C2312yes—
154C2×#217C2311yescharacteristic
155C2×#217C2314yes—
156C2×#217C2314yes—
157C2×#217C2314yes—
158C2×#217C2314yes—
159C2×#217C2312yes—
160#938—44no—
161#937—24no—
162#937—44no—
163#936—44no—
164C4×#67—44no—
165C2×(C2×D3)⋊C4—28no—
166C2×(C2×D3)⋊C4C2312yes—
167C2×(C2×D3)⋊C4C2312yes—
168C2×(C2×D3)⋊C4C2314yes—
169C2×(C2×D3)⋊C4C2314yes—
170C2×(C2×D3)⋊C4C2312yes—
171C2×(C2×D3)⋊C4C2314yes—
172#926—44no—
173C2×C4⋊Dic3—28no—
174C2×C4⋊Dic3C2312yes—
175C2×C4⋊Dic3C2314yes—
176C2×C4⋊Dic3C2314yes—
177C2×C4⋊Dic3C2314yes—
178#924—44no—
179C2×Dic3⋊C4C2312yes—
180C2×Dic3⋊C4C2314yes—
181C2×C4×Dic3C2312yes—
182C2×C4×Dic3C2314yes—
183#897—28no—
184#897—28no—
185#897—216no—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2312yes—
189C3⋊#95C2312yes—
190C3⋊#95C2312yes—
191C3⋊#95C2312yes—
192C3⋊#95C2314yes—
193C3⋊#95C2314yes—
194C3⋊#95C2314yes—
195C3⋊#95C2314yes—
196C3⋊#95C2314yes—
197C22×#41C2×D312yes—
198C23×Q8—31no—
199C24×C4—31no—
200#547—28no—
201C2×C4⋊Q8C2×D311yescharacteristic, complemented
202C2×#124—32no—
203C2×#123C2×D312yes—
204C2×#123C2×D312yescomplemented
205C2×C22⋊Q8—32no—
206C2×C22⋊Q8—32no—
207C2×C22⋊Q8—34no—
208C2×C22⋊Q8—32no—
209C2×C22⋊Q8—68no—
210C2×C22⋊Q8C2×D312yescomplemented
211C2×#121—32no—
212C2×#121C2×D311yescharacteristic
213C2×#121C2×D311yescharacteristic, complemented
214C2×#120—31no—
215C2×#120—32no—
216C2×C4×D4—32no—
217C2×C4×D4C2×D311yescharacteristic
218C2×C4×D4C2×D311yescharacteristic, complemented
219C2×#117—32no—
220C22×C4⋊C4—32no—
221C22×C4⋊C4C2×D311yescharacteristic
222C22×C4⋊C4C2×D311yescharacteristic, complemented
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—32no—
233#393—34no—
234#392—34no—
235#391—34no—
236#391—32no—
237#391—32no—
238#390—34no—
239#390—34no—
240#389—32no—
241#388—34no—
242#387—34no—
243#386—31no—
244#386—32no—
245#386—32no—
246#386—32no—
247#386—32no—
248#386—34no—
249#386—34no—
250#386—34no—
251#386—32no—
252#385—32no—
253#385—31no—
254#385—32no—
255#381—32no—
256#380—34no—
257#380—34no—
258#380—31no—
259#380—32no—
260#379—31no—
261C4×C4⋊C4—32no—
262C4×C22⋊C4—31no—
263C4×C22⋊C4—32no—
264C24×C3C2412yes—
265C24×C3C2411yescharacteristic
266C24×C3C2411yescharacteristic
267C23×D3—22no—
268C23×D3—24no—
269C23×D3—22no—
270C23×D3—22no—
271C23×D3—42no—
272C23×D3C2412yes—
273C3×#41—432no—
274C2×C3×Q8—24no—
275C2×C3×Q8—24no—
276C2×C3×Q8—42no—
277C2×C3×D4—22no—
278C2×C3×D4—22no—
279C2×C3×D4—24no—
280C2×C3×D4—24no—
281C2×C3×D4—24no—
282C2×C3×D4—24no—
283C2×C3×D4—22no—
284C2×C3×D4—24no—
285C2×C3×D4—24no—
286C2×C3×D4—42no—
287C2×C3×D4#4114yes—
288C22×C3×C4—24no—
289C22×C3×C4—24no—
290C22×C3×C4—24no—
291C22×C3×C4—24no—
292C22×C3×C4—22no—
293C22×C3×C4—24no—
294C22×C3×C4—24no—
295C22×C3×C4—24no—
296C22×C3×C4—24no—
297C22×C3×C4—42no—
298C22×C3×C4—42no—
299C22×C3×C4C2×D418yes—
300C22×C3×C4C2×D414yes—
301C22×C3×C4C2411yescharacteristic
302C22×C3×C4C2412yes—
303C22×C3×C4C2411yescharacteristic
304C22×C3×C4C2411yescharacteristic
305C22×C3×C4C2412yes—
306C22×C3×C4C2412yes—
307C22×C3×C4C2411yescharacteristic
308C22×C3×C4C2411yescharacteristic
309C2×#67—24no—
310C2×#67—24no—
311C2×#67—28no—
312C2×#67—42no—
313C2×#67—44no—
314C2×#67—44no—
315C22×Dic3—22no—
316C22×Dic3—24no—
317C22×Dic3—44no—
318C22×Dic3—42no—
319C22×Dic3C2412yes—
320C22×Dic3C2414yes—
321C22×Dic3C2412yes—
322C22×Dic3C2412yes—
323C22×Dic3C2414yes—
324C2×C4×D3—24no—
325C2×C4×D3—24no—
326C2×C4×D3—24no—
327C2×C4×D3—24no—
328C2×C4×D3—42no—
329C2×C4×D3—42no—
330C2×C4×D3—416no—
331C2×Dic6—24no—
332C2×Dic6—24no—
333C2×Dic6—24no—
334C2×Dic6—24no—
335C2×Dic6—44no—
336C2×Dic6—416no—
337C3×C4⋊C4—22no—
338C3×C4⋊C4—24no—
339C3×C4⋊C4—22no—
340C3×C4⋊C4—24no—
341C3×C4⋊C4C2×D414yes—
342C3×C4⋊C4C2×D414yes—
343C3×C4⋊C4C2×D418yes—
344C3×C22⋊C4—22no—
345C3×C22⋊C4—24no—
346C3×C22⋊C4—22no—
347C3×C22⋊C4—24no—
348C3×C22⋊C4—24no—
349C3×C42—22no—
350#217—22no—
351#217—22no—
352#217—24no—
353#217—44no—
354#217—42no—
355#217—44no—
356#217—44no—
357#217—44no—
358(C2×D3)⋊C4—24no—
359(C2×D3)⋊C4—28no—
360(C2×D3)⋊C4—28no—
361(C2×D3)⋊C4—24no—
362(C2×D3)⋊C4—42no—
363(C2×D3)⋊C4—44no—
364C4⋊Dic3—28no—
365C4⋊Dic3—28no—
366C4⋊Dic3—24no—
367C4⋊Dic3—44no—
368Dic3⋊C4—44no—
369Dic3⋊C4—42no—
370C4×Dic3—24no—
371C4×Dic3—44no—
372C25—31no—
373C2×#41—28no—
374C2×#41—28no—
375C2×#41—44no—
376C22×Q8—32no—
377C22×Q8—32no—
378C22×Q8—64no—
379C22×Q8—124no—
380C22×Q8C22×D312yes—
381C22×D4—32no—
382C22×D4—34no—
383C22×D4C22×D311yescharacteristic
384C22×D4C22×D312yes—
385C22×D4C22×D312yes—
386C22×D4C22×D311yescharacteristic
387C23×C4—32no—
388C23×C4—31no—
389C23×C4—32no—
390C23×C4—32no—
391C23×C4—64no—
392C23×C4—124no—
393C23×C4C22×D311yescharacteristic
394C23×C4C22×D312yes—
395C23×C4C22×D312yes—
396C23×C4C22×D312yes—
397C23×C4C22×D311yescharacteristic
398C4⋊Q8—24no—
399#124—124no—
400#123—28no—
401#123—28no—
402C22⋊Q8—28no—
403C22⋊Q8—68no—
404C22⋊Q8—68no—
405C22⋊Q8—616no—
406C22⋊Q8—124no—
407#121—24no—
408#121—24no—
409#121—124no—
410#120—64no—
411#120—124no—
412C4×D4—24no—
413C4×D4—24no—
414C4×D4—124no—
415#117—124no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—34no—
418C2×C4⋊C4—34no—
419C2×C4⋊C4—32no—
420C2×C4⋊C4—34no—
421C2×C4⋊C4—32no—
422C2×C4⋊C4—34no—
423C2×C4⋊C4—68no—
424C2×C4⋊C4#6718yescomplemented
425C2×C4⋊C4C22×D311yescharacteristic
426C2×C4⋊C4C22×D312yes—
427C2×C4⋊C4C22×D311yescharacteristic
428C2×C4⋊C4C22×D312yes—
429C2×C4⋊C4C22×D311yescharacteristic
430C2×C4⋊C4C22×D311yescharacteristic
431C2×C4⋊C4C22×D312yes—
432C2×C22⋊C4—31no—
433C2×C22⋊C4—32no—
434C2×C22⋊C4—31no—
435C2×C22⋊C4—34no—
436C2×C22⋊C4—34no—
437C2×C22⋊C4—32no—
438C2×C22⋊C4—32no—
439C2×C22⋊C4—32no—
440C2×C22⋊C4—34no—
441C2×C22⋊C4—34no—
442C2×C22⋊C4—34no—
443C2×C22⋊C4—34no—
444C2×C22⋊C4—32no—
445C2×C22⋊C4—34no—
446C2×C22⋊C4—68no—
447C2×C22⋊C4C22×D311yescharacteristic
448C2×C22⋊C4C22×D311yescharacteristic
449C2×C22⋊C4C22×D312yes—
450C2×C22⋊C4C22×D312yes—
451C2×C22⋊C4C22×D312yes—
452C2×C42—32no—
453C2×C42—34no—
454C2×C42C22×D311yescharacteristic
455#95—32no—
456#95—32no—
457#95—32no—
458#95—34no—
459#95—34no—
460#95—32no—
461#95—34no—
462#95—34no—
463#95—34no—
464#95—34no—
465#95—34no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—21no—
469C23×C3—22no—
470C23×C3—21no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—24no—
475C23×C3—22no—
476C23×C3—24no—
477C23×C3C22×D412yes—
478C23×C3C2×#4112yes—
479C23×C3C2×#4112yes—
480C23×C3H(5,𝔽2)12yes—
481C23×C3C2511yescharacteristic
482C22×D3—28no—
483C22×D3—22no—
484C22×D3—22no—
485C22×D3—22no—
486C22×D3—22no—
487C22×D3—22no—
488C22×D3—22no—
489C22×D3—48no—
490C22×D3—48no—
491C22×D3—44no—
492C22×D3—44no—
493C22×D32−1+414yes—
494C3×Q8—48no—
495C3×D4—28no—
496C3×D4—48no—
497C3×D4—48no—
498C3×D4—44no—
499C2×C3×C4—216no—
500C2×C3×C4—21no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—21no—
507C2×C3×C4—28no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—48no—
516C2×C3×C4—48no—
517C2×C3×C4—44no—
518C2×C3×C4C22×D414yes—
519C2×C3×C4C22×D414yes—
520C2×C3×C4C22×D412yes—
521C2×C3×C4C22×D412yes—
522C2×C3×C4C2×#4112yes—
523C2×C3×C4H(5,𝔽2)14yes—
524#67—48no—
525#67—88no—
526C2×Dic3—22no—
527C2×Dic3—24no—
528C2×Dic3—22no—
529C2×Dic3—22no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—24no—
533C2×Dic3—24no—
534C2×Dic3—24no—
535C2×Dic3—22no—
536C2×Dic3—24no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—24no—
541C2×Dic3—48no—
542C2×Dic3—44no—
543C4×D3—48no—
544C4×D3—48no—
545Dic6—48no—
546Dic6—48no—
547C24—32no—
548C24—64no—
549C24—62no—
550C24—62no—
551C24—62no—
552C24—122no—
553C24C23×D312yes—
554C24C23×D311yescharacteristic
555C24C23×D311yescharacteristic
556#41—432no—
557C2×Q8—24no—
558C2×Q8—24no—
559C2×Q8—42no—
560C2×Q8—64no—
561C2×Q8—64no—
562C2×Q8—64no—
563C2×Q8—64no—
564C2×Q8—124no—
565C2×Q8—1216no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—24no—
569C2×D4—24no—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—24no—
573C2×D4—22no—
574C2×D4—24no—
575C2×D4—42no—
576C2×D4—64no—
577C2×D4—64no—
578C2×D4—68no—
579C2×D4—122no—
580C2×D4—124no—
581C2×D4—124no—
582C2×D4#23714yes—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—32no—
593C22×C4—34no—
594C22×C4—32no—
595C22×C4—34no—
596C22×C4—32no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—64no—
600C22×C4—62no—
601C22×C4—64no—
602C22×C4—64no—
603C22×C4—64no—
604C22×C4—64no—
605C22×C4—122no—
606C22×C4—122no—
607C22×C4—1216no—
608C22×C4—122no—
609C22×C4—124no—
610C22×C4C2×#6718yes—
611C22×C4C2×#6714yes—
612C22×C4C23×D311yescharacteristic
613C22×C4C23×D312yes—
614C22×C4C23×D311yescharacteristic
615C22×C4C23×D311yescharacteristic
616C22×C4C23×D311yescharacteristic
617C22×C4C23×D312yes—
618C22×C4C23×D312yes—
619C22×C4C23×D311yescharacteristic
620C4⋊C4—22no—
621C4⋊C4—24no—
622C4⋊C4—22no—
623C4⋊C4—24no—
624C4⋊C4—64no—
625C4⋊C4—68no—
626C4⋊C4—68no—
627C4⋊C4—124no—
628C4⋊C4—122no—
629C4⋊C4—124no—
630C4⋊C4C2×#6714yes—
631C4⋊C4C2×#6714yes—
632C4⋊C4C2×#6718yes—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—64no—
639C22⋊C4—62no—
640C22⋊C4—62no—
641C22⋊C4—64no—
642C22⋊C4—64no—
643C22⋊C4—68no—
644C22⋊C4—68no—
645C22⋊C4—122no—
646C22⋊C4—124no—
647C22⋊C4—122no—
648C22⋊C4—124no—
649C22⋊C4—124no—
650C22⋊C4—124no—
651C22⋊C4—124no—
652C42—22no—
653C42—64no—
654C42—124no—
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—24no—
658C22×C3—24no—
659C22×C3—22no—
660C22×C3—24no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—44no—
668C22×C3—44no—
669C22×C3#54614yes—
670C22×C3C23×D411yescharacteristic
671C22×C3C22×#4111yescharacteristic
672C22×C3C2×H(5,𝔽2)11yescharacteristic
673C22×C3C2×H(5,𝔽2)12yes—
674C22×C3C2×2−1+412yes—
675C2×D3—24no—
676C2×D3—24no—
677C2×D3—24no—
678C2×D3—416no—
679C2×D3—42no—
680C2×D3—42no—
681C2×D3—42no—
682C2×D3—42no—
683C3×C4—22no—
684C3×C4—24no—
685C3×C4—24no—
686C3×C4—22no—
687C3×C4—41no—
688C3×C4—42no—
689C3×C4—41no—
690C3×C4#53514yes—
691Dic3—44no—
692Dic3—42no—
693Dic3—42no—
694Dic3—42no—
695Dic3—44no—
696C23—22no—
697C23—22no—
698C23—21no—
699C23—22no—
700C23—22no—
701C23—21no—
702C23—22no—
703C23—22no—
704C23—24no—
705C23—24no—
706C23—22no—
707C23—34no—
708C23—68no—
709C23—62no—
710C23—62no—
711C23—62no—
712C23—62no—
713C23—62no—
714C23—62no—
715C23—128no—
716C23—128no—
717C23—124no—
718C23—124no—
719C23C2×#23712yes—
720C23C2×#23712yes—
721C23#100412yes—
722C23C22×#6712yes—
723C23C24×D311yescharacteristic
724Q8—48no—
725Q8—128no—
726Q8—128no—
727D4—28no—
728D4—48no—
729D4—48no—
730D4—44no—
731D4—128no—
732D4—248no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—216no—
741C2×C4—28no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—48no—
750C2×C4—48no—
751C2×C4—44no—
752C2×C4—62no—
753C2×C4—62no—
754C2×C4—64no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—64no—
758C2×C4—62no—
759C2×C4—64no—
760C2×C4—62no—
761C2×C4—64no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—64no—
765C2×C4—64no—
766C2×C4—62no—
767C2×C4—128no—
768C2×C4—124no—
769C2×C4—128no—
770C2×C4—128no—
771C2×C4C2×#23712yes—
772C2×C4#100914yes—
773C2×C4C22×#6712yes—
774C2×C4C22×#6714yes—
775C2×C4C22×#6714yes—
776C2×C4C22×#6712yes—
777C2×C3—24no—
778C2×C3—42no—
779C2×C3—82no—
780C2×C3C2×#53511yescharacteristic
781C2×C3C2×#54611yescharacteristic
782C2×C3#348611yescharacteristic
783C2×C3#352012yes—
784C2×C3#353612yes—
785D3—44no—
786C22—24no—
787C22—24no—
788C22—22no—
789C22—22no—
790C22—24no—
791C22—22no—
792C22—42no—
793C22—41no—
794C22—41no—
795C22—44no—
796C22—44no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—64no—
801C22—64no—
802C22—64no—
803C22—1216no—
804C22—122no—
805C22—122no—
806C22—122no—
807C22—122no—
808C22#580614yes—
809C22C22×#23711yescharacteristic
810C22C2×#100411yescharacteristic
811C22C2×#100912yes—
812C22D3×2−1+412yes—
813C22C23×#6711yescharacteristic
814C4—24no—
815C4—24no—
816C4—22no—
817C4—22no—
818C4—42no—
819C4—41no—
820C4—41no—
821C4—122no—
822C4—124no—
823C4—122no—
824C4—122no—
825C4—124no—
826C4#583014yes—
827C3#3890511yescharacteristic, complemented, Sylow
828C2—24no—
829C2—42no—
830C2—82no—
831C2—124no—
832C2#8668512yes—
833C2#8670512yes—
834C2C2×#580611yescharacteristic
835C2C2×#583011yescharacteristic
836C2#8729411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#547C2
hypercenterC2×#547D3
hypocenterC3#38905
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. C22×#897C2semidirect
3. #84096C2semidirect
4. #84087C2semidirect
5. #83258C2semidirect
6. #82894C2semidirect
7. #82878C2semidirect
8. #82866C2semidirect
9. #82797C2semidirect
10. #82723C2semidirect
11. #82668C2semidirect
12. #82654C2semidirect
13. #82408C2semidirect
14. C4×#937C2semidirect
15. #82349C2semidirect
16. #82194C2semidirect
17. #82159C2semidirect
23. C2×C3×C4⋊Q8C22semidirect
25. C2×C3×#123C22semidirect
26. C2×C3×C22⋊Q8C22semidirect
28. C2×C3×#121C22semidirect
30. C2×C3×C4×D4C22semidirect
32. C22×C3×C4⋊C4C22semidirect
36. C2×#936C22semidirect
41. C2×#924C22semidirect
47. #5229C22semidirect
49. #5221C22semidirect
58. #5212C22semidirect
59. #5212C22semidirect
66. #4986C22semidirect
67. #4984C22semidirect
68. #4981C22semidirect
69. #4980C22semidirect
70. #4979C22semidirect
71. Dic3×C4⋊C4C22semidirect
72. #4973C22semidirect
78. #4953C22semidirect
79. #4949C22semidirect
80. #4947C22semidirect
81. #4947C22semidirect
85. #4929C22semidirect
86. C2×#547D3semidirect
138. C2×C3×C4⋊C4D4semidirect
201. C2×C4⋊Q8C2×D3semidirect
204. C2×#123C2×D3semidirect
210. C2×C22⋊Q8C2×D3semidirect
213. C2×#121C2×D3semidirect
218. C2×C4×D4C2×D3semidirect
222. C22×C4⋊C4C2×D3semidirect
424. C2×C4⋊C4#67semidirect
827. C3#38905semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5472
C22×#8972
#840962
#840872
#832582
#828942
#828782
#828662
#827972
#827232
#826682
#826542
#824082
C4×#9372
#823492
#821942
#821592
#389053