Finite Group Databasebeta

← #10842608

Subgroups — #10842608

Order 768.

1078 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5173C211yesmaximal, characteristic
2C2×#5173C211yesmaximal, characteristic
3#83254C211yesmaximal, characteristic, complemented
4C2×#5090C211yesmaximal, characteristic, complemented
5C2×#4790C211yesmaximal, characteristic, complemented
6#76301C211yesmaximal, characteristic
7C3×#2013C211yesmaximal, characteristic, complemented
8#72049C211yesmaximal, characteristic, complemented
9#72048C211yesmaximal, characteristic, complemented
10#70281C211yesmaximal, characteristic, complemented
11#70275C211yesmaximal, characteristic, complemented
12#70243C211yesmaximal, characteristic, complemented
13#69653C211yesmaximal, characteristic, complemented
14#68684C211yesmaximal, characteristic, complemented
15#68615C211yesmaximal, characteristic, complemented
16#25151—31nomaximal, Sylow
17C22×#237C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C2×Q8×Dic3C2211yescharacteristic
24C22×#216C2211yescharacteristic
25C22×#216C2211yescharacteristic
26C2×#887C2211yescharacteristic
27C2×C4×Dic6C2211yescharacteristic
28C2×C3×#103C2211yescharacteristic
29C2×C3×#103C2211yescharacteristic
30C3×#390C2211yescharacteristic
31#5229C2211yescharacteristic
32C2×#835C2211yescharacteristic
33C2×#835C2211yescharacteristic
34#5221C2211yescharacteristic
35C2×#832C2211yescharacteristic
36C2×#832C2211yescharacteristic
37#5173—24no—
38#5173—24no—
39C2×(C2×D3)⋊C8C2211yescharacteristic
40C2×(C2×D3)⋊C8C2211yescharacteristic
41C2×#817C2211yescharacteristic
42C2×#816C2211yescharacteristic
43C2×#816C2211yescharacteristic
44C2×C8×Dic3C2211yescharacteristic
45#5090—24no—
46#4994—21no—
47#4990—21no—
48#4987C2211yescharacteristic
49#4982—21no—
50#4976—21no—
51C2×#807C2211yescharacteristic
52#4957—21no—
53#4957—21no—
54#4942—21no—
55Dic3×C22⋊C4—21no—
56C4×(C2×D3)⋊C4C2211yescharacteristic
57#4928C2211yescharacteristic
58C2×C4⋊(C3⋊C8)C2211yescharacteristic
59#4790—24no—
60C3×#336C2211yescharacteristic
61#4551C2211yescharacteristic
62#4550C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#462—31no—
65C2×#452—31no—
66C2×#452—31no—
67C2×C4×Q16—31no—
68#2429—31no—
69#2341—31no—
70#2067—31no—
71#2036—31no—
72#2035—31no—
73#2013D311yescharacteristic, complemented
74#1968—31no—
75#1923—31no—
76#1880—31no—
77#1878—31no—
78#1865—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C22×#67—21no—
83C23×Dic3—21no—
84C2×#237—22no—
85C2×#237—22no—
86C2×#237—22no—
87C2×#237—22no—
88C2×#237—41no—
89C2×#237—41no—
90C22×C4×D3C2311yescharacteristic
91C22×Dic6C2311yescharacteristic
92C2×C3×SD16—22no—
93C2×C3×SD16—22no—
94C2×C3×SD16—22no—
95C2×C3×SD16—22no—
96C2×C3×SD16—41no—
97C2×C3×SD16—41no—
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C3×C4⋊Q8—22no—
101C3×C4⋊Q8—41no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C22⋊C4—21no—
106C2×C3×C22⋊C4—21no—
107C2×C3×C42C2311yescharacteristic
108C2×#217—21no—
109C2×#217—21no—
110#946—22no—
111#946—22no—
112#946—41no—
113#946—41no—
114Q8×Dic3—22no—
115Q8×Dic3—41no—
116C2×#216—22no—
117C2×#216—22no—
118C2×#216—22no—
119C2×#216—22no—
120C2×#216—22no—
121C2×#216D414yes—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4D411yescharacteristic
126C2×(C2×D3)⋊C4D411yescharacteristic
127C2×C4⋊Dic3—21no—
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×C4×Dic3—21no—
137C2×C4×Dic3—21no—
138C2×C4×Dic3—21no—
139C2×C4×Dic3C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142#887—22no—
143#887—41no—
144C4×Dic6—22no—
145C4×Dic6—41no—
146C3×#103—22no—
147C3×#103—41no—
148#835—22no—
149#835—22no—
150#832—22no—
151#832—22no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95D411yescharacteristic
157C3⋊#95D411yescharacteristic
158(C2×D3)⋊C8—22no—
159(C2×D3)⋊C8—22no—
160#817—41no—
161#816—22no—
162#816D414yes—
163C8×Dic3—22no—
164#807—22no—
165C4⋊(C3⋊C8)—22no—
166C22×#41—31no—
167C22×Q16—31no—
168C22×Q16—31no—
169C22×SD16C2×D311yescharacteristic
170C22×SD16C2×D311yescharacteristic
171C2×C4⋊Q8C2×D311yescharacteristic
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—31no—
174C2×C4×Q8—31no—
175C2×C4×Q8—31no—
176C2×C4×Q8—31no—
177#462—64no—
178#452—64no—
179#452—64no—
180C4×Q16—64no—
181C2×#107—31no—
182C2×#106—31no—
183C2×C4⋊C8—31no—
184C2×#103—31no—
185C2×#103—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103C2×D311yescharacteristic
189C2×#103C2×D311yescharacteristic
190C2×#102—31no—
191C2×#102—31no—
192C2×C22⋊C8—31no—
193C2×C22⋊C8—31no—
194C2×C4×C8—31no—
195#398—61no—
196#396—61no—
197#391—31no—
198#390—31no—
199#390—61no—
200#390—61no—
201#390C2×D311yescharacteristic
202#389—31no—
203#389—61no—
204#388—61no—
205#380—31no—
206#380—61no—
207C4×C22⋊C4—31no—
208C4×C22⋊C4—61no—
209#340—31no—
210#340—31no—
211#336—31no—
212#336C2×D311yescharacteristic
213C24×C3—21no—
214C23×D3C2×D411yescharacteristic
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8C2×D412yes—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4#4112yes—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2411yescharacteristic
239C2×#67—24no—
240C2×#67—42no—
241C2×#67—42no—
242C22×Dic3—21no—
243C22×Dic3—24no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—42no—
248C22×Dic3—42no—
249C22×Dic3C2×D411yescharacteristic
250C22×Dic3C2×D411yescharacteristic
251C22×Dic3C2×D411yescharacteristic
252#237—44no—
253#237—44no—
254#237—44no—
255#237—44no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6C2×D412yes—
266C2×Dic6C2×D412yes—
267C2×Dic6#4112yes—
268C3×SD16—44no—
269C3×SD16—44no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8C2×D412yes—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—42no—
279C3×C4⋊C4—42no—
280C3×C22⋊C4—42no—
281C3×C22⋊C4—81no—
282C3×C42—21no—
283C3×C42—21no—
284#217—42no—
285#217—81no—
286#216—28no—
287#216—44no—
288(C2×D3)⋊C4—22no—
289(C2×D3)⋊C4—22no—
290(C2×D3)⋊C4—42no—
291(C2×D3)⋊C4—42no—
292(C2×D3)⋊C4—81no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—42no—
299C4⋊Dic3C2×D412yes—
300Dic3⋊C4—42no—
301Dic3⋊C4—42no—
302Dic3⋊C4—42no—
303Dic3⋊C4—42no—
304Dic3⋊C4—42no—
305C4×Dic3—21no—
306C4×Dic3—21no—
307C4×Dic3—42no—
308C4×Dic3—42no—
309C4×Dic3—42no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8C2×D412yes—
316C2×#41—62no—
317C2×#41—62no—
318C2×#41—62no—
319C2×#41—62no—
320C2×#41—121no—
321C2×#41—121no—
322C22×Q8—31no—
323C22×Q8C22×D311yescharacteristic
324C22×Q8C22×D311yescharacteristic
325C22×D4—61no—
326C22×D4C22×D311yescharacteristic
327C23×C4—31no—
328C23×C4—61no—
329C2×Q16—34no—
330C2×Q16—62no—
331C2×Q16—62no—
332C2×Q16—62no—
333C2×Q16—62no—
334C2×Q16—62no—
335C2×SD16—22no—
336C2×SD16—22no—
337C2×SD16—22no—
338C2×SD16—22no—
339C2×SD16—41no—
340C2×SD16—41no—
341C22×C8—31no—
342C22×C8—31no—
343C22×C8C22×D311yescharacteristic
344C22×C8C22×D311yescharacteristic
345C4⋊Q8—22no—
346C4⋊Q8—41no—
347C22⋊Q8—62no—
348C22⋊Q8—62no—
349C22⋊Q8—121no—
350C22⋊Q8—121no—
351C4×Q8—62no—
352C4×Q8—62no—
353C4×Q8—62no—
354C4×Q8—121no—
355C4×Q8—121no—
356C4×Q8—121no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4C22×D311yescharacteristic
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—31no—
372C2×C22⋊C4—31no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C42—31no—
379C2×C42—61no—
380C2×C42—61no—
381C2×C42—61no—
382C2×C42C22×D311yescharacteristic
383#107—62no—
384#106—121no—
385C4⋊C8—62no—
386#103—22no—
387#103—34no—
388#103—41no—
389#103—62no—
390#103—62no—
391#103—62no—
392#102—62no—
393#102—62no—
394C22⋊C8—62no—
395C22⋊C8—62no—
396C4×C8—62no—
397#95—31no—
398#95—31no—
399#95—61no—
400#95—61no—
401#95—61no—
402#95—61no—
403C23×C3—22no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3C22×D411yescharacteristic
411C22×D3—21no—
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—21no—
416C22×D3—21no—
417C22×D3—21no—
418C3×Q8—22no—
419C3×Q8—22no—
420C3×Q8—41no—
421C3×Q8—41no—
422C3×Q8—41no—
423C3×Q8—41no—
424C3×Q8—41no—
425C3×Q8—41no—
426C3×D4—22no—
427C3×D4—22no—
428C3×D4—41no—
429C3×D4—41no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—22no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4#13512yes—
445C2×C3×C4C22×D411yescharacteristic
446C2×C3×C4C22×D411yescharacteristic
447C2×C3×C4C2×#4111yescharacteristic
448C2×C3×C4C2×#4111yescharacteristic
449C2×C3×C4H(5,𝔽2)11yescharacteristic
450C2×C3×C4H(5,𝔽2)11yescharacteristic
451#67—48no—
452C2×Dic3—22no—
453C2×Dic3—21no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—22no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—48no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3#13712yes—
474C4×D3—41no—
475C4×D3—41no—
476C4×D3—41no—
477C4×D3—41no—
478Dic6—22no—
479Dic6—22no—
480Dic6—22no—
481Dic6#12114yes—
482C3×C8—22no—
483C3×C8—41no—
484C3⋊C8—22no—
485C3⋊C8—41no—
486C24—21no—
487C24—31no—
488#41—124no—
489#41—124no—
490#41—124no—
491#41—124no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—32no—
504C2×Q8—32no—
505C2×Q8—32no—
506C2×Q8—61no—
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8D3×D412yes—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—64no—
516C2×D4—122no—
517C2×D4—122no—
518C2×D4#23712yes—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—31no—
523C22×C4—31no—
524C22×C4—31no—
525C22×C4—61no—
526C22×C4—64no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—122no—
537C22×C4—122no—
538C22×C4D3×D411yescharacteristic
539C22×C4D3×D411yescharacteristic
540C22×C4C23×D311yescharacteristic
541Q16—68no—
542Q16—124no—
543SD16—44no—
544SD16—44no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—32no—
551C2×C8—61no—
552C2×C8—61no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8D3×D412yes—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—32no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—122no—
568C4⋊C4—122no—
569C4⋊C4—122no—
570C4⋊C4—122no—
571C4⋊C4—122no—
572C4⋊C4—122no—
573C22⋊C4—42no—
574C22⋊C4—62no—
575C22⋊C4—62no—
576C22⋊C4—81no—
577C22⋊C4—122no—
578C22⋊C4—122no—
579C22⋊C4—122no—
580C22⋊C4—241no—
581C22⋊C4—241no—
582C42—21no—
583C42—21no—
584C42—61no—
585C42—61no—
586C42—122no—
587C42—122no—
588C42—122no—
589C22×C3—42no—
590C22×C3—42no—
591C22×C3—42no—
592C22×C3—81no—
593C22×C3—81no—
594C22×C3—81no—
595C22×C3—81no—
596C22×C3#52511yescharacteristic
597C22×C3D4211yescharacteristic
598C22×C3D4211yescharacteristic
599C22×C3C2×#13511yescharacteristic
600C22×C3C2×#13711yescharacteristic
601C22×C3#57711yescharacteristic
602C22×C3#57811yescharacteristic
603C2×D3—41no—
604C2×D3—41no—
605C2×D3—41no—
606C2×D3—41no—
607C2×D3—41no—
608C2×D3—41no—
609C2×D3—41no—
610C3×C4—22no—
611C3×C4—42no—
612C3×C4—41no—
613C3×C4—81no—
614C3×C4—81no—
615C3×C4C2×#12111yescharacteristic
616C3×C4#53811yescharacteristic
617C3×C4#54611yescharacteristic
618C3×C4#54611yescharacteristic
619Dic3—24no—
620Dic3—22no—
621Dic3—41no—
622Dic3—41no—
623Dic3—42no—
624Dic3—81no—
625Dic3—81no—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—61no—
634C23—61no—
635C23—61no—
636C23—61no—
637C23—61no—
638C23—61no—
639C23—61no—
640C23C2×D3×D411yescharacteristic
641Q8—22no—
642Q8—22no—
643Q8—34no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—62no—
651Q8—62no—
652Q8—62no—
653D4—22no—
654D4—22no—
655D4—41no—
656D4—41no—
657D4—128no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—32no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—61no—
674C2×C4—62no—
675C2×C4—61no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—61no—
679C2×C4—62no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—128no—
686C2×C4—121no—
687C2×C4—121no—
688C2×C4—121no—
689C2×C4—121no—
690C2×C4—121no—
691C2×C4—121no—
692C2×C4—121no—
693C2×C4—121no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4#91612yes—
699C2×C4C2×D3×D411yescharacteristic
700C2×C4C2×D3×D411yescharacteristic
701C2×C4C2×#23711yescharacteristic
702C2×C4#100411yescharacteristic
703C2×C4#100411yescharacteristic
704C2×C4D3×#4111yescharacteristic
705C8—22no—
706C8—41no—
707C8—62no—
708C8—121no—
709C2×C3—82no—
710C2×C3#242411yescharacteristic
711C2×C3#310711yescharacteristic
712C2×C3#312011yescharacteristic
713C2×C3#327011yescharacteristic
714C2×C3#327811yescharacteristic
715C2×C3#328411yescharacteristic
716C2×C3#328511yescharacteristic
717D3—81no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—121no—
726C22—121no—
727C22—121no—
728C22—121no—
729C22—121no—
730C22—121no—
731C22—121no—
732C22#559011yescharacteristic
733C22#560611yescharacteristic
734C22#571711yescharacteristic
735C22C2×#91611yescharacteristic
736C22#576211yescharacteristic
737C22D3×#13711yescharacteristic
738C22#577911yescharacteristic
739C4—22no—
740C4—41no—
741C4—42no—
742C4—64no—
743C4—62no—
744C4—81no—
745C4—81no—
746C4—121no—
747C4—122no—
748C4—121no—
749C4—241no—
750C4—241no—
751C4#559111yescharacteristic
752C4#559111yescharacteristic
753C4D3×#12111yescharacteristic
754C4#561311yescharacteristic
755C3#2515111yescharacteristic, complemented, Sylow
756C2—82no—
757C2—241no—
758C2#7675611yescharacteristic
759C2#8006611yescharacteristic
760C2#8006711yescharacteristic
761C2#8040911yescharacteristic
762C2#8041211yescharacteristic
763C2#8177211yescharacteristic
764C2#8188411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2013C2
socleC23×C3C22×D4
prime radicalC22×#237C22
hypercenter#2013D3
hypocenterC3#25151
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2013

Complements

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

NH ≅ G/Ntype
3. #83254C2semidirect
4. C2×#5090C2semidirect
5. C2×#4790C2semidirect
7. C3×#2013C2semidirect
8. #72049C2semidirect
9. #72048C2semidirect
10. #70281C2semidirect
11. #70275C2semidirect
12. #70243C2semidirect
13. #69653C2semidirect
14. #68684C2semidirect
15. #68615C2semidirect
73. #2013D3semidirect
755. C3#25151semidirect

Maximal subgroups

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

subgroupindex
C2×#51732
#832542
C2×#50902
C2×#47902
#763012
C3×#20132
#720492
#720482
#702812
#702752
#702432
#696532
#686842
#686152
#251513