Finite Group Databasebeta

← #10847430

Subgroups — #10847430

Order 768.

1226 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5600C211yesmaximal, characteristic, complemented
2C2×#5114C211yesmaximal, characteristic, complemented
3C2×#5038C211yesmaximal, characteristic
4#73999C211yesmaximal, characteristic, complemented
5C3×#1893C211yesmaximal, characteristic, complemented
6C2×#4550C211yesmaximal, characteristic, complemented
7#70214C211yesmaximal, characteristic, complemented
8#70178C211yesmaximal, characteristic, complemented
9#70172C211yesmaximal, characteristic, complemented
10#70170C211yesmaximal, characteristic, complemented
11#69514C211yesmaximal, characteristic, complemented
12#68909C211yesmaximal, characteristic, complemented
13#68906C211yesmaximal, characteristic, complemented
14#68899C211yesmaximal, characteristic, complemented
15#68828C211yesmaximal, characteristic, complemented
16#25500—31nomaximal, Sylow
17C23×C3×C8C2211yescharacteristic
18C2×C3×#121C2211yescharacteristic
19C2×#936C2211yescharacteristic
20C2×#935—21no—
21C2×D4×Dic3—21no—
22C2×D4×Dic3C2211yescharacteristic
23C22×#213C2211yescharacteristic
24C2×#930C2211yescharacteristic
25C2×#924C2211yescharacteristic
26C22×C4×Dic3C2211yescharacteristic
27C23×C3⋊C8C2211yescharacteristic
28C22×#204C2211yescharacteristic
29#5600—24no—
30#5600—24no—
31C2×#890C2211yescharacteristic
32C2×#887C2211yescharacteristic
33C2×#886—21no—
34C2×#879—21no—
35C2×#877—21no—
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C3×#380C2211yescharacteristic
39C2×#832C2211yescharacteristic
40#5114—24no—
41C2×#821C2211yescharacteristic
42C2×#817C2211yescharacteristic
43C2×#816C2211yescharacteristic
44#5038—24no—
45#4988C2211yescharacteristic
46#4988C2211yescharacteristic
47#4984C2211yescharacteristic
48#4984C2211yescharacteristic
49C2×#810C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#807C2211yescharacteristic
53#4958—21no—
54#4670—21no—
55#4670—21no—
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58#4550C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#529—31no—
65C2×#466—31no—
66C2×#465—31no—
67#2854—31no—
68#2059—31no—
69#2042—31no—
70#2025—31no—
71#2012—31no—
72#1893D311yescharacteristic, complemented
73#1892—31no—
74#1880—31no—
75#1879—31no—
76#1864—31no—
77#1863—31no—
78C2×#336—31no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67—21no—
83C23×Dic3—21no—
84C23×Dic3D411yescharacteristic
85C23×Dic3D411yescharacteristic
86C22×D12C2311yescharacteristic
87C22×Dic6C2311yescharacteristic
88C22×C3×C8—22no—
89C22×C3×C8—22no—
90C22×C3×C8—41no—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×#121—22no—
94C3×#121D414yes—
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×#217—21no—
101C2×#217—21no—
102C2×#217—21no—
103C2×#217—21no—
104#936—22no—
105#936—22no—
106#935—28no—
107D4×Dic3—28no—
108D4×Dic3—22no—
109D4×Dic3—22no—
110C2×#213—22no—
111C2×#213—22no—
112C2×#213—41no—
113#930—22no—
114#930—22no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×C4⋊Dic3—21no—
121C2×C4⋊Dic3—21no—
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3C2311yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125#924—22no—
126#924D414yes—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×C4×Dic3—22no—
131C2×C4×Dic3—22no—
132C2×C4×Dic3—21no—
133C2×C4×Dic3D411yescharacteristic
134C2×C4×Dic3D411yescharacteristic
135C2×C4×Dic3C2311yescharacteristic
136C2×C4×Dic3C2311yescharacteristic
137C22×C3⋊C8—22no—
138C22×C3⋊C8—22no—
139C22×C3⋊C8—41no—
140C22×C3⋊C8C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C2×#204—22no—
143C2×#204—22no—
144C2×#204—41no—
145#890—22no—
146#890—22no—
147#887—22no—
148#887—22no—
149#886—44no—
150#879—28no—
151#877—28no—
152C3×#102—22no—
153C3×#102—41no—
154C3×#95—21no—
155#832—22no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158#821—22no—
159#817—22no—
160#816—22no—
161#810—22no—
162#810—41no—
163#809—22no—
164#807—22no—
165C22×SD16—31no—
166C22×D8—31no—
167C23×C8—31no—
168C23×C8C2×D311yescharacteristic
169#529—64no—
170#529—64no—
171C2×#126—61no—
172C2×#125—31no—
173C2×#124—31no—
174C2×#123—61no—
175C2×#123—61no—
176C2×C22⋊Q8—31no—
177C2×#121—31no—
178C2×#121C2×D311yescharacteristic
179C2×C4×Q8—31no—
180C2×C4×D4—31no—
181C2×C4×D4—61no—
182C2×#117—61no—
183C22×C42—31no—
184#466—64no—
185#465—64no—
186C2×#107—31no—
187C2×#106—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102C2×D311yescharacteristic
195C2×#102C2×D311yescharacteristic
196#390—31no—
197#390—31no—
198#389—31no—
199#389—31no—
200#388—61no—
201#388—61no—
202#386—61no—
203#380C2×D311yescharacteristic
204#340—31no—
205#340—31no—
206#340C2×D311yescharacteristic
207#340C2×D311yescharacteristic
208#336—31no—
209#336—31no—
210#336—31no—
211#336—31no—
212C24×C3—21no—
213C24×C3C2×D411yescharacteristic
214C23×D3—21no—
215C2×C3×D4—24no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—42no—
222C2×C3×D4—42no—
223C2×C3×D4C2×D412yes—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4C2×D412yes—
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D412yes—
234C22×C3×C4C2411yescharacteristic
235C2×#67—42no—
236C2×#67—42no—
237C2×#67—42no—
238C22×Dic3—24no—
239C22×Dic3—22no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—22no—
243C22×Dic3—21no—
244C22×Dic3—21no—
245C22×Dic3—22no—
246C22×Dic3—21no—
247C22×Dic3—41no—
248C22×Dic3—42no—
249C22×Dic3—42no—
250C22×Dic3C2×D411yescharacteristic
251C22×Dic3C2×D411yescharacteristic
252C22×Dic3C2×D411yescharacteristic
253C22×Dic3C2×D411yescharacteristic
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×Dic6—21no—
261C2×Dic6—21no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6C2×D412yes—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—44no—
272C2×C3×C8#4112yes—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4C2×D412yes—
279C3×C22⋊C4—24no—
280C3×C22⋊C4—42no—
281#217—24no—
282#217—24no—
283#217—24no—
284#217—24no—
285#213—44no—
286(C2×D3)⋊C4—42no—
287(C2×D3)⋊C4—42no—
288(C2×D3)⋊C4—42no—
289(C2×D3)⋊C4—42no—
290(C2×D3)⋊C4—42no—
291C4⋊Dic3—24no—
292C4⋊Dic3—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3—42no—
296C4⋊Dic3—42no—
297C4⋊Dic3C2×D412yes—
298Dic3⋊C4—24no—
299Dic3⋊C4—24no—
300Dic3⋊C4—24no—
301C4×Dic3—24no—
302C4×Dic3—22no—
303C4×Dic3—22no—
304C4×Dic3—21no—
305C4×Dic3—21no—
306C4×Dic3—21no—
307C4×Dic3—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—44no—
314C2×C3⋊C8#4112yes—
315#204—44no—
316C22×Q8—31no—
317C22×D4—21no—
318C22×D4—31no—
319C22×D4—61no—
320C22×D4C22×D311yescharacteristic
321C23×C4—31no—
322C23×C4—31no—
323C23×C4—61no—
324C23×C4C22×D311yescharacteristic
325C2×SD16—62no—
326C2×SD16—62no—
327C2×SD16—121no—
328C2×D8—62no—
329C2×D8—62no—
330C2×D8—121no—
331C22×C8—22no—
332C22×C8—22no—
333C22×C8—31no—
334C22×C8—31no—
335C22×C8—41no—
336C22×C8—62no—
337C22×C8—62no—
338C22×C8—121no—
339C22×C8C22×D311yescharacteristic
340C22×C8C22×D311yescharacteristic
341#126—68no—
342#125—62no—
343#125—62no—
344#124—62no—
345#124—62no—
346#123—68no—
347#123—124no—
348C22⋊Q8—34no—
349C22⋊Q8—62no—
350#121—22no—
351#121—62no—
352#121—62no—
353#121D1214yes—
354C4×Q8—62no—
355C4×Q8—62no—
356C4×D4—62no—
357C4×D4—68no—
358C4×D4—62no—
359#117—68no—
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×C4⋊C4C22×D311yescharacteristic
370C2×C4⋊C4C22×D311yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C42—31no—
383C2×C42—31no—
384C2×C42—31no—
385C2×C42—31no—
386C2×C42—61no—
387C2×C42—62no—
388C2×C42—62no—
389#107—62no—
390#106—62no—
391#103—62no—
392#103—62no—
393#103—121no—
394#102—22no—
395#102—41no—
396#102—62no—
397#102—62no—
398#102—62no—
399#95—21no—
400#95—61no—
401#95—61no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—22no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3#12012yes—
414C23×C3#13512yes—
415C23×C3AGL(1,ℤ/8)12yes—
416C23×C3C22×D411yescharacteristic
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C3×D4—22no—
425C3×D4—22no—
426C3×D4—48no—
427C3×D4—41no—
428C3×D4—41no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
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#12012yes—
445C2×C3×C4C22×D411yescharacteristic
446C2×C3×C4C22×D411yescharacteristic
447C2×C3×C4C2×#4111yescharacteristic
448C2×C3×C4C2×#4111yescharacteristic
449C2×C3×C4H(5,𝔽2)11yescharacteristic
450C2×C3×C42−1+411yescharacteristic
451#67—84no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—44no—
466C2×Dic3—48no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—44no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3#13512yes—
476D12—41no—
477D12—41no—
478D12—41no—
479D12—41no—
480Dic6—22no—
481Dic6—22no—
482Dic6—41no—
483Dic6—41no—
484C3×C8—22no—
485C3×C8—41no—
486C3⋊C8—22no—
487C3⋊C8—41no—
488C24—21no—
489C24—61no—
490C24D3×D411yescharacteristic
491C2×Q8—32no—
492C2×Q8—61no—
493C2×Q8—61no—
494C2×Q8—61no—
495C2×Q8—61no—
496C2×Q8—61no—
497C2×D4—24no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—61no—
506C2×D4—61no—
507C2×D4—61no—
508C2×D4—61no—
509C2×D4—61no—
510C2×D4—61no—
511C2×D4—122no—
512C2×D4—122no—
513C2×D4—122no—
514C2×D4C2×D1212yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—31no—
523C22×C4—31no—
524C22×C4—31no—
525C22×C4—31no—
526C22×C4—62no—
527C22×C4—64no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—122no—
536C22×C4—121no—
537C22×C4—122no—
538C22×C4C2×D1212yes—
539C22×C4D3×D411yescharacteristic
540C22×C4D3×D412yes—
541C22×C4C23×D311yescharacteristic
542SD16—124no—
543D8—124no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—32no—
550C2×C8—44no—
551C2×C8—61no—
552C2×C8—61no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—124no—
557C2×C8#23712yes—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—32no—
564C4⋊C4—64no—
565C4⋊C4—64no—
566C4⋊C4—64no—
567C4⋊C4—64no—
568C4⋊C4—61no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—122no—
572C4⋊C4—122no—
573C4⋊C4C2×D1212yes—
574C22⋊C4—24no—
575C22⋊C4—42no—
576C22⋊C4—64no—
577C22⋊C4—64no—
578C22⋊C4—64no—
579C22⋊C4—64no—
580C22⋊C4—122no—
581C22⋊C4—122no—
582C22⋊C4—122no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C42—64no—
586C42—62no—
587C42—62no—
588C42—61no—
589C42—61no—
590C42—61no—
591C42—61no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—42no—
599C22×C3—42no—
600C22×C3—42no—
601C22×C3—81no—
602C22×C3—81no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3#44914yes—
606C22×C3C2×#12011yescharacteristic
607C22×C3#53211yescharacteristic
608C22×C3#53711yescharacteristic
609C22×C3C2×#13511yescharacteristic
610C22×C3C2×#13511yescharacteristic
611C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
612C22×C3#57511yescharacteristic
613C2×D3—81no—
614C2×D3—81no—
615C2×D3—81no—
616C2×D3—81no—
617C2×D3—81no—
618C2×D3—81no—
619C2×D3—81no—
620C3×C4—22no—
621C3×C4—42no—
622C3×C4—81no—
623C3×C4—81no—
624C3×C4#54611yescharacteristic
625C3×C4#54611yescharacteristic
626C3×C4#54711yescharacteristic
627C3×C4#54711yescharacteristic
628Dic3—22no—
629Dic3—42no—
630Dic3—41no—
631Dic3—41no—
632Dic3—41no—
633Dic3—42no—
634Dic3—81no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—22no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—121no—
647C23—121no—
648C23—121no—
649C23—121no—
650C23—121no—
651C23—121no—
652C23—121no—
653C23#88212yes—
654C23#91112yes—
655C23#91612yes—
656C23C2×D3×D411yescharacteristic
657Q8—62no—
658Q8—62no—
659Q8—121no—
660Q8—121no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—41no—
665D4—41no—
666D4—121no—
667D4—121no—
668D4—121no—
669D4—121no—
670D4—244no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—32no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—124no—
701C2×C4—128no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—124no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4#88212yes—
711C2×C4C22×D1211yescharacteristic
712C2×C4C2×D3×D411yescharacteristic
713C2×C4C2×#23711yescharacteristic
714C2×C4#100411yescharacteristic
715C2×C4D3×#4111yescharacteristic
716C2×C4#101011yescharacteristic
717C8—22no—
718C8—41no—
719C8—62no—
720C8—121no—
721C2×C3—24no—
722C2×C3—82no—
723C2×C3#243011yescharacteristic
724C2×C3C2×#44911yescharacteristic
725C2×C3#300211yescharacteristic
726C2×C3#316811yescharacteristic
727C2×C3#318011yescharacteristic
728C2×C3#324711yescharacteristic
729C2×C3#325011yescharacteristic
730D3—161no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—241no—
745C22—241no—
746C22—241no—
747C22—241no—
748C22—241no—
749C22—241no—
750C22—241no—
751C22#478114yes—
752C22C2×#88211yescharacteristic
753C22#559611yescharacteristic
754C22#559711yescharacteristic
755C22C2×#91111yescharacteristic
756C22C2×#91611yescharacteristic
757C22D3×#13511yescharacteristic
758C22#576811yescharacteristic
759C4—22no—
760C4—42no—
761C4—62no—
762C4—81no—
763C4—81no—
764C4—121no—
765C4—121no—
766C4—122no—
767C4—121no—
768C4—122no—
769C4—241no—
770C4#555411yescharacteristic
771C4#555511yescharacteristic
772C4#559111yescharacteristic
773C4#565511yescharacteristic
774C3#2550011yescharacteristic, complemented, Sylow
775C2—24no—
776C2—82no—
777C2—481no—
778C2#7469911yescharacteristic
779C2C2×#478111yescharacteristic
780C2#7883311yescharacteristic
781C2#8063311yescharacteristic
782C2#8064311yescharacteristic
783C2#8070111yescharacteristic
784C2#8070311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1893C2
socleC23×C3C22×D4
prime radicalC2×#5038C2
hypercenter#1893D3
hypocenterC3#25500
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
1. C2×#5600C2semidirect
2. C2×#5114C2semidirect
4. #73999C2semidirect
5. C3×#1893C2semidirect
6. C2×#4550C2semidirect
7. #70214C2semidirect
8. #70178C2semidirect
9. #70172C2semidirect
10. #70170C2semidirect
11. #69514C2semidirect
12. #68909C2semidirect
13. #68906C2semidirect
14. #68899C2semidirect
15. #68828C2semidirect
72. #1893D3semidirect
774. C3#25500semidirect

Maximal subgroups

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

subgroupindex
C2×#56002
C2×#51142
C2×#50382
#739992
C3×#18932
C2×#45502
#702142
#701782
#701722
#701702
#695142
#689092
#689062
#688992
#688282
#255003