Finite Group Databasebeta

← #10876312

Subgroups — #10876312

Order 768.

1124 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#380C211yesmaximal, characteristic
2D3×#380C211yesmaximal, characteristic
3C3×#2077C211yesmaximal, characteristic, complemented
4#70579C211yesmaximal, characteristic, complemented
5#70579C211yesmaximal, characteristic, complemented
6#69955C211yesmaximal, characteristic
7#69940C211yesmaximal, characteristic, complemented
8#69520C211yesmaximal, characteristic, complemented
9#69507C211yesmaximal, characteristic, complemented
10#68875C211yesmaximal, characteristic, complemented
11#68875C211yesmaximal, characteristic, complemented
12#68872C211yesmaximal, characteristic, complemented
13#68872C211yesmaximal, characteristic, complemented
14#68871C211yesmaximal, characteristic, complemented
15#68871C211yesmaximal, characteristic, complemented
16#27601—31nomaximal, Sylow
17C23×C4×D3C2211yescharacteristic
18C2×D3×C4⋊C4C2211yescharacteristic
19C2×D3×C4⋊C4C2211yescharacteristic
20C2×D3×C4⋊C4C2211yescharacteristic
21C2×D3×C4⋊C4C2211yescharacteristic
22C2×D3×C22⋊C4—21no—
23C2×D3×C22⋊C4—21no—
24C2×C3×#106C2211yescharacteristic, complemented
25C2×C3×C22⋊C8C2211yescharacteristic
26C3×#380C2211yescharacteristic
27C3×#380C2211yescharacteristic
28#5212C2211yescharacteristic
29#5212C2211yescharacteristic
30C2×#830C2211yescharacteristic
31C2×(C2×D3)⋊C8C2211yescharacteristic
32C2×(C2×D3)⋊C8C2211yescharacteristic
33C2×(C2×D3)⋊C8C2211yescharacteristic
34C2×(C2×D3)⋊C8C2211yescharacteristic
35C2×#817C2211yescharacteristic, complemented
36#4987C2211yescharacteristic
37#4987C2211yescharacteristic
38#4987C2211yescharacteristic
39#4987C2211yescharacteristic
40C2×#808C2211yescharacteristic, complemented
41C2×#808C2211yescharacteristic, complemented
42#4942—21no—
43#4942—21no—
44#4667—21no—
45#4667—21no—
46D3×#95—21no—
47D3×#95—21no—
48C3×#340C2211yescharacteristic, complemented
49C3×#340C2211yescharacteristic, complemented
50C3×#340C2211yescharacteristic, complemented
51#4551C2211yescharacteristic, complemented
52#4551C2211yescharacteristic, complemented
53#4551C2211yescharacteristic, complemented
54#4529C2211yescharacteristic, complemented
55#4529C2211yescharacteristic, complemented
56#4529C2211yescharacteristic, complemented
57#4529C2211yescharacteristic, complemented
58#4529C2211yescharacteristic, complemented
59#4529C2211yescharacteristic, complemented
60C2×#380—31no—
61C2×#380—31no—
62#2077—31no—
63#2077—31no—
64#2077—31no—
65#2077D311yescharacteristic, complemented
66#1853—31no—
67#1853—31no—
68#1853—31no—
69#1853—31no—
70#1824—31no—
71#1824—31no—
72#1823—31no—
73#1823—31no—
74#1779—31no—
75C24×D3D411yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×Dic3D411yescharacteristic
78C22×C4×D3—22no—
79C22×C4×D3—22no—
80C22×C4×D3—22no—
81C22×C4×D3—22no—
82C22×C4×D3—21no—
83C22×C4×D3—21no—
84C22×C4×D3—21no—
85C22×C4×D3—21no—
86C22×C4×D3—41no—
87C22×C4×D3—41no—
88C22×C4×D3D411yescharacteristic
89C22×C4×D3D411yescharacteristic
90C22×C4×D3C2311yescharacteristic
91C22×C4×D3C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C2×C3×C4⋊C4C2311yescharacteristic
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×(C2×D3)⋊C4—21no—
103C2×(C2×D3)⋊C4—21no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4—21no—
106C2×C4⋊Dic3C2311yescharacteristic
107C2×C4⋊Dic3C2311yescharacteristic
108C2×C4⋊Dic3C2311yescharacteristic
109C2×C4⋊Dic3C2311yescharacteristic
110C2×Dic3⋊C4—21no—
111C2×Dic3⋊C4—21no—
112C2×Dic3⋊C4—21no—
113C2×Dic3⋊C4—21no—
114C22×C3⋊C8C2311yescharacteristic
115C22×C3⋊C8C2311yescharacteristic
116D3×C4⋊C4—22no—
117D3×C4⋊C4—22no—
118D3×C4⋊C4—22no—
119D3×C4⋊C4—22no—
120D3×C4⋊C4—41no—
121D3×C4⋊C4—41no—
122D3×C4⋊C4—41no—
123D3×C4⋊C4—41no—
124D3×C22⋊C4—44no—
125D3×C22⋊C4—44no—
126C3×#106—41no—
127C3×C22⋊C8—41no—
128C3×#95—21no—
129C3×#95—21no—
130C3⋊#95—21no—
131C3⋊#95—21no—
132C3⋊#95—21no—
133C3⋊#95—21no—
134C3⋊#95—21no—
135C3⋊#95—21no—
136#830—41no—
137(C2×D3)⋊C8—22no—
138(C2×D3)⋊C8—22no—
139(C2×D3)⋊C8—22no—
140(C2×D3)⋊C8—22no—
141#817—41no—
142#808—41no—
143#808—41no—
144C24×C4—31no—
145C22×C4⋊C4—31no—
146C22×C4⋊C4—31no—
147C22×C4⋊C4—31no—
148C22×C4⋊C4—31no—
149C22×C22⋊C4—61no—
150C22×C22⋊C4—61no—
151C2×#106—31no—
152C2×#106—31no—
153C2×#106—31no—
154C2×#106C2×D311yescharacteristic, complemented
155C2×C22⋊C8—31no—
156C2×C22⋊C8—31no—
157C2×C22⋊C8—31no—
158C2×C22⋊C8—31no—
159C2×C22⋊C8—31no—
160C2×C22⋊C8C2×D311yescharacteristic
161#380—31no—
162#380—31no—
163#380—31no—
164#380—31no—
165#380—31no—
166#380—31no—
167#380—61no—
168#380—61no—
169#380—61no—
170#380—61no—
171#380C2×D311yescharacteristic
172#380C2×D311yescharacteristic
173C2×#95—61no—
174C2×#95—61no—
175#340—31no—
176#340—31no—
177#340—31no—
178#340—31no—
179#340—31no—
180#340—31no—
181#340—31no—
182#340—31no—
183#340—31no—
184#340C2×D311yescharacteristic, complemented
185#340C2×D311yescharacteristic, complemented
186#340C2×D311yescharacteristic, complemented
187C24×C3C2×D411yescharacteristic
188C23×D3—22no—
189C23×D3—22no—
190C23×D3—22no—
191C23×D3—22no—
192C23×D3—41no—
193C23×D3—41no—
194C23×D3SD1614yes—
195C23×D3C2×D411yescharacteristic
196C23×D3C2×D411yescharacteristic
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4C2×D411yescharacteristic
208C22×C3×C4C2411yescharacteristic
209C22×Dic3—22no—
210C22×Dic3—22no—
211C22×Dic3—21no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—21no—
215C22×Dic3—41no—
216C22×Dic3C2×D411yescharacteristic
217C22×Dic3C2×D411yescharacteristic
218C2×C4×D3—21no—
219C2×C4×D3—21no—
220C2×C4×D3—21no—
221C2×C4×D3—21no—
222C2×C4×D3—21no—
223C2×C4×D3—21no—
224C2×C4×D3—21no—
225C2×C4×D3—21no—
226C2×C4×D3—22no—
227C2×C4×D3—22no—
228C2×C4×D3—22no—
229C2×C4×D3—22no—
230C2×C4×D3—44no—
231C2×C4×D3—44no—
232C2×C4×D3—44no—
233C2×C4×D3—44no—
234C2×C4×D3—41no—
235C2×C4×D3—41no—
236C2×C4×D3—42no—
237C2×C4×D3—42no—
238C2×C4×D3—42no—
239C2×C4×D3—42no—
240C2×C4×D3—42no—
241C2×C4×D3—42no—
242C2×C4×D3—42no—
243C2×C4×D3—42no—
244C2×C4×D3—42no—
245C2×C4×D3—42no—
246C2×C4×D3—42no—
247C2×C4×D3—42no—
248C2×C4×D3#4112yes—
249C2×C4×D3#4112yes—
250C2×C4×D3#4112yes—
251C2×C4×D3#4112yes—
252C2×C3×C8—21no—
253C2×C3×C8—21no—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C22⋊C4—42no—
267C3×C22⋊C4—42no—
268#217—42no—
269#217—42no—
270(C2×D3)⋊C4—42no—
271(C2×D3)⋊C4—42no—
272(C2×D3)⋊C4—42no—
273(C2×D3)⋊C4—42no—
274C4⋊Dic3—21no—
275C4⋊Dic3—21no—
276C4⋊Dic3—21no—
277C4⋊Dic3—21no—
278C4⋊Dic3—21no—
279C4⋊Dic3—21no—
280C4⋊Dic3—21no—
281C4⋊Dic3—21no—
282Dic3⋊C4—42no—
283Dic3⋊C4—42no—
284Dic3⋊C4—42no—
285Dic3⋊C4—42no—
286C2×C3⋊C8—21no—
287C2×C3⋊C8—21no—
288C2×C3⋊C8—21no—
289C2×C3⋊C8—21no—
290C2×C3⋊C8—21no—
291C2×C3⋊C8—21no—
292C25—31no—
293C23×C4—31no—
294C23×C4—31no—
295C23×C4—31no—
296C23×C4—31no—
297C23×C4—31no—
298C23×C4—62no—
299C23×C4—62no—
300C23×C4—62no—
301C23×C4—62no—
302C23×C4—61no—
303C23×C4—61no—
304C23×C4—61no—
305C23×C4—61no—
306C23×C4—121no—
307C23×C4—121no—
308C23×C4C22×D311yescharacteristic
309C22×C8—31no—
310C22×C8—31no—
311C22×C8C22×D311yescharacteristic
312C22×C8C22×D311yescharacteristic
313C2×C4⋊C4—31no—
314C2×C4⋊C4—31no—
315C2×C4⋊C4—31no—
316C2×C4⋊C4—31no—
317C2×C4⋊C4—62no—
318C2×C4⋊C4—62no—
319C2×C4⋊C4—62no—
320C2×C4⋊C4—62no—
321C2×C4⋊C4—61no—
322C2×C4⋊C4—61no—
323C2×C4⋊C4—61no—
324C2×C4⋊C4—61no—
325C2×C4⋊C4—121no—
326C2×C4⋊C4—121no—
327C2×C4⋊C4—121no—
328C2×C4⋊C4—121no—
329C2×C4⋊C4C22×D311yescharacteristic
330C2×C4⋊C4C22×D311yescharacteristic
331C2×C4⋊C4C22×D311yescharacteristic
332C2×C4⋊C4C22×D311yescharacteristic
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—61no—
336C2×C22⋊C4—61no—
337C2×C22⋊C4—61no—
338C2×C22⋊C4—61no—
339C2×C22⋊C4—61no—
340C2×C22⋊C4—61no—
341C2×C22⋊C4—124no—
342C2×C22⋊C4—124no—
343#106—41no—
344#106—121no—
345#106—121no—
346#106—121no—
347C22⋊C8—41no—
348C22⋊C8—62no—
349C22⋊C8—62no—
350C22⋊C8—62no—
351C22⋊C8—62no—
352C22⋊C8—121no—
353#95—21no—
354#95—21no—
355#95—61no—
356#95—61no—
357#95—61no—
358#95—61no—
359#95—61no—
360#95—61no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—21no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3C2×SD1612yes—
368C23×C3C22×D411yescharacteristic
369C22×D3—21no—
370C22×D3—21no—
371C22×D3—21no—
372C22×D3—21no—
373C22×D3—21no—
374C22×D3—21no—
375C22×D3—21no—
376C22×D3—21no—
377C22×D3—28no—
378C22×D3—28no—
379C22×D3—44no—
380C22×D3—44no—
381C22×D3—44no—
382C22×D3—44no—
383C22×D3—44no—
384C22×D3#12312yes—
385C22×D3#12312yes—
386C22×D3C2×SD1612yes—
387C22×D3C2×SD1612yes—
388C22×D3AGL(1,ℤ/8)12yes—
389C22×D3#13712yes—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4C2×#4111yescharacteristic
410C2×C3×C4C2×#4111yescharacteristic
411C2×C3×C4C2×#4111yescharacteristic
412C2×C3×C4C2×#4111yescharacteristic
413C2×C3×C4H(5,𝔽2)11yescharacteristic
414C2×C3×C4H(5,𝔽2)11yescharacteristic
415C2×Dic3—21no—
416C2×Dic3—21no—
417C2×Dic3—21no—
418C2×Dic3—21no—
419C2×Dic3—44no—
420C2×Dic3—41no—
421C2×Dic3—41no—
422C2×Dic3—41no—
423C2×Dic3—41no—
424C2×Dic3—41no—
425C2×Dic3—41no—
426C2×Dic3—41no—
427C2×Dic3—41no—
428C2×Dic3—41no—
429C2×Dic3—41no—
430C2×Dic3—41no—
431C2×Dic3—41no—
432C2×Dic3#12312yes—
433C2×Dic3#12312yes—
434C4×D3—22no—
435C4×D3—22no—
436C4×D3—22no—
437C4×D3—22no—
438C4×D3—22no—
439C4×D3—22no—
440C4×D3—22no—
441C4×D3—22no—
442C4×D3—44no—
443C4×D3—44no—
444C4×D3—84no—
445C4×D3—84no—
446C4×D3—84no—
447C4×D3—84no—
448C3×C8—41no—
449C3×C8—41no—
450C3⋊C8—41no—
451C3⋊C8—41no—
452C24—31no—
453C24—31no—
454C24—34no—
455C24—62no—
456C24—62no—
457C24—62no—
458C24—62no—
459C24—121no—
460C24—121no—
461C24D3×D411yescharacteristic
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—31no—
473C22×C4—31no—
474C22×C4—32no—
475C22×C4—32no—
476C22×C4—32no—
477C22×C4—32no—
478C22×C4—62no—
479C22×C4—62no—
480C22×C4—62no—
481C22×C4—62no—
482C22×C4—62no—
483C22×C4—62no—
484C22×C4—61no—
485C22×C4—61no—
486C22×C4—61no—
487C22×C4—61no—
488C22×C4—61no—
489C22×C4—61no—
490C22×C4—61no—
491C22×C4—61no—
492C22×C4—61no—
493C22×C4—61no—
494C22×C4—61no—
495C22×C4—61no—
496C22×C4—121no—
497C22×C4—121no—
498C22×C4—124no—
499C22×C4—124no—
500C22×C4—124no—
501C22×C4—124no—
502C22×C4—122no—
503C22×C4—122no—
504C22×C4—122no—
505C22×C4—122no—
506C22×C4—122no—
507C22×C4—122no—
508C22×C4—122no—
509C22×C4—122no—
510C22×C4—122no—
511C22×C4—122no—
512C22×C4—122no—
513C22×C4—122no—
514C22×C4—121no—
515C22×C4D3×D411yescharacteristic
516C22×C4C23×D311yescharacteristic
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—61no—
524C2×C8—61no—
525C2×C8—61no—
526C2×C8—61no—
527C2×C8—61no—
528C2×C8—61no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—61no—
538C4⋊C4—61no—
539C4⋊C4—61no—
540C4⋊C4—61no—
541C4⋊C4—61no—
542C4⋊C4—61no—
543C4⋊C4—61no—
544C4⋊C4—61no—
545C4⋊C4—122no—
546C4⋊C4—122no—
547C4⋊C4—122no—
548C4⋊C4—122no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—122no—
552C22⋊C4—122no—
553C22⋊C4—122no—
554C22⋊C4—122no—
555C22⋊C4—122no—
556C22⋊C4—122no—
557C22×C3—22no—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—41no—
561C22×C3—41no—
562C22×C3—41no—
563C22×C3—41no—
564C22×C3C2×#12311yescharacteristic
565C22×C3C2×#12311yescharacteristic
566C22×C3#53411yescharacteristic
567C22×C3C22×SD1611yescharacteristic
568C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
569C22×C3C2×#13711yescharacteristic
570C22×C3#57511yescharacteristic
571C2×D3—22no—
572C2×D3—22no—
573C2×D3—22no—
574C2×D3—22no—
575C2×D3—22no—
576C2×D3—22no—
577C2×D3—22no—
578C2×D3—22no—
579C2×D3—22no—
580C2×D3—22no—
581C2×D3—22no—
582C2×D3—22no—
583C2×D3—416no—
584C2×D3#48114yes—
585C2×D3#48314yes—
586C3×C4—41no—
587C3×C4—81no—
588C3×C4—81no—
589C3×C4—81no—
590C3×C4—81no—
591C3×C4#55111yescharacteristic
592C3×C4#55111yescharacteristic
593C3×C4#55111yescharacteristic
594C3×C4#55111yescharacteristic
595Dic3—22no—
596Dic3—22no—
597Dic3—81no—
598Dic3—81no—
599Dic3—81no—
600Dic3—81no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—32no—
608C23—32no—
609C23—32no—
610C23—32no—
611C23—32no—
612C23—32no—
613C23—68no—
614C23—68no—
615C23—61no—
616C23—61no—
617C23—61no—
618C23—61no—
619C23—61no—
620C23—61no—
621C23—61no—
622C23—61no—
623C23—124no—
624C23—124no—
625C23—124no—
626C23—124no—
627C23—124no—
628C23D3×SD1612yes—
629C23C2×D3×D411yescharacteristic
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—32no—
634C2×C4—32no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—62no—
658C2×C4—62no—
659C2×C4—62no—
660C2×C4—62no—
661C2×C4—62no—
662C2×C4—62no—
663C2×C4—124no—
664C2×C4—124no—
665C2×C4—124no—
666C2×C4—121no—
667C2×C4—121no—
668C2×C4—121no—
669C2×C4—121no—
670C2×C4—121no—
671C2×C4—121no—
672C2×C4—121no—
673C2×C4—121no—
674C2×C4—121no—
675C2×C4—121no—
676C2×C4—121no—
677C2×C4—121no—
678C2×C4—244no—
679C2×C4—244no—
680C2×C4—244no—
681C2×C4—244no—
682C2×C4#100411yescharacteristic
683C2×C4D3×#4111yescharacteristic
684C2×C4D3×#4111yescharacteristic
685C2×C4D3×#4111yescharacteristic
686C2×C4D3×#4111yescharacteristic
687C2×C4#100911yescharacteristic
688C8—41no—
689C8—41no—
690C8—121no—
691C8—121no—
692C2×C3—42no—
693C2×C3#248311yescharacteristic
694C2×C3C2×#48311yescharacteristic
695C2×C3C2×#48111yescharacteristic
696C2×C3#309411yescharacteristic
697C2×C3#309511yescharacteristic
698C2×C3#318711yescharacteristic
699C2×C3#319311yescharacteristic
700D3—24no—
701D3—24no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—34no—
706C22—34no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—62no—
712C22—62no—
713C22—62no—
714C22—62no—
715C22—62no—
716C22—62no—
717C22—62no—
718C22—62no—
719C22—62no—
720C22—62no—
721C22—62no—
722C22—62no—
723C22—1216no—
724C22#560511yescharacteristic
725C22D3×#12311yescharacteristic
726C22D3×#12311yescharacteristic
727C22C2×D3×SD1611yescharacteristic
728C22#576811yescharacteristic
729C22D3×AGL(1,ℤ/8)11yescharacteristic
730C22D3×#13711yescharacteristic
731C4—41no—
732C4—62no—
733C4—62no—
734C4—81no—
735C4—81no—
736C4—81no—
737C4—81no—
738C4—241no—
739C4—241no—
740C4—241no—
741C4—241no—
742C4#565911yescharacteristic
743C4#567911yescharacteristic
744C4#570511yescharacteristic
745C4#570511yescharacteristic
746C3#2760111yescharacteristic, complemented, Sylow
747C2—42no—
748C2—64no—
749C2—64no—
750C2#7767711yescharacteristic
751C2#8066311yescharacteristic
752C2#8081111yescharacteristic
753C2D3×#48111yescharacteristic
754C2#8137311yescharacteristic
755C2D3×#48311yescharacteristic
756C2#8151711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2077C2
socleC23×C3C22×D4
prime radicalC24×D3D4
hypercenter#2077D3
hypocenterC3#27601
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2077

Complements

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

NH ≅ G/Ntype
3. C3×#2077C2semidirect
4. #70579C2semidirect
5. #70579C2semidirect
7. #69940C2semidirect
8. #69520C2semidirect
9. #69507C2semidirect
10. #68875C2semidirect
11. #68875C2semidirect
12. #68872C2semidirect
13. #68872C2semidirect
14. #68871C2semidirect
15. #68871C2semidirect
24. C2×C3×#106C22semidirect
35. C2×#817C22semidirect
40. C2×#808C22semidirect
41. C2×#808C22semidirect
48. C3×#340C22semidirect
49. C3×#340C22semidirect
50. C3×#340C22semidirect
51. #4551C22semidirect
52. #4551C22semidirect
53. #4551C22semidirect
54. #4529C22semidirect
55. #4529C22semidirect
56. #4529C22semidirect
57. #4529C22semidirect
58. #4529C22semidirect
59. #4529C22semidirect
65. #2077D3semidirect
154. C2×#106C2×D3semidirect
184. #340C2×D3semidirect
185. #340C2×D3semidirect
186. #340C2×D3semidirect
746. C3#27601semidirect

Maximal subgroups

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

subgroupindex
D3×#3802
C3×#20772
#705792
#699552
#699402
#695202
#695072
#688752
#688722
#688712
#276013