Finite Group Databasebeta

← #10846090

Subgroups — #10846090

Order 768.

984 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2536C211yesmaximal, characteristic
2C2×#5052C211yesmaximal, characteristic, complemented
3C2×#5051C211yesmaximal, characteristic, complemented
4C2×#5031C211yesmaximal, characteristic, complemented
5#82379C211yesmaximal, characteristic
6C2×#5011C211yesmaximal, characteristic
7#71700C211yesmaximal, characteristic, complemented
8#71700C211yesmaximal, characteristic, complemented
9#71631C211yesmaximal, characteristic, complemented
10#69552C211yesmaximal, characteristic, complemented
11#69540C211yesmaximal, characteristic, complemented
12#69527C211yesmaximal, characteristic, complemented
13#69526C211yesmaximal, characteristic, complemented
14#69516C211yesmaximal, characteristic, complemented
15#69514C211yesmaximal, characteristic, complemented
16#25398—31nomaximal, Sylow
17C2×C3×C22⋊Q8C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C22×#216C2211yescharacteristic
22C22×#216C2211yescharacteristic
23C2×#924C2211yescharacteristic
24C2×#924C2211yescharacteristic
25C2×#924C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C22×#208C2211yescharacteristic
28C23×C3⋊C8C2211yescharacteristic
29C2×#869C2211yescharacteristic
30C3×#398—21no—
31C3×#394—21no—
32C3×#388—21no—
33C3×#388—21no—
34C3×#382C2211yescharacteristic
35C3×#380C2211yescharacteristic
36C3×#380C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#835C2211yescharacteristic
39#5221—21no—
40C2×#830C2211yescharacteristic
41C2×#830C2211yescharacteristic
42#5052—24no—
43#5051—24no—
44#5031—24no—
45#5011—24no—
46#4975—21no—
47C2×#810C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#810C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#810C2211yescharacteristic
52C2×#810C2211yescharacteristic
53C2×#808C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4949—21no—
56#4949—21no—
57C4×C4⋊Dic3C2211yescharacteristic
58C2×C4⋊(C3⋊C8)C2211yescharacteristic
59C2×#803C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#470—31no—
65C2×#467—31no—
66C2×#462—31no—
67C2×#435—31no—
68#2542—31no—
69#2536D311yescharacteristic
70#2036—31no—
71#2035—31no—
72#2001—31no—
73#2001—31no—
74#1960—31no—
75#1949—31no—
76#1894—31no—
77#1892—31no—
78#1763—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4D411yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×Dic6C2311yescharacteristic
84C22×Dic6C2311yescharacteristic
85C3×C22⋊Q8—22no—
86C3×C22⋊Q8—22no—
87C3×C22⋊Q8—41no—
88C3×C22⋊Q8—41no—
89C3×C4×Q8—22no—
90C3×C4×Q8—22no—
91C3×C4×D4—22no—
92C3×C4×D4—22no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4D411yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—21no—
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—21no—
104C2×C3×C22⋊C4D411yescharacteristic
105C2×C3×C22⋊C4D411yescharacteristic
106C2×C3×C42—21no—
107C2×C3×C42C2311yescharacteristic
108C2×#217—21no—
109C2×#217—21no—
110C2×#217—21no—
111C2×#217—21no—
112C2×#216—22no—
113C2×#216—22no—
114C2×#216—22no—
115C2×#216—22no—
116C2×#216—41no—
117C2×#216—41no—
118C2×C4⋊Dic3—21no—
119C2×C4⋊Dic3—21no—
120C2×C4⋊Dic3C2311yescharacteristic
121C2×C4⋊Dic3C2311yescharacteristic
122#924—22no—
123#924—22no—
124#924—22no—
125#924—22no—
126#924—41no—
127#924—41no—
128#924—41no—
129#924—41no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×C4×Dic3—21no—
135C2×#208—22no—
136C2×#208—22no—
137C2×#208—41no—
138C22×C3⋊C8—22no—
139C22×C3⋊C8—22no—
140C22×C3⋊C8—41no—
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145#869—22no—
146#869—22no—
147C3×#95—21no—
148C3×#95—21no—
149C3×#95—21no—
150C3×#95—21no—
151#835—22no—
152#835D414yescomplemented
153C3⋊#95—21no—
154#830—22no—
155#830—22no—
156#810—22no—
157#810—22no—
158#810—22no—
159#810—22no—
160#810—41no—
161#810—41no—
162#808—22no—
163#807—22no—
164C4⋊(C3⋊C8)D414yes—
165#803—22no—
166C22×Q16—31no—
167C22×Q16—31no—
168C22×M16—31no—
169C23×C8—31no—
170C2×C4⋊Q8—31no—
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
175C2×C22⋊Q8C2×D311yescharacteristic
176C2×C22⋊Q8C2×D311yescharacteristic
177C2×C4×Q8C2×D311yescharacteristic
178C2×C4×D4C2×D311yescharacteristic
179#470—64no—
180#467—64no—
181#462—64no—
182#435—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×C4⋊C8—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×#97—31no—
197#399—61no—
198#399—61no—
199#398—21no—
200#394—21no—
201#390—61no—
202#388—21no—
203#388—21no—
204#384—61no—
205#382C2×D311yescharacteristic
206#380C2×D311yescharacteristic
207#380C2×D311yescharacteristic
208C4×C4⋊C4—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213C24×C3C2×D411yescharacteristic
214C24×C3C2×D411yescharacteristic
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8C2×D412yes—
221C2×C3×D4—22no—
222C2×C3×D4—22no—
223C2×C3×D4—41no—
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×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2411yescharacteristic
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C2×Dic6—21no—
250C2×Dic6—21no—
251C2×Dic6—21no—
252C2×Dic6—21no—
253C2×Dic6—21no—
254C2×Dic6—21no—
255C2×Dic6—21no—
256C2×Dic6—21no—
257C2×Dic6—21no—
258C2×Dic6—21no—
259C2×Dic6—21no—
260C2×Dic6—21no—
261C3×C4⋊C4—22no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—42no—
269C3×C4⋊C4—42no—
270C3×C4⋊C4—42no—
271C3×C22⋊C4—22no—
272C3×C22⋊C4—22no—
273C3×C22⋊C4—42no—
274C3×C22⋊C4—42no—
275C3×C22⋊C4—42no—
276C3×C22⋊C4—42no—
277C3×C42—42no—
278C3×C42C2×D412yes—
279C3×C42#4112yes—
280#217—42no—
281#217—42no—
282#217—42no—
283#217—42no—
284#216—44no—
285#216—44no—
286C4⋊Dic3—21no—
287C4⋊Dic3—21no—
288C4⋊Dic3—42no—
289C4⋊Dic3—42no—
290C4⋊Dic3C2×D412yes—
291C4⋊Dic3#4112yes—
292Dic3⋊C4—42no—
293Dic3⋊C4—42no—
294Dic3⋊C4—42no—
295Dic3⋊C4—42no—
296C4×Dic3—42no—
297#208—44no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—44no—
308C2×C3⋊C8C2×D412yes—
309C2×C3⋊C8C2×D412yes—
310C2×C3⋊C8C2×D412yes—
311C22×Q8—31no—
312C22×Q8—31no—
313C22×Q8C22×D311yescharacteristic
314C22×D4#6711yescharacteristic
315C23×C4C22×D311yescharacteristic
316C23×C4C22×D311yescharacteristic
317C2×Q16—62no—
318C2×Q16—62no—
319C2×Q16—62no—
320C2×Q16—62no—
321C2×Q16—121no—
322C2×Q16—121no—
323C2×M16—62no—
324C2×M16—62no—
325C2×M16—121no—
326C22×C8—31no—
327C22×C8—31no—
328C22×C8—31no—
329C22×C8—31no—
330C22×C8—62no—
331C22×C8—62no—
332C22×C8—121no—
333C4⋊Q8—62no—
334C4⋊Q8—62no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337C22⋊Q8—41no—
338C22⋊Q8—41no—
339C22⋊Q8—62no—
340C22⋊Q8—62no—
341C22⋊Q8—62no—
342C22⋊Q8—62no—
343C22⋊Q8—121no—
344C22⋊Q8—121no—
345C22⋊Q8—121no—
346C22⋊Q8—121no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×D4—22no—
350C4×D4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—61no—
357C2×C4⋊C4—61no—
358C2×C4⋊C4—61no—
359C2×C4⋊C4—61no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4#6711yescharacteristic
363C2×C4⋊C4C22×D311yescharacteristic
364C2×C4⋊C4C22×D311yescharacteristic
365C2×C4⋊C4C22×D311yescharacteristic
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—61no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4#6711yescharacteristic
375C2×C22⋊C4#6711yescharacteristic
376C2×C42—21no—
377C2×C42—61no—
378C2×C42C22×D311yescharacteristic
379#107—62no—
380#106—62no—
381C4⋊C8—34no—
382#103—34no—
383#103—62no—
384#103—62no—
385#103—62no—
386#103—62no—
387#103—62no—
388#103—121no—
389#103—121no—
390C22⋊C8—62no—
391C22⋊C8—62no—
392#97—62no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—61no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3#13712yes—
412C23×C3C22×D411yescharacteristic
413C3×Q8—22no—
414C3×Q8—22no—
415C3×Q8—41no—
416C3×Q8—41no—
417C3×D4—44no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—22no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
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—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4#12112yes—
449C2×C3×C4#12112yes—
450C2×C3×C4C22×D411yescharacteristic
451C2×C3×C4C22×D411yescharacteristic
452C2×C3×C4C2×#4111yescharacteristic
453C2×C3×C4C2×#4111yescharacteristic
454C2×C3×C4H(5,𝔽2)11yescharacteristic
455C2×C3×C4H(5,𝔽2)11yescharacteristic
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468Dic6—41no—
469Dic6—41no—
470Dic6—41no—
471Dic6—41no—
472Dic6—41no—
473Dic6—41no—
474Dic6—41no—
475Dic6—41no—
476C3⋊C8—22no—
477C3⋊C8—22no—
478C3⋊C8—22no—
479C3⋊C8—41no—
480C24C2×#6711yescharacteristic
481C24C2×#6711yescharacteristic
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—61no—
488C2×Q8—61no—
489C2×Q8—61no—
490C2×Q8—61no—
491C2×Q8—61no—
492C2×Q8—61no—
493C2×Q8—61no—
494C2×Q8—61no—
495C2×Q8—61no—
496C2×Q8—61no—
497C2×Q8—61no—
498C2×Q8—61no—
499C2×Q8D3×D412yes—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—41no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4C2×#6711yescharacteristic
524C22×C4C2×#6711yescharacteristic
525C22×C4C2×#6711yescharacteristic
526C22×C4C2×#6711yescharacteristic
527C22×C4C23×D311yescharacteristic
528Q16—124no—
529Q16—124no—
530M16—124no—
531C2×C8—32no—
532C2×C8—32no—
533C2×C8—32no—
534C2×C8—61no—
535C2×C8—61no—
536C2×C8—61no—
537C2×C8—61no—
538C2×C8—61no—
539C2×C8—61no—
540C2×C8—61no—
541C2×C8—61no—
542C2×C8—61no—
543C2×C8—124no—
544C4⋊C4—22no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—32no—
552C4⋊C4—32no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—122no—
559C4⋊C4—122no—
560C4⋊C4—122no—
561C4⋊C4—122no—
562C4⋊C4—122no—
563C4⋊C4—122no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—122no—
571C22⋊C4—122no—
572C22⋊C4—122no—
573C22⋊C4—122no—
574C42—42no—
575C42—122no—
576C42D3×D412yes—
577C42#23712yes—
578C22×C3—22no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3C2×#12111yescharacteristic
593C22×C3D4211yescharacteristic
594C22×C3#54611yescharacteristic
595C22×C3C2×#13711yescharacteristic
596C22×C3#57511yescharacteristic
597C22×C3#57811yescharacteristic
598C22×C3#57811yescharacteristic
599C3×C4—22no—
600C3×C4—22no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—42no—
604C3×C4—81no—
605C3×C4—81no—
606C3×C4—81no—
607C3×C4#53211yescharacteristic
608C3×C4#54011yescharacteristic
609C3×C4D4211yescharacteristic
610C3×C4#55011yescharacteristic
611Dic3—42no—
612Dic3—42no—
613Dic3—81no—
614Dic3—81no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23#95112yes—
629C23C22×#6711yescharacteristic
630Q8—22no—
631Q8—22no—
632Q8—41no—
633Q8—41no—
634Q8—121no—
635Q8—121no—
636Q8—121no—
637Q8—121no—
638Q8—121no—
639Q8—121no—
640Q8—121no—
641Q8—121no—
642D4—44no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
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—62no—
674C2×C4—62no—
675C2×C4—121no—
676C2×C4—121no—
677C2×C4—121no—
678C2×C4—121no—
679C2×C4—121no—
680C2×C4—121no—
681C2×C4—121no—
682C2×C4—121no—
683C2×C4—121no—
684C2×C4—121no—
685C2×C4#93912yes—
686C2×C4#93912yes—
687C2×C4C2×D3×D411yescharacteristic
688C2×C4C2×D3×D411yescharacteristic
689C2×C4C2×#23711yescharacteristic
690C2×C4#100411yescharacteristic
691C2×C4D3×#4111yescharacteristic
692C2×C4#100911yescharacteristic
693C8—62no—
694C8—62no—
695C8—62no—
696C8—121no—
697C2×C3—42no—
698C2×C3—81no—
699C2×C3#242811yescharacteristic
700C2×C3#305611yescharacteristic
701C2×C3#305911yescharacteristic
702C2×C3#326911yescharacteristic
703C2×C3#327011yescharacteristic
704C2×C3#331211yescharacteristic
705C2×C3#331511yescharacteristic
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22D4×#6711yescharacteristic
721C22C2×#93911yescharacteristic
722C22#582211yescharacteristic
723C22C2×#95111yescharacteristic
724C22#582911yescharacteristic
725C22#583811yescharacteristic
726C22#583811yescharacteristic
727C4—22no—
728C4—22no—
729C4—41no—
730C4—41no—
731C4—42no—
732C4—81no—
733C4—81no—
734C4—81no—
735C4—122no—
736C4—122no—
737C4—241no—
738C4—241no—
739C4#559611yescharacteristic
740C4#559911yescharacteristic
741C4#560911yescharacteristic
742C4#561911yescharacteristic
743C3#2539811yescharacteristic, complemented, Sylow
744C2—42no—
745C2—81no—
746C2#8264911yescharacteristic
747C2#8292511yescharacteristic
748C2#8339911yescharacteristic
749C2#8354311yescharacteristic
750C2#8354611yescharacteristic
751C2#8360011yescharacteristic
752C2#8360311yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2536C2
socleC23×C3C22×D4
prime radicalC22×C3×D4D4
hypercenter#2536D3
hypocenterC3#25398
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2536

Complements

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

NH ≅ G/Ntype
2. C2×#5052C2semidirect
3. C2×#5051C2semidirect
4. C2×#5031C2semidirect
7. #71700C2semidirect
8. #71700C2semidirect
9. #71631C2semidirect
10. #69552C2semidirect
11. #69540C2semidirect
12. #69527C2semidirect
13. #69526C2semidirect
14. #69516C2semidirect
15. #69514C2semidirect
152. #835D4semidirect
743. C3#25398semidirect

Maximal subgroups

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

subgroupindex
C3×#25362
C2×#50522
C2×#50512
C2×#50312
#823792
C2×#50112
#717002
#716312
#695522
#695402
#695272
#695262
#695162
#695142
#253983