Finite Group Databasebeta

← #10846082

Subgroups — #10846082

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
1C2×C3×#462C211yesmaximal, characteristic, complemented
2C2×#5189C211yesmaximal, characteristic, complemented
3C2×#5188C211yesmaximal, characteristic, complemented
4#83259C211yesmaximal, characteristic
5#82499C211yesmaximal, characteristic
6C2×#4836C211yesmaximal, characteristic
7#72071C211yesmaximal, characteristic, complemented
8#72071C211yesmaximal, characteristic, complemented
9#71786C211yesmaximal, characteristic, complemented
10#71631C211yesmaximal, characteristic, complemented
11#70455C211yesmaximal, characteristic, complemented
12#70271C211yesmaximal, characteristic, complemented
13#70270C211yesmaximal, characteristic, complemented
14#70244C211yesmaximal, characteristic, complemented
15#70243C211yesmaximal, characteristic, complemented
16#25398—31nomaximal, Sylow
17C22×C3×Q16C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×C3×C4×Q8C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C2×#946C2211yescharacteristic
24C2×#946C2211yescharacteristic
25C2×#946C2211yescharacteristic
26C2×#946C2211yescharacteristic
27C22×ΓL(1,𝔽25)C2211yescharacteristic
28C22×D3×C8C2211yescharacteristic
29C2×C4×D12C2211yescharacteristic
30C3×#462—24no—
31C2×C3×C4⋊C8C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×#835C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40#5189—24no—
41#5188—24no—
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×#818C2211yescharacteristic
45C2×#817C2211yescharacteristic
46#4993—21no—
47#4993—21no—
48#4991—21no—
49#4988—21no—
50#4987C2211yescharacteristic
51#4987C2211yescharacteristic
52#4981—21no—
53#4975—21no—
54#4940—21no—
55#4940—21no—
56#4936C2211yescharacteristic
57C4×C4⋊Dic3C2211yescharacteristic
58C2×#803C2211yescharacteristic
59#4836—24no—
60#4551C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#470—31no—
65C2×#467—31no—
66C2×#462D311yescharacteristic, complemented
67C2×#435—31no—
68#2542—31no—
69#2536—31no—
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×Q8C2311yescharacteristic
81C22×C3×Q8C2311yescharacteristic
82C22×D12D411yescharacteristic
83C22×C4×D3C2311yescharacteristic
84C22×C4×D3C2311yescharacteristic
85C2×C3×Q16—22no—
86C2×C3×Q16—22no—
87C2×C3×Q16—22no—
88C2×C3×Q16—22no—
89C2×C3×Q16—41no—
90C2×C3×Q16—41no—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×C4⋊Q8—22no—
94C3×C4⋊Q8—22no—
95C3×C4×Q8—22no—
96C3×C4×Q8—22no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4—21no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C42—21no—
102C2×C3×C42C2311yescharacteristic
103#946—22no—
104#946—22no—
105#946—22no—
106#946—22no—
107#946—22no—
108#946—22no—
109#946—41no—
110#946—41no—
111#946—41no—
112#946—41no—
113#946—41no—
114#946—41no—
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×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4D411yescharacteristic
124C2×(C2×D3)⋊C4D411yescharacteristic
125C2×C4⋊Dic3D411yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×C4×Dic3—21no—
137C22×C3⋊C8C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139C2×ΓL(1,𝔽25)—22no—
140C2×ΓL(1,𝔽25)—22no—
141C2×ΓL(1,𝔽25)—41no—
142C2×D3×C8—22no—
143C2×D3×C8—22no—
144C2×D3×C8—41no—
145C4×D12—22no—
146C4×D12—22no—
147C3×C4⋊C8D414yes—
148C3×#103—22no—
149C3×#103—22no—
150#835—22no—
151#835—22no—
152#835—22no—
153#835—41no—
154#835—41no—
155#835D414yescomplemented
156C3⋊#95—21no—
157C3⋊#95—21no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161(C2×D3)⋊C8—22no—
162(C2×D3)⋊C8—22no—
163#818—22no—
164#817—22no—
165#803—22no—
166C22×Q16C2×D311yescharacteristic
167C22×Q16C2×D311yescharacteristic
168C22×M16—31no—
169C23×C8—31no—
170C2×C4⋊Q8C2×D311yescharacteristic
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
175C2×C22⋊Q8—31no—
176C2×C22⋊Q8—31no—
177C2×C4×Q8C2×D311yescharacteristic
178C2×C4×D4—31no—
179#470—64no—
180#467—64no—
181#462—24no—
182#435—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×C4⋊C8C2×D311yescharacteristic
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#103—31no—
192C2×#103C2×D311yescharacteristic
193C2×#103C2×D311yescharacteristic
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×#97—31no—
197#399—61no—
198#399—61no—
199#398—61no—
200#394—61no—
201#390—61no—
202#388—61no—
203#388—61no—
204#384—61no—
205#382—31no—
206#380—31no—
207#380—31no—
208C4×C4⋊C4—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213C23×D3C2×D411yescharacteristic
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×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8C2×D412yes—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2411yescharacteristic
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3C2×D411yescharacteristic
245C22×Dic3C2×D411yescharacteristic
246C2×D12—22no—
247C2×D12—22no—
248C2×D12—41no—
249C2×C4×D3—21no—
250C2×C4×D3—21no—
251C2×C4×D3—21no—
252C2×C4×D3—21no—
253C2×C4×D3—21no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C3×Q16—44no—
262C3×Q16—44no—
263C2×C3×C8—21no—
264C2×C3×C8—21no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8C2×D412yes—
268C2×C3×C8C2×D412yes—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—42no—
272C3×C4⋊C4—42no—
273C3×C4⋊C4—42no—
274C3×C42—42no—
275C3×C42C2×D412yes—
276C3×C42#4112yes—
277(C2×D3)⋊C4—22no—
278(C2×D3)⋊C4—22no—
279(C2×D3)⋊C4—42no—
280(C2×D3)⋊C4—42no—
281(C2×D3)⋊C4—42no—
282(C2×D3)⋊C4—42no—
283(C2×D3)⋊C4—42no—
284(C2×D3)⋊C4—42no—
285(C2×D3)⋊C4—42no—
286(C2×D3)⋊C4—42no—
287C4⋊Dic3—22no—
288C4⋊Dic3—21no—
289C4⋊Dic3—21no—
290C4⋊Dic3—21no—
291C4⋊Dic3—21no—
292C4⋊Dic3—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3C2×D412yes—
295C4⋊Dic3#4112yes—
296Dic3⋊C4—42no—
297Dic3⋊C4—42no—
298Dic3⋊C4—42no—
299Dic3⋊C4—42no—
300Dic3⋊C4—42no—
301Dic3⋊C4—42no—
302C4×Dic3—42no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8C2×D412yes—
309ΓL(1,𝔽25)—44no—
310D3×C8—44no—
311C22×Q8C22×D311yescharacteristic
312C22×Q8C22×D311yescharacteristic
313C22×Q8C22×D311yescharacteristic
314C22×D4—31no—
315C23×C4—31no—
316C23×C4—31no—
317C2×Q16—22no—
318C2×Q16—22no—
319C2×Q16—22no—
320C2×Q16—22no—
321C2×Q16—41no—
322C2×Q16—41no—
323C2×M16—62no—
324C2×M16—62no—
325C2×M16—121no—
326C22×C8—31no—
327C22×C8—31no—
328C22×C8—62no—
329C22×C8—62no—
330C22×C8—121no—
331C22×C8C22×D311yescharacteristic
332C22×C8C22×D311yescharacteristic
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C22⋊Q8—62no—
336C22⋊Q8—62no—
337C22⋊Q8—62no—
338C22⋊Q8—62no—
339C22⋊Q8—62no—
340C22⋊Q8—62no—
341C22⋊Q8—121no—
342C22⋊Q8—121no—
343C22⋊Q8—121no—
344C22⋊Q8—121no—
345C22⋊Q8—121no—
346C22⋊Q8—121no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×D4—62no—
350C4×D4—62no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—31no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—61no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4C22×D311yescharacteristic
366C2×C22⋊C4—31no—
367C2×C22⋊C4—31no—
368C2×C22⋊C4—61no—
369C2×C22⋊C4—61no—
370C2×C22⋊C4—61no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C42—21no—
377C2×C42—61no—
378C2×C42C22×D311yescharacteristic
379#107—62no—
380#106—62no—
381C4⋊C8#6714yes—
382#103—22no—
383#103—22no—
384#103—34no—
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—61no—
394#95—61no—
395#95—61no—
396#95—61no—
397#95—61no—
398C23×C3C22×D411yescharacteristic
399C22×D3—21no—
400C22×D3—21no—
401C22×D3—21no—
402C22×D3—21no—
403C22×D3—21no—
404C22×D3—21no—
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—21no—
408C22×D3—21no—
409C22×D3—21no—
410C22×D3—21no—
411C22×D3—21no—
412C22×D3#13712yes—
413C3×Q8—22no—
414C3×Q8—22no—
415C3×Q8—41no—
416C3×Q8—41no—
417C3×Q8—41no—
418C3×Q8—41no—
419C3×Q8—41no—
420C3×Q8—41no—
421C3×Q8—41no—
422C3×Q8—41no—
423C3×Q8—41no—
424C3×Q8—41no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—22no—
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#12112yes—
442C2×C3×C4#12112yes—
443C2×C3×C4C22×D411yescharacteristic
444C2×C3×C4C22×D411yescharacteristic
445C2×C3×C4C2×#4111yescharacteristic
446C2×C3×C4C2×#4111yescharacteristic
447C2×C3×C4H(5,𝔽2)11yescharacteristic
448C2×C3×C4H(5,𝔽2)11yescharacteristic
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—41no—
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—
467D12—44no—
468C4×D3—41no—
469C4×D3—41no—
470C4×D3—41no—
471C4×D3—41no—
472C4×D3—41no—
473C4×D3—41no—
474C4×D3—41no—
475C4×D3—41no—
476C3×C8—22no—
477C3×C8—22no—
478C3⋊C8—22no—
479C3⋊C8—41no—
480C24—31no—
481C24—31no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8D3×D412yes—
500C2×D4—62no—
501C2×D4—62no—
502C2×D4—121no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—31no—
508C22×C4—31no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4D3×D411yescharacteristic
526C22×C4D3×D411yescharacteristic
527C22×C4C23×D311yescharacteristic
528Q16—44no—
529Q16—44no—
530M16—124no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—32no—
536C2×C8—61no—
537C2×C8—61no—
538C2×C8—61no—
539C2×C8—61no—
540C2×C8—61no—
541C2×C8—124no—
542C2×C8C2×#6712yes—
543C2×C8C2×#6712yes—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—32no—
547C4⋊C4—32no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—62no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
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—62no—
565C22⋊C4—62no—
566C22⋊C4—122no—
567C22⋊C4—122no—
568C22⋊C4—122no—
569C22⋊C4—122no—
570C22⋊C4—122no—
571C22⋊C4—122no—
572C22⋊C4—122no—
573C22⋊C4—122no—
574C42—42no—
575C42—122no—
576C42#23712yes—
577C42C2×#6712yes—
578C22×C3C2×#12111yescharacteristic
579C22×C3D4211yescharacteristic
580C22×C3#54611yescharacteristic
581C22×C3C2×#13711yescharacteristic
582C22×C3#57511yescharacteristic
583C22×C3#57811yescharacteristic
584C22×C3#57811yescharacteristic
585C2×D3—22no—
586C2×D3—22no—
587C2×D3—22no—
588C2×D3—41no—
589C2×D3—41no—
590C2×D3—41no—
591C2×D3—41no—
592C2×D3—41no—
593C2×D3—41no—
594C2×D3—41no—
595C2×D3—41no—
596C2×D3—41no—
597C2×D3—41no—
598C2×D3—41no—
599C3×C4—22no—
600C3×C4—22no—
601C3×C4—42no—
602C3×C4—81no—
603C3×C4—81no—
604C3×C4—81no—
605C3×C4#53211yescharacteristic
606C3×C4#54011yescharacteristic
607C3×C4D4211yescharacteristic
608C3×C4#55011yescharacteristic
609Dic3—41no—
610Dic3—41no—
611Dic3—42no—
612Dic3—42no—
613Dic3—81no—
614Dic3—81no—
615C23—32no—
616C23—61no—
617C23—61no—
618C23—61no—
619C23—61no—
620C23—61no—
621C23—61no—
622C23—61no—
623C23—61no—
624C23—61no—
625C23—61no—
626C23—61no—
627C23—61no—
628C23—61no—
629C23C2×D3×D411yescharacteristic
630Q8—22no—
631Q8—22no—
632Q8—41no—
633Q8—41no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8—41no—
642D4—124no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—62no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—62no—
665C2×C4—61no—
666C2×C4—61no—
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—121no—
679C2×C4—121no—
680C2×C4—121no—
681C2×C4—121no—
682C2×C4—121no—
683C2×C4—121no—
684C2×C4—121no—
685C2×C4#93812yes—
686C2×C4#93812yes—
687C2×C4C2×D3×D411yescharacteristic
688C2×C4C2×#23711yescharacteristic
689C2×C4#100411yescharacteristic
690C2×C4D3×#4111yescharacteristic
691C2×C4#100911yescharacteristic
692C2×C4C22×#6711yescharacteristic
693C8—22no—
694C8—22no—
695C8—62no—
696C8—121no—
697C2×C3#242811yescharacteristic
698C2×C3#305611yescharacteristic
699C2×C3#305911yescharacteristic
700C2×C3#326911yescharacteristic
701C2×C3#327011yescharacteristic
702C2×C3#331211yescharacteristic
703C2×C3#331511yescharacteristic
704D3—42no—
705D3—81no—
706C22—62no—
707C22—62no—
708C22—62no—
709C22—121no—
710C22—121no—
711C22—121no—
712C22—121no—
713C22—121no—
714C22—121no—
715C22—121no—
716C22—121no—
717C22—121no—
718C22—121no—
719C22—121no—
720C22#560911yescharacteristic
721C22#561211yescharacteristic
722C22#576611yescharacteristic
723C22#576611yescharacteristic
724C22D3×#13711yescharacteristic
725C22#577711yescharacteristic
726C22C2×#93811yescharacteristic
727C4—22no—
728C4—22no—
729C4—42no—
730C4—81no—
731C4—81no—
732C4—81no—
733C4—122no—
734C4—122no—
735C4—121no—
736C4—121no—
737C4—241no—
738C4—241no—
739C4#559611yescharacteristic
740C4#561911yescharacteristic
741C4D4×#6711yescharacteristic
742C4#583411yescharacteristic
743C3#2539811yescharacteristic, complemented, Sylow
744C2—122no—
745C2—241no—
746C2#8048911yescharacteristic
747C2#8049311yescharacteristic
748C2#8049411yescharacteristic
749C2#8050011yescharacteristic
750C2#8264811yescharacteristic
751C2#8388711yescharacteristic
752C2#8398511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#462C2
socleC23×C3C22×D4
prime radicalC22×D12D4
hypercenterC2×#462D3
hypocenterC3#25398
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C2×C3×#462C2semidirect
2. C2×#5189C2semidirect
3. C2×#5188C2semidirect
7. #72071C2semidirect
8. #72071C2semidirect
9. #71786C2semidirect
10. #71631C2semidirect
11. #70455C2semidirect
12. #70271C2semidirect
13. #70270C2semidirect
14. #70244C2semidirect
15. #70243C2semidirect
66. C2×#462D3semidirect
155. #835D4semidirect
743. C3#25398semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4622
C2×#51892
C2×#51882
#832592
#824992
C2×#48362
#720712
#717862
#716312
#704552
#702712
#702702
#702442
#702432
#253983