Finite Group Databasebeta

← #10845923

Subgroups — #10845923

Order 768.

1018 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
1C2×#5188C211yesmaximal, characteristic, complemented
2C2×#5182C211yesmaximal, characteristic, complemented
3#82780C211yesmaximal, characteristic
4#82778C211yesmaximal, characteristic
5C2×#5051C211yesmaximal, characteristic, complemented
6C2×#67⋊C8C211yesmaximal, characteristic
7C3×#2001C211yesmaximal, characteristic, complemented
8#71696C211yesmaximal, characteristic, complemented
9#70275C211yesmaximal, characteristic, complemented
10#70273C211yesmaximal, characteristic, complemented
11#70225C211yesmaximal, characteristic, complemented
12Dic3×#103C211yesmaximal, characteristic, complemented
13#69937C211yesmaximal, characteristic, complemented
14#68882C211yesmaximal, characteristic, complemented
15#68795C211yesmaximal, characteristic, complemented
16#25386—31nomaximal, Sylow
17C22×C3×Q16C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×Q8×Dic3C2211yescharacteristic
23C2×#944C2211yescharacteristic
24C22×#216C2211yescharacteristic
25C2×C4×#67C2211yescharacteristic
26C2×#924C2211yescharacteristic
27C23×C3⋊C8C2211yescharacteristic
28C22×D3×C8C2211yescharacteristic
29C2×#897C2211yescharacteristic
30C2×C3×#103C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×C22⋊C8C2211yescharacteristic
33C2×#835C2211yescharacteristic
34C2×#835C2211yescharacteristic
35C2×#835C2211yescharacteristic
36#5212C2211yescharacteristic
37#5188—24no—
38#5182—24no—
39C2×(C2×D3)⋊C8C2211yescharacteristic
40C2×#818C2211yescharacteristic
41C2×#816C2211yescharacteristic
42C2×#816C2211yescharacteristic
43C2×Dic3⋊C8C2211yescharacteristic
44C2×C8×Dic3C2211yescharacteristic
45#5051—24no—
46#4994—21no—
47#4993—21no—
48#4987C2211yescharacteristic
49#4976—21no—
50#4975—21no—
51#4975C2211yescharacteristic
52Dic3×C4⋊C4C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4957—21no—
56#4957—21no—
57#4949—21no—
58#4948—21no—
59#67⋊C8—24no—
60C3×#340C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#467—31no—
65C2×#467—31no—
66C2×#462—31no—
67C2×C8×D4—31no—
68#2542—31no—
69#2538—31no—
70#2036—31no—
71#2036—31no—
72#2001—31no—
73#2001D311yescharacteristic, complemented
74#1956—31no—
75#1947—31no—
76#1892—31no—
77#1892—31no—
78C4×#103—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67D411yescharacteristic
83C22×C4×D3C2311yescharacteristic
84C22×Dic6C2311yescharacteristic
85C2×C3×Q16—22no—
86C2×C3×Q16—22no—
87C2×C3×Q16—41no—
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C3×C22⋊Q8—22no—
91C3×C22⋊Q8—22no—
92C3×C22⋊Q8—41no—
93C3×C22⋊Q8—41no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—21no—
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×#217D411yescharacteristic
103#946—22no—
104#946—22no—
105#946—41no—
106#946—41no—
107Q8×Dic3—22no—
108Q8×Dic3—22no—
109#944—22no—
110#944—22no—
111C2×#216—22no—
112C2×#216—22no—
113C2×#216—41no—
114C4×#67—22no—
115C4×#67—22no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4D411yescharacteristic
121C2×C4⋊Dic3—21no—
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3C2311yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126#924—22no—
127#924—41no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4D411yescharacteristic
136C2×C4×Dic3—21no—
137C2×C4×Dic3—21no—
138C2×C4×Dic3C2311yescharacteristic
139C22×C3⋊C8—22no—
140C22×C3⋊C8—22no—
141C22×C3⋊C8—41no—
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C2×D3×C8—22no—
145C2×D3×C8—22no—
146C2×D3×C8—41no—
147#897—22no—
148#897—41no—
149C3×#103—22no—
150C3×#103—41no—
151C3×C22⋊C8—22no—
152#835—22no—
153#835—22no—
154#835D414yescomplemented
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158(C2×D3)⋊C8—22no—
159#818—22no—
160#816—22no—
161#816—41no—
162Dic3⋊C8D414yes—
163C8×Dic3—22no—
164#810—22no—
165#807—22no—
166C22×Q16—31no—
167C22×Q16C2×D311yescharacteristic
168C23×C8—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×Q8—31no—
178C2×C4×D4—31no—
179#467—64no—
180#467—64no—
181#462—64no—
182C8×D4—64no—
183C2×#107—31no—
184C2×#107—31no—
185C2×C4⋊C8—31no—
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⋊C8C2×D311yescharacteristic
196C2×C4×C8—31no—
197#399—61no—
198#399—61no—
199#396—61no—
200#396—61no—
201#390—61no—
202#390—61no—
203#389—61no—
204#384—31no—
205#384—61no—
206#380—31no—
207#380—31no—
208C4×C4⋊C4—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340C2×D311yescharacteristic
213C24×C3C2×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×Q8C2×D412yes—
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×C4C2×D411yescharacteristic
238C22×C3×C4C2411yescharacteristic
239C2×#67—22no—
240C2×#67—22no—
241C2×#67Q1614yescomplemented
242C22×Dic3—21no—
243C22×Dic3—21no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3C2×D411yescharacteristic
247C22×Dic3C2×D411yescharacteristic
248C22×Dic3C2×D411yescharacteristic
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×Dic6—21no—
256C2×Dic6—21no—
257C2×Dic6—21no—
258C2×Dic6—21no—
259C2×Dic6—21no—
260C2×Dic6—21no—
261C3×Q16—44no—
262C2×C3×C8—21no—
263C2×C3×C8—21no—
264C2×C3×C8—21no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8C2×D412yes—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—42no—
272C3×C4⋊C4—42no—
273C3×C4⋊C4#4112yes—
274C3×C22⋊C4—42no—
275C3×C22⋊C4—42no—
276#217—22no—
277#217—42no—
278#217—81no—
279#216—44no—
280(C2×D3)⋊C4—22no—
281(C2×D3)⋊C4—42no—
282(C2×D3)⋊C4—42no—
283(C2×D3)⋊C4—42no—
284(C2×D3)⋊C4—81no—
285C4⋊Dic3—21no—
286C4⋊Dic3—21no—
287C4⋊Dic3—21no—
288C4⋊Dic3—21no—
289C4⋊Dic3—21no—
290C4⋊Dic3—42no—
291C4⋊Dic3—42no—
292C4⋊Dic3C2×D412yes—
293Dic3⋊C4—22no—
294Dic3⋊C4—42no—
295Dic3⋊C4—42no—
296Dic3⋊C4—42no—
297Dic3⋊C4—42no—
298Dic3⋊C4—42no—
299Dic3⋊C4—42no—
300Dic3⋊C4—81no—
301C4×Dic3—42no—
302C4×Dic3—42no—
303C4×Dic3C2×D412yes—
304C4×Dic3#4112yes—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—44no—
310C2×C3⋊C8C2×D412yes—
311C2×C3⋊C8C2×D412yes—
312D3×C8—44no—
313C22×Q8—31no—
314C22×Q8C22×D311yescharacteristic
315C22×Q8C22×D311yescharacteristic
316C22×D4—31no—
317C23×C4—31no—
318C23×C4C22×D311yescharacteristic
319C2×Q16—22no—
320C2×Q16—22no—
321C2×Q16—41no—
322C2×Q16—62no—
323C2×Q16—62no—
324C2×Q16—121no—
325C22×C8—31no—
326C22×C8—31no—
327C22×C8—62no—
328C22×C8—62no—
329C22×C8—62no—
330C22×C8—62no—
331C22×C8—121no—
332C22×C8—121no—
333C22×C8C22×D311yescharacteristic
334C22×C8C22×D311yescharacteristic
335C4⋊Q8—62no—
336C4⋊Q8—62no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C22⋊Q8—41no—
340C22⋊Q8—41no—
341C22⋊Q8—62no—
342C22⋊Q8—62no—
343C22⋊Q8—62no—
344C22⋊Q8—62no—
345C22⋊Q8—121no—
346C22⋊Q8—121no—
347C22⋊Q8—121no—
348C22⋊Q8—121no—
349C4×Q8—62no—
350C4×Q8—62no—
351C4×D4—62no—
352C4×D4—62no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
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⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4C22×D311yescharacteristic
369C2×C4⋊C4C22×D311yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—31no—
373C2×C22⋊C4—31no—
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×C42—31no—
381C2×C42—61no—
382C2×C42—61no—
383#107—62no—
384#107—62no—
385C4⋊C8—34no—
386#103—22no—
387#103—34no—
388#103—41no—
389#103—62no—
390#103—62no—
391#103—62no—
392#103—62no—
393#103—121no—
394C22⋊C8—22no—
395C22⋊C8—62no—
396C4×C8—62no—
397#95—61no—
398#95—61no—
399#95—61no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3C2×Q1612yes—
407C23×C3C22×D411yescharacteristic
408C22×D3—21no—
409C22×D3—21no—
410C22×D3—21no—
411C22×D3—21no—
412C22×D3—21no—
413C22×D3—21no—
414C22×D3C2×Q1612yes—
415C3×Q8—22no—
416C3×Q8—22no—
417C3×Q8—41no—
418C3×Q8—41no—
419C3×Q8—41no—
420C3×Q8—41no—
421C3×Q8—41no—
422C3×Q8—41no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—21no—
428C2×C3×C4—41no—
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×C4C22×D411yescharacteristic
443C2×C3×C4C22×D411yescharacteristic
444C2×C3×C4C2×#4111yescharacteristic
445C2×C3×C4C2×#4111yescharacteristic
446C2×C3×C4H(5,𝔽2)11yescharacteristic
447C2×C3×C4H(5,𝔽2)11yescharacteristic
448#67—28no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—22no—
454C2×Dic3—21no—
455C2×Dic3—41no—
456C2×Dic3—41no—
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#12112yes—
467C2×Dic3#12112yes—
468C2×Dic3C2×Q1612yes—
469C2×Dic3#13512yes—
470C4×D3—41no—
471C4×D3—41no—
472C4×D3—41no—
473C4×D3—41no—
474Dic6—41no—
475Dic6—41no—
476Dic6—41no—
477Dic6—41no—
478C3×C8—22no—
479C3×C8—41no—
480C3⋊C8—22no—
481C3⋊C8—22no—
482C24—31no—
483C24D3×D411yescharacteristic
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—61no—
496C2×Q8—61no—
497C2×Q8—61no—
498C2×Q8—61no—
499C2×Q8—61no—
500C2×Q8—61no—
501C2×Q8D3×D412yes—
502C2×D4—34no—
503C2×D4—62no—
504C2×D4—62no—
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—31no—
516C22×C4—31no—
517C22×C4—31no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4D3×D411yescharacteristic
529C22×C4C23×D311yescharacteristic
530Q16—44no—
531Q16—124no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—32no—
538C2×C8—32no—
539C2×C8—61no—
540C2×C8—61no—
541C2×C8—61no—
542C2×C8—61no—
543C2×C8—124no—
544C2×C8—124no—
545C2×C8D3×D412yes—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—32no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—62no—
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—
564C4⋊C4—122no—
565C4⋊C4—122no—
566C4⋊C4—241no—
567C4⋊C4#23712yes—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—62no—
571C22⋊C4—62no—
572C22⋊C4—122no—
573C22⋊C4—122no—
574C22⋊C4—122no—
575C22⋊C4—122no—
576C22⋊C4—241no—
577C22⋊C4—241no—
578C42—32no—
579C42—32no—
580C42—122no—
581C42—122no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3C2×#12111yescharacteristic
590C22×C3D4211yescharacteristic
591C22×C3#54611yescharacteristic
592C22×C3C22×Q1611yescharacteristic
593C22×C3C2×#13511yescharacteristic
594C22×C3#57711yescharacteristic
595C22×C3#57811yescharacteristic
596C2×D3—22no—
597C2×D3—22no—
598C2×D3—22no—
599C2×D3—41no—
600C2×D3—41no—
601C2×D3—41no—
602C2×D3—41no—
603C3×C4—41no—
604C3×C4—42no—
605C3×C4—42no—
606C3×C4—81no—
607C3×C4—81no—
608C3×C4#53211yescharacteristic
609C3×C4#54011yescharacteristic
610C3×C4D4211yescharacteristic
611C3×C4#55011yescharacteristic
612Dic3—22no—
613Dic3—41no—
614Dic3—42no—
615Dic3—81no—
616Dic3—81no—
617Dic3—81no—
618Dic3#46714yescomplemented
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—32no—
626C23—61no—
627C23—61no—
628C23—61no—
629C23—61no—
630C23—61no—
631C23—61no—
632C23D3×Q1612yes—
633C23C2×D3×D411yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—41no—
637Q8—41no—
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8—41no—
642Q8—121no—
643Q8—121no—
644Q8—121no—
645Q8—121no—
646D4—68no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—32no—
653C2×C4—32no—
654C2×C4—32no—
655C2×C4—32no—
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—61no—
671C2×C4—61no—
672C2×C4—62no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
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—121no—
686C2×C4—121no—
687C2×C4—121no—
688C2×C4—121no—
689C2×C4—121no—
690C2×C4—121no—
691C2×C4C2×D3×D411yescharacteristic
692C2×C4C2×D3×D411yescharacteristic
693C2×C4C2×#23711yescharacteristic
694C2×C4#100411yescharacteristic
695C2×C4#100411yescharacteristic
696C2×C4D3×#4111yescharacteristic
697C8—22no—
698C8—41no—
699C8—62no—
700C8—62no—
701C2×C3—42no—
702C2×C3#242811yescharacteristic
703C2×C3C2×#46711yescharacteristic
704C2×C3#306311yescharacteristic
705C2×C3#328411yescharacteristic
706C2×C3D4×Q1611yescharacteristic
707C2×C3#329911yescharacteristic
708C2×C3#330211yescharacteristic
709D3—42no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—62no—
718C22—62no—
719C22—62no—
720C22—121no—
721C22—121no—
722C22—121no—
723C22—121no—
724C22#559011yescharacteristic
725C22#559111yescharacteristic
726C22D3×#12111yescharacteristic
727C22C2×D3×Q1611yescharacteristic
728C22D3×#13511yescharacteristic
729C22#577811yescharacteristic
730C22#577911yescharacteristic
731C4—34no—
732C4—42no—
733C4—41no—
734C4—42no—
735C4—62no—
736C4—81no—
737C4—81no—
738C4—121no—
739C4—122no—
740C4—241no—
741C4—241no—
742C4—241no—
743C4#559011yescharacteristic
744C4#559611yescharacteristic
745C4#561511yescharacteristic
746C4#571811yescharacteristic
747C3#2538611yescharacteristic, complemented, Sylow
748C2—42no—
749C2—122no—
750C2#7667111yescharacteristic
751C2#8019311yescharacteristic
752C2#8021111yescharacteristic
753C2#8024811yescharacteristic
754C2#8027011yescharacteristic
755C2D3×#46711yescharacteristic
756C2#8090711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2001C2
socleC23×C3C22×D4
prime radicalC22×#67D4
hypercenter#2001D3
hypocenterC3#25386
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

Complements

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

NH ≅ G/Ntype
1. C2×#5188C2semidirect
2. C2×#5182C2semidirect
5. C2×#5051C2semidirect
7. C3×#2001C2semidirect
8. #71696C2semidirect
9. #70275C2semidirect
10. #70273C2semidirect
11. #70225C2semidirect
12. Dic3×#103C2semidirect
13. #69937C2semidirect
14. #68882C2semidirect
15. #68795C2semidirect
73. #2001D3semidirect
154. #835D4semidirect
241. C2×#67Q16semidirect
618. Dic3#467semidirect
747. C3#25386semidirect

Maximal subgroups

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

subgroupindex
C2×#51882
C2×#51822
#827802
#827782
C2×#50512
C2×#67⋊C82
C3×#20012
#716962
#702752
#702732
#702252
Dic3×#1032
#699372
#688822
#687952
#253863