Finite Group Databasebeta

← #10846279

Subgroups — #10846279

Order 768.

1038 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×#5168C211yesmaximal, characteristic, complemented
2#82495C211yesmaximal, characteristic, complemented
3C2×C4×#216C211yesmaximal, characteristic, complemented
4C2×#4813C211yesmaximal, characteristic, complemented
5C2×#4775C211yesmaximal, characteristic
6#76443C211yesmaximal, characteristic, complemented
7C3×#1880C211yesmaximal, characteristic, complemented
8#72054C211yesmaximal, characteristic, complemented
9#70279C211yesmaximal, characteristic, complemented
10#70178C211yesmaximal, characteristic, complemented
11#69647C211yesmaximal, characteristic, complemented
12#68887C211yesmaximal, characteristic, complemented
13#68859C211yesmaximal, characteristic, complemented
14#68686C211yesmaximal, characteristic, complemented
15#68647C211yesmaximal, characteristic, complemented
16#25412—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C2×C3×C4×Q8C2211yescharacteristic
19C2×#947C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C22×#216C2211yescharacteristic
22C2×#938C2211yescharacteristic
23C2×#936C2211yescharacteristic
24C22×#213C2211yescharacteristic
25C22×#204C2211yescharacteristic
26C22×D3×C8C2211yescharacteristic
27C2×#897C2211yescharacteristic
28C2×#895C2211yescharacteristic
29C2×C4×Dic6C2211yescharacteristic
30C2×C3×#103C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C3×#390C2211yescharacteristic
33C2×#835C2211yescharacteristic
34C2×#832C2211yescharacteristic
35#5168—24no—
36C2×#821C2211yescharacteristic
37C2×(C2×D3)⋊C8C2211yescharacteristic
38C2×#816C2211yescharacteristic
39C2×C8×Dic3C2211yescharacteristic
40C4×#216—24no—
41#4994—21no—
42#4991—21no—
43#4984C2211yescharacteristic
44#4972C2211yescharacteristic
45C2×#810C2211yescharacteristic
46C2×#809C2211yescharacteristic
47C2×#807C2211yescharacteristic
48C2×#807C2211yescharacteristic
49#4959—21no—
50#4957—21no—
51#4951—21no—
52#4948—21no—
53#4940—21no—
54#4939—21no—
55#4939C2211yescharacteristic
56C4×(C2×D3)⋊C4C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4813—24no—
59#4775—24no—
60C3×#340C2211yescharacteristic
61C3×#336C2211yescharacteristic
62#4551C2211yescharacteristic
63#4550C2211yescharacteristic
64C2×#495—31no—
65C2×#467—31no—
66C2×#466—31no—
67C2×C4×Q16—31no—
68#2426—31no—
69#2426—31no—
70#2042—31no—
71#2042—31no—
72#2000—31no—
73#2000—31no—
74#1970—31no—
75#1942—31no—
76#1880—31no—
77#1880D311yescharacteristic, complemented
78C8×C22⋊C4—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C22×#67—21no—
82C22×D12—21no—
83C22×D12C2311yescharacteristic
84C22×C4×D3C2311yescharacteristic
85C22×Dic6C2311yescharacteristic
86C2×C3×SD16—22no—
87C2×C3×SD16—22no—
88C2×C3×SD16—41no—
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C3×C4×Q8—22no—
92C3×C4×Q8—41no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C22⋊C4—21no—
97C2×C3×C22⋊C4—21no—
98C2×C3×C42—21no—
99C2×C3×C42C2311yescharacteristic
100C2×#217—21no—
101C2×#217—21no—
102C2×#217—21no—
103#947—22no—
104#947—41no—
105#946—22no—
106#946—41no—
107C2×#216—22no—
108C2×#216—22no—
109C2×#216D414yescomplemented
110#938—22no—
111#938—41no—
112#936—22no—
113#936—41no—
114C2×#213—22no—
115C2×#213—22no—
116C2×#213—22no—
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)⋊C4—21no—
124C2×(C2×D3)⋊C4D411yescharacteristic
125C2×(C2×D3)⋊C4D411yescharacteristic
126C2×C4⋊Dic3—21no—
127C2×C4⋊Dic3—21no—
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×C4×Dic3—21no—
134C2×C4×Dic3C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137C2×#204—22no—
138C2×#204—22no—
139C2×#204—41no—
140C2×D3×C8—22no—
141C2×D3×C8—22no—
142C2×D3×C8—22no—
143#897—22no—
144#897—41no—
145#895—22no—
146#895—41no—
147C4×Dic6—22no—
148C4×Dic6—41no—
149C3×#103—22no—
150C3×#102—22no—
151#835—22no—
152#832—41no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95D411yescharacteristic
156C3⋊#95D411yescharacteristic
157#821—22no—
158(C2×D3)⋊C8—22no—
159#816—22no—
160C8×Dic3—22no—
161#810—22no—
162#809—41no—
163#807—22no—
164#807D414yes—
165C4×C3⋊C8—22no—
166C22×Q16—31no—
167C22×SD16—31no—
168C22×SD16C2×D311yescharacteristic
169C22×D8—31no—
170C23×C8—31no—
171C2×#124—31no—
172C2×#124—31no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×C4×Q8—31no—
178C2×C4×Q8C2×D311yescharacteristic
179#495—64no—
180#467—64no—
181#466—64no—
182C4×Q16—64no—
183C2×#107—31no—
184C2×#107—31no—
185C2×#103—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103C2×D311yescharacteristic
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102C2×D311yescharacteristic
193C2×C22⋊C8—31no—
194C2×C4×C8—31no—
195C2×C4×C8—31no—
196#396—61no—
197#396—61no—
198#394—61no—
199#394—61no—
200#390—31no—
201#390—61no—
202#390—61no—
203#390C2×D311yescharacteristic
204#389—31no—
205#389—31no—
206#388—61no—
207#388—61no—
208C4×C22⋊C4—31no—
209#340—31no—
210#340C2×D311yescharacteristic
211#336—31no—
212#336C2×D311yescharacteristic
213C24×C3—21no—
214C23×D3—21no—
215C23×D3C2×D411yescharacteristic
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8C2×D412yes—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2411yescharacteristic
234C2×#67—42no—
235C2×#67—42no—
236C2×#67—81no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3C2×D411yescharacteristic
241C22×Dic3C2×D411yescharacteristic
242C22×Dic3C2×D411yescharacteristic
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—42no—
250C2×D12—42no—
251C2×D12—81no—
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×Dic6—21no—
259C2×Dic6—21no—
260C2×Dic6—21no—
261C2×Dic6—21no—
262C2×Dic6—21no—
263C2×Dic6C2×D412yes—
264C3×SD16—44no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8#4112yes—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—42no—
275C3×C4⋊C4C2×D412yes—
276C3×C22⋊C4—42no—
277C3×C22⋊C4—81no—
278C3×C42—21no—
279C3×C42—21no—
280C3×C42—42no—
281#217—42no—
282#217—42no—
283#217—42no—
284#216—28no—
285#213—44no—
286(C2×D3)⋊C4—22no—
287(C2×D3)⋊C4—22no—
288(C2×D3)⋊C4—42no—
289(C2×D3)⋊C4—42no—
290(C2×D3)⋊C4—42no—
291(C2×D3)⋊C4—42no—
292(C2×D3)⋊C4—42no—
293(C2×D3)⋊C4—42no—
294(C2×D3)⋊C4—81no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—42no—
299C4⋊Dic3—81no—
300C4⋊Dic3C2×D412yes—
301Dic3⋊C4—42no—
302Dic3⋊C4—42no—
303Dic3⋊C4—81no—
304C4×Dic3—21no—
305C4×Dic3—21no—
306C4×Dic3—42no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8C2×D412yes—
311C2×C3⋊C8C2×D412yes—
312C2×C3⋊C8#4112yes—
313#204—44no—
314D3×C8—44no—
315C22×Q8—31no—
316C22×Q8C22×D311yescharacteristic
317C22×D4—31no—
318C22×D4—61no—
319C22×D4—61no—
320C22×D4C22×D311yescharacteristic
321C23×C4—31no—
322C2×Q16—34no—
323C2×Q16—62no—
324C2×Q16—62no—
325C2×SD16—22no—
326C2×SD16—22no—
327C2×SD16—41no—
328C2×SD16—62no—
329C2×SD16—62no—
330C2×SD16—121no—
331C2×D8—62no—
332C2×D8—62no—
333C2×D8—62no—
334C22×C8—31no—
335C22×C8—31no—
336C22×C8—62no—
337C22×C8—62no—
338C22×C8—62no—
339C22×C8C22×D311yescharacteristic
340C22×C8C22×D311yescharacteristic
341#124—62no—
342#124—62no—
343#124—121no—
344#124—121no—
345C22⋊Q8—62no—
346C22⋊Q8—62no—
347C22⋊Q8—121no—
348C22⋊Q8—121no—
349#121—62no—
350#121—62no—
351#121—121no—
352#121—121no—
353C4×Q8—22no—
354C4×Q8—41no—
355C4×Q8—62no—
356C4×Q8—121no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
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×C4⋊C4C22×D311yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—31no—
370C2×C22⋊C4—31no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
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×C42—21no—
382C2×C42—31no—
383C2×C42—61no—
384C2×C42C22×D311yescharacteristic
385#107—34no—
386#107—62no—
387#103—22no—
388#103—62no—
389#103—62no—
390#103—62no—
391#102—22no—
392#102—62no—
393#102—121no—
394#102—121no—
395C22⋊C8—62no—
396C4×C8—62no—
397C4×C8—62no—
398#95—31no—
399#95—31no—
400#95—61no—
401#95—61no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3C22×D411yescharacteristic
410C22×D3—21no—
411C22×D3—21no—
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—21no—
416C22×D3—41no—
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3#13512yes—
424C3×Q8—22no—
425C3×Q8—22no—
426C3×Q8—41no—
427C3×Q8—41no—
428C3×D4—41no—
429C3×D4—41no—
430C3×D4—41no—
431C3×D4—41no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
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#13512yes—
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C22×D411yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×C3×C4H(5,𝔽2)11yescharacteristic
452C2×C3×C4H(5,𝔽2)11yescharacteristic
453#67—84no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—22no—
458C2×Dic3—21no—
459C2×Dic3—22no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472D12—41no—
473D12—41no—
474D12—41no—
475D12—41no—
476D12—84no—
477C4×D3—41no—
478C4×D3—41no—
479C4×D3—41no—
480C4×D3—41no—
481Dic6—22no—
482Dic6—22no—
483Dic6—41no—
484Dic6—41no—
485C3×C8—22no—
486C3×C8—41no—
487C3⋊C8—41no—
488C3⋊C8#12114yes—
489C24—21no—
490C24—31no—
491C24—61no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—32no—
498C2×Q8—61no—
499C2×Q8—61no—
500C2×Q8—61no—
501C2×Q8—61no—
502C2×Q8—61no—
503C2×Q8D3×D412yes—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—61no—
511C2×D4—61no—
512C2×D4—61no—
513C2×D4—61no—
514C2×D4—61no—
515C2×D4—61no—
516C2×D4—122no—
517C2×D4—122no—
518C2×D4—122no—
519C2×D4—122no—
520C2×D4—241no—
521C2×D4—241no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—31no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4D3×D411yescharacteristic
538C22×C4D3×D411yescharacteristic
539C22×C4C23×D311yescharacteristic
540Q16—68no—
541SD16—44no—
542SD16—124no—
543D8—124no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—32no—
550C2×C8—32no—
551C2×C8—32no—
552C2×C8—61no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8—124no—
556C2×C8#23512yes—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—32no—
561C4⋊C4—42no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—122no—
566C4⋊C4—122no—
567C4⋊C4—122no—
568C4⋊C4—241no—
569C4⋊C4—241no—
570C4⋊C4D3×D412yes—
571C22⋊C4—42no—
572C22⋊C4—62no—
573C22⋊C4—62no—
574C22⋊C4—81no—
575C22⋊C4—122no—
576C22⋊C4—122no—
577C22⋊C4—122no—
578C22⋊C4—122no—
579C22⋊C4—122no—
580C22⋊C4—122no—
581C22⋊C4—122no—
582C22⋊C4—122no—
583C22⋊C4—122no—
584C22⋊C4—241no—
585C42—21no—
586C42—21no—
587C42—42no—
588C42—61no—
589C42—61no—
590C42—122no—
591C22×C3—81no—
592C22×C3—81no—
593C22×C3—81no—
594C22×C3—81no—
595C22×C3—81no—
596C22×C3—81no—
597C22×C3—81no—
598C22×C3#53211yescharacteristic
599C22×C3D4211yescharacteristic
600C22×C3D4211yescharacteristic
601C22×C3C2×#13511yescharacteristic
602C22×C3C2×#13511yescharacteristic
603C22×C3#57611yescharacteristic
604C22×C3#57811yescharacteristic
605C2×D3—22no—
606C2×D3—22no—
607C2×D3—22no—
608C2×D3—41no—
609C2×D3—41no—
610C2×D3—41no—
611C2×D3—41no—
612C2×D3—81no—
613C2×D3—81no—
614C2×D3—81no—
615C2×D3—81no—
616C2×D3—81no—
617C2×D3—81no—
618C2×D3—81no—
619C3×C4—22no—
620C3×C4—42no—
621C3×C4—42no—
622C3×C4—41no—
623C3×C4—81no—
624C3×C4C2×#12111yescharacteristic
625C3×C4#54011yescharacteristic
626C3×C4#54611yescharacteristic
627C3×C4#55011yescharacteristic
628Dic3—42no—
629Dic3—41no—
630Dic3—42no—
631Dic3—41no—
632Dic3—41no—
633Dic3—81no—
634C23—32no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—61no—
643C23—61no—
644C23—61no—
645C23—61no—
646C23—61no—
647C23—61no—
648C23—121no—
649C23—121no—
650C23—121no—
651C23—121no—
652C23—121no—
653C23—121no—
654C23—121no—
655C23C2×D3×D411yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—41no—
659Q8—41no—
660Q8—62no—
661Q8—62no—
662Q8—121no—
663Q8—121no—
664D4—41no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—121no—
669D4—121no—
670D4—121no—
671D4—121no—
672D4—244no—
673D4—244no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—62no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—62no—
698C2×C4—61no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4#91612yes—
711C2×C4C2×#23511yescharacteristic
712C2×C4C2×D3×D411yescharacteristic
713C2×C4C2×D3×D411yescharacteristic
714C2×C4#100411yescharacteristic
715C2×C4D3×#4111yescharacteristic
716C2×C4#100911yescharacteristic
717C8—22no—
718C8—34no—
719C8—41no—
720C8—121no—
721C2×C3—161no—
722C2×C3#242811yescharacteristic
723C2×C3#316811yescharacteristic
724C2×C3#317511yescharacteristic
725C2×C3#328011yescharacteristic
726C2×C3#328511yescharacteristic
727C2×C3#328511yescharacteristic
728C2×C3#328711yescharacteristic
729D3—42no—
730D3—161no—
731C22—62no—
732C22—62no—
733C22—62no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—121no—
742C22—121no—
743C22—121no—
744C22—121no—
745C22—241no—
746C22—241no—
747C22—241no—
748C22—241no—
749C22—241no—
750C22—241no—
751C22—241no—
752C22#554811yescharacteristic
753C22#559011yescharacteristic
754C22#560911yescharacteristic
755C22C2×#91611yescharacteristic
756C22D3×#13511yescharacteristic
757C22#577411yescharacteristic
758C22#577911yescharacteristic
759C4—22no—
760C4—42no—
761C4—41no—
762C4—42no—
763C4—81no—
764C4—121no—
765C4—121no—
766C4—122no—
767C4—122no—
768C4—121no—
769C4—241no—
770C4#549011yescharacteristic
771C4#555311yescharacteristic
772C4D3×#12111yescharacteristic
773C4#566311yescharacteristic
774C3#2541211yescharacteristic, complemented, Sylow
775C2—122no—
776C2—161no—
777C2—481no—
778C2#7469811yescharacteristic
779C2#7966311yescharacteristic
780C2#7976811yescharacteristic
781C2#8006711yescharacteristic
782C2#8010111yescharacteristic
783C2#8039411yescharacteristic
784C2#8061411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1880C2
socleC23×C3C22×D4
prime radicalC2×#4775C2
hypercenter#1880D3
hypocenterC3#25412
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
1. C2×#5168C2semidirect
2. #82495C2semidirect
3. C2×C4×#216C2semidirect
4. C2×#4813C2semidirect
6. #76443C2semidirect
7. C3×#1880C2semidirect
8. #72054C2semidirect
9. #70279C2semidirect
10. #70178C2semidirect
11. #69647C2semidirect
12. #68887C2semidirect
13. #68859C2semidirect
14. #68686C2semidirect
15. #68647C2semidirect
77. #1880D3semidirect
109. C2×#216D4semidirect
774. C3#25412semidirect

Maximal subgroups

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

subgroupindex
C2×#51682
#824952
C2×C4×#2162
C2×#48132
C2×#47752
#764432
C3×#18802
#720542
#702792
#701782
#696472
#688872
#688592
#686862
#686472
#254123