Finite Group Databasebeta

← #10846259

Subgroups — #10846259

Order 768.

1052 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×SD16C211yesmaximal, characteristic, complemented
2C2×#5171C211yesmaximal, characteristic, complemented
3C2×#5168C211yesmaximal, characteristic, complemented
4#82495C211yesmaximal, characteristic, complemented
5#82408C211yesmaximal, characteristic, complemented
6C2×#4864C211yesmaximal, characteristic, complemented
7#71632C211yesmaximal, characteristic, complemented
8#71613C211yesmaximal, characteristic, complemented
9#70560C211yesmaximal, characteristic, complemented
10#70273C211yesmaximal, characteristic, complemented
11#70245C211yesmaximal, characteristic, complemented
12#70204C211yesmaximal, characteristic
13#70178C211yesmaximal, characteristic, complemented
14C8×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
15#69774C211yesmaximal, characteristic, complemented
16#25411—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C2×C3×C4×Q8C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#947C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C22×#216C2211yescharacteristic
23C2×#938C2211yescharacteristic
24C2×#936C2211yescharacteristic
25C22×#213C2211yescharacteristic
26C22×#204C2211yescharacteristic
27C22×D3×C8C2211yescharacteristic
28C2×#897C2211yescharacteristic
29C2×#895C2211yescharacteristic
30C3×C4×SD16—24no—
31C2×C3×#106C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×C4×C8C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#832C2211yescharacteristic
37#5213—21no—
38#5212—21no—
39#5171—24no—
40#5168—24no—
41C2×#821C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×#817C2211yescharacteristic
44C2×#816C2211yescharacteristic
45C2×C8×Dic3C2211yescharacteristic
46#4994—21no—
47#4991—21no—
48#4984C2211yescharacteristic
49#4984C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#809C2211yescharacteristic
52#4961—21no—
53#4953—21no—
54#4940—21no—
55#4939—21no—
56#4939C2211yescharacteristic
57C4×(C2×D3)⋊C4C2211yescharacteristic
58#4929C2211yescharacteristic
59#4864—24no—
60#4550C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#495—31no—
65C2×#465—31no—
66C2×#465—31no—
67C2×C4×SD16D311yescharacteristic, complemented
68#2427—31no—
69#2426—31no—
70#2042—31no—
71#2042—31no—
72#2001—31no—
73#1999—31no—
74#1968—31no—
75#1941—31no—
76#1879—31no—
77#1878—31no—
78C8×C22⋊C4—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C22×#67—21no—
83C22×D12—21no—
84C22×D12C2311yescharacteristic
85C22×C4×D3C2311yescharacteristic
86C22×Dic6C2311yescharacteristic
87C2×C3×SD16—22no—
88C2×C3×SD16—22no—
89C2×C3×SD16D414yescomplemented
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C3×C4×Q8—22no—
93C3×C4×Q8—41no—
94C3×C4×D4—22no—
95C3×C4×D4—41no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C22⋊C4—21no—
100C2×C3×C42—21no—
101C2×C3×C42C2311yescharacteristic
102C2×#217—21no—
103C2×#217—21no—
104C2×#217—21no—
105#947—22no—
106#947—41no—
107#946—22no—
108#946—41no—
109C2×#216—22no—
110C2×#216—22no—
111C2×#216—41no—
112#938—22no—
113#938—41no—
114#936—22no—
115#936—41no—
116C2×#213—22no—
117C2×#213—22no—
118C2×#213—41no—
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)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4D411yescharacteristic
127C2×(C2×D3)⋊C4D411yescharacteristic
128C2×C4⋊Dic3—21no—
129C2×C4⋊Dic3—21no—
130C2×C4⋊Dic3—21no—
131C2×C4⋊Dic3C2311yescharacteristic
132C2×C4⋊Dic3C2311yescharacteristic
133C2×Dic3⋊C4—21no—
134C2×C4×Dic3C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137C2×#204—22no—
138C2×#204—22no—
139C2×#204—22no—
140C2×D3×C8—22no—
141C2×D3×C8—22no—
142C2×D3×C8—22no—
143#897—22no—
144#897—41no—
145#895—22no—
146#895—41no—
147C3×#106D414yescomplemented
148C3×#103—22no—
149C3×#102—22no—
150C3×C4×C8—22no—
151#835—22no—
152#832—22no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95D411yescharacteristic
158C3⋊#95D411yescharacteristic
159#821—41no—
160(C2×D3)⋊C8—22no—
161#817—22no—
162#816—41no—
163C8×Dic3—22no—
164#810—22no—
165#809—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×Q8C2×D311yescharacteristic
178C2×C4×D4C2×D311yescharacteristic
179#495—64no—
180#465—64no—
181#465—64no—
182C4×SD16—24no—
183C2×#106—31no—
184C2×#106C2×D311yescharacteristic
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×C8C2×D311yescharacteristic
196#397—61no—
197#396—61no—
198#394—61no—
199#394—61no—
200#391—31no—
201#390—31no—
202#390—61no—
203#389—31no—
204#389—31no—
205#388—61no—
206#386—61no—
207#380—61no—
208C4×C22⋊C4—31no—
209#340—31no—
210#340—31no—
211#336—31no—
212#336—31no—
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×D4C2×D412yes—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—42no—
232C22×C3×C4—42no—
233C22×C3×C4—81no—
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2411yescharacteristic
237C2×#67—42no—
238C2×#67—42no—
239C2×#67—81no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3C2×D411yescharacteristic
244C22×Dic3C2×D411yescharacteristic
245C22×Dic3C2×D411yescharacteristic
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—42no—
253C2×D12—42no—
254C2×D12—81no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×Dic6—21no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C3×SD16—28no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8C2×D412yes—
272C2×C3×C8C2×D412yes—
273C2×C3×C8#4112yes—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—42no—
277C3×C4⋊C4C2×D412yes—
278C3×C4⋊C4C2×D412yes—
279C3×C22⋊C4—42no—
280C3×C42—21no—
281C3×C42—21no—
282C3×C42—42no—
283#217—42no—
284#217—42no—
285#217—42no—
286#216—44no—
287#213—44no—
288(C2×D3)⋊C4—22no—
289(C2×D3)⋊C4—22no—
290(C2×D3)⋊C4—42no—
291(C2×D3)⋊C4—42no—
292(C2×D3)⋊C4—42no—
293(C2×D3)⋊C4—42no—
294(C2×D3)⋊C4—42no—
295(C2×D3)⋊C4—42no—
296(C2×D3)⋊C4—81no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3—42no—
302C4⋊Dic3—81no—
303C4⋊Dic3—81no—
304Dic3⋊C4—42no—
305C4×Dic3—21no—
306C4×Dic3—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
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—21no—
322C23×C4—31no—
323C2×Q16—62no—
324C2×Q16—62no—
325C2×Q16—121no—
326C2×SD16—22no—
327C2×SD16—22no—
328C2×SD16—62no—
329C2×SD16—62no—
330C2×SD16—62no—
331C2×SD16D1214yescomplemented
332C2×D8—62no—
333C2×D8—62no—
334C2×D8—121no—
335C22×C8—31no—
336C22×C8—31no—
337C22×C8—62no—
338C22×C8—62no—
339C22×C8—62no—
340C22×C8C22×D311yescharacteristic
341C22×C8C22×D311yescharacteristic
342#124—62no—
343#124—62no—
344#124—121no—
345#124—121no—
346C22⋊Q8—62no—
347C22⋊Q8—62no—
348C22⋊Q8—121no—
349C22⋊Q8—121no—
350#121—62no—
351#121—62no—
352#121—121no—
353#121—121no—
354C4×Q8—22no—
355C4×Q8—41no—
356C4×D4—22no—
357C4×D4—41no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—31no—
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—31no—
369C2×C22⋊C4—31no—
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×C22⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C42—21no—
381C2×C42—31no—
382C2×C42C22×D311yescharacteristic
383#106—62no—
384#106#6714yescomplemented
385#103—22no—
386#103—62no—
387#103—62no—
388#103—121no—
389#102—22no—
390#102—62no—
391#102—62no—
392#102—121no—
393C22⋊C8—62no—
394C4×C8—22no—
395C4×C8—62no—
396#95—31no—
397#95—31no—
398#95—61no—
399#95—61no—
400#95—61no—
401#95—61no—
402C23×C3—22no—
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—22no—
429C3×D4—22no—
430C3×D4—41no—
431C3×D4—41no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
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—84no—
447C2×C3×C4#13512yes—
448C2×C3×C4C22×D411yescharacteristic
449C2×C3×C4C22×D411yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×C3×C4C2×#4111yescharacteristic
452C2×C3×C4H(5,𝔽2)11yescharacteristic
453C2×C3×C4H(5,𝔽2)11yescharacteristic
454#67—84no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473D12—41no—
474D12—41no—
475D12—41no—
476D12—41no—
477D12—84no—
478C4×D3—41no—
479C4×D3—41no—
480C4×D3—41no—
481C4×D3—41no—
482Dic6—41no—
483Dic6—41no—
484Dic6—41no—
485Dic6—41no—
486C3×C8—41no—
487C3×C8#12114yes—
488C3⋊C8—22no—
489C3⋊C8—41no—
490C24—21no—
491C24—31no—
492C24—61no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—61no—
499C2×Q8—61no—
500C2×Q8—61no—
501C2×Q8—61no—
502C2×Q8—61no—
503C2×Q8—61no—
504C2×Q8C2×D1212yes—
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—
522C2×D4C2×D1212yes—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—31no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—81no—
541C22×C4D3×D411yescharacteristic
542C22×C4D3×D411yescharacteristic
543C22×C4C23×D311yescharacteristic
544Q16—124no—
545SD16—28no—
546SD16—124no—
547D8—124no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—32no—
552C2×C8—61no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—61no—
557C2×C8—124no—
558C2×C8C2×D1212yes—
559C2×C8#23512yes—
560C2×C8C2×#6712yes—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—42no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—61no—
568C4⋊C4—122no—
569C4⋊C4—122no—
570C4⋊C4—241no—
571C4⋊C4—241no—
572C4⋊C4C2×#6712yes—
573C4⋊C4C2×#6712yes—
574C22⋊C4—42no—
575C22⋊C4—62no—
576C22⋊C4—62no—
577C22⋊C4—122no—
578C22⋊C4—122no—
579C22⋊C4—122no—
580C22⋊C4—122no—
581C22⋊C4—122no—
582C22⋊C4—122no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C22⋊C4—122no—
586C22⋊C4—241no—
587C42—21no—
588C42—21no—
589C42—42no—
590C42—61no—
591C42—61no—
592C22×C3—42no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—81no—
596C22×C3—81no—
597C22×C3—81no—
598C22×C3—81no—
599C22×C3#53211yescharacteristic
600C22×C3D4211yescharacteristic
601C22×C3D4211yescharacteristic
602C22×C3C2×#13511yescharacteristic
603C22×C3C2×#13511yescharacteristic
604C22×C3#57711yescharacteristic
605C22×C3#57711yescharacteristic
606C2×D3—22no—
607C2×D3—22no—
608C2×D3—22no—
609C2×D3—41no—
610C2×D3—41no—
611C2×D3—41no—
612C2×D3—41no—
613C2×D3—81no—
614C2×D3—81no—
615C2×D3—81no—
616C2×D3—81no—
617C2×D3—81no—
618C2×D3—81no—
619C2×D3—81no—
620C3×C4—22no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4—41no—
624C3×C4—42no—
625C3×C4C2×#12111yescharacteristic
626C3×C4#54011yescharacteristic
627C3×C4#54611yescharacteristic
628C3×C4#55011yescharacteristic
629Dic3—41no—
630Dic3—41no—
631Dic3—41no—
632Dic3—81no—
633Dic3—81no—
634Dic3—81no—
635C23—22no—
636C23—32no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—61no—
644C23—61no—
645C23—61no—
646C23—61no—
647C23—61no—
648C23—61no—
649C23—121no—
650C23—121no—
651C23—121no—
652C23—121no—
653C23—121no—
654C23—121no—
655C23—121no—
656C23C2×D3×D411yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661Q8—121no—
662Q8—121no—
663Q8—121no—
664Q8—121no—
665D4—22no—
666D4—22no—
667D4—41no—
668D4—41no—
669D4—121no—
670D4—121no—
671D4—121no—
672D4—121no—
673D4—244no—
674D4—244no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—84no—
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—121no—
711C2×C4—121no—
712C2×C4#91612yes—
713C2×C4C22×D1211yescharacteristic
714C2×C4C2×#23511yescharacteristic
715C2×C4#100411yescharacteristic
716C2×C4D3×#4111yescharacteristic
717C2×C4#100911yescharacteristic
718C2×C4C22×#6711yescharacteristic
719C8—41no—
720C8—62no—
721C8—121no—
722C8#93014yes—
723C2×C3—82no—
724C2×C3#242811yescharacteristic
725C2×C3#316811yescharacteristic
726C2×C3#317311yescharacteristic
727C2×C3#328211yescharacteristic
728C2×C3#328211yescharacteristic
729C2×C3#328211yescharacteristic
730C2×C3#328411yescharacteristic
731D3—42no—
732D3—161no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—62no—
737C22—62no—
738C22—62no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—121no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—241no—
748C22—241no—
749C22—241no—
750C22—241no—
751C22—241no—
752C22—241no—
753C22—241no—
754C22#554811yescharacteristic
755C22D4×D1211yescharacteristic
756C22C2×#91611yescharacteristic
757C22#576211yescharacteristic
758C22D3×#13511yescharacteristic
759C22#577011yescharacteristic
760C22D4×#6711yescharacteristic
761C4—22no—
762C4—42no—
763C4—41no—
764C4—42no—
765C4—42no—
766C4—121no—
767C4—121no—
768C4—121no—
769C4—241no—
770C4—241no—
771C4—241no—
772C4#555411yescharacteristic
773C4#556211yescharacteristic
774C4C2×#93011yescharacteristic
775C4#583411yescharacteristic
776C3#2541111yescharacteristic, complemented, Sylow
777C2—82no—
778C2—122no—
779C2—481no—
780C2#7966311yescharacteristic
781C2#7966611yescharacteristic
782C2#7967411yescharacteristic
783C2#7967511yescharacteristic
784C2#8240911yescharacteristic
785C2#8386711yescharacteristic
786C2#8391911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×C4×SD16C2
socleC23×C3C22×D4
prime radical#70204C2
hypercenterC2×C4×SD16D3
hypocenterC3#25411
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×SD16C2semidirect
2. C2×#5171C2semidirect
3. C2×#5168C2semidirect
4. #82495C2semidirect
5. #82408C2semidirect
6. C2×#4864C2semidirect
7. #71632C2semidirect
8. #71613C2semidirect
9. #70560C2semidirect
10. #70273C2semidirect
11. #70245C2semidirect
13. #70178C2semidirect
14. C8×(C2×D3)⋊C4C2semidirect
15. #69774C2semidirect
67. C2×C4×SD16D3semidirect
89. C2×C3×SD16D4semidirect
147. C3×#106D4semidirect
331. C2×SD16D12semidirect
384. #106#67semidirect
776. C3#25411semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×SD162
C2×#51712
C2×#51682
#824952
#824082
C2×#48642
#716322
#716132
#705602
#702732
#702452
#702042
#701782
C8×(C2×D3)⋊C42
#697742
#254113