Finite Group Databasebeta

← #10833967

Subgroups — #10833967

Order 768.

1098 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4840C211yesmaximal, characteristic, complemented
2C2×#4773C211yesmaximal, characteristic
3#76428C211yesmaximal, characteristic, complemented
4#76249C211yesmaximal, characteristic, complemented
5C3×#2067C211yesmaximal, characteristic, complemented
6#70633C211yesmaximal, characteristic, complemented
7#70628C211yesmaximal, characteristic, complemented
8#70481C211yesmaximal, characteristic, complemented
9#70198C211yesmaximal, characteristic, complemented
10#70191C211yesmaximal, characteristic, complemented
11#70186C211yesmaximal, characteristic, complemented
12#69650C211yesmaximal, characteristic, complemented
13#69629C211yesmaximal, characteristic, complemented
14#68881C211yesmaximal, characteristic, complemented
15#68856C211yesmaximal, characteristic, complemented
16#24512—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C22×#213C2211yescharacteristic
19C22×D24C2211yescharacteristic
20C2×#895C2211yescharacteristic
21C2×#892C2211yescharacteristic
22C2×#872C2211yescharacteristic
23C2×C3×#107C2211yescharacteristic, complemented
24C2×C3×C4⋊C8C2211yescharacteristic, complemented
25C2×C3×#102C2211yescharacteristic
26C2×C3×#102C2211yescharacteristic
27C3×#390C2211yescharacteristic
28C3×#389C2211yescharacteristic, complemented
29#5221C2211yescharacteristic
30C2×#832C2211yescharacteristic
31C2×#821C2211yescharacteristic
32C2×#821C2211yescharacteristic, complemented
33C2×(C2×D3)⋊C8C2211yescharacteristic
34C2×(C2×D3)⋊C8C2211yescharacteristic
35C2×#815C2211yescharacteristic, complemented
36C2×C8×Dic3C2211yescharacteristic, complemented
37#4993—21no—
38#4991—21no—
39#4988C2211yescharacteristic
40#4988C2211yescharacteristic, complemented
41#4987C2211yescharacteristic
42#4972C2211yescharacteristic, complemented
43C2×#809C2211yescharacteristic
44C2×#809C2211yescharacteristic
45C2×#809C2211yescharacteristic, complemented
46C2×#808C2211yescharacteristic, complemented
47#4957—21no—
48#4957—21no—
49#4955—21no—
50#4955—21no—
51#4939C2211yescharacteristic
52#4939C2211yescharacteristic, complemented
53C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
54#4840—24no—
55#4773—24no—
56#4675—21no—
57#4672—21no—
58C3×#340C2211yescharacteristic, complemented
59#4551C2211yescharacteristic, complemented
60#4529C2211yescharacteristic, complemented
61#4529C2211yescharacteristic, complemented
62C2×#447—31no—
63C2×#433—31no—
64#2624—31no—
65#2309—31no—
66#2067D311yescharacteristic, complemented
67#2065—31no—
68#2054—31no—
69#2054—31no—
70#1972—31no—
71#1970—31no—
72#1936—31no—
73#1934—31no—
74#1875—31no—
75#1854—31no—
76#1786—31no—
77C24×D3—21no—
78C22×C3×D4C2311yescharacteristic
79C22×#67—21no—
80C2×D3×D4—22no—
81C2×D3×D4—22no—
82C2×D3×D4—22no—
83C2×D3×D4—22no—
84C2×D3×D4—41no—
85C2×D3×D4—41no—
86C22×D12—21no—
87C22×D12C2311yescharacteristic
88C22×D12C2311yescharacteristic
89C22×C4×D3C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4C2311yescharacteristic
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C22⋊C4—21no—
97C2×C3×C22⋊C4—21no—
98C2×C3×C42C2311yescharacteristic
99C2×#217—21no—
100C2×#217—21no—
101C2×#213—22no—
102C2×#213—22no—
103C2×#213—41no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—21no—
107C2×(C2×D3)⋊C4—21no—
108C2×(C2×D3)⋊C4—21no—
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4D411yescharacteristic
116C2×(C2×D3)⋊C4D411yescharacteristic
117C2×C4⋊Dic3C2311yescharacteristic
118C2×C4⋊Dic3C2311yescharacteristic
119C2×Dic3⋊C4—21no—
120C2×Dic3⋊C4D411yescharacteristic
121C2×Dic3⋊C4D411yescharacteristic
122C2×C4×Dic3—21no—
123C2×C4×Dic3C2311yescharacteristic
124C22×C3⋊C8C2311yescharacteristic
125C22×C3⋊C8C2311yescharacteristic
126C2×D24—22no—
127C2×D24—22no—
128C2×D24—41no—
129#895—22no—
130#895—22no—
131#892—41no—
132#892—41no—
133#872—22no—
134#872—22no—
135C3×#107—41no—
136C3×C4⋊C8—22no—
137C3×#102—22no—
138C3×#102—41no—
139C3×#95—21no—
140#832—22no—
141C3⋊#95—21no—
142C3⋊#95—21no—
143#821—22no—
144#821—41no—
145(C2×D3)⋊C8—22no—
146(C2×D3)⋊C8D414yes—
147#815—22no—
148C8×Dic3—22no—
149#809—22no—
150#809—41no—
151#809—41no—
152#808—41no—
153C4⋊(C3⋊C8)—22no—
154C23×D4—31no—
155C22×D8—31no—
156C22×D8—31no—
157C2×#121—31no—
158C2×#117—31no—
159C2×#117—31no—
160#447—64no—
161#433—64no—
162C2×#107C2×D311yescharacteristic, complemented
163C2×#106—31no—
164C2×C4⋊C8—31no—
165C2×C4⋊C8C2×D311yescharacteristic, complemented
166C2×#102—31no—
167C2×#102—31no—
168C2×#102—31no—
169C2×#102—31no—
170C2×#102—31no—
171C2×#102—31no—
172C2×#102C2×D311yescharacteristic
173C2×#102C2×D311yescharacteristic
174C2×C22⋊C8—31no—
175C2×C22⋊C8—31no—
176C2×#97—31no—
177C2×C4×C8—31no—
178#399—61no—
179#397—61no—
180#394—61no—
181#394—61no—
182#390—31no—
183#390—31no—
184#390—31no—
185#390—31no—
186#390—31no—
187#390—61no—
188#390—61no—
189#390C2×D311yescharacteristic
190#389—31no—
191#389C2×D311yescharacteristic, complemented
192#380—31no—
193#379—61no—
194#379—61no—
195#340—31no—
196#340—31no—
197#340—31no—
198#340C2×D311yescharacteristic, complemented
199C24×C3—21no—
200C23×D3—21no—
201C23×D3—24no—
202C23×D3—21no—
203C23×D3—42no—
204C23×D3—42no—
205C23×D3—81no—
206C23×D3—81no—
207C23×D3—81no—
208C23×D3—81no—
209C23×D3C2×D411yescharacteristic
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4#4112yes—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4C2×D411yescharacteristic
220C22×C3×C4C2×D411yescharacteristic
221C22×C3×C4C2411yescharacteristic
222C2×#67—24no—
223C2×#67—42no—
224C2×#67—42no—
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3C2×D411yescharacteristic
228C22×Dic3C2×D411yescharacteristic
229C22×Dic3C2×D411yescharacteristic
230D3×D4—44no—
231D3×D4—44no—
232D3×D4—44no—
233D3×D4—44no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—21no—
237C2×D12—21no—
238C2×D12—21no—
239C2×D12—21no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—42no—
246C2×D12—81no—
247C2×D12—81no—
248C2×D12#4112yes—
249C2×C4×D3—21no—
250C2×C4×D3—21no—
251C2×C4×D3—21no—
252C2×C4×D3—21no—
253C2×C4×D3C2×D412yes—
254C2×C4×D3#4112yes—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8C2×D412yes—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—81no—
268C3×C22⋊C4—81no—
269C3×C22⋊C4—81no—
270C3×C42—21no—
271C3×C42—21no—
272#217—81no—
273#217—81no—
274#213—44no—
275(C2×D3)⋊C4—22no—
276(C2×D3)⋊C4—22no—
277(C2×D3)⋊C4—42no—
278(C2×D3)⋊C4—42no—
279(C2×D3)⋊C4—81no—
280(C2×D3)⋊C4—81no—
281(C2×D3)⋊C4—81no—
282(C2×D3)⋊C4—81no—
283(C2×D3)⋊C4—81no—
284(C2×D3)⋊C4—81no—
285(C2×D3)⋊C4—81no—
286(C2×D3)⋊C4—81no—
287(C2×D3)⋊C4—81no—
288C4⋊Dic3—21no—
289C4⋊Dic3—21no—
290C4⋊Dic3—21no—
291C4⋊Dic3—21no—
292Dic3⋊C4—22no—
293Dic3⋊C4—22no—
294Dic3⋊C4—81no—
295C4×Dic3—21no—
296C4×Dic3—21no—
297C4×Dic3—42no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8C2×D412yes—
304D24—44no—
305C25—61no—
306C22×D4—31no—
307C22×D4—31no—
308C22×D4—61no—
309C22×D4—62no—
310C22×D4—62no—
311C22×D4—61no—
312C22×D4—62no—
313C22×D4—62no—
314C22×D4—121no—
315C22×D4—121no—
316C22×D4C22×D311yescharacteristic
317C23×C4—31no—
318C2×D8—62no—
319C2×D8—62no—
320C2×D8—62no—
321C2×D8—62no—
322C2×D8—121no—
323C2×D8—121no—
324C22×C8—31no—
325C22×C8—31no—
326C22×C8C22×D311yescharacteristic
327C22×C8C22×D311yescharacteristic
328#121—62no—
329#121—62no—
330#117—62no—
331#117—62no—
332#117—121no—
333#117—121no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—31no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—31no—
338C2×C4⋊C4—31no—
339C2×C4⋊C4—61no—
340C2×C4⋊C4C22×D311yescharacteristic
341C2×C4⋊C4C22×D311yescharacteristic
342C2×C4⋊C4C22×D311yescharacteristic
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—31no—
346C2×C22⋊C4—31no—
347C2×C22⋊C4—61no—
348C2×C22⋊C4—61no—
349C2×C22⋊C4—61no—
350C2×C22⋊C4—61no—
351C2×C22⋊C4—61no—
352C2×C22⋊C4—61no—
353C2×C22⋊C4—61no—
354C2×C22⋊C4—61no—
355C2×C22⋊C4—61no—
356C2×C22⋊C4—61no—
357C2×C22⋊C4—61no—
358C2×C22⋊C4—61no—
359C2×C22⋊C4—61no—
360C2×C42—31no—
361C2×C42—61no—
362C2×C42C22×D311yescharacteristic
363#107—41no—
364#106—121no—
365C4⋊C8—22no—
366C4⋊C8—62no—
367#102—22no—
368#102—41no—
369#102—62no—
370#102—62no—
371#102—62no—
372#102—121no—
373#102—121no—
374#102—121no—
375C22⋊C8—34no—
376C22⋊C8—62no—
377#97—62no—
378C4×C8—62no—
379#95—21no—
380#95—61no—
381#95—61no—
382C23×C3—22no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3C22×D411yescharacteristic
390C22×D3—21no—
391C22×D3—21no—
392C22×D3—21no—
393C22×D3—21no—
394C22×D3—21no—
395C22×D3—21no—
396C22×D3—22no—
397C22×D3—48no—
398C22×D3—41no—
399C22×D3—41no—
400C22×D3—41no—
401C22×D3—41no—
402C22×D3—41no—
403C22×D3—41no—
404C22×D3—41no—
405C22×D3—41no—
406C22×D3—41no—
407C22×D3—41no—
408C22×D3—41no—
409C22×D3—41no—
410C22×D3—41no—
411C22×D3—84no—
412C22×D3—84no—
413C22×D3—84no—
414C22×D3—84no—
415C22×D3—84no—
416C22×D3—84no—
417C22×D3#12112yes—
418C3×D4—22no—
419C3×D4—22no—
420C3×D4—41no—
421C3×D4—41no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
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×C4C22×D411yescharacteristic
438C2×C3×C4C2×#4111yescharacteristic
439C2×C3×C4C2×#4111yescharacteristic
440C2×C3×C4C2×#4111yescharacteristic
441C2×C3×C4H(5,𝔽2)11yescharacteristic
442C2×C3×C4H(5,𝔽2)11yescharacteristic
443#67—48no—
444C2×Dic3—21no—
445C2×Dic3—21no—
446C2×Dic3—21no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3#12112yes—
459D12—22no—
460D12—22no—
461D12—41no—
462D12—41no—
463D12—41no—
464D12—41no—
465D12—41no—
466D12—41no—
467D12—84no—
468C4×D3—22no—
469C4×D3—22no—
470C4×D3—22no—
471C4×D3—22no—
472C3×C8—22no—
473C3×C8—41no—
474C3⋊C8—22no—
475C3⋊C8—41no—
476C24—21no—
477C24—31no—
478C24—64no—
479C24—61no—
480C24—61no—
481C24—122no—
482C24—122no—
483C24—241no—
484C24—241no—
485C24—241no—
486C24—241no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—32no—
493C2×D4—64no—
494C2×D4—61no—
495C2×D4—61no—
496C2×D4—61no—
497C2×D4—61no—
498C2×D4—61no—
499C2×D4—61no—
500C2×D4—61no—
501C2×D4—61no—
502C2×D4—61no—
503C2×D4—61no—
504C2×D4—61no—
505C2×D4—122no—
506C2×D4—122no—
507C2×D4—124no—
508C2×D4—124no—
509C2×D4—124no—
510C2×D4—124no—
511C2×D4—122no—
512C2×D4—241no—
513C2×D4—241no—
514C2×D4#23912yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—31no—
519C22×C4—32no—
520C22×C4—32no—
521C22×C4—31no—
522C22×C4—31no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4D3×D411yescharacteristic
530C22×C4D3×D411yescharacteristic
531C22×C4C23×D311yescharacteristic
532D8—124no—
533D8—124no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—32no—
540C2×C8—61no—
541C2×C8—61no—
542C2×C8—61no—
543C2×C8—61no—
544C2×C8—61no—
545C2×C8D3×D412yes—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—62no—
553C4⋊C4—62no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—81no—
559C4⋊C4—241no—
560C22⋊C4—62no—
561C22⋊C4—62no—
562C22⋊C4—81no—
563C22⋊C4—81no—
564C22⋊C4—122no—
565C22⋊C4—122no—
566C22⋊C4—241no—
567C22⋊C4—241no—
568C22⋊C4—241no—
569C22⋊C4—241no—
570C22⋊C4—241no—
571C22⋊C4—241no—
572C22⋊C4—241no—
573C22⋊C4—241no—
574C22⋊C4—241no—
575C22⋊C4—241no—
576C22⋊C4—241no—
577C42—21no—
578C42—21no—
579C42—61no—
580C42—61no—
581C42—122no—
582C22×C3—42no—
583C22×C3—42no—
584C22×C3—42no—
585C22×C3—81no—
586C22×C3—81no—
587C22×C3—81no—
588C22×C3—81no—
589C22×C3C2×#12111yescharacteristic
590C22×C3#52511yescharacteristic
591C22×C3#53511yescharacteristic
592C22×C3#57611yescharacteristic
593C22×C3#57611yescharacteristic
594C22×C3#57611yescharacteristic
595C22×C3#57711yescharacteristic
596C2×D3—22no—
597C2×D3—22no—
598C2×D3—22no—
599C2×D3—41no—
600C2×D3—41no—
601C2×D3—41no—
602C2×D3—41no—
603C2×D3—42no—
604C2×D3—42no—
605C2×D3—42no—
606C2×D3—816no—
607C2×D3—81no—
608C2×D3—81no—
609C2×D3—81no—
610C2×D3—81no—
611C2×D3—81no—
612C2×D3—81no—
613C2×D3—81no—
614C2×D3—81no—
615C2×D3—81no—
616C2×D3—81no—
617C2×D3—81no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—81no—
621C3×C4—81no—
622C3×C4—81no—
623C3×C4#54611yescharacteristic
624C3×C4#54611yescharacteristic
625C3×C4#55111yescharacteristic
626C3×C4#55111yescharacteristic
627Dic3—22no—
628Dic3—41no—
629Dic3—41no—
630Dic3—81no—
631Dic3—81no—
632C23—22no—
633C23—32no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—61no—
641C23—61no—
642C23—61no—
643C23—61no—
644C23—61no—
645C23—61no—
646C23—62no—
647C23—128no—
648C23—121no—
649C23—121no—
650C23—121no—
651C23—121no—
652C23—121no—
653C23—121no—
654C23—121no—
655C23—121no—
656C23—121no—
657C23—121no—
658C23—121no—
659C23—121no—
660C23—121no—
661C23—244no—
662C23—244no—
663C23—244no—
664C23—244no—
665C23—244no—
666C23—244no—
667C23C2×D3×D411yescharacteristic
668D4—22no—
669D4—22no—
670D4—41no—
671D4—41no—
672D4—62no—
673D4—62no—
674D4—128no—
675D4—121no—
676D4—121no—
677D4—121no—
678D4—121no—
679D4—121no—
680D4—121no—
681D4—244no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—32no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4C2×D3×D411yescharacteristic
717C2×C4#100411yescharacteristic
718C2×C4C2×#23911yescharacteristic
719C2×C4D3×#4111yescharacteristic
720C2×C4D3×#4111yescharacteristic
721C2×C4#100911yescharacteristic
722C8—22no—
723C8—41no—
724C8—62no—
725C8—121no—
726C2×C3—82no—
727C2×C3#241111yescharacteristic
728C2×C3#305811yescharacteristic
729C2×C3#306211yescharacteristic
730C2×C3#311811yescharacteristic
731C2×C3#312211yescharacteristic
732C2×C3#322011yescharacteristic
733C2×C3#322411yescharacteristic
734D3—42no—
735D3—82no—
736D3—161no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—62no—
741C22—62no—
742C22—62no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—122no—
752C22—122no—
753C22—122no—
754C22—2416no—
755C22—241no—
756C22—241no—
757C22—241no—
758C22—241no—
759C22—241no—
760C22—241no—
761C22—241no—
762C22—241no—
763C22—241no—
764C22—241no—
765C22—241no—
766C22D3×#12111yescharacteristic
767C22#560711yescharacteristic
768C22#562711yescharacteristic
769C22#575711yescharacteristic
770C22#576911yescharacteristic
771C22#577411yescharacteristic
772C22#577811yescharacteristic
773C4—41no—
774C4—41no—
775C4—62no—
776C4—81no—
777C4—81no—
778C4—81no—
779C4—121no—
780C4—121no—
781C4—241no—
782C4—241no—
783C4#561011yescharacteristic
784C4#563011yescharacteristic
785C4#563711yescharacteristic
786C4#570511yescharacteristic
787C3#2451211yescharacteristic, complemented, Sylow
788C2—82no—
789C2—122no—
790C2—242no—
791C2—481no—
792C2#7741411yescharacteristic
793C2#8034011yescharacteristic
794C2#8061011yescharacteristic
795C2#8071611yescharacteristic
796C2#8080911yescharacteristic
797C2#8095211yescharacteristic
798C2#8114611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2067C2
socleC23×C3C22×D4
prime radicalC2×#4773C2
hypercenter#2067D3
hypocenterC3#24512
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2067

Complements

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

NH ≅ G/Ntype
1. C2×#4840C2semidirect
3. #76428C2semidirect
4. #76249C2semidirect
5. C3×#2067C2semidirect
6. #70633C2semidirect
7. #70628C2semidirect
8. #70481C2semidirect
9. #70198C2semidirect
10. #70191C2semidirect
11. #70186C2semidirect
12. #69650C2semidirect
13. #69629C2semidirect
14. #68881C2semidirect
15. #68856C2semidirect
23. C2×C3×#107C22semidirect
24. C2×C3×C4⋊C8C22semidirect
28. C3×#389C22semidirect
32. C2×#821C22semidirect
35. C2×#815C22semidirect
36. C2×C8×Dic3C22semidirect
40. #4988C22semidirect
42. #4972C22semidirect
45. C2×#809C22semidirect
46. C2×#808C22semidirect
52. #4939C22semidirect
53. C2×C4⋊(C3⋊C8)C22semidirect
58. C3×#340C22semidirect
59. #4551C22semidirect
60. #4529C22semidirect
61. #4529C22semidirect
66. #2067D3semidirect
162. C2×#107C2×D3semidirect
165. C2×C4⋊C8C2×D3semidirect
191. #389C2×D3semidirect
198. #340C2×D3semidirect
787. C3#24512semidirect

Maximal subgroups

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

subgroupindex
C2×#48402
C2×#47732
#764282
#762492
C3×#20672
#706332
#706282
#704812
#701982
#701912
#701862
#696502
#696292
#688812
#688562
#245123