Finite Group Databasebeta

← #10852247

Subgroups — #10852247

Order 768.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4890C211yesmaximal, characteristic, complemented
2C2×D3×#102C211yesmaximal, characteristic
3#76431C211yesmaximal, characteristic
4#74326C211yesmaximal, characteristic, complemented
5C3×#2093C211yesmaximal, characteristic, complemented
6#70638C211yesmaximal, characteristic, complemented
7#70632C211yesmaximal, characteristic, complemented
8#70630C211yesmaximal, characteristic, complemented
9#70198C211yesmaximal, characteristic
10#70180C211yesmaximal, characteristic, complemented
11#70163C211yesmaximal, characteristic, complemented
12#69653C211yesmaximal, characteristic, complemented
13#69584C211yesmaximal, characteristic, complemented
14#68670C211yesmaximal, characteristic, complemented
15#68666C211yesmaximal, characteristic, complemented
16#25950—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C22×D3×C8C2211yescharacteristic
19C2×#896—21no—
20C2×#893C2211yescharacteristic
21C2×D3×C4⋊C4C2211yescharacteristic
22C2×#888C2211yescharacteristic, complemented
23C2×D3×C22⋊C4—21no—
24C2×C4×D12C2211yescharacteristic
25C2×C3×#107C2211yescharacteristic, complemented
26C2×C3×#107C2211yescharacteristic, complemented
27C2×C3×#102C2211yescharacteristic
28C2×C3×#102C2211yescharacteristic
29C3×#390C2211yescharacteristic
30C3×#384C2211yescharacteristic, complemented
31#5221C2211yescharacteristic
32C2×#832C2211yescharacteristic
33C2×#832C2211yescharacteristic
34C2×#821C2211yescharacteristic
35C2×#821C2211yescharacteristic
36C2×(C2×D3)⋊C8C2211yescharacteristic
37C2×#818C2211yescharacteristic, complemented
38C2×Dic3⋊C8C2211yescharacteristic, complemented
39#4989—21no—
40#4987C2211yescharacteristic
41#4987C2211yescharacteristic
42#4983—21no—
43#4979—21no—
44#4972C2211yescharacteristic, complemented
45C2×#809C2211yescharacteristic
46C2×#809C2211yescharacteristic
47C2×#807C2211yescharacteristic, complemented
48#4956—21no—
49#4956—21no—
50#4955—21no—
51C4×(C2×D3)⋊C4C2211yescharacteristic
52#4928C2211yescharacteristic, complemented
53C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
54#4890—24no—
55D3×#102—24no—
56C3×#336C2211yescharacteristic, complemented
57#4551C2211yescharacteristic, complemented
58#4550C2211yescharacteristic, complemented
59#4529C2211yescharacteristic, complemented
60#4529C2211yescharacteristic, complemented
61#4529C2211yescharacteristic, complemented
62C2×#474—31no—
63C22×#102—31no—
64#2440—31no—
65D4×C22⋊C4—31no—
66#2093D311yescharacteristic, complemented
67#2067—31no—
68#2067—31no—
69#2023—31no—
70#1862—31no—
71#1862—31no—
72#1852—31no—
73#1850—31no—
74#1808—31no—
75#1802—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—41no—
84C2×D3×D4—41no—
85C2×D3×D4Q814yescomplemented
86C22×D12C2311yescharacteristic
87C22×C4×D3—21no—
88C22×C4×D3—21no—
89C22×C4×D3—21no—
90C22×C4×D3C2311yescharacteristic
91C22×Dic6—21no—
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C22⋊C4—21no—
100C2×C3×C22⋊C4—21no—
101C2×C3×C42C2311yescharacteristic
102C2×#217—21no—
103C2×#217—21no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—21no—
107C2×(C2×D3)⋊C4—21no—
108C2×(C2×D3)⋊C4D411yescharacteristic
109C2×(C2×D3)⋊C4D411yescharacteristic
110C2×C4⋊Dic3C2311yescharacteristic
111C2×C4⋊Dic3C2311yescharacteristic
112C2×C4⋊Dic3C2311yescharacteristic
113C2×Dic3⋊C4—21no—
114C2×Dic3⋊C4—21no—
115C2×Dic3⋊C4—21no—
116C2×Dic3⋊C4—21no—
117C2×C4×Dic3C2311yescharacteristic
118C22×C3⋊C8C2311yescharacteristic
119C22×C3⋊C8C2311yescharacteristic
120C2×D3×C8—22no—
121C2×D3×C8—22no—
122C2×D3×C8—41no—
123#896—44no—
124#893—22no—
125#893—41no—
126D3×C4⋊C4—22no—
127D3×C4⋊C4—41no—
128#888—22no—
129#888—41no—
130D3×C22⋊C4—44no—
131C4×D12—22no—
132C4×D12—41no—
133C3×#107—22no—
134C3×#107—41no—
135C3×#102—22no—
136C3×#102—41no—
137#832—22no—
138#832—41no—
139C3⋊#95—21no—
140C3⋊#95—21no—
141C3⋊#95—21no—
142C3⋊#95—21no—
143C3⋊#95D411yescharacteristic
144C3⋊#95D411yescharacteristic
145#821—22no—
146#821D414yes—
147(C2×D3)⋊C8—22no—
148#818—41no—
149Dic3⋊C8—22no—
150#809—22no—
151#809—22no—
152#807—22no—
153C4⋊(C3⋊C8)—41no—
154C23×D4—31no—
155C23×C8—31no—
156C2×C4⋊Q8—31no—
157C2×C22⋊Q8—61no—
158C2×C4×D4—31no—
159C2×C4×D4—31no—
160C22×C4⋊C4—31no—
161C22×C22⋊C4—61no—
162#474—64no—
163C2×#107—31no—
164C2×#107—31no—
165C2×#107C2×D311yescharacteristic, complemented
166C2×#107C2×D311yescharacteristic, complemented
167C2×C4⋊C8—31no—
168C2×C4⋊C8—31no—
169C2×#102—31no—
170C2×#102—31no—
171C2×#102—31no—
172C2×#102—31no—
173C2×#102—31no—
174C2×#102—31no—
175C2×#102—64no—
176C2×#102C2×D311yescharacteristic
177C2×#102C2×D311yescharacteristic
178C2×C22⋊C8—31no—
179#398—61no—
180#395—61no—
181#390—31no—
182#390C2×D311yescharacteristic
183#389—31no—
184#389—31no—
185#386—61no—
186#386—61no—
187#385—61no—
188#384C2×D311yescharacteristic, complemented
189#380—31no—
190#380—31no—
191#379—61no—
192C4×C22⋊C4—31no—
193#340—31no—
194#340—31no—
195#340—31no—
196#340—31no—
197#336—31no—
198#336C2×D311yescharacteristic, complemented
199C24×C3—21no—
200C23×D3—21no—
201C23×D3—24no—
202C23×D3—42no—
203C23×D3—42no—
204C23×D3—42no—
205C23×D3—42no—
206C23×D3—81no—
207C23×D3—81no—
208C23×D3C2×D411yescharacteristic
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4C2×Q812yes—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4C2×D411yescharacteristic
220C22×C3×C4C2411yescharacteristic
221C2×#67—24no—
222C2×#67—42no—
223C2×#67—42no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3C2×D411yescharacteristic
228C22×Dic3C2×D411yescharacteristic
229C22×Dic3C2×D411yescharacteristic
230D3×D4—28no—
231D3×D4—44no—
232D3×D4—44no—
233D3×D4—44no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—21no—
237C2×D12C2×D412yes—
238C2×D12C2×Q812yes—
239C2×D12#4112yes—
240C2×C4×D3—21no—
241C2×C4×D3—21no—
242C2×C4×D3—21no—
243C2×C4×D3—21no—
244C2×C4×D3—42no—
245C2×C4×D3—42no—
246C2×C4×D3—42no—
247C2×C4×D3—42no—
248C2×C4×D3—42no—
249C2×C4×D3—42no—
250C2×C4×D3—81no—
251C2×C4×D3—81no—
252C2×C4×D3—81no—
253C2×C4×D3C2×Q812yes—
254C2×C4×D3#4112yes—
255C2×Dic6—42no—
256C2×Dic6—42no—
257C2×Dic6—81no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8—21no—
262C2×C3×C8—21no—
263C2×C3×C8C2×D412yes—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—42no—
271C3×C4⋊C4—81no—
272C3×C22⋊C4—42no—
273C3×C22⋊C4—81no—
274C3×C42—21no—
275C3×C42—21no—
276#217—42no—
277#217—81no—
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)⋊C4D814yes—
284C4⋊Dic3—21no—
285C4⋊Dic3—21no—
286C4⋊Dic3—21no—
287C4⋊Dic3—21no—
288C4⋊Dic3—21no—
289C4⋊Dic3C2×D412yes—
290Dic3⋊C4—42no—
291Dic3⋊C4—42no—
292Dic3⋊C4—42no—
293Dic3⋊C4—42no—
294C4×Dic3—21no—
295C4×Dic3—21no—
296C2×C3⋊C8—21no—
297C2×C3⋊C8—21no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302D3×C8—44no—
303C25—61no—
304C22×Q8—61no—
305C22×D4—34no—
306C22×D4—31no—
307C22×D4—62no—
308C22×D4—61no—
309C22×D4—62no—
310C22×D4—62no—
311C22×D4—121no—
312C22×D4—121no—
313C22×D4C22×D311yescharacteristic
314C23×C4—31no—
315C23×C4—61no—
316C23×C4—61no—
317C23×C4—61no—
318C22×C8—31no—
319C22×C8—31no—
320C22×C8—62no—
321C22×C8—62no—
322C22×C8—121no—
323C22×C8C22×D311yescharacteristic
324C22×C8C22×D311yescharacteristic
325C4⋊Q8—62no—
326C4⋊Q8—121no—
327C22⋊Q8—124no—
328C4×D4—62no—
329C4×D4—62no—
330C4×D4—121no—
331C4×D4—121no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—31no—
335C2×C4⋊C4—31no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—62no—
338C2×C4⋊C4—61no—
339C2×C4⋊C4—61no—
340C2×C4⋊C4—61no—
341C2×C4⋊C4—61no—
342C2×C4⋊C4—121no—
343C2×C4⋊C4C22×D311yescharacteristic
344C2×C4⋊C4C22×D311yescharacteristic
345C2×C4⋊C4C22×D311yescharacteristic
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—31no—
349C2×C22⋊C4—31no—
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—124no—
357C2×C42—31no—
358C2×C42C22×D311yescharacteristic
359#107—22no—
360#107—41no—
361#107—62no—
362#107—121no—
363C4⋊C8—62no—
364C4⋊C8—121no—
365#102—22no—
366#102—34no—
367#102—41no—
368#102—62no—
369#102—62no—
370#102—62no—
371#102—62no—
372#102—121no—
373C22⋊C8—62no—
374#95—31no—
375#95—31no—
376#95—61no—
377#95—61no—
378#95—61no—
379#95—61no—
380C23×C3—22no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3C22×D411yescharacteristic
388C22×D3—21no—
389C22×D3—21no—
390C22×D3—21no—
391C22×D3—21no—
392C22×D3—22no—
393C22×D3—22no—
394C22×D3—22no—
395C22×D3—48no—
396C22×D3—41no—
397C22×D3—41no—
398C22×D3—41no—
399C22×D3—41no—
400C22×D3—48no—
401C22×D3—84no—
402C22×D3—84no—
403C22×D3—84no—
404C22×D3—84no—
405C22×D3—84no—
406C22×D3C22⋊Q812yes—
407C22×D3C2×D812yes—
408C22×D3#13712yes—
409C3×D4—22no—
410C3×D4—22no—
411C3×D4—41no—
412C3×D4—41no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4C2×D812yes—
428C2×C3×C4C22×D411yescharacteristic
429C2×C3×C4C22×Q811yescharacteristic
430C2×C3×C4C2×#4111yescharacteristic
431C2×C3×C4C2×#4111yescharacteristic
432C2×C3×C4H(5,𝔽2)11yescharacteristic
433C2×C3×C4H(5,𝔽2)11yescharacteristic
434#67—48no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—21no—
439C2×Dic3—21no—
440C2×Dic3—22no—
441C2×Dic3—21no—
442C2×Dic3—21no—
443C2×Dic3—41no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3—41no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—41no—
450C2×Dic3—41no—
451C2×Dic3C22⋊Q812yes—
452C2×Dic3C2×D812yes—
453D12—22no—
454D12—22no—
455D12—22no—
456D12C22⋊Q814yescomplemented
457C4×D3—22no—
458C4×D3—22no—
459C4×D3—22no—
460C4×D3—22no—
461C4×D3—84no—
462C4×D3—84no—
463C4×D3—84no—
464Dic6—84no—
465C3×C8—22no—
466C3×C8—41no—
467C3⋊C8—41no—
468C3⋊C8—41no—
469C24—21no—
470C24—31no—
471C24—64no—
472C24—61no—
473C24—122no—
474C24—122no—
475C24—122no—
476C24—122no—
477C24—241no—
478C24—241no—
479C2×Q8—122no—
480C2×Q8—122no—
481C2×Q8—241no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—32no—
488C2×D4—32no—
489C2×D4—32no—
490C2×D4—64no—
491C2×D4—68no—
492C2×D4—61no—
493C2×D4—61no—
494C2×D4—61no—
495C2×D4—124no—
496C2×D4—124no—
497C2×D4—124no—
498C2×D4—122no—
499C2×D4—122no—
500C2×D4D3×Q812yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—31no—
505C22×C4—31no—
506C22×C4—32no—
507C22×C4—32no—
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—122no—
517C22×C4—122no—
518C22×C4—122no—
519C22×C4—122no—
520C22×C4—122no—
521C22×C4—122no—
522C22×C4—241no—
523C22×C4—241no—
524C22×C4—241no—
525C22×C4D3×D411yescharacteristic
526C22×C4D3×D411yescharacteristic
527C22×C4C23×D311yescharacteristic
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—61no—
534C2×C8—61no—
535C2×C8—61no—
536C2×C8—61no—
537C2×C8—61no—
538C2×C8—61no—
539C2×C8—124no—
540C2×C8D3×D412yes—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—32no—
548C4⋊C4—42no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—81no—
555C4⋊C4—122no—
556C4⋊C4—122no—
557C4⋊C4—122no—
558C4⋊C4—122no—
559C22⋊C4—34no—
560C22⋊C4—42no—
561C22⋊C4—62no—
562C22⋊C4—81no—
563C22⋊C4—122no—
564C22⋊C4—122no—
565C22⋊C4—122no—
566C22⋊C4—122no—
567C22⋊C4—122no—
568C22⋊C4—241no—
569C42—21no—
570C42—21no—
571C42—61no—
572C42—61no—
573C22×C3—42no—
574C22×C3—42no—
575C22×C3—42no—
576C22×C3—81no—
577C22×C3—81no—
578C22×C3—81no—
579C22×C3—81no—
580C22×C3C2×C22⋊Q811yescharacteristic
581C22×C3D4211yescharacteristic
582C22×C3#54611yescharacteristic
583C22×C3C22×D811yescharacteristic
584C22×C3C2×#13711yescharacteristic
585C22×C3#57611yescharacteristic
586C22×C3#57711yescharacteristic
587C2×D3—22no—
588C2×D3—22no—
589C2×D3—22no—
590C2×D3—22no—
591C2×D3—22no—
592C2×D3—22no—
593C2×D3—24no—
594C2×D3—42no—
595C2×D3—42no—
596C2×D3—42no—
597C2×D3—42no—
598C2×D3—42no—
599C2×D3—42no—
600C2×D3—816no—
601C2×D3#47414yescomplemented
602C3×C4—22no—
603C3×C4—41no—
604C3×C4—81no—
605C3×C4—81no—
606C3×C4—81no—
607C3×C4C2×C22⋊Q811yescharacteristic
608C3×C4#54311yescharacteristic
609C3×C4#54611yescharacteristic
610C3×C4#55111yescharacteristic
611Dic3—22no—
612Dic3—22no—
613Dic3—41no—
614Dic3—42no—
615Dic3—81no—
616Dic3—81no—
617C23—22no—
618C23—32no—
619C23—32no—
620C23—32no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—61no—
628C23—61no—
629C23—61no—
630C23—61no—
631C23—62no—
632C23—62no—
633C23—62no—
634C23—128no—
635C23—128no—
636C23—121no—
637C23—121no—
638C23—121no—
639C23—121no—
640C23—244no—
641C23—244no—
642C23—244no—
643C23—244no—
644C23—244no—
645C23C2×D3×D411yescharacteristic
646Q8—244no—
647D4—22no—
648D4—22no—
649D4—34no—
650D4—41no—
651D4—41no—
652D4—62no—
653D4—62no—
654D4—62no—
655D4—128no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—32no—
662C2×C4—32no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—61no—
681C2×C4—62no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—121no—
685C2×C4—121no—
686C2×C4—121no—
687C2×C4—121no—
688C2×C4—121no—
689C2×C4—121no—
690C2×C4—121no—
691C2×C4—121no—
692C2×C4—244no—
693C2×C4—244no—
694C2×C4—244no—
695C2×C4D3×D812yes—
696C2×C4C2×D3×D411yescharacteristic
697C2×C4#100411yescharacteristic
698C2×C4C2×D3×Q811yescharacteristic
699C2×C4D3×#4111yescharacteristic
700C2×C4D3×#4111yescharacteristic
701C2×C4#100911yescharacteristic
702C8—22no—
703C8—41no—
704C8—121no—
705C8—121no—
706C2×C3—82no—
707C2×C3#243711yescharacteristic
708C2×C3C2×#47411yescharacteristic
709C2×C3#308111yescharacteristic
710C2×C3#326611yescharacteristic
711C2×C3D4×D811yescharacteristic
712C2×C3#329411yescharacteristic
713C2×C3#331411yescharacteristic
714D3—24no—
715D3—44no—
716C22—34no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—62no—
721C22—62no—
722C22—62no—
723C22—62no—
724C22—62no—
725C22—62no—
726C22—64no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—122no—
732C22—122no—
733C22—122no—
734C22—122no—
735C22—122no—
736C22—122no—
737C22—2416no—
738C22D3×C22⋊Q811yescharacteristic
739C22#565411yescharacteristic
740C22#571711yescharacteristic
741C22C2×D3×D811yescharacteristic
742C22#575711yescharacteristic
743C22D3×#13711yescharacteristic
744C22#577811yescharacteristic
745C4—22no—
746C4—41no—
747C4—62no—
748C4—62no—
749C4—81no—
750C4—81no—
751C4—81no—
752C4—122no—
753C4—121no—
754C4—241no—
755C4—241no—
756C4D3×C22⋊Q811yescharacteristic
757C4#563411yescharacteristic
758C4#565411yescharacteristic
759C4#565911yescharacteristic
760C3#2595011yescharacteristic, complemented, Sylow
761C2—64no—
762C2—82no—
763C2—124no—
764C2#7810211yescharacteristic
765C2D3×#47411yescharacteristic
766C2#8096711yescharacteristic
767C2#8128911yescharacteristic
768C2#8130211yescharacteristic
769C2#8178911yescharacteristic
770C2#8188111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2093C2
socleC23×C3C22×D4
prime radicalC22×D3×D4C22
hypercenter#2093D3
hypocenterC3#25950
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2093

Complements

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

NH ≅ G/Ntype
1. C2×#4890C2semidirect
4. #74326C2semidirect
5. C3×#2093C2semidirect
6. #70638C2semidirect
7. #70632C2semidirect
8. #70630C2semidirect
10. #70180C2semidirect
11. #70163C2semidirect
12. #69653C2semidirect
13. #69584C2semidirect
14. #68670C2semidirect
15. #68666C2semidirect
22. C2×#888C22semidirect
25. C2×C3×#107C22semidirect
26. C2×C3×#107C22semidirect
30. C3×#384C22semidirect
37. C2×#818C22semidirect
38. C2×Dic3⋊C8C22semidirect
44. #4972C22semidirect
47. C2×#807C22semidirect
52. #4928C22semidirect
53. C2×C4⋊(C3⋊C8)C22semidirect
56. C3×#336C22semidirect
57. #4551C22semidirect
58. #4550C22semidirect
59. #4529C22semidirect
60. #4529C22semidirect
61. #4529C22semidirect
66. #2093D3semidirect
85. C2×D3×D4Q8semidirect
165. C2×#107C2×D3semidirect
166. C2×#107C2×D3semidirect
188. #384C2×D3semidirect
198. #336C2×D3semidirect
456. D12C22⋊Q8semidirect
601. C2×D3#474semidirect
760. C3#25950semidirect

Maximal subgroups

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

subgroupindex
C2×#48902
C2×D3×#1022
#764312
#743262
C3×#20932
#706382
#706322
#706302
#701982
#701802
#701632
#696532
#695842
#686702
#686662
#259503