Finite Group Databasebeta

← #10845965

Subgroups — #10845965

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×#4887C211yesmaximal, characteristic, complemented
2C2×#4864C211yesmaximal, characteristic, complemented
3C2×#4845C211yesmaximal, characteristic, complemented
4C2×#4834C211yesmaximal, characteristic, complemented
5#74240C211yesmaximal, characteristic, complemented
6#73798C211yesmaximal, characteristic
7C3×#1949C211yesmaximal, characteristic, complemented
8#70634C211yesmaximal, characteristic, complemented
9#70582C211yesmaximal, characteristic, complemented
10#69551C211yesmaximal, characteristic, complemented
11C4×#810C211yesmaximal, characteristic, complemented
12#68888C211yesmaximal, characteristic, complemented
13#68887C211yesmaximal, characteristic, complemented
14#68883C211yesmaximal, characteristic, complemented
15#68882C211yesmaximal, characteristic, complemented
16#25389—31nomaximal, Sylow
17C22×Dic12C2211yescharacteristic
18C22×#204C2211yescharacteristic
19C22×D3×C8C2211yescharacteristic
20C22×D3×C8C2211yescharacteristic
21C2×#897C2211yescharacteristic
22C2×#897C2211yescharacteristic
23C2×#897C2211yescharacteristic
24C2×#897C2211yescharacteristic
25C2×#895C2211yescharacteristic
26C2×#895C2211yescharacteristic
27C2×#875C2211yescharacteristic
28C2×C4×D12C2211yescharacteristic
29C2×C4×Dic6C2211yescharacteristic
30C2×C3×#107C2211yescharacteristic
31C2×C3×#106C2211yescharacteristic
32C2×C3×C4⋊C8C2211yescharacteristic
33C3×#382C2211yescharacteristic
34C3×C4×C4⋊C4C2211yescharacteristic
35C2×#821C2211yescharacteristic
36C2×(C2×D3)⋊C8C2211yescharacteristic
37C2×(C2×D3)⋊C8C2211yescharacteristic
38C2×#816C2211yescharacteristic
39#4987C2211yescharacteristic
40#4987C2211yescharacteristic
41C2×#810C2211yescharacteristic
42C2×#810C2211yescharacteristic
43C2×#810C2211yescharacteristic
44C2×#810C2211yescharacteristic
45C2×#809C2211yescharacteristic
46C2×#809C2211yescharacteristic
47#4939—21no—
48#4939—21no—
49C2×C4×C3⋊C8C2211yescharacteristic
50#4887—24no—
51#4864—24no—
52#4845—24no—
53#4834—24no—
54#4677—21no—
55#4672—21no—
56#4671—21no—
57#4670—21no—
58#4670—21no—
59#4661—21no—
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#467—31no—
65C2×#465—31no—
66C2×#464—31no—
67C2×C8×D4—31no—
68#2540—31no—
69#2536—31no—
70#2035—31no—
71#2033—31no—
72#2001—31no—
73#2000—31no—
74#1958—31no—
75#1949D311yescharacteristic, complemented
76#1893—31no—
77#1892—31no—
78C4×#103—31no—
79C22×D12—21no—
80C22×D12—21no—
81C22×D12D411yescharacteristic
82C22×D12C2311yescharacteristic
83C22×C4×D3C2311yescharacteristic
84C22×C4×D3C2311yescharacteristic
85C22×Dic6C2311yescharacteristic
86C22×Dic6C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C2×C3×C4⋊C4C2311yescharacteristic
90C2×C3×C4⋊C4C2311yescharacteristic
91C2×C3×C4⋊C4C2311yescharacteristic
92C2×C3×C4⋊C4C2311yescharacteristic
93C2×C3×C42—21no—
94C2×C3×C42C2311yescharacteristic
95C2×(C2×D3)⋊C4—21no—
96C2×(C2×D3)⋊C4—21no—
97C2×(C2×D3)⋊C4—21no—
98C2×(C2×D3)⋊C4—21no—
99C2×(C2×D3)⋊C4—21no—
100C2×(C2×D3)⋊C4—21no—
101C2×(C2×D3)⋊C4—21no—
102C2×(C2×D3)⋊C4—21no—
103C2×(C2×D3)⋊C4—21no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4D411yescharacteristic
106C2×(C2×D3)⋊C4D411yescharacteristic
107C2×C4⋊Dic3—21no—
108C2×C4⋊Dic3—21no—
109C2×C4⋊Dic3—21no—
110C2×C4⋊Dic3—21no—
111C2×C4⋊Dic3D411yescharacteristic
112C2×C4⋊Dic3C2311yescharacteristic
113C2×Dic3⋊C4—21no—
114C2×C4×Dic3—21no—
115C22×C3⋊C8C2311yescharacteristic
116C22×C3⋊C8C2311yescharacteristic
117C2×Dic12—22no—
118C2×Dic12—22no—
119C2×Dic12—41no—
120C2×#204—22no—
121C2×#204—22no—
122C2×#204—41no—
123C2×D3×C8—22no—
124C2×D3×C8—22no—
125C2×D3×C8—22no—
126C2×D3×C8—22no—
127C2×D3×C8—41no—
128C2×D3×C8—41no—
129#897—22no—
130#897—22no—
131#897—22no—
132#897—22no—
133#897—41no—
134#897—41no—
135#897—41no—
136#897—41no—
137#895—22no—
138#895—22no—
139#895—41no—
140#895—41no—
141#875—22no—
142#875—22no—
143C4×D12—22no—
144C4×D12—22no—
145C4×Dic6—22no—
146C4×Dic6—22no—
147C3×#107—22no—
148C3×#106—22no—
149C3×C4⋊C8D414yescomplemented
150C3×#95—21no—
151C3×#95—21no—
152C3×#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155#821—22no—
156(C2×D3)⋊C8—22no—
157(C2×D3)⋊C8—22no—
158#816—22no—
159#810—22no—
160#810—22no—
161#810—41no—
162#810D414yescomplemented
163#809—22no—
164#809—41no—
165C4×C3⋊C8—22no—
166C22×Q16—31no—
167C22×SD16—31no—
168C23×C8—31no—
169C23×C8—31no—
170C2×#124—31no—
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×C4×Q8—31no—
178C2×C4×D4—31no—
179#467—64no—
180#465—64no—
181#464—64no—
182C8×D4—64no—
183C2×#107C2×D311yescharacteristic
184C2×#106C2×D311yescharacteristic
185C2×C4⋊C8C2×D311yescharacteristic
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×C4×C8—31no—
197#399—61no—
198#398—61no—
199#394—61no—
200#392—61no—
201#390—61no—
202#390—61no—
203#388—61no—
204#388—61no—
205#382C2×D311yescharacteristic
206#380—31no—
207#380—31no—
208C4×C4⋊C4C2×D311yescharacteristic
209#340—31no—
210#340—31no—
211#340C2×D311yescharacteristic
212#340C2×D311yescharacteristic
213C23×D3—21no—
214C23×D3C2×D411yescharacteristic
215C23×D3C2×D411yescharacteristic
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4C2×D411yescharacteristic
221C22×C3×C4C2×D411yescharacteristic
222C22×C3×C4C2411yescharacteristic
223C22×Dic3—21no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3C2×D411yescharacteristic
227C22×Dic3C2×D411yescharacteristic
228C2×D12—22no—
229C2×D12—22no—
230C2×D12—22no—
231C2×D12—21no—
232C2×D12—21no—
233C2×D12—21no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—21no—
237C2×D12—42no—
238C2×D12—42no—
239C2×D12—42no—
240C2×D12—42no—
241C2×D12—81no—
242C2×D12—81no—
243C2×C4×D3—21no—
244C2×C4×D3—21no—
245C2×C4×D3—21no—
246C2×C4×D3—21no—
247C2×C4×D3—21no—
248C2×C4×D3—21no—
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—
261C2×Dic6—21no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6C2×D412yes—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8C2×D412yes—
272C2×C3×C8C2×D412yes—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4C2×D412yes—
280C3×C4⋊C4#4112yes—
281C3×C42—81no—
282C3×C42C2×D412yes—
283C3×C42#4112yes—
284(C2×D3)⋊C4—22no—
285(C2×D3)⋊C4—22no—
286(C2×D3)⋊C4—42no—
287(C2×D3)⋊C4—42no—
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—42no—
295(C2×D3)⋊C4—42no—
296C4⋊Dic3—22no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3—42no—
300C4⋊Dic3—42no—
301C4⋊Dic3—42no—
302C4⋊Dic3—42no—
303Dic3⋊C4—42no—
304C4×Dic3—42no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8C2×D412yes—
311Dic12—44no—
312#204—44no—
313D3×C8—44no—
314D3×C8—44no—
315C22×Q8—31no—
316C22×Q8—31no—
317C22×D4—31no—
318C22×D4—31no—
319C22×D4—61no—
320C22×D4—61no—
321C23×C4—31no—
322C23×C4—31no—
323C2×Q16—62no—
324C2×Q16—62no—
325C2×Q16—121no—
326C2×SD16—62no—
327C2×SD16—62no—
328C2×SD16—121no—
329C22×C8—31no—
330C22×C8—31no—
331C22×C8—62no—
332C22×C8—62no—
333C22×C8—62no—
334C22×C8—62no—
335C22×C8—121no—
336C22×C8—121no—
337C22×C8C22×D311yescharacteristic
338C22×C8C22×D311yescharacteristic
339#124—62no—
340#124—62no—
341C22⋊Q8—62no—
342C22⋊Q8—62no—
343C22⋊Q8—62no—
344C22⋊Q8—62no—
345C22⋊Q8—121no—
346C22⋊Q8—121no—
347C22⋊Q8—121no—
348C22⋊Q8—121no—
349#121—62no—
350#121—62no—
351#121—121no—
352#121—121no—
353C4×Q8—62no—
354C4×Q8—62no—
355C4×D4—62no—
356C4×D4—62no—
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⋊C4C22×D311yescharacteristic
365C2×C4⋊C4C22×D311yescharacteristic
366C2×C4⋊C4C22×D311yescharacteristic
367C2×C4⋊C4C22×D311yescharacteristic
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—61no—
382C2×C42C22×D311yescharacteristic
383#107—22no—
384#106—22no—
385C4⋊C8D1214yescomplemented
386#103—34no—
387#103—62no—
388#103—62no—
389#103—62no—
390#103—121no—
391#102—62no—
392#102—62no—
393#102—121no—
394C22⋊C8—62no—
395C22⋊C8—62no—
396C4×C8—62no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—61no—
401#95—61no—
402C23×C3C22×D411yescharacteristic
403C22×D3—21no—
404C22×D3—21no—
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—21no—
408C22×D3—21no—
409C22×D3—21no—
410C22×D3—21no—
411C22×D3—21no—
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—41no—
416C22×D3—41no—
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3#13512yes—
423C22×D3#13512yes—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
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#12112yes—
441C2×C3×C4#12112yes—
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
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—22no—
452C2×Dic3—21no—
453C2×Dic3—21no—
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—
463D12—28no—
464D12—41no—
465D12—41no—
466D12—41no—
467D12—41no—
468D12—84no—
469D12—84no—
470C4×D3—41no—
471C4×D3—41no—
472C4×D3—41no—
473C4×D3—41no—
474C4×D3—41no—
475C4×D3—41no—
476C4×D3—41no—
477C4×D3—41no—
478Dic6—22no—
479Dic6—22no—
480Dic6—41no—
481Dic6—41no—
482Dic6—41no—
483Dic6—41no—
484Dic6—41no—
485Dic6—41no—
486C3×C8—22no—
487C3×C8—22no—
488C3⋊C8—22no—
489C3⋊C8—41no—
490C24—31no—
491C24—31no—
492C24—61no—
493C2×Q8—32no—
494C2×Q8—61no—
495C2×Q8—61no—
496C2×Q8—61no—
497C2×Q8—61no—
498C2×Q8—61no—
499C2×Q8—61no—
500C2×Q8—61no—
501C2×Q8—61no—
502C2×Q8—61no—
503C2×Q8—61no—
504C2×Q8—61no—
505C2×D4—62no—
506C2×D4—62no—
507C2×D4—62no—
508C2×D4—61no—
509C2×D4—61no—
510C2×D4—61no—
511C2×D4—61no—
512C2×D4—61no—
513C2×D4—61no—
514C2×D4—122no—
515C2×D4—122no—
516C2×D4—122no—
517C2×D4—122no—
518C2×D4—241no—
519C2×D4—241no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—31no—
525C22×C4—31no—
526C22×C4—61no—
527C22×C4—61no—
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×C4—61no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4D3×D411yescharacteristic
542C22×C4D3×D411yescharacteristic
543C22×C4C23×D311yescharacteristic
544Q16—124no—
545SD16—124no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—32no—
551C2×C8—61no—
552C2×C8—61no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—124no—
557C2×C8—124no—
558C2×C8C2×D1212yes—
559C2×C8C2×D1212yes—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—62no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—122no—
570C4⋊C4—122no—
571C4⋊C4—122no—
572C4⋊C4—122no—
573C4⋊C4—122no—
574C4⋊C4D3×D412yes—
575C4⋊C4#23912yes—
576C22⋊C4—62no—
577C22⋊C4—62no—
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—122no—
587C22⋊C4—122no—
588C42—81no—
589C42—122no—
590C42C2×D1212yes—
591C42#23912yes—
592C22×C3C2×#12111yescharacteristic
593C22×C3D4211yescharacteristic
594C22×C3#54611yescharacteristic
595C22×C3C2×#13511yescharacteristic
596C22×C3C2×#13511yescharacteristic
597C22×C3#57711yescharacteristic
598C22×C3#57811yescharacteristic
599C2×D3—22no—
600C2×D3—22no—
601C2×D3—22no—
602C2×D3—22no—
603C2×D3—22no—
604C2×D3—22no—
605C2×D3—41no—
606C2×D3—41no—
607C2×D3—41no—
608C2×D3—41no—
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—22no—
622C3×C4—42no—
623C3×C4—42no—
624C3×C4—81no—
625C3×C4—81no—
626C3×C4#53211yescharacteristic
627C3×C4#54011yescharacteristic
628C3×C4D4211yescharacteristic
629C3×C4#55011yescharacteristic
630Dic3—42no—
631Dic3—41no—
632Dic3—41no—
633Dic3—81no—
634Dic3—81no—
635C23—32no—
636C23—32no—
637C23—61no—
638C23—61no—
639C23—61no—
640C23—61no—
641C23—61no—
642C23—61no—
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—62no—
658Q8—62no—
659Q8—121no—
660Q8—121no—
661Q8—121no—
662Q8—121no—
663Q8—121no—
664Q8—121no—
665D4—68no—
666D4—121no—
667D4—121no—
668D4—121no—
669D4—121no—
670D4—244no—
671D4—244no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
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—62no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
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#89512yes—
712C2×C4#89512yes—
713C2×C4C22×D1211yescharacteristic
714C2×C4C2×D3×D411yescharacteristic
715C2×C4C2×#23911yescharacteristic
716C2×C4C2×#23911yescharacteristic
717C2×C4#100911yescharacteristic
718C2×C4#100911yescharacteristic
719C8—22no—
720C8—22no—
721C8—62no—
722C8—121no—
723C2×C3#242811yescharacteristic
724C2×C3#305011yescharacteristic
725C2×C3#306311yescharacteristic
726C2×C3#328211yescharacteristic
727C2×C3#328511yescharacteristic
728C2×C3#329611yescharacteristic
729C2×C3#330011yescharacteristic
730D3—42no—
731D3—42no—
732D3—161no—
733C22—62no—
734C22—62no—
735C22—62no—
736C22—62no—
737C22—62no—
738C22—62no—
739C22—121no—
740C22—121no—
741C22—121no—
742C22—121no—
743C22—121no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—241no—
748C22—241no—
749C22—241no—
750C22—241no—
751C22—241no—
752C22—241no—
753C22—241no—
754C22C2×#89511yescharacteristic
755C22#560911yescharacteristic
756C22#563011yescharacteristic
757C22D3×#13511yescharacteristic
758C22D3×#13511yescharacteristic
759C22#577511yescharacteristic
760C22#577911yescharacteristic
761C4—22no—
762C4—22no—
763C4—42no—
764C4—42no—
765C4—81no—
766C4—81no—
767C4—121no—
768C4—121no—
769C4—122no—
770C4—241no—
771C4—241no—
772C4D4×D1211yescharacteristic
773C4#557711yescharacteristic
774C4#569711yescharacteristic
775C4#572511yescharacteristic
776C3#2538911yescharacteristic, complemented, Sylow
777C2—122no—
778C2—122no—
779C2—481no—
780C2#7622011yescharacteristic
781C2#7918011yescharacteristic
782C2#7921411yescharacteristic
783C2#8055811yescharacteristic
784C2#8061411yescharacteristic
785C2#8118611yescharacteristic
786C2#8124511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1949C2
socleC23×C3C22×D4
prime radical#73798C2
hypercenter#1949D3
hypocenterC3#25389
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
1. C2×#4887C2semidirect
2. C2×#4864C2semidirect
3. C2×#4845C2semidirect
4. C2×#4834C2semidirect
5. #74240C2semidirect
7. C3×#1949C2semidirect
8. #70634C2semidirect
9. #70582C2semidirect
10. #69551C2semidirect
11. C4×#810C2semidirect
12. #68888C2semidirect
13. #68887C2semidirect
14. #68883C2semidirect
15. #68882C2semidirect
75. #1949D3semidirect
149. C3×C4⋊C8D4semidirect
162. #810D4semidirect
385. C4⋊C8D12semidirect
776. C3#25389semidirect

Maximal subgroups

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

subgroupindex
C2×#48872
C2×#48642
C2×#48452
C2×#48342
#742402
#737982
C3×#19492
#706342
#705822
#695512
C4×#8102
#688882
#688872
#688832
#688822
#253893