Finite Group Databasebeta

← #10810939

Subgroups — #10810939

Order 768.

1438 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#916C211yesmaximal, characteristic
2#82457C211yesmaximal, characteristic, complemented
3C2×#5030C211yesmaximal, characteristic, complemented
4C2×#4789C211yesmaximal, characteristic, complemented
5#76301C211yesmaximal, characteristic, complemented
6C3×#1880C211yesmaximal, characteristic, complemented
7#72048C211yesmaximal, characteristic, complemented
8#70267C211yesmaximal, characteristic, complemented
9#70199C211yesmaximal, characteristic, complemented
10#70191C211yesmaximal, characteristic, complemented
11#69648C211yesmaximal, characteristic, complemented
12#68909C211yesmaximal, characteristic, complemented
13#68868C211yesmaximal, characteristic, complemented
14#68686C211yesmaximal, characteristic, complemented
15#68648C211yesmaximal, characteristic, complemented
16#22441—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×#237C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C2×C3×C4×Q8C2211yescharacteristic
21C2×Q8×Dic3C2211yescharacteristic
22C22×#216C2211yescharacteristic
23C22×#213C2211yescharacteristic
24C2×#916—24no—
25C2×#916—24no—
26C2×#916C418yescomplemented
27C22×#204C2211yescharacteristic
28C22×D3×C8C2211yescharacteristic
29C2×#887C2211yescharacteristic
30C2×C4×Dic6C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C3×#390C2211yescharacteristic
34C2×#835C2211yescharacteristic
35#5221C2211yescharacteristic
36C2×#832C2211yescharacteristic
37C2×#821C2211yescharacteristic
38C2×(C2×D3)⋊C8C2211yescharacteristic
39C2×#816C2211yescharacteristic
40C2×#815C2211yescharacteristic
41#5030—24no—
42#4988—21no—
43#4988C2211yescharacteristic
44#4987—21no—
45#4987C2211yescharacteristic
46#4987C2211yescharacteristic
47C2×#810C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#808C2211yescharacteristic
50C2×#808C2211yescharacteristic
51#4957—21no—
52#4957—21no—
53#4942—21no—
54Dic3×C22⋊C4—21no—
55#4939—21no—
56#4939C2211yescharacteristic
57C4×(C2×D3)⋊C4—21no—
58C4×(C2×D3)⋊C4C2211yescharacteristic
59C2×#803C2211yescharacteristic
60#4789—24no—
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63#4551C2211yescharacteristic
64#4550C2211yescharacteristic
65C22×#135—31no—
66C2×#441—31no—
67C2×#441—31no—
68#2341—31no—
69#2341—31no—
70#1972—31no—
71#1972—31no—
72#1880—31no—
73#1880—31no—
74#1880—31no—
75#1880D311yescharacteristic, complemented
76#1807—31no—
77#1788—31no—
78#1788—31no—
79#1752—31no—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C22×#67—21no—
83C23×Dic3—21no—
84C2×#239—22no—
85C2×#239—22no—
86C2×#239—22no—
87C2×#239—41no—
88C2×#239—41no—
89C2×#239C2×C414yes—
90C2×#237—22no—
91C2×#237—22no—
92C2×#237—22no—
93C2×#237—41no—
94C2×#237—41no—
95C2×#237C2×C414yes—
96C22×D12—21no—
97C22×D12C2311yescharacteristic
98C22×C4×D3—21no—
99C22×C4×D3C2311yescharacteristic
100C22×Dic6C2311yescharacteristic
101C2×C3×SD16—22no—
102C2×C3×SD16—22no—
103C2×C3×SD16C2×C414yes—
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C3×C4×Q8—22no—
107C3×C4×Q8—41no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C42—21no—
114C2×C3×C42C2311yescharacteristic
115C2×#217—21no—
116C2×#217—21no—
117Q8×Dic3—22no—
118Q8×Dic3—41no—
119C2×#216C2×C414yes—
120C2×#216D414yes—
121C2×#216D414yes—
122C2×#213—22no—
123C2×#213—22no—
124C2×#213C2×C414yes—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4D411yescharacteristic
132C2×(C2×D3)⋊C4D411yescharacteristic
133C2×C4⋊Dic3—21no—
134C2×C4⋊Dic3C2311yescharacteristic
135C2×C4⋊Dic3C2311yescharacteristic
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×C4×Dic3—21no—
139C2×C4×Dic3—21no—
140C2×C4×Dic3—21no—
141C2×C4×Dic3C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144#916—232no—
145C2×#204—22no—
146C2×#204—22no—
147C2×#204C2×C414yes—
148C2×D3×C8—22no—
149C2×D3×C8—22no—
150C2×D3×C8C2×C414yes—
151#887—22no—
152#887—41no—
153C4×Dic6—22no—
154C4×Dic6—41no—
155C3×#103—22no—
156C3×#102—41no—
157#835—22no—
158#832—41no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95D411yescharacteristic
162C3⋊#95D411yescharacteristic
163#821—41no—
164(C2×D3)⋊C8—22no—
165#816—22no—
166#815—22no—
167#810—22no—
168#809—41no—
169#808—22no—
170#808—22no—
171#803—22no—
172C22×#41—31no—
173C22×#41—31no—
174C2×#135—38no—
175C2×#135—64no—
176C2×#135—64no—
177C22×Q16—31no—
178C22×SD16—31no—
179C22×SD16C2×D311yescharacteristic
180C22×D8—31no—
181C23×C8—31no—
182C2×C4×Q8—31no—
183C2×C4×Q8—31no—
184C2×C4×Q8—31no—
185C2×C4×Q8C2×D311yescharacteristic
186#441—64no—
187#441—64no—
188C2×#106—31no—
189C2×#106—31no—
190C2×#103—31no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103C2×D311yescharacteristic
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102C2×D311yescharacteristic
198C2×C22⋊C8—31no—
199C2×#97—31no—
200C2×#97—31no—
201#390—31no—
202#390—31no—
203#390—31no—
204#390—61no—
205#390—61no—
206#390—61no—
207#390—61no—
208#390C2×D311yescharacteristic
209#380—31no—
210#380—31no—
211#380—61no—
212#380—61no—
213C4×C22⋊C4—31no—
214C4×C22⋊C4—61no—
215C4×C22⋊C4—61no—
216#340—31no—
217#340C2×D311yescharacteristic
218#336—31no—
219#336C2×D311yescharacteristic
220C24×C3—21no—
221C23×D3—21no—
222C23×D3C2×D411yescharacteristic
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8C22×C412yes—
227C2×C3×Q8C2×D412yes—
228C2×C3×Q8C2×D412yes—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4C22×C412yes—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2411yescharacteristic
241C2×#67—24no—
242C2×#67—42no—
243C2×#67—42no—
244C22×Dic3—21no—
245C22×Dic3—24no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—42no—
249C22×Dic3—42no—
250C22×Dic3C2×D411yescharacteristic
251C22×Dic3C2×D411yescharacteristic
252C22×Dic3C2×D411yescharacteristic
253#239—28no—
254#239—44no—
255#239—44no—
256#239—44no—
257#237—28no—
258#237—44no—
259#237—44no—
260#237—44no—
261C2×D12—21no—
262C2×D12—21no—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—24no—
266C2×D12—21no—
267C2×D12—42no—
268C2×D12—42no—
269C2×D12C22×C412yes—
270C2×C4×D3—21no—
271C2×C4×D3—21no—
272C2×C4×D3—21no—
273C2×C4×D3—21no—
274C2×C4×D3—24no—
275C2×C4×D3—42no—
276C2×C4×D3—42no—
277C2×C4×D3C22×C412yes—
278C2×C4×D3#4112yes—
279C2×Dic6—21no—
280C2×Dic6—21no—
281C2×Dic6—21no—
282C2×Dic6C22×C412yes—
283C2×Dic6C2×D412yes—
284C2×Dic6C2×D412yes—
285C3×SD16—28no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8C22×C412yes—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—42no—
297C3×C22⋊C4—42no—
298C3×C22⋊C4—81no—
299C3×C42—21no—
300C3×C42—21no—
301C3×C42—42no—
302#217—42no—
303#217—81no—
304#216C22⋊C4116yescomplemented
305#213—28no—
306(C2×D3)⋊C4—41no—
307(C2×D3)⋊C4—41no—
308(C2×D3)⋊C4—42no—
309(C2×D3)⋊C4—42no—
310(C2×D3)⋊C4—81no—
311(C2×D3)⋊C4—81no—
312(C2×D3)⋊C4—81no—
313(C2×D3)⋊C4—81no—
314C4⋊Dic3—21no—
315C4⋊Dic3—21no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3—42no—
319Dic3⋊C4—42no—
320Dic3⋊C4—42no—
321C4×Dic3—21no—
322C4×Dic3—21no—
323C4×Dic3—42no—
324C4×Dic3—42no—
325C4×Dic3—42no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×C3⋊C8—21no—
329C2×C3⋊C8C22×C412yes—
330C2×C3⋊C8C2×D412yes—
331C2×C3⋊C8C2×D412yes—
332#204—28no—
333D3×C8—28no—
334C2×#41—34no—
335C2×#41—34no—
336C2×#41—62no—
337C2×#41—62no—
338C2×#41—62no—
339C2×#41—62no—
340C2×#41—62no—
341C2×#41—62no—
342C2×#41—121no—
343C2×#41—121no—
344C2×#41—121no—
345C2×#41—121no—
346C22×Q8—31no—
347C22×Q8C22×D311yescharacteristic
348C22×D4—31no—
349C22×D4—61no—
350C22×D4—61no—
351C22×D4C22×D311yescharacteristic
352C23×C4—31no—
353C23×C4—61no—
354C23×C4—61no—
355#135—632no—
356C2×Q16—34no—
357C2×Q16—34no—
358C2×Q16—34no—
359C2×SD16—22no—
360C2×SD16—22no—
361C2×SD16—34no—
362C2×SD16—62no—
363C2×SD16—62no—
364C2×SD16C4×D314yes—
365C2×D8—34no—
366C2×D8—62no—
367C2×D8—62no—
368C22×C8—31no—
369C22×C8—34no—
370C22×C8—31no—
371C22×C8—62no—
372C22×C8—62no—
373C22×C8C22×D311yescharacteristic
374C22×C8C22×D311yescharacteristic
375C4×Q8—22no—
376C4×Q8—41no—
377C4×Q8—62no—
378C4×Q8—62no—
379C4×Q8—62no—
380C4×Q8—121no—
381C4×Q8—121no—
382C4×Q8—121no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—61no—
387C2×C4⋊C4—61no—
388C2×C4⋊C4—61no—
389C2×C4⋊C4C22×D311yescharacteristic
390C2×C4⋊C4C22×D311yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—31no—
394C2×C22⋊C4—31no—
395C2×C22⋊C4—61no—
396C2×C22⋊C4—61no—
397C2×C22⋊C4—61no—
398C2×C22⋊C4—61no—
399C2×C22⋊C4—61no—
400C2×C22⋊C4—61no—
401C2×C22⋊C4—61no—
402C2×C22⋊C4—61no—
403C2×C42—21no—
404C2×C42—31no—
405C2×C42—61no—
406C2×C42—61no—
407C2×C42—61no—
408C2×C42C22×D311yescharacteristic
409#106—62no—
410#106—62no—
411#103—22no—
412#103—62no—
413#103—62no—
414#103—62no—
415#102—41no—
416#102—121no—
417#102—121no—
418#102—121no—
419C22⋊C8—62no—
420#97—62no—
421#97—62no—
422#95—31no—
423#95—31no—
424#95—61no—
425#95—61no—
426C23×C3—22no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3C22×D411yescharacteristic
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—21no—
440C22×D3—22no—
441C22×D3—41no—
442C22×D3—41no—
443C22×D3—41no—
444C22×D3—41no—
445C22×D3—41no—
446C22×D3—41no—
447C22×D3C4×D412yes—
448C3×Q8—22no—
449C3×Q8—22no—
450C3×Q8—22no—
451C3×Q8C2×C22⋊C414yes—
452C3×D4—22no—
453C3×D4—22no—
454C3×D4—41no—
455C3×D4—41no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4C23×C411yescharacteristic
472C2×C3×C4C22×D411yescharacteristic
473C2×C3×C4C22×D411yescharacteristic
474C2×C3×C4C2×#4111yescharacteristic
475C2×C3×C4H(5,𝔽2)11yescharacteristic
476C2×C3×C4H(5,𝔽2)11yescharacteristic
477#67—48no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—48no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3C4×D412yes—
497D12—22no—
498D12—22no—
499D12—48no—
500D12—41no—
501D12—41no—
502C4×D3—22no—
503C4×D3—22no—
504C4×D3—22no—
505C4×D3—22no—
506C4×D3—48no—
507Dic6—22no—
508Dic6—22no—
509Dic6—22no—
510Dic6C2×C22⋊C414yes—
511C3×C8—22no—
512C3×C8—41no—
513C3⋊C8—41no—
514C3⋊C8C2×C22⋊C414yes—
515C24—21no—
516C24—31no—
517C24—61no—
518#41—68no—
519#41—68no—
520#41—124no—
521#41—124no—
522#41—124no—
523#41—124no—
524#41—124no—
525#41—124no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—32no—
530C2×Q8—32no—
531C2×Q8—32no—
532C2×Q8—61no—
533C2×Q8—61no—
534C2×Q8—61no—
535C2×Q8C2×C4×D312yes—
536C2×Q8D3×D412yes—
537C2×Q8D3×D412yes—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—32no—
544C2×D4—64no—
545C2×D4—64no—
546C2×D4—61no—
547C2×D4—61no—
548C2×D4—61no—
549C2×D4—61no—
550C2×D4—61no—
551C2×D4—122no—
552C2×D4—122no—
553C2×D4—122no—
554C2×D4—122no—
555C2×D4C2×C4×D312yes—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—31no—
560C22×C4—32no—
561C22×C4—32no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—64no—
565C22×C4—64no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—122no—
574C22×C4—122no—
575C22×C4—122no—
576C22×C4—122no—
577C22×C4D3×D411yescharacteristic
578C22×C4D3×D411yescharacteristic
579C22×C4C23×D311yescharacteristic
580Q16—316no—
581SD16—28no—
582SD16—68no—
583D8—68no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—32no—
590C2×C8—32no—
591C2×C8—32no—
592C2×C8—68no—
593C2×C8—61no—
594C2×C8—61no—
595C2×C8—61no—
596C2×C8C2×C4×D312yes—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—42no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—122no—
607C4⋊C4—122no—
608C4⋊C4—122no—
609C22⋊C4—42no—
610C22⋊C4—81no—
611C22⋊C4—121no—
612C22⋊C4—121no—
613C22⋊C4—122no—
614C22⋊C4—122no—
615C22⋊C4—122no—
616C22⋊C4—241no—
617C22⋊C4—241no—
618C22⋊C4—241no—
619C22⋊C4—241no—
620C22⋊C4—241no—
621C42—21no—
622C42—21no—
623C42—42no—
624C42—61no—
625C42—61no—
626C42—122no—
627C42—122no—
628C42—122no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3—42no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3C2×C4×D411yescharacteristic
637C22×C3D4211yescharacteristic
638C22×C3D4211yescharacteristic
639C22×C3#57511yescharacteristic
640C22×C3#57511yescharacteristic
641C22×C3#57711yescharacteristic
642C22×C3#57711yescharacteristic
643C2×D3—22no—
644C2×D3—22no—
645C2×D3—22no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—42no—
651C2×D3—42no—
652C2×D3—42no—
653C2×D3—81no—
654C2×D3—81no—
655C2×D3—81no—
656C2×D3—81no—
657C3×C4—24no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—81no—
661C3×C4—81no—
662C3×C4C22×C22⋊C411yescharacteristic
663C3×C4#51811yescharacteristic
664C3×C4#54611yescharacteristic
665C3×C4#54611yescharacteristic
666Dic3—24no—
667Dic3—22no—
668Dic3—41no—
669Dic3—41no—
670Dic3—81no—
671Dic3—81no—
672C23—22no—
673C23—32no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—61no—
681C23—61no—
682C23—61no—
683C23—61no—
684C23—61no—
685C23—61no—
686C23—62no—
687C23—121no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23C2×D3×D411yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—22no—
697Q8—34no—
698Q8—62no—
699Q8—62no—
700Q8—62no—
701Q8D3×C22⋊C414yes—
702D4—22no—
703D4—22no—
704D4—41no—
705D4—41no—
706D4—62no—
707D4—62no—
708D4—128no—
709D4—128no—
710D4—121no—
711D4—121no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—32no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—61no—
731C2×C4—62no—
732C2×C4—61no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—62no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—128no—
744C2×C4—128no—
745C2×C4—121no—
746C2×C4—121no—
747C2×C4—121no—
748C2×C4—121no—
749C2×C4—121no—
750C2×C4—121no—
751C2×C4C22×C4×D311yescharacteristic
752C2×C4C2×D3×D411yescharacteristic
753C2×C4C2×D3×D411yescharacteristic
754C2×C4#100411yescharacteristic
755C2×C4D3×#4111yescharacteristic
756C2×C4#100911yescharacteristic
757C8—22no—
758C8—34no—
759C8—41no—
760C8—121no—
761C2×C3—82no—
762C2×C3D4×C22⋊C411yescharacteristic
763C2×C3#294311yescharacteristic
764C2×C3#295211yescharacteristic
765C2×C3#327111yescharacteristic
766C2×C3#327111yescharacteristic
767C2×C3#327111yescharacteristic
768C2×C3#327111yescharacteristic
769D3—42no—
770D3—82no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—62no—
775C22—62no—
776C22—62no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—121no—
782C22—121no—
783C22—121no—
784C22—121no—
785C22—122no—
786C22—122no—
787C22—122no—
788C22—241no—
789C22—241no—
790C22—241no—
791C22—241no—
792C22C4×D3×D411yescharacteristic
793C22#559011yescharacteristic
794C22#560911yescharacteristic
795C22#576211yescharacteristic
796C22#577011yescharacteristic
797C22#577311yescharacteristic
798C22#577711yescharacteristic
799C4—24no—
800C4—41no—
801C4—41no—
802C4—62no—
803C4—64no—
804C4—81no—
805C4—81no—
806C4—121no—
807C4—121no—
808C4—241no—
809C4—241no—
810C4C2×D3×C22⋊C411yescharacteristic
811C4#554511yescharacteristic
812C4#561011yescharacteristic
813C4#565411yescharacteristic
814C3#2244111yescharacteristic, complemented, Sylow
815C2—82no—
816C2—122no—
817C2—242no—
818C2#7487811yescharacteristic
819C2#7965011yescharacteristic
820C2#7977211yescharacteristic
821C2#8006511yescharacteristic
822C2#8009811yescharacteristic
823C2#8040711yescharacteristic
824C2#8061211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1880C2
socleC23×C3C22×D4
prime radicalC22×#916C2
cosocleC22×C3×C4C24
hypercenter#1880D3
hypocenterC3#22441
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
2. #82457C2semidirect
3. C2×#5030C2semidirect
4. C2×#4789C2semidirect
5. #76301C2semidirect
6. C3×#1880C2semidirect
7. #72048C2semidirect
8. #70267C2semidirect
9. #70199C2semidirect
10. #70191C2semidirect
11. #69648C2semidirect
12. #68909C2semidirect
13. #68868C2semidirect
14. #68686C2semidirect
15. #68648C2semidirect
26. C2×#916C4semidirect
75. #1880D3semidirect
304. #216C22⋊C4semidirect
814. C3#22441semidirect

Maximal subgroups

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

subgroupindex
C22×#9162
#824572
C2×#50302
C2×#47892
#763012
C3×#18802
#720482
#702672
#701992
#701912
#696482
#689092
#688682
#686862
#686482
#224413