Finite Group Databasebeta

← #10702999

Subgroups — #10702999

Order 768.

1210 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#102C211yesmaximal, characteristic
2C2×#5221C211yesmaximal, characteristic
3C22×#832C211yesmaximal, characteristic
4C2×#4551C211yesmaximal, characteristic, complemented
5C2×#4550C211yesmaximal, characteristic, complemented
6#71563C211yesmaximal, characteristic, complemented
7C2×#4529C211yesmaximal, characteristic, complemented
8#11189—31nomaximal, Sylow
9C23×C3×D4C2211yescharacteristic
10C23×C3×C8C2211yescharacteristic
11C22×C3×C4⋊C4C2211yescharacteristic
12C22×#217—21no—
13C22×#217—21no—
14C22×C4⋊Dic3C2211yescharacteristic
15C22×C4⋊Dic3C2211yescharacteristic
16C22×C4×Dic3C2211yescharacteristic
17C23×C3⋊C8C2211yescharacteristic
18C2×C3×#102—22no—
19C2×C3×#102—22no—
20C2×C3×#102C414yescomplemented
21#5221—22no—
22#5221—22no—
23C2×#832—22no—
24C2×#832—22no—
25C2×#832—22no—
26C2×C3⋊#95—21no—
27C2×C3⋊#95—21no—
28#4551—22no—
29#4550—22no—
30#4529—22no—
31C22×#102—31no—
32C22×#102D311yescharacteristic
33C2×#390—31no—
34C2×#340—31no—
35C2×#340—31no—
36C2×#336—31no—
37C4⋊#95—31no—
38C25×C3—21no—
39C22×C3×D4—21no—
40C22×C3×D4—21no—
41C22×C3×D4—21no—
42C22×C3×D4—21no—
43C22×C3×D4—21no—
44C22×C3×D4—21no—
45C22×C3×D4—21no—
46C22×C3×D4—21no—
47C22×C3×D4—21no—
48C22×C3×D4—21no—
49C22×C3×D4—21no—
50C22×C3×D4C2×C412yes—
51C22×C3×D4D412yes—
52C22×C3×D4D412yes—
53C23×C3×C4—21no—
54C23×C3×C4C2311yescharacteristic
55C23×Dic3—21no—
56C23×Dic3—21no—
57C23×Dic3D411yescharacteristic
58C23×Dic3D411yescharacteristic
59C22×C3×C8—21no—
60C22×C3×C8—21no—
61C22×C3×C8—21no—
62C22×C3×C8—21no—
63C22×C3×C8—21no—
64C22×C3×C8—21no—
65C22×C3×C8C2×C412yes—
66C2×C3×C4⋊C4—21no—
67C2×C3×C4⋊C4—21no—
68C2×C3×C4⋊C4—21no—
69C2×C3×C4⋊C4—21no—
70C2×C3×C4⋊C4—21no—
71C2×C3×C4⋊C4C2×C412yes—
72C2×#217—24no—
73C2×#217—24no—
74C2×#217—42no—
75C2×#217—42no—
76C2×#217—42no—
77C2×#217—42no—
78C2×C4⋊Dic3—21no—
79C2×C4⋊Dic3—21no—
80C2×C4⋊Dic3—21no—
81C2×C4⋊Dic3—21no—
82C2×C4⋊Dic3—21no—
83C2×C4⋊Dic3—21no—
84C2×C4⋊Dic3—21no—
85C2×C4⋊Dic3—21no—
86C2×C4⋊Dic3—21no—
87C2×C4⋊Dic3—21no—
88C2×C4⋊Dic3D412yes—
89C2×C4⋊Dic3D412yes—
90C2×C4×Dic3—21no—
91C2×C4×Dic3—21no—
92C2×C4×Dic3—21no—
93C2×C4×Dic3—21no—
94C2×C4×Dic3—21no—
95C2×C4×Dic3—21no—
96C22×C3⋊C8—21no—
97C22×C3⋊C8—21no—
98C22×C3⋊C8—21no—
99C22×C3⋊C8—21no—
100C22×C3⋊C8—21no—
101C22×C3⋊C8—21no—
102C22×C3⋊C8D412yes—
103C3×#102—28no—
104#832—28no—
105C3⋊#95—42no—
106C3⋊#95—42no—
107C23×D4C2×D311yescharacteristic
108C23×C8—31no—
109C23×C8C2×D311yescharacteristic
110C22×C4⋊C4—31no—
111C22×C4⋊C4—31no—
112C22×C4⋊C4C2×D311yescharacteristic
113C22×C22⋊C4—61no—
114C22×C22⋊C4—61no—
115C22×C42—31no—
116C2×#102—22no—
117C2×#102—22no—
118C2×#102—62no—
119C2×#102—62no—
120C2×#102—62no—
121C2×#102Dic314yescomplemented
122#390—62no—
123#390—62no—
124C2×#95—61no—
125C2×#95—61no—
126#340—62no—
127#340—62no—
128#336—62no—
129C24×C3—22no—
130C24×C3—22no—
131C24×C3—22no—
132C24×C3—41no—
133C24×C3—41no—
134C24×C3—41no—
135C24×C3—41no—
136C24×C3—41no—
137C24×C3—41no—
138C24×C3—41no—
139C24×C3—41no—
140C24×C3—41no—
141C24×C3—41no—
142C24×C3—41no—
143C24×C3—41no—
144C24×C3C2×D411yescharacteristic
145C2×C3×D4—22no—
146C2×C3×D4—22no—
147C2×C3×D4—22no—
148C2×C3×D4—22no—
149C2×C3×D4—22no—
150C2×C3×D4—22no—
151C2×C3×D4—22no—
152C2×C3×D4—22no—
153C2×C3×D4—22no—
154C2×C3×D4—22no—
155C2×C3×D4—22no—
156C2×C3×D4—22no—
157C2×C3×D4—22no—
158C2×C3×D4—22no—
159C2×C3×D4—22no—
160C2×C3×D4—41no—
161C2×C3×D4—41no—
162C2×C3×D4—41no—
163C2×C3×D4—41no—
164C2×C3×D4—41no—
165C2×C3×D4—41no—
166C2×C3×D4—41no—
167C2×C3×D4—41no—
168C2×C3×D4—41no—
169C2×C3×D4—41no—
170C2×C3×D4—41no—
171C2×C3×D4—41no—
172C2×C3×D4C22⋊C414yes—
173C22×C3×C4—22no—
174C22×C3×C4—41no—
175C22×C3×C4—41no—
176C22×C3×C4—41no—
177C22×C3×C4—41no—
178C22×C3×C4—41no—
179C22×C3×C4—41no—
180C22×C3×C4C22×C411yescharacteristic
181C22×C3×C4C2×D411yescharacteristic
182C22×C3×C4C2×D411yescharacteristic
183C22×C3×C4C2×D411yescharacteristic
184C22×C3×C4C2×D411yescharacteristic
185C22×C3×C4C2×D411yescharacteristic
186C22×C3×C4#4111yescharacteristic
187C22×C3×C4#4111yescharacteristic
188C22×C3×C4#4111yescharacteristic
189C22×C3×C4#4111yescharacteristic
190C22×C3×C4#4111yescharacteristic
191C22×C3×C4#4111yescharacteristic
192C22×C3×C4#4111yescharacteristic
193C22×C3×C4#4111yescharacteristic
194C22×Dic3—21no—
195C22×Dic3—21no—
196C22×Dic3—21no—
197C22×Dic3—21no—
198C22×Dic3—21no—
199C22×Dic3—21no—
200C22×Dic3—21no—
201C22×Dic3—21no—
202C22×Dic3—21no—
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3—21no—
206C22×Dic3—22no—
207C22×Dic3—22no—
208C22×Dic3—41no—
209C22×Dic3—41no—
210C22×Dic3—41no—
211C22×Dic3—41no—
212C22×Dic3—41no—
213C22×Dic3—41no—
214C22×Dic3—41no—
215C22×Dic3—41no—
216C22×Dic3—41no—
217C22×Dic3—41no—
218C22×Dic3—41no—
219C22×Dic3—41no—
220C22×Dic3D812yes—
221C22×Dic3SD1612yes—
222C2×C3×C8—22no—
223C2×C3×C8—22no—
224C2×C3×C8—22no—
225C2×C3×C8—41no—
226C2×C3×C8—41no—
227C2×C3×C8—41no—
228C2×C3×C8—41no—
229C3×C4⋊C4—22no—
230C3×C4⋊C4—22no—
231C3×C4⋊C4—41no—
232C3×C4⋊C4—41no—
233#217—48no—
234#217—48no—
235C4⋊Dic3—22no—
236C4⋊Dic3—22no—
237C4⋊Dic3—22no—
238C4⋊Dic3—22no—
239C4⋊Dic3—41no—
240C4⋊Dic3—41no—
241C4⋊Dic3—41no—
242C4⋊Dic3—41no—
243C4×Dic3—41no—
244C4×Dic3—41no—
245C4×Dic3—41no—
246C4×Dic3—41no—
247C2×C3⋊C8—22no—
248C2×C3⋊C8—22no—
249C2×C3⋊C8—22no—
250C2×C3⋊C8—41no—
251C2×C3⋊C8—41no—
252C2×C3⋊C8—41no—
253C2×C3⋊C8—41no—
254C25—21no—
255C22×D4—21no—
256C22×D4—21no—
257C22×D4—21no—
258C22×D4—21no—
259C22×D4—21no—
260C22×D4—21no—
261C22×D4—21no—
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4—21no—
266C22×D4C2×Dic312yes—
267C22×D4#6712yes—
268C22×D4#6712yes—
269C23×C4—21no—
270C23×C4—31no—
271C23×C4—31no—
272C23×C4—61no—
273C23×C4—61no—
274C23×C4C22×D311yescharacteristic
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—32no—
282C22×C8—61no—
283C22×C8—61no—
284C22×C8—61no—
285C22×C8—61no—
286C22×C8—61no—
287C22×C8—61no—
288C22×C8C2×Dic312yes—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—32no—
295C2×C4⋊C4—32no—
296C2×C4⋊C4—61no—
297C2×C4⋊C4—61no—
298C2×C4⋊C4—61no—
299C2×C4⋊C4—61no—
300C2×C4⋊C4—61no—
301C2×C4⋊C4—61no—
302C2×C4⋊C4—61no—
303C2×C4⋊C4—61no—
304C2×C4⋊C4—61no—
305C2×C4⋊C4—61no—
306C2×C4⋊C4C2×Dic312yes—
307C2×C22⋊C4—64no—
308C2×C22⋊C4—64no—
309C2×C22⋊C4—122no—
310C2×C22⋊C4—122no—
311C2×C22⋊C4—122no—
312C2×C22⋊C4—122no—
313C2×C42—61no—
314C2×C42—61no—
315C2×C42—61no—
316C2×C42—61no—
317C2×C42—61no—
318C2×C42—61no—
319#102—28no—
320#102—68no—
321#95—122no—
322#95—122no—
323C23×C3—24no—
324C23×C3—42no—
325C23×C3—42no—
326C23×C3—42no—
327C23×C3—42no—
328C23×C3—42no—
329C23×C3—42no—
330C23×C3—42no—
331C23×C3—42no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—42no—
339C23×C3—42no—
340C23×C3—42no—
341C23×C3—42no—
342C23×C3—81no—
343C23×C3—81no—
344C23×C3—81no—
345C23×C3—81no—
346C23×C3—81no—
347C23×C3—81no—
348C23×C3—81no—
349C23×C3—81no—
350C23×C3—81no—
351C23×C3—81no—
352C23×C3—81no—
353C23×C3—81no—
354C23×C3—81no—
355C23×C3—81no—
356C23×C3—81no—
357C23×C3—81no—
358C23×C3C4×D411yescharacteristic
359C23×C3#12011yescharacteristic
360C23×C3#12111yescharacteristic
361C23×C3#12111yescharacteristic
362C23×C3#12111yescharacteristic
363C23×C3#12311yescharacteristic
364C23×C3#12411yescharacteristic
365C23×C3C2×D811yescharacteristic
366C23×C3C2×SD1611yescharacteristic
367C23×C3#13511yescharacteristic
368C23×C3#13511yescharacteristic
369C23×C3AGL(1,ℤ/8)11yescharacteristic
370C23×C3AGL(1,ℤ/8)11yescharacteristic
371C23×C3AGL(1,ℤ/8)11yescharacteristic
372C23×C3#13711yescharacteristic
373C3×D4—24no—
374C3×D4—24no—
375C3×D4—42no—
376C3×D4—42no—
377C3×D4—42no—
378C3×D4—42no—
379C3×D4—42no—
380C3×D4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—42no—
383C2×C3×C4—42no—
384C2×C3×C4—81no—
385C2×C3×C4—81no—
386C2×C3×C4—81no—
387C2×C3×C4—81no—
388C2×C3×C4C2×C22⋊C411yescharacteristic
389C2×C3×C4#11711yescharacteristic
390C2×C3×C4#11711yescharacteristic
391C2×C3×C4C4×D411yescharacteristic
392C2×C3×C4C4×D411yescharacteristic
393C2×C3×C4C4×D411yescharacteristic
394C2×C3×C4#12011yescharacteristic
395C2×C3×C4#12111yescharacteristic
396C2×C3×C4#12111yescharacteristic
397C2×C3×C4#12111yescharacteristic
398C2×C3×C4#12111yescharacteristic
399C2×C3×C4#12111yescharacteristic
400C2×C3×C4#12311yescharacteristic
401C2×C3×C4#12311yescharacteristic
402C2×C3×C4#12311yescharacteristic
403C2×C3×C4#12311yescharacteristic
404C2×C3×C4#12311yescharacteristic
405C2×C3×C4#12311yescharacteristic
406C2×C3×C4#12311yescharacteristic
407C2×C3×C4#12311yescharacteristic
408C2×C3×C4#12311yescharacteristic
409C2×C3×C4#12411yescharacteristic
410C2×C3×C4#12411yescharacteristic
411C2×C3×C4#12411yescharacteristic
412C2×C3×C4#12611yescharacteristic
413C2×C3×C4#12611yescharacteristic
414C2×C3×C4#12611yescharacteristic
415C2×C3×C4#12611yescharacteristic
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—41no—
423C2×Dic3—41no—
424C2×Dic3—41no—
425C2×Dic3—41no—
426C2×Dic3—41no—
427C2×Dic3—41no—
428C2×Dic3—41no—
429C2×Dic3—41no—
430C2×Dic3—42no—
431C2×Dic3—42no—
432C2×Dic3—42no—
433C2×Dic3—42no—
434C2×Dic3—42no—
435C2×Dic3—42no—
436C2×Dic3—81no—
437C2×Dic3—81no—
438C2×Dic3—81no—
439C2×Dic3—81no—
440C2×Dic3—81no—
441C2×Dic3—81no—
442C2×Dic3—81no—
443C2×Dic3—81no—
444C3×C8—42no—
445C3⋊C8—42no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—41no—
450C24—41no—
451C24—41no—
452C24—41no—
453C24—41no—
454C24—41no—
455C24—41no—
456C24—41no—
457C24—41no—
458C24—41no—
459C24—41no—
460C24—41no—
461C24D3×D411yescharacteristic
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4#21714yes—
490C22×C4—22no—
491C22×C4—32no—
492C22×C4—32no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—61no—
500C22×C4—61no—
501C22×C4—61no—
502C22×C4—61no—
503C22×C4—61no—
504C22×C4—61no—
505C22×C4—61no—
506C22×C4—61no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4—62no—
512C22×C4—62no—
513C22×C4—121no—
514C22×C4—121no—
515C22×C4—121no—
516C22×C4—121no—
517C22×C4—121no—
518C22×C4—121no—
519C22×C4—121no—
520C22×C4—121no—
521C22×C4—121no—
522C22×C4—121no—
523C22×C4—121no—
524C22×C4—121no—
525C22×C4#23511yescharacteristic
526C22×C4#23511yescharacteristic
527C22×C4#23511yescharacteristic
528C22×C4#23511yescharacteristic
529C22×C4D3×D411yescharacteristic
530C22×C4D3×D411yescharacteristic
531C22×C4D3×D411yescharacteristic
532C22×C4#23711yescharacteristic
533C22×C4#23711yescharacteristic
534C22×C4#23711yescharacteristic
535C22×C4#23711yescharacteristic
536C22×C4C22×Dic311yescharacteristic
537C22×C4C2×#6711yescharacteristic
538C22×C4C2×#6711yescharacteristic
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—62no—
547C2×C8—62no—
548C2×C8—62no—
549C2×C8—121no—
550C2×C8—121no—
551C2×C8—121no—
552C2×C8—121no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—62no—
558C4⋊C4—62no—
559C4⋊C4—62no—
560C4⋊C4—62no—
561C4⋊C4—121no—
562C4⋊C4—121no—
563C4⋊C4—121no—
564C4⋊C4—121no—
565C22⋊C4—128no—
566C22⋊C4—128no—
567C42—121no—
568C42—121no—
569C42—121no—
570C42—121no—
571C22×C3—44no—
572C22×C3—44no—
573C22×C3—44no—
574C22×C3—82no—
575C22×C3—82no—
576C22×C3—82no—
577C22×C3—82no—
578C22×C3—82no—
579C22×C3—82no—
580C22×C3—82no—
581C22×C3—82no—
582C22×C3—82no—
583C22×C3—82no—
584C22×C3—82no—
585C22×C3—82no—
586C22×C3#38611yescharacteristic
587C22×C3#38811yescharacteristic
588C22×C3#38811yescharacteristic
589C22×C3#39411yescharacteristic
590C22×C3#39411yescharacteristic
591C22×C3#39411yescharacteristic
592C22×C3#39711yescharacteristic
593C22×C3C4×D811yescharacteristic
594C22×C3C4×SD1611yescharacteristic
595C22×C3#44011yescharacteristic
596C22×C3#44211yescharacteristic
597C22×C3#44711yescharacteristic
598C22×C3#44911yescharacteristic
599C22×C3#45011yescharacteristic
600C22×C3#45211yescharacteristic
601C22×C3#45911yescharacteristic
602C22×C3#45911yescharacteristic
603C22×C3#46011yescharacteristic
604C22×C3#46111yescharacteristic
605C22×C3#46311yescharacteristic
606C22×C3#46311yescharacteristic
607C22×C3#46311yescharacteristic
608C22×C3#46411yescharacteristic
609C22×C3#46511yescharacteristic
610C22×C3#46611yescharacteristic
611C22×C3#46811yescharacteristic
612C22×C3#46911yescharacteristic
613C22×C3#48011yescharacteristic
614C22×C3#48111yescharacteristic
615C22×C3#48211yescharacteristic
616C22×C3#48211yescharacteristic
617C22×C3#48611yescharacteristic
618C22×C3#48811yescharacteristic
619C22×C3#48911yescharacteristic
620C22×C3#49011yescharacteristic
621C3×C4—82no—
622C3×C4#38111yescharacteristic
623C3×C4#38611yescharacteristic
624C3×C4#38811yescharacteristic
625C3×C4#38811yescharacteristic
626C3×C4#39411yescharacteristic
627C3×C4#39711yescharacteristic
628C3×C4#39711yescharacteristic
629C3×C4#39711yescharacteristic
630Dic3—42no—
631Dic3—42no—
632Dic3—82no—
633Dic3—82no—
634C23—24no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—81no—
654C23—81no—
655C23—81no—
656C23—81no—
657C23—81no—
658C23—81no—
659C23—81no—
660C23—81no—
661C23—81no—
662C23—81no—
663C23—81no—
664C23—81no—
665C23—81no—
666C23—81no—
667C23—81no—
668C23—81no—
669C23#88311yescharacteristic
670C23#88411yescharacteristic
671C23#88411yescharacteristic
672C23#88511yescharacteristic
673C23D3×D811yescharacteristic
674C23#91111yescharacteristic
675C23#91111yescharacteristic
676C23#91211yescharacteristic
677C23D3×SD1611yescharacteristic
678C23#91411yescharacteristic
679C23#91511yescharacteristic
680C23#91611yescharacteristic
681C23D4×Dic311yescharacteristic
682C23#93711yescharacteristic
683C23#93911yescharacteristic
684D4—24no—
685D4—24no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—62no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—122no—
714C2×C4—122no—
715C2×C4—122no—
716C2×C4—122no—
717C2×C4—122no—
718C2×C4—122no—
719C2×C4—241no—
720C2×C4—241no—
721C2×C4—241no—
722C2×C4—241no—
723C2×C4—241no—
724C2×C4—241no—
725C2×C4—241no—
726C2×C4—241no—
727C2×C4#87911yescharacteristic
728C2×C4#87911yescharacteristic
729C2×C4#87911yescharacteristic
730C2×C4#87911yescharacteristic
731C2×C4#88311yescharacteristic
732C2×C4#88311yescharacteristic
733C2×C4#88311yescharacteristic
734C2×C4#88411yescharacteristic
735C2×C4#88411yescharacteristic
736C2×C4#88511yescharacteristic
737C2×C4#88511yescharacteristic
738C2×C4#88511yescharacteristic
739C2×C4#92611yescharacteristic
740C2×C4#92611yescharacteristic
741C2×C4#92911yescharacteristic
742C2×C4#92911yescharacteristic
743C2×C4#92911yescharacteristic
744C2×C4#92911yescharacteristic
745C2×C4D4×Dic311yescharacteristic
746C2×C4D4×Dic311yescharacteristic
747C2×C4D4×Dic311yescharacteristic
748C2×C4#93511yescharacteristic
749C2×C4#93511yescharacteristic
750C2×C4#93711yescharacteristic
751C2×C4#93911yescharacteristic
752C2×C4#93911yescharacteristic
753C2×C4#93911yescharacteristic
754C2×C4C2×#21711yescharacteristic
755C8—42no—
756C8—122no—
757C2×C3—84no—
758C2×C3#144011yescharacteristic
759C2×C3#187711yescharacteristic
760C2×C3#187911yescharacteristic
761C2×C3#192511yescharacteristic
762C2×C3#192611yescharacteristic
763C2×C3#193411yescharacteristic
764C2×C3#193611yescharacteristic
765C2×C3#203311yescharacteristic
766C2×C3#203411yescharacteristic
767C2×C3#204111yescharacteristic
768C2×C3#204211yescharacteristic
769C2×C3#205411yescharacteristic
770C2×C3#205511yescharacteristic
771C2×C3#207111yescharacteristic
772C2×C3#207311yescharacteristic
773C22—44no—
774C22—44no—
775C22—44no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22#476011yescharacteristic
789C22#476211yescharacteristic
790C22#476411yescharacteristic
791C22#476511yescharacteristic
792C22#476711yescharacteristic
793C22#476811yescharacteristic
794C22#477411yescharacteristic
795C22#477511yescharacteristic
796C22#477711yescharacteristic
797C22#477811yescharacteristic
798C22#477911yescharacteristic
799C22#478011yescharacteristic
800C22#478211yescharacteristic
801C22#478411yescharacteristic
802C22#478611yescharacteristic
803C22#478711yescharacteristic
804C22#495111yescharacteristic
805C22#495111yescharacteristic
806C22#495211yescharacteristic
807C22#495911yescharacteristic
808C22#495911yescharacteristic
809C22#495911yescharacteristic
810C22Dic3×D811yescharacteristic
811C22#515011yescharacteristic
812C22#515211yescharacteristic
813C22#515311yescharacteristic
814C22#515611yescharacteristic
815C22#515811yescharacteristic
816C22Dic3×SD1611yescharacteristic
817C22#516211yescharacteristic
818C22#516411yescharacteristic
819C22#516511yescharacteristic
820C22#516911yescharacteristic
821C22#517311yescharacteristic
822C22#522011yescharacteristic
823C4—82no—
824C4—122no—
825C4—122no—
826C4—242no—
827C4—242no—
828C4#495111yescharacteristic
829C4#495111yescharacteristic
830C4#495211yescharacteristic
831C4#495211yescharacteristic
832C4#495211yescharacteristic
833C4#495911yescharacteristic
834C4#521111yescharacteristic
835C4#522011yescharacteristic
836C3#1118911yescharacteristic, complemented, Sylow
837C2—84no—
838C2#7015511yescharacteristic
839C2#7015611yescharacteristic
840C2#7016511yescharacteristic
841C2#7016611yescharacteristic
842C2#7018511yescharacteristic
843C2#7018711yescharacteristic
844C2#7020611yescharacteristic
845C2#7020711yescharacteristic
846C2#7021111yescharacteristic
847C2#7021211yescharacteristic
848C2#7021611yescharacteristic
849C2#7021711yescharacteristic
850C2#7154811yescharacteristic
851C2#7203711yescharacteristic
852C2#7204711yescharacteristic
subgroupG/H
centerC24D3×D4
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC22×C3×#102C2
socleC24×C3C2×D4
prime radicalC23×C3×D4C22
cosocleC23×C3×C4C23
hypercenterC22×#102D3
hypocenterC3#11189
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
4. C2×#4551C2semidirect
5. C2×#4550C2semidirect
6. #71563C2semidirect
7. C2×#4529C2semidirect
20. C2×C3×#102C4semidirect
121. C2×#102Dic3semidirect
836. C3#11189semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1022
C2×#52212
C22×#8322
C2×#45512
C2×#45502
#715632
C2×#45292
#111893