Finite Group Databasebeta

← #10703000

Subgroups — #10703000

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
1C2×C3×#390C211yesmaximal, characteristic
2C22×#832C211yesmaximal, characteristic
3C22×#832C211yesmaximal, characteristic
4C2×#4529C211yesmaximal, characteristic, complemented
5C2×#4529C211yesmaximal, characteristic, complemented
6#71535C211yesmaximal, characteristic, complemented
7C2×#4524C211yesmaximal, characteristic, complemented
8#11189—31nomaximal, Sylow
9C23×C3×D4C2211yescharacteristic
10C22×C3×C4⋊C4C2211yescharacteristic
11C22×C3×C22⋊C4—21no—
12C22×C3×C22⋊C4—21no—
13C22×C3×C42C2211yescharacteristic
14C22×C4⋊Dic3C2211yescharacteristic
15C22×C4⋊Dic3C2211yescharacteristic
16C23×C3⋊C8C2211yescharacteristic
17C23×C3⋊C8C2211yescharacteristic
18C3×#390—22no—
19C3×#390—22no—
20C2×#832—22no—
21C2×#832—22no—
22C2×#832—22no—
23C2×#832—22no—
24C2×#832—22no—
25C2×#832C414yescomplemented
26C2×C3⋊#95—21no—
27C2×C3⋊#95—21no—
28#4529—22no—
29#4529—22no—
30#4524—22no—
31C22×#102—31no—
32C22×#102—31no—
33C2×#390D311yescharacteristic
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×C4D411yescharacteristic
55C23×C3×C4D411yescharacteristic
56C23×C3×C4C2311yescharacteristic
57C23×Dic3—21no—
58C23×Dic3—21no—
59C2×C3×C4⋊C4—21no—
60C2×C3×C4⋊C4—21no—
61C2×C3×C4⋊C4—21no—
62C2×C3×C4⋊C4—21no—
63C2×C3×C4⋊C4—21no—
64C2×C3×C4⋊C4D412yes—
65C2×C3×C22⋊C4—24no—
66C2×C3×C22⋊C4—24no—
67C2×C3×C22⋊C4—42no—
68C2×C3×C22⋊C4—42no—
69C2×C3×C22⋊C4—42no—
70C2×C3×C22⋊C4—42no—
71C2×C3×C42—21no—
72C2×C3×C42—21no—
73C2×C3×C42—21no—
74C2×C3×C42—21no—
75C2×C3×C42—21no—
76C2×C3×C42—21no—
77C2×C4⋊Dic3—21no—
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⋊Dic3C2×C412yes—
88C2×C4⋊Dic3D412yes—
89C22×C3⋊C8—21no—
90C22×C3⋊C8—21no—
91C22×C3⋊C8—21no—
92C22×C3⋊C8—21no—
93C22×C3⋊C8—21no—
94C22×C3⋊C8—21no—
95C22×C3⋊C8—21no—
96C22×C3⋊C8—21no—
97C22×C3⋊C8—21no—
98C22×C3⋊C8—21no—
99C22×C3⋊C8—21no—
100C22×C3⋊C8—21no—
101C22×C3⋊C8C2×C412yes—
102C22×C3⋊C8D412yes—
103#832—28no—
104#832—28no—
105C3⋊#95—42no—
106C3⋊#95—42no—
107C23×D4C2×D311yescharacteristic
108C23×C8—31no—
109C23×C8—31no—
110C22×C4⋊C4—31no—
111C22×C4⋊C4—31no—
112C22×C4⋊C4C2×D311yescharacteristic
113C22×C22⋊C4—21no—
114C22×C22⋊C4—21no—
115C22×C42C2×D311yescharacteristic
116C2×#102—34no—
117C2×#102—62no—
118C2×#102—62no—
119C2×#102—62no—
120C2×#102—62no—
121C2×#102—62no—
122#390—22no—
123#390—22no—
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—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—22no—
186C22×C3×C4—41no—
187C22×C3×C4—41no—
188C22×C3×C4—41no—
189C22×C3×C4—41no—
190C22×C3×C4—41no—
191C22×C3×C4—41no—
192C22×C3×C4D812yes—
193C22×C3×C4SD1612yes—
194C22×C3×C4C22×C411yescharacteristic
195C22×C3×C4C2×D411yescharacteristic
196C22×C3×C4C2×D411yescharacteristic
197C22×C3×C4C2×D411yescharacteristic
198C22×C3×C4C2×D411yescharacteristic
199C22×C3×C4C2×D411yescharacteristic
200C22×C3×C4#4111yescharacteristic
201C22×C3×C4#4111yescharacteristic
202C22×C3×C4#4111yescharacteristic
203C22×C3×C4#4111yescharacteristic
204C22×C3×C4#4111yescharacteristic
205C22×C3×C4#4111yescharacteristic
206C22×C3×C4#4111yescharacteristic
207C22×C3×C4#4111yescharacteristic
208C22×Dic3—22no—
209C22×Dic3—22no—
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×Dic3—41no—
221C22×Dic3—41no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—41no—
225C3×C4⋊C4—41no—
226C3×C22⋊C4—48no—
227C3×C22⋊C4—48no—
228C3×C42—41no—
229C3×C42—41no—
230C3×C42—41no—
231C3×C42—41no—
232C4⋊Dic3—22no—
233C4⋊Dic3—22no—
234C4⋊Dic3—22no—
235C4⋊Dic3—22no—
236C4⋊Dic3—41no—
237C4⋊Dic3—41no—
238C4⋊Dic3—41no—
239C4⋊Dic3—41no—
240C2×C3⋊C8—22no—
241C2×C3⋊C8—22no—
242C2×C3⋊C8—22no—
243C2×C3⋊C8—22no—
244C2×C3⋊C8—22no—
245C2×C3⋊C8—22no—
246C2×C3⋊C8—41no—
247C2×C3⋊C8—41no—
248C2×C3⋊C8—41no—
249C2×C3⋊C8—41no—
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×D4C4×D312yes—
267C22×D4D1212yes—
268C22×D4#6712yes—
269C23×C4—21no—
270C23×C4—61no—
271C23×C4—61no—
272C23×C4#6711yescharacteristic
273C23×C4#6711yescharacteristic
274C23×C4C22×D311yescharacteristic
275C22×C8—32no—
276C22×C8—32no—
277C22×C8—61no—
278C22×C8—61no—
279C22×C8—61no—
280C22×C8—61no—
281C22×C8—61no—
282C22×C8—61no—
283C22×C8—61no—
284C22×C8—61no—
285C22×C8—61no—
286C22×C8—61no—
287C22×C8—61no—
288C22×C8—61no—
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⋊C4#6712yes—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4—42no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319#102—68no—
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—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4—42no—
398C2×C3×C4—81no—
399C2×C3×C4—81no—
400C2×C3×C4—81no—
401C2×C3×C4—81no—
402C2×C3×C4C2×C22⋊C411yescharacteristic
403C2×C3×C4#11711yescharacteristic
404C2×C3×C4#11711yescharacteristic
405C2×C3×C4C4×D411yescharacteristic
406C2×C3×C4C4×D411yescharacteristic
407C2×C3×C4C4×D411yescharacteristic
408C2×C3×C4#12011yescharacteristic
409C2×C3×C4#12111yescharacteristic
410C2×C3×C4#12111yescharacteristic
411C2×C3×C4#12111yescharacteristic
412C2×C3×C4#12111yescharacteristic
413C2×C3×C4#12111yescharacteristic
414C2×C3×C4#12311yescharacteristic
415C2×C3×C4#12311yescharacteristic
416C2×C3×C4#12311yescharacteristic
417C2×C3×C4#12311yescharacteristic
418C2×C3×C4#12311yescharacteristic
419C2×C3×C4#12311yescharacteristic
420C2×C3×C4#12311yescharacteristic
421C2×C3×C4#12311yescharacteristic
422C2×C3×C4#12311yescharacteristic
423C2×C3×C4#12411yescharacteristic
424C2×C3×C4#12411yescharacteristic
425C2×C3×C4#12411yescharacteristic
426C2×C3×C4#12611yescharacteristic
427C2×C3×C4#12611yescharacteristic
428C2×C3×C4#12611yescharacteristic
429C2×C3×C4#12611yescharacteristic
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—
461C24C2×#6711yescharacteristic
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(C2×D3)⋊C414yes—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—62no—
510C22×C4—62no—
511C22×C4—121no—
512C22×C4—121no—
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#21312yes—
524C22×C4#21412yes—
525C22×C4C2×C4×D311yescharacteristic
526C22×C4C2×D1211yescharacteristic
527C22×C4#23511yescharacteristic
528C22×C4#23511yescharacteristic
529C22×C4D3×D411yescharacteristic
530C22×C4D3×D411yescharacteristic
531C22×C4#23711yescharacteristic
532C22×C4#23711yescharacteristic
533C22×C4#23711yescharacteristic
534C22×C4#23711yescharacteristic
535C22×C4#23711yescharacteristic
536C22×C4#23711yescharacteristic
537C22×C4C2×#6711yescharacteristic
538C22×C4C2×#6711yescharacteristic
539C2×C8—62no—
540C2×C8—62no—
541C2×C8—62no—
542C2×C8—62no—
543C2×C8—62no—
544C2×C8—62no—
545C2×C8—121no—
546C2×C8—121no—
547C2×C8—121no—
548C2×C8—121no—
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—48no—
566C22⋊C4—48no—
567C42—41no—
568C42—41no—
569C42—41no—
570C42—41no—
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—42no—
622C3×C4—42no—
623C3×C4—82no—
624C3×C4#38111yescharacteristic
625C3×C4#38611yescharacteristic
626C3×C4#38811yescharacteristic
627C3×C4#38811yescharacteristic
628C3×C4#39411yescharacteristic
629C3×C4#39711yescharacteristic
630C3×C4#39711yescharacteristic
631C3×C4#39711yescharacteristic
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—
669C23C4×#6711yescharacteristic
670C23#93011yescharacteristic
671C23C2×#21311yescharacteristic
672C23#93211yescharacteristic
673C23#93211yescharacteristic
674C23C2×#21411yescharacteristic
675C23#93511yescharacteristic
676C23#93611yescharacteristic
677C23#93811yescharacteristic
678C23#93911yescharacteristic
679C23#94911yescharacteristic
680C23#95011yescharacteristic
681C23#95011yescharacteristic
682C23#95111yescharacteristic
683C23#95311yescharacteristic
684D4—24no—
685D4—24no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—42no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
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#87711yescharacteristic
728C2×C4#87711yescharacteristic
729C2×C4#87911yescharacteristic
730C2×C4#87911yescharacteristic
731C2×C4#87911yescharacteristic
732C2×C4#87911yescharacteristic
733C2×C4#67⋊C411yescharacteristic
734C2×C4#67⋊C411yescharacteristic
735C2×C4#88211yescharacteristic
736C2×C4#88311yescharacteristic
737C2×C4#88311yescharacteristic
738C2×C4#88511yescharacteristic
739C2×C4#88511yescharacteristic
740C2×C4#88611yescharacteristic
741C2×C4#88611yescharacteristic
742C2×C4#88611yescharacteristic
743C2×C4C2×(C2×D3)⋊C411yescharacteristic
744C2×C4C4×#6711yescharacteristic
745C2×C4#92911yescharacteristic
746C2×C4#93011yescharacteristic
747C2×C4#93511yescharacteristic
748C2×C4#93511yescharacteristic
749C2×C4#93511yescharacteristic
750C2×C4#93611yescharacteristic
751C2×C4#93811yescharacteristic
752C2×C4#93911yescharacteristic
753C2×C4#93911yescharacteristic
754C2×C4#93911yescharacteristic
755C8—122no—
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#494411yescharacteristic
789C22#494511yescharacteristic
790C22#495311yescharacteristic
791C22#496111yescharacteristic
792C22C4×#21311yescharacteristic
793C22#501411yescharacteristic
794C22#501511yescharacteristic
795C22#501611yescharacteristic
796C22#501611yescharacteristic
797C22C4×#21411yescharacteristic
798C22#501811yescharacteristic
799C22#501911yescharacteristic
800C22#503311yescharacteristic
801C22#503411yescharacteristic
802C22#503511yescharacteristic
803C22#503511yescharacteristic
804C22#503811yescharacteristic
805C22#503911yescharacteristic
806C22#504111yescharacteristic
807C22#504211yescharacteristic
808C22#505411yescharacteristic
809C22#505511yescharacteristic
810C22#505611yescharacteristic
811C22#505711yescharacteristic
812C22#507011yescharacteristic
813C22#507111yescharacteristic
814C22#507211yescharacteristic
815C22#507511yescharacteristic
816C22#521311yescharacteristic
817C22#521711yescharacteristic
818C22#521811yescharacteristic
819C22#522211yescharacteristic
820C22#522211yescharacteristic
821C22#523811yescharacteristic
822C22#523911yescharacteristic
823C4—42no—
824C4—42no—
825C4—82no—
826C4—242no—
827C4—242no—
828C4#494311yescharacteristic
829C4#494411yescharacteristic
830C4#494511yescharacteristic
831C4#495211yescharacteristic
832C4#495211yescharacteristic
833C4#495311yescharacteristic
834C4#495811yescharacteristic
835C4#496111yescharacteristic
836C3#1118911yescharacteristic, complemented, Sylow
837C2—84no—
838C2#6963611yescharacteristic
839C2#6963711yescharacteristic
840C2#6964011yescharacteristic
841C2#6964111yescharacteristic
842C2#6964411yescharacteristic
843C2#6964511yescharacteristic
844C2#6965011yescharacteristic
845C2#6965111yescharacteristic
846C2#7154911yescharacteristic
847C2#7161211yescharacteristic
848C2#7161311yescharacteristic
849C2#7167911yescharacteristic
850C2#7168011yescharacteristic
851C2#7172211yescharacteristic
852C2#7176211yescharacteristic
subgroupG/H
centerC24C2×#67
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC2×C3×#390C2
socleC24×C3C2×D4
prime radicalC23×C3×D4C22
cosocleC23×C3×C4C23
hypercenterC2×#390D3
hypocenterC3#11189
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
4. C2×#4529C2semidirect
5. C2×#4529C2semidirect
6. #71535C2semidirect
7. C2×#4524C2semidirect
25. C2×#832C4semidirect
836. C3#11189semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3902
C22×#8322
C2×#45292
#715352
C2×#45242
#111893