Finite Group Databasebeta

← #10702998

Subgroups — #10702998

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×#809C211yesmaximal, characteristic
2C22×#809C211yesmaximal, characteristic
3C2×#4939C211yesmaximal, characteristic
4C3×C4⋊#95C211yesmaximal, characteristic, complemented
5C2×#4529C211yesmaximal, characteristic, complemented
6C2×#4529C211yesmaximal, characteristic, complemented
7C2×#4524C211yesmaximal, characteristic, complemented
8#11189—31nomaximal, Sylow
9C23×D12C2211yescharacteristic
10C22×C3×C4⋊C4C2211yescharacteristic
11C22×C3×C4⋊C4C2211yescharacteristic
12C22×C3×C42C2211yescharacteristic
13C22×(C2×D3)⋊C4—21no—
14C22×(C2×D3)⋊C4—21no—
15C22×C4⋊Dic3C2211yescharacteristic
16C23×C3⋊C8C2211yescharacteristic
17C23×C3⋊C8C2211yescharacteristic
18C2×C3×#95—21no—
19C2×C3×#95—21no—
20C2×#809—22no—
21C2×#809—22no—
22C2×#809—22no—
23C2×#809—22no—
24C2×#809—22no—
25C2×#809C414yescomplemented
26#4939—22no—
27#4939—22no—
28#4529—22no—
29#4529—22no—
30#4524—22no—
31C22×#102—31no—
32C22×#102—31no—
33C2×#390—31no—
34C2×#340—31no—
35C2×#340—31no—
36C2×#336—31no—
37C4⋊#95D311yescharacteristic, complemented
38C24×D3—21no—
39C23×C3×C4—21no—
40C23×C3×C4—21no—
41C23×C3×C4D411yescharacteristic
42C23×C3×C4D411yescharacteristic
43C23×C3×C4C2311yescharacteristic
44C23×Dic3—21no—
45C22×D12—21no—
46C22×D12—21no—
47C22×D12—21no—
48C22×D12—21no—
49C22×D12—21no—
50C22×D12—21no—
51C22×D12—21no—
52C22×D12—21no—
53C22×D12—21no—
54C22×D12—21no—
55C22×D12—21no—
56C22×D12C2×C412yes—
57C22×D12D412yes—
58C22×D12D412yes—
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⋊C4—21no—
65C2×C3×C4⋊C4—21no—
66C2×C3×C4⋊C4—21no—
67C2×C3×C4⋊C4—21no—
68C2×C3×C4⋊C4—21no—
69C2×C3×C4⋊C4C2×C412yes—
70C2×C3×C4⋊C4D412yes—
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×(C2×D3)⋊C4—24no—
78C2×(C2×D3)⋊C4—24no—
79C2×(C2×D3)⋊C4—42no—
80C2×(C2×D3)⋊C4—42no—
81C2×(C2×D3)⋊C4—42no—
82C2×(C2×D3)⋊C4—42no—
83C2×C4⋊Dic3—21no—
84C2×C4⋊Dic3—21no—
85C2×C4⋊Dic3—21no—
86C2×C4⋊Dic3—21no—
87C2×C4⋊Dic3—21no—
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—
103C3×#95—42no—
104C3×#95—42no—
105#809—28no—
106#809—28no—
107C23×D4—31no—
108C23×C8—31no—
109C23×C8—31no—
110C22×C4⋊C4—31no—
111C22×C4⋊C4C2×D311yescharacteristic
112C22×C4⋊C4C2×D311yescharacteristic
113C22×C22⋊C4—61no—
114C22×C22⋊C4—61no—
115C22×C42C2×D311yescharacteristic
116C2×#102—34no—
117C2×#102—62no—
118C2×#102—62no—
119C2×#102—62no—
120C2×#102—62no—
121C2×#102—62no—
122#390—62no—
123#390—62no—
124C2×#95—21no—
125C2×#95—21no—
126#340—62no—
127#340—62no—
128#336—62no—
129C24×C3C2×D411yescharacteristic
130C23×D3—22no—
131C23×D3—22no—
132C23×D3—22no—
133C23×D3—41no—
134C23×D3—41no—
135C23×D3—41no—
136C23×D3—41no—
137C23×D3—41no—
138C23×D3—41no—
139C23×D3—41no—
140C23×D3—41no—
141C23×D3—41no—
142C23×D3—41no—
143C23×D3—41no—
144C23×D3—41no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—22no—
158C22×C3×C4—22no—
159C22×C3×C4—41no—
160C22×C3×C4—41no—
161C22×C3×C4—41no—
162C22×C3×C4—41no—
163C22×C3×C4—41no—
164C22×C3×C4—41no—
165C22×C3×C4—41no—
166C22×C3×C4—41no—
167C22×C3×C4—41no—
168C22×C3×C4—41no—
169C22×C3×C4—41no—
170C22×C3×C4—41no—
171C22×C3×C4D812yes—
172C22×C3×C4SD1612yes—
173C22×C3×C4C22×C411yescharacteristic
174C22×C3×C4C2×D411yescharacteristic
175C22×C3×C4C2×D411yescharacteristic
176C22×C3×C4C2×D411yescharacteristic
177C22×C3×C4C2×D411yescharacteristic
178C22×C3×C4C2×D411yescharacteristic
179C22×C3×C4#4111yescharacteristic
180C22×C3×C4#4111yescharacteristic
181C22×C3×C4#4111yescharacteristic
182C22×C3×C4#4111yescharacteristic
183C22×C3×C4#4111yescharacteristic
184C22×C3×C4#4111yescharacteristic
185C22×C3×C4#4111yescharacteristic
186C22×C3×C4#4111yescharacteristic
187C22×Dic3—22no—
188C22×Dic3—41no—
189C22×Dic3—41no—
190C22×Dic3—41no—
191C22×Dic3—41no—
192C22×Dic3—41no—
193C22×Dic3—41no—
194C2×D12—22no—
195C2×D12—22no—
196C2×D12—22no—
197C2×D12—22no—
198C2×D12—22no—
199C2×D12—22no—
200C2×D12—22no—
201C2×D12—22no—
202C2×D12—22no—
203C2×D12—22no—
204C2×D12—22no—
205C2×D12—22no—
206C2×D12—22no—
207C2×D12—22no—
208C2×D12—22no—
209C2×D12—41no—
210C2×D12—41no—
211C2×D12—41no—
212C2×D12—41no—
213C2×D12—41no—
214C2×D12—41no—
215C2×D12—41no—
216C2×D12—41no—
217C2×D12—41no—
218C2×D12—41no—
219C2×D12—41no—
220C2×D12—41no—
221C2×D12C22⋊C414yes—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—22no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4—41no—
227C3×C4⋊C4—41no—
228C3×C4⋊C4—41no—
229C3×C4⋊C4—41no—
230C3×C42—41no—
231C3×C42—41no—
232C3×C42—41no—
233C3×C42—41no—
234(C2×D3)⋊C4—48no—
235(C2×D3)⋊C4—48no—
236C4⋊Dic3—22no—
237C4⋊Dic3—22no—
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—61no—
255C22×D4—32no—
256C22×D4—32no—
257C22×D4—32no—
258C22×D4—61no—
259C22×D4—61no—
260C22×D4—61no—
261C22×D4—61no—
262C22×D4—61no—
263C22×D4—61no—
264C22×D4—61no—
265C22×D4—61no—
266C22×D4—61no—
267C22×D4—61no—
268C22×D4—61no—
269C23×C4—21no—
270C23×C4—21no—
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—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—32no—
300C2×C4⋊C4—61no—
301C2×C4⋊C4—61no—
302C2×C4⋊C4—61no—
303C2×C4⋊C4—61no—
304C2×C4⋊C4—61no—
305C2×C4⋊C4C4×D312yes—
306C2×C4⋊C4D1212yes—
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—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319#102—68no—
320#102—68no—
321#95—42no—
322#95—42no—
323C23×C3C4×D411yescharacteristic
324C23×C3#12011yescharacteristic
325C23×C3#12111yescharacteristic
326C23×C3#12111yescharacteristic
327C23×C3#12111yescharacteristic
328C23×C3#12311yescharacteristic
329C23×C3#12411yescharacteristic
330C23×C3C2×D811yescharacteristic
331C23×C3C2×SD1611yescharacteristic
332C23×C3#13511yescharacteristic
333C23×C3#13511yescharacteristic
334C23×C3AGL(1,ℤ/8)11yescharacteristic
335C23×C3AGL(1,ℤ/8)11yescharacteristic
336C23×C3AGL(1,ℤ/8)11yescharacteristic
337C23×C3#13711yescharacteristic
338C22×D3—24no—
339C22×D3—42no—
340C22×D3—42no—
341C22×D3—42no—
342C22×D3—42no—
343C22×D3—42no—
344C22×D3—42no—
345C22×D3—42no—
346C22×D3—42no—
347C22×D3—42no—
348C22×D3—42no—
349C22×D3—42no—
350C22×D3—42no—
351C22×D3—42no—
352C22×D3—42no—
353C22×D3—42no—
354C22×D3—42no—
355C22×D3—42no—
356C22×D3—42no—
357C22×D3—81no—
358C22×D3—81no—
359C22×D3—81no—
360C22×D3—81no—
361C22×D3—81no—
362C22×D3—81no—
363C22×D3—81no—
364C22×D3—81no—
365C22×D3—81no—
366C22×D3—81no—
367C22×D3—81no—
368C22×D3—81no—
369C22×D3—81no—
370C22×D3—81no—
371C22×D3—81no—
372C22×D3—81no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—81no—
394C2×C3×C4—81no—
395C2×C3×C4—81no—
396C2×C3×C4—81no—
397C2×C3×C4—81no—
398C2×C3×C4—81no—
399C2×C3×C4—81no—
400C2×C3×C4—81no—
401C2×C3×C4C2×C22⋊C411yescharacteristic
402C2×C3×C4#11711yescharacteristic
403C2×C3×C4#11711yescharacteristic
404C2×C3×C4C4×D411yescharacteristic
405C2×C3×C4C4×D411yescharacteristic
406C2×C3×C4C4×D411yescharacteristic
407C2×C3×C4#12011yescharacteristic
408C2×C3×C4#12111yescharacteristic
409C2×C3×C4#12111yescharacteristic
410C2×C3×C4#12111yescharacteristic
411C2×C3×C4#12111yescharacteristic
412C2×C3×C4#12111yescharacteristic
413C2×C3×C4#12311yescharacteristic
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#12411yescharacteristic
423C2×C3×C4#12411yescharacteristic
424C2×C3×C4#12411yescharacteristic
425C2×C3×C4#12611yescharacteristic
426C2×C3×C4#12611yescharacteristic
427C2×C3×C4#12611yescharacteristic
428C2×C3×C4#12611yescharacteristic
429C2×Dic3—42no—
430C2×Dic3—42no—
431C2×Dic3—42no—
432C2×Dic3—81no—
433C2×Dic3—81no—
434C2×Dic3—81no—
435C2×Dic3—81no—
436D12—24no—
437D12—24no—
438D12—42no—
439D12—42no—
440D12—42no—
441D12—42no—
442D12—42no—
443D12—42no—
444C3⋊C8—42no—
445C3⋊C8—42no—
446C24—62no—
447C24—62no—
448C24—62no—
449C24—121no—
450C24—121no—
451C24—121no—
452C24—121no—
453C24—121no—
454C24—121no—
455C24—121no—
456C24—121no—
457C24—121no—
458C24—121no—
459C24—121no—
460C24—121no—
461C24C2×#6711yescharacteristic
462C2×D4—34no—
463C2×D4—62no—
464C2×D4—62no—
465C2×D4—62no—
466C2×D4—62no—
467C2×D4—62no—
468C2×D4—62no—
469C2×D4—62no—
470C2×D4—62no—
471C2×D4—62no—
472C2×D4—62no—
473C2×D4—62no—
474C2×D4—62no—
475C2×D4—62no—
476C2×D4—62no—
477C2×D4—62no—
478C2×D4—121no—
479C2×D4—121no—
480C2×D4—121no—
481C2×D4—121no—
482C2×D4—121no—
483C2×D4—121no—
484C2×D4—121no—
485C2×D4—121no—
486C2×D4—121no—
487C2×D4—121no—
488C2×D4—121no—
489C2×D4—121no—
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—22no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—62no—
517C22×C4—121no—
518C22×C4—121no—
519C22×C4—121no—
520C22×C4—121no—
521C22×C4—121no—
522C22×C4—121no—
523C22×C4#21312yes—
524C22×C4#21512yes—
525C22×C4C2×C4×D311yescharacteristic
526C22×C4C2×D1211yescharacteristic
527C22×C4#23511yescharacteristic
528C22×C4#23511yescharacteristic
529C22×C4#23511yescharacteristic
530C22×C4#23511yescharacteristic
531C22×C4D3×D411yescharacteristic
532C22×C4D3×D411yescharacteristic
533C22×C4D3×D411yescharacteristic
534C22×C4D3×D411yescharacteristic
535C22×C4#23711yescharacteristic
536C22×C4#23711yescharacteristic
537C22×C4#23911yescharacteristic
538C22×C4#23911yescharacteristic
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—22no—
556C4⋊C4—22no—
557C4⋊C4—41no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—62no—
562C4⋊C4—62no—
563C4⋊C4—121no—
564C4⋊C4—121no—
565C22⋊C4—128no—
566C22⋊C4—128no—
567C42—41no—
568C42—41no—
569C42—41no—
570C42—41no—
571C22×C3#38611yescharacteristic
572C22×C3#38811yescharacteristic
573C22×C3#38811yescharacteristic
574C22×C3#39411yescharacteristic
575C22×C3#39411yescharacteristic
576C22×C3#39411yescharacteristic
577C22×C3#39711yescharacteristic
578C22×C3C4×D811yescharacteristic
579C22×C3C4×SD1611yescharacteristic
580C22×C3#44011yescharacteristic
581C22×C3#44211yescharacteristic
582C22×C3#44711yescharacteristic
583C22×C3#44911yescharacteristic
584C22×C3#45011yescharacteristic
585C22×C3#45211yescharacteristic
586C22×C3#45911yescharacteristic
587C22×C3#45911yescharacteristic
588C22×C3#46011yescharacteristic
589C22×C3#46111yescharacteristic
590C22×C3#46311yescharacteristic
591C22×C3#46311yescharacteristic
592C22×C3#46311yescharacteristic
593C22×C3#46411yescharacteristic
594C22×C3#46511yescharacteristic
595C22×C3#46611yescharacteristic
596C22×C3#46811yescharacteristic
597C22×C3#46911yescharacteristic
598C22×C3#48011yescharacteristic
599C22×C3#48111yescharacteristic
600C22×C3#48211yescharacteristic
601C22×C3#48211yescharacteristic
602C22×C3#48611yescharacteristic
603C22×C3#48811yescharacteristic
604C22×C3#48911yescharacteristic
605C22×C3#49011yescharacteristic
606C2×D3—44no—
607C2×D3—44no—
608C2×D3—44no—
609C2×D3—82no—
610C2×D3—82no—
611C2×D3—82no—
612C2×D3—82no—
613C2×D3—82no—
614C2×D3—82no—
615C2×D3—82no—
616C2×D3—82no—
617C2×D3—82no—
618C2×D3—82no—
619C2×D3—82no—
620C2×D3—82no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4—82no—
624C3×C4—82no—
625C3×C4#38111yescharacteristic
626C3×C4#38611yescharacteristic
627C3×C4#38811yescharacteristic
628C3×C4#38811yescharacteristic
629C3×C4#39411yescharacteristic
630C3×C4#39711yescharacteristic
631C3×C4#39711yescharacteristic
632C3×C4#39711yescharacteristic
633Dic3—82no—
634C23—64no—
635C23—122no—
636C23—122no—
637C23—122no—
638C23—122no—
639C23—122no—
640C23—122no—
641C23—122no—
642C23—122no—
643C23—122no—
644C23—122no—
645C23—122no—
646C23—122no—
647C23—122no—
648C23—122no—
649C23—122no—
650C23—122no—
651C23—122no—
652C23—122no—
653C23—241no—
654C23—241no—
655C23—241no—
656C23—241no—
657C23—241no—
658C23—241no—
659C23—241no—
660C23—241no—
661C23—241no—
662C23—241no—
663C23—241no—
664C23—241no—
665C23—241no—
666C23—241no—
667C23—241no—
668C23—241no—
669C23C4×#6711yescharacteristic
670C23#92911yescharacteristic
671C23#93011yescharacteristic
672C23C2×#21311yescharacteristic
673C23#93211yescharacteristic
674C23#93711yescharacteristic
675C23#93811yescharacteristic
676C23#93911yescharacteristic
677C23C2×#21511yescharacteristic
678C23#94211yescharacteristic
679C23#94711yescharacteristic
680C23#94911yescharacteristic
681C23#94911yescharacteristic
682C23#95011yescharacteristic
683C23#95011yescharacteristic
684D4—64no—
685D4—64no—
686D4—122no—
687D4—122no—
688D4—122no—
689D4—122no—
690D4—122no—
691D4—122no—
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—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—122no—
721C2×C4—122no—
722C2×C4—122no—
723C2×C4—241no—
724C2×C4—241no—
725C2×C4—241no—
726C2×C4—241no—
727C2×C4#87211yescharacteristic
728C2×C4C4×D1211yescharacteristic
729C2×C4#87511yescharacteristic
730C2×C4#87611yescharacteristic
731C2×C4D3×C22⋊C411yescharacteristic
732C2×C4#67⋊C411yescharacteristic
733C2×C4#88211yescharacteristic
734C2×C4#88311yescharacteristic
735C2×C4#88311yescharacteristic
736C2×C4#88311yescharacteristic
737C2×C4#88411yescharacteristic
738C2×C4#88411yescharacteristic
739C2×C4#88411yescharacteristic
740C2×C4#88511yescharacteristic
741C2×C4#88511yescharacteristic
742C2×C4#88611yescharacteristic
743C2×C4#89211yescharacteristic
744C2×C4#89311yescharacteristic
745C2×C4#89411yescharacteristic
746C2×C4#89411yescharacteristic
747C2×C4#89411yescharacteristic
748C2×C4#89411yescharacteristic
749C2×C4#89411yescharacteristic
750C2×C4#89511yescharacteristic
751C2×C4#89511yescharacteristic
752C2×C4#89811yescharacteristic
753C2×C4#89811yescharacteristic
754C2×C4#89811yescharacteristic
755C8—122no—
756C8—122no—
757C2×C3#144011yescharacteristic
758C2×C3#187711yescharacteristic
759C2×C3#187911yescharacteristic
760C2×C3#192511yescharacteristic
761C2×C3#192611yescharacteristic
762C2×C3#193411yescharacteristic
763C2×C3#193611yescharacteristic
764C2×C3#203311yescharacteristic
765C2×C3#203411yescharacteristic
766C2×C3#204111yescharacteristic
767C2×C3#204211yescharacteristic
768C2×C3#205411yescharacteristic
769C2×C3#205511yescharacteristic
770C2×C3#207111yescharacteristic
771C2×C3#207311yescharacteristic
772D3—84no—
773C22—124no—
774C22—124no—
775C22—124no—
776C22—242no—
777C22—242no—
778C22—242no—
779C22—242no—
780C22—242no—
781C22—242no—
782C22—242no—
783C22—242no—
784C22—242no—
785C22—242no—
786C22—242no—
787C22—242no—
788C22#494011yescharacteristic
789C22#495611yescharacteristic
790C22#495911yescharacteristic
791C22#496111yescharacteristic
792C22#496711yescharacteristic
793C22#496811yescharacteristic
794C22#499011yescharacteristic
795C22#499111yescharacteristic
796C22#499211yescharacteristic
797C22#500311yescharacteristic
798C22#500311yescharacteristic
799C22C4×#21311yescharacteristic
800C22#501411yescharacteristic
801C22#501511yescharacteristic
802C22#501611yescharacteristic
803C22C4×#21511yescharacteristic
804C22#502611yescharacteristic
805C22#502711yescharacteristic
806C22#502811yescharacteristic
807C22#503611yescharacteristic
808C22#503711yescharacteristic
809C22#503811yescharacteristic
810C22#503911yescharacteristic
811C22#504611yescharacteristic
812C22#504711yescharacteristic
813C22#504811yescharacteristic
814C22#504911yescharacteristic
815C22#505711yescharacteristic
816C22#505711yescharacteristic
817C22#506711yescharacteristic
818C22#506811yescharacteristic
819C22#507211yescharacteristic
820C22#508311yescharacteristic
821C22#508811yescharacteristic
822C22#508911yescharacteristic
823C4—42no—
824C4—42no—
825C4—82no—
826C4—82no—
827C4—242no—
828C4#466411yescharacteristic
829C4#466511yescharacteristic
830C4#466911yescharacteristic
831C4#467011yescharacteristic
832C4#467211yescharacteristic
833C4#467411yescharacteristic
834C4#467511yescharacteristic
835C4#467511yescharacteristic
836C3#1118911yescharacteristic, complemented, Sylow
837C2—244no—
838C2#6942911yescharacteristic
839C2#6946211yescharacteristic
840C2#6946311yescharacteristic
841C2#6952311yescharacteristic
842C2#6952411yescharacteristic
843C2#6955711yescharacteristic
844C2#6958511yescharacteristic
845C2#6961511yescharacteristic
846C2#6961711yescharacteristic
847C2#6962711yescharacteristic
848C2#6962811yescharacteristic
849C2#6965011yescharacteristic
850C2#6965711yescharacteristic
851C2#6968011yescharacteristic
852C2#6968711yescharacteristic
subgroupG/H
centerC24C2×#67
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC3×C4⋊#95C2
socleC24×C3C2×D4
prime radicalC23×D12C22
cosocleC23×C3×C4C23
hypercenterC4⋊#95D3
hypocenterC3#11189
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C42 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C3×C4⋊#95C2semidirect
5. C2×#4529C2semidirect
6. C2×#4529C2semidirect
7. C2×#4524C2semidirect
25. C2×#809C4semidirect
37. C4⋊#95D3semidirect
836. C3#11189semidirect

Maximal subgroups

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

subgroupindex
C22×#8092
C2×#49392
C3×C4⋊#952
C2×#45292
C2×#45242
#111893