Finite Group Databasebeta

← #10702105

Subgroups — #10702105

Order 768.

1262 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C2×D3)⋊C8C211yesmaximal, characteristic
2C22×(C2×D3)⋊C8C211yesmaximal, characteristic
3C22×Dic3⋊C8C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
5C2×C3×#336C211yesmaximal, characteristic, complemented
6C2×#4550C211yesmaximal, characteristic, complemented
7C2×#4524C211yesmaximal, characteristic, complemented
8#11042—31nomaximal, Sylow
9C23×C4×D3C2211yescharacteristic
10C23×C3×C8C2211yescharacteristic
11C23×C3×C8C2211yescharacteristic
12C22×C3×C42C2211yescharacteristic
13C22×(C2×D3)⋊C4C411yescharacteristic
14C22×(C2×D3)⋊C4C411yescharacteristic
15C22×C4×Dic3C2211yescharacteristic
16C23×C3⋊C8C2211yescharacteristic
17C23×C3⋊C8C2211yescharacteristic
18C2×C3⋊#95C411yescharacteristic
19C2×C3⋊#95C411yescharacteristic
20C2×(C2×D3)⋊C8—22no—
21C2×(C2×D3)⋊C8—22no—
22C2×(C2×D3)⋊C8—22no—
23C2×(C2×D3)⋊C8—22no—
24C2×(C2×D3)⋊C8—22no—
25C2×(C2×D3)⋊C8—22no—
26C2×Dic3⋊C8—22no—
27C2×Dic3⋊C8—22no—
28C2×Dic3⋊C8—22no—
29C4×(C2×D3)⋊C4—22no—
30C4×(C2×D3)⋊C4—22no—
31C3×#336—22no—
32#4550—22no—
33#4524—22no—
34C22×C4⋊C8—31no—
35C22×C22⋊C8—31no—
36C22×C22⋊C8—31no—
37C2×C4×C22⋊C4—31no—
38C2×#336—31no—
39C2×#336—31no—
40C2×#336D311yescharacteristic, complemented
41C24×D3C2×C411yescharacteristic
42C23×C3×C4C2×C411yescharacteristic
43C23×C3×C4C2×C411yescharacteristic
44C23×C3×C4C2311yescharacteristic
45C23×Dic3C2×C411yescharacteristic
46C23×Dic3C2×C411yescharacteristic
47C23×Dic3C2×C411yescharacteristic
48C22×C4×D3—21no—
49C22×C4×D3—21no—
50C22×C4×D3—21no—
51C22×C4×D3—21no—
52C22×C4×D3—21no—
53C22×C4×D3—21no—
54C22×C4×D3—21no—
55C22×C4×D3—21no—
56C22×C4×D3—21no—
57C22×C4×D3—21no—
58C22×C4×D3—21no—
59C22×C4×D3—21no—
60C22×C4×D3D412yes—
61C22×C4×D3Q812yes—
62C22×C3×C8—21no—
63C22×C3×C8—21no—
64C22×C3×C8—21no—
65C22×C3×C8—21no—
66C22×C3×C8—21no—
67C22×C3×C8—21no—
68C22×C3×C8—21no—
69C22×C3×C8—21no—
70C22×C3×C8—21no—
71C22×C3×C8—21no—
72C22×C3×C8—21no—
73C22×C3×C8—21no—
74C22×C3×C8D412yes—
75C22×C3×C8D412yes—
76C2×C3×C42—21no—
77C2×C3×C42—21no—
78C2×C3×C42—21no—
79C2×C3×C42—21no—
80C2×C3×C42—21no—
81C2×C3×C42—21no—
82C2×(C2×D3)⋊C4—22no—
83C2×(C2×D3)⋊C4—22no—
84C2×(C2×D3)⋊C4—22no—
85C2×(C2×D3)⋊C4—22no—
86C2×(C2×D3)⋊C4—22no—
87C2×(C2×D3)⋊C4C814yescomplemented
88C2×C4×Dic3—21no—
89C2×C4×Dic3—21no—
90C2×C4×Dic3—21no—
91C2×C4×Dic3—21no—
92C2×C4×Dic3D412yes—
93C2×C4×Dic3D412yes—
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⋊C8—21no—
102C22×C3⋊C8—21no—
103C22×C3⋊C8—21no—
104C22×C3⋊C8—21no—
105C22×C3⋊C8—21no—
106C22×C3⋊C8D412yes—
107C22×C3⋊C8D412yes—
108C3⋊#95—22no—
109C3⋊#95—22no—
110(C2×D3)⋊C8—28no—
111(C2×D3)⋊C8—28no—
112Dic3⋊C8—28no—
113C24×C4—31no—
114C23×C8—31no—
115C23×C8—31no—
116C23×C8C2×D311yescharacteristic
117C23×C8C2×D311yescharacteristic
118C22×C22⋊C4—31no—
119C22×C22⋊C4—31no—
120C22×C42—31no—
121C22×C42C2×D311yescharacteristic
122C2×C4⋊C8—62no—
123C2×C4⋊C8—62no—
124C2×C4⋊C8—62no—
125C2×C22⋊C8—62no—
126C2×C22⋊C8—62no—
127C2×C22⋊C8—62no—
128C2×C22⋊C8—62no—
129C2×C22⋊C8—62no—
130C2×C22⋊C8—62no—
131C4×C22⋊C4—62no—
132C4×C22⋊C4—62no—
133C2×#95—31no—
134C2×#95—31no—
135#336—22no—
136#336—62no—
137#336—62no—
138C24×C3C22×C411yescharacteristic
139C23×D3—21no—
140C23×D3—21no—
141C23×D3—21no—
142C23×D3—21no—
143C23×D3—21no—
144C23×D3—21no—
145C23×D3—21no—
146C23×D3—21no—
147C23×D3—21no—
148C23×D3—21no—
149C23×D3—21no—
150C23×D3—21no—
151C23×D3C4⋊C412yes—
152C23×D3C2×C812yes—
153C23×D3M1612yes—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4C2×C812yes—
167C22×C3×C4M1612yes—
168C22×C3×C4C2×D411yescharacteristic
169C22×C3×C4C2×D411yescharacteristic
170C22×C3×C4C2×D411yescharacteristic
171C22×C3×C4C2×D411yescharacteristic
172C22×C3×C4C2×D411yescharacteristic
173C22×C3×C4C2×D411yescharacteristic
174C22×C3×C4C2×D411yescharacteristic
175C22×C3×C4C2×Q811yescharacteristic
176C22×C3×C4#4111yescharacteristic
177C22×C3×C4#4111yescharacteristic
178C22×C3×C4#4111yescharacteristic
179C22×C3×C4#4111yescharacteristic
180C22×C3×C4#4111yescharacteristic
181C22×C3×C4#4111yescharacteristic
182C22×Dic3—21no—
183C22×Dic3—21no—
184C22×Dic3—21no—
185C22×Dic3—21no—
186C22×Dic3—21no—
187C22×Dic3—21no—
188C22×Dic3—21no—
189C22×Dic3—21no—
190C22×Dic3—21no—
191C22×Dic3—21no—
192C22×Dic3—21no—
193C22×Dic3—21no—
194C22×Dic3—21no—
195C22×Dic3—21no—
196C22×Dic3—21no—
197C22×Dic3—21no—
198C22×Dic3C22⋊C412yes—
199C22×Dic3C22⋊C412yes—
200C22×Dic3C4⋊C412yes—
201C22×Dic3C2×C812yes—
202C22×Dic3M1612yes—
203C2×C4×D3—22no—
204C2×C4×D3—22no—
205C2×C4×D3—22no—
206C2×C4×D3—22no—
207C2×C4×D3—22no—
208C2×C4×D3—22no—
209C2×C4×D3—22no—
210C2×C4×D3—22no—
211C2×C4×D3—22no—
212C2×C4×D3—22no—
213C2×C4×D3—22no—
214C2×C4×D3—22no—
215C2×C4×D3—41no—
216C2×C4×D3—41no—
217C2×C4×D3—41no—
218C2×C4×D3—41no—
219C2×C4×D3—41no—
220C2×C4×D3—41no—
221C2×C4×D3—41no—
222C2×C4×D3—41no—
223C2×C4×D3—41no—
224C2×C4×D3—41no—
225C2×C4×D3—41no—
226C2×C4×D3—41no—
227C2×C4×D3—41no—
228C2×C4×D3—41no—
229C2×C4×D3—41no—
230C2×C4×D3—41no—
231C2×C3×C8—22no—
232C2×C3×C8—22no—
233C2×C3×C8—22no—
234C2×C3×C8—22no—
235C2×C3×C8—22no—
236C2×C3×C8—22no—
237C2×C3×C8—41no—
238C2×C3×C8—41no—
239C2×C3×C8—41no—
240C2×C3×C8—41no—
241C2×C3×C8—41no—
242C2×C3×C8—41no—
243C2×C3×C8—41no—
244C2×C3×C8—41no—
245C3×C42—41no—
246C3×C42—41no—
247C3×C42—41no—
248C3×C42—41no—
249(C2×D3)⋊C4—28no—
250(C2×D3)⋊C4—28no—
251C4×Dic3—22no—
252C4×Dic3—22no—
253C4×Dic3—22no—
254C4×Dic3—22no—
255C2×C3⋊C8—22no—
256C2×C3⋊C8—22no—
257C2×C3⋊C8—22no—
258C2×C3⋊C8—22no—
259C2×C3⋊C8—22no—
260C2×C3⋊C8—22no—
261C2×C3⋊C8—41no—
262C2×C3⋊C8—41no—
263C2×C3⋊C8—41no—
264C2×C3⋊C8—41no—
265C2×C3⋊C8—41no—
266C2×C3⋊C8—41no—
267C2×C3⋊C8—41no—
268C2×C3⋊C8—41no—
269C25—31no—
270C23×C4—31no—
271C23×C4—31no—
272C23×C4—31no—
273C23×C4—32no—
274C23×C4—32no—
275C23×C4—61no—
276C23×C4—61no—
277C23×C4—61no—
278C23×C4—61no—
279C23×C4—61no—
280C23×C4—61no—
281C23×C4—61no—
282C23×C4—61no—
283C23×C4—61no—
284C23×C4—61no—
285C23×C4—61no—
286C23×C4—61no—
287C23×C4C4×D311yescharacteristic
288C23×C4C4×D311yescharacteristic
289C23×C4C22×D311yescharacteristic
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—21no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—21no—
302C22×C8—32no—
303C22×C8—32no—
304C22×C8—61no—
305C22×C8—61no—
306C22×C8—61no—
307C22×C8—61no—
308C22×C8—61no—
309C22×C8—61no—
310C22×C8—61no—
311C22×C8—61no—
312C22×C8—61no—
313C22×C8—61no—
314C22×C8—61no—
315C22×C8—61no—
316C22×C8D1212yes—
317C22×C8#6712yes—
318C2×C22⋊C4—34no—
319C2×C22⋊C4—62no—
320C2×C22⋊C4—62no—
321C2×C22⋊C4—62no—
322C2×C22⋊C4—62no—
323C2×C22⋊C4—62no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—32no—
331C2×C42—32no—
332C2×C42—61no—
333C2×C42—61no—
334C2×C42—61no—
335C2×C42—61no—
336C4⋊C8—68no—
337C22⋊C8—68no—
338C22⋊C8—68no—
339#95—62no—
340#95—62no—
341C23×C3C2×C22⋊C411yescharacteristic
342C23×C3C2×C4⋊C411yescharacteristic
343C23×C3#11711yescharacteristic
344C23×C3C4×D411yescharacteristic
345C23×C3C4×D411yescharacteristic
346C23×C3C4×D411yescharacteristic
347C23×C3C4×D411yescharacteristic
348C23×C3C22×C811yescharacteristic
349C23×C3C2×M1611yescharacteristic
350C23×C3C2×M1611yescharacteristic
351C23×C3C2×M1611yescharacteristic
352C23×C3#13111yescharacteristic
353C23×C3#13111yescharacteristic
354C23×C3#13111yescharacteristic
355C23×C3#13111yescharacteristic
356C22×D3—22no—
357C22×D3—22no—
358C22×D3—22no—
359C22×D3—22no—
360C22×D3—22no—
361C22×D3—22no—
362C22×D3—22no—
363C22×D3—22no—
364C22×D3—22no—
365C22×D3—22no—
366C22×D3—22no—
367C22×D3—22no—
368C22×D3—22no—
369C22×D3—22no—
370C22×D3—22no—
371C22×D3—22no—
372C22×D3—22no—
373C22×D3—22no—
374C22×D3—41no—
375C22×D3—41no—
376C22×D3—41no—
377C22×D3—41no—
378C22×D3—41no—
379C22×D3—41no—
380C22×D3—41no—
381C22×D3—41no—
382C22×D3—41no—
383C22×D3—41no—
384C22×D3—41no—
385C22×D3—41no—
386C22×D3—41no—
387C22×D3—41no—
388C22×D3—41no—
389C22×D3—41no—
390C22×D3C4⋊C814yescomplemented
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4#12011yescharacteristic
406C2×C3×C4#12011yescharacteristic
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#12111yescharacteristic
414C2×C3×C4#12111yescharacteristic
415C2×C3×C4#12111yescharacteristic
416C2×C3×C4C22⋊Q811yescharacteristic
417C2×C3×C4C22⋊Q811yescharacteristic
418C2×C3×C4C22⋊Q811yescharacteristic
419C2×C3×C4C22⋊Q811yescharacteristic
420C2×C3×C4C22⋊Q811yescharacteristic
421C2×C3×C4C22⋊Q811yescharacteristic
422C2×C3×C4#12311yescharacteristic
423C2×C3×C4#12311yescharacteristic
424C2×C3×C4#12311yescharacteristic
425C2×C3×C4#12311yescharacteristic
426C2×C3×C4#12311yescharacteristic
427C2×C3×C4#12411yescharacteristic
428C2×C3×C4#12411yescharacteristic
429C2×C3×C4#12411yescharacteristic
430C2×C3×C4#12611yescharacteristic
431C2×C3×C4#12611yescharacteristic
432C2×C3×C4#12711yescharacteristic
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—22no—
445C2×Dic3—41no—
446C2×Dic3—41no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—41no—
450C2×Dic3—41no—
451C2×Dic3—41no—
452C2×Dic3—41no—
453C2×Dic3C22⋊C814yescomplemented
454C4×D3—42no—
455C4×D3—42no—
456C4×D3—42no—
457C4×D3—42no—
458C4×D3—42no—
459C4×D3—42no—
460C4×D3—42no—
461C4×D3—42no—
462C3×C8—42no—
463C3×C8—42no—
464C3⋊C8—42no—
465C3⋊C8—42no—
466C24—32no—
467C24—32no—
468C24—32no—
469C24—61no—
470C24—61no—
471C24—61no—
472C24—61no—
473C24—61no—
474C24—61no—
475C24—61no—
476C24—61no—
477C24—61no—
478C24—61no—
479C24—61no—
480C24—61no—
481C24C2×C4×D311yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—32no—
495C22×C4—32no—
496C22×C4—32no—
497C22×C4—32no—
498C22×C4—32no—
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—61no—
512C22×C4—61no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—62no—
516C22×C4—62no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—121no—
528C22×C4—121no—
529C22×C4—121no—
530C22×C4—121no—
531C22×C4—121no—
532C22×C4—121no—
533C22×C4—121no—
534C22×C4—121no—
535C22×C4—121no—
536C22×C4—121no—
537C22×C4—121no—
538C22×C4—121no—
539C22×C4—121no—
540C22×C4—121no—
541C22×C4—121no—
542C22×C4—121no—
543C22×C4D3×C812yes—
544C22×C4ΓL(1,𝔽25)12yes—
545C22×C4C2×D1211yescharacteristic
546C22×C4#23511yescharacteristic
547C22×C4#23511yescharacteristic
548C22×C4#23511yescharacteristic
549C22×C4#23511yescharacteristic
550C22×C4D3×D411yescharacteristic
551C22×C4D3×D411yescharacteristic
552C22×C4D3×D411yescharacteristic
553C22×C4D3×D411yescharacteristic
554C22×C4D3×D411yescharacteristic
555C22×C4#23711yescharacteristic
556C22×C4D3×Q811yescharacteristic
557C22×C4#23911yescharacteristic
558C22×C4C2×#6711yescharacteristic
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8—41no—
568C2×C8—41no—
569C2×C8—41no—
570C2×C8—41no—
571C2×C8—41no—
572C2×C8—41no—
573C2×C8—62no—
574C2×C8—62no—
575C2×C8—62no—
576C2×C8—62no—
577C2×C8—62no—
578C2×C8—62no—
579C2×C8—121no—
580C2×C8—121no—
581C2×C8—121no—
582C2×C8—121no—
583C2×C8—121no—
584C2×C8—121no—
585C2×C8—121no—
586C2×C8—121no—
587C22⋊C4—68no—
588C22⋊C4—68no—
589C42—41no—
590C42—41no—
591C42—41no—
592C42—41no—
593C42—62no—
594C42—62no—
595C42—62no—
596C42—62no—
597C22×C3#38011yescharacteristic
598C22×C3#38511yescharacteristic
599C22×C3#38511yescharacteristic
600C22×C3#38611yescharacteristic
601C22×C3#38811yescharacteristic
602C22×C3#38811yescharacteristic
603C22×C3#39011yescharacteristic
604C22×C3C2×C22⋊C811yescharacteristic
605C22×C3#40711yescharacteristic
606C22×C3#40811yescharacteristic
607C22×C3#40811yescharacteristic
608C22×C3C2×C4⋊C811yescharacteristic
609C22×C3#42311yescharacteristic
610C22×C3#42411yescharacteristic
611C22×C3#42411yescharacteristic
612C22×C3#43111yescharacteristic
613C22×C3#43211yescharacteristic
614C22×C3#43311yescharacteristic
615C22×C3#43311yescharacteristic
616C22×C3C8×D411yescharacteristic
617C22×C3C8×D411yescharacteristic
618C22×C3C8×D411yescharacteristic
619C22×C3C8×D411yescharacteristic
620C22×C3#43511yescharacteristic
621C22×C3#43511yescharacteristic
622C22×C3#43511yescharacteristic
623C22×C3#43511yescharacteristic
624C22×C3#43511yescharacteristic
625C22×C3#43511yescharacteristic
626C22×C3#43511yescharacteristic
627C22×C3#43511yescharacteristic
628C22×C3#43611yescharacteristic
629C22×C3#43611yescharacteristic
630C22×C3#43611yescharacteristic
631C22×C3#43611yescharacteristic
632C2×D3—24no—
633C2×D3—24no—
634C2×D3—24no—
635C2×D3—42no—
636C2×D3—42no—
637C2×D3—42no—
638C2×D3—42no—
639C2×D3—42no—
640C2×D3—42no—
641C2×D3—42no—
642C2×D3—42no—
643C2×D3—42no—
644C2×D3—42no—
645C2×D3—42no—
646C2×D3—42no—
647C3×C4—42no—
648C3×C4—42no—
649C3×C4#39211yescharacteristic
650C3×C4#39311yescharacteristic
651C3×C4#39411yescharacteristic
652C3×C4#39411yescharacteristic
653C3×C4#39611yescharacteristic
654C3×C4#39611yescharacteristic
655C3×C4#39711yescharacteristic
656C3×C4#39911yescharacteristic
657Dic3—24no—
658Dic3—42no—
659Dic3—42no—
660C23—34no—
661C23—62no—
662C23—62no—
663C23—62no—
664C23—62no—
665C23—62no—
666C23—62no—
667C23—62no—
668C23—62no—
669C23—62no—
670C23—62no—
671C23—62no—
672C23—62no—
673C23—62no—
674C23—62no—
675C23—62no—
676C23—62no—
677C23—62no—
678C23—62no—
679C23—121no—
680C23—121no—
681C23—121no—
682C23—121no—
683C23—121no—
684C23—121no—
685C23—121no—
686C23—121no—
687C23—121no—
688C23—121no—
689C23—121no—
690C23—121no—
691C23—121no—
692C23—121no—
693C23—121no—
694C23—121no—
695C23#87211yescharacteristic
696C23C4×D1211yescharacteristic
697C23D3×C22⋊C411yescharacteristic
698C23#67⋊C411yescharacteristic
699C23D3×C4⋊C411yescharacteristic
700C23#89311yescharacteristic
701C23C2×D3×C811yescharacteristic
702C23C2×ΓL(1,𝔽25)11yescharacteristic
703C23#90111yescharacteristic
704C23#90111yescharacteristic
705C23D3×M1611yescharacteristic
706C23D3×M1611yescharacteristic
707C23#90711yescharacteristic
708C23#90711yescharacteristic
709C23C4×#6711yescharacteristic
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—34no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—62no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4—122no—
746C2×C4—122no—
747C2×C4—122no—
748C2×C4—122no—
749C2×C4—122no—
750C2×C4—122no—
751C2×C4—122no—
752C2×C4—122no—
753C2×C4#87511yescharacteristic
754C2×C4#87611yescharacteristic
755C2×C4#88211yescharacteristic
756C2×C4#88211yescharacteristic
757C2×C4#88311yescharacteristic
758C2×C4#88411yescharacteristic
759C2×C4#88411yescharacteristic
760C2×C4#88411yescharacteristic
761C2×C4#88411yescharacteristic
762C2×C4#88411yescharacteristic
763C2×C4#88511yescharacteristic
764C2×C4#88511yescharacteristic
765C2×C4#89411yescharacteristic
766C2×C4#89411yescharacteristic
767C2×C4#89411yescharacteristic
768C2×C4#89511yescharacteristic
769C2×C4#89611yescharacteristic
770C2×C4#89611yescharacteristic
771C2×C4#89611yescharacteristic
772C2×C4#89611yescharacteristic
773C2×C4#89711yescharacteristic
774C2×C4#89811yescharacteristic
775C2×C4#92911yescharacteristic
776C2×C4#93011yescharacteristic
777C2×C4#93711yescharacteristic
778C2×C4#93911yescharacteristic
779C2×C4#94011yescharacteristic
780C2×C4#94611yescharacteristic
781C8—42no—
782C8—42no—
783C8—122no—
784C8—122no—
785C2×C3#143911yescharacteristic
786C2×C3#179711yescharacteristic
787C2×C3#179811yescharacteristic
788C2×C3#185011yescharacteristic
789C2×C3#185011yescharacteristic
790C2×C3#185111yescharacteristic
791C2×C3#185111yescharacteristic
792C2×C3#186911yescharacteristic
793C2×C3#187011yescharacteristic
794C2×C3#192311yescharacteristic
795C2×C3#192311yescharacteristic
796C2×C3#192411yescharacteristic
797C2×C3#192411yescharacteristic
798C2×C3#195411yescharacteristic
799C2×C3#195511yescharacteristic
800D3—44no—
801C22—64no—
802C22—64no—
803C22—64no—
804C22—122no—
805C22—122no—
806C22—122no—
807C22—122no—
808C22—122no—
809C22—122no—
810C22—122no—
811C22—122no—
812C22—122no—
813C22—122no—
814C22—122no—
815C22—122no—
816C22#466511yescharacteristic
817C22#466711yescharacteristic
818C22#466811yescharacteristic
819C22#466911yescharacteristic
820C22#468511yescharacteristic
821C22C8×D1211yescharacteristic
822C22#468811yescharacteristic
823C22#469011yescharacteristic
824C22#470511yescharacteristic
825C22#470611yescharacteristic
826C22#470611yescharacteristic
827C22#470911yescharacteristic
828C22D3×C22⋊C811yescharacteristic
829C22#67⋊C811yescharacteristic
830C22#472611yescharacteristic
831C22#472711yescharacteristic
832C22#472711yescharacteristic
833C22#472811yescharacteristic
834C22#472911yescharacteristic
835C22#473011yescharacteristic
836C22D3×C4⋊C811yescharacteristic
837C22#483411yescharacteristic
838C22#483611yescharacteristic
839C22#483611yescharacteristic
840C22#483711yescharacteristic
841C22#483811yescharacteristic
842C22#483911yescharacteristic
843C22#483911yescharacteristic
844C22#494011yescharacteristic
845C22#495711yescharacteristic
846C22#498911yescharacteristic
847C22C8×#6711yescharacteristic
848C22#511111yescharacteristic
849C22#512711yescharacteristic
850C22#512811yescharacteristic
851C4—42no—
852C4—42no—
853C4—64no—
854C4—122no—
855C4—122no—
856C4#467211yescharacteristic
857C4#467311yescharacteristic
858C4#467511yescharacteristic
859C4#467611yescharacteristic
860C4#495911yescharacteristic
861C4#496011yescharacteristic
862C4#499311yescharacteristic
863C4#499411yescharacteristic
864C3#1104211yescharacteristic, complemented, Sylow
865C2—124no—
866C2#6865711yescharacteristic
867C2#6865811yescharacteristic
868C2#6866211yescharacteristic
869C2#6866311yescharacteristic
870C2#6866611yescharacteristic
871C2#6866711yescharacteristic
872C2#6866811yescharacteristic
873C2#6866911yescharacteristic
874C2#6942811yescharacteristic
875C2#6978511yescharacteristic
876C2#6983511yescharacteristic
877C2#6991611yescharacteristic
878C2#6991711yescharacteristic
879C2#7047711yescharacteristic
880C2#7047811yescharacteristic
subgroupG/H
center, FrattiniC23×C4C22×D3
commutatorC23×C3C22×C8
FittingC2×C3×#336C2
socleC24×C3C22×C4
prime radicalC24×D3C2×C4
cosocleC23×C3×C4C23
hypercenterC2×#336D3
hypocenterC3#11042
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C4 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
3. C22×Dic3⋊C8C2semidirect
5. C2×C3×#336C2semidirect
6. C2×#4550C2semidirect
7. C2×#4524C2semidirect
40. C2×#336D3semidirect
87. C2×(C2×D3)⋊C4C8semidirect
390. C22×D3C4⋊C8semidirect
453. C2×Dic3C22⋊C8semidirect
864. C3#11042semidirect

Maximal subgroups

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

subgroupindex
C22×(C2×D3)⋊C82
C22×Dic3⋊C82
C2×C4×(C2×D3)⋊C42
C2×C3×#3362
C2×#45502
C2×#45242
#110423