Finite Group Databasebeta

← #10702241

Subgroups — #10702241

Order 768.

1282 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#389C211yesmaximal, characteristic, complemented
2C22×#809C211yesmaximal, characteristic
3C22×#809C211yesmaximal, characteristic
4C2×#4939C211yesmaximal, characteristic
5C2×#4529C211yesmaximal, characteristic, complemented
6C2×#4529C211yesmaximal, characteristic, complemented
7C2×#4524C211yesmaximal, characteristic, complemented
8#11066—31nomaximal, Sylow
9C23×D12C2211yescharacteristic
10C22×C3×C4⋊C4—21no—
11C22×C3×C4⋊C4C2211yescharacteristic
12C22×C3×C4⋊C4C2211yescharacteristic
13C22×C3×C42C2211yescharacteristic
14C22×(C2×D3)⋊C4—21no—
15C22×(C2×D3)⋊C4—21no—
16C22×C4⋊Dic3C2211yescharacteristic
17C23×C3⋊C8C2211yescharacteristic
18C23×C3⋊C8C2211yescharacteristic
19C3×#389—22no—
20C3×#389—22no—
21C2×C3×#95—21no—
22C2×#809—22no—
23C2×#809—22no—
24C2×#809—22no—
25C2×#809—22no—
26C2×#809—22no—
27C2×#809C414yescomplemented
28#4939—22no—
29#4939—22no—
30#4529—22no—
31#4529—22no—
32#4524—22no—
33C22×#102—31no—
34C22×#102—31no—
35C2×#390—31no—
36C2×#389D311yescharacteristic, complemented
37C2×#340—31no—
38C2×#340—31no—
39C2×#336—31no—
40C24×D3—21no—
41C23×C3×C4—21no—
42C23×C3×C4—21no—
43C23×C3×C4D411yescharacteristic
44C23×C3×C4D411yescharacteristic
45C23×C3×C4C2311yescharacteristic
46C23×Dic3—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×D12—21no—
57C22×D12—21no—
58C22×D12C2×C412yes—
59C22×D12D412yes—
60C22×D12Q812yes—
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—24no—
69C2×C3×C4⋊C4—21no—
70C2×C3×C4⋊C4—42no—
71C2×C3×C4⋊C4—42no—
72C2×C3×C4⋊C4C2×C412yes—
73C2×C3×C4⋊C4D412yes—
74C2×C3×C4⋊C4D412yes—
75C2×C3×C4⋊C4D412yes—
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—24no—
83C2×(C2×D3)⋊C4—24no—
84C2×(C2×D3)⋊C4—42no—
85C2×(C2×D3)⋊C4—42no—
86C2×(C2×D3)⋊C4—42no—
87C2×(C2×D3)⋊C4—42no—
88C2×C4⋊Dic3—21no—
89C2×C4⋊Dic3—21no—
90C2×C4⋊Dic3—21no—
91C2×C4⋊Dic3—21no—
92C2×C4⋊Dic3—21no—
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⋊C8C2×C412yes—
107C22×C3⋊C8D412yes—
108C3×#95—24no—
109#809—28no—
110#809—28no—
111C23×D4—31no—
112C23×C8—31no—
113C23×C8—31no—
114C22×C4⋊C4—21no—
115C22×C4⋊C4—31no—
116C22×C4⋊C4C2×D311yescharacteristic
117C22×C4⋊C4C2×D311yescharacteristic
118C22×C22⋊C4—61no—
119C22×C22⋊C4—61no—
120C22×C42C2×D311yescharacteristic
121C2×#102—34no—
122C2×#102—62no—
123C2×#102—62no—
124C2×#102—62no—
125C2×#102—62no—
126C2×#102—62no—
127#390—62no—
128#390—62no—
129#389—22no—
130#389—22no—
131C2×#95—21no—
132#340—62no—
133#340—62no—
134#336—62no—
135C24×C3C2×D411yescharacteristic
136C23×D3—22no—
137C23×D3—22no—
138C23×D3—22no—
139C23×D3—41no—
140C23×D3—41no—
141C23×D3—41no—
142C23×D3—41no—
143C23×D3—41no—
144C23×D3—41no—
145C23×D3—41no—
146C23×D3—41no—
147C23×D3—41no—
148C23×D3—41no—
149C23×D3—41no—
150C23×D3—41no—
151C22×C3×C4—22no—
152C22×C3×C4—21no—
153C22×C3×C4—22no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—22no—
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×C4—22no—
167C22×C3×C4—41no—
168C22×C3×C4—41no—
169C22×C3×C4—41no—
170C22×C3×C4—41no—
171C22×C3×C4—41no—
172C22×C3×C4—41no—
173C22×C3×C4—41no—
174C22×C3×C4—41no—
175C22×C3×C4—41no—
176C22×C3×C4—41no—
177C22×C3×C4D812yes—
178C22×C3×C4SD1612yes—
179C22×C3×C4C22×C411yescharacteristic
180C22×C3×C4C2×D411yescharacteristic
181C22×C3×C4C2×D411yescharacteristic
182C22×C3×C4C2×D411yescharacteristic
183C22×C3×C4C2×D411yescharacteristic
184C22×C3×C4C2×D411yescharacteristic
185C22×C3×C4C2×D411yescharacteristic
186C22×C3×C4C2×Q811yescharacteristic
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×Dic3—22no—
194C22×Dic3—41no—
195C22×Dic3—41no—
196C22×Dic3—41no—
197C22×Dic3—41no—
198C22×Dic3—41no—
199C22×Dic3—41no—
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—22no—
210C2×D12—22no—
211C2×D12—22no—
212C2×D12—22no—
213C2×D12—22no—
214C2×D12—22no—
215C2×D12—41no—
216C2×D12—41no—
217C2×D12—41no—
218C2×D12—41no—
219C2×D12—41no—
220C2×D12—41no—
221C2×D12—41no—
222C2×D12—41no—
223C2×D12—41no—
224C2×D12—41no—
225C2×D12—41no—
226C2×D12—41no—
227C2×D12C4⋊C414yescomplemented
228C3×C4⋊C4—22no—
229C3×C4⋊C4—22no—
230C3×C4⋊C4—22no—
231C3×C4⋊C4—22no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—48no—
234C3×C4⋊C4—41no—
235C3×C4⋊C4—41no—
236C3×C4⋊C4C22⋊C414yescomplemented
237C3×C42—41no—
238C3×C42—41no—
239C3×C42—41no—
240C3×C42—41no—
241(C2×D3)⋊C4—48no—
242(C2×D3)⋊C4—48no—
243C4⋊Dic3—22no—
244C4⋊Dic3—22no—
245C4⋊Dic3—41no—
246C4⋊Dic3—41no—
247C2×C3⋊C8—22no—
248C2×C3⋊C8—22no—
249C2×C3⋊C8—22no—
250C2×C3⋊C8—22no—
251C2×C3⋊C8—22no—
252C2×C3⋊C8—22no—
253C2×C3⋊C8—41no—
254C2×C3⋊C8—41no—
255C2×C3⋊C8—41no—
256C2×C3⋊C8—41no—
257C2×C3⋊C8—41no—
258C2×C3⋊C8—41no—
259C2×C3⋊C8—41no—
260C2×C3⋊C8—41no—
261C25—61no—
262C22×D4—32no—
263C22×D4—32no—
264C22×D4—32no—
265C22×D4—61no—
266C22×D4—61no—
267C22×D4—61no—
268C22×D4—61no—
269C22×D4—61no—
270C22×D4—61no—
271C22×D4—61no—
272C22×D4—61no—
273C22×D4—61no—
274C22×D4—61no—
275C22×D4—61no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—61no—
279C23×C4#6711yescharacteristic
280C23×C4#6711yescharacteristic
281C23×C4C22×D311yescharacteristic
282C22×C8—32no—
283C22×C8—32no—
284C22×C8—61no—
285C22×C8—61no—
286C22×C8—61no—
287C22×C8—61no—
288C22×C8—61no—
289C22×C8—61no—
290C22×C8—61no—
291C22×C8—61no—
292C22×C8—61no—
293C22×C8—61no—
294C22×C8—61no—
295C22×C8—61no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—32no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—61no—
309C2×C4⋊C4—61no—
310C2×C4⋊C4—61no—
311C2×C4⋊C4—61no—
312C2×C4⋊C4—61no—
313C2×C4⋊C4C4×D312yes—
314C2×C4⋊C4D1212yes—
315C2×C4⋊C4#6712yes—
316C2×C4⋊C4#6712yes—
317C2×C22⋊C4—64no—
318C2×C22⋊C4—64no—
319C2×C22⋊C4—122no—
320C2×C22⋊C4—122no—
321C2×C22⋊C4—122no—
322C2×C22⋊C4—122no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329#102—68no—
330#102—68no—
331#95—24no—
332C23×C3C4×D411yescharacteristic
333C23×C3#12011yescharacteristic
334C23×C3#12011yescharacteristic
335C23×C3#12111yescharacteristic
336C23×C3#12111yescharacteristic
337C23×C3C22⋊Q811yescharacteristic
338C23×C3#12411yescharacteristic
339C23×C3C2×D811yescharacteristic
340C23×C3C2×SD1611yescharacteristic
341C23×C3#13511yescharacteristic
342C23×C3#13511yescharacteristic
343C23×C3AGL(1,ℤ/8)11yescharacteristic
344C23×C3AGL(1,ℤ/8)11yescharacteristic
345C23×C3AGL(1,ℤ/8)11yescharacteristic
346C23×C3#13711yescharacteristic
347C22×D3—24no—
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—42no—
358C22×D3—42no—
359C22×D3—42no—
360C22×D3—42no—
361C22×D3—42no—
362C22×D3—42no—
363C22×D3—42no—
364C22×D3—42no—
365C22×D3—42no—
366C22×D3—81no—
367C22×D3—81no—
368C22×D3—81no—
369C22×D3—81no—
370C22×D3—81no—
371C22×D3—81no—
372C22×D3—81no—
373C22×D3—81no—
374C22×D3—81no—
375C22×D3—81no—
376C22×D3—81no—
377C22×D3—81no—
378C22×D3—81no—
379C22×D3—81no—
380C22×D3—81no—
381C22×D3—81no—
382C2×C3×C4—24no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—42no—
398C2×C3×C4—41no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—81no—
407C2×C3×C4—81no—
408C2×C3×C4—81no—
409C2×C3×C4—81no—
410C2×C3×C4C2×C22⋊C411yescharacteristic
411C2×C3×C4C2×C4⋊C411yescharacteristic
412C2×C3×C4#11711yescharacteristic
413C2×C3×C4C4×D411yescharacteristic
414C2×C3×C4C4×D411yescharacteristic
415C2×C3×C4C4×D411yescharacteristic
416C2×C3×C4#12011yescharacteristic
417C2×C3×C4#12111yescharacteristic
418C2×C3×C4#12111yescharacteristic
419C2×C3×C4#12111yescharacteristic
420C2×C3×C4#12111yescharacteristic
421C2×C3×C4#12111yescharacteristic
422C2×C3×C4#12111yescharacteristic
423C2×C3×C4C22⋊Q811yescharacteristic
424C2×C3×C4C22⋊Q811yescharacteristic
425C2×C3×C4C22⋊Q811yescharacteristic
426C2×C3×C4C22⋊Q811yescharacteristic
427C2×C3×C4C22⋊Q811yescharacteristic
428C2×C3×C4#12311yescharacteristic
429C2×C3×C4#12311yescharacteristic
430C2×C3×C4#12311yescharacteristic
431C2×C3×C4#12311yescharacteristic
432C2×C3×C4#12311yescharacteristic
433C2×C3×C4#12411yescharacteristic
434C2×C3×C4#12411yescharacteristic
435C2×C3×C4#12611yescharacteristic
436C2×C3×C4#12611yescharacteristic
437C2×C3×C4#12711yescharacteristic
438C2×Dic3—42no—
439C2×Dic3—42no—
440C2×Dic3—42no—
441C2×Dic3—81no—
442C2×Dic3—81no—
443C2×Dic3—81no—
444C2×Dic3—81no—
445D12—24no—
446D12—24no—
447D12—42no—
448D12—42no—
449D12—42no—
450D12—42no—
451D12—42no—
452D12—42no—
453C3⋊C8—42no—
454C3⋊C8—42no—
455C24—62no—
456C24—62no—
457C24—62no—
458C24—121no—
459C24—121no—
460C24—121no—
461C24—121no—
462C24—121no—
463C24—121no—
464C24—121no—
465C24—121no—
466C24—121no—
467C24—121no—
468C24—121no—
469C24—121no—
470C24C2×#6711yescharacteristic
471C2×D4—34no—
472C2×D4—62no—
473C2×D4—62no—
474C2×D4—62no—
475C2×D4—62no—
476C2×D4—62no—
477C2×D4—62no—
478C2×D4—62no—
479C2×D4—62no—
480C2×D4—62no—
481C2×D4—62no—
482C2×D4—62no—
483C2×D4—62no—
484C2×D4—62no—
485C2×D4—62no—
486C2×D4—62no—
487C2×D4—121no—
488C2×D4—121no—
489C2×D4—121no—
490C2×D4—121no—
491C2×D4—121no—
492C2×D4—121no—
493C2×D4—121no—
494C2×D4—121no—
495C2×D4—121no—
496C2×D4—121no—
497C2×D4—121no—
498C2×D4—121no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—62no—
526C22×C4—121no—
527C22×C4—121no—
528C22×C4—121no—
529C22×C4—121no—
530C22×C4—121no—
531C22×C4—121no—
532C22×C4#21312yes—
533C22×C4#21512yes—
534C22×C4C2×C4×D311yescharacteristic
535C22×C4C2×D1211yescharacteristic
536C22×C4#23511yescharacteristic
537C22×C4#23511yescharacteristic
538C22×C4D3×D411yescharacteristic
539C22×C4D3×D411yescharacteristic
540C22×C4D3×D411yescharacteristic
541C22×C4#23711yescharacteristic
542C22×C4D3×Q811yescharacteristic
543C22×C4#23911yescharacteristic
544C22×C4#23911yescharacteristic
545C22×C4#23911yescharacteristic
546C22×C4C2×#6711yescharacteristic
547C22×C4C2×#6711yescharacteristic
548C2×C8—62no—
549C2×C8—62no—
550C2×C8—62no—
551C2×C8—62no—
552C2×C8—62no—
553C2×C8—62no—
554C2×C8—121no—
555C2×C8—121no—
556C2×C8—121no—
557C2×C8—121no—
558C2×C8—121no—
559C2×C8—121no—
560C2×C8—121no—
561C2×C8—121no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—48no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—62no—
571C4⋊C4—62no—
572C4⋊C4—121no—
573C4⋊C4—121no—
574C4⋊C4(C2×D3)⋊C414yescomplemented
575C22⋊C4—128no—
576C22⋊C4—128no—
577C42—41no—
578C42—41no—
579C42—41no—
580C42—41no—
581C22×C3#38511yescharacteristic
582C22×C3#38611yescharacteristic
583C22×C3#38811yescharacteristic
584C22×C3#39211yescharacteristic
585C22×C3#39311yescharacteristic
586C22×C3#39411yescharacteristic
587C22×C3#39611yescharacteristic
588C22×C3C4×D811yescharacteristic
589C22×C3C4×SD1611yescharacteristic
590C22×C3#44011yescharacteristic
591C22×C3#44211yescharacteristic
592C22×C3#44711yescharacteristic
593C22×C3#44711yescharacteristic
594C22×C3#44811yescharacteristic
595C22×C3#44911yescharacteristic
596C22×C3#44911yescharacteristic
597C22×C3#44911yescharacteristic
598C22×C3#45011yescharacteristic
599C22×C3#45211yescharacteristic
600C22×C3#45911yescharacteristic
601C22×C3#46011yescharacteristic
602C22×C3#46311yescharacteristic
603C22×C3#46411yescharacteristic
604C22×C3#46511yescharacteristic
605C22×C3#46611yescharacteristic
606C22×C3#46811yescharacteristic
607C22×C3#46911yescharacteristic
608C22×C3#47411yescharacteristic
609C22×C3#47611yescharacteristic
610C22×C3#47811yescharacteristic
611C22×C3#47811yescharacteristic
612C22×C3#48611yescharacteristic
613C22×C3#48811yescharacteristic
614C22×C3#48911yescharacteristic
615C22×C3#49011yescharacteristic
616C2×D3—44no—
617C2×D3—44no—
618C2×D3—44no—
619C2×D3—82no—
620C2×D3—82no—
621C2×D3—82no—
622C2×D3—82no—
623C2×D3—82no—
624C2×D3—82no—
625C2×D3—82no—
626C2×D3—82no—
627C2×D3—82no—
628C2×D3—82no—
629C2×D3—82no—
630C2×D3—82no—
631C3×C4—44no—
632C3×C4—42no—
633C3×C4—42no—
634C3×C4—82no—
635C3×C4#38011yescharacteristic
636C3×C4#38511yescharacteristic
637C3×C4#38811yescharacteristic
638C3×C4#39011yescharacteristic
639C3×C4#39411yescharacteristic
640C3×C4#39611yescharacteristic
641C3×C4#39711yescharacteristic
642C3×C4#39911yescharacteristic
643Dic3—82no—
644C23—64no—
645C23—122no—
646C23—122no—
647C23—122no—
648C23—122no—
649C23—122no—
650C23—122no—
651C23—122no—
652C23—122no—
653C23—122no—
654C23—122no—
655C23—122no—
656C23—122no—
657C23—122no—
658C23—122no—
659C23—122no—
660C23—122no—
661C23—122no—
662C23—122no—
663C23—241no—
664C23—241no—
665C23—241no—
666C23—241no—
667C23—241no—
668C23—241no—
669C23—241no—
670C23—241no—
671C23—241no—
672C23—241no—
673C23—241no—
674C23—241no—
675C23—241no—
676C23—241no—
677C23—241no—
678C23—241no—
679C23C4×#6711yescharacteristic
680C23#93011yescharacteristic
681C23C2×#21311yescharacteristic
682C23#93211yescharacteristic
683C23#93711yescharacteristic
684C23#93911yescharacteristic
685C23C2×#21511yescharacteristic
686C23#94211yescharacteristic
687C23#94611yescharacteristic
688C23#94711yescharacteristic
689C23#94911yescharacteristic
690C23#94911yescharacteristic
691C23#95011yescharacteristic
692C23#95011yescharacteristic
693C23#95311yescharacteristic
694D4—64no—
695D4—64no—
696D4—122no—
697D4—122no—
698D4—122no—
699D4—122no—
700D4—122no—
701D4—122no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—122no—
731C2×C4—122no—
732C2×C4—122no—
733C2×C4—241no—
734C2×C4—241no—
735C2×C4—241no—
736C2×C4—241no—
737C2×C4D3×C4⋊C411yescharacteristic
738C2×C4#89211yescharacteristic
739C2×C4#89311yescharacteristic
740C2×C4#89311yescharacteristic
741C2×C4#89411yescharacteristic
742C2×C4#89411yescharacteristic
743C2×C4#89411yescharacteristic
744C2×C4#89411yescharacteristic
745C2×C4#89511yescharacteristic
746C2×C4#89511yescharacteristic
747C2×C4#89511yescharacteristic
748C2×C4#89611yescharacteristic
749C2×C4#89611yescharacteristic
750C2×C4#89711yescharacteristic
751C2×C4#89811yescharacteristic
752C2×C4#89811yescharacteristic
753C2×C4C2×(C2×D3)⋊C411yescharacteristic
754C2×C4C4×#6711yescharacteristic
755C2×C4#92911yescharacteristic
756C2×C4#93011yescharacteristic
757C2×C4#93711yescharacteristic
758C2×C4#93811yescharacteristic
759C2×C4#93911yescharacteristic
760C2×C4#94011yescharacteristic
761C2×C4#94611yescharacteristic
762C2×C4#94611yescharacteristic
763C2×C4#94711yescharacteristic
764C2×C4#94711yescharacteristic
765C8—122no—
766C8—122no—
767C2×C3#143911yescharacteristic
768C2×C3#186211yescharacteristic
769C2×C3#186411yescharacteristic
770C2×C3#187911yescharacteristic
771C2×C3#188011yescharacteristic
772C2×C3#193411yescharacteristic
773C2×C3#193611yescharacteristic
774C2×C3#199911yescharacteristic
775C2×C3#200011yescharacteristic
776C2×C3#202311yescharacteristic
777C2×C3#202511yescharacteristic
778C2×C3#204111yescharacteristic
779C2×C3#204211yescharacteristic
780C2×C3#206511yescharacteristic
781C2×C3#206711yescharacteristic
782D3—84no—
783C22—124no—
784C22—124no—
785C22—124no—
786C22—242no—
787C22—242no—
788C22—242no—
789C22—242no—
790C22—242no—
791C22—242no—
792C22—242no—
793C22—242no—
794C22—242no—
795C22—242no—
796C22—242no—
797C22—242no—
798C22#498911yescharacteristic
799C22#499011yescharacteristic
800C22#499111yescharacteristic
801C22#499411yescharacteristic
802C22C4×#21311yescharacteristic
803C22#501411yescharacteristic
804C22#501511yescharacteristic
805C22#501611yescharacteristic
806C22C4×#21511yescharacteristic
807C22#502611yescharacteristic
808C22#502711yescharacteristic
809C22#502811yescharacteristic
810C22#503611yescharacteristic
811C22#503711yescharacteristic
812C22#503811yescharacteristic
813C22#503911yescharacteristic
814C22#504611yescharacteristic
815C22#504711yescharacteristic
816C22#504811yescharacteristic
817C22#504911yescharacteristic
818C22#506611yescharacteristic
819C22#506611yescharacteristic
820C22#506711yescharacteristic
821C22#506811yescharacteristic
822C22#508411yescharacteristic
823C22#508711yescharacteristic
824C22#508811yescharacteristic
825C22#508911yescharacteristic
826C22#521311yescharacteristic
827C22#521711yescharacteristic
828C22#522311yescharacteristic
829C22#522711yescharacteristic
830C22#523111yescharacteristic
831C22#523811yescharacteristic
832C22#523811yescharacteristic
833C4—42no—
834C4—42no—
835C4—44no—
836C4—82no—
837C4—242no—
838C4#498711yescharacteristic
839C4#498811yescharacteristic
840C4#498911yescharacteristic
841C4#499011yescharacteristic
842C4#499111yescharacteristic
843C4#499211yescharacteristic
844C4#499311yescharacteristic
845C4#499411yescharacteristic
846C3#1106611yescharacteristic, complemented, Sylow
847C2—244no—
848C2#6961511yescharacteristic
849C2#6961711yescharacteristic
850C2#6962511yescharacteristic
851C2#6962611yescharacteristic
852C2#6962711yescharacteristic
853C2#6962811yescharacteristic
854C2#6962911yescharacteristic
855C2#6963011yescharacteristic
856C2#7157011yescharacteristic
857C2#7161311yescharacteristic
858C2#7163311yescharacteristic
859C2#7168411yescharacteristic
860C2#7169911yescharacteristic
861C2#7174311yescharacteristic
862C2#7179211yescharacteristic
subgroupG/H
centerC24C2×#67
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC2×C3×#389C2
socleC24×C3C2×D4
prime radicalC23×D12C22
cosocleC23×C3×C4C23
hypercenterC2×#389D3
hypocenterC3#11066
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C2×C3×#389C2semidirect
5. C2×#4529C2semidirect
6. C2×#4529C2semidirect
7. C2×#4524C2semidirect
27. C2×#809C4semidirect
36. C2×#389D3semidirect
227. C2×D12C4⋊C4semidirect
236. C3×C4⋊C4C22⋊C4semidirect
574. C4⋊C4(C2×D3)⋊C4semidirect
846. C3#11066semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3892
C22×#8092
C2×#49392
C2×#45292
C2×#45242
#110663