Finite Group Databasebeta

← #25019985

Subgroups — #25019985

Order 11008.

1810 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic43C211yesmaximal, characteristic
2C2×#14582806C211yesmaximal, characteristic
3C2×#14582798C211yesmaximal, characteristic
4C2×C4×C4⋊Dic43C211yesmaximal, characteristic
5#19132860C212yesmaximal
6#19132852C212yesmaximal
7#19132829C212yesmaximal
8#19132829C212yesmaximal
9#19132825C211yesmaximal, characteristic
10#19132824C211yesmaximal, characteristic
11C2×C43×#391C211yesmaximal, characteristic
12C2×Q8×Dic43—24no—
13C2×Q8×Dic43—24no—
14C2×Q8×Dic43—24no—
15C22×C4⋊Dic43C2211yescharacteristic
16C22×C4⋊Dic43C2211yescharacteristic
17C22×C4⋊Dic43C2212yes—
18C22×C4⋊Dic43C2212yes—
19C22×C4⋊Dic43C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22C22×C4×Dic43C2212yes—
23C22×C4×Dic43C2211yescharacteristic
24#14582806—24no—
25#14582798—24no—
26C4×C4⋊Dic43—24no—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2211yescharacteristic
34C2×C43⋊#95C2212yes—
35C2×C43⋊#95C2212yes—
36C23×Q8×C43C2211yescharacteristic
37C22×C4⋊C4×C43C2211yescharacteristic
38C22×C42×C43C2211yescharacteristic
39C43×#391C418yescomplemented
40C2×#95×C43C2212yes—
41C2×#95×C43C2212yes—
42C23×Dic43C2312yes—
43C23×Dic43C2312yes—
44C23×Dic43C2311yescharacteristic
45C23×Dic43C2311yescharacteristic
46C23×Dic43C2311yescharacteristic
47C23×Dic43C2311yescharacteristic
48Q8×Dic43—232no—
49C2×C4⋊Dic43—24no—
50C2×C4⋊Dic43—22no—
51C2×C4⋊Dic43—22no—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—24no—
54C2×C4⋊Dic43—24no—
55C2×C4⋊Dic43—22no—
56C2×C4⋊Dic43—22no—
57C2×C4⋊Dic43—22no—
58C2×C4⋊Dic43—22no—
59C2×C4⋊Dic43—22no—
60C2×C4⋊Dic43—22no—
61C2×C4⋊Dic43—22no—
62C2×C4⋊Dic43—24no—
63C2×C4⋊Dic43—24no—
64C2×C4⋊Dic43—42no—
65C2×C4⋊Dic43D414yes—
66C2×C4⋊Dic43Q814yescomplemented
67C2×C4×Dic43—24no—
68C2×C4×Dic43—22no—
69C2×C4×Dic43—22no—
70C2×C4×Dic43—24no—
71C2×C4×Dic43—24no—
72C2×C4×Dic43—22no—
73C2×C4×Dic43—22no—
74C2×C4×Dic43—22no—
75C2×C4×Dic43D414yes—
76C43⋊#95—24no—
77C43⋊#95—24no—
78C43⋊#95—24no—
79C43⋊#95—24no—
80C43⋊#95—22no—
81C43⋊#95—22no—
82C43⋊#95—24no—
83C43⋊#95—42no—
84C43⋊#95—42no—
85C22×Q8×C43—22no—
86C22×Q8×C43—22no—
87C22×Q8×C43—22no—
88C22×Q8×C43—22no—
89C22×Q8×C43C2×C414yes—
90C22×Q8×C43D414yes—
91C22×Q8×C43Q814yes—
92C23×C4×C43C2311yescharacteristic
93C23×C4×C43C2312yes—
94C23×C4×C43C2312yes—
95C23×C4×C43C2311yescharacteristic
96C23×C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43—22no—
98C2×C4⋊C4×C43—22no—
99C2×C4⋊C4×C43C2×C414yes—
100C2×C42×C43—22no—
101C2×C42×C43—22no—
102C2×C42×C43C2×C414yes—
103#95×C43C2×C418yes—
104#95×C43C2×C418yes—
105C24×C43C2411yescharacteristic
106C2×Q8×C43—28no—
107C2×Q8×C43—28no—
108C2×Q8×C43—28no—
109C2×Q8×C43—28no—
110C2×Q8×C43—28no—
111C2×Q8×C43—28no—
112C2×Q8×C43C4⋊C4116yescomplemented
113C22×C4×C43—21no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—21no—
117C22×C4×C43—22no—
118C22×C4×C43—21no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—21no—
128C22×C4×C43—22no—
129C22×C4×C43—21no—
130C22×C4×C43—22no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43C22×C412yes—
134C22×C4×C43C22×C414yes—
135C22×C4×C43C22×C414yes—
136C22×C4×C43C22×C412yes—
137C22×C4×C43C22×C412yes—
138C22×C4×C43C2×D414yes—
139C22×C4×C43C2×D412yes—
140C22×C4×C43C2×D412yes—
141C22×C4×C43C2×D412yes—
142C22×C4×C43C2×Q814yes—
143C22×C4×C43C2×Q812yes—
144C22×C4×C43C2×Q812yes—
145C22×C4×C43#4112yes—
146C22×C4×C43#4112yes—
147C22×C4×C43#4112yes—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—22no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—22no—
159C22×Dic43—21no—
160C22×Dic43—22no—
161C22×Dic43—22no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—22no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—22no—
168C22×Dic43—22no—
169C22×Dic43—22no—
170C22×Dic43—22no—
171C22×Dic43—21no—
172C22×Dic43—22no—
173C22×Dic43—21no—
174C22×Dic43—22no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—21no—
180C22×Dic43—22no—
181C22×Dic43—21no—
182C22×Dic43—22no—
183C22×Dic43C2×D414yes—
184C22×Dic43C2×D412yes—
185C22×Dic43C2×D412yes—
186C22×Dic43C2×Q812yes—
187C22×Dic43C2×Q812yes—
188C22×Dic43#4112yes—
189C22×Dic43#4112yes—
190C4⋊C4×C43—28no—
191C42×C43—28no—
192C4⋊Dic43—28no—
193C4⋊Dic43—216no—
194C4⋊Dic43—28no—
195C4⋊Dic43—28no—
196C4⋊Dic43—48no—
197C4⋊Dic43—44no—
198C4×Dic43—216no—
199C4×Dic43—28no—
200C4×Dic43—44no—
201C23×C43C23×C411yescharacteristic
202C23×C43C22×D411yescharacteristic
203C23×C43C22×D411yescharacteristic
204C23×C43C22×D411yescharacteristic
205C23×C43C22×Q811yescharacteristic
206C23×C43C22×Q811yescharacteristic
207C23×C43C2×#4111yescharacteristic
208C23×C43C2×#4111yescharacteristic
209C23×C43C2×#4111yescharacteristic
210C23×C43C2×#4111yescharacteristic
211C23×C43C2×#4111yescharacteristic
212C23×C43H(5,𝔽2)11yescharacteristic
213C23×C432−1+411yescharacteristic
214C23×C432−1+411yescharacteristic
215C23×C432−1+411yescharacteristic
216Q8×C43—232no—
217C2×C4×C43—22no—
218C2×C4×C43—24no—
219C2×C4×C43—24no—
220C2×C4×C43—22no—
221C2×C4×C43—24no—
222C2×C4×C43—22no—
223C2×C4×C43—24no—
224C2×C4×C43—24no—
225C2×C4×C43—24no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
232C2×C4×C43—22no—
233C2×C4×C43—22no—
234C2×C4×C43—24no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43C2×C4⋊C418yes—
244C2×C4×C43C2×C4⋊C414yes—
245C2×C4×C43C4×D414yes—
246C2×C4×C43C4×D414yes—
247C2×C4×C43C4×Q814yescomplemented
248C2×C4×C43#12014yes—
249C2×C4×C43C22⋊Q814yes—
250C2×C4×C43C22⋊Q814yes—
251C2×C4×C43#12314yes—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—24no—
259C2×Dic43—22no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—24no—
266C2×Dic43—24no—
267C2×Dic43—22no—
268C2×Dic43—22no—
269C2×Dic43—22no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—42no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—42no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—42no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—42no—
285C2×Dic43—41no—
286C2×Dic43—42no—
287C2×Dic43—42no—
288C2×Dic43—42no—
289C2×Dic43—42no—
290C2×Dic43—42no—
291C2×Dic43—42no—
292C2×Dic43—42no—
293C2×Dic43C22⋊Q814yes—
294#14017—431nomaximal, Sylow
295C22×C43C22×C4⋊C411yescharacteristic
296C22×C43C2×C4×D411yescharacteristic
297C22×C43C2×C4×D411yescharacteristic
298C22×C43C2×C4×Q811yescharacteristic
299C22×C43C4×#4111yescharacteristic
300C22×C43#51911yescharacteristic
301C22×C43#52011yescharacteristic
302C22×C43C2×#12011yescharacteristic
303C22×C43C2×C22⋊Q811yescharacteristic
304C22×C43C2×C22⋊Q811yescharacteristic
305C22×C43C2×C22⋊Q811yescharacteristic
306C22×C43C2×#12311yescharacteristic
307C22×C43#52511yescharacteristic
308C22×C43#52911yescharacteristic
309C22×C43#53311yescharacteristic
310C22×C43#53611yescharacteristic
311C22×C43#53711yescharacteristic
312C22×C43#54111yescharacteristic
313C22×C43#54211yescharacteristic
314C22×C43#54611yescharacteristic
315C22×C43#54711yescharacteristic
316C22×C43#54811yescharacteristic
317C22×C43#54811yescharacteristic
318C22×C43#54811yescharacteristic
319C22×C43D4×Q811yescharacteristic
320C22×C43D4×Q811yescharacteristic
321C22×C43#55011yescharacteristic
322C22×C43#55611yescharacteristic
323C22×C43#55611yescharacteristic
324C22×C43#55711yescharacteristic
325C22×C43#55711yescharacteristic
326C22×C43#55711yescharacteristic
327C22×C43#55711yescharacteristic
328C22×C43Q8211yescharacteristic
329C22×C43#55911yescharacteristic
330C4×C43—28no—
331C4×C43—24no—
332C4×C43—42no—
333C4×C43—44no—
334C4×C43#38518yes—
335Dic43—24no—
336Dic43—42no—
337Dic43—44no—
338Dic43—42no—
339Dic43—42no—
340Dic43—82no—
341C22×C4×Q8—431no—
342C2×#391—431no—
343C2×#391D4311yescharacteristic
344C2×#389—431no—
345C2×C4×C4⋊C4—431no—
346#1444—432no—
347#1442—432no—
348#1436—432no—
349#1436—432no—
350C4⋊#95—431no—
351C4⋊#95—431no—
352C2×C43C2×#38511yescharacteristic
353C2×C43C4×C22⋊Q811yescharacteristic
354C2×C43#232311yescharacteristic
355C2×C43Q8×C4⋊C411yescharacteristic
356C2×C43#235111yescharacteristic
357C2×C43#236511yescharacteristic
358C2×C43#236711yescharacteristic
359C2×C43#240711yescharacteristic
360C2×C43#240911yescharacteristic
361C2×C43#244611yescharacteristic
362C2×C43#244811yescharacteristic
363C2×C43#245111yescharacteristic
364C2×C43#245311yescharacteristic
365C2×C43#258111yescharacteristic
366C2×C43#258211yescharacteristic
367C23×Q8C2×D4311yescharacteristic
368C2×C4×Q8—864no—
369C2×C4×Q8—864no—
370C2×C4×Q8—864no—
371C22×C4⋊C4—431no—
372C22×C4⋊C4—431no—
373C22×C4⋊C4—432no—
374C22×C4⋊C4—431no—
375C22×C4⋊C4—431no—
376C22×C4⋊C4—432no—
377C22×C4⋊C4C2×D4311yescharacteristic
378C22×C42—431no—
379C22×C42—432no—
380C22×C42—431no—
381C22×C42C2×D4311yescharacteristic
382#391—864no—
383#391Dic4318yescomplemented
384#389—864no—
385C4×C4⋊C4—864no—
386C2×#95—432no—
387C2×#95—432no—
388C2×#95—431no—
389C2×#95—432no—
390C2×#95—432no—
391C2×#95—432no—
392C2×#95—431no—
393C2×#95—432no—
394C2×#95—432no—
395C2×#95C2×D4312yes—
396C2×#95C2×D4312yes—
397C43#1401711yescharacteristic, complemented, Sylow
398C22×Q8—22no—
399C22×Q8—22no—
400C22×Q8—22no—
401C22×Q8—22no—
402C22×Q8Dic8614yes—
403C22×Q8D17214yes—
404C22×Q8C2×Dic4314yes—
405C23×C4—431no—
406C23×C4—431no—
407C23×C4—432no—
408C23×C4—431no—
409C23×C4—431no—
410C23×C4—432no—
411C23×C4C22×D4312yes—
412C23×C4C22×D4311yescharacteristic
413C23×C4C22×D4312yes—
414C23×C4C22×D4311yescharacteristic
415C23×C4C22×D4311yescharacteristic
416C4×Q8—8632no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—434no—
420C2×C4⋊C4—434no—
421C2×C4⋊C4—864no—
422C2×C4⋊C4—864no—
423C2×C4⋊C4—862no—
424C2×C4⋊C4—862no—
425C2×C4⋊C4—862no—
426C2×C4⋊C4—862no—
427C2×C4⋊C4—864no—
428C2×C4⋊C4—862no—
429C2×C4⋊C4—862no—
430C2×C4⋊C4—862no—
431C2×C4⋊C4—864no—
432C2×C4⋊C4—864no—
433C2×C4⋊C4—862no—
434C2×C4⋊C4—862no—
435C2×C4⋊C4—862no—
436C2×C4⋊C4—1722no—
437C2×C4⋊C4C2×Dic4314yes—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—434no—
441C2×C42—864no—
442C2×C42—864no—
443C2×C42—864no—
444C2×C42—862no—
445C2×C42—862no—
446C2×C42—862no—
447C2×C42—862no—
448C2×C42—862no—
449C2×C42C2×Dic4314yes—
450#95—864no—
451#95—862no—
452#95—862no—
453#95—864no—
454#95—864no—
455#95—864no—
456#95—864no—
457#95—1722no—
458#95—1722no—
459#95C2×Dic4318yes—
460#95C2×Dic4318yes—
461C24C23×D4311yescharacteristic
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8—28no—
468C2×Q8C4⋊Dic43116yescomplemented
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—432no—
490C22×C4—432no—
491C22×C4—432no—
492C22×C4—432no—
493C22×C4—434no—
494C22×C4—432no—
495C22×C4—432no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—862no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—861no—
508C22×C4—862no—
509C22×C4—861no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4—862no—
513C22×C4—862no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—862no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—862no—
521C22×C4—861no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—862no—
525C22×C4—862no—
526C22×C4—862no—
527C22×C4—862no—
528C22×C4—862no—
529C22×C4—862no—
530C22×C4—862no—
531C22×C4C2×Dic8614yes—
532C22×C4C2×Dic8612yes—
533C22×C4C2×D17214yes—
534C22×C4C2×D17212yes—
535C22×C4D4×D4312yes—
536C22×C4D4×D4312yes—
537C22×C4#1062190012yes—
538C22×C4#1062190012yes—
539C22×C4Q8×D4312yes—
540C22×C4#1062190212yes—
541C22×C4C22×Dic4312yes—
542C22×C4C22×Dic4314yes—
543C22×C4C22×Dic4314yes—
544C22×C4C22×Dic4312yes—
545C22×C4C22×Dic4312yes—
546C4⋊C4—28no—
547C4⋊C4—868no—
548C4⋊C4—8616no—
549C4⋊C4—868no—
550C4⋊C4—868no—
551C4⋊C4—1728no—
552C4⋊C4—1724no—
553C42—28no—
554C42—8616no—
555C42—868no—
556C42—1724no—
557C23C23×Dic4311yescharacteristic
558C23C2×D4×D4311yescharacteristic
559C23C2×D4×D4311yescharacteristic
560C23C22×D17211yescharacteristic
561C23C2×Q8×D4311yescharacteristic
562C23C22×Dic8611yescharacteristic
563C23#41×D4311yescharacteristic
564C23#41×D4311yescharacteristic
565C23C2×#1062190011yescharacteristic
566C23C2×#1062190011yescharacteristic
567C23C2×#1062190211yescharacteristic
568C23#1306337111yescharacteristic
569C23#1306337211yescharacteristic
570C23#1306337311yescharacteristic
571C23#1306337311yescharacteristic
572Q8—232no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—434no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—864no—
607C2×C4—862no—
608C2×C4—862no—
609C2×C4—862no—
610C2×C4—864no—
611C2×C4—862no—
612C2×C4—862no—
613C2×C4—862no—
614C2×C4—862no—
615C2×C4—862no—
616C2×C4—862no—
617C2×C4—864no—
618C2×C4—1722no—
619C2×C4—1722no—
620C2×C4—1722no—
621C2×C4—1722no—
622C2×C4—1722no—
623C2×C4—1722no—
624C2×C4—1722no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1722no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1722no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1722no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1722no—
640C2×C4—1721no—
641C2×C4C2×C4⋊Dic4318yes—
642C2×C4C2×C4⋊Dic4314yes—
643C2×C4D4×Dic4314yes—
644C2×C4D4×Dic4314yes—
645C2×C4Q8×Dic4314yescomplemented
646C2×C4#1306329514yes—
647C2×C4#1306330214yes—
648C2×C4#1306330214yes—
649C2×C4#1306330914yes—
650C22C22×C4⋊Dic4311yescharacteristic
651C22C2×D4×Dic4311yescharacteristic
652C22C2×D4×Dic4311yescharacteristic
653C22C2×Q8×Dic4311yescharacteristic
654C22#41×Dic4311yescharacteristic
655C22#1458337711yescharacteristic
656C22#1458338211yescharacteristic
657C22C2×#1306329511yescharacteristic
658C22C22⋊Q8×D4311yescharacteristic
659C22C2×#1306330211yescharacteristic
660C22C2×#1306330211yescharacteristic
661C22C2×#1306330911yescharacteristic
662C22#1458341211yescharacteristic
663C22#1458343511yescharacteristic
664C22#1458345111yescharacteristic
665C22#1458347211yescharacteristic
666C22#1458347911yescharacteristic
667C22#1458350911yescharacteristic
668C22#1458352211yescharacteristic
669C22#1458354211yescharacteristic
670C22#1458355211yescharacteristic
671C22#1458355711yescharacteristic
672C22#1458356111yescharacteristic
673C22#1458356111yescharacteristic
674C22#1458356411yescharacteristic
675C22Q8×D17211yescharacteristic
676C22#1458357111yescharacteristic
677C22#1458361811yescharacteristic
678C22#1458362311yescharacteristic
679C22#1458362411yescharacteristic
680C22#1458362511yescharacteristic
681C22#1458362511yescharacteristic
682C22#1458362811yescharacteristic
683C22Q8×Dic8611yescharacteristic
684C22#1458363111yescharacteristic
685C4—24no—
686C4—28no—
687C4—44no—
688C4—42no—
689C4—864no—
690C4—3442no—
691C4—1724no—
692C4—1722no—
693C4—1722no—
694C4—1722no—
695C4#1458277418yes—
696C2C2×#1458277411yescharacteristic
697C2C22⋊Q8×Dic4311yescharacteristic
698C2#1913727911yescharacteristic
699C2Q8×C4⋊Dic4311yescharacteristic
700C2#1913751611yescharacteristic
701C2#1913765511yescharacteristic
702C2#1913767011yescharacteristic
703C2#1913794311yescharacteristic
704C2#1913795811yescharacteristic
705C2#1913836911yescharacteristic
706C2#1913839111yescharacteristic
707C2#1913843711yescharacteristic
708C2#1913845911yescharacteristic
709C2#1913995911yescharacteristic
710C2#1913996611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#391C2
socle, prime radical, cosocleC24×C43C24
hypercenterC2×#391D43
hypocenterC43#14017
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
39. C43×#391C4semidirect
66. C2×C4⋊Dic43Q8semidirect
112. C2×Q8×C43C4⋊C4semidirect
247. C2×C4×C43C4×Q8semidirect
383. #391Dic43semidirect
397. C43#14017semidirect
468. C2×Q8C4⋊Dic43semidirect
645. C2×C4Q8×Dic43semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic432
C2×#145828062
C2×#145827982
C2×C4×C4⋊Dic432
#191328602
#191328522
#191328292
#191328252
#191328242
C2×C43×#3912
#1401743