Finite Group Databasebeta

← #25257649

Subgroups — #25257649

Order 11008.

5106 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063373C211yesmaximal, characteristic
2C2×#14583381C211yesmaximal, characteristic, complemented
3C2×C4×#10621902C211yesmaximal, characteristic, complemented
4Q8×C22⋊Dic43C211yesmaximal, characteristic, complemented
5Q8×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
6Q8×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
7#19137426C213yesmaximal, complemented
8#19137424C213yesmaximal, complemented
9#19137424C213yesmaximal, complemented
10#19137423C213yesmaximal, complemented
11#19137184C213yesmaximal, complemented
12#19137178C213yesmaximal, complemented
13#19137081C213yesmaximal, complemented
14#391×D43C213yesmaximal, complemented
15Q8×C22⋊C4×C43C211yesmaximal, characteristic, complemented
16C2×#13063373—28no—
17C2×#13063373—28no—
18C2×#13063373C4116yescomplemented
19C22×#10621902C2213yes—
20C22×#10621902C2211yescharacteristic
21C22×#10621898C2213yes—
22C22×#10621898C2213yes—
23C22×Q8×D43C2213yes—
24C22×Q8×D43C2211yescharacteristic
25#14583381—28no—
26C4×#10621902—28no—
27C2×Q8×Dic43C2211yescharacteristic
28C2×Q8×Dic43C2211yescharacteristic
29C2×C4×D172C2213yes—
30C2×C4×D172C2213yes—
31C2×#13063287C2213yes—
32C2×#13063287C2213yes—
33C2×#13063283C2213yes—
34C2×#13063282C2213yes—
35C2×C4⋊C4×D43C2213yes—
36C2×C42×D43C2213yes—
37#14582806C2213yes—
38#14582806C2213yes—
39#14582805C2213yes—
40#14582805C2213yes—
41#14582804C2213yes—
42#14582804C2213yes—
43#14582803C2213yes—
44#14582803C2216yes—
45#14582803C2213yes—
46#14582799C2211yescharacteristic
47#14582799C2213yes—
48#14582777C2213yes—
49#14582777C2213yes—
50#14582777C2216yes—
51#14582775C2213yes—
52#14582775C2213yes—
53#14582775C2216yes—
54#14582761C2216yes—
55#14582761C2216yes—
56#14582759C2213yes—
57#14582756C2213yes—
58#14582756C2213yes—
59C4×(C2×D43)⋊C4C2213yes—
60C4×(C2×D43)⋊C4C2213yes—
61C4×C22⋊Dic43C2213yes—
62#95×D43C2216yes—
63#95×D43C2216yes—
64C23×Q8×C43C2211yescharacteristic
65C2×C4×Q8×C43C2211yescharacteristic
66C2×C4×Q8×C43C2211yescharacteristic
67C43×#391C2213yes—
68C43×#391C2213yes—
69C43×#380C2213yes—
70C4×C22⋊C4×C43C2213yes—
71#13063373—2128no—
72C2×#10621902—212no—
73C2×#10621902—212no—
74C2×#10621902C2×C418yes—
75C2×#10621902C2×C4124yescomplemented
76C2×#10621902D418yes—
77C2×#10621902D418yes—
78C2×#10621898—212no—
79C2×#10621898—212no—
80C2×#10621898—212no—
81C2×#10621898—212no—
82C2×#10621898C2×C4124yescomplemented
83C2×#10621898C2×C4124yescomplemented
84C22×Dic86C2313yes—
85C22×Dic86C2313yes—
86C2×Q8×D43—24no—
87C2×Q8×D43—24no—
88C2×Q8×D43—212no—
89C2×Q8×D43—212no—
90C2×Q8×D43C2×C418yescomplemented
91C2×Q8×D43C2×C4124yescomplemented
92C22×D172C2313yes—
93C22×D172C2313yes—
94C22×C22⋊D43C2311yescharacteristic
95C22×C22⋊D43C2313yes—
96C22×C4×D43C2313yes—
97C22×C4×D43C2313yes—
98C22×C4×D43C2316yes—
99C22×C4×D43C2313yes—
100C22×C4×D43C2316yes—
101C22×C4×D43C2313yes—
102Q8×Dic43—24no—
103Q8×Dic43—24no—
104C4×D172—212no—
105C4×D172—212no—
106#13063287—212no—
107#13063287—212no—
108#13063283—212no—
109#13063282—212no—
110C2×C4⋊Dic43C2313yes—
111C2×C4⋊Dic43C2313yes—
112C2×Dic43⋊C4C2313yes—
113C2×Dic43⋊C4C2311yescharacteristic
114C4⋊C4×D43—212no—
115C2×C22⋊Dic43C2311yescharacteristic
116C2×C22⋊Dic43C2313yes—
117C2×(C2×D43)⋊C4C2311yescharacteristic
118C2×(C2×D43)⋊C4C2311yescharacteristic
119C2×(C2×D43)⋊C4C2313yes—
120C2×(C2×D43)⋊C4C2313yes—
121C2×(C2×D43)⋊C4C2316yes—
122C2×(C2×D43)⋊C4C2313yes—
123C2×(C2×D43)⋊C4C2313yes—
124C2×C4×Dic43C2311yescharacteristic
125C2×C4×Dic43C2313yes—
126C2×C4×Dic43C2313yes—
127C2×C4×Dic43C2313yes—
128C42×D43—212no—
129C43⋊#95C2313yes—
130C43⋊#95C2313yes—
131C43⋊#95C2316yes—
132C43⋊#95C2316yes—
133C43⋊#95C2313yes—
134C43⋊#95C2313yes—
135C43⋊#95C2313yes—
136C43⋊#95C2316yes—
137C43⋊#95C2313yes—
138C22×Q8×C43—24no—
139C22×Q8×C43—24no—
140C22×Q8×C43C2×C418yescomplemented
141C22×Q8×C43C2313yes—
142C22×Q8×C43C2311yescharacteristic
143C23×C4×C43C2313yes—
144C4×Q8×C43—24no—
145C4×Q8×C43—24no—
146C2×C4⋊C4×C43C2313yes—
147C2×C4⋊C4×C43C2313yes—
148C2×C22⋊C4×C43C2311yescharacteristic
149C2×C22⋊C4×C43C2313yes—
150C2×C42×C43C2313yes—
151C2×C42×C43C2313yes—
152#95×C43C2313yes—
153#95×C43C2313yes—
154#95×C43C2316yes—
155C24×C43C2411yescharacteristic
156C23×D43C2411yescharacteristic
157C23×D43C2413yes—
158C2×Q8×C43—232no—
159C2×Q8×C43—26no—
160C2×Q8×C43—26no—
161C2×Q8×C43C22×C4112yes—
162C2×Q8×C43C22×C414yes—
163C2×Q8×C43C2×D414yes—
164C2×Q8×C43C2×D414yes—
165C22×C4×C43—26no—
166C22×C4×C43—26no—
167C22×C4×C43C22×C4112yes—
168C22×C4×C43C2411yescharacteristic
169C22×C4×C43C2413yes—
170C22×C4×C43C2413yes—
171C22×C4×C43C2413yes—
172C22×C4×C43C2411yescharacteristic
173C22×C4×C43C2413yes—
174C2×C22⋊D43—22no—
175C2×C22⋊D43—22no—
176C2×C22⋊D43—26no—
177C2×C22⋊D43—26no—
178C2×C22⋊D43C22×C414yes—
179C2×C22⋊D43C22×C4112yes—
180C22×Dic43C2411yescharacteristic
181C22×Dic43C2413yes—
182C22×Dic43C2413yes—
183C22×Dic43C2413yes—
184C22×Dic43C2411yescharacteristic
185C22×Dic43C2411yescharacteristic
186#10621902—296no—
187#10621902C22⋊C4164yescomplemented
188Q8×D43—232no—
189Q8×D43—296no—
190#10621898—296no—
191#10621898—296no—
192C2×D172—26no—
193C2×D172—26no—
194C2×D172C22×C4112yes—
195C2×D172C22×C4112yes—
196C2×D172C2×D4112yes—
197C2×D172C2×D4112yes—
198C2×C4×D43—26no—
199C2×C4×D43—26no—
200C2×C4×D43—26no—
201C2×C4×D43—26no—
202C2×C4×D43—212no—
203C2×C4×D43—212no—
204C2×C4×D43—26no—
205C2×C4×D43—26no—
206C2×C4×D43—212no—
207C2×C4×D43—43no—
208C2×C4×D43—43no—
209C2×C4×D43—46no—
210C2×C4×D43—46no—
211C2×C4×D43C22×C4112yes—
212C2×C4×D43C22×C4124yes—
213C2×C4×D43C22×C4112yes—
214C2×C4×D43C2×D4112yes—
215C2×C4×D43C2×D4112yes—
216C2×Dic86—26no—
217C2×Dic86—26no—
218C2×Dic86—26no—
219C2×Dic86—26no—
220C2×Dic86C22×C4112yes—
221C2×Dic86C22×C4112yes—
222C4⋊C4×C43—26no—
223C4⋊C4×C43—26no—
224C22⋊C4×C43—22no—
225C22⋊C4×C43—43no—
226C42×C43—26no—
227C42×C43—26no—
228C22⋊Dic43—22no—
229C22⋊Dic43—43no—
230(C2×D43)⋊C4—22no—
231(C2×D43)⋊C4—22no—
232(C2×D43)⋊C4—26no—
233(C2×D43)⋊C4—26no—
234(C2×D43)⋊C4—212no—
235(C2×D43)⋊C4—43no—
236(C2×D43)⋊C4—43no—
237C4⋊Dic43—26no—
238C4⋊Dic43—26no—
239Dic43⋊C4—26no—
240Dic43⋊C4—22no—
241C4×Dic43—26no—
242C4×Dic43—26no—
243C4×Dic43—22no—
244C4×Dic43—26no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43C23×C412yes—
252C23×C43C2511yescharacteristic
253C22×D43—23no—
254C22×D43—23no—
255C22×D43—23no—
256C22×D43—23no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43C23×C412yes—
264C22×D43C23×C416yes—
265C22×D43C22×D416yes—
266C22×D43C22×D416yes—
267Q8×C43—224no—
268Q8×C43C2×C22⋊C4116yes—
269C2×C4×C43—21no—
270C2×C4×C43—23no—
271C2×C4×C43—23no—
272C2×C4×C43—21no—
273C2×C4×C43—224no—
274C2×C4×C43—23no—
275C2×C4×C43—21no—
276C2×C4×C43—23no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—23no—
280C2×C4×C43—23no—
281C2×C4×C43—23no—
282C2×C4×C43—23no—
283C2×C4×C43C23×C416yes—
284C2×C4×C43C23×C416yes—
285C2×C4×C43C22×D416yes—
286C2×C4×C43C22×D416yes—
287C2×C4×C432−1+412yescomplemented
288C22⋊D43—224no—
289C22⋊D43—28no—
290C2×Dic43—21no—
291C2×Dic43—23no—
292C2×Dic43—23no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—23no—
296C2×Dic43—23no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—23no—
300C2×Dic43—23no—
301C2×Dic43—23no—
302C2×Dic43—23no—
303C2×Dic43C23×C416yes—
304C2×Dic43C23×C412yes—
305C2×Dic43C22×D412yes—
306C2×Dic43C22×D412yes—
307C2×Dic432−1+412yescomplemented
308D172—224no—
309D172C2×C22⋊C4148yes—
310C4×D43—248no—
311C4×D43—224no—
312C4×D43—412no—
313C4×D43—412no—
314C4×D43—812no—
315C4×D43C2×C22⋊C4148yes—
316Dic86—224no—
317Dic86—224no—
318#34259—431nomaximal, Sylow
319C22×C43—22no—
320C22×C43—22no—
321C22×C43—22no—
322C22×C43—41no—
323C22×C43—41no—
324C22×C43—41no—
325C22×C43—41no—
326C22×C43C24×C411yescharacteristic
327C22×C43C23×D411yescharacteristic
328C22×C43C23×D411yescharacteristic
329C22×C43C2×2−1+411yescharacteristic
330C22×C43C2×2−1+411yescharacteristic
331C22×C43#58511yescharacteristic
332C22×C43#58511yescharacteristic
333C2×D43—26no—
334C2×D43—26no—
335C2×D43—26no—
336C2×D43—26no—
337C2×D43—26no—
338C2×D43—26no—
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—22no—
342C2×D43—41no—
343C2×D43—41no—
344C2×D43—41no—
345C2×D43—41no—
346C2×D43C22×C22⋊C4112yes—
347C4×C43—26no—
348C4×C43—22no—
349C4×C43—43no—
350C4×C43—41no—
351C4×C43—43no—
352C4×C43C22×C22⋊C4112yes—
353Dic43—26no—
354Dic43—22no—
355Dic43—43no—
356Dic43—41no—
357Dic43—43no—
358Dic43C22×C22⋊C414yes—
359C22×2−1+4—431no—
360C2×#520—431no—
361C2×C4×#41—431no—
362Q8×C22⋊C4—431no—
363Q8×C22⋊C4—431no—
364Q8×C22⋊C4—431no—
365Q8×C22⋊C4D4311yescharacteristic, complemented
366#2339—433no—
367#2339—433no—
368#2339—433no—
369#2339—433no—
370#2311—433no—
371#2310—433no—
372#2297—433no—
373C2×#391—433no—
374C2×C43—42no—
375C2×C43C23×C22⋊C411yescharacteristic
376C2×C43C4×2−1+411yescharacteristic
377C2×C43C4×2−1+411yescharacteristic
378C2×C43#348911yescharacteristic
379C2×C43#348911yescharacteristic
380C2×C43#349911yescharacteristic
381C2×C43#350011yescharacteristic
382D43—212no—
383D43—42no—
384C2×2−1+4—4316no—
385C2×2−1+4—868no—
386C2×2−1+4—868no—
387C22×#41—431no—
388C22×#41—433no—
389C22×#41—433no—
390C22×#41—433no—
391C23×Q8—433no—
392C23×Q8—431no—
393C23×Q8C2×D4311yescharacteristic
394#520—868no—
395C4×#41—868no—
396C2×C4×Q8—431no—
397C2×C4×Q8—431no—
398C2×C4×Q8C2×D4311yescharacteristic
399C2×C4×Q8C2×D4311yescharacteristic
400C2×C4×D4—433no—
401C2×C4×D4—433no—
402C2×C4×D4—433no—
403C2×C4×D4—433no—
404C2×#117—433no—
405C2×#117—433no—
406C22×C4⋊C4—433no—
407C22×C42—433no—
408#391—433no—
409#391—433no—
410#391—433no—
411#391—433no—
412#391—433no—
413#391—433no—
414#391—433no—
415#391—436no—
416#391—433no—
417#391C2×D4313yes—
418#391C2×D4313yes—
419#390—433no—
420#390—431no—
421#386—436no—
422#386—433no—
423#386—433no—
424#386—436no—
425#386—433no—
426#386—433no—
427#381—436no—
428#381—436no—
429#380—433no—
430#380—433no—
431#380—433no—
432#380C2×D4313yes—
433C4×C22⋊C4—433no—
434C4×C22⋊C4—433no—
435C4×C22⋊C4—433no—
436C4×C22⋊C4C2×D4313yes—
437C2×#95—436no—
438C2×#95—436no—
439C43#3425911yescharacteristic, complemented, Sylow
4402−1+4—86128no—
441C2×#41—438no—
442C2×#41—4324no—
443C2×#41—438no—
444C2×#41—438no—
445C2×#41—4324no—
446C2×#41—4324no—
447C2×#41—8612no—
448C2×#41—8612no—
449C2×#41—8612no—
450C2×#41—8612no—
451C2×#41—8612no—
452C2×#41—8612no—
453C22×Q8—24no—
454C22×Q8—24no—
455C22×Q8—4324no—
456C22×Q8—438no—
457C22×Q8—433no—
458C22×Q8—433no—
459C22×Q8—8612no—
460C22×Q8—8612no—
461C22×Q8—864no—
462C22×Q8—864no—
463C22×Q8C4×D4318yescomplemented
464C22×Q8C22×D4313yes—
465C22×Q8C22×D4311yescharacteristic
466C22×D4—433no—
467C22×D4—431no—
468C22×D4—433no—
469C22×D4—433no—
470C23×C4—433no—
471C23×C4—436no—
472C23×C4—433no—
473C23×C4—433no—
474C23×C4—433no—
475C23×C4—436no—
476C23×C4C22×D4313yes—
477C4×Q8—24no—
478C4×Q8—24no—
479C4×Q8—864no—
480C4×Q8—864no—
481C4×D4—8612no—
482C4×D4—8612no—
483C4×D4—8612no—
484C4×D4—8612no—
485#117—8612no—
486#117—8612no—
487C2×C4⋊C4—433no—
488C2×C4⋊C4—433no—
489C2×C4⋊C4—431no—
490C2×C4⋊C4—433no—
491C2×C4⋊C4—8612no—
492C2×C4⋊C4C22×D4313yes—
493C2×C4⋊C4C22×D4313yes—
494C2×C22⋊C4—431no—
495C2×C22⋊C4—433no—
496C2×C22⋊C4—436no—
497C2×C22⋊C4—433no—
498C2×C22⋊C4—431no—
499C2×C22⋊C4—431no—
500C2×C22⋊C4—433no—
501C2×C22⋊C4—433no—
502C2×C22⋊C4—433no—
503C2×C22⋊C4C22×D4311yescharacteristic
504C2×C22⋊C4C22×D4313yes—
505C2×C42—433no—
506C2×C42—433no—
507C2×C42—433no—
508C2×C42—431no—
509C2×C42—8612no—
510C2×C42C22×D4313yes—
511C2×C42C22×D4313yes—
512#95—433no—
513#95—433no—
514#95—433no—
515#95—436no—
516#95—436no—
517#95—436no—
518#95—433no—
519#95—433no—
520#95—433no—
521#95C22×D4313yes—
522#95C22×D4316yes—
523#95C22×D4313yes—
524C24—433no—
525C24—431no—
526C24C23×D4311yescharacteristic
527#41—4364no—
528#41—8696no—
529#41—8696no—
530#41—8696no—
531C2×Q8—232no—
532C2×Q8—26no—
533C2×Q8—26no—
534C2×Q8—4312no—
535C2×Q8—4312no—
536C2×Q8—866no—
537C2×Q8—866no—
538C2×Q8—8696no—
539C2×Q8—8632no—
540C2×Q8—866no—
541C2×Q8—866no—
542C2×Q8C2×C4×D43112yes—
543C2×Q8C2×C4×D4314yes—
544C2×Q8D4×D4314yes—
545C2×Q8D4×D4314yes—
546C2×D4—434no—
547C2×D4—4312no—
548C2×D4—4312no—
549C2×D4—4312no—
550C2×D4—4312no—
551C2×D4—4312no—
552C2×D4—866no—
553C2×D4—866no—
554C2×D4—862no—
555C2×D4—862no—
556C2×D4—866no—
557C2×D4—866no—
558C22×C4—26no—
559C22×C4—26no—
560C22×C4—431no—
561C22×C4—4312no—
562C22×C4—4312no—
563C22×C4—4312no—
564C22×C4—433no—
565C22×C4—431no—
566C22×C4—4324no—
567C22×C4—4312no—
568C22×C4—431no—
569C22×C4—433no—
570C22×C4—433no—
571C22×C4—866no—
572C22×C4—8612no—
573C22×C4—8612no—
574C22×C4—8612no—
575C22×C4—866no—
576C22×C4—866no—
577C22×C4—866no—
578C22×C4—866no—
579C22×C4—866no—
580C22×C4—1726no—
581C22×C4—1726no—
582C22×C4—1723no—
583C22×C4—1723no—
584C22×C4C2×C4×D43112yes—
585C22×C4C23×D4313yes—
586C22×C4C23×D4311yescharacteristic
587C22×C4C23×D4313yes—
588C22×C4C23×D4313yes—
589C22×C4C23×D4311yescharacteristic
590C22×C4C23×D4313yes—
591C4⋊C4—26no—
592C4⋊C4—26no—
593C4⋊C4—866no—
594C4⋊C4—862no—
595C4⋊C4—866no—
596C4⋊C4—866no—
597C22⋊C4—22no—
598C22⋊C4—43no—
599C22⋊C4—862no—
600C22⋊C4—866no—
601C22⋊C4—8612no—
602C22⋊C4—866no—
603C22⋊C4—862no—
604C22⋊C4—862no—
605C22⋊C4—1723no—
606C22⋊C4—1723no—
607C22⋊C4—1723no—
608C42—26no—
609C42—26no—
610C42—862no—
611C42—866no—
612C42—866no—
613C42—866no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—436no—
621C23—436no—
622C23—436no—
623C23—432no—
624C23—863no—
625C23—863no—
626C23—863no—
627C23—863no—
628C23—861no—
629C23—861no—
630C23—861no—
631C23—861no—
632C23—861no—
633C23—861no—
634C23C22×C4×D4312yes—
635C23C24×D4311yescharacteristic
636Q8—224no—
637Q8—8624no—
638Q8—8624no—
639Q8C22⋊C4×D43116yes—
640D4—4348no—
641D4—8624no—
642D4—868no—
643D4—8624no—
644C2×C4—21no—
645C2×C4—23no—
646C2×C4—23no—
647C2×C4—21no—
648C2×C4—224no—
649C2×C4—21no—
650C2×C4—23no—
651C2×C4—23no—
652C2×C4—21no—
653C2×C4—23no—
654C2×C4—21no—
655C2×C4—23no—
656C2×C4—23no—
657C2×C4—23no—
658C2×C4—432no—
659C2×C4—432no—
660C2×C4—432no—
661C2×C4—4348no—
662C2×C4—436no—
663C2×C4—432no—
664C2×C4—8648no—
665C2×C4—861no—
666C2×C4—863no—
667C2×C4—863no—
668C2×C4—861no—
669C2×C4—8624no—
670C2×C4—861no—
671C2×C4—863no—
672C2×C4—863no—
673C2×C4—861no—
674C2×C4—861no—
675C2×C4—863no—
676C2×C4—863no—
677C2×C4—863no—
678C2×C4—863no—
679C2×C4—34412no—
680C2×C4—17212no—
681C2×C4—17212no—
682C2×C4C22×C4×D4316yes—
683C2×C4C22×C4×D4316yes—
684C2×C4C2×D4×D4316yes—
685C2×C4C2×D4×D4316yes—
686C2×C4#1306337312yescomplemented
687C22—22no—
688C22—22no—
689C22—22no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—4312no—
695C22—866no—
696C22—866no—
697C22—866no—
698C22—866no—
699C22—866no—
700C22—866no—
701C22—862no—
702C22—862no—
703C22—862no—
704C22—1721no—
705C22—1721no—
706C22—1721no—
707C22—1721no—
708C22C23×C4×D4311yescharacteristic
709C22C22×D4×D4311yescharacteristic
710C22C22×D4×D4311yescharacteristic
711C222−1+4×D4311yescharacteristic
712C22C2×#1306337311yescharacteristic
713C22#1458373511yescharacteristic
714C22#1458373611yescharacteristic
715C4—26no—
716C4—22no—
717C4—41no—
718C4—43no—
719C4—43no—
720C4—434no—
721C4—866no—
722C4—862no—
723C4—1721no—
724C4—1723no—
725C4—1723no—
726C4C2×C22⋊C4×D43112yes—
727C2—42no—
728C2—8612no—
729C2—1722no—
730C2C22×C22⋊C4×D4311yescharacteristic
731C2#1914780411yescharacteristic
732C2C4×#1306337311yescharacteristic
733C2#1914827211yescharacteristic
734C2#1914827411yescharacteristic
735C2#1914837911yescharacteristic
736C2#1914838611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingQ8×C22⋊C4×C43C2
socle, cosocleC23×C43C25
prime radicalC22×#13063373C2
hypercenterQ8×C22⋊C4D43
hypocenterC43#34259
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#14583381C2semidirect
3. C2×C4×#10621902C2semidirect
4. Q8×C22⋊Dic43C2semidirect
5. Q8×(C2×D43)⋊C4C2semidirect
6. Q8×(C2×D43)⋊C4C2semidirect
7. #19137426C2semidirect
8. #19137424C2semidirect
9. #19137424C2semidirect
10. #19137423C2semidirect
11. #19137184C2semidirect
12. #19137178C2semidirect
13. #19137081C2semidirect
14. #391×D43C2semidirect
15. Q8×C22⋊C4×C43C2semidirect
18. C2×#13063373C4semidirect
75. C2×#10621902C2×C4semidirect
82. C2×#10621898C2×C4semidirect
83. C2×#10621898C2×C4semidirect
90. C2×Q8×D43C2×C4semidirect
91. C2×Q8×D43C2×C4semidirect
140. C22×Q8×C43C2×C4semidirect
187. #10621902C22⋊C4semidirect
287. C2×C4×C432−1+4semidirect
307. C2×Dic432−1+4semidirect
365. Q8×C22⋊C4D43semidirect
439. C43#34259semidirect
463. C22×Q8C4×D43semidirect
686. C2×C4#13063373semidirect

Maximal subgroups

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

subgroupindex
C22×#130633732
C2×#145833812
C2×C4×#106219022
Q8×C22⋊Dic432
Q8×(C2×D43)⋊C42
#191374262
#191374242
#191374232
#191371842
#191371782
#191370812
#391×D432
Q8×C22⋊C4×C432
#3425943