Finite Group Databasebeta

← #25257631

Subgroups — #25257631

Order 11008.

5050 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063373C211yesmaximal, characteristic
2C2×#14583375C211yesmaximal, characteristic, complemented
3C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
4#19137435C213yesmaximal, complemented
5#19137433C211yesmaximal, characteristic, complemented
6#19137433C211yesmaximal, characteristic, complemented
7#19137432C213yesmaximal, complemented
8Q8×C22⋊Dic43C211yesmaximal, characteristic, complemented
9#19137429C213yesmaximal, complemented
10#19137429C213yesmaximal, complemented
11#19137186C213yesmaximal, complemented
12#19137184C213yesmaximal, complemented
13#19137084C213yesmaximal, complemented
14#19137081C213yesmaximal, 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#14583375—28no—
26C2×Q8×Dic43C2211yescharacteristic
27C2×Q8×Dic43C2211yescharacteristic
28C2×C4×Dic86C2213yes—
29C2×C4×Dic86C2213yes—
30C2×#13063290C2213yes—
31C2×#13063290C2213yes—
32C4×Q8×D43—28no—
33C2×#13063283C2213yes—
34C2×#13063282C2213yes—
35C2×C4⋊C4×D43C2213yes—
36C2×C42×D43C2213yes—
37#14582806C2213yes—
38#14582806C2213yes—
39#14582803C2213yes—
40#14582803C2213yes—
41#14582803C2216yes—
42#14582801C2213yes—
43#14582801C2213yes—
44#14582800C2213yes—
45#14582800C2213yes—
46#14582799C2213yes—
47#14582799C2213yes—
48#14582799C2216yes—
49#14582777C2213yes—
50#14582777C2213yes—
51#14582777C2216yes—
52#14582775C2211yescharacteristic
53#14582775C2213yes—
54#14582759C2213yes—
55#14582758C2216yes—
56#14582758C2216yes—
57#14582756C2213yes—
58#14582756C2213yes—
59C4×(C2×D43)⋊C4C2213yes—
60C4×(C2×D43)⋊C4C2213yes—
61C4×C22⋊Dic43C2213yes—
62#14582746C2216yes—
63#14582746C2216yes—
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—24no—
73C2×#10621902—24no—
74C2×#10621902—212no—
75C2×#10621902—212no—
76C2×#10621902C2×C4124yes—
77C2×#10621902C2×C418yescomplemented
78C2×#10621898—212no—
79C2×#10621898—212no—
80C2×#10621898—212no—
81C2×#10621898—212no—
82C2×#10621898C2×C4124yes—
83C2×#10621898C2×C4124yescomplemented
84C22×Dic86C2313yes—
85C22×Dic86C2313yes—
86C2×Q8×D43—212no—
87C2×Q8×D43—212no—
88C2×Q8×D43C2×C418yes—
89C2×Q8×D43C2×C4124yescomplemented
90C2×Q8×D43D418yes—
91C2×Q8×D43D418yes—
92C22×D172C2313yes—
93C22×D172C2313yes—
94C22×C22⋊D43C2313yes—
95C22×C22⋊D43C2311yescharacteristic
96C22×C4×D43C2311yescharacteristic
97C22×C4×D43C2316yes—
98C22×C4×D43C2313yes—
99C22×C4×D43C2313yes—
100C22×C4×D43C2313yes—
101Q8×Dic43—24no—
102Q8×Dic43—24no—
103C4×Dic86—212no—
104C4×Dic86—212no—
105#13063290—212no—
106#13063290—212no—
107#13063283—212no—
108#13063282—212no—
109C2×C4⋊Dic43C2313yes—
110C2×C4⋊Dic43C2313yes—
111C2×Dic43⋊C4C2316yes—
112C2×Dic43⋊C4C2313yes—
113C2×Dic43⋊C4C2313yes—
114C4⋊C4×D43—212no—
115C2×C22⋊Dic43C2311yescharacteristic
116C2×C22⋊Dic43C2313yes—
117C2×(C2×D43)⋊C4C2313yes—
118C2×(C2×D43)⋊C4C2313yes—
119C2×(C2×D43)⋊C4C2311yescharacteristic
120C2×(C2×D43)⋊C4C2313yes—
121C2×(C2×D43)⋊C4C2313yes—
122C2×(C2×D43)⋊C4C2316yes—
123C2×(C2×D43)⋊C4C2316yes—
124C2×(C2×D43)⋊C4C2313yes—
125C2×C4×Dic43C2313yes—
126C2×C4×Dic43C2313yes—
127C2×C4×Dic43C2316yes—
128C2×C4×Dic43C2313yes—
129C2×C4×Dic43C2313yes—
130C42×D43—212no—
131C43⋊#95C2311yescharacteristic
132C43⋊#95C2311yescharacteristic
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×D43C2413yes—
157C23×D43C2411yescharacteristic
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—26no—
175C2×C22⋊D43—26no—
176C2×C22⋊D43—22no—
177C2×C22⋊D43—22no—
178C2×C22⋊D43C22×C414yes—
179C2×C22⋊D43C22×C4112yes—
180C22×Dic43C2411yescharacteristic
181C22×Dic43C2413yes—
182C22×Dic43C2413yes—
183C22×Dic43C2411yescharacteristic
184C22×Dic43C2411yescharacteristic
185C22×Dic43C2413yes—
186#10621902—232no—
187#10621902—296no—
188Q8×D43—296no—
189Q8×D43C22⋊C4164yescomplemented
190#10621898—296no—
191#10621898—296no—
192C2×D172—26no—
193C2×D172—26no—
194C2×D172—26no—
195C2×D172—26no—
196C2×D172C22×C4112yes—
197C2×D172C22×C4112yes—
198C2×C4×D43—26no—
199C2×C4×D43—26no—
200C2×C4×D43—22no—
201C2×C4×D43—212no—
202C2×C4×D43—212no—
203C2×C4×D43—22no—
204C2×C4×D43—22no—
205C2×C4×D43—26no—
206C2×C4×D43—43no—
207C2×C4×D43—43no—
208C2×C4×D43C22×C4112yes—
209C2×C4×D43C22×C4124yes—
210C2×C4×D43C22×C4112yes—
211C2×C4×D43C2×D4112yes—
212C2×C4×D43C2×D4112yes—
213C2×Dic86—26no—
214C2×Dic86—26no—
215C2×Dic86C22×C4112yes—
216C2×Dic86C22×C4112yes—
217C2×Dic86C2×D4112yes—
218C2×Dic86C2×D4112yes—
219C4⋊C4×C43—26no—
220C4⋊C4×C43—26no—
221C22⋊C4×C43—22no—
222C22⋊C4×C43—43no—
223C42×C43—26no—
224C42×C43—26no—
225C22⋊Dic43—22no—
226C22⋊Dic43—43no—
227(C2×D43)⋊C4—26no—
228(C2×D43)⋊C4—26no—
229(C2×D43)⋊C4—22no—
230(C2×D43)⋊C4—26no—
231(C2×D43)⋊C4—43no—
232(C2×D43)⋊C4—46no—
233(C2×D43)⋊C4—46no—
234(C2×D43)⋊C4—43no—
235C4⋊Dic43—26no—
236C4⋊Dic43—26no—
237Dic43⋊C4—212no—
238Dic43⋊C4—26no—
239Dic43⋊C4—26no—
240C4×Dic43—26no—
241C4×Dic43—26no—
242C4×Dic43—26no—
243C4×Dic43—26no—
244C4×Dic43—212no—
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—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—23no—
258C22×D43—23no—
259C22×D43—23no—
260C22×D43—23no—
261C22×D43—23no—
262C22×D43—23no—
263C22×D43C23×C416yes—
264C22×D43C23×C412yes—
265C22×D43C22×D412yes—
266C22×D43C22×D412yes—
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—23no—
276C2×C4×C43—21no—
277C2×C4×C43—23no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
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—28no—
289C22⋊D43—224no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—23no—
296C2×Dic43—23no—
297C2×Dic43—23no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—23no—
301C2×Dic43—23no—
302C2×Dic43—23no—
303C2×Dic43C23×C412yes—
304C2×Dic43C23×C416yes—
305C2×Dic43C22×D416yes—
306C2×Dic43C22×D416yes—
307C2×Dic432−1+412yescomplemented
308D172—224no—
309D172—224no—
310C4×D43—28no—
311C4×D43—224no—
312C4×D43—248no—
313C4×D43—412no—
314C4×D43C2×C22⋊C4148yes—
315Dic86—224no—
316Dic86C2×C22⋊C4148yes—
317#34257—431nomaximal, Sylow
318C22×C43—22no—
319C22×C43—22no—
320C22×C43—22no—
321C22×C43—41no—
322C22×C43—41no—
323C22×C43—41no—
324C22×C43—41no—
325C22×C43C24×C411yescharacteristic
326C22×C43C23×D411yescharacteristic
327C22×C43C23×D411yescharacteristic
328C22×C43C2×2−1+411yescharacteristic
329C22×C43C2×2−1+411yescharacteristic
330C22×C43#58511yescharacteristic
331C22×C43#58511yescharacteristic
332C2×D43—22no—
333C2×D43—22no—
334C2×D43—22no—
335C2×D43—22no—
336C2×D43—22no—
337C2×D43—22no—
338C2×D43—26no—
339C2×D43—26no—
340C2×D43—26no—
341C2×D43—43no—
342C2×D43—43no—
343C2×D43—43no—
344C2×D43—43no—
345C2×D43C22×C22⋊C414yes—
346C4×C43—26no—
347C4×C43—22no—
348C4×C43—43no—
349C4×C43—43no—
350C4×C43—41no—
351C4×C43C22×C22⋊C4112yes—
352Dic43—22no—
353Dic43—22no—
354Dic43—43no—
355Dic43—41no—
356Dic43—43no—
357Dic43C22×C22⋊C4112yes—
358C22×2−1+4—431no—
359C2×#519—431no—
360C22×C4×Q8—431no—
361#2341—433no—
362#2341—433no—
363#2341—431no—
364#2341—431no—
365Q8×C22⋊C4—433no—
366Q8×C22⋊C4—433no—
367Q8×C22⋊C4—431no—
368Q8×C22⋊C4D4311yescharacteristic, complemented
369#2311—433no—
370#2311—433no—
371#2297—433no—
372#2297—433no—
373C2×C43—42no—
374C2×C43C23×C22⋊C411yescharacteristic
375C2×C43C4×2−1+411yescharacteristic
376C2×C43C4×2−1+411yescharacteristic
377C2×C43#348611yescharacteristic
378C2×C43#348711yescharacteristic
379C2×C43#349711yescharacteristic
380C2×C43#349711yescharacteristic
381D43—24no—
382D43—46no—
383C2×2−1+4—4316no—
384C2×2−1+4—868no—
385C2×2−1+4—868no—
386C22×#41—433no—
387C22×#41—431no—
388C22×#41—433no—
389C22×#41—433no—
390C23×Q8—431no—
391C23×Q8—433no—
392C23×Q8C2×D4311yescharacteristic
393#519—868no—
394C2×C4×Q8—431no—
395C2×C4×Q8—431no—
396C2×C4×Q8—433no—
397C2×C4×Q8—433no—
398C2×C4×Q8—433no—
399C2×C4×Q8—433no—
400C2×C4×Q8—868no—
401C2×C4×Q8C2×D4311yescharacteristic
402C2×C4×Q8C2×D4311yescharacteristic
403C2×#117—433no—
404C2×#117—433no—
405C22×C4⋊C4—433no—
406C22×C42—433no—
407#391—433no—
408#391—433no—
409#391—436no—
410#391—433no—
411#391—433no—
412#391C2×D4313yes—
413#391C2×D4313yes—
414#390—433no—
415#390—433no—
416#390—436no—
417#390—433no—
418#390—433no—
419#390—433no—
420#390—433no—
421#386—433no—
422#386—431no—
423#386—436no—
424#386—433no—
425#386—433no—
426#380—433no—
427#380—433no—
428#380—433no—
429#380—436no—
430#380—436no—
431#380C2×D4313yes—
432C4×C22⋊C4—433no—
433C4×C22⋊C4—433no—
434C4×C22⋊C4—433no—
435C4×C22⋊C4—436no—
436C4×C22⋊C4—436no—
437C4×C22⋊C4C2×D4313yes—
438C43#3425711yescharacteristic, complemented, Sylow
4392−1+4—86128no—
440C2×#41—4324no—
441C2×#41—438no—
442C2×#41—4324no—
443C2×#41—4324no—
444C2×#41—8612no—
445C2×#41—8612no—
446C2×#41—8612no—
447C2×#41—8612no—
448C2×#41—8612no—
449C2×#41—8612no—
450C2×#41—864no—
451C2×#41—864no—
452C22×Q8—24no—
453C22×Q8—24no—
454C22×Q8—438no—
455C22×Q8—438no—
456C22×Q8—438no—
457C22×Q8—4324no—
458C22×Q8—433no—
459C22×Q8—433no—
460C22×Q8—8612no—
461C22×Q8—8612no—
462C22×Q8C4×D4318yescomplemented
463C22×Q8C22×D4313yes—
464C22×Q8C22×D4311yescharacteristic
465C22×D4—431no—
466C22×D4—433no—
467C22×D4—433no—
468C22×D4—433no—
469C23×C4—433no—
470C23×C4—436no—
471C23×C4—433no—
472C23×C4—431no—
473C23×C4—433no—
474C23×C4C22×D4313yes—
475C4×Q8—24no—
476C4×Q8—24no—
477C4×Q8—8612no—
478C4×Q8—8612no—
479C4×Q8—8612no—
480C4×Q8—8612no—
481C4×Q8—864no—
482C4×Q8—864no—
483#117—8612no—
484#117—8612no—
485C2×C4⋊C4—436no—
486C2×C4⋊C4—433no—
487C2×C4⋊C4—433no—
488C2×C4⋊C4—433no—
489C2×C4⋊C4—433no—
490C2×C4⋊C4—8612no—
491C2×C4⋊C4C22×D4313yes—
492C2×C4⋊C4C22×D4313yes—
493C2×C22⋊C4—431no—
494C2×C22⋊C4—433no—
495C2×C22⋊C4—431no—
496C2×C22⋊C4—433no—
497C2×C22⋊C4—433no—
498C2×C22⋊C4—433no—
499C2×C22⋊C4—433no—
500C2×C22⋊C4—436no—
501C2×C22⋊C4—436no—
502C2×C22⋊C4—433no—
503C2×C22⋊C4C22×D4311yescharacteristic
504C2×C22⋊C4C22×D4313yes—
505C2×C42—436no—
506C2×C42—433no—
507C2×C42—433no—
508C2×C42—433no—
509C2×C42—433no—
510C2×C42—8612no—
511C2×C42C22×D4313yes—
512C2×C42C22×D4313yes—
513#95—431no—
514#95—431no—
515#95—433no—
516#95—433no—
517#95—433no—
518#95—436no—
519#95—433no—
520#95C22×D4313yes—
521#95C22×D4316yes—
522#95C22×D4313yes—
523C24—431no—
524C24—433no—
525C24C23×D4311yescharacteristic
526#41—8696no—
527#41—8696no—
528#41—8696no—
529#41—8632no—
530C2×Q8—232no—
531C2×Q8—26no—
532C2×Q8—26no—
533C2×Q8—4364no—
534C2×Q8—4312no—
535C2×Q8—4312no—
536C2×Q8—4312no—
537C2×Q8—4312no—
538C2×Q8—866no—
539C2×Q8—866no—
540C2×Q8—8696no—
541C2×Q8C2×C4×D43112yes—
542C2×Q8C2×C4×D4314yes—
543C2×Q8D4×D4314yes—
544C2×Q8D4×D4314yes—
545C2×D4—4312no—
546C2×D4—434no—
547C2×D4—4312no—
548C2×D4—4312no—
549C2×D4—866no—
550C2×D4—866no—
551C2×D4—866no—
552C2×D4—866no—
553C2×D4—862no—
554C2×D4—862no—
555C2×D4—866no—
556C2×D4—866no—
557C22×C4—26no—
558C22×C4—26no—
559C22×C4—433no—
560C22×C4—4312no—
561C22×C4—4312no—
562C22×C4—4312no—
563C22×C4—431no—
564C22×C4—431no—
565C22×C4—4324no—
566C22×C4—4312no—
567C22×C4—431no—
568C22×C4—433no—
569C22×C4—433no—
570C22×C4—8612no—
571C22×C4—8612no—
572C22×C4—862no—
573C22×C4—862no—
574C22×C4—866no—
575C22×C4—866no—
576C22×C4—866no—
577C22×C4—862no—
578C22×C4—1723no—
579C22×C4—1723no—
580C22×C4C2×C4×D43112yes—
581C22×C4C23×D4313yes—
582C22×C4C23×D4313yes—
583C22×C4C23×D4311yescharacteristic
584C22×C4C23×D4313yes—
585C22×C4C23×D4311yescharacteristic
586C22×C4C23×D4313yes—
587C4⋊C4—26no—
588C4⋊C4—26no—
589C4⋊C4—8612no—
590C4⋊C4—866no—
591C4⋊C4—866no—
592C4⋊C4—866no—
593C4⋊C4—866no—
594C22⋊C4—22no—
595C22⋊C4—43no—
596C22⋊C4—866no—
597C22⋊C4—862no—
598C22⋊C4—866no—
599C22⋊C4—862no—
600C22⋊C4—866no—
601C22⋊C4—1726no—
602C22⋊C4—1723no—
603C22⋊C4—1723no—
604C22⋊C4—1726no—
605C22⋊C4—1723no—
606C42—26no—
607C42—26no—
608C42—866no—
609C42—866no—
610C42—8612no—
611C42—866no—
612C42—866no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—432no—
620C23—432no—
621C23—432no—
622C23—436no—
623C23—861no—
624C23—861no—
625C23—861no—
626C23—861no—
627C23—863no—
628C23—863no—
629C23—863no—
630C23—863no—
631C23—863no—
632C23—863no—
633C23C22×C4×D4312yes—
634C23C24×D4311yescharacteristic
635Q8—224no—
636Q8—4348no—
637Q8—8624no—
638Q8C22⋊C4×D43116yes—
639D4—8624no—
640D4—8624no—
641D4—868no—
642D4—8624no—
643C2×C4—21no—
644C2×C4—23no—
645C2×C4—23no—
646C2×C4—21no—
647C2×C4—224no—
648C2×C4—21no—
649C2×C4—23no—
650C2×C4—23no—
651C2×C4—23no—
652C2×C4—21no—
653C2×C4—23no—
654C2×C4—23no—
655C2×C4—21no—
656C2×C4—23no—
657C2×C4—436no—
658C2×C4—436no—
659C2×C4—436no—
660C2×C4—4348no—
661C2×C4—432no—
662C2×C4—432no—
663C2×C4—8648no—
664C2×C4—868no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—8624no—
670C2×C4—861no—
671C2×C4—863no—
672C2×C4—863no—
673C2×C4—861no—
674C2×C4—863no—
675C2×C4—861no—
676C2×C4—863no—
677C2×C4—863no—
678C2×C4—863no—
679C2×C4—17212no—
680C2×C4C22×C4×D4316yes—
681C2×C4C22×C4×D4316yes—
682C2×C4C2×D4×D4316yes—
683C2×C4C2×D4×D4316yes—
684C2×C4#1306337312yescomplemented
685C22—22no—
686C22—22no—
687C22—22no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—434no—
693C22—862no—
694C22—862no—
695C22—862no—
696C22—862no—
697C22—862no—
698C22—862no—
699C22—866no—
700C22—866no—
701C22—866no—
702C22—1723no—
703C22—1723no—
704C22—1723no—
705C22—1723no—
706C22C23×C4×D4311yescharacteristic
707C22C22×D4×D4311yescharacteristic
708C22C22×D4×D4311yescharacteristic
709C222−1+4×D4311yescharacteristic
710C22C2×#1306337311yescharacteristic
711C22#1458373511yescharacteristic
712C22#1458373611yescharacteristic
713C4—22no—
714C4—26no—
715C4—43no—
716C4—41no—
717C4—43no—
718C4—4312no—
719C4—862no—
720C4—862no—
721C4—1721no—
722C4—1723no—
723C4—1723no—
724C4C2×C22⋊C4×D43112yes—
725C2—42no—
726C2—864no—
727C2—1726no—
728C2C22×C22⋊C4×D4311yescharacteristic
729C2#1914780411yescharacteristic
730C2C4×#1306337311yescharacteristic
731C2#1914824511yescharacteristic
732C2#1914825211yescharacteristic
733C2#1914836311yescharacteristic
734C2#1914836511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingQ8×C22⋊C4×C43C2
socle, cosocleC23×C43C25
prime radicalC22×#13063373C2
hypercenterQ8×C22⋊C4D43
hypocenterC43#34257
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×#14583375C2semidirect
3. C2×C4×Q8×D43C2semidirect
4. #19137435C2semidirect
5. #19137433C2semidirect
6. #19137433C2semidirect
7. #19137432C2semidirect
8. Q8×C22⋊Dic43C2semidirect
9. #19137429C2semidirect
10. #19137429C2semidirect
11. #19137186C2semidirect
12. #19137184C2semidirect
13. #19137084C2semidirect
14. #19137081C2semidirect
15. Q8×C22⋊C4×C43C2semidirect
18. C2×#13063373C4semidirect
77. C2×#10621902C2×C4semidirect
83. C2×#10621898C2×C4semidirect
89. C2×Q8×D43C2×C4semidirect
140. C22×Q8×C43C2×C4semidirect
189. Q8×D43C22⋊C4semidirect
287. C2×C4×C432−1+4semidirect
307. C2×Dic432−1+4semidirect
368. Q8×C22⋊C4D43semidirect
438. C43#34257semidirect
462. C22×Q8C4×D43semidirect
684. 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×#145833752
C2×C4×Q8×D432
#191374352
#191374332
#191374322
Q8×C22⋊Dic432
#191374292
#191371862
#191371842
#191370842
#191370812
Q8×C22⋊C4×C432
#3425743