Finite Group Databasebeta

← #25156574

Subgroups — #25156574

Order 11008.

1022 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
1C2×#14583094C211yesmaximal, characteristic
2C2×C4×#10621882C211yesmaximal, characteristic, complemented
3#19138360C211yesmaximal, characteristic, complemented
4#19136124C211yesmaximal, characteristic, complemented
5#19136086C211yesmaximal, characteristic, complemented
6#19135999C211yesmaximal, characteristic, complemented
7#19135829C211yesmaximal, characteristic, complemented
8#19135277C211yesmaximal, characteristic, complemented
9#19135154C211yesmaximal, characteristic, complemented
10#19134943C211yesmaximal, characteristic, complemented
11#19134943C211yesmaximal, characteristic, complemented
12#19134943C211yesmaximal, characteristic, complemented
13#19134842C211yesmaximal, characteristic, complemented
14#19134841C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C43C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063322C2211yescharacteristic
19C2×#13063310—21no—
20C2×C4×D172C2211yescharacteristic
21#14583094—24no—
22C4×#10621882—24no—
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582817—21no—
36#14582816—21no—
37#14582801C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582777—21no—
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50C2×C4×D4×C43C2211yescharacteristic
51C2×C4×D4×C43C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C22×C4⋊C4×C43—21no—
54C43×#389C2211yescharacteristic
55C43×#389C2211yescharacteristic
56C43×#385—21no—
57C43×#385—21no—
58C43×#384C2211yescharacteristic
59C43×#380—21no—
60C4×C4⋊C4×C43C2211yescharacteristic
61C22×D172—21no—
62C22×D172—21no—
63C22×D172C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C4×D43—21no—
66C2×#10621882—22no—
67C2×#10621882—22no—
68C2×#10621882—22no—
69C2×#10621882—22no—
70C2×#10621882—22no—
71C2×#10621882D414yes—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063322—22no—
77#13063322—41no—
78#13063310—44no—
79C4×D172—22no—
80C4×D172—41no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91#13063258—22no—
92#13063258—41no—
93C4⋊(C43⋊C8)—22no—
94#13063246—22no—
95#13063246—22no—
96#13063245—22no—
97#13063245—22no—
98#13063245—22no—
99#13063245—22no—
100#13063245—22no—
101#13063245—41no—
102C4×C43⋊C8—22no—
103C43⋊#95—21no—
104C22×D4×C43C2311yescharacteristic
105C23×C4×C43—21no—
106C23×C4×C43—21no—
107C23×C4×C43—21no—
108C4×D4×C43—22no—
109C4×D4×C43—22no—
110C4×D4×C43—22no—
111C4×D4×C43—22no—
112C4×D4×C43—41no—
113C4×D4×C43—41no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43—44no—
119C2×C4⋊C4×C43D411yescharacteristic
120C2×C4⋊C4×C43D411yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C42×C43C2311yescharacteristic
128C2×C42×C43C2311yescharacteristic
129C2×C42×C43C2311yescharacteristic
130#95×C43—21no—
131#95×C43—21no—
132#95×C43D411yescharacteristic
133#95×C43D411yescharacteristic
134C24×C43—21no—
135C23×D43—21no—
136C23×D43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43C2×D412yes—
141C2×D4×C43#4112yes—
142C2×D4×C43#4112yes—
143C22×C4×C43—24no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—42no—
148C22×C4×C43—42no—
149C22×C4×C43—42no—
150C22×C4×C43—42no—
151C22×C4×C43—42no—
152C22×C4×C43—42no—
153C22×C4×C43—81no—
154C22×C4×C43—81no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C22×Dic43—21no—
163C22×Dic43—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—42no—
176C2×D172—42no—
177C2×D172—42no—
178C2×D172—42no—
179C2×D172—81no—
180C2×D172—81no—
181C2×D172C2×D412yes—
182C2×C4×D43—42no—
183C2×C4×D43—42no—
184C2×C4×D43—81no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—41no—
191C4⋊C4×C43—42no—
192C4⋊C4×C43—42no—
193C4⋊C4×C43—42no—
194C4⋊C4×C43—81no—
195C4⋊C4×C43D814yescomplemented
196C4⋊C4×C43#4112yes—
197C22⋊C4×C43—24no—
198C22⋊C4×C43—42no—
199C22⋊C4×C43—42no—
200C42×C43—21no—
201C42×C43—21no—
202C42×C43—21no—
203C42×C43—21no—
204C42×C43—21no—
205C42×C43—21no—
206#10621882—28no—
207#10621882—44no—
208(C2×D43)⋊C4—42no—
209(C2×D43)⋊C4—42no—
210(C2×D43)⋊C4—42no—
211(C2×D43)⋊C4—42no—
212(C2×D43)⋊C4—81no—
213(C2×D43)⋊C4—81no—
214(C2×D43)⋊C4—81no—
215C4⋊Dic43—21no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219Dic43⋊C4—42no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8C2×D412yes—
232C23×C43—22no—
233C23×C43—22no—
234C23×C43—22no—
235C23×C43—41no—
236C23×C43—41no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43C22×D411yescharacteristic
240C22×D43—22no—
241C22×D43—41no—
242C22×D43—41no—
243C22×D43—41no—
244C22×D43—41no—
245C22×D43—41no—
246C22×D43—41no—
247C22×D43—41no—
248C22×D43—41no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43—41no—
253C22×D43—41no—
254D4×C43—22no—
255D4×C43—22no—
256D4×C43—22no—
257D4×C43#12314yescomplemented
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—22no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—48no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—84no—
284C2×C4×C43—84no—
285C2×C4×C43C2×D812yes—
286C2×C4×C43C2×D812yes—
287C2×C4×C43C2×D812yes—
288C2×C4×C43C22×D411yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43C2×#4111yescharacteristic
292C2×C4×C43H(5,𝔽2)11yescharacteristic
293C2×C4×C432−1+411yescharacteristic
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300D172—22no—
301D172—22no—
302D172—41no—
303D172—41no—
304D172—41no—
305D172—41no—
306D172—41no—
307D172—41no—
308D172—84no—
309D172—84no—
310C4×D43—84no—
311C43⋊C8—22no—
312C43⋊C8—41no—
313C43⋊C8—41no—
314C43⋊C8—41no—
315#26158—431nomaximal, Sylow
316C22×C43—24no—
317C22×C43—42no—
318C22×C43—42no—
319C22×C43—42no—
320C22×C43—42no—
321C22×C43—42no—
322C22×C43—42no—
323C22×C43#52511yescharacteristic
324C22×C43D4211yescharacteristic
325C22×C43#54811yescharacteristic
326C22×C43C22×D811yescharacteristic
327C22×C43#57511yescharacteristic
328C22×C43#57611yescharacteristic
329C22×C43#57711yescharacteristic
330C2×D43—42no—
331C2×D43—42no—
332C2×D43—42no—
333C2×D43—81no—
334C2×D43—81no—
335C2×D43—81no—
336C2×D43—81no—
337C2×D43—81no—
338C2×D43—81no—
339C2×D43—81no—
340C2×D43—81no—
341C2×D43—81no—
342C2×D43—81no—
343C2×D43—81no—
344C4×C43—22no—
345C4×C43—22no—
346C4×C43—22no—
347C4×C43—42no—
348C4×C43—41no—
349C4×C43—41no—
350C4×C43—41no—
351C4×C43—81no—
352C4×C43—81no—
353C4×C43C2×#12311yescharacteristic
354C4×C43#53911yescharacteristic
355C4×C43#54711yescharacteristic
356C4×C43#55311yescharacteristic
357Dic43—81no—
358Dic43—81no—
359C2×#459—431no—
360C2×C4×D8—431no—
361#2445—431no—
362D4×C4⋊C4D4311yescharacteristic, complemented
363#2093—431no—
364#2086—431no—
365#2071—431no—
366#2041—431no—
367#1934—431no—
368#1916—431no—
369#1879—431no—
370#1879—431no—
371#1879—431no—
372#1862—431no—
373#1862—431no—
374C2×C43—44no—
375C2×C43#244311yescharacteristic
376C2×C43#310011yescharacteristic
377C2×C43#311911yescharacteristic
378C2×C43#326711yescharacteristic
379C2×C43D4×D811yescharacteristic
380C2×C43#335811yescharacteristic
381C2×C43#337011yescharacteristic
382D43—82no—
383D43—161no—
384C22×D8—431no—
385C22×D8—431no—
386C2×#127—431no—
387C2×#123—861no—
388C2×C4×D4—431no—
389C2×C4×D4C2×D4311yescharacteristic
390C2×C4×D4C2×D4311yescharacteristic
391C2×C4×D4C2×D4311yescharacteristic
392C22×C4⋊C4—21no—
393#459—864no—
394C4×D8—864no—
395C2×#107—431no—
396C2×#107—431no—
397C2×C4⋊C8—431no—
398C2×#102—431no—
399C2×#102—431no—
400C2×#102—431no—
401C2×#102—431no—
402C2×#102—431no—
403C2×#102—431no—
404C2×#102—431no—
405C2×#102—431no—
406C2×C4×C8—431no—
407#394—861no—
408#394—861no—
409#390—431no—
410#390—431no—
411#390—431no—
412#389—431no—
413#389C2×D4311yescharacteristic
414#389C2×D4311yescharacteristic
415#386—861no—
416#385—21no—
417#385—21no—
418#384C2×D4311yescharacteristic
419#380—21no—
420C4×C4⋊C4C2×D4311yescharacteristic
421#340—431no—
422#340—431no—
423#340—431no—
424#340—431no—
425#336—431no—
426#336—431no—
427#336—431no—
428#336—431no—
429C43#2615811yescharacteristic, complemented, Sylow
430C22×D4—431no—
431C22×D4—431no—
432C22×D4—861no—
433C22×D4—861no—
434C22×D4C22×D4311yescharacteristic
435C23×C4—21no—
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—861no—
439C2×D8—434no—
440C2×D8—862no—
441C2×D8—862no—
442C2×D8—862no—
443C2×D8—862no—
444C2×D8—862no—
445C22×C8—431no—
446C22×C8—431no—
447C22×C8—431no—
448C22×C8—431no—
449#127—862no—
450#127—1721no—
451#123—1724no—
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—22no—
455C4×D4—22no—
456C4×D4—41no—
457C4×D4—41no—
458C4×D4—862no—
459C4×D4—1721no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—44no—
465C2×C4⋊C4—431no—
466C2×C4⋊C4—431no—
467C2×C4⋊C4—861no—
468C2×C4⋊C4C22⋊D4311yescharacteristic
469C2×C4⋊C4C22⋊D4311yescharacteristic
470C2×C4⋊C4C22×D4311yescharacteristic
471C2×C4⋊C4C22×D4311yescharacteristic
472C2×C4⋊C4C22×D4311yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—861no—
477C2×C22⋊C4—861no—
478C2×C22⋊C4—861no—
479C2×C22⋊C4—861no—
480C2×C22⋊C4—861no—
481C2×C22⋊C4—861no—
482C2×C22⋊C4—861no—
483C2×C42C22×D4311yescharacteristic
484C2×C42C22×D4311yescharacteristic
485C2×C42C22×D4311yescharacteristic
486#107—862no—
487#107—1721no—
488C4⋊C8—862no—
489#102—862no—
490#102—862no—
491#102—862no—
492#102—862no—
493#102—862no—
494#102—862no—
495#102—862no—
496#102—1721no—
497C4×C8—862no—
498#95—21no—
499#95—21no—
500#95—861no—
501#95C22⋊D4311yescharacteristic
502#95C22⋊D4311yescharacteristic
503C24—21no—
504C24—861no—
505C24—861no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—432no—
510C2×D4—861no—
511C2×D4—861no—
512C2×D4—861no—
513C2×D4—861no—
514C2×D4—861no—
515C2×D4—861no—
516C2×D4—861no—
517C2×D4—861no—
518C2×D4—861no—
519C2×D4—861no—
520C2×D4—861no—
521C2×D4—3441no—
522C2×D4—3441no—
523C2×D4—1722no—
524C2×D4—1722no—
525C2×D4—1722no—
526C2×D4—1722no—
527C2×D4#1062189812yes—
528C2×D4D4×D4312yes—
529C2×D4#1062190212yes—
530C22×C4—24no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—81no—
541C22×C4—81no—
542C22×C4—861no—
543C22×C4—861no—
544C22×C4—3441no—
545C22×C4—1722no—
546C22×C4—1722no—
547C22×C4C2×C22⋊D4311yescharacteristic
548C22×C4C2×C22⋊D4311yescharacteristic
549C22×C4C2×C22⋊D4311yescharacteristic
550C22×C4C2×C22⋊D4311yescharacteristic
551C22×C4C2×C22⋊D4311yescharacteristic
552C22×C4C2×C22⋊D4311yescharacteristic
553C22×C4C23×D4311yescharacteristic
554D8—868no—
555D8—1724no—
556C2×C8—432no—
557C2×C8—861no—
558C2×C8—861no—
559C2×C8—861no—
560C2×C8—861no—
561C2×C8—861no—
562C2×C8—861no—
563C2×C8—861no—
564C2×C8—861no—
565C2×C8—861no—
566C2×C8—861no—
567C2×C8—861no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—41no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—81no—
578C4⋊C4—861no—
579C4⋊C4—861no—
580C4⋊C4—861no—
581C4⋊C4—861no—
582C4⋊C4—1722no—
583C4⋊C4#1062188214yescomplemented
584C4⋊C4#1062189812yes—
585C22⋊C4—24no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—3441no—
589C22⋊C4—3441no—
590C22⋊C4—3441no—
591C22⋊C4—1722no—
592C22⋊C4—1722no—
593C22⋊C4—1722no—
594C22⋊C4—1722no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—862no—
609C23—1721no—
610C23—1721no—
611C23—1721no—
612C23—1721no—
613C23—1721no—
614C23—1721no—
615C23—1721no—
616C23—1721no—
617C23—1721no—
618C23—1721no—
619C23—1721no—
620C23—1721no—
621C23—1721no—
622C23C22×C22⋊D4311yescharacteristic
623D4—22no—
624D4—22no—
625D4—22no—
626D4—862no—
627D4—862no—
628D4—3444no—
629D4—3444no—
630D4—1721no—
631D4—1721no—
632D4—1721no—
633D4—1721no—
634D4—1721no—
635D4—1721no—
636D4#1306331014yescomplemented
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—48no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—84no—
663C2×C4—84no—
664C2×C4—3444no—
665C2×C4—1721no—
666C2×C4—1721no—
667C2×C4—1721no—
668C2×C4—1721no—
669C2×C4—1721no—
670C2×C4—1721no—
671C2×C4C2×#1062188212yes—
672C2×C4C2×#1062188212yes—
673C2×C4C2×#1062188212yes—
674C2×C4C2×D4×D4311yescharacteristic
675C2×C4C2×#1062189811yescharacteristic
676C2×C4C2×#1062189811yescharacteristic
677C2×C4C2×#1062190211yescharacteristic
678C2×C4#1306337011yescharacteristic
679C2×C4#1306337311yescharacteristic
680C8—862no—
681C8—1721no—
682C8—1721no—
683C8—1721no—
684C22—24no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—3441no—
692C22—3441no—
693C22—3441no—
694C22—3441no—
695C22—3441no—
696C22—3441no—
697C22—3441no—
698C22—3441no—
699C22—3441no—
700C22—3441no—
701C22—3441no—
702C22—1722no—
703C22—1722no—
704C22—1722no—
705C22#1458341011yescharacteristic
706C22D4×C22⋊D4311yescharacteristic
707C22#1458356011yescharacteristic
708C22C22×#1062188211yescharacteristic
709C22#1458369711yescharacteristic
710C22#1458370211yescharacteristic
711C22#1458370711yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—41no—
716C4—41no—
717C4—41no—
718C4—42no—
719C4—81no—
720C4—81no—
721C4—3441no—
722C4—3441no—
723C4C2×#1306331011yescharacteristic
724C4#1458349611yescharacteristic
725C4#1458355011yescharacteristic
726C4#1458359711yescharacteristic
727C2—44no—
728C2—3442no—
729C2—6881no—
730C2#1913833011yescharacteristic
731C2#1914459511yescharacteristic
732C2#1914479411yescharacteristic
733C2#1914612111yescharacteristic
734C2D4×#1062188211yescharacteristic
735C2#1914723011yescharacteristic
736C2#1914734811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingD4×C4⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583094C2
hypercenterD4×C4⋊C4D43
hypocenterC43#26158
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621882C2semidirect
3. #19138360C2semidirect
4. #19136124C2semidirect
5. #19136086C2semidirect
6. #19135999C2semidirect
7. #19135829C2semidirect
8. #19135277C2semidirect
9. #19135154C2semidirect
10. #19134943C2semidirect
11. #19134943C2semidirect
12. #19134943C2semidirect
13. #19134842C2semidirect
14. #19134841C2semidirect
15. D4×C4⋊C4×C43C2semidirect
195. C4⋊C4×C43D8semidirect
257. D4×C43#123semidirect
362. D4×C4⋊C4D43semidirect
429. C43#26158semidirect
583. C4⋊C4#10621882semidirect
636. D4#13063310semidirect

Maximal subgroups

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

subgroupindex
C2×#145830942
C2×C4×#106218822
#191383602
#191361242
#191360862
#191359992
#191358292
#191352772
#191351542
#191349432
#191348422
#191348412
D4×C4⋊C4×C432
#2615843