Finite Group Databasebeta

← C2×C4⋊C4×C22⋊D43 #25255881

Subgroups — C2×C4⋊C4×C22⋊D43 #25255881

Order 11008.

4718 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D43C212yesmaximal
2C22×C4×C22⋊D43C211yesmaximal, characteristic
3C22×C4⋊C4×D43C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D43C2116yesmaximal, direct product factor
5C2×#14582794C212yesmaximal, complemented
6C2×#14582772C212yesmaximal, complemented
7C2×#14582770C212yesmaximal, complemented
8C2×#14582768C211yesmaximal, characteristic, complemented
9C2×#14582759C211yesmaximal, characteristic, complemented
10C2×#14582756C211yesmaximal, characteristic, complemented
11C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
12C23×C4⋊C4×C43C211yesmaximal, characteristic, complemented
13C23×C22⋊D43C2211yescharacteristic
14C23×C4×D43C2212yes—
15C23×C4×D43C2211yescharacteristic
16C2×C4×C22⋊D43—216no—
17C2×C4×C22⋊D43C4116yescomplemented
18C2×C4×C22⋊D43C22116yes—
19C2×C4×C22⋊D43C2218yes—
20C22×C4⋊Dic43C2211yescharacteristic
21C22×C4⋊Dic43C2211yescharacteristic
22C22×Dic43⋊C4C2212yes—
23C22×Dic43⋊C4C2212yes—
24C22×Dic43⋊C4C2212yes—
25C22×Dic43⋊C4C2211yescharacteristic
26C2×C4⋊C4×D43—28no—
27C2×C4⋊C4×D43C2218yescomplemented
28C22×C22⋊Dic43C2212yes—
29C22×C22⋊Dic43C2211yescharacteristic
30C22×(C2×D43)⋊C4C2212yes—
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×C4×Dic43C2212yes—
33C22×C4×Dic43C2211yescharacteristic
34#14582794C22116yescomplemented
35#14582772C22116yescomplemented
36#14582770C22116yescomplemented
37#14582768C2218yescomplemented
38#14582759C2218yescomplemented
39#14582756C2218yescomplemented
40C4⋊C4×Dic43C2218yescomplemented
41C2×C43⋊#95C2212yes—
42C2×C43⋊#95C2212yes—
43C2×C43⋊#95C2212yes—
44C24×C4×C43C2212yes—
45C24×C4×C43C2211yescharacteristic
46C22×C4⋊C4×C43—28no—
47C22×C4⋊C4×C43C2212yes—
48C22×C4⋊C4×C43C2211yescharacteristic
49C22×C4⋊C4×C43C2211yescharacteristic
50C22×C4⋊C4×C43C2218yescomplemented
51C24×D43C2311yescharacteristic
52C22×C22⋊D43C2×C418yes—
53C22×C22⋊D43D418yes—
54C22×C22⋊D43Q818yes—
55C22×C22⋊D43C2314yes—
56C23×Dic43C2312yes—
57C23×Dic43C2312yes—
58C23×Dic43C2311yescharacteristic
59C23×Dic43C2311yescharacteristic
60C23×Dic43C2311yescharacteristic
61C22×C4×D43—24no—
62C22×C4×D43—24no—
63C22×C4×D43—28no—
64C22×C4×D43—28no—
65C22×C4×D43—44no—
66C22×C4×D43C2×C418yescomplemented
67C22×C4×D43C2318yes—
68C22×C4×D43C2314yes—
69C4×C22⋊D43—264no—
70C4×C22⋊D43C2×C4164yescomplemented
71C2×C4⋊Dic43—24no—
72C2×C4⋊Dic43—24no—
73C2×C4⋊Dic43C2314yes—
74C2×C4⋊Dic43C2314yes—
75C2×Dic43⋊C4—28no—
76C2×Dic43⋊C4—28no—
77C2×Dic43⋊C4—44no—
78C2×Dic43⋊C4C2×C418yescomplemented
79C2×Dic43⋊C4C2318yes—
80C2×Dic43⋊C4C2318yes—
81C2×Dic43⋊C4C2318yes—
82C2×Dic43⋊C4C2314yes—
83C4⋊C4×D43—232no—
84C2×C22⋊Dic43—28no—
85C2×C22⋊Dic43C2×C418yescomplemented
86C2×C22⋊Dic43C2318yes—
87C2×C22⋊Dic43C2314yes—
88C2×(C2×D43)⋊C4—28no—
89C2×(C2×D43)⋊C4C2×C418yescomplemented
90C2×(C2×D43)⋊C4C2318yes—
91C2×(C2×D43)⋊C4C2314yes—
92C2×C4×Dic43—28no—
93C2×C4×Dic43C2×C418yescomplemented
94C2×C4×Dic43C2318yes—
95C2×C4×Dic43C2314yes—
96C43⋊#95C2318yes—
97C43⋊#95C2318yes—
98C43⋊#95C2318yes—
99C25×C43C2311yescharacteristic
100C23×C4×C43—24no—
101C23×C4×C43—24no—
102C23×C4×C43—28no—
103C23×C4×C43—28no—
104C23×C4×C43—44no—
105C23×C4×C43C2×C418yescomplemented
106C23×C4×C43C2312yes—
107C23×C4×C43C2318yes—
108C23×C4×C43C2311yescharacteristic
109C23×C4×C43C2314yes—
110C23×C4×C43C2312yes—
111C23×C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43—28no—
113C2×C4⋊C4×C43—24no—
114C2×C4⋊C4×C43—232no—
115C2×C4⋊C4×C43D418yescomplemented
116C2×C4⋊C4×C43C2318yes—
117C2×C4⋊C4×C43C2314yes—
118C2×C4⋊C4×C43C2314yes—
119C24×C43—22no—
120C24×C43—22no—
121C24×C43—22no—
122C24×C43—22no—
123C24×C43C22×C414yes—
124C24×C43C2×D414yes—
125C24×C43C2×Q814yes—
126C24×C43C2412yes—
127C24×C43C2411yescharacteristic
128C23×D43—22no—
129C23×D43—22no—
130C23×D43—22no—
131C23×D43—22no—
132C23×D43C22×C414yes—
133C23×D43C2×D414yes—
134C23×D43C2×Q814yes—
135C23×D43C2412yes—
136C22×C4×C43—232no—
137C22×C4×C43—28no—
138C22×C4×C43—28no—
139C22×C4×C43—216no—
140C22×C4×C43—22no—
141C22×C4×C43—24no—
142C22×C4×C43—24no—
143C22×C4×C43—24no—
144C22×C4×C43—216no—
145C22×C4×C43—22no—
146C22×C4×C43—24no—
147C22×C4×C43—24no—
148C22×C4×C43—48no—
149C22×C4×C43—432no—
150C22×C4×C43C22×C414yes—
151C22×C4×C43C22×C414yes—
152C22×C4×C43C22×C4116yescomplemented
153C22×C4×C43C2×D418yes—
154C22×C4×C43C2×D414yes—
155C22×C4×C43#4114yes—
156C22×C4×C43C2414yes—
157C22×C4×C43C2412yes—
158C22×C4×C43C2414yes—
159C22×C4×C43C2412yes—
160C2×C22⋊D43C4⋊C4164yesdirect product factor
161C2×C22⋊D43C22×C4116yes—
162C2×C22⋊D43C2×D4116yes—
163C2×C22⋊D43C2×Q8116yes—
164C22×Dic43—22no—
165C22×Dic43—24no—
166C22×Dic43—24no—
167C22×Dic43—24no—
168C22×Dic43—22no—
169C22×Dic43—24no—
170C22×Dic43—22no—
171C22×Dic43—24no—
172C22×Dic43—22no—
173C22×Dic43—24no—
174C22×Dic43C22×C414yes—
175C22×Dic43C22×C414yes—
176C22×Dic43C22×C414yes—
177C22×Dic43C2×D414yes—
178C22×Dic43C2×Q814yes—
179C22×Dic43C2414yes—
180C22×Dic43C2414yes—
181C22×Dic43C2412yes—
182C22×Dic43C2412yes—
183C22×Dic43C2412yes—
184C2×C4×D43—232no—
185C2×C4×D43—28no—
186C2×C4×D43—28no—
187C2×C4×D43—216no—
188C2×C4×D43—216no—
189C2×C4×D43—48no—
190C2×C4×D43—432no—
191C2×C4×D43C22×C4116yescomplemented
192C4⋊C4×C43—216no—
193C4⋊C4×C43—28no—
194C4⋊C4×C43C2×D4116yescomplemented
195C22⋊Dic43—216no—
196C22⋊Dic43C22×C4116yescomplemented
197(C2×D43)⋊C4—216no—
198(C2×D43)⋊C4C22×C4116yescomplemented
199C4⋊Dic43—28no—
200C4⋊Dic43—28no—
201Dic43⋊C4—216no—
202Dic43⋊C4—216no—
203Dic43⋊C4—48no—
204Dic43⋊C4C22×C4116yescomplemented
205C4×Dic43—216no—
206C4×Dic43C22×C4116yescomplemented
207C23×C43—28no—
208C23×C43—28no—
209C23×C43—28no—
210C23×C43—28no—
211C23×C43—28no—
212C23×C43—28no—
213C23×C43—22no—
214C23×C43—22no—
215C23×C43—22no—
216C23×C43—22no—
217C23×C43C2×C4⋊C4116yescomplemented
218C23×C43C23×C414yes—
219C23×C43C23×C412yes—
220C23×C43C22×D414yes—
221C23×C43C22×D412yes—
222C23×C43C22×D412yes—
223C23×C43C22×Q814yes—
224C23×C43C22×Q812yes—
225C23×C43C2×#4112yes—
226C23×C43H(5,𝔽2)12yes—
227C23×C432−1+412yes—
228C23×C43C2511yescharacteristic
229C22×D43—28no—
230C22×D43—28no—
231C22×D43—28no—
232C22×D43—28no—
233C22×D43—28no—
234C22×D43—28no—
235C22×D43—22no—
236C22×D43—22no—
237C22×D43—22no—
238C22×D43—22no—
239C22×D43C2×C4⋊C4116yescomplemented
240C22×D43C23×C414yes—
241C22×D43C22×D414yes—
242C22×D43C22×Q814yes—
243C2×C4×C43—28no—
244C2×C4×C43—216no—
245C2×C4×C43—24no—
246C2×C4×C43—22no—
247C2×C4×C43—22no—
248C2×C4×C43—24no—
249C2×C4×C43—232no—
250C2×C4×C43—24no—
251C2×C4×C43—24no—
252C2×C4×C43—24no—
253C2×C4×C43—432no—
254C2×C4×C43—48no—
255C2×C4×C43C4×D4116yescomplemented
256C2×C4×C43C23×C414yes—
257C2×C4×C43C23×C414yes—
258C2×C4×C43C22×D418yes—
259C2×C4×C43C22×D414yes—
260C2×C4×C43C2×#4114yes—
261C22⋊D43C2×C4⋊C4164yesdirect product factor
262C2×Dic43—28no—
263C2×Dic43—28no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—24no—
269C2×Dic43—24no—
270C2×Dic43—24no—
271C2×Dic43—24no—
272C2×Dic43—24no—
273C2×Dic43—24no—
274C2×Dic43—48no—
275C2×Dic43—48no—
276C2×Dic43C2×C4⋊C4116yescomplemented
277C2×Dic43C23×C414yes—
278C2×Dic43C23×C414yes—
279C2×Dic43C23×C414yes—
280C2×Dic43C22×D414yes—
281C2×Dic43C22×Q814yes—
282C4×D43—232no—
283C4×D43—432no—
284C2×D4×C4⋊C4—431nomaximal, Sylow
285C22×C43—232no—
286C22×C43—24no—
287C22×C43—24no—
288C22×C43—24no—
289C22×C43—24no—
290C22×C43—24no—
291C22×C43—24no—
292C22×C43C22×C4⋊C414yes—
293C22×C43C22×C4⋊C418yescomplemented
294C22×C43C2×C4×D414yes—
295C22×C43#52014yes—
296C22×C43D4214yes—
297C22×C43#54714yes—
298C22×C43D4×Q814yes—
299C22×C43#55414yes—
300C22×C43C24×C411yescharacteristic
301C22×C43C23×D411yescharacteristic
302C22×C43C23×D411yescharacteristic
303C22×C43C23×Q811yescharacteristic
304C22×C43C22×#4111yescharacteristic
305C22×C43C2×H(5,𝔽2)11yescharacteristic
306C22×C43C2×2−1+411yescharacteristic
307C2×D43—232no—
308C2×D43—24no—
309C2×D43—24no—
310C2×D43—24no—
311C2×D43—24no—
312C2×D43—24no—
313C2×D43—24no—
314C2×D43C22×C4⋊C418yescomplemented
315C4×C43—24no—
316C4×C43—28no—
317C4×C43—44no—
318C4×C43C2×C4×D418yescomplemented
319Dic43—24no—
320Dic43—24no—
321Dic43—44no—
322Dic43—44no—
323Dic43C22×C4⋊C418yescomplemented
324C22×C4×D4—431no—
325C22×C4×D4—432no—
326C23×C4⋊C4—431no—
327C23×C4⋊C4D4311yescharacteristic, complemented
328D4×C4⋊C4—4316no—
329C2×#389—432no—
330C2×#385—432no—
331C2×#385—432no—
332C2×#384—431no—
333C2×#380—431no—
334C2×#380—431no—
335C2×C4×C4⋊C4—431no—
336C2×C43—28no—
337C2×C43D4×C4⋊C418yescomplemented
338C2×C43C23×C4⋊C411yescharacteristic
339C2×C43C22×C4×D411yescharacteristic
340C2×C43C2×#52011yescharacteristic
341C2×C43C2×D4211yescharacteristic
342C2×C43C2×#54711yescharacteristic
343C2×C43C2×D4×Q811yescharacteristic
344C2×C43C2×#55411yescharacteristic
345D43—28no—
346C23×D4—431no—
347C24×C4—431no—
348C24×C4—432no—
349C24×C4C2×D4312yes—
350C24×C4C2×D4311yescharacteristic
351C2×C4×D4—438no—
352C2×C4×D4—4316no—
353C2×C4×D4—4316no—
354C2×C4×D4—8616no—
355C22×C4⋊C4—28no—
356C22×C4⋊C4—431no—
357C22×C4⋊C4—432no—
358C22×C4⋊C4—432no—
359C22×C4⋊C4—431no—
360C22×C4⋊C4—431no—
361C22×C4⋊C4—432no—
362C22×C4⋊C4—438no—
363C22×C4⋊C4—868no—
364C22×C4⋊C4C2×D4311yescharacteristic
365C22×C4⋊C4C2×D4312yes—
366C22×C4⋊C4C2×D4311yescharacteristic
367C22×C4⋊C4C2×D4318yescomplemented
368C22×C22⋊C4—431no—
369C22×C22⋊C4—431no—
370C22×C22⋊C4—432no—
371C22×C22⋊C4—432no—
372C22×C42—431no—
373C22×C42—432no—
374#389—4316no—
375#385—4316no—
376#385—4316no—
377#384—438no—
378#380—438no—
379#380—438no—
380C4×C4⋊C4—438no—
381C2×#95—432no—
382C2×#95—432no—
383C2×#95—432no—
384C43C2×D4×C4⋊C411yescharacteristic, complemented, Sylow
385C25—431no—
386C25C22×D4311yescharacteristic
387C22×D4—438no—
388C22×D4—438no—
389C22×D4—438no—
390C22×D4—434no—
391C23×C4—24no—
392C23×C4—24no—
393C23×C4—28no—
394C23×C4—28no—
395C23×C4—44no—
396C23×C4—431no—
397C23×C4—431no—
398C23×C4—431no—
399C23×C4—438no—
400C23×C4—434no—
401C23×C4—432no—
402C23×C4—432no—
403C23×C4—438no—
404C23×C4—868no—
405C23×C4—864no—
406C23×C4—864no—
407C23×C4—868no—
408C23×C4—1724no—
409C23×C4C4×D4318yescomplemented
410C23×C4C22×D4312yes—
411C23×C4C22×D4318yes—
412C23×C4C22×D4311yescharacteristic
413C23×C4C22×D4314yes—
414C23×C4C22×D4312yes—
415C23×C4C22×D4311yescharacteristic
416C4×D4—4364no—
417C4×D4—8664no—
418C2×C4⋊C4—28no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—232no—
421C2×C4⋊C4—438no—
422C2×C4⋊C4—434no—
423C2×C4⋊C4—438no—
424C2×C4⋊C4—434no—
425C2×C4⋊C4—438no—
426C2×C4⋊C4—434no—
427C2×C4⋊C4—438no—
428C2×C4⋊C4—868no—
429C2×C4⋊C4—864no—
430C2×C4⋊C4—868no—
431C2×C4⋊C4—864no—
432C2×C4⋊C4—8632no—
433C2×C4⋊C4—1724no—
434C2×C4⋊C4C22⋊D4318yesdirect product factor
435C2×C4⋊C4C22×D4314yes—
436C2×C4⋊C4C22×D4318yes—
437C2×C4⋊C4C22×D4314yes—
438C2×C22⋊C4—438no—
439C2×C22⋊C4—434no—
440C2×C22⋊C4—438no—
441C2×C22⋊C4—434no—
442C2×C22⋊C4—438no—
443C2×C22⋊C4—438no—
444C2×C22⋊C4—868no—
445C2×C22⋊C4—868no—
446C2×C42—438no—
447C2×C42—434no—
448C2×C42—438no—
449C2×C42—868no—
450#95—438no—
451#95—438no—
452#95—438no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—434no—
458C24—434no—
459C24—434no—
460C24—432no—
461C24—862no—
462C24—862no—
463C24—862no—
464C24—862no—
465C24C2×C4×D4314yes—
466C24D4×D4314yes—
467C24Q8×D4314yes—
468C24C23×D4312yes—
469C24C23×D4311yescharacteristic
470C2×D4—4364no—
471C2×D4—4316no—
472C2×D4—4316no—
473C2×D4—4316no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—232no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—24no—
482C22×C4—216no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—216no—
486C22×C4—48no—
487C22×C4—432no—
488C22×C4—434no—
489C22×C4—434no—
490C22×C4—434no—
491C22×C4—432no—
492C22×C4—434no—
493C22×C4—434no—
494C22×C4—432no—
495C22×C4—432no—
496C22×C4—4316no—
497C22×C4—434no—
498C22×C4—434no—
499C22×C4—8616no—
500C22×C4—862no—
501C22×C4—862no—
502C22×C4—862no—
503C22×C4—862no—
504C22×C4—8632no—
505C22×C4—868no—
506C22×C4—868no—
507C22×C4—864no—
508C22×C4—864no—
509C22×C4—864no—
510C22×C4—864no—
511C22×C4—864no—
512C22×C4—864no—
513C22×C4—8616no—
514C22×C4—1728no—
515C22×C4—17232no—
516C22×C4C2×C4×D4314yes—
517C22×C4C2×C4×D4314yes—
518C22×C4C2×C4×D43116yescomplemented
519C22×C4#1062189814yes—
520C22×C4C2×C22⋊D4318yes—
521C22×C4C2×C22⋊D4314yes—
522C22×C4C23×D4314yes—
523C22×C4C23×D4312yes—
524C22×C4C23×D4314yes—
525C22×C4C23×D4312yes—
526C4⋊C4—216no—
527C4⋊C4—28no—
528C4⋊C4—4316no—
529C4⋊C4—8616no—
530C4⋊C4—8616no—
531C4⋊C4—868no—
532C4⋊C4—868no—
533C4⋊C4—1728no—
534C4⋊C4C2×C22⋊D43116yesdirect product factor
535C22⋊C4—4316no—
536C22⋊C4—4316no—
537C22⋊C4—8616no—
538C22⋊C4—8616no—
539C42—4316no—
540C42—8616no—
541C23—28no—
542C23—28no—
543C23—28no—
544C23—28no—
545C23—22no—
546C23—22no—
547C23—22no—
548C23—22no—
549C23—28no—
550C23—28no—
551C23—4316no—
552C23—434no—
553C23—434no—
554C23—434no—
555C23—868no—
556C23—868no—
557C23—868no—
558C23—868no—
559C23—862no—
560C23—862no—
561C23—862no—
562C23—862no—
563C23—868no—
564C23—868no—
565C23C4⋊C4×D43116yescomplemented
566C23C22×C4×D4314yes—
567C23C22×C4×D4312yes—
568C23C2×D4×D4314yes—
569C23C2×D4×D4312yes—
570C23C22×C22⋊D4312yes—
571C23C2×Q8×D4314yes—
572C23C2×Q8×D4312yes—
573C23C2×#1062189812yes—
574C23#1306337012yes—
575C23#1306337312yes—
576C23C24×D4311yescharacteristic
577D4—4364no—
578C2×C4—28no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—216no—
584C2×C4—232no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—432no—
589C2×C4—48no—
590C2×C4—4316no—
591C2×C4—434no—
592C2×C4—434no—
593C2×C4—434no—
594C2×C4—434no—
595C2×C4—434no—
596C2×C4—868no—
597C2×C4—868no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—8632no—
603C2×C4—864no—
604C2×C4—864no—
605C2×C4—864no—
606C2×C4—864no—
607C2×C4—864no—
608C2×C4—864no—
609C2×C4—17232no—
610C2×C4—1728no—
611C2×C4—1728no—
612C2×C4C4×C22⋊D43116yescomplemented
613C2×C4C22×C4×D4314yes—
614C2×C4C22×C4×D4314yes—
615C2×C4C22×C22⋊D4318yes—
616C2×C4C22×C22⋊D4314yes—
617C2×C4C2×#1062189814yes—
618C22—24no—
619C22—24no—
620C22—24no—
621C22—24no—
622C22—24no—
623C22—232no—
624C22—24no—
625C22—438no—
626C22—864no—
627C22—864no—
628C22—864no—
629C22—864no—
630C22—864no—
631C22—8632no—
632C22—864no—
633C22C2×C4⋊C4×D4314yes—
634C22C2×C4⋊C4×D4318yescomplemented
635C22C2×C4×C22⋊D4314yes—
636C22#1458338014yes—
637C22D4×C22⋊D4314yes—
638C22#1458355014yes—
639C22Q8×C22⋊D4314yes—
640C22#1458360414yes—
641C22C23×C4×D4311yescharacteristic
642C22C22×D4×D4311yescharacteristic
643C22C23×C22⋊D4311yescharacteristic
644C22C22×Q8×D4311yescharacteristic
645C22C22×#1062189811yescharacteristic
646C22C2×#1306337011yescharacteristic
647C22C2×#1306337311yescharacteristic
648C4—28no—
649C4—24no—
650C4—44no—
651C4—438no—
652C4—864no—
653C4—864no—
654C4—1724no—
655C4—1724no—
656C4C2×C4×C22⋊D4318yescomplemented
657C2—28no—
658C2—868no—
659C2C4⋊C4×C22⋊D4318yesdirect product factor
660C2C22×C4⋊C4×D4311yescharacteristic
661C2C22×C4×C22⋊D4311yescharacteristic
662C2C2×#1458338011yescharacteristic
663C2C2×D4×C22⋊D4311yescharacteristic
664C2C2×#1458355011yescharacteristic
665C2C2×Q8×C22⋊D4311yescharacteristic
666C2C2×#1458360411yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC23×C4⋊C4×C43C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC23×C4⋊C4D43
hypocenterC43C2×D4×C4⋊C4
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊C4×D43C2semidirect
4. C4⋊C4×C22⋊D43C2direct (N × H)
5. C2×#14582794C2semidirect
6. C2×#14582772C2semidirect
7. C2×#14582770C2semidirect
8. C2×#14582768C2semidirect
9. C2×#14582759C2semidirect
10. C2×#14582756C2semidirect
11. C2×C4⋊C4×Dic43C2semidirect
12. C23×C4⋊C4×C43C2semidirect
17. C2×C4×C22⋊D43C4semidirect
27. C2×C4⋊C4×D43C22semidirect
34. #14582794C22semidirect
35. #14582772C22semidirect
36. #14582770C22semidirect
37. #14582768C22semidirect
38. #14582759C22semidirect
39. #14582756C22semidirect
40. C4⋊C4×Dic43C22semidirect
50. C22×C4⋊C4×C43C22semidirect
66. C22×C4×D43C2×C4semidirect
70. C4×C22⋊D43C2×C4semidirect
78. C2×Dic43⋊C4C2×C4semidirect
85. C2×C22⋊Dic43C2×C4semidirect
89. C2×(C2×D43)⋊C4C2×C4semidirect
93. C2×C4×Dic43C2×C4semidirect
105. C23×C4×C43C2×C4semidirect
115. C2×C4⋊C4×C43D4semidirect
152. C22×C4×C43C22×C4semidirect
160. C2×C22⋊D43C4⋊C4direct (N × H)
191. C2×C4×D43C22×C4semidirect
194. C4⋊C4×C43C2×D4semidirect
196. C22⋊Dic43C22×C4semidirect
198. (C2×D43)⋊C4C22×C4semidirect
204. Dic43⋊C4C22×C4semidirect
206. C4×Dic43C22×C4semidirect
217. C23×C43C2×C4⋊C4semidirect
239. C22×D43C2×C4⋊C4semidirect
255. C2×C4×C43C4×D4semidirect
261. C22⋊D43C2×C4⋊C4direct (N × H)
276. C2×Dic43C2×C4⋊C4semidirect
293. C22×C43C22×C4⋊C4semidirect
314. C2×D43C22×C4⋊C4semidirect
318. C4×C43C2×C4×D4semidirect
323. Dic43C22×C4⋊C4semidirect
327. C23×C4⋊C4D43semidirect
337. C2×C43D4×C4⋊C4semidirect
367. C22×C4⋊C4C2×D43semidirect
384. C43C2×D4×C4⋊C4semidirect
409. C23×C4C4×D43semidirect
434. C2×C4⋊C4C22⋊D43direct (N × H)
518. C22×C4C2×C4×D43semidirect
534. C4⋊C4C2×C22⋊D43direct (N × H)
565. C23C4⋊C4×D43semidirect
612. C2×C4C4×C22⋊D43semidirect
634. C22C2×C4⋊C4×D43semidirect
656. C4C2×C4×C22⋊D43semidirect
659. C2C4⋊C4×C22⋊D43direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D432
C22×C4⋊C4×D432
C4⋊C4×C22⋊D432
C2×#145827942
C2×#145827722
C2×#145827702
C2×#145827682
C2×#145827592
C2×#145827562
C2×C4⋊C4×Dic432
C23×C4⋊C4×C432
C2×D4×C4⋊C443