Finite Group Databasebeta

← C2×C4×#13063298 #25255021

Subgroups — C2×C4×#13063298 #25255021

Order 11008.

5022 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063298C211yesmaximal, characteristic
2C22×C4×D172C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D43C211yesmaximal, characteristic, complemented
4C22×C4×C22⋊D43C211yesmaximal, characteristic, complemented
5C22×C42×D43C211yesmaximal, characteristic, complemented
6C4×#13063298C2116yesmaximal, direct product factor
7C2×#14582799C211yesmaximal, characteristic, complemented
8C2×#14582796C211yesmaximal, characteristic, complemented
9C2×#14582792C211yesmaximal, characteristic, complemented
10C2×#14582788C211yesmaximal, characteristic, complemented
11C2×#14582777C211yesmaximal, characteristic, complemented
12C2×#14582775C211yesmaximal, characteristic, complemented
13C2×#14582758C211yesmaximal, characteristic, complemented
14C2×C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
17C23×D172C2211yescharacteristic
18C23×C22⋊D43C2211yescharacteristic
19C23×C22⋊D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22C23×C4×D43C2211yescharacteristic
23C23×C4×D43C2211yescharacteristic
24C2×#13063298C4116yesdirect product factor
25C2×#13063298C2218yes—
26C2×C4×D172—28no—
27C2×C4×D172C2218yescomplemented
28C2×C4×C22⋊D43—28no—
29C2×C4×C22⋊D43—28no—
30C2×C4×C22⋊D43C2218yescomplemented
31C2×C4×C22⋊D43C2218yescomplemented
32C22×C4⋊Dic43C2211yescharacteristic
33C22×Dic43⋊C4C2211yescharacteristic
34C22×Dic43⋊C4C2211yescharacteristic
35C22×Dic43⋊C4C2211yescharacteristic
36C22×Dic43⋊C4C2211yescharacteristic
37C22×C22⋊Dic43C2211yescharacteristic
38C22×C22⋊Dic43C2211yescharacteristic
39C22×(C2×D43)⋊C4C2211yescharacteristic
40C22×(C2×D43)⋊C4C2211yescharacteristic
41C22×(C2×D43)⋊C4C2211yescharacteristic
42C22×(C2×D43)⋊C4C2211yescharacteristic
43C22×(C2×D43)⋊C4C2211yescharacteristic
44C22×(C2×D43)⋊C4C2211yescharacteristic
45C22×C4×Dic43C2211yescharacteristic
46C22×C4×Dic43C2211yescharacteristic
47C22×C4×Dic43C2211yescharacteristic
48C22×C4×Dic43C2211yescharacteristic
49C2×C42×D43—28no—
50C2×C42×D43C2218yescomplemented
51#14582799C2218yescomplemented
52#14582796C2218yescomplemented
53#14582792C2218yescomplemented
54#14582788C2218yescomplemented
55#14582777C2218yescomplemented
56#14582775C2218yescomplemented
57#14582758C2218yescomplemented
58C4×Dic43⋊C4C2218yescomplemented
59C4×(C2×D43)⋊C4C2218yescomplemented
60C2×C43⋊#95C2211yescharacteristic
61C2×C43⋊#95C2211yescharacteristic
62C2×C43⋊#95C2211yescharacteristic
63C2×C43⋊#95C2211yescharacteristic
64C24×C4×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C22×C22⋊C4×C43C2211yescharacteristic
67C22×C42×C43C2211yescharacteristic
68C22×C42×C43C2211yescharacteristic
69C4×C22⋊C4×C43C2218yescomplemented
70C2×#95×C43C2211yescharacteristic
71C2×#95×C43C2211yescharacteristic
72C24×D43C2311yescharacteristic
73C24×D43C2311yescharacteristic
74C22×D172—24no—
75C22×D172—24no—
76C22×D172C2×C418yescomplemented
77C22×D172C2314yes—
78C22×C22⋊D43—24no—
79C22×C22⋊D43—24no—
80C22×C22⋊D43—24no—
81C22×C22⋊D43—24no—
82C22×C22⋊D43C2×C418yescomplemented
83C22×C22⋊D43C2×C418yescomplemented
84C22×C22⋊D43C2314yes—
85C22×C22⋊D43C2314yes—
86C23×Dic43C2311yescharacteristic
87C23×Dic43C2311yescharacteristic
88C23×Dic43C2311yescharacteristic
89C23×Dic43C2311yescharacteristic
90C23×Dic43C2311yescharacteristic
91C23×Dic43C2311yescharacteristic
92C22×C4×D43—24no—
93C22×C4×D43—24no—
94C22×C4×D43—24no—
95C22×C4×D43—24no—
96C22×C4×D43—24no—
97C22×C4×D43—24no—
98C22×C4×D43—24no—
99C22×C4×D43—24no—
100C22×C4×D43—24no—
101C22×C4×D43—24no—
102C22×C4×D43C2×C418yescomplemented
103C22×C4×D43D418yescomplemented
104C22×C4×D43C2314yes—
105C22×C4×D43C2314yes—
106C22×C4×D43C2314yes—
107C22×C4×D43C2314yes—
108#13063298C2×C4164yesdirect product factor
109C4×D172—232no—
110C4×C22⋊D43—232no—
111C4×C22⋊D43—232no—
112C2×C4⋊Dic43—24no—
113C2×C4⋊Dic43C2314yes—
114C2×Dic43⋊C4—24no—
115C2×Dic43⋊C4—24no—
116C2×Dic43⋊C4—24no—
117C2×Dic43⋊C4C2×C418yescomplemented
118C2×Dic43⋊C4C2314yes—
119C2×Dic43⋊C4C2314yes—
120C2×Dic43⋊C4C2314yes—
121C2×Dic43⋊C4C2314yes—
122C2×C22⋊Dic43—24no—
123C2×C22⋊Dic43—24no—
124C2×C22⋊Dic43C2314yes—
125C2×C22⋊Dic43C2314yes—
126C2×(C2×D43)⋊C4—24no—
127C2×(C2×D43)⋊C4—24no—
128C2×(C2×D43)⋊C4—24no—
129C2×(C2×D43)⋊C4—24no—
130C2×(C2×D43)⋊C4—24no—
131C2×(C2×D43)⋊C4C2×C418yescomplemented
132C2×(C2×D43)⋊C4C2314yes—
133C2×(C2×D43)⋊C4C2314yes—
134C2×(C2×D43)⋊C4C2314yes—
135C2×(C2×D43)⋊C4C2314yes—
136C2×(C2×D43)⋊C4C2314yes—
137C2×(C2×D43)⋊C4C2314yes—
138C2×C4×Dic43—24no—
139C2×C4×Dic43—24no—
140C2×C4×Dic43—24no—
141C2×C4×Dic43D418yescomplemented
142C2×C4×Dic43C2314yes—
143C2×C4×Dic43C2314yes—
144C2×C4×Dic43C2314yes—
145C2×C4×Dic43C2314yes—
146C42×D43—232no—
147C43⋊#95C2314yes—
148C43⋊#95C2314yes—
149C43⋊#95C2314yes—
150C43⋊#95C2314yes—
151C25×C43C2311yescharacteristic
152C23×C4×C43—24no—
153C23×C4×C43—24no—
154C23×C4×C43—24no—
155C23×C4×C43C2311yescharacteristic
156C23×C4×C43C2311yescharacteristic
157C23×C4×C43C2314yes—
158C23×C4×C43C2311yescharacteristic
159C23×C4×C43C2311yescharacteristic
160C23×C4×C43C2311yescharacteristic
161C23×C4×C43C2311yescharacteristic
162C2×C22⋊C4×C43—24no—
163C2×C22⋊C4×C43C2×C418yescomplemented
164C2×C22⋊C4×C43C2314yes—
165C2×C22⋊C4×C43C2314yes—
166C2×C42×C43—24no—
167C2×C42×C43—24no—
168C2×C42×C43C2314yes—
169C2×C42×C43C2314yes—
170#95×C43C2314yes—
171#95×C43C2314yes—
172C24×C43—22no—
173C24×C43—22no—
174C24×C43—22no—
175C24×C43—22no—
176C24×C43—22no—
177C24×C43—22no—
178C24×C43C22×C414yes—
179C24×C43C2412yes—
180C24×C43C2411yescharacteristic
181C23×D43—22no—
182C23×D43—22no—
183C23×D43—22no—
184C23×D43—22no—
185C23×D43—22no—
186C23×D43—22no—
187C23×D43—22no—
188C23×D43—22no—
189C23×D43—22no—
190C23×D43—22no—
191C23×D43C22×C414yes—
192C23×D43C22×C414yes—
193C23×D43C2×D414yes—
194C23×D43#4114yes—
195C23×D43C2412yes—
196C23×D43C2412yes—
197C22×C4×C43—28no—
198C22×C4×C43—28no—
199C22×C4×C43—28no—
200C22×C4×C43—22no—
201C22×C4×C43—22no—
202C22×C4×C43—22no—
203C22×C4×C43—22no—
204C22×C4×C43—22no—
205C22×C4×C43—22no—
206C22×C4×C43—22no—
207C22×C4×C43—22no—
208C22×C4×C43—22no—
209C22×C4×C43—22no—
210C22×C4×C43—22no—
211C22×C4×C43—22no—
212C22×C4×C43—416no—
213C22×C4×C43C22×C414yes—
214C22×C4×C43C22×C414yes—
215C22×C4×C43C2×D414yes—
216C22×C4×C43C2×D414yes—
217C22×C4×C43#4114yes—
218C22×C4×C43#4114yes—
219C22×C4×C43C2412yes—
220C22×C4×C43C2412yes—
221C22×C4×C43C2412yes—
222C22×C4×C43C2412yes—
223C22×C4×C43C2412yes—
224C22×C4×C43C2412yes—
225C2×C22⋊D43—232no—
226C2×C22⋊D43—28no—
227C2×C22⋊D43—28no—
228C2×C22⋊D43—232no—
229C2×C22⋊D43—28no—
230C2×C22⋊D43—28no—
231C2×C22⋊D43C22×C4116yescomplemented
232C2×C22⋊D43C22×C4116yescomplemented
233C22×Dic43—22no—
234C22×Dic43—22no—
235C22×Dic43—22no—
236C22×Dic43—22no—
237C22×Dic43—22no—
238C22×Dic43—22no—
239C22×Dic43—22no—
240C22×Dic43—22no—
241C22×Dic43—22no—
242C22×Dic43—22no—
243C22×Dic43—22no—
244C22×Dic43—22no—
245C22×Dic43C22×C414yes—
246C22×Dic43C22×C414yes—
247C22×Dic43C2×D414yes—
248C22×Dic43C2×D414yes—
249C22×Dic43C2×D414yes—
250C22×Dic43#4114yes—
251C22×Dic43C2412yes—
252C22×Dic43C2412yes—
253C22×Dic43C2412yes—
254C22×Dic43C2412yes—
255C22×Dic43C2412yes—
256C22×Dic43C2412yes—
257C2×D172—232no—
258C2×D172—28no—
259C2×D172—28no—
260C2×D172C22×C4116yescomplemented
261C2×C4×D43—232no—
262C2×C4×D43—232no—
263C2×C4×D43—28no—
264C2×C4×D43—28no—
265C2×C4×D43—28no—
266C2×C4×D43—232no—
267C2×C4×D43—28no—
268C2×C4×D43—28no—
269C2×C4×D43—28no—
270C2×C4×D43—28no—
271C2×C4×D43—28no—
272C2×C4×D43—28no—
273C2×C4×D43—28no—
274C2×C4×D43—416no—
275C2×C4×D43C22×C4116yescomplemented
276C2×C4×D43C2×D4116yescomplemented
277C22⋊C4×C43—28no—
278C22⋊C4×C43C22×C4116yescomplemented
279C42×C43—28no—
280C42×C43—28no—
281C22⋊Dic43—28no—
282C22⋊Dic43—28no—
283(C2×D43)⋊C4—28no—
284(C2×D43)⋊C4—28no—
285(C2×D43)⋊C4—28no—
286(C2×D43)⋊C4—28no—
287(C2×D43)⋊C4—28no—
288(C2×D43)⋊C4C22×C4116yescomplemented
289C4⋊Dic43—28no—
290Dic43⋊C4—28no—
291Dic43⋊C4—28no—
292Dic43⋊C4—28no—
293Dic43⋊C4C22×C4116yescomplemented
294C4×Dic43—28no—
295C4×Dic43—28no—
296C4×Dic43—28no—
297C4×Dic43C2×D4116yescomplemented
298C23×C43—28no—
299C23×C43—28no—
300C23×C43—28no—
301C23×C43—22no—
302C23×C43—22no—
303C23×C43—22no—
304C23×C43—22no—
305C23×C43—22no—
306C23×C43—22no—
307C23×C43—44no—
308C23×C43—44no—
309C23×C43—44no—
310C23×C43—44no—
311C23×C43C23×C414yes—
312C23×C43C23×C412yes—
313C23×C43C22×D412yes—
314C23×C43C22×D412yes—
315C23×C43C2×#4112yes—
316C23×C43C2×#4112yes—
317C23×C43C2×#4112yes—
318C23×C43C2×#4112yes—
319C23×C43C2511yescharacteristic
320C22×D43—28no—
321C22×D43—28no—
322C22×D43—28no—
323C22×D43—28no—
324C22×D43—28no—
325C22×D43—28no—
326C22×D43—22no—
327C22×D43—22no—
328C22×D43—22no—
329C22×D43—22no—
330C22×D43—28no—
331C22×D43—28no—
332C22×D43—28no—
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—22no—
336C22×D43—22no—
337C22×D43—22no—
338C22×D43—22no—
339C22×D43—44no—
340C22×D43—44no—
341C22×D43—44no—
342C22×D43—44no—
343C22×D43C4×D4116yescomplemented
344C22×D43C23×C414yes—
345C22×D43C23×C414yes—
346C22×D43C22×D414yes—
347C22×D43C2×#4114yes—
348C2×C4×C43—28no—
349C2×C4×C43—28no—
350C2×C4×C43—28no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—44no—
364C2×C4×C43—44no—
365C2×C4×C43—416no—
366C2×C4×C43#121116yescomplemented
367C2×C4×C43C23×C414yes—
368C2×C4×C43C23×C414yes—
369C2×C4×C43C22×D414yes—
370C2×C4×C43C22×D414yes—
371C2×C4×C43C2×#4114yes—
372C2×C4×C43C2×#4114yes—
373C22⋊D43—232no—
374C22⋊D43—232no—
375C2×Dic43—28no—
376C2×Dic43—28no—
377C2×Dic43—28no—
378C2×Dic43—22no—
379C2×Dic43—22no—
380C2×Dic43—22no—
381C2×Dic43—22no—
382C2×Dic43—22no—
383C2×Dic43—22no—
384C2×Dic43—22no—
385C2×Dic43—22no—
386C2×Dic43—22no—
387C2×Dic43—22no—
388C2×Dic43—22no—
389C2×Dic43—22no—
390C2×Dic43—44no—
391C2×Dic43—44no—
392C2×Dic43C4×D4116yescomplemented
393C2×Dic43C23×C414yes—
394C2×Dic43C23×C414yes—
395C2×Dic43C22×D414yes—
396C2×Dic43C22×D414yes—
397C2×Dic43C22×D414yes—
398C2×Dic43C2×#4114yes—
399D172—232no—
400C4×D43—232no—
401C4×D43—232no—
402C4×D43—232no—
403C4×D43—416no—
404C2×C4×#121—431nomaximal, Sylow
405C22×C43—24no—
406C22×C43—24no—
407C22×C43—24no—
408C22×C43—42no—
409C22×C43—42no—
410C22×C43—42no—
411C22×C43—42no—
412C22×C43—416no—
413C22×C43C2×C4×D414yes—
414C22×C43C2×C4×D414yes—
415C22×C43C4×#4114yes—
416C22×C43C2×#12114yes—
417C22×C43#52514yes—
418C22×C43#52914yes—
419C22×C43#53214yes—
420C22×C43C24×C411yescharacteristic
421C22×C43C23×D411yescharacteristic
422C22×C43C23×D411yescharacteristic
423C22×C43C22×#4111yescharacteristic
424C22×C43C22×#4111yescharacteristic
425C22×C43C22×#4111yescharacteristic
426C22×C43C22×#4111yescharacteristic
427C2×D43—24no—
428C2×D43—24no—
429C2×D43—24no—
430C2×D43—24no—
431C2×D43—24no—
432C2×D43—24no—
433C2×D43—232no—
434C2×D43—24no—
435C2×D43—24no—
436C2×D43—24no—
437C2×D43—42no—
438C2×D43—42no—
439C2×D43—42no—
440C2×D43—42no—
441C2×D43—416no—
442C2×D43C2×C4×D418yescomplemented
443C4×C43—24no—
444C4×C43—24no—
445C4×C43—24no—
446C4×C43—42no—
447C4×C43—42no—
448C4×C43C2×#12118yescomplemented
449Dic43—24no—
450Dic43—24no—
451Dic43—24no—
452Dic43—42no—
453Dic43—42no—
454Dic43C2×C4×D418yescomplemented
455C22×#121—431no—
456C22×C4×D4—431no—
457C22×C4×D4—431no—
458C22×C4×D4—431no—
459C23×C42—431no—
460C4×#121—4316no—
461C2×#390—431no—
462C2×#389—431no—
463C2×#388—431no—
464C2×#388—431no—
465C2×#386—431no—
466C2×#386—431no—
467C2×#380—431no—
468C2×C4×C4⋊C4—431no—
469C2×C4×C22⋊C4—431no—
470C2×C4×C22⋊C4D4311yescharacteristic, complemented
471C2×C43—44no—
472C2×C43C4×#12118yescomplemented
473C2×C43C22×C4×D411yescharacteristic
474C2×C43C22×C4×D411yescharacteristic
475C2×C43C2×C4×#4111yescharacteristic
476C2×C43C22×#12111yescharacteristic
477C2×C43C2×#52511yescharacteristic
478C2×C43C2×#52911yescharacteristic
479C2×C43C2×#53211yescharacteristic
480D43—28no—
481D43—44no—
482C23×D4—431no—
483C23×D4—431no—
484C23×D4—431no—
485C24×C4—431no—
486C24×C4—431no—
487C24×C4—431no—
488C24×C4—431no—
489C24×C4C2×D4311yescharacteristic
490C2×#121—438no—
491C2×#121—4316no—
492C2×C4×D4—438no—
493C2×C4×D4—438no—
494C2×C4×D4—438no—
495C2×C4×D4—868no—
496C2×C4×D4—868no—
497C2×C4×D4—868no—
498C22×C4⋊C4—431no—
499C22×C4⋊C4—431no—
500C22×C4⋊C4—431no—
501C22×C4⋊C4—431no—
502C22×C4⋊C4—431no—
503C22×C22⋊C4—431no—
504C22×C22⋊C4—431no—
505C22×C22⋊C4—431no—
506C22×C22⋊C4—431no—
507C22×C22⋊C4—431no—
508C22×C22⋊C4—431no—
509C22×C22⋊C4—431no—
510C22×C22⋊C4—431no—
511C22×C22⋊C4C2×D4311yescharacteristic
512C22×C22⋊C4C2×D4311yescharacteristic
513C22×C42—431no—
514C22×C42—431no—
515C22×C42—431no—
516C22×C42—431no—
517C22×C42—438no—
518C22×C42—868no—
519C22×C42C2×D4311yescharacteristic
520C22×C42C2×D4311yescharacteristic
521#390—438no—
522#389—438no—
523#388—438no—
524#388—438no—
525#386—438no—
526#386—438no—
527#380—438no—
528C4×C4⋊C4—438no—
529C4×C22⋊C4—438no—
530C4×C22⋊C4C2×D4318yescomplemented
531C2×#95—431no—
532C2×#95—431no—
533C2×#95—431no—
534C2×#95—431no—
535C2×#95C2×D4311yescharacteristic
536C2×#95C2×D4311yescharacteristic
537C43C2×C4×#12111yescharacteristic, complemented, Sylow
538C25—431no—
539C25—431no—
540C25C22×D4311yescharacteristic
541C22×D4—438no—
542C22×D4—438no—
543C22×D4—434no—
544C22×D4—434no—
545C22×D4—438no—
546C22×D4—434no—
547C22×D4—864no—
548C22×D4—864no—
549C22×D4—864no—
550C22×D4—864no—
551C22×D4—864no—
552C22×D4—864no—
553C23×C4—24no—
554C23×C4—24no—
555C23×C4—24no—
556C23×C4—431no—
557C23×C4—431no—
558C23×C4—431no—
559C23×C4—431no—
560C23×C4—438no—
561C23×C4—438no—
562C23×C4—434no—
563C23×C4—434no—
564C23×C4—431no—
565C23×C4—431no—
566C23×C4—434no—
567C23×C4—434no—
568C23×C4—864no—
569C23×C4—864no—
570C23×C4—864no—
571C23×C4—864no—
572C23×C4—864no—
573C23×C4—864no—
574C23×C4—864no—
575C23×C4—864no—
576C23×C4—864no—
577C23×C4—864no—
578C23×C4C22×D4311yescharacteristic
579C23×C4C22×D4311yescharacteristic
580C23×C4C22×D4314yes—
581C23×C4C22×D4311yescharacteristic
582C23×C4C22×D4311yescharacteristic
583C23×C4C22×D4311yescharacteristic
584C23×C4C22×D4311yescharacteristic
585#121—4364no—
586C4×D4—8632no—
587C4×D4—8632no—
588C4×D4—8632no—
589C2×C4⋊C4—438no—
590C2×C4⋊C4—434no—
591C2×C4⋊C4—434no—
592C2×C4⋊C4—434no—
593C2×C4⋊C4—434no—
594C2×C4⋊C4—434no—
595C2×C4⋊C4—864no—
596C2×C4⋊C4—864no—
597C2×C4⋊C4—864no—
598C2×C4⋊C4—864no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—438no—
601C2×C22⋊C4—434no—
602C2×C22⋊C4—434no—
603C2×C22⋊C4—434no—
604C2×C22⋊C4—434no—
605C2×C22⋊C4—434no—
606C2×C22⋊C4—434no—
607C2×C22⋊C4—434no—
608C2×C22⋊C4—434no—
609C2×C22⋊C4—864no—
610C2×C22⋊C4—864no—
611C2×C22⋊C4—864no—
612C2×C22⋊C4—864no—
613C2×C22⋊C4—864no—
614C2×C22⋊C4—864no—
615C2×C22⋊C4—864no—
616C2×C22⋊C4C4×D4318yescomplemented
617C2×C22⋊C4C22×D4314yes—
618C2×C22⋊C4C22×D4314yes—
619C2×C42—24no—
620C2×C42—24no—
621C2×C42—438no—
622C2×C42—434no—
623C2×C42—434no—
624C2×C42—434no—
625C2×C42—434no—
626C2×C42—8632no—
627C2×C42—864no—
628C2×C42—864no—
629C2×C42—864no—
630C2×C42C22×D4314yes—
631C2×C42C22×D4314yes—
632#95—434no—
633#95—434no—
634#95—434no—
635#95—434no—
636#95C22×D4314yes—
637#95C22×D4314yes—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—434no—
645C24—434no—
646C24—434no—
647C24—432no—
648C24—434no—
649C24—432no—
650C24—862no—
651C24—862no—
652C24—862no—
653C24—862no—
654C24—862no—
655C24—862no—
656C24—862no—
657C24—862no—
658C24—862no—
659C24—862no—
660C24C2×C4×D4314yes—
661C24C23×D4312yes—
662C24C23×D4311yescharacteristic
663C2×D4—4316no—
664C2×D4—4316no—
665C2×D4—4316no—
666C2×D4—868no—
667C2×D4—8632no—
668C2×D4—868no—
669C2×D4—868no—
670C2×D4—8632no—
671C2×D4—868no—
672C2×D4—868no—
673C2×D4—8632no—
674C2×D4—868no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—28no—
688C22×C4—28no—
689C22×C4—28no—
690C22×C4—416no—
691C22×C4—434no—
692C22×C4—434no—
693C22×C4—434no—
694C22×C4—432no—
695C22×C4—434no—
696C22×C4—434no—
697C22×C4—434no—
698C22×C4—432no—
699C22×C4—432no—
700C22×C4—432no—
701C22×C4—4316no—
702C22×C4—4316no—
703C22×C4—432no—
704C22×C4—432no—
705C22×C4—868no—
706C22×C4—868no—
707C22×C4—8632no—
708C22×C4—868no—
709C22×C4—868no—
710C22×C4—8632no—
711C22×C4—862no—
712C22×C4—862no—
713C22×C4—862no—
714C22×C4—862no—
715C22×C4—862no—
716C22×C4—862no—
717C22×C4—8632no—
718C22×C4—868no—
719C22×C4—868no—
720C22×C4—868no—
721C22×C4—862no—
722C22×C4—862no—
723C22×C4—862no—
724C22×C4—862no—
725C22×C4—862no—
726C22×C4—862no—
727C22×C4—868no—
728C22×C4—868no—
729C22×C4—868no—
730C22×C4—17216no—
731C22×C4C2×C4×D4314yes—
732C22×C4C2×C4×D4314yes—
733C22×C4#1062189814yes—
734C22×C4#1062189814yes—
735C22×C4D4×D4314yes—
736C22×C4D4×D4314yes—
737C22×C4C23×D4312yes—
738C22×C4C23×D4312yes—
739C22×C4C23×D4312yes—
740C22×C4C23×D4312yes—
741C22×C4C23×D4312yes—
742C22×C4C23×D4312yes—
743C4⋊C4—4316no—
744C4⋊C4—868no—
745C4⋊C4—868no—
746C4⋊C4—868no—
747C4⋊C4—868no—
748C22⋊C4—28no—
749C22⋊C4—4316no—
750C22⋊C4—868no—
751C22⋊C4—868no—
752C22⋊C4—868no—
753C22⋊C4—868no—
754C22⋊C4—868no—
755C22⋊C4—868no—
756C22⋊C4—868no—
757C22⋊C4C2×C4×D43116yescomplemented
758C42—28no—
759C42—28no—
760C42—4316no—
761C42—868no—
762C42—868no—
763C42—868no—
764C23—28no—
765C23—28no—
766C23—28no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—4316no—
778C23—434no—
779C23—434no—
780C23—434no—
781C23—434no—
782C23—868no—
783C23—868no—
784C23—868no—
785C23—868no—
786C23—868no—
787C23—868no—
788C23—862no—
789C23—862no—
790C23—862no—
791C23—862no—
792C23—868no—
793C23—868no—
794C23—868no—
795C23—862no—
796C23—862no—
797C23—862no—
798C23—862no—
799C23—862no—
800C23—862no—
801C23—1724no—
802C23—1724no—
803C23—1724no—
804C23—1724no—
805C23C22×C4×D4314yes—
806C23C22×C4×D4312yes—
807C23C2×D4×D4312yes—
808C23C2×D4×D4312yes—
809C23#41×D4312yes—
810C23#41×D4312yes—
811C23C2×#1062189812yes—
812C23C2×#1062189812yes—
813C23C24×D4311yescharacteristic
814D4—8632no—
815D4—8632no—
816D4—8632no—
817C2×C4—28no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—416no—
835C2×C4—4316no—
836C2×C4—434no—
837C2×C4—434no—
838C2×C4—434no—
839C2×C4—434no—
840C2×C4—434no—
841C2×C4—434no—
842C2×C4—8632no—
843C2×C4—8632no—
844C2×C4—868no—
845C2×C4—868no—
846C2×C4—868no—
847C2×C4—862no—
848C2×C4—862no—
849C2×C4—862no—
850C2×C4—862no—
851C2×C4—862no—
852C2×C4—862no—
853C2×C4—8632no—
854C2×C4—862no—
855C2×C4—862no—
856C2×C4—862no—
857C2×C4—862no—
858C2×C4—862no—
859C2×C4—862no—
860C2×C4—1724no—
861C2×C4—1724no—
862C2×C4—17216no—
863C2×C4#13063298116yesdirect product factor
864C2×C4C22×C4×D4314yes—
865C2×C4C22×C4×D4314yes—
866C2×C4C2×D4×D4314yes—
867C2×C4C2×D4×D4314yes—
868C2×C4C2×#1062189814yes—
869C2×C4C2×#1062189814yes—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—416no—
877C22—42no—
878C22—438no—
879C22—864no—
880C22—864no—
881C22—864no—
882C22—8632no—
883C22—864no—
884C22—864no—
885C22—864no—
886C22—864no—
887C22—864no—
888C22—864no—
889C22—1722no—
890C22—1722no—
891C22—1722no—
892C22—17216no—
893C22—1722no—
894C22C4×D4×D4314yes—
895C22C4×D4×D4314yes—
896C22C4×#1062189814yes—
897C22C2×#1306329814yes—
898C22#1458340814yes—
899C22#1458342714yes—
900C22#1458344614yes—
901C22C23×C4×D4311yescharacteristic
902C22C22×D4×D4311yescharacteristic
903C22C22×D4×D4311yescharacteristic
904C22C2×#41×D4311yescharacteristic
905C22C2×#41×D4311yescharacteristic
906C22C22×#1062189811yescharacteristic
907C22C22×#1062189811yescharacteristic
908C4—24no—
909C4—24no—
910C4—24no—
911C4—42no—
912C4—42no—
913C4—438no—
914C4—864no—
915C4—864no—
916C4—864no—
917C4—1722no—
918C4—1722no—
919C4C2×#1306329818yesdirect product factor
920C2—44no—
921C2—868no—
922C2—1724no—
923C2C4×#1306329818yesdirect product factor
924C2C2×C4×D4×D4311yescharacteristic
925C2C2×C4×D4×D4311yescharacteristic
926C2C2×C4×#1062189811yescharacteristic
927C2C22×#1306329811yescharacteristic
928C2C2×#1458340811yescharacteristic
929C2C2×#1458342711yescharacteristic
930C2C2×#1458344611yescharacteristic
subgroupG/H
centerC23×C4C22×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C4×C22⋊C4×C43C2
socleC24×C43C24
prime radicalC22×#13063298C2
cosocleC23×C43C25
hypercenterC2×C4×C22⋊C4D43
hypocenterC43C2×C4×#121
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×D172C2semidirect
3. C22×C4×C22⋊D43C2semidirect
4. C22×C4×C22⋊D43C2semidirect
5. C22×C42×D43C2semidirect
6. C4×#13063298C2direct (N × H)
7. C2×#14582799C2semidirect
8. C2×#14582796C2semidirect
9. C2×#14582792C2semidirect
10. C2×#14582788C2semidirect
11. C2×#14582777C2semidirect
12. C2×#14582775C2semidirect
13. C2×#14582758C2semidirect
14. C2×C4×Dic43⋊C4C2semidirect
15. C2×C4×(C2×D43)⋊C4C2semidirect
16. C2×C4×C22⋊C4×C43C2semidirect
24. C2×#13063298C4direct (N × H)
27. C2×C4×D172C22semidirect
30. C2×C4×C22⋊D43C22semidirect
31. C2×C4×C22⋊D43C22semidirect
50. C2×C42×D43C22semidirect
51. #14582799C22semidirect
52. #14582796C22semidirect
53. #14582792C22semidirect
54. #14582788C22semidirect
55. #14582777C22semidirect
56. #14582775C22semidirect
57. #14582758C22semidirect
58. C4×Dic43⋊C4C22semidirect
59. C4×(C2×D43)⋊C4C22semidirect
69. C4×C22⋊C4×C43C22semidirect
76. C22×D172C2×C4semidirect
82. C22×C22⋊D43C2×C4semidirect
83. C22×C22⋊D43C2×C4semidirect
102. C22×C4×D43C2×C4semidirect
103. C22×C4×D43D4semidirect
108. #13063298C2×C4direct (N × H)
117. C2×Dic43⋊C4C2×C4semidirect
131. C2×(C2×D43)⋊C4C2×C4semidirect
141. C2×C4×Dic43D4semidirect
163. C2×C22⋊C4×C43C2×C4semidirect
231. C2×C22⋊D43C22×C4semidirect
232. C2×C22⋊D43C22×C4semidirect
260. C2×D172C22×C4semidirect
275. C2×C4×D43C22×C4semidirect
276. C2×C4×D43C2×D4semidirect
278. C22⋊C4×C43C22×C4semidirect
288. (C2×D43)⋊C4C22×C4semidirect
293. Dic43⋊C4C22×C4semidirect
297. C4×Dic43C2×D4semidirect
343. C22×D43C4×D4semidirect
366. C2×C4×C43#121semidirect
392. C2×Dic43C4×D4semidirect
442. C2×D43C2×C4×D4semidirect
448. C4×C43C2×#121semidirect
454. Dic43C2×C4×D4semidirect
470. C2×C4×C22⋊C4D43semidirect
472. C2×C43C4×#121semidirect
530. C4×C22⋊C4C2×D43semidirect
537. C43C2×C4×#121semidirect
616. C2×C22⋊C4C4×D43semidirect
757. C22⋊C4C2×C4×D43semidirect
863. C2×C4#13063298direct (N × H)
919. C4C2×#13063298direct (N × H)
923. C2C4×#13063298direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130632982
C22×C4×D1722
C22×C4×C22⋊D432
C22×C42×D432
C4×#130632982
C2×#145827992
C2×#145827962
C2×#145827922
C2×#145827882
C2×#145827772
C2×#145827752
C2×#145827582
C2×C4×Dic43⋊C42
C2×C4×(C2×D43)⋊C42
C2×C4×C22⋊C4×C432
C2×C4×#12143