Finite Group Databasebeta

← C2×#19137265 #25255326

Subgroups — C2×#19137265 #25255326

Order 11008.

3718 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063307C211yesmaximal, characteristic
2C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
3C22×C4⋊C4×D43C211yesmaximal, characteristic, complemented
4#19137265C2116yesmaximal, direct product factor
5C2×#14582797C211yesmaximal, characteristic, complemented
6C2×#14582794C211yesmaximal, characteristic, complemented
7C2×#14582793C211yesmaximal, characteristic, complemented
8C2×#14582786C211yesmaximal, characteristic, complemented
9C2×#14582782C211yesmaximal, characteristic, complemented
10C2×#14582775C211yesmaximal, characteristic
11C2×#14582774C211yesmaximal, characteristic, complemented
12C2×#14582773C211yesmaximal, characteristic, complemented
13C2×#14582771C211yesmaximal, characteristic, complemented
14C2×#14582761C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
16C2×C43×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22C2×#13063307C4116yescomplemented
23C2×#13063307C2218yes—
24C2×(C22⋊D43)⋊C4—28no—
25C2×(C22⋊D43)⋊C4C2218yes—
26C22×C4⋊Dic43C2211yescharacteristic
27C22×C4⋊Dic43C2211yescharacteristic
28C22×C4⋊Dic43C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C22×Dic43⋊C4C2211yescharacteristic
32C22×Dic43⋊C4C2211yescharacteristic
33C22×Dic43⋊C4C2211yescharacteristic
34C2×C4⋊C4×D43—28no—
35C2×C4⋊C4×D43C2218yescomplemented
36C22×C22⋊Dic43C2211yescharacteristic
37C22×C22⋊Dic43C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×(C2×D43)⋊C4C2211yescharacteristic
40C22×(C2×D43)⋊C4C2211yescharacteristic
41C22×C4×Dic43C2211yescharacteristic
42C22×C4×Dic43C2211yescharacteristic
43#14582797C2218yescomplemented
44#14582794C2218yescomplemented
45#14582793C2218yescomplemented
46#14582786C2218yescomplemented
47#14582782C2218yescomplemented
48#14582775C2218yes—
49#14582774C2218yescomplemented
50#14582773C2218yescomplemented
51#14582771C2218yescomplemented
52#14582761C2218yescomplemented
53C4×(C2×D43)⋊C4C2218yescomplemented
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C2×C43⋊#95C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C22⋊C4×C43C2211yescharacteristic
64C22×C22⋊C4×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C22×C42×C43C2211yescharacteristic
67C43×#388C2218yescomplemented
68C2×#95×C43C2211yescharacteristic
69C2×#95×C43C2211yescharacteristic
70C24×D43C2311yescharacteristic
71C22×C22⋊D43—24no—
72C22×C22⋊D43—24no—
73C22×C22⋊D43C2×C418yes—
74C22×C22⋊D43C2314yes—
75C23×Dic43—24no—
76C23×Dic43—42no—
77C23×Dic43—42no—
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2314yes—
86C22×C4×D43—24no—
87C22×C4×D43—24no—
88C22×C4×D43—24no—
89C22×C4×D43—42no—
90C22×C4×D43—42no—
91C22×C4×D43—42no—
92C22×C4×D43—42no—
93C22×C4×D43C2×C418yescomplemented
94C22×C4×D43D418yes—
95C22×C4×D43C2314yes—
96C22×C4×D43C2314yes—
97C22×C4×D43C2314yes—
98#13063307C2×C4164yescomplemented
99(C22⋊D43)⋊C4—232no—
100C2×C4⋊Dic43—24no—
101C2×C4⋊Dic43—42no—
102C2×C4⋊Dic43C2×C418yescomplemented
103C2×C4⋊Dic43C2314yes—
104C2×C4⋊Dic43C2314yes—
105C2×C4⋊Dic43C2314yes—
106C2×Dic43⋊C4—24no—
107C2×Dic43⋊C4—24no—
108C2×Dic43⋊C4—24no—
109C2×Dic43⋊C4—42no—
110C2×Dic43⋊C4C2×C418yescomplemented
111C2×Dic43⋊C4C2314yes—
112C2×Dic43⋊C4C2314yes—
113C2×Dic43⋊C4C2314yes—
114C2×Dic43⋊C4C2314yes—
115C2×Dic43⋊C4C2314yes—
116C4⋊C4×D43—232no—
117C2×C22⋊Dic43—42no—
118C2×C22⋊Dic43C2×C418yescomplemented
119C2×C22⋊Dic43C2314yes—
120C2×C22⋊Dic43C2314yes—
121C2×(C2×D43)⋊C4—24no—
122C2×(C2×D43)⋊C4—24no—
123C2×(C2×D43)⋊C4C2×C418yescomplemented
124C2×(C2×D43)⋊C4C2314yes—
125C2×(C2×D43)⋊C4C2314yes—
126C2×(C2×D43)⋊C4C2314yes—
127C2×C4×Dic43—24no—
128C2×C4×Dic43—42no—
129C2×C4×Dic43C2314yes—
130C2×C4×Dic43C2314yes—
131C43⋊#95C2314yes—
132C43⋊#95C2314yes—
133C43⋊#95C2314yes—
134C43⋊#95C2314yes—
135C43⋊#95C2314yes—
136C43⋊#95C2314yes—
137C43⋊#95C2314yes—
138C43⋊#95C2314yes—
139C25×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43—24no—
147C2×C4⋊C4×C43C2314yes—
148C2×C22⋊C4×C43—24no—
149C2×C22⋊C4×C43—42no—
150C2×C22⋊C4×C43C2×C418yescomplemented
151C2×C22⋊C4×C43C2314yes—
152C2×C22⋊C4×C43C2314yes—
153C2×C22⋊C4×C43C2314yes—
154C2×C42×C43—42no—
155C2×C42×C43C2314yes—
156#95×C43C2314yes—
157#95×C43C2314yes—
158C24×C43—22no—
159C24×C43—22no—
160C24×C43—22no—
161C24×C43—22no—
162C24×C43—22no—
163C24×C43—22no—
164C24×C43C22×C414yes—
165C24×C43C2412yes—
166C24×C43C2411yescharacteristic
167C23×D43—22no—
168C23×D43—22no—
169C23×D43—22no—
170C23×D43—22no—
171C23×D43C22×C414yes—
172C23×D43C2×D414yes—
173C23×D43#4114yes—
174C23×D43C2412yes—
175C22×C4×C43—22no—
176C22×C4×C43—22no—
177C22×C4×C43—22no—
178C22×C4×C43—22no—
179C22×C4×C43—22no—
180C22×C4×C43—22no—
181C22×C4×C43—22no—
182C22×C4×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43—22no—
185C22×C4×C43—22no—
186C22×C4×C43—22no—
187C22×C4×C43—22no—
188C22×C4×C43—22no—
189C22×C4×C43—22no—
190C22×C4×C43C22×C414yes—
191C22×C4×C43C22×C414yes—
192C22×C4×C43C2×D414yes—
193C22×C4×C43C2412yes—
194C22×C4×C43C2412yes—
195C22×C4×C43C2412yes—
196C22×C4×C43C2412yes—
197C22×C4×C43C2412yes—
198C22×C4×C43C2412yes—
199C2×C22⋊D43—232no—
200C2×C22⋊D43—28no—
201C2×C22⋊D43—28no—
202C2×C22⋊D43C22×C4116yes—
203C22×Dic43—28no—
204C22×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43—22no—
209C22×Dic43—22no—
210C22×Dic43—22no—
211C22×Dic43—22no—
212C22×Dic43—22no—
213C22×Dic43—22no—
214C22×Dic43—22no—
215C22×Dic43—22no—
216C22×Dic43—22no—
217C22×Dic43—22no—
218C22×Dic43—22no—
219C22×Dic43—22no—
220C22×Dic43—22no—
221C22×Dic43—44no—
222C22×Dic43—44no—
223C22×Dic43—416no—
224C22×Dic43C22×C414yes—
225C22×Dic43C22×C414yes—
226C22×Dic43C22×C414yes—
227C22×Dic43C2×D414yes—
228C22×Dic43C2412yes—
229C22×Dic43C2412yes—
230C22×Dic43C2412yes—
231C22×Dic43C2412yes—
232C22×Dic43C2412yes—
233C22×Dic43C2412yes—
234C22×Dic43C2412yes—
235C2×C4×D43—232no—
236C2×C4×D43—28no—
237C2×C4×D43—28no—
238C2×C4×D43—28no—
239C2×C4×D43—416no—
240C2×C4×D43—44no—
241C2×C4×D43—44no—
242C2×C4×D43—44no—
243C2×C4×D43—44no—
244C2×C4×D43—416no—
245C2×C4×D43C22×C4116yescomplemented
246C2×C4×D43C2×D4116yes—
247C4⋊C4×C43—28no—
248C22⋊C4×C43—28no—
249C22⋊C4×C43—44no—
250C22⋊C4×C43C22×C4116yescomplemented
251C42×C43—44no—
252C22⋊Dic43—44no—
253C22⋊Dic43C22×C4116yescomplemented
254(C2×D43)⋊C4—28no—
255(C2×D43)⋊C4—28no—
256(C2×D43)⋊C4C22×C4116yescomplemented
257C4⋊Dic43—28no—
258C4⋊Dic43—44no—
259C4⋊Dic43C22×C4116yescomplemented
260Dic43⋊C4—28no—
261Dic43⋊C4—28no—
262Dic43⋊C4—28no—
263Dic43⋊C4—44no—
264Dic43⋊C4C22×C4116yescomplemented
265C4×Dic43—28no—
266C4×Dic43—44no—
267C23×C43—28no—
268C23×C43—28no—
269C23×C43—28no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—44no—
277C23×C43—44no—
278C23×C43—44no—
279C23×C43—44no—
280C23×C43C23×C414yes—
281C23×C43C23×C412yes—
282C23×C43C22×D412yes—
283C23×C43C2×#4112yes—
284C23×C43H(5,𝔽2)12yes—
285C23×C43H(5,𝔽2)12yes—
286C23×C432−1+412yes—
287C23×C432−1+412yes—
288C23×C43C2511yescharacteristic
289C22×D43—28no—
290C22×D43—28no—
291C22×D43—28no—
292C22×D43—28no—
293C22×D43—28no—
294C22×D43—28no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43C4×D4116yes—
300C22×D43C23×C414yes—
301C22×D43C22×D414yes—
302C22×D43C2×#4114yes—
303C2×C4×C43—28no—
304C2×C4×C43—28no—
305C2×C4×C43—28no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—44no—
322C2×C4×C43—44no—
323C2×C4×C43—44no—
324C2×C4×C43C23×C414yes—
325C2×C4×C43C23×C414yes—
326C2×C4×C43C22×D414yes—
327C22⋊D43—232no—
328C2×Dic43—28no—
329C2×Dic43—28no—
330C2×Dic43—28no—
331C2×Dic43—28no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—416no—
350C2×Dic43—44no—
351C2×Dic43—44no—
352C2×Dic43—44no—
353C2×Dic43C23×C414yes—
354C2×Dic43C23×C414yes—
355C2×Dic43C23×C414yes—
356C2×Dic43C22×D414yes—
357C4×D43—232no—
358C4×D43—416no—
359C4×D43—416no—
360C2×#2322—431nomaximal, Sylow
361C22×C43—24no—
362C22×C43—24no—
363C22×C43—24no—
364C22×C43—416no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43C2×C4×D414yes—
370C22×C43#52014yes—
371C22×C43#52014yes—
372C22×C43#53414yes—
373C22×C43#53614yes—
374C22×C43#53914yes—
375C22×C43#53914yes—
376C22×C43C24×C411yescharacteristic
377C22×C43C23×D411yescharacteristic
378C22×C43C22×#4111yescharacteristic
379C22×C43C2×H(5,𝔽2)11yescharacteristic
380C22×C43C2×H(5,𝔽2)11yescharacteristic
381C22×C43C2×2−1+411yescharacteristic
382C22×C43C2×2−1+411yescharacteristic
383C2×D43—232no—
384C2×D43—24no—
385C2×D43—24no—
386C2×D43—24no—
387C2×D43—24no—
388C2×D43—24no—
389C2×D43—24no—
390C2×D43C2×C4×D418yes—
391C4×C43—24no—
392C4×C43—24no—
393C4×C43—24no—
394C4×C43—42no—
395C4×C43—42no—
396C4×C43—42no—
397Dic43—24no—
398Dic43—24no—
399Dic43—24no—
400Dic43—24no—
401Dic43—42no—
402Dic43—42no—
403Dic43—42no—
404C22×#123—431no—
405C22×C4×D4—431no—
406C23×C4⋊C4—431no—
407#2322—4316no—
408C2×#389—431no—
409C2×#389—431no—
410C2×#388—431no—
411C2×#388D4311yescharacteristic, complemented
412C2×#387—431no—
413C2×#387—431no—
414C2×#386—431no—
415C2×#385—431no—
416C2×#385—431no—
417C2×#385—431no—
418C2×#381—431no—
419C2×C4×C22⋊C4—431no—
420C2×C43—44no—
421C2×C43#232218yescomplemented
422C2×C43C22×C4×D411yescharacteristic
423C2×C43C2×#52011yescharacteristic
424C2×C43C2×#52011yescharacteristic
425C2×C43C2×#53411yescharacteristic
426C2×C43C2×#53611yescharacteristic
427C2×C43C2×#53911yescharacteristic
428C2×C43C2×#53911yescharacteristic
429D43—28no—
430C23×D4—431no—
431C24×C4—431no—
432C24×C4—431no—
433C24×C4—431no—
434C24×C4—431no—
435C2×#123—438no—
436C2×#123—4316no—
437C2×C4×D4—438no—
438C2×C4×D4—868no—
439C22×C4⋊C4—431no—
440C22×C4⋊C4—431no—
441C22×C4⋊C4—431no—
442C22×C4⋊C4—431no—
443C22×C4⋊C4—431no—
444C22×C4⋊C4—431no—
445C22×C4⋊C4—431no—
446C22×C4⋊C4—431no—
447C22×C4⋊C4—438no—
448C22×C4⋊C4—868no—
449C22×C4⋊C4C2×D4311yescharacteristic
450C22×C22⋊C4—431no—
451C22×C22⋊C4—431no—
452C22×C22⋊C4—431no—
453C22×C22⋊C4—431no—
454C22×C22⋊C4—431no—
455C22×C22⋊C4C2×D4311yescharacteristic
456C22×C22⋊C4C2×D4311yescharacteristic
457C22×C22⋊C4C2×D4311yescharacteristic
458C22×C42—431no—
459C22×C42—431no—
460C22×C42C2×D4311yescharacteristic
461#389—438no—
462#389—438no—
463#388—438no—
464#388C2×D4318yescomplemented
465#387—438no—
466#387—438no—
467#386—438no—
468#385—438no—
469#385—438no—
470#385—438no—
471#381—438no—
472C4×C22⋊C4—438no—
473C2×#95—431no—
474C2×#95—431no—
475C2×#95—431no—
476C2×#95—431no—
477C2×#95—431no—
478C2×#95—431no—
479C2×#95—431no—
480C2×#95—431no—
481C2×#95C2×D4311yescharacteristic
482C2×#95C2×D4311yescharacteristic
483C43C2×#232211yescharacteristic, complemented, Sylow
484C25—431no—
485C25C22×D4311yescharacteristic
486C22×D4—438no—
487C22×D4—434no—
488C22×D4—864no—
489C22×D4—864no—
490C23×C4—431no—
491C23×C4—431no—
492C23×C4—431no—
493C23×C4—431no—
494C23×C4—438no—
495C23×C4—434no—
496C23×C4—438no—
497C23×C4—434no—
498C23×C4—431no—
499C23×C4—431no—
500C23×C4—431no—
501C23×C4—434no—
502C23×C4—434no—
503C23×C4—864no—
504C23×C4—864no—
505C23×C4—864no—
506C23×C4—864no—
507C23×C4—1722no—
508C23×C4—1722no—
509C23×C4—1722no—
510C23×C4—1722no—
511C23×C4—1722no—
512C23×C4—1722no—
513C23×C4C22×D4311yescharacteristic
514C23×C4C22×D4311yescharacteristic
515C23×C4C22×D4311yescharacteristic
516C23×C4C22×D4311yescharacteristic
517C23×C4C22×D4311yescharacteristic
518C23×C4C22×D4311yescharacteristic
519#123—4364no—
520C4×D4—8632no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—438no—
523C2×C4⋊C4—438no—
524C2×C4⋊C4—434no—
525C2×C4⋊C4—434no—
526C2×C4⋊C4—434no—
527C2×C4⋊C4—434no—
528C2×C4⋊C4—434no—
529C2×C4⋊C4—434no—
530C2×C4⋊C4—434no—
531C2×C4⋊C4—434no—
532C2×C4⋊C4—8632no—
533C2×C4⋊C4—864no—
534C2×C4⋊C4—864no—
535C2×C4⋊C4—864no—
536C2×C4⋊C4—864no—
537C2×C4⋊C4—1722no—
538C2×C4⋊C4—1722no—
539C2×C4⋊C4C22×D4314yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—438no—
543C2×C22⋊C4—434no—
544C2×C22⋊C4—438no—
545C2×C22⋊C4—434no—
546C2×C22⋊C4—434no—
547C2×C22⋊C4—434no—
548C2×C22⋊C4—434no—
549C2×C22⋊C4—864no—
550C2×C22⋊C4—864no—
551C2×C22⋊C4—1722no—
552C2×C22⋊C4C4×D4318yescomplemented
553C2×C22⋊C4C22×D4314yes—
554C2×C22⋊C4C22×D4314yes—
555C2×C22⋊C4C22×D4314yes—
556C2×C42—42no—
557C2×C42—434no—
558C2×C42—434no—
559C2×C42—864no—
560C2×C42—1722no—
561C2×C42C22×D4314yes—
562#95—434no—
563#95—434no—
564#95—434no—
565#95—434no—
566#95—434no—
567#95—434no—
568#95—434no—
569#95—434no—
570#95C22×D4314yes—
571#95C22×D4314yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—434no—
579C24—434no—
580C24—434no—
581C24—432no—
582C24—862no—
583C24—862no—
584C24—862no—
585C24—862no—
586C24C2×C4×D4314yes—
587C24C23×D4312yes—
588C24C23×D4311yescharacteristic
589C2×D4—4316no—
590C2×D4—868no—
591C2×D4—8632no—
592C2×D4—868no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—434no—
609C22×C4—434no—
610C22×C4—434no—
611C22×C4—434no—
612C22×C4—432no—
613C22×C4—432no—
614C22×C4—432no—
615C22×C4—432no—
616C22×C4—4316no—
617C22×C4—4316no—
618C22×C4—432no—
619C22×C4—432no—
620C22×C4—432no—
621C22×C4—868no—
622C22×C4—8632no—
623C22×C4—868no—
624C22×C4—868no—
625C22×C4—868no—
626C22×C4—862no—
627C22×C4—862no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—862no—
631C22×C4—862no—
632C22×C4—862no—
633C22×C4—862no—
634C22×C4—862no—
635C22×C4—862no—
636C22×C4—862no—
637C22×C4—862no—
638C22×C4—862no—
639C22×C4—862no—
640C22×C4—862no—
641C22×C4—862no—
642C22×C4—862no—
643C22×C4—17216no—
644C22×C4—1724no—
645C22×C4—1724no—
646C22×C4—1724no—
647C22×C4—1724no—
648C22×C4—17216no—
649C22×C4—1724no—
650C22×C4—1724no—
651C22×C4—17216no—
652C22×C4C2×C4×D4314yes—
653C22×C4C2×C4×D4314yes—
654C22×C4D4×D4314yes—
655C22×C4C23×D4312yes—
656C22×C4C23×D4312yes—
657C22×C4C23×D4312yes—
658C22×C4C23×D4312yes—
659C22×C4C23×D4312yes—
660C22×C4C23×D4312yes—
661C4⋊C4—28no—
662C4⋊C4—4316no—
663C4⋊C4—4316no—
664C4⋊C4—868no—
665C4⋊C4—868no—
666C4⋊C4—868no—
667C4⋊C4—868no—
668C4⋊C4—1724no—
669C4⋊C4—1724no—
670C22⋊C4—28no—
671C22⋊C4—44no—
672C22⋊C4—4316no—
673C22⋊C4—4316no—
674C22⋊C4—868no—
675C22⋊C4—868no—
676C22⋊C4—1724no—
677C22⋊C4C2×C4×D43116yescomplemented
678C42—44no—
679C42—868no—
680C42—1724no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—4316no—
695C23—434no—
696C23—434no—
697C23—434no—
698C23—868no—
699C23—868no—
700C23—868no—
701C23—868no—
702C23—862no—
703C23—862no—
704C23—862no—
705C23—862no—
706C23—868no—
707C23—868no—
708C23C22×C4×D4314yes—
709C23C22×C4×D4312yes—
710C23C2×D4×D4312yes—
711C23#41×D4312yes—
712C23#1306337012yes—
713C23#1306337112yes—
714C23#1306337212yes—
715C23#1306337212yes—
716C23C24×D4311yescharacteristic
717D4—8632no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—434no—
740C2×C4—434no—
741C2×C4—434no—
742C2×C4—434no—
743C2×C4—8632no—
744C2×C4—868no—
745C2×C4—868no—
746C2×C4—868no—
747C2×C4—868no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—17216no—
766C2×C4—17216no—
767C2×C4—17216no—
768C2×C4—1724no—
769C2×C4—1724no—
770C2×C4—1724no—
771C2×C4C22×C4×D4314yes—
772C2×C4C22×C4×D4314yes—
773C2×C4C2×D4×D4314yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—416no—
782C22—438no—
783C22—864no—
784C22—864no—
785C22—864no—
786C22—864no—
787C22—864no—
788C22—864no—
789C22—8632no—
790C22C4×D4×D4314yes—
791C22#1458337814yes—
792C22#1458337914yes—
793C22#1458345714yes—
794C22#1458346914yes—
795C22#1458349014yes—
796C22#1458349214yes—
797C22C23×C4×D4311yescharacteristic
798C22C22×D4×D4311yescharacteristic
799C22C2×#41×D4311yescharacteristic
800C22C2×#1306337011yescharacteristic
801C22C2×#1306337111yescharacteristic
802C22C2×#1306337211yescharacteristic
803C22C2×#1306337211yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—864no—
811C4—864no—
812C4—864no—
813C4—864no—
814C4—1722no—
815C4—1722no—
816C4—1722no—
817C2—44no—
818C2—868no—
819C2#1913726518yesdirect product factor
820C2C2×C4×D4×D4311yescharacteristic
821C2C2×#1458337811yescharacteristic
822C2C2×#1458337911yescharacteristic
823C2C2×#1458345711yescharacteristic
824C2C2×#1458346911yescharacteristic
825C2C2×#1458349011yescharacteristic
826C2C2×#1458349211yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#388C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC2×#388D43
hypocenterC43C2×#2322
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊C4×D43C2semidirect
4. #19137265C2direct (N × H)
5. C2×#14582797C2semidirect
6. C2×#14582794C2semidirect
7. C2×#14582793C2semidirect
8. C2×#14582786C2semidirect
9. C2×#14582782C2semidirect
11. C2×#14582774C2semidirect
12. C2×#14582773C2semidirect
13. C2×#14582771C2semidirect
14. C2×#14582761C2semidirect
15. C2×C4×(C2×D43)⋊C4C2semidirect
16. C2×C43×#388C2semidirect
22. C2×#13063307C4semidirect
35. C2×C4⋊C4×D43C22semidirect
43. #14582797C22semidirect
44. #14582794C22semidirect
45. #14582793C22semidirect
46. #14582786C22semidirect
47. #14582782C22semidirect
49. #14582774C22semidirect
50. #14582773C22semidirect
51. #14582771C22semidirect
52. #14582761C22semidirect
53. C4×(C2×D43)⋊C4C22semidirect
67. C43×#388C22semidirect
93. C22×C4×D43C2×C4semidirect
98. #13063307C2×C4semidirect
102. C2×C4⋊Dic43C2×C4semidirect
110. C2×Dic43⋊C4C2×C4semidirect
118. C2×C22⋊Dic43C2×C4semidirect
123. C2×(C2×D43)⋊C4C2×C4semidirect
150. C2×C22⋊C4×C43C2×C4semidirect
245. C2×C4×D43C22×C4semidirect
250. C22⋊C4×C43C22×C4semidirect
253. C22⋊Dic43C22×C4semidirect
256. (C2×D43)⋊C4C22×C4semidirect
259. C4⋊Dic43C22×C4semidirect
264. Dic43⋊C4C22×C4semidirect
411. C2×#388D43semidirect
421. C2×C43#2322semidirect
464. #388C2×D43semidirect
483. C43C2×#2322semidirect
552. C2×C22⋊C4C4×D43semidirect
677. C22⋊C4C2×C4×D43semidirect
819. C2#19137265direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633072
C22×(C22⋊D43)⋊C42
C22×C4⋊C4×D432
#191372652
C2×#145827972
C2×#145827942
C2×#145827932
C2×#145827862
C2×#145827822
C2×#145827752
C2×#145827742
C2×#145827732
C2×#145827712
C2×#145827612
C2×C4×(C2×D43)⋊C42
C2×C43×#3882
C2×#232243