Finite Group Databasebeta

← C2×#19137577 #25256089

Subgroups — C2×#19137577 #25256089

Order 11008.

5942 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063295C211yesmaximal, characteristic
2C22×C4×D172C211yesmaximal, characteristic, complemented
3C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic, complemented
4C23×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
5C22×C22⋊C4×D43C211yesmaximal, characteristic, complemented
6#19137577C2116yesmaximal, direct product factor
7C2×#14582801C211yesmaximal, characteristic, complemented
8C2×#14582791C211yesmaximal, characteristic, complemented
9C2×#14582790C211yesmaximal, characteristic, complemented
10C2×#14582778C211yesmaximal, characteristic, complemented
11C2×#14582777C211yesmaximal, characteristic, complemented
12C2×#14582777C211yesmaximal, characteristic, complemented
13C2×#14582774C211yesmaximal, characteristic, complemented
14C2×#14582773C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
17C25×D43C2211yescharacteristic
18C23×D172C2211yescharacteristic
19C23×D172C2211yescharacteristic
20C23×C22⋊D43C2211yescharacteristic
21C24×Dic43C2211yescharacteristic
22C23×C4×D43C2211yescharacteristic
23C23×C4×D43C2211yescharacteristic
24C23×C4×D43C2211yescharacteristic, complemented
25C2×#13063295C4116yescomplemented
26C2×#13063295C2218yes—
27C2×C4×D172—28no—
28C2×C4×D172C2218yescomplemented
29C2×(C22⋊D43)⋊C4—28no—
30C2×(C22⋊D43)⋊C4C2218yescomplemented
31C22×C4⋊Dic43C2211yescharacteristic, complemented
32C22×C4⋊Dic43C2211yescharacteristic, complemented
33C22×Dic43⋊C4C2211yescharacteristic, complemented
34C22×C22⋊Dic43C2211yescharacteristic
35C22×(C2×D43)⋊C4—28no—
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×(C2×D43)⋊C4C2211yescharacteristic
40C22×(C2×D43)⋊C4C2211yescharacteristic
41C22×(C2×D43)⋊C4C2211yescharacteristic
42C22×(C2×D43)⋊C4C2211yescharacteristic
43C22×(C2×D43)⋊C4C2211yescharacteristic
44C22×(C2×D43)⋊C4C2218yescomplemented
45C22×(C2×D43)⋊C4C2211yescharacteristic, complemented
46C22×(C2×D43)⋊C4C2211yescharacteristic, complemented
47C22×(C2×D43)⋊C4C2211yescharacteristic, complemented
48C2×C22⋊C4×D43—28no—
49C2×C22⋊C4×D43C2218yescomplemented
50C22×C4×Dic43C2211yescharacteristic, complemented
51#14582801C2218yescomplemented
52#14582791C2218yescomplemented
53#14582790C2218yescomplemented
54#14582778C2218yescomplemented
55#14582777C2218yescomplemented
56#14582777C2218yescomplemented
57#14582774C2218yescomplemented
58#14582773C2218yescomplemented
59C4×(C2×D43)⋊C4C2218yescomplemented
60C2×C43⋊#95C2211yescharacteristic, complemented
61C2×C43⋊#95C2211yescharacteristic, complemented
62C2×C43⋊#95C2211yescharacteristic, complemented
63C2×C43⋊#95C2211yescharacteristic, complemented
64C24×C4×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C22×C22⋊C4×C43C2211yescharacteristic
67C22×C42×C43C2211yescharacteristic, complemented
68C22×C42×C43C2211yescharacteristic, complemented
69C4×C22⋊C4×C43C2218yescomplemented
70C2×#95×C43C2211yescharacteristic, complemented
71C2×#95×C43C2211yescharacteristic, complemented
72C24×D43—24no—
73C24×D43—24no—
74C24×D43—24no—
75C24×D43—24no—
76C24×D43—42no—
77C24×D43—42no—
78C24×D43C2×C418yescomplemented
79C24×D43C2311yescharacteristic
80C24×D43C2311yescharacteristic
81C24×D43C2314yes—
82C24×D43C2311yescharacteristic
83C22×D172—24no—
84C22×D172—24no—
85C22×D172—42no—
86C22×D172—42no—
87C22×D172C2×C418yescomplemented
88C22×D172C2×C418yescomplemented
89C22×D172C2314yes—
90C22×D172C2314yes—
91C22×C22⋊D43—24no—
92C22×C22⋊D43—24no—
93C22×C22⋊D43C2×C418yescomplemented
94C22×C22⋊D43C2314yes—
95C23×Dic43—24no—
96C23×Dic43—24no—
97C23×Dic43—42no—
98C23×Dic43C2311yescharacteristic
99C23×Dic43C2311yescharacteristic
100C23×Dic43C2311yescharacteristic
101C23×Dic43C2314yes—
102C23×Dic43C2311yescharacteristic
103C23×Dic43C2311yescharacteristic
104C22×C4×D43—24no—
105C22×C4×D43—24no—
106C22×C4×D43—24no—
107C22×C4×D43—24no—
108C22×C4×D43—24no—
109C22×C4×D43—24no—
110C22×C4×D43—42no—
111C22×C4×D43—42no—
112C22×C4×D43—42no—
113C22×C4×D43C2314yes—
114C22×C4×D43C2314yes—
115C22×C4×D43C2314yescomplemented
116#13063295C2×C4164yescomplemented
117C4×D172—232no—
118(C22⋊D43)⋊C4—232no—
119C2×C4⋊Dic43—24no—
120C2×C4⋊Dic43—42no—
121C2×C4⋊Dic43C2314yescomplemented
122C2×C4⋊Dic43C2314yescomplemented
123C2×Dic43⋊C4—24no—
124C2×Dic43⋊C4C2314yescomplemented
125C2×C22⋊Dic43—24no—
126C2×C22⋊Dic43C2314yes—
127C2×(C2×D43)⋊C4—24no—
128C2×(C2×D43)⋊C4—24no—
129C2×(C2×D43)⋊C4—24no—
130C2×(C2×D43)⋊C4—24no—
131C2×(C2×D43)⋊C4—24no—
132C2×(C2×D43)⋊C4—24no—
133C2×(C2×D43)⋊C4—24no—
134C2×(C2×D43)⋊C4—232no—
135C2×(C2×D43)⋊C4—42no—
136C2×(C2×D43)⋊C4C2×C418yescomplemented
137C2×(C2×D43)⋊C4C2×C418yescomplemented
138C2×(C2×D43)⋊C4D418yescomplemented
139C2×(C2×D43)⋊C4C2314yes—
140C2×(C2×D43)⋊C4C2314yes—
141C2×(C2×D43)⋊C4C2314yes—
142C2×(C2×D43)⋊C4C2314yes—
143C2×(C2×D43)⋊C4C2314yes—
144C2×(C2×D43)⋊C4C2314yes—
145C2×(C2×D43)⋊C4C2314yes—
146C2×(C2×D43)⋊C4C2314yes—
147C2×(C2×D43)⋊C4C2314yescomplemented
148C2×(C2×D43)⋊C4C2314yescomplemented
149C2×(C2×D43)⋊C4C2314yescomplemented
150C22⋊C4×D43—232no—
151C2×C4×Dic43—24no—
152C2×C4×Dic43C2314yescomplemented
153C43⋊#95C2314yescomplemented
154C43⋊#95C2314yescomplemented
155C43⋊#95C2314yescomplemented
156C43⋊#95C2314yescomplemented
157C25×C43C2311yescharacteristic
158C23×C4×C43—24no—
159C23×C4×C43—24no—
160C23×C4×C43—42no—
161C23×C4×C43C2311yescharacteristic
162C23×C4×C43C2314yes—
163C23×C4×C43C2311yescharacteristic
164C23×C4×C43C2311yescharacteristic
165C23×C4×C43C2311yescharacteristic
166C23×C4×C43C2311yescharacteristic
167C23×C4×C43C2311yescharacteristic
168C2×C22⋊C4×C43C2×C418yescomplemented
169C2×C22⋊C4×C43D418yescomplemented
170C2×C22⋊C4×C43C2314yes—
171C2×C22⋊C4×C43C2314yes—
172C2×C42×C43—24no—
173C2×C42×C43—42no—
174C2×C42×C43C2314yescomplemented
175C2×C42×C43C2314yescomplemented
176#95×C43C2314yescomplemented
177#95×C43C2314yescomplemented
178C24×C43—22no—
179C24×C43—22no—
180C24×C43—22no—
181C24×C43—22no—
182C24×C43C22×C414yes—
183C24×C43C2×D414yes—
184C24×C43#4114yes—
185C24×C43C2412yes—
186C24×C43C2411yescharacteristic
187C23×D43—22no—
188C23×D43—22no—
189C23×D43—22no—
190C23×D43—22no—
191C23×D43—232no—
192C23×D43—28no—
193C23×D43—22no—
194C23×D43—22no—
195C23×D43—22no—
196C23×D43—22no—
197C23×D43—22no—
198C23×D43—22no—
199C23×D43—28no—
200C23×D43—22no—
201C23×D43—22no—
202C23×D43—22no—
203C23×D43—22no—
204C23×D43—22no—
205C23×D43—22no—
206C23×D43—232no—
207C23×D43—28no—
208C23×D43—28no—
209C23×D43—416no—
210C23×D43—44no—
211C23×D43—44no—
212C23×D43—416no—
213C23×D43—416no—
214C23×D43—416no—
215C23×D43—416no—
216C23×D43C22×C414yes—
217C23×D43C22×C414yes—
218C23×D43C22×C414yes—
219C23×D43C22×C4116yescomplemented
220C23×D43C2×D414yes—
221C23×D43#4114yes—
222C23×D43C2412yes—
223C23×D43C2412yes—
224C23×D43C2412yes—
225C22×C4×C43—28no—
226C22×C4×C43—22no—
227C22×C4×C43—22no—
228C22×C4×C43—22no—
229C22×C4×C43—22no—
230C22×C4×C43—22no—
231C22×C4×C43—22no—
232C22×C4×C43—28no—
233C22×C4×C43—22no—
234C22×C4×C43—22no—
235C22×C4×C43—22no—
236C22×C4×C43—22no—
237C22×C4×C43—22no—
238C22×C4×C43—22no—
239C22×C4×C43—22no—
240C22×C4×C43—44no—
241C22×C4×C43—416no—
242C22×C4×C43C22×C414yes—
243C22×C4×C43C22×C414yes—
244C22×C4×C43C2×D414yes—
245C22×C4×C43C2×D414yes—
246C22×C4×C43C2×D414yes—
247C22×C4×C43C2412yes—
248C22×C4×C43C2412yes—
249C22×C4×C43C2412yes—
250C22×C4×C43C2412yes—
251C22×C4×C43C2412yes—
252C22×C4×C43C2412yes—
253C2×C22⋊D43—232no—
254C2×C22⋊D43—28no—
255C2×C22⋊D43—28no—
256C2×C22⋊D43C22×C4116yescomplemented
257C22×Dic43—28no—
258C22×Dic43—22no—
259C22×Dic43—22no—
260C22×Dic43—22no—
261C22×Dic43—22no—
262C22×Dic43—22no—
263C22×Dic43—22no—
264C22×Dic43—22no—
265C22×Dic43—28no—
266C22×Dic43—22no—
267C22×Dic43—22no—
268C22×Dic43—22no—
269C22×Dic43—22no—
270C22×Dic43—22no—
271C22×Dic43—22no—
272C22×Dic43—44no—
273C22×Dic43—416no—
274C22×Dic43C22×C414yes—
275C22×Dic43C2×D414yes—
276C22×Dic43C2412yes—
277C22×Dic43C2412yes—
278C22×Dic43C2412yes—
279C22×Dic43C2412yes—
280C22×Dic43C2412yes—
281C2×D172—232no—
282C2×D172—28no—
283C2×D172—28no—
284C2×D172—416no—
285C2×D172—44no—
286C2×D172—44no—
287C2×D172C22×C4116yescomplemented
288C2×D172C22×C4116yescomplemented
289C2×C4×D43—28no—
290C2×C4×D43—28no—
291C2×C4×D43—28no—
292C2×C4×D43—28no—
293C2×C4×D43—28no—
294C2×C4×D43—28no—
295C2×C4×D43—44no—
296C2×C4×D43—44no—
297C2×C4×D43—44no—
298C2×C4×D43—416no—
299C2×C4×D43—416no—
300C2×C4×D43—416no—
301C22⋊C4×C43C22×C4116yescomplemented
302C22⋊C4×C43C2×D4116yescomplemented
303C42×C43—28no—
304C42×C43—44no—
305C22⋊Dic43—28no—
306(C2×D43)⋊C4—28no—
307(C2×D43)⋊C4—28no—
308(C2×D43)⋊C4—28no—
309(C2×D43)⋊C4—28no—
310(C2×D43)⋊C4—28no—
311(C2×D43)⋊C4—28no—
312(C2×D43)⋊C4—28no—
313(C2×D43)⋊C4—44no—
314(C2×D43)⋊C4C22×C4116yescomplemented
315(C2×D43)⋊C4C22×C4116yescomplemented
316(C2×D43)⋊C4C2×D4116yescomplemented
317C4⋊Dic43—28no—
318C4⋊Dic43—44no—
319Dic43⋊C4—28no—
320C4×Dic43—28no—
321C23×C43—28no—
322C23×C43—28no—
323C23×C43—28no—
324C23×C43—28no—
325C23×C43—28no—
326C23×C43—28no—
327C23×C43—22no—
328C23×C43—22no—
329C23×C43—22no—
330C23×C43—22no—
331C23×C43C4×D4116yescomplemented
332C23×C43C23×C414yes—
333C23×C43C23×C412yes—
334C23×C43C22×D412yes—
335C23×C43C22×D414yes—
336C23×C43C22×D412yes—
337C23×C43C2×#4112yes—
338C23×C43C2×#4114yes—
339C23×C43C2×#4112yes—
340C23×C43H(5,𝔽2)12yes—
341C23×C43H(5,𝔽2)12yes—
342C23×C43C2511yescharacteristic
343C22×D43—28no—
344C22×D43—28no—
345C22×D43—28no—
346C22×D43—28no—
347C22×D43—28no—
348C22×D43—28no—
349C22×D43—22no—
350C22×D43—22no—
351C22×D43—22no—
352C22×D43—22no—
353C22×D43—28no—
354C22×D43—28no—
355C22×D43—28no—
356C22×D43—28no—
357C22×D43—232no—
358C22×D43—28no—
359C22×D43—28no—
360C22×D43—22no—
361C22×D43—22no—
362C22×D43—22no—
363C22×D43—22no—
364C22×D43—22no—
365C22×D43—22no—
366C22×D43—22no—
367C22×D43—22no—
368C22×D43—22no—
369C22×D43—22no—
370C22×D43—22no—
371C22×D43—22no—
372C22×D43—232no—
373C22×D43—416no—
374C22×D43—4128no—
375C22×D43—416no—
376C22×D43—416no—
377C22×D43—416no—
378C22×D43—416no—
379C22×D43—44no—
380C22×D43—44no—
381C22×D43—44no—
382C22×D43—44no—
383C22×D43—44no—
384C22×D43—44no—
385C22×D43—44no—
386C22×D43—44no—
387C22×D43C4×D4116yescomplemented
388C22×D43C23×C414yes—
389C22×D43C23×C414yes—
390C22×D43C23×C414yes—
391C22×D43C22×D414yes—
392C22×D43C2×#4114yes—
393C2×C4×C43—28no—
394C2×C4×C43—28no—
395C2×C4×C43—28no—
396C2×C4×C43—28no—
397C2×C4×C43—28no—
398C2×C4×C43—22no—
399C2×C4×C43—22no—
400C2×C4×C43—22no—
401C2×C4×C43—22no—
402C2×C4×C43—22no—
403C2×C4×C43—22no—
404C2×C4×C43—22no—
405C2×C4×C43—22no—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
408C2×C4×C43—22no—
409C2×C4×C43—22no—
410C2×C4×C43—22no—
411C2×C4×C43—416no—
412C2×C4×C43—44no—
413C2×C4×C43C23×C414yes—
414C2×C4×C43C23×C414yes—
415C2×C4×C43C22×D414yes—
416C2×C4×C43C22×D414yes—
417C2×C4×C43C22×D414yes—
418C22⋊D43—232no—
419C2×Dic43—28no—
420C2×Dic43—28no—
421C2×Dic43—22no—
422C2×Dic43—22no—
423C2×Dic43—22no—
424C2×Dic43—22no—
425C2×Dic43—22no—
426C2×Dic43—22no—
427C2×Dic43—22no—
428C2×Dic43—22no—
429C2×Dic43—22no—
430C2×Dic43—22no—
431C2×Dic43—22no—
432C2×Dic43—22no—
433C2×Dic43—22no—
434C2×Dic43—416no—
435C2×Dic43—44no—
436C2×Dic43—44no—
437C2×Dic43—44no—
438C2×Dic43C23×C414yes—
439C2×Dic43C22×D414yes—
440D172—232no—
441D172—416no—
442C4×D43—416no—
443C4×D43—416no—
444C4×D43—416no—
445C2×#2358—431nomaximal, Sylow
446C22×C43—232no—
447C22×C43—24no—
448C22×C43—24no—
449C22×C43—24no—
450C22×C43—24no—
451C22×C43—24no—
452C22×C43—24no—
453C22×C43C2×C4×D414yes—
454C22×C43C2×C4×D414yes—
455C22×C43C2×C4×D418yescomplemented
456C22×C43#51814yes—
457C22×C43D4214yes—
458C22×C43#54614yes—
459C22×C43#54614yes—
460C22×C43#55114yes—
461C22×C43C24×C411yescharacteristic
462C22×C43C23×D411yescharacteristic
463C22×C43C23×D411yescharacteristic
464C22×C43C22×#4111yescharacteristic
465C22×C43C22×#4111yescharacteristic
466C22×C43C2×H(5,𝔽2)11yescharacteristic
467C22×C43C2×H(5,𝔽2)11yescharacteristic
468C2×D43—232no—
469C2×D43—24no—
470C2×D43—24no—
471C2×D43—24no—
472C2×D43—24no—
473C2×D43—24no—
474C2×D43—24no—
475C2×D43—24no—
476C2×D43—24no—
477C2×D43—24no—
478C2×D43—24no—
479C2×D43—24no—
480C2×D43—24no—
481C2×D43—464no—
482C2×D43—416no—
483C2×D43—416no—
484C2×D43—42no—
485C2×D43—42no—
486C2×D43—42no—
487C2×D43—42no—
488C2×D43—42no—
489C2×D43—42no—
490C2×D43—42no—
491C2×D43—42no—
492C2×D43C2×C4×D418yescomplemented
493C4×C43—24no—
494C4×C43—24no—
495C4×C43—24no—
496C4×C43—24no—
497C4×C43—24no—
498C4×C43—42no—
499Dic43—24no—
500Dic43—24no—
501Dic43—42no—
502Dic43—42no—
503Dic43—42no—
504C22×#120—431no—
505C22×C4×D4—431no—
506C22×C4×D4—431no—
507C23×C22⋊C4—431no—
508C23×C22⋊C4—431no—
509#2358—4316no—
510C2×#390—431no—
511C2×#388—431no—
512C2×#388—431no—
513C2×#386—431no—
514C2×#386—431no—
515C2×#386—431no—
516C2×#385—431no—
517C2×#385—431no—
518C2×C4×C22⋊C4—431no—
519C2×C4×C22⋊C4D4311yescharacteristic, complemented
520C2×C43—28no—
521C2×C43#235818yescomplemented
522C2×C43C22×C4×D411yescharacteristic
523C2×C43C22×C4×D411yescharacteristic
524C2×C43C2×#51811yescharacteristic
525C2×C43C2×D4211yescharacteristic
526C2×C43C2×#54611yescharacteristic
527C2×C43C2×#54611yescharacteristic
528C2×C43C2×#55111yescharacteristic
529D43—28no—
530D43—44no—
531D43—44no—
532C26—431no—
533C23×D4—431no—
534C23×D4—431no—
535C23×D4—431no—
536C24×C4—431no—
537C24×C4—431no—
538C24×C4—431no—
539C24×C4—431no—
540C24×C4C2×D4311yescharacteristic
541C2×#120—438no—
542C2×#120—4316no—
543C2×C4×D4—438no—
544C2×C4×D4—438no—
545C2×C4×D4—868no—
546C2×C4×D4—868no—
547C22×C4⋊C4—431no—
548C22×C4⋊C4—431no—
549C22×C4⋊C4—431no—
550C22×C22⋊C4—431no—
551C22×C22⋊C4—431no—
552C22×C22⋊C4—431no—
553C22×C22⋊C4—431no—
554C22×C22⋊C4—431no—
555C22×C22⋊C4—431no—
556C22×C22⋊C4—431no—
557C22×C22⋊C4—431no—
558C22×C22⋊C4—431no—
559C22×C22⋊C4—438no—
560C22×C22⋊C4—431no—
561C22×C22⋊C4—431no—
562C22×C22⋊C4—431no—
563C22×C22⋊C4—438no—
564C22×C22⋊C4—868no—
565C22×C22⋊C4—868no—
566C22×C22⋊C4C2×D4311yescharacteristic
567C22×C22⋊C4C2×D4311yescharacteristic
568C22×C42—431no—
569C22×C42C2×D4311yescharacteristic, complemented
570C22×C42C2×D4311yescharacteristic, complemented
571#390—438no—
572#388—438no—
573#388—438no—
574#386—438no—
575#386—438no—
576#386—438no—
577#385—438no—
578#385—438no—
579C4×C22⋊C4—438no—
580C4×C22⋊C4C2×D4318yescomplemented
581C2×#95—431no—
582C2×#95—431no—
583C2×#95—431no—
584C2×#95—431no—
585C2×#95C2×D4311yescharacteristic, complemented
586C2×#95C2×D4311yescharacteristic, complemented
587C43C2×#235811yescharacteristic, complemented, Sylow
588C25—431no—
589C25—431no—
590C25—431no—
591C25—438no—
592C25—434no—
593C25—864no—
594C25—864no—
595C25—864no—
596C25—864no—
597C25—1722no—
598C25—1722no—
599C25C22×D4311yescharacteristic
600C22×D4—438no—
601C22×D4—434no—
602C22×D4—438no—
603C22×D4—438no—
604C22×D4—434no—
605C22×D4—434no—
606C22×D4—864no—
607C22×D4—864no—
608C22×D4—864no—
609C22×D4—864no—
610C22×D4—1722no—
611C22×D4—1722no—
612C23×C4—24no—
613C23×C4—24no—
614C23×C4—42no—
615C23×C4—431no—
616C23×C4—431no—
617C23×C4—431no—
618C23×C4—431no—
619C23×C4—431no—
620C23×C4—434no—
621C23×C4—434no—
622C23×C4—434no—
623C23×C4—434no—
624C23×C4—864no—
625C23×C4—864no—
626C23×C4—864no—
627C23×C4—864no—
628C23×C4—864no—
629C23×C4—864no—
630C23×C4—864no—
631C23×C4—864no—
632C23×C4—1722no—
633C23×C4—1722no—
634C23×C4—1722no—
635C23×C4—1722no—
636C23×C4C22×D4311yescharacteristic
637C23×C4C22×D4314yes—
638C23×C4C22×D4311yescharacteristic
639C23×C4C22×D4311yescharacteristic
640C23×C4C22×D4311yescharacteristic
641C23×C4C22×D4311yescharacteristic
642C23×C4C22×D4311yescharacteristic
643#120—4364no—
644C4×D4—8632no—
645C4×D4—8632no—
646C2×C4⋊C4—434no—
647C2×C4⋊C4—434no—
648C2×C4⋊C4—434no—
649C2×C4⋊C4—864no—
650C2×C4⋊C4—864no—
651C2×C4⋊C4—1722no—
652C2×C22⋊C4—438no—
653C2×C22⋊C4—438no—
654C2×C22⋊C4—438no—
655C2×C22⋊C4—434no—
656C2×C22⋊C4—434no—
657C2×C22⋊C4—434no—
658C2×C22⋊C4—434no—
659C2×C22⋊C4—434no—
660C2×C22⋊C4—434no—
661C2×C22⋊C4—434no—
662C2×C22⋊C4—434no—
663C2×C22⋊C4—434no—
664C2×C22⋊C4—434no—
665C2×C22⋊C4—434no—
666C2×C22⋊C4—434no—
667C2×C22⋊C4—8632no—
668C2×C22⋊C4—864no—
669C2×C22⋊C4—864no—
670C2×C22⋊C4—864no—
671C2×C22⋊C4—864no—
672C2×C22⋊C4—864no—
673C2×C22⋊C4—864no—
674C2×C22⋊C4—864no—
675C2×C22⋊C4—864no—
676C2×C22⋊C4—8632no—
677C2×C22⋊C4—1722no—
678C2×C22⋊C4C4×D4318yescomplemented
679C2×C22⋊C4D17218yescomplemented
680C2×C22⋊C4C22×D4314yes—
681C2×C22⋊C4C22×D4314yes—
682C2×C42—24no—
683C2×C42—42no—
684C2×C42—434no—
685C2×C42—864no—
686C2×C42C22×D4314yescomplemented
687C2×C42C22×D4314yescomplemented
688#95—434no—
689#95—434no—
690#95—434no—
691#95—434no—
692#95C22×D4314yescomplemented
693#95C22×D4314yescomplemented
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—434no—
699C24—434no—
700C24—434no—
701C24—432no—
702C24—434no—
703C24—434no—
704C24—432no—
705C24—432no—
706C24—4316no—
707C24—868no—
708C24—8632no—
709C24—868no—
710C24—862no—
711C24—862no—
712C24—862no—
713C24—862no—
714C24—8632no—
715C24—862no—
716C24—862no—
717C24—868no—
718C24—862no—
719C24—862no—
720C24—862no—
721C24—862no—
722C24—862no—
723C24—868no—
724C24—862no—
725C24—862no—
726C24—862no—
727C24—862no—
728C24—862no—
729C24—17216no—
730C24—1724no—
731C24—1724no—
732C24—17216no—
733C24—17216no—
734C24—17216no—
735C24—17216no—
736C24C2×C4×D4314yes—
737C24C2×D17214yes—
738C24#1062189814yes—
739C24C23×D4312yes—
740C24C23×D4311yescharacteristic
741C2×D4—4316no—
742C2×D4—4316no—
743C2×D4—4316no—
744C2×D4—868no—
745C2×D4—8632no—
746C2×D4—868no—
747C2×D4—8632no—
748C2×D4—868no—
749C2×D4—868no—
750C2×D4—17216no—
751C2×D4—1724no—
752C2×D4—1724no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—28no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—28no—
768C22×C4—44no—
769C22×C4—416no—
770C22×C4—434no—
771C22×C4—434no—
772C22×C4—432no—
773C22×C4—432no—
774C22×C4—432no—
775C22×C4—432no—
776C22×C4—432no—
777C22×C4—868no—
778C22×C4—868no—
779C22×C4—868no—
780C22×C4—868no—
781C22×C4—862no—
782C22×C4—862no—
783C22×C4—862no—
784C22×C4—862no—
785C22×C4—862no—
786C22×C4—862no—
787C22×C4—862no—
788C22×C4—862no—
789C22×C4—862no—
790C22×C4—868no—
791C22×C4—862no—
792C22×C4—862no—
793C22×C4—862no—
794C22×C4—862no—
795C22×C4—868no—
796C22×C4—868no—
797C22×C4—868no—
798C22×C4—1724no—
799C22×C4—1724no—
800C22×C4—1724no—
801C22×C4—17216no—
802C22×C4—17216no—
803C22×C4—17216no—
804C22×C4—1724no—
805C22×C4—17216no—
806C22×C4C2×C4×D4314yes—
807C22×C4C2×C4×D4314yes—
808C22×C4C2×D17214yes—
809C22×C4C2×D17214yes—
810C22×C4D4×D4314yes—
811C22×C4C23×D4312yes—
812C22×C4C23×D4312yes—
813C22×C4C23×D4312yes—
814C22×C4C23×D4312yes—
815C22×C4C23×D4312yes—
816C22×C4C23×D4312yes—
817C4⋊C4—868no—
818C4⋊C4—868no—
819C4⋊C4—1724no—
820C22⋊C4—4316no—
821C22⋊C4—4316no—
822C22⋊C4—4316no—
823C22⋊C4—868no—
824C22⋊C4—868no—
825C22⋊C4—868no—
826C22⋊C4—868no—
827C22⋊C4—868no—
828C22⋊C4—868no—
829C22⋊C4—868no—
830C22⋊C4—868no—
831C22⋊C4—1724no—
832C22⋊C4C2×C4×D43116yescomplemented
833C22⋊C4C2×D172116yescomplemented
834C42—28no—
835C42—44no—
836C42—868no—
837C23—28no—
838C23—28no—
839C23—28no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—28no—
845C23—28no—
846C23—28no—
847C23—4316no—
848C23—434no—
849C23—434no—
850C23—434no—
851C23—434no—
852C23—434no—
853C23—8632no—
854C23—868no—
855C23—868no—
856C23—868no—
857C23—862no—
858C23—862no—
859C23—862no—
860C23—862no—
861C23—868no—
862C23—868no—
863C23—868no—
864C23—868no—
865C23—868no—
866C23—868no—
867C23—868no—
868C23—8632no—
869C23—868no—
870C23—868no—
871C23—862no—
872C23—862no—
873C23—862no—
874C23—862no—
875C23—862no—
876C23—862no—
877C23—862no—
878C23—862no—
879C23—862no—
880C23—862no—
881C23—862no—
882C23—862no—
883C23—17216no—
884C23—17216no—
885C23—17216no—
886C23—17216no—
887C23—172128no—
888C23—17216no—
889C23—1724no—
890C23—1724no—
891C23—1724no—
892C23—1724no—
893C23—1724no—
894C23—1724no—
895C23—1724no—
896C23—1724no—
897C23C4×D172116yescomplemented
898C23C22×C4×D4314yes—
899C23C22×C4×D4312yes—
900C23C2×D4×D4312yes—
901C23C22×D17214yes—
902C23C22×D17212yes—
903C23#41×D4312yes—
904C23C2×#1062189814yes—
905C23C2×#1062189812yes—
906C23#1306337012yes—
907C23#1306337112yes—
908C23C24×D4311yescharacteristic
909D4—8632no—
910D4—8632no—
911D4—17216no—
912C2×C4—28no—
913C2×C4—28no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—28no—
925C2×C4—28no—
926C2×C4—28no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—416no—
931C2×C4—44no—
932C2×C4—434no—
933C2×C4—434no—
934C2×C4—868no—
935C2×C4—862no—
936C2×C4—862no—
937C2×C4—862no—
938C2×C4—862no—
939C2×C4—868no—
940C2×C4—862no—
941C2×C4—862no—
942C2×C4—862no—
943C2×C4—862no—
944C2×C4—862no—
945C2×C4—862no—
946C2×C4—862no—
947C2×C4—862no—
948C2×C4—862no—
949C2×C4—17216no—
950C2×C4—17216no—
951C2×C4—17216no—
952C2×C4—17216no—
953C2×C4—1724no—
954C2×C4—1724no—
955C2×C4—1724no—
956C2×C4C22×C4×D4314yes—
957C2×C4C22×C4×D4314yes—
958C2×C4C2×D4×D4314yes—
959C2×C4C22×D17214yes—
960C2×C4C22×D17214yes—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—24no—
965C22—232no—
966C22—24no—
967C22—24no—
968C22—438no—
969C22—864no—
970C22—864no—
971C22—864no—
972C22—864no—
973C22—8632no—
974C22—864no—
975C22—864no—
976C22—864no—
977C22—864no—
978C22—864no—
979C22—864no—
980C22—864no—
981C22—864no—
982C22—17264no—
983C22—1722no—
984C22—1722no—
985C22—1722no—
986C22—1722no—
987C22—1722no—
988C22—1722no—
989C22—17216no—
990C22—17216no—
991C22—1722no—
992C22—1722no—
993C22C4×D4×D4314yes—
994C22C2×C4×D17214yes—
995C22C2×C4×D17218yescomplemented
996C22#1458337114yes—
997C22D4×D17214yes—
998C22#1458353914yes—
999C22#1458354414yes—
1000C22#1458357314yes—
1001C22C23×C4×D4311yescharacteristic
1002C22C22×D4×D4311yescharacteristic
1003C22C23×D17211yescharacteristic
1004C22C2×#41×D4311yescharacteristic
1005C22C22×#1062189811yescharacteristic
1006C22C2×#1306337011yescharacteristic
1007C22C2×#1306337111yescharacteristic
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—24no—
1012C4—24no—
1013C4—42no—
1014C4—864no—
1015C4—864no—
1016C4—1722no—
1017C4—1722no—
1018C4—1722no—
1019C2—28no—
1020C2—868no—
1021C2—1724no—
1022C2—1724no—
1023C2#1913757718yesdirect product factor
1024C2C2×C4×D4×D4311yescharacteristic
1025C2C22×C4×D17211yescharacteristic
1026C2C2×#1458337111yescharacteristic
1027C2C2×D4×D17211yescharacteristic
1028C2C2×#1458353911yescharacteristic
1029C2C2×#1458354411yescharacteristic
1030C2C2×#1458357311yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C4×C22⋊C4×C43C2
socleC24×C43C24
prime radicalC22×#13063295C2
cosocleC23×C43C25
hypercenterC2×C4×C22⋊C4D43
hypocenterC43C2×#2358
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×D172C2semidirect
3. C22×(C22⋊D43)⋊C4C2semidirect
4. C23×(C2×D43)⋊C4C2semidirect
5. C22×C22⋊C4×D43C2semidirect
6. #19137577C2direct (N × H)
7. C2×#14582801C2semidirect
8. C2×#14582791C2semidirect
9. C2×#14582790C2semidirect
10. C2×#14582778C2semidirect
11. C2×#14582777C2semidirect
12. C2×#14582777C2semidirect
13. C2×#14582774C2semidirect
14. C2×#14582773C2semidirect
15. C2×C4×(C2×D43)⋊C4C2semidirect
16. C2×C4×C22⋊C4×C43C2semidirect
24. C23×C4×D43C22semidirect
25. C2×#13063295C4semidirect
28. C2×C4×D172C22semidirect
30. C2×(C22⋊D43)⋊C4C22semidirect
31. C22×C4⋊Dic43C22semidirect
32. C22×C4⋊Dic43C22semidirect
33. C22×Dic43⋊C4C22semidirect
44. C22×(C2×D43)⋊C4C22semidirect
45. C22×(C2×D43)⋊C4C22semidirect
46. C22×(C2×D43)⋊C4C22semidirect
47. C22×(C2×D43)⋊C4C22semidirect
49. C2×C22⋊C4×D43C22semidirect
50. C22×C4×Dic43C22semidirect
51. #14582801C22semidirect
52. #14582791C22semidirect
53. #14582790C22semidirect
54. #14582778C22semidirect
55. #14582777C22semidirect
56. #14582777C22semidirect
57. #14582774C22semidirect
58. #14582773C22semidirect
59. C4×(C2×D43)⋊C4C22semidirect
60. C2×C43⋊#95C22semidirect
61. C2×C43⋊#95C22semidirect
62. C2×C43⋊#95C22semidirect
63. C2×C43⋊#95C22semidirect
67. C22×C42×C43C22semidirect
68. C22×C42×C43C22semidirect
69. C4×C22⋊C4×C43C22semidirect
70. C2×#95×C43C22semidirect
71. C2×#95×C43C22semidirect
78. C24×D43C2×C4semidirect
87. C22×D172C2×C4semidirect
88. C22×D172C2×C4semidirect
93. C22×C22⋊D43C2×C4semidirect
115. C22×C4×D43C23semidirect
116. #13063295C2×C4semidirect
121. C2×C4⋊Dic43C23semidirect
122. C2×C4⋊Dic43C23semidirect
124. C2×Dic43⋊C4C23semidirect
136. C2×(C2×D43)⋊C4C2×C4semidirect
137. C2×(C2×D43)⋊C4C2×C4semidirect
138. C2×(C2×D43)⋊C4D4semidirect
147. C2×(C2×D43)⋊C4C23semidirect
148. C2×(C2×D43)⋊C4C23semidirect
149. C2×(C2×D43)⋊C4C23semidirect
152. C2×C4×Dic43C23semidirect
153. C43⋊#95C23semidirect
154. C43⋊#95C23semidirect
155. C43⋊#95C23semidirect
156. C43⋊#95C23semidirect
168. C2×C22⋊C4×C43C2×C4semidirect
169. C2×C22⋊C4×C43D4semidirect
174. C2×C42×C43C23semidirect
175. C2×C42×C43C23semidirect
176. #95×C43C23semidirect
177. #95×C43C23semidirect
219. C23×D43C22×C4semidirect
256. C2×C22⋊D43C22×C4semidirect
287. C2×D172C22×C4semidirect
288. C2×D172C22×C4semidirect
301. C22⋊C4×C43C22×C4semidirect
302. C22⋊C4×C43C2×D4semidirect
314. (C2×D43)⋊C4C22×C4semidirect
315. (C2×D43)⋊C4C22×C4semidirect
316. (C2×D43)⋊C4C2×D4semidirect
331. C23×C43C4×D4semidirect
387. C22×D43C4×D4semidirect
455. C22×C43C2×C4×D4semidirect
492. C2×D43C2×C4×D4semidirect
519. C2×C4×C22⋊C4D43semidirect
521. C2×C43#2358semidirect
569. C22×C42C2×D43semidirect
570. C22×C42C2×D43semidirect
580. C4×C22⋊C4C2×D43semidirect
585. C2×#95C2×D43semidirect
586. C2×#95C2×D43semidirect
587. C43C2×#2358semidirect
678. C2×C22⋊C4C4×D43semidirect
679. C2×C22⋊C4D172semidirect
686. C2×C42C22×D43semidirect
687. C2×C42C22×D43semidirect
692. #95C22×D43semidirect
693. #95C22×D43semidirect
832. C22⋊C4C2×C4×D43semidirect
833. C22⋊C4C2×D172semidirect
897. C23C4×D172semidirect
995. C22C2×C4×D172semidirect
1023. C2#19137577direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130632952
C22×C4×D1722
C22×(C22⋊D43)⋊C42
C23×(C2×D43)⋊C42
C22×C22⋊C4×D432
#191375772
C2×#145828012
C2×#145827912
C2×#145827902
C2×#145827782
C2×#145827772
C2×#145827742
C2×#145827732
C2×C4×(C2×D43)⋊C42
C2×C4×C22⋊C4×C432
C2×#235843