Finite Group Databasebeta

← C2×#19137571 #25256083

Subgroups — C2×#19137571 #25256083

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×#13063287C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D43C211yesmaximal, characteristic, complemented
4C23×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
5C22×C22⋊C4×D43C211yesmaximal, characteristic, complemented
6#19137571C2116yesmaximal, direct product factor
7C2×#14582800C211yesmaximal, characteristic, complemented
8C2×#14582789C211yesmaximal, characteristic, complemented
9C2×#14582788C211yesmaximal, characteristic, complemented
10C2×#14582777C211yesmaximal, characteristic, complemented
11C2×#14582777C211yesmaximal, characteristic, complemented
12C2×#14582776C211yesmaximal, characteristic, complemented
13C2×#14582770C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
15C2×#14582746C211yesmaximal, characteristic, complemented
16C2×C43×#385C211yesmaximal, 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×#13063287—28no—
28C2×#13063287C2218yescomplemented
29C2×C4×C22⋊D43—28no—
30C2×C4×C22⋊D43C2218yescomplemented
31C22×Dic43⋊C4C2211yescharacteristic, complemented
32C22×C22⋊Dic43C2211yescharacteristic
33C22×(C2×D43)⋊C4—28no—
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
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)⋊C4C2218yescomplemented
43C22×(C2×D43)⋊C4C2211yescharacteristic, complemented
44C22×(C2×D43)⋊C4C2211yescharacteristic, complemented
45C22×(C2×D43)⋊C4C2211yescharacteristic, complemented
46C2×C22⋊C4×D43—28no—
47C2×C22⋊C4×D43C2218yescomplemented
48C22×C4×Dic43C2211yescharacteristic, complemented
49C22×C4×Dic43C2211yescharacteristic, complemented
50C22×C4×Dic43C2211yescharacteristic, complemented
51#14582800C2218yescomplemented
52#14582789C2218yescomplemented
53#14582788C2218yescomplemented
54#14582777C2218yescomplemented
55#14582777C2218yescomplemented
56#14582776C2218yescomplemented
57#14582770C2218yescomplemented
58C22⋊C4×Dic43C2218yescomplemented
59#14582746C2218yescomplemented
60C2×C43⋊#95C2211yescharacteristic, complemented
61C2×C43⋊#95C2211yescharacteristic, complemented
62C2×C43⋊#95C2211yescharacteristic, complemented
63C2×C43⋊#95C2211yescharacteristic, complemented
64C24×C4×C43C2211yescharacteristic
65C22×C4⋊C4×C43C2211yescharacteristic, complemented
66C22×C4⋊C4×C43C2211yescharacteristic, complemented
67C22×C22⋊C4×C43C2211yescharacteristic
68C22×C22⋊C4×C43C2211yescharacteristic
69C43×#385C2218yescomplemented
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×Dic43C2314yes—
100C23×Dic43C2311yescharacteristic
101C23×Dic43C2311yescharacteristic
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
117#13063287—232no—
118C4×C22⋊D43—232no—
119C2×Dic43⋊C4—24no—
120C2×Dic43⋊C4C2314yescomplemented
121C2×C22⋊Dic43D418yescomplemented
122C2×C22⋊Dic43C2314yes—
123C2×(C2×D43)⋊C4—24no—
124C2×(C2×D43)⋊C4—24no—
125C2×(C2×D43)⋊C4—24no—
126C2×(C2×D43)⋊C4—24no—
127C2×(C2×D43)⋊C4—24no—
128C2×(C2×D43)⋊C4—24no—
129C2×(C2×D43)⋊C4—24no—
130C2×(C2×D43)⋊C4—232no—
131C2×(C2×D43)⋊C4—42no—
132C2×(C2×D43)⋊C4C2×C418yescomplemented
133C2×(C2×D43)⋊C4C2×C418yescomplemented
134C2×(C2×D43)⋊C4D418yescomplemented
135C2×(C2×D43)⋊C4C2314yes—
136C2×(C2×D43)⋊C4C2314yes—
137C2×(C2×D43)⋊C4C2314yes—
138C2×(C2×D43)⋊C4C2314yes—
139C2×(C2×D43)⋊C4C2314yes—
140C2×(C2×D43)⋊C4C2314yes—
141C2×(C2×D43)⋊C4C2314yes—
142C2×(C2×D43)⋊C4C2314yes—
143C2×(C2×D43)⋊C4C2314yescomplemented
144C2×(C2×D43)⋊C4C2314yescomplemented
145C2×(C2×D43)⋊C4C2314yescomplemented
146C22⋊C4×D43—232no—
147C2×C4×Dic43—24no—
148C2×C4×Dic43—24no—
149C2×C4×Dic43—42no—
150C2×C4×Dic43C2314yescomplemented
151C2×C4×Dic43C2314yescomplemented
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×C43C2311yescharacteristic
163C23×C4×C43C2311yescharacteristic
164C23×C4×C43C2314yes—
165C23×C4×C43C2311yescharacteristic
166C23×C4×C43C2311yescharacteristic
167C23×C4×C43C2311yescharacteristic
168C2×C4⋊C4×C43—24no—
169C2×C4⋊C4×C43—42no—
170C2×C4⋊C4×C43C2314yescomplemented
171C2×C4⋊C4×C43C2314yescomplemented
172C2×C22⋊C4×C43—24no—
173C2×C22⋊C4×C43C2×C418yescomplemented
174C2×C22⋊C4×C43C2314yes—
175C2×C22⋊C4×C43C2314yes—
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—22no—
233C22×C4×C43—28no—
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—22no—
241C22×C4×C43—22no—
242C22×C4×C43—44no—
243C22×C4×C43—416no—
244C22×C4×C43C22×C414yes—
245C22×C4×C43C22×C414yes—
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—28no—
265C22×Dic43—22no—
266C22×Dic43—22no—
267C22×Dic43—22no—
268C22×Dic43—22no—
269C22×Dic43—22no—
270C22×Dic43—44no—
271C22×Dic43—416no—
272C22×Dic43C22×C414yes—
273C22×Dic43C2×D414yes—
274C22×Dic43C2×D414yes—
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—
301C4⋊C4×C43—28no—
302C4⋊C4×C43—44no—
303C22⋊C4×C43—28no—
304C22⋊C4×C43C22×C4116yescomplemented
305C22⋊Dic43C2×D4116yescomplemented
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
317Dic43⋊C4—28no—
318C4×Dic43—28no—
319C4×Dic43—28no—
320C4×Dic43—44no—
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×D414yes—
335C23×C43C22×D412yes—
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—22no—
397C2×C4×C43—22no—
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×C43—44no—
414C2×C4×C43—44no—
415C2×C4×C43C23×C414yes—
416C2×C4×C43C23×C414yes—
417C2×C4×C43C22×D414yes—
418C22⋊D43—232no—
419C2×Dic43—28no—
420C2×Dic43—28no—
421C2×Dic43—28no—
422C2×Dic43—28no—
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×Dic43C23×C414yes—
437C2×Dic43C22×D414yes—
438C2×Dic43C22×D414yes—
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—42no—
497C4×C43—42no—
498C4×C43—42no—
499Dic43—24no—
500Dic43—24no—
501Dic43—24no—
502Dic43—24no—
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×#385D4311yescharacteristic, complemented
518C2×C4×C22⋊C4—431no—
519C2×C4×C22⋊C4—431no—
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⋊C4C2×D4311yescharacteristic, complemented
549C22×C4⋊C4C2×D4311yescharacteristic, complemented
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×C42—431no—
570C22×C42—431no—
571#390—438no—
572#388—438no—
573#388—438no—
574#386—438no—
575#386—438no—
576#386—438no—
577#385—438no—
578#385C2×D4318yescomplemented
579C4×C22⋊C4—438no—
580C4×C22⋊C4—438no—
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×D4311yescharacteristic
638C23×C4C22×D4311yescharacteristic
639C23×C4C22×D4314yes—
640C23×C4C22×D4311yescharacteristic
641C23×C4C22×D4311yescharacteristic
642C23×C4C22×D4311yescharacteristic
643#120—4364no—
644C4×D4—8632no—
645C4×D4—8632no—
646C2×C4⋊C4—24no—
647C2×C4⋊C4—42no—
648C2×C4⋊C4—434no—
649C2×C4⋊C4—864no—
650C2×C4⋊C4C22×D4314yescomplemented
651C2×C4⋊C4C22×D4314yescomplemented
652C2×C22⋊C4—24no—
653C2×C22⋊C4—438no—
654C2×C22⋊C4—434no—
655C2×C22⋊C4—438no—
656C2×C22⋊C4—438no—
657C2×C22⋊C4—438no—
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—434no—
668C2×C22⋊C4—434no—
669C2×C22⋊C4—8632no—
670C2×C22⋊C4—8632no—
671C2×C22⋊C4—864no—
672C2×C22⋊C4—864no—
673C2×C22⋊C4—864no—
674C2×C22⋊C4—864no—
675C2×C22⋊C4—864no—
676C2×C22⋊C4—864no—
677C2×C22⋊C4—864no—
678C2×C22⋊C4—1722no—
679C2×C22⋊C4C4×D4318yescomplemented
680C2×C22⋊C4C22×D4314yes—
681C2×C22⋊C4C22×D4314yes—
682C2×C42—434no—
683C2×C42—434no—
684C2×C42—434no—
685C2×C42—864no—
686C2×C42—864no—
687C2×C42—1722no—
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—868no—
716C24—862no—
717C24—862no—
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—
737C24D4×D4314yes—
738C24#1062190214yes—
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—22no—
768C22×C4—22no—
769C22×C4—28no—
770C22×C4—44no—
771C22×C4—416no—
772C22×C4—434no—
773C22×C4—434no—
774C22×C4—434no—
775C22×C4—434no—
776C22×C4—432no—
777C22×C4—432no—
778C22×C4—432no—
779C22×C4—432no—
780C22×C4—432no—
781C22×C4—868no—
782C22×C4—868no—
783C22×C4—868no—
784C22×C4—868no—
785C22×C4—868no—
786C22×C4—868no—
787C22×C4—862no—
788C22×C4—862no—
789C22×C4—862no—
790C22×C4—862no—
791C22×C4—862no—
792C22×C4—862no—
793C22×C4—862no—
794C22×C4—862no—
795C22×C4—862no—
796C22×C4—868no—
797C22×C4—862no—
798C22×C4—862no—
799C22×C4—868no—
800C22×C4—1724no—
801C22×C4—1724no—
802C22×C4—1724no—
803C22×C4—17216no—
804C22×C4—17216no—
805C22×C4—17216no—
806C22×C4—1724no—
807C22×C4—17216no—
808C22×C4C2×C4×D4314yes—
809C22×C4C2×C4×D4314yes—
810C22×C4D4×D4314yes—
811C22×C4C23×D4312yes—
812C22×C4C23×D4312yes—
813C22×C4C23×D4312yes—
814C22×C4C23×D4312yes—
815C22×C4C23×D4312yes—
816C22×C4C23×D4312yes—
817C4⋊C4—28no—
818C4⋊C4—44no—
819C4⋊C4—868no—
820C22⋊C4—28no—
821C22⋊C4—4316no—
822C22⋊C4—4316no—
823C22⋊C4—4316no—
824C22⋊C4—4316no—
825C22⋊C4—868no—
826C22⋊C4—868no—
827C22⋊C4—868no—
828C22⋊C4—868no—
829C22⋊C4—868no—
830C22⋊C4—868no—
831C22⋊C4—868no—
832C22⋊C4—1724no—
833C22⋊C4C2×C4×D43116yescomplemented
834C42—868no—
835C42—868no—
836C42—1724no—
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—172128no—
887C23—17216no—
888C23—17216no—
889C23—1724no—
890C23—1724no—
891C23—1724no—
892C23—1724no—
893C23—1724no—
894C23—1724no—
895C23—1724no—
896C23—1724no—
897C23#13063287116yescomplemented
898C23C22×C4×D4314yes—
899C23C22×C4×D4312yes—
900C23C2×D4×D4314yes—
901C23C2×D4×D4312yes—
902C23C2×D4×D4312yes—
903C23#41×D4312yes—
904C23C2×#1062190214yes—
905C23C2×#1062190212yes—
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—28no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—416no—
931C2×C4—44no—
932C2×C4—44no—
933C2×C4—44no—
934C2×C4—434no—
935C2×C4—434no—
936C2×C4—434no—
937C2×C4—434no—
938C2×C4—868no—
939C2×C4—862no—
940C2×C4—862no—
941C2×C4—862no—
942C2×C4—862no—
943C2×C4—862no—
944C2×C4—862no—
945C2×C4—862no—
946C2×C4—862no—
947C2×C4—868no—
948C2×C4—868no—
949C2×C4—868no—
950C2×C4—862no—
951C2×C4—862no—
952C2×C4—862no—
953C2×C4—17216no—
954C2×C4—17216no—
955C2×C4—17216no—
956C2×C4—17216no—
957C2×C4—1724no—
958C2×C4C22×C4×D4314yes—
959C2×C4C22×C4×D4314yes—
960C2×C4C2×D4×D4314yes—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—232no—
965C22—24no—
966C22—24no—
967C22—24no—
968C22—438no—
969C22—864no—
970C22—864no—
971C22—864no—
972C22—8632no—
973C22—864no—
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—17216no—
988C22—17216no—
989C22—1722no—
990C22—1722no—
991C22—1722no—
992C22—1722no—
993C22C4×D4×D4314yes—
994C22C2×#1306328714yes—
995C22C2×#1306328718yescomplemented
996C22#1458337114yes—
997C22#1458353114yes—
998C22#1458354014yes—
999C22#1458354114yes—
1000C22#1458357614yes—
1001C22C23×C4×D4311yescharacteristic
1002C22C22×D4×D4311yescharacteristic
1003C22C22×D4×D4311yescharacteristic
1004C22C2×#41×D4311yescharacteristic
1005C22C22×#1062190211yescharacteristic
1006C22C2×#1306337011yescharacteristic
1007C22C2×#1306337111yescharacteristic
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—864no—
1015C4—864no—
1016C4—864no—
1017C4—864no—
1018C4—1722no—
1019C2—28no—
1020C2—868no—
1021C2—1724no—
1022C2—1724no—
1023C2#1913757118yesdirect product factor
1024C2C2×C4×D4×D4311yescharacteristic
1025C2C22×#1306328711yescharacteristic
1026C2C2×#1458337111yescharacteristic
1027C2C2×#1458353111yescharacteristic
1028C2C2×#1458354011yescharacteristic
1029C2C2×#1458354111yescharacteristic
1030C2C2×#1458357611yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#385C2
socleC24×C43C24
prime radicalC22×#13063295C2
cosocleC23×C43C25
hypercenterC2×#385D43
hypocenterC43C2×#2358
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#13063287C2semidirect
3. C22×C4×C22⋊D43C2semidirect
4. C23×(C2×D43)⋊C4C2semidirect
5. C22×C22⋊C4×D43C2semidirect
6. #19137571C2direct (N × H)
7. C2×#14582800C2semidirect
8. C2×#14582789C2semidirect
9. C2×#14582788C2semidirect
10. C2×#14582777C2semidirect
11. C2×#14582777C2semidirect
12. C2×#14582776C2semidirect
13. C2×#14582770C2semidirect
14. C2×C22⋊C4×Dic43C2semidirect
15. C2×#14582746C2semidirect
16. C2×C43×#385C2semidirect
24. C23×C4×D43C22semidirect
25. C2×#13063295C4semidirect
28. C2×#13063287C22semidirect
30. C2×C4×C22⋊D43C22semidirect
31. C22×Dic43⋊C4C22semidirect
42. C22×(C2×D43)⋊C4C22semidirect
43. C22×(C2×D43)⋊C4C22semidirect
44. C22×(C2×D43)⋊C4C22semidirect
45. C22×(C2×D43)⋊C4C22semidirect
47. C2×C22⋊C4×D43C22semidirect
48. C22×C4×Dic43C22semidirect
49. C22×C4×Dic43C22semidirect
50. C22×C4×Dic43C22semidirect
51. #14582800C22semidirect
52. #14582789C22semidirect
53. #14582788C22semidirect
54. #14582777C22semidirect
55. #14582777C22semidirect
56. #14582776C22semidirect
57. #14582770C22semidirect
58. C22⋊C4×Dic43C22semidirect
59. #14582746C22semidirect
60. C2×C43⋊#95C22semidirect
61. C2×C43⋊#95C22semidirect
62. C2×C43⋊#95C22semidirect
63. C2×C43⋊#95C22semidirect
65. C22×C4⋊C4×C43C22semidirect
66. C22×C4⋊C4×C43C22semidirect
69. C43×#385C22semidirect
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
120. C2×Dic43⋊C4C23semidirect
121. C2×C22⋊Dic43D4semidirect
132. C2×(C2×D43)⋊C4C2×C4semidirect
133. C2×(C2×D43)⋊C4C2×C4semidirect
134. C2×(C2×D43)⋊C4D4semidirect
143. C2×(C2×D43)⋊C4C23semidirect
144. C2×(C2×D43)⋊C4C23semidirect
145. C2×(C2×D43)⋊C4C23semidirect
150. C2×C4×Dic43C23semidirect
151. C2×C4×Dic43C23semidirect
152. C2×C4×Dic43C23semidirect
153. C43⋊#95C23semidirect
154. C43⋊#95C23semidirect
155. C43⋊#95C23semidirect
156. C43⋊#95C23semidirect
170. C2×C4⋊C4×C43C23semidirect
171. C2×C4⋊C4×C43C23semidirect
173. C2×C22⋊C4×C43C2×C4semidirect
176. #95×C43C23semidirect
177. #95×C43C23semidirect
219. C23×D43C22×C4semidirect
256. C2×C22⋊D43C22×C4semidirect
287. C2×D172C22×C4semidirect
288. C2×D172C22×C4semidirect
304. C22⋊C4×C43C22×C4semidirect
305. C22⋊Dic43C2×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
517. C2×#385D43semidirect
521. C2×C43#2358semidirect
548. C22×C4⋊C4C2×D43semidirect
549. C22×C4⋊C4C2×D43semidirect
578. #385C2×D43semidirect
585. C2×#95C2×D43semidirect
586. C2×#95C2×D43semidirect
587. C43C2×#2358semidirect
650. C2×C4⋊C4C22×D43semidirect
651. C2×C4⋊C4C22×D43semidirect
679. C2×C22⋊C4C4×D43semidirect
692. #95C22×D43semidirect
693. #95C22×D43semidirect
833. C22⋊C4C2×C4×D43semidirect
897. C23#13063287semidirect
995. C22C2×#13063287semidirect
1023. C2#19137571direct (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×#130632872
C22×C4×C22⋊D432
C23×(C2×D43)⋊C42
C22×C22⋊C4×D432
#191375712
C2×#145828002
C2×#145827892
C2×#145827882
C2×#145827772
C2×#145827762
C2×#145827702
C2×C22⋊C4×Dic432
C2×#145827462
C2×C43×#3852
C2×#235843