Finite Group Databasebeta

← C2×#19139952 #25267810

Subgroups — C2×#19139952 #25267810

Order 11008.

3222 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063290C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D43C211yesmaximal, characteristic
3#19139952C2116yesmaximal, direct product factor
4C2×#14582835C211yesmaximal, characteristic, complemented
5C2×#14582834C211yesmaximal, characteristic, complemented
6C2×#14582812C211yesmaximal, characteristic, complemented
7C2×#14582811C211yesmaximal, characteristic, complemented
8C2×#14582799C211yesmaximal, characteristic
9C2×#14582799C211yesmaximal, characteristic
10C2×#14582796C211yesmaximal, characteristic, complemented
11C2×#14582794C211yesmaximal, characteristic, complemented
12C2×#14582773C211yesmaximal, characteristic, complemented
13C2×#14582772C211yesmaximal, characteristic, complemented
14C2×#14582770C211yesmaximal, characteristic, complemented
15C2×#14582763C211yesmaximal, characteristic, complemented
16C2×C43×#385C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C23×C22⋊D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C2×#13063290—28no—
21C2×#13063290C2218yescomplemented
22C2×C4×C22⋊D43—28no—
23C2×C4×C22⋊D43C2218yes—
24C22×C4⋊Dic43C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊C4C2211yescharacteristic
30C22×Dic43⋊C4C2211yescharacteristic
31C22×Dic43⋊C4C2211yescharacteristic
32C22×C22⋊Dic43C2211yescharacteristic
33C22×C22⋊Dic43C2211yescharacteristic
34C22×C22⋊Dic43C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×(C2×D43)⋊C4C2211yescharacteristic
40C22×C4×Dic43C2211yescharacteristic
41C22×C4×Dic43C2211yescharacteristic
42C22×C4×Dic43C2211yescharacteristic
43#14582835C2218yescomplemented
44#14582834C2218yescomplemented
45#14582812C2218yescomplemented
46#14582811C2218yescomplemented
47#14582799C2218yes—
48#14582799C2218yes—
49#14582796C2218yescomplemented
50#14582794C2218yescomplemented
51#14582773C2218yescomplemented
52#14582772C2218yescomplemented
53#14582770C2218yescomplemented
54#14582763C2218yescomplemented
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C24×C4×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C22⋊C4×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C43×#385C2218yescomplemented
67C2×#95×C43C2211yescharacteristic
68C2×#95×C43C2211yescharacteristic
69C24×D43C2311yescharacteristic
70C22×Dic86—24no—
71C22×Dic86—24no—
72C22×Dic86—24no—
73C22×Dic86C2314yes—
74C22×C22⋊D43—24no—
75C22×C22⋊D43—24no—
76C22×C22⋊D43Q818yescomplemented
77C22×C22⋊D43C2314yes—
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C22×C4×D43—24no—
86C22×C4×D43—42no—
87C22×C4×D43—42no—
88C22×C4×D43C2314yes—
89#13063290—232no—
90C4×C22⋊D43—232no—
91C2×C4⋊Dic43—42no—
92C2×C4⋊Dic43C2314yes—
93C2×Dic43⋊C4—24no—
94C2×Dic43⋊C4—24no—
95C2×Dic43⋊C4—24no—
96C2×Dic43⋊C4—24no—
97C2×Dic43⋊C4—24no—
98C2×Dic43⋊C4—42no—
99C2×Dic43⋊C4—42no—
100C2×Dic43⋊C4C2314yes—
101C2×Dic43⋊C4C2314yes—
102C2×Dic43⋊C4C2314yes—
103C2×Dic43⋊C4C2314yes—
104C2×Dic43⋊C4C2314yes—
105C2×Dic43⋊C4C2314yes—
106C2×Dic43⋊C4C2314yes—
107C2×C22⋊Dic43—24no—
108C2×C22⋊Dic43—24no—
109C2×C22⋊Dic43—42no—
110C2×C22⋊Dic43C2314yes—
111C2×C22⋊Dic43C2314yes—
112C2×C22⋊Dic43C2314yes—
113C2×(C2×D43)⋊C4—24no—
114C2×(C2×D43)⋊C4—24no—
115C2×(C2×D43)⋊C4—24no—
116C2×(C2×D43)⋊C4—42no—
117C2×(C2×D43)⋊C4—42no—
118C2×(C2×D43)⋊C4C2314yes—
119C2×(C2×D43)⋊C4C2314yes—
120C2×(C2×D43)⋊C4C2314yes—
121C2×(C2×D43)⋊C4C2314yes—
122C2×(C2×D43)⋊C4C2314yes—
123C2×C4×Dic43—24no—
124C2×C4×Dic43—24no—
125C2×C4×Dic43D418yes—
126C2×C4×Dic43C2314yes—
127C2×C4×Dic43C2314yes—
128C2×C4×Dic43C2314yes—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C43⋊#95C2314yes—
132C43⋊#95C2314yes—
133C43⋊#95C2314yes—
134C43⋊#95C2314yes—
135C25×C43C2311yescharacteristic
136C23×C4×C43—24no—
137C23×C4×C43—42no—
138C23×C4×C43—42no—
139C23×C4×C43C2311yescharacteristic
140C23×C4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C23×C4×C43C2311yescharacteristic
145C23×C4×C43C2314yes—
146C2×C4⋊C4×C43—24no—
147C2×C4⋊C4×C43—42no—
148C2×C4⋊C4×C43C2314yes—
149C2×C4⋊C4×C43C2314yes—
150C2×C22⋊C4×C43—24no—
151C2×C22⋊C4×C43—42no—
152C2×C22⋊C4×C43C2314yes—
153C2×C22⋊C4×C43C2314yes—
154#95×C43C2314yes—
155#95×C43C2314yes—
156C24×C43—22no—
157C24×C43—22no—
158C24×C43—22no—
159C24×C43—22no—
160C24×C43—22no—
161C24×C43—22no—
162C24×C43C2×Q814yes—
163C24×C43C2412yes—
164C24×C43C2411yescharacteristic
165C23×D43—22no—
166C23×D43—22no—
167C23×D43—22no—
168C23×D43—22no—
169C23×D43—22no—
170C23×D43—22no—
171C23×D43C2×Q814yes—
172C23×D43C2412yes—
173C22×C4×C43—28no—
174C22×C4×C43—22no—
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×C43—44no—
191C22×C4×C43—44no—
192C22×C4×C43—416no—
193C22×C4×C43C2×D414yes—
194C22×C4×C43#4114yes—
195C22×C4×C43C2412yes—
196C22×C4×C43C2412yes—
197C22×C4×C43C2412yes—
198C22×C4×C43C2412yes—
199C22×C4×C43C2412yes—
200C22×C4×C43C2412yes—
201C2×C22⋊D43—232no—
202C2×C22⋊D43—28no—
203C2×C22⋊D43—28no—
204C2×C22⋊D43C2×Q8116yescomplemented
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×Dic43C2×D414yes—
222C22×Dic43C2×D414yes—
223C22×Dic43C2×Q814yes—
224C22×Dic43#4114yes—
225C22×Dic43#4114yes—
226C22×Dic43C2412yes—
227C22×Dic43C2412yes—
228C22×Dic43C2412yes—
229C22×Dic43C2412yes—
230C22×Dic43C2412yes—
231C22×Dic43C2412yes—
232C22×Dic43C2412yes—
233C2×C4×D43—28no—
234C2×C4×D43—44no—
235C2×C4×D43—44no—
236C2×C4×D43—416no—
237C2×Dic86—232no—
238C2×Dic86—28no—
239C2×Dic86—28no—
240C2×Dic86—28no—
241C4⋊C4×C43—28no—
242C4⋊C4×C43—44no—
243C22⋊C4×C43—28no—
244C22⋊C4×C43—44no—
245C22⋊Dic43—28no—
246C22⋊Dic43—28no—
247C22⋊Dic43—44no—
248(C2×D43)⋊C4—28no—
249(C2×D43)⋊C4—28no—
250(C2×D43)⋊C4—28no—
251(C2×D43)⋊C4—44no—
252(C2×D43)⋊C4—44no—
253C4⋊Dic43—44no—
254Dic43⋊C4—28no—
255Dic43⋊C4—28no—
256Dic43⋊C4—28no—
257Dic43⋊C4—28no—
258Dic43⋊C4—28no—
259Dic43⋊C4—44no—
260Dic43⋊C4—44no—
261C4×Dic43—28no—
262C4×Dic43—28no—
263C4×Dic43C2×D4116yes—
264C23×C43—28no—
265C23×C43—28no—
266C23×C43—28no—
267C23×C43—22no—
268C23×C43—22no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—44no—
274C23×C43—44no—
275C23×C43—44no—
276C23×C43—44no—
277C23×C43C22×D412yes—
278C23×C43C22×Q814yes—
279C23×C43C22×Q812yes—
280C23×C43C2×#4112yes—
281C23×C43C2×#4112yes—
282C23×C43C2×#4112yes—
283C23×C43H(5,𝔽2)12yes—
284C23×C43H(5,𝔽2)12yes—
285C23×C43C2511yescharacteristic
286C22×D43—28no—
287C22×D43—28no—
288C22×D43—28no—
289C22×D43—22no—
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—44no—
296C22×D43—44no—
297C22×D43—44no—
298C22×D43—44no—
299C22×D43C22×Q814yes—
300C2×C4×C43—28no—
301C2×C4×C43—28no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
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—416no—
319C2×C4×C43—44no—
320C2×C4×C43—44no—
321C2×C4×C43—44no—
322C2×C4×C43—44no—
323C2×C4×C43C22×D414yes—
324C2×C4×C43C2×#4114yes—
325C22⋊D43—232no—
326C2×Dic43—28no—
327C2×Dic43—28no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
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—44no—
345C2×Dic43—44no—
346C2×Dic43—44no—
347C2×Dic43—44no—
348C2×Dic43C22⋊Q8116yes—
349C2×Dic43C22×D414yes—
350C2×Dic43C22×D414yes—
351C2×Dic43C22×Q814yes—
352C2×Dic43C2×#4114yes—
353C2×Dic43C2×#4114yes—
354C4×D43—416no—
355Dic86—232no—
356C2×#2580—431nomaximal, Sylow
357C22×C43—24no—
358C22×C43—24no—
359C22×C43—24no—
360C22×C43—416no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43C2×C22⋊Q814yes—
366C22×C43#52514yes—
367C22×C43#53514yes—
368C22×C43#55414yes—
369C22×C43#55414yes—
370C22×C43#55914yes—
371C22×C43#55914yes—
372C22×C43C23×D411yescharacteristic
373C22×C43C23×Q811yescharacteristic
374C22×C43C22×#4111yescharacteristic
375C22×C43C22×#4111yescharacteristic
376C22×C43C22×#4111yescharacteristic
377C22×C43C2×H(5,𝔽2)11yescharacteristic
378C22×C43C2×H(5,𝔽2)11yescharacteristic
379C2×D43—24no—
380C2×D43—24no—
381C2×D43—24no—
382C2×D43—416no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—42no—
386C2×D43—42no—
387C4×C43—24no—
388C4×C43—24no—
389C4×C43—42no—
390C4×C43—42no—
391C4×C43—42no—
392C4×C43—42no—
393Dic43—24no—
394Dic43—24no—
395Dic43—42no—
396Dic43—42no—
397Dic43—42no—
398Dic43—42no—
399Dic43C2×C22⋊Q818yes—
400C22×C4×Q8—431no—
401C22×C4×D4—431no—
402#2580—4316no—
403C2×#399—431no—
404C2×#399—431no—
405C2×#393—431no—
406C2×#393—431no—
407C2×#390—431no—
408C2×#390—431no—
409C2×#389—431no—
410C2×#389—431no—
411C2×#385—431no—
412C2×#385—431no—
413C2×#385—431no—
414C2×#385D4311yescharacteristic, complemented
415C2×#382—431no—
416C2×C43—44no—
417C2×C43#258018yescomplemented
418C2×C43C22×C22⋊Q811yescharacteristic
419C2×C43C2×#52511yescharacteristic
420C2×C43C2×#53511yescharacteristic
421C2×C43C2×#55411yescharacteristic
422C2×C43C2×#55411yescharacteristic
423C2×C43C2×#55911yescharacteristic
424C2×C43C2×#55911yescharacteristic
425D43—44no—
426C23×Q8—431no—
427C23×D4—431no—
428C24×C4—431no—
429C24×C4C2×D4311yescharacteristic
430C2×C4×Q8—438no—
431C2×C4×Q8—868no—
432C2×C4×D4—438no—
433C2×C4×D4—868no—
434C22×C4⋊C4—431no—
435C22×C4⋊C4—431no—
436C22×C4⋊C4—431no—
437C22×C4⋊C4—431no—
438C22×C4⋊C4—431no—
439C22×C4⋊C4—431no—
440C22×C4⋊C4—431no—
441C22×C4⋊C4—431no—
442C22×C4⋊C4C2×D4311yescharacteristic
443C22×C4⋊C4C2×D4311yescharacteristic
444C22×C22⋊C4—431no—
445C22×C22⋊C4—431no—
446C22×C22⋊C4—431no—
447C22×C22⋊C4—431no—
448C22×C22⋊C4—431no—
449C22×C22⋊C4—431no—
450C22×C22⋊C4—431no—
451C22×C22⋊C4—431no—
452C22×C22⋊C4C2×D4311yescharacteristic
453C22×C22⋊C4C2×D4311yescharacteristic
454C22×C42—431no—
455C22×C42—431no—
456C22×C42—431no—
457#399—438no—
458#399—438no—
459#393—438no—
460#393—438no—
461#390—438no—
462#390—438no—
463#389—438no—
464#389—438no—
465#385—438no—
466#385—438no—
467#385—438no—
468#385C2×D4318yescomplemented
469#382—438no—
470C2×#95—431no—
471C2×#95—431no—
472C2×#95—431no—
473C2×#95—431no—
474C2×#95—431no—
475C2×#95—431no—
476C2×#95C2×D4311yescharacteristic
477C2×#95C2×D4311yescharacteristic
478C43C2×#258011yescharacteristic, complemented, Sylow
479C25—431no—
480C25C22×D4311yescharacteristic
481C22×Q8—434no—
482C22×Q8—864no—
483C22×Q8—864no—
484C22×Q8—864no—
485C22×D4—438no—
486C22×D4—434no—
487C22×D4—864no—
488C22×D4—864no—
489C23×C4—24no—
490C23×C4—42no—
491C23×C4—42no—
492C23×C4—431no—
493C23×C4—431no—
494C23×C4—431no—
495C23×C4—431no—
496C23×C4—431no—
497C23×C4—431no—
498C23×C4—431no—
499C23×C4—434no—
500C23×C4—864no—
501C23×C4—1722no—
502C23×C4—1722no—
503C23×C4C22×D4311yescharacteristic
504C23×C4C22×D4311yescharacteristic
505C23×C4C22×D4311yescharacteristic
506C23×C4C22×D4311yescharacteristic
507C23×C4C22×D4311yescharacteristic
508C23×C4C22×D4311yescharacteristic
509C23×C4C22×D4314yes—
510C4×Q8—8632no—
511C4×D4—8632no—
512C2×C4⋊C4—24no—
513C2×C4⋊C4—42no—
514C2×C4⋊C4—434no—
515C2×C4⋊C4—434no—
516C2×C4⋊C4—434no—
517C2×C4⋊C4—434no—
518C2×C4⋊C4—434no—
519C2×C4⋊C4—434no—
520C2×C4⋊C4—434no—
521C2×C4⋊C4—434no—
522C2×C4⋊C4—864no—
523C2×C4⋊C4—864no—
524C2×C4⋊C4—864no—
525C2×C4⋊C4—864no—
526C2×C4⋊C4—864no—
527C2×C4⋊C4—1722no—
528C2×C4⋊C4—1722no—
529C2×C4⋊C4—1722no—
530C2×C4⋊C4C22×D4314yes—
531C2×C4⋊C4C22×D4314yes—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—434no—
535C2×C22⋊C4—434no—
536C2×C22⋊C4—434no—
537C2×C22⋊C4—434no—
538C2×C22⋊C4—434no—
539C2×C22⋊C4—434no—
540C2×C22⋊C4—434no—
541C2×C22⋊C4—434no—
542C2×C22⋊C4—864no—
543C2×C22⋊C4—864no—
544C2×C22⋊C4—864no—
545C2×C22⋊C4—864no—
546C2×C22⋊C4—864no—
547C2×C22⋊C4—1722no—
548C2×C22⋊C4—1722no—
549C2×C22⋊C4—1722no—
550C2×C22⋊C4C22×D4314yes—
551C2×C22⋊C4C22×D4314yes—
552C2×C42—438no—
553C2×C42—434no—
554C2×C42—434no—
555C2×C42—434no—
556C2×C42—864no—
557C2×C42—864no—
558#95—434no—
559#95—434no—
560#95—434no—
561#95—434no—
562#95—434no—
563#95—434no—
564#95C22×D4314yes—
565#95C22×D4314yes—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—434no—
573C24—432no—
574C24—862no—
575C24—862no—
576C24—862no—
577C24—862no—
578C24—862no—
579C24—862no—
580C24Q8×D4314yes—
581C24C23×D4312yes—
582C24C23×D4311yescharacteristic
583C2×Q8—868no—
584C2×Q8—868no—
585C2×Q8—8632no—
586C2×Q8—868no—
587C2×D4—4316no—
588C2×D4—868no—
589C2×D4—8632no—
590C2×D4—868no—
591C22×C4—22no—
592C22×C4—22no—
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—28no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—416no—
611C22×C4—434no—
612C22×C4—434no—
613C22×C4—434no—
614C22×C4—432no—
615C22×C4—434no—
616C22×C4—434no—
617C22×C4—432no—
618C22×C4—432no—
619C22×C4—432no—
620C22×C4—432no—
621C22×C4—432no—
622C22×C4—432no—
623C22×C4—862no—
624C22×C4—862no—
625C22×C4—862no—
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—868no—
640C22×C4—1724no—
641C22×C4—1724no—
642C22×C4—17216no—
643C22×C4#1062189814yes—
644C22×C4D4×D4314yes—
645C22×C4C23×D4312yes—
646C22×C4C23×D4312yes—
647C22×C4C23×D4312yes—
648C22×C4C23×D4312yes—
649C22×C4C23×D4312yes—
650C22×C4C23×D4312yes—
651C4⋊C4—28no—
652C4⋊C4—44no—
653C4⋊C4—868no—
654C4⋊C4—868no—
655C4⋊C4—868no—
656C4⋊C4—868no—
657C4⋊C4—868no—
658C4⋊C4—1724no—
659C4⋊C4—1724no—
660C4⋊C4—1724no—
661C22⋊C4—28no—
662C22⋊C4—44no—
663C22⋊C4—868no—
664C22⋊C4—868no—
665C22⋊C4—868no—
666C22⋊C4—868no—
667C22⋊C4—868no—
668C22⋊C4—1724no—
669C22⋊C4—1724no—
670C22⋊C4—1724no—
671C42—4316no—
672C42—868no—
673C42—868no—
674C23—28no—
675C23—28no—
676C23—28no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—434no—
688C23—868no—
689C23—868no—
690C23—868no—
691C23—862no—
692C23—862no—
693C23—862no—
694C23—862no—
695C23—862no—
696C23—862no—
697C23—1724no—
698C23—1724no—
699C23—1724no—
700C23—1724no—
701C23C2×D4×D4312yes—
702C23C2×Q8×D4314yes—
703C23C2×Q8×D4312yes—
704C23#41×D4312yes—
705C23#41×D4312yes—
706C23C2×#1062189812yes—
707C23#1306337012yes—
708C23#1306337012yes—
709C23C24×D4311yescharacteristic
710Q8—8632no—
711D4—8632no—
712C2×C4—28no—
713C2×C4—22no—
714C2×C4—28no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
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—416no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—4316no—
736C2×C4—434no—
737C2×C4—434no—
738C2×C4—434no—
739C2×C4—434no—
740C2×C4—434no—
741C2×C4—868no—
742C2×C4—868no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—862no—
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—17216no—
760C2×C4—1724no—
761C2×C4—1724no—
762C2×C4—1724no—
763C2×C4—1724no—
764C2×C4C2×D4×D4314yes—
765C2×C4C2×#1062189814yes—
766C22—24no—
767C22—24no—
768C22—24no—
769C22—42no—
770C22—416no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—864no—
775C22—864no—
776C22—864no—
777C22—1722no—
778C22—17216no—
779C22—1722no—
780C22—1722no—
781C22—1722no—
782C22C22⋊Q8×D4314yes—
783C22#1458340814yes—
784C22#1458346414yes—
785C22#1458360314yes—
786C22#1458360414yes—
787C22#1458363214yes—
788C22#1458363314yes—
789C22C22×D4×D4311yescharacteristic
790C22C22×Q8×D4311yescharacteristic
791C22C2×#41×D4311yescharacteristic
792C22C2×#41×D4311yescharacteristic
793C22C22×#1062189811yescharacteristic
794C22C2×#1306337011yescharacteristic
795C22C2×#1306337011yescharacteristic
796C4—24no—
797C4—24no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—438no—
803C4—864no—
804C4—864no—
805C4—1722no—
806C4—1722no—
807C4—1722no—
808C4—1722no—
809C2—44no—
810C2—1724no—
811C2#1913995218yesdirect product factor
812C2C2×C22⋊Q8×D4311yescharacteristic
813C2C2×#1458340811yescharacteristic
814C2C2×#1458346411yescharacteristic
815C2C2×#1458360311yescharacteristic
816C2C2×#1458360411yescharacteristic
817C2C2×#1458363211yescharacteristic
818C2C2×#1458363311yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#385C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#385D43
hypocenterC43C2×#2580
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#13063290C2semidirect
3. #19139952C2direct (N × H)
4. C2×#14582835C2semidirect
5. C2×#14582834C2semidirect
6. C2×#14582812C2semidirect
7. C2×#14582811C2semidirect
10. C2×#14582796C2semidirect
11. C2×#14582794C2semidirect
12. C2×#14582773C2semidirect
13. C2×#14582772C2semidirect
14. C2×#14582770C2semidirect
15. C2×#14582763C2semidirect
16. C2×C43×#385C2semidirect
21. C2×#13063290C22semidirect
43. #14582835C22semidirect
44. #14582834C22semidirect
45. #14582812C22semidirect
46. #14582811C22semidirect
49. #14582796C22semidirect
50. #14582794C22semidirect
51. #14582773C22semidirect
52. #14582772C22semidirect
53. #14582770C22semidirect
54. #14582763C22semidirect
66. C43×#385C22semidirect
76. C22×C22⋊D43Q8semidirect
204. C2×C22⋊D43C2×Q8semidirect
414. C2×#385D43semidirect
417. C2×C43#2580semidirect
468. #385C2×D43semidirect
478. C43C2×#2580semidirect
811. C2#19139952direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130632902
C22×C4×C22⋊D432
#191399522
C2×#145828352
C2×#145828342
C2×#145828122
C2×#145828112
C2×#145827992
C2×#145827962
C2×#145827942
C2×#145827732
C2×#145827722
C2×#145827702
C2×#145827632
C2×C43×#3852
C2×#258043