Finite Group Databasebeta

← C2×#19142733 #25302918

Subgroups — C2×#19142733 #25302918

Order 11008.

2434 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142733C2116yesmaximal, direct product factor
2C2×#14582834C211yesmaximal, characteristic, complemented
3C2×#14582826C211yesmaximal, characteristic, complemented
4C2×#14582825C211yesmaximal, characteristic, complemented
5C2×#14582821C211yesmaximal, characteristic, complemented
6C2×#14582821C211yesmaximal, characteristic, complemented
7C2×#14582817C211yesmaximal, characteristic, complemented
8C2×#14582817C211yesmaximal, characteristic, complemented
9C2×#14582816C211yesmaximal, characteristic, complemented
10C2×#14582816C211yesmaximal, characteristic, complemented
11C2×#14582816C211yesmaximal, characteristic, complemented
12C2×#14582809C211yesmaximal, characteristic
13C2×#14582800C211yesmaximal, characteristic, complemented
14C2×#14582788C211yesmaximal, characteristic, complemented
15C2×#14582781C211yesmaximal, characteristic, complemented
16C2×C43×#398C211yesmaximal, characteristic, complemented
17C23×D172C2211yescharacteristic
18C23×D172C2211yescharacteristic
19C23×D172C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21C22×Dic43⋊C4C2211yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×(C2×D43)⋊C4C2211yescharacteristic
25C22×(C2×D43)⋊C4C2211yescharacteristic
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×(C2×D43)⋊C4C2211yescharacteristic
35C22×(C2×D43)⋊C4C2211yescharacteristic
36C22×(C2×D43)⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×C4×Dic43C2211yescharacteristic
40#14582834C2218yescomplemented
41#14582826C2218yescomplemented
42#14582825C2218yescomplemented
43#14582821C2218yescomplemented
44#14582821C2218yescomplemented
45#14582817C2218yescomplemented
46#14582817C2218yescomplemented
47#14582816C2218yescomplemented
48#14582816C2218yescomplemented
49#14582816C2218yescomplemented
50#14582809C2218yes—
51#14582800C2218yescomplemented
52#14582788C2218yescomplemented
53#14582781C2218yescomplemented
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C22×C4⋊C4×C43C2211yescharacteristic
60C22×C4⋊C4×C43C2211yescharacteristic
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C43×#398C2218yescomplemented
64C2×#95×C43C2211yescharacteristic
65C2×#95×C43C2211yescharacteristic
66C2×#95×C43C2211yescharacteristic
67C24×D43C2311yescharacteristic
68C24×D43C2311yescharacteristic
69C24×D43C2311yescharacteristic
70C22×D172—24no—
71C22×D172—42no—
72C22×D172—42no—
73C22×D172—42no—
74C22×D172—42no—
75C22×D172—42no—
76C22×D172—42no—
77C22×D172—42no—
78C22×D172—42no—
79C22×D172C2314yes—
80C22×D172C2314yes—
81C22×D172C2314yes—
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2311yescharacteristic
87C2×C4⋊Dic43—42no—
88C2×C4⋊Dic43C2314yes—
89C2×Dic43⋊C4—24no—
90C2×Dic43⋊C4—42no—
91C2×Dic43⋊C4—42no—
92C2×Dic43⋊C4C2314yes—
93C2×Dic43⋊C4C2314yes—
94C2×Dic43⋊C4C2314yes—
95C2×(C2×D43)⋊C4—24no—
96C2×(C2×D43)⋊C4—42no—
97C2×(C2×D43)⋊C4—42no—
98C2×(C2×D43)⋊C4—42no—
99C2×(C2×D43)⋊C4—42no—
100C2×(C2×D43)⋊C4—42no—
101C2×(C2×D43)⋊C4—42no—
102C2×(C2×D43)⋊C4—42no—
103C2×(C2×D43)⋊C4—42no—
104C2×(C2×D43)⋊C4—42no—
105C2×(C2×D43)⋊C4—42no—
106C2×(C2×D43)⋊C4—42no—
107C2×(C2×D43)⋊C4—42no—
108C2×(C2×D43)⋊C4—42no—
109C2×(C2×D43)⋊C4—42no—
110C2×(C2×D43)⋊C4C2314yes—
111C2×(C2×D43)⋊C4C2314yes—
112C2×(C2×D43)⋊C4C2314yes—
113C2×(C2×D43)⋊C4C2314yes—
114C2×(C2×D43)⋊C4C2314yes—
115C2×(C2×D43)⋊C4C2314yes—
116C2×(C2×D43)⋊C4C2314yes—
117C2×(C2×D43)⋊C4C2314yes—
118C2×(C2×D43)⋊C4C2314yes—
119C2×(C2×D43)⋊C4C2314yes—
120C2×(C2×D43)⋊C4C2314yes—
121C2×(C2×D43)⋊C4C2314yes—
122C2×(C2×D43)⋊C4C2314yes—
123C2×(C2×D43)⋊C4C2314yes—
124C2×(C2×D43)⋊C4C2314yes—
125C2×C4×Dic43—42no—
126C2×C4×Dic43C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C43⋊#95C2314yes—
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43—42no—
140C2×C4⋊C4×C43—42no—
141C2×C4⋊C4×C43—42no—
142C2×C4⋊C4×C43—42no—
143C2×C4⋊C4×C43C2314yes—
144C2×C4⋊C4×C43C2314yes—
145C2×C4⋊C4×C43C2314yes—
146C2×C4⋊C4×C43C2314yes—
147#95×C43C2314yes—
148#95×C43C2314yes—
149#95×C43C2314yes—
150C24×C43C2411yescharacteristic
151C23×D43—22no—
152C23×D43—22no—
153C23×D43—22no—
154C23×D43—22no—
155C23×D43—22no—
156C23×D43—22no—
157C23×D43—22no—
158C23×D43—22no—
159C23×D43—22no—
160C23×D43—22no—
161C23×D43—22no—
162C23×D43—22no—
163C23×D43—22no—
164C23×D43—22no—
165C23×D43—22no—
166C23×D43—22no—
167C23×D43—22no—
168C23×D43—22no—
169C23×D43—22no—
170C23×D43—22no—
171C23×D43—22no—
172C23×D43C2412yes—
173C23×D43C2412yes—
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×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—22no—
195C22×C4×C43#4114yes—
196C22×C4×C43C2412yes—
197C22×C4×C43C2412yes—
198C22×C4×C43C2412yes—
199C22×C4×C43C2412yes—
200C22×C4×C43C2412yes—
201C22×C4×C43C2412yes—
202C22×C4×C43C2412yes—
203C22×Dic43—22no—
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×Dic43C2412yes—
219C22×Dic43C2412yes—
220C22×Dic43C2412yes—
221C22×Dic43C2412yes—
222C22×Dic43C2412yes—
223C2×D172—28no—
224C2×D172—44no—
225C2×D172—44no—
226C2×D172—44no—
227C2×D172—44no—
228C2×D172—44no—
229C2×D172—44no—
230C2×D172—44no—
231C2×D172—44no—
232C2×D172—416no—
233C2×D172—416no—
234C2×D172—416no—
235C4⋊C4×C43—44no—
236C4⋊C4×C43—44no—
237C4⋊C4×C43—44no—
238C4⋊C4×C43—44no—
239(C2×D43)⋊C4—28no—
240(C2×D43)⋊C4—44no—
241(C2×D43)⋊C4—44no—
242(C2×D43)⋊C4—44no—
243(C2×D43)⋊C4—44no—
244(C2×D43)⋊C4—44no—
245(C2×D43)⋊C4—44no—
246(C2×D43)⋊C4—44no—
247(C2×D43)⋊C4—44no—
248(C2×D43)⋊C4—44no—
249(C2×D43)⋊C4—44no—
250(C2×D43)⋊C4—44no—
251(C2×D43)⋊C4—44no—
252(C2×D43)⋊C4—44no—
253(C2×D43)⋊C4—44no—
254C4⋊Dic43—44no—
255Dic43⋊C4—28no—
256Dic43⋊C4—44no—
257Dic43⋊C4—44no—
258C4×Dic43—44no—
259C23×C43C2×#4112yes—
260C23×C43H(5,𝔽2)12yes—
261C23×C43H(5,𝔽2)12yes—
262C23×C43H(5,𝔽2)12yes—
263C23×C43H(5,𝔽2)12yes—
264C23×C43H(5,𝔽2)12yes—
265C23×C432−1+412yes—
266C23×C43C2511yescharacteristic
267C22×D43—22no—
268C22×D43—22no—
269C22×D43—22no—
270C22×D43—22no—
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—44no—
289C22×D43—44no—
290C22×D43—44no—
291C22×D43—44no—
292C22×D43—44no—
293C22×D43—44no—
294C22×D43—44no—
295C22×D43—44no—
296C22×D43—44no—
297C22×D43—44no—
298C22×D43—44no—
299C22×D43—44no—
300C22×D43—44no—
301C22×D43—44no—
302C22×D43—44no—
303C22×D43—44no—
304C22×D43—44no—
305C22×D43—44no—
306C22×D43—44no—
307C22×D43—44no—
308C22×D43—44no—
309C2×C4×C43—28no—
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—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—44no—
331C2×C4×C43—44no—
332C2×C4×C43—44no—
333C2×C4×C43—44no—
334C2×C4×C43—44no—
335C2×C4×C43—44no—
336C2×C4×C43C2×#4114yes—
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—22no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—44no—
353C2×Dic43—44no—
354C2×Dic43—44no—
355C2×Dic43—44no—
356C2×Dic43—44no—
357D172—416no—
358D172—416no—
359D172—416no—
360C2×#2829—431nomaximal, Sylow
361C22×C43#53814yes—
362C22×C43#54014yes—
363C22×C43#54214yes—
364C22×C43#56014yes—
365C22×C43#56014yes—
366C22×C43#56214yes—
367C22×C43#56214yes—
368C22×C43C22×#4111yescharacteristic
369C22×C43C2×H(5,𝔽2)11yescharacteristic
370C22×C43C2×H(5,𝔽2)11yescharacteristic
371C22×C43C2×H(5,𝔽2)11yescharacteristic
372C22×C43C2×H(5,𝔽2)11yescharacteristic
373C22×C43C2×H(5,𝔽2)11yescharacteristic
374C22×C43C2×2−1+411yescharacteristic
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—42no—
390C2×D43—42no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—42no—
396C2×D43—88no—
397C2×D43—88no—
398C2×D43—88no—
399C4×C43—24no—
400C4×C43—42no—
401C4×C43—42no—
402C4×C43—42no—
403C4×C43—42no—
404C4×C43—42no—
405C4×C43—42no—
406Dic43—42no—
407Dic43—42no—
408Dic43—42no—
409Dic43—42no—
410Dic43—42no—
411#2829—4316no—
412C2×#399—431no—
413C2×#398D4311yescharacteristic, complemented
414C2×#397—431no—
415C2×#397—431no—
416C2×#396—431no—
417C2×#396—431no—
418C2×#394—431no—
419C2×#394—431no—
420C2×#394—431no—
421C2×#394—431no—
422C2×#394—431no—
423C2×#392—431no—
424C2×#390—431no—
425C2×#388—431no—
426C2×#387—431no—
427C2×C43#282918yescomplemented
428C2×C43C2×#53811yescharacteristic
429C2×C43C2×#54011yescharacteristic
430C2×C43C2×#54211yescharacteristic
431C2×C43C2×#56011yescharacteristic
432C2×C43C2×#56011yescharacteristic
433C2×C43C2×#56211yescharacteristic
434C2×C43C2×#56211yescharacteristic
435D43—82no—
436D43—82no—
437D43—82no—
438C23×D4—431no—
439C23×D4—431no—
440C23×D4—431no—
441C22×C4⋊C4—431no—
442C22×C4⋊C4—431no—
443C22×C4⋊C4—431no—
444C22×C4⋊C4—431no—
445C22×C4⋊C4C2×D4311yescharacteristic
446C22×C4⋊C4C2×D4311yescharacteristic
447C22×C4⋊C4C2×D4311yescharacteristic
448C22×C4⋊C4C2×D4311yescharacteristic
449C22×C22⋊C4—431no—
450C22×C22⋊C4—431no—
451C22×C22⋊C4—431no—
452C22×C22⋊C4—431no—
453C22×C22⋊C4—431no—
454C22×C22⋊C4—431no—
455C22×C22⋊C4—431no—
456C22×C22⋊C4—431no—
457C22×C22⋊C4—431no—
458C22×C22⋊C4—431no—
459C22×C22⋊C4—431no—
460C22×C22⋊C4—431no—
461C22×C22⋊C4—431no—
462C22×C22⋊C4—431no—
463C22×C22⋊C4—431no—
464C22×C42—431no—
465#399—438no—
466#398C2×D4318yescomplemented
467#397—438no—
468#397—438no—
469#396—438no—
470#396—438no—
471#394—438no—
472#394—438no—
473#394—438no—
474#394—438no—
475#394—438no—
476#392—438no—
477#390—438no—
478#388—438no—
479#387—438no—
480C2×#95—431no—
481C2×#95—431no—
482C2×#95—431no—
483C2×#95—431no—
484C2×#95—431no—
485C2×#95C2×D4311yescharacteristic
486C2×#95C2×D4311yescharacteristic
487C2×#95C2×D4311yescharacteristic
488C43C2×#282911yescharacteristic, complemented, Sylow
489C25—431no—
490C25—431no—
491C25—431no—
492C22×D4—434no—
493C22×D4—434no—
494C22×D4—434no—
495C22×D4—864no—
496C22×D4—1722no—
497C22×D4—1722no—
498C22×D4—1722no—
499C22×D4—1722no—
500C22×D4—1722no—
501C22×D4—1722no—
502C22×D4—1722no—
503C22×D4—1722no—
504C23×C4—431no—
505C23×C4—431no—
506C23×C4—431no—
507C23×C4—431no—
508C23×C4—431no—
509C23×C4C22×D4311yescharacteristic
510C23×C4C22×D4311yescharacteristic
511C23×C4C22×D4311yescharacteristic
512C23×C4C22×D4311yescharacteristic
513C23×C4C22×D4311yescharacteristic
514C23×C4C22×D4311yescharacteristic
515C23×C4C22×D4311yescharacteristic
516C2×C4⋊C4—42no—
517C2×C4⋊C4—42no—
518C2×C4⋊C4—42no—
519C2×C4⋊C4—42no—
520C2×C4⋊C4—434no—
521C2×C4⋊C4—434no—
522C2×C4⋊C4—434no—
523C2×C4⋊C4—434no—
524C2×C4⋊C4—864no—
525C2×C4⋊C4—1722no—
526C2×C4⋊C4—1722no—
527C2×C4⋊C4—1722no—
528C2×C4⋊C4C22×D4314yes—
529C2×C4⋊C4C22×D4314yes—
530C2×C4⋊C4C22×D4314yes—
531C2×C4⋊C4C22×D4314yes—
532C2×C22⋊C4—434no—
533C2×C22⋊C4—434no—
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—434no—
543C2×C22⋊C4—434no—
544C2×C22⋊C4—434no—
545C2×C22⋊C4—434no—
546C2×C22⋊C4—434no—
547C2×C22⋊C4—864no—
548C2×C22⋊C4—1722no—
549C2×C22⋊C4—1722no—
550C2×C22⋊C4—1722no—
551C2×C22⋊C4—1722no—
552C2×C22⋊C4—1722no—
553C2×C22⋊C4—1722no—
554C2×C22⋊C4—1722no—
555C2×C22⋊C4—1722no—
556C2×C22⋊C4—1722no—
557C2×C22⋊C4—1722no—
558C2×C22⋊C4—1722no—
559C2×C22⋊C4—1722no—
560C2×C22⋊C4—1722no—
561C2×C22⋊C4—1722no—
562C2×C42—434no—
563C2×C42—1722no—
564#95—434no—
565#95—434no—
566#95—434no—
567#95—434no—
568#95—434no—
569#95C22×D4314yes—
570#95C22×D4314yes—
571#95C22×D4314yes—
572C24—432no—
573C24—432no—
574C24—432no—
575C24—862no—
576C24—862no—
577C24—862no—
578C24—862no—
579C24—862no—
580C24—862no—
581C24—862no—
582C24—862no—
583C24—862no—
584C24—862no—
585C24—862no—
586C24—862no—
587C24—862no—
588C24—862no—
589C24—862no—
590C24—862no—
591C24—862no—
592C24—862no—
593C24—862no—
594C24—862no—
595C24—862no—
596C24C23×D4311yescharacteristic
597C2×D4—868no—
598C2×D4—1724no—
599C2×D4—1724no—
600C2×D4—1724no—
601C2×D4—1724no—
602C2×D4—1724no—
603C2×D4—1724no—
604C2×D4—1724no—
605C2×D4—1724no—
606C2×D4—17216no—
607C2×D4—17216no—
608C2×D4—17216no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—432no—
630C22×C4—432no—
631C22×C4—432no—
632C22×C4—432no—
633C22×C4—432no—
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—862no—
644C22×C4—862no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—862no—
648C22×C4—862no—
649C22×C4#1062190214yes—
650C22×C4C23×D4312yes—
651C22×C4C23×D4312yes—
652C22×C4C23×D4312yes—
653C22×C4C23×D4312yes—
654C22×C4C23×D4312yes—
655C22×C4C23×D4312yes—
656C22×C4C23×D4312yes—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—868no—
662C4⋊C4—1724no—
663C4⋊C4—1724no—
664C4⋊C4—1724no—
665C22⋊C4—868no—
666C22⋊C4—1724no—
667C22⋊C4—1724no—
668C22⋊C4—1724no—
669C22⋊C4—1724no—
670C22⋊C4—1724no—
671C22⋊C4—1724no—
672C22⋊C4—1724no—
673C22⋊C4—1724no—
674C22⋊C4—1724no—
675C22⋊C4—1724no—
676C22⋊C4—1724no—
677C22⋊C4—1724no—
678C22⋊C4—1724no—
679C22⋊C4—1724no—
680C42—1724no—
681C23—862no—
682C23—862no—
683C23—862no—
684C23—862no—
685C23—862no—
686C23—862no—
687C23—862no—
688C23—862no—
689C23—862no—
690C23—862no—
691C23—862no—
692C23—862no—
693C23—862no—
694C23—862no—
695C23—862no—
696C23—862no—
697C23—862no—
698C23—862no—
699C23—862no—
700C23—862no—
701C23—862no—
702C23—1724no—
703C23—1724no—
704C23—1724no—
705C23—1724no—
706C23—1724no—
707C23—1724no—
708C23—1724no—
709C23—1724no—
710C23—1724no—
711C23—1724no—
712C23—1724no—
713C23—1724no—
714C23—1724no—
715C23—1724no—
716C23—1724no—
717C23—1724no—
718C23—1724no—
719C23—1724no—
720C23—1724no—
721C23—1724no—
722C23—1724no—
723C23C2×#1062190212yes—
724C23#1306337012yes—
725C23#1306337012yes—
726C23#1306337112yes—
727C23#1306337112yes—
728C23#1306337112yes—
729C23#1306337312yes—
730C23C24×D4311yescharacteristic
731D4—17216no—
732D4—17216no—
733D4—17216no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—28no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—862no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—862no—
776C2×C4—1724no—
777C2×C4—1724no—
778C2×C4—1724no—
779C2×C4—1724no—
780C2×C4—1724no—
781C2×C4C2×#1062190214yes—
782C22—3448no—
783C22—3448no—
784C22—3448no—
785C22—1722no—
786C22—1722no—
787C22—1722no—
788C22—1722no—
789C22—1722no—
790C22—1722no—
791C22—1722no—
792C22—1722no—
793C22—1722no—
794C22—1722no—
795C22—1722no—
796C22—1722no—
797C22—1722no—
798C22—1722no—
799C22—1722no—
800C22—1722no—
801C22—1722no—
802C22—1722no—
803C22—1722no—
804C22—1722no—
805C22—1722no—
806C22#1458348914yes—
807C22#1458350514yes—
808C22#1458352314yes—
809C22#1458363714yes—
810C22#1458363914yes—
811C22#1458364514yes—
812C22#1458364714yes—
813C22C22×#1062190211yescharacteristic
814C22C2×#1306337011yescharacteristic
815C22C2×#1306337011yescharacteristic
816C22C2×#1306337111yescharacteristic
817C22C2×#1306337111yescharacteristic
818C22C2×#1306337111yescharacteristic
819C22C2×#1306337311yescharacteristic
820C4—24no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—42no—
826C4—42no—
827C4—1722no—
828C4—1722no—
829C4—1722no—
830C4—1722no—
831C4—1722no—
832C2—3442no—
833C2—3442no—
834C2—3442no—
835C2#1914273318yesdirect product factor
836C2C2×#1458348911yescharacteristic
837C2C2×#1458350511yescharacteristic
838C2C2×#1458352311yescharacteristic
839C2C2×#1458363711yescharacteristic
840C2C2×#1458363911yescharacteristic
841C2C2×#1458364511yescharacteristic
842C2C2×#1458364711yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#398C2
socleC24×C43C24
prime radicalC2×#14582809C2
hypercenterC2×#398D43
hypocenterC43C2×#2829
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. #19142733C2direct (N × H)
2. C2×#14582834C2semidirect
3. C2×#14582826C2semidirect
4. C2×#14582825C2semidirect
5. C2×#14582821C2semidirect
6. C2×#14582821C2semidirect
7. C2×#14582817C2semidirect
8. C2×#14582817C2semidirect
9. C2×#14582816C2semidirect
10. C2×#14582816C2semidirect
11. C2×#14582816C2semidirect
13. C2×#14582800C2semidirect
14. C2×#14582788C2semidirect
15. C2×#14582781C2semidirect
16. C2×C43×#398C2semidirect
40. #14582834C22semidirect
41. #14582826C22semidirect
42. #14582825C22semidirect
43. #14582821C22semidirect
44. #14582821C22semidirect
45. #14582817C22semidirect
46. #14582817C22semidirect
47. #14582816C22semidirect
48. #14582816C22semidirect
49. #14582816C22semidirect
51. #14582800C22semidirect
52. #14582788C22semidirect
53. #14582781C22semidirect
63. C43×#398C22semidirect
413. C2×#398D43semidirect
427. C2×C43#2829semidirect
466. #398C2×D43semidirect
488. C43C2×#2829semidirect
835. C2#19142733direct (N × H)

Maximal subgroups

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

subgroupindex
#191427332
C2×#145828342
C2×#145828262
C2×#145828252
C2×#145828212
C2×#145828172
C2×#145828162
C2×#145828092
C2×#145828002
C2×#145827882
C2×#145827812
C2×C43×#3982
C2×#282943