Finite Group Databasebeta

← C2×#19138259 #25264023

Subgroups — C2×#19138259 #25264023

Order 11008.

4926 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063305C211yesmaximal, characteristic, complemented
2C22×#13063302C211yesmaximal, characteristic, complemented
3C23×(C2×D43)⋊C4C211yesmaximal, characteristic
4C22×C22⋊C4×D43C211yesmaximal, characteristic
5#19138259C2116yesmaximal, direct product factor
6C2×#14582836C211yesmaximal, characteristic, complemented
7C2×#14582821C211yesmaximal, characteristic, complemented
8C2×#14582821C211yesmaximal, characteristic, complemented
9C2×#14582812C211yesmaximal, characteristic, complemented
10C2×#14582774C211yesmaximal, characteristic, complemented
11C2×#14582773C211yesmaximal, characteristic, complemented
12C2×#14582773C211yesmaximal, characteristic, complemented
13C2×#14582759C211yesmaximal, characteristic, complemented
14C2×#14582756C211yesmaximal, characteristic, complemented
15C2×#14582754C211yesmaximal, characteristic
16C2×C43×#385C211yesmaximal, characteristic, complemented
17C25×D43C2211yescharacteristic
18C23×Dic86C2211yescharacteristic, complemented
19C24×Dic43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22C2×#13063305—28no—
23C2×#13063305C2218yescomplemented
24C2×#13063302—28no—
25C2×#13063302C2218yescomplemented
26C22×C4⋊Dic43C2211yescharacteristic, complemented
27C22×C4⋊Dic43C2211yescharacteristic, complemented
28C22×C4⋊Dic43C2211yescharacteristic, complemented
29C22×C4⋊Dic43C2211yescharacteristic, complemented
30C22×C4⋊Dic43C2211yescharacteristic, complemented
31C22×Dic43⋊C4C2211yescharacteristic, complemented
32C22×Dic43⋊C4C2211yescharacteristic, complemented
33C22×C22⋊Dic43C2211yescharacteristic
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)⋊C4C2218yes—
44C22×(C2×D43)⋊C4C2211yescharacteristic
45C22×(C2×D43)⋊C4C2211yescharacteristic
46C22×(C2×D43)⋊C4C2211yescharacteristic
47C2×C22⋊C4×D43—28no—
48C2×C22⋊C4×D43C2218yes—
49#14582836C2218yescomplemented
50#14582821C2218yescomplemented
51#14582821C2218yescomplemented
52#14582812C2218yescomplemented
53#14582774C2218yescomplemented
54#14582773C2218yescomplemented
55#14582773C2218yescomplemented
56#14582759C2218yescomplemented
57#14582756C2218yescomplemented
58#14582754C2218yes—
59C2×C43⋊#95C2211yescharacteristic, complemented
60C2×C43⋊#95C2211yescharacteristic, complemented
61C2×C43⋊#95C2211yescharacteristic, complemented
62C2×C43⋊#95C2211yescharacteristic, complemented
63C24×C4×C43C2211yescharacteristic
64C22×C4⋊C4×C43C2211yescharacteristic, complemented
65C22×C4⋊C4×C43C2211yescharacteristic, complemented
66C22×C22⋊C4×C43C2211yescharacteristic
67C22×C22⋊C4×C43C2211yescharacteristic
68C43×#385C2218yescomplemented
69C2×#95×C43C2211yescharacteristic, complemented
70C2×#95×C43C2211yescharacteristic, complemented
71C24×D43—24no—
72C24×D43—24no—
73C24×D43—24no—
74C24×D43—24no—
75C24×D43—42no—
76C24×D43—42no—
77C24×D43Q818yescomplemented
78C24×D43C2311yescharacteristic
79C24×D43C2314yes—
80C24×D43C2311yescharacteristic
81C22×Dic86—24no—
82C22×Dic86—24no—
83C22×Dic86—42no—
84C22×Dic86C2314yescomplemented
85C23×Dic43—24no—
86C23×Dic43—24no—
87C23×Dic43—42no—
88C23×Dic43C2311yescharacteristic
89C23×Dic43C2311yescharacteristic
90C23×Dic43C2311yescharacteristic
91C23×Dic43C2311yescharacteristic
92C23×Dic43C2311yescharacteristic
93C23×Dic43C2314yes—
94C23×Dic43C2311yescharacteristic
95C22×C4×D43—24no—
96C22×C4×D43—24no—
97C22×C4×D43—24no—
98C22×C4×D43—24no—
99C22×C4×D43—42no—
100C22×C4×D43—42no—
101C22×C4×D43C2314yes—
102C22×C4×D43C2314yes—
103#13063305—232no—
104#13063302—232no—
105C2×C4⋊Dic43—24no—
106C2×C4⋊Dic43—24no—
107C2×C4⋊Dic43—24no—
108C2×C4⋊Dic43—42no—
109C2×C4⋊Dic43—42no—
110C2×C4⋊Dic43C2314yescomplemented
111C2×C4⋊Dic43C2314yescomplemented
112C2×C4⋊Dic43C2314yescomplemented
113C2×C4⋊Dic43C2314yescomplemented
114C2×C4⋊Dic43C2314yescomplemented
115C2×Dic43⋊C4—24no—
116C2×Dic43⋊C4—24no—
117C2×Dic43⋊C4C2314yescomplemented
118C2×Dic43⋊C4C2314yescomplemented
119C2×C22⋊Dic43—24no—
120C2×C22⋊Dic43—24no—
121C2×C22⋊Dic43C2314yes—
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)⋊C4—42no—
133C2×(C2×D43)⋊C4D418yes—
134C2×(C2×D43)⋊C4C2314yes—
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)⋊C4C2314yes—
144C22⋊C4×D43—232no—
145C43⋊#95C2314yescomplemented
146C43⋊#95C2314yescomplemented
147C43⋊#95C2314yescomplemented
148C43⋊#95C2314yescomplemented
149C25×C43C2311yescharacteristic
150C23×C4×C43—24no—
151C23×C4×C43—24no—
152C23×C4×C43—42no—
153C23×C4×C43C2311yescharacteristic
154C23×C4×C43C2311yescharacteristic
155C23×C4×C43C2311yescharacteristic
156C23×C4×C43C2314yes—
157C23×C4×C43C2311yescharacteristic
158C23×C4×C43C2311yescharacteristic
159C23×C4×C43C2311yescharacteristic
160C2×C4⋊C4×C43—24no—
161C2×C4⋊C4×C43—42no—
162C2×C4⋊C4×C43C2314yescomplemented
163C2×C4⋊C4×C43C2314yescomplemented
164C2×C22⋊C4×C43—24no—
165C2×C22⋊C4×C43D418yes—
166C2×C22⋊C4×C43C2314yes—
167C2×C22⋊C4×C43C2314yes—
168#95×C43C2314yescomplemented
169#95×C43C2314yescomplemented
170C24×C43—22no—
171C24×C43—22no—
172C24×C43—22no—
173C24×C43—22no—
174C24×C43C2×D414yes—
175C24×C43C2×Q814yes—
176C24×C43#4114yes—
177C24×C43C2412yes—
178C24×C43C2411yescharacteristic
179C23×D43—22no—
180C23×D43—22no—
181C23×D43—22no—
182C23×D43—22no—
183C23×D43—232no—
184C23×D43—28no—
185C23×D43—22no—
186C23×D43—22no—
187C23×D43—28no—
188C23×D43—22no—
189C23×D43—22no—
190C23×D43—22no—
191C23×D43—22no—
192C23×D43—232no—
193C23×D43—28no—
194C23×D43—28no—
195C23×D43—416no—
196C23×D43—44no—
197C23×D43—44no—
198C23×D43—416no—
199C23×D43—416no—
200C23×D43—416no—
201C23×D43—416no—
202C23×D43C2×D414yes—
203C23×D43C2×Q814yes—
204C23×D43C2×Q814yes—
205C23×D43C2×Q8116yescomplemented
206C23×D43#4114yes—
207C23×D43C2412yes—
208C23×D43C2412yes—
209C22×C4×C43—28no—
210C22×C4×C43—22no—
211C22×C4×C43—22no—
212C22×C4×C43—22no—
213C22×C4×C43—22no—
214C22×C4×C43—22no—
215C22×C4×C43—22no—
216C22×C4×C43—22no—
217C22×C4×C43—28no—
218C22×C4×C43—22no—
219C22×C4×C43—22no—
220C22×C4×C43—22no—
221C22×C4×C43—22no—
222C22×C4×C43—22no—
223C22×C4×C43—22no—
224C22×C4×C43—22no—
225C22×C4×C43—22no—
226C22×C4×C43—44no—
227C22×C4×C43—416no—
228C22×C4×C43C2×D414yes—
229C22×C4×C43C2×D414yes—
230C22×C4×C43C2×D414yes—
231C22×C4×C43C2412yes—
232C22×C4×C43C2412yes—
233C22×C4×C43C2412yes—
234C22×C4×C43C2412yes—
235C22×C4×C43C2412yes—
236C22×C4×C43C2412yes—
237C22×Dic43—28no—
238C22×Dic43—22no—
239C22×Dic43—22no—
240C22×Dic43—22no—
241C22×Dic43—22no—
242C22×Dic43—22no—
243C22×Dic43—22no—
244C22×Dic43—22no—
245C22×Dic43—22no—
246C22×Dic43—22no—
247C22×Dic43—28no—
248C22×Dic43—22no—
249C22×Dic43—22no—
250C22×Dic43—22no—
251C22×Dic43—22no—
252C22×Dic43—22no—
253C22×Dic43—22no—
254C22×Dic43—22no—
255C22×Dic43—22no—
256C22×Dic43—44no—
257C22×Dic43—416no—
258C22×Dic43C2×D414yes—
259C22×Dic43C2412yes—
260C22×Dic43C2412yes—
261C22×Dic43C2412yes—
262C22×Dic43C2412yes—
263C22×Dic43C2412yes—
264C22×Dic43C2412yes—
265C2×C4×D43—28no—
266C2×C4×D43—28no—
267C2×C4×D43—28no—
268C2×C4×D43—28no—
269C2×C4×D43—44no—
270C2×C4×D43—44no—
271C2×C4×D43—416no—
272C2×C4×D43—416no—
273C2×Dic86—28no—
274C2×Dic86—28no—
275C2×Dic86—44no—
276C2×Dic86—416no—
277C4⋊C4×C43—28no—
278C4⋊C4×C43—44no—
279C22⋊C4×C43—28no—
280C22⋊C4×C43C2×D4116yes—
281C22⋊Dic43—28no—
282C22⋊Dic43—28no—
283(C2×D43)⋊C4—28no—
284(C2×D43)⋊C4—28no—
285(C2×D43)⋊C4—28no—
286(C2×D43)⋊C4—28no—
287(C2×D43)⋊C4—28no—
288(C2×D43)⋊C4—28no—
289(C2×D43)⋊C4—28no—
290(C2×D43)⋊C4—44no—
291(C2×D43)⋊C4—44no—
292(C2×D43)⋊C4C2×D4116yes—
293C4⋊Dic43—28no—
294C4⋊Dic43—28no—
295C4⋊Dic43—28no—
296C4⋊Dic43—44no—
297C4⋊Dic43—44no—
298Dic43⋊C4—28no—
299Dic43⋊C4—28no—
300C23×C43—28no—
301C23×C43—28no—
302C23×C43—28no—
303C23×C43—28no—
304C23×C43—28no—
305C23×C43—28no—
306C23×C43—22no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43C22⋊Q8116yescomplemented
311C23×C43C22×D412yes—
312C23×C43C22×D414yes—
313C23×C43C22×D412yes—
314C23×C43C22×Q814yes—
315C23×C43C22×Q812yes—
316C23×C43C2×#4112yes—
317C23×C43C2×#4114yes—
318C23×C43C2×#4112yes—
319C23×C43H(5,𝔽2)12yes—
320C23×C43H(5,𝔽2)12yes—
321C23×C43C2511yescharacteristic
322C22×D43—28no—
323C22×D43—28no—
324C22×D43—28no—
325C22×D43—28no—
326C22×D43—28no—
327C22×D43—28no—
328C22×D43—22no—
329C22×D43—22no—
330C22×D43—22no—
331C22×D43—22no—
332C22×D43—28no—
333C22×D43—28no—
334C22×D43—232no—
335C22×D43—28no—
336C22×D43—22no—
337C22×D43—22no—
338C22×D43—22no—
339C22×D43—22no—
340C22×D43—22no—
341C22×D43—22no—
342C22×D43—232no—
343C22×D43—416no—
344C22×D43—4128no—
345C22×D43—416no—
346C22×D43—416no—
347C22×D43—416no—
348C22×D43—416no—
349C22×D43—44no—
350C22×D43—44no—
351C22×D43—44no—
352C22×D43—44no—
353C22×D43C22⋊Q8116yescomplemented
354C22×D43C22×D414yes—
355C22×D43C22×Q814yes—
356C22×D43C22×Q814yes—
357C22×D43C2×#4114yes—
358C2×C4×C43—28no—
359C2×C4×C43—28no—
360C2×C4×C43—28no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—22no—
365C2×C4×C43—22no—
366C2×C4×C43—22no—
367C2×C4×C43—22no—
368C2×C4×C43—22no—
369C2×C4×C43—22no—
370C2×C4×C43—22no—
371C2×C4×C43—22no—
372C2×C4×C43—22no—
373C2×C4×C43—22no—
374C2×C4×C43—22no—
375C2×C4×C43—22no—
376C2×C4×C43—416no—
377C2×C4×C43—44no—
378C2×C4×C43—44no—
379C2×C4×C43—44no—
380C2×C4×C43C22×D414yes—
381C2×C4×C43C22×D414yes—
382C2×C4×C43C22×D414yes—
383C2×Dic43—28no—
384C2×Dic43—22no—
385C2×Dic43—22no—
386C2×Dic43—22no—
387C2×Dic43—22no—
388C2×Dic43—22no—
389C2×Dic43—22no—
390C2×Dic43—22no—
391C2×Dic43—22no—
392C2×Dic43—22no—
393C2×Dic43—22no—
394C2×Dic43—22no—
395C2×Dic43—22no—
396C2×Dic43—22no—
397C2×Dic43—22no—
398C2×Dic43—22no—
399C2×Dic43—22no—
400C2×Dic43—22no—
401C2×Dic43—416no—
402C2×Dic43—44no—
403C2×Dic43—44no—
404C2×Dic43—44no—
405C2×Dic43—44no—
406C2×Dic43—44no—
407C2×Dic43C22×D414yes—
408C4×D43—416no—
409C4×D43—416no—
410Dic86—416no—
411C2×#2437—431nomaximal, Sylow
412C22×C43—24no—
413C22×C43—24no—
414C22×C43—232no—
415C22×C43—24no—
416C22×C43—24no—
417C22×C43—24no—
418C22×C43—24no—
419C22×C43C2×C22⋊Q814yes—
420C22×C43C2×C22⋊Q814yes—
421C22×C43C2×C22⋊Q818yescomplemented
422C22×C43#54314yes—
423C22×C43D4214yes—
424C22×C43#54614yes—
425C22×C43#54614yes—
426C22×C43#55114yes—
427C22×C43C23×D411yescharacteristic
428C22×C43C23×D411yescharacteristic
429C22×C43C23×Q811yescharacteristic
430C22×C43C22×#4111yescharacteristic
431C22×C43C22×#4111yescharacteristic
432C22×C43C2×H(5,𝔽2)11yescharacteristic
433C22×C43C2×H(5,𝔽2)11yescharacteristic
434C2×D43—24no—
435C2×D43—24no—
436C2×D43—232no—
437C2×D43—24no—
438C2×D43—24no—
439C2×D43—24no—
440C2×D43—24no—
441C2×D43—24no—
442C2×D43—24no—
443C2×D43—24no—
444C2×D43—464no—
445C2×D43—416no—
446C2×D43—42no—
447C2×D43—42no—
448C2×D43—42no—
449C2×D43—42no—
450C2×D43C2×C22⋊Q818yescomplemented
451C4×C43—24no—
452C4×C43—24no—
453C4×C43—24no—
454C4×C43—42no—
455C4×C43—42no—
456C4×C43—42no—
457Dic43—24no—
458Dic43—42no—
459Dic43—42no—
460Dic43—42no—
461Dic43—42no—
462Dic43—42no—
463C22×C22⋊Q8—431no—
464C22×C22⋊Q8—431no—
465C23×C22⋊C4—431no—
466C23×C22⋊C4—431no—
467#2437—4316no—
468C2×#399—431no—
469C2×#396—431no—
470C2×#396—431no—
471C2×#393—431no—
472C2×#385—431no—
473C2×#385—431no—
474C2×#385—431no—
475C2×#385D4311yescharacteristic, complemented
476C2×#380—431no—
477C2×#380—431no—
478C2×#379—431no—
479C2×C43—28no—
480C2×C43#243718yescomplemented
481C2×C43C22×C22⋊Q811yescharacteristic
482C2×C43C22×C22⋊Q811yescharacteristic
483C2×C43C2×#54311yescharacteristic
484C2×C43C2×D4211yescharacteristic
485C2×C43C2×#54611yescharacteristic
486C2×C43C2×#54611yescharacteristic
487C2×C43C2×#55111yescharacteristic
488D43—28no—
489D43—44no—
490C26—431no—
491C23×Q8—431no—
492C24×C4—431no—
493C24×C4—431no—
494C24×C4—431no—
495C24×C4C2×D4311yescharacteristic
496C2×C22⋊Q8—438no—
497C2×C22⋊Q8—438no—
498C2×C22⋊Q8—868no—
499C2×C22⋊Q8—868no—
500C22×C4⋊C4—431no—
501C22×C4⋊C4—431no—
502C22×C4⋊C4—431no—
503C22×C4⋊C4—431no—
504C22×C4⋊C4—431no—
505C22×C4⋊C4—431no—
506C22×C4⋊C4—431no—
507C22×C4⋊C4C2×D4311yescharacteristic, complemented
508C22×C4⋊C4C2×D4311yescharacteristic, complemented
509C22×C22⋊C4—431no—
510C22×C22⋊C4—431no—
511C22×C22⋊C4—431no—
512C22×C22⋊C4—431no—
513C22×C22⋊C4—431no—
514C22×C22⋊C4—431no—
515C22×C22⋊C4—431no—
516C22×C22⋊C4—438no—
517C22×C22⋊C4—431no—
518C22×C22⋊C4—431no—
519C22×C22⋊C4—431no—
520C22×C22⋊C4—431no—
521C22×C22⋊C4—431no—
522C22×C22⋊C4—438no—
523C22×C22⋊C4—868no—
524C22×C22⋊C4—868no—
525C22×C22⋊C4C2×D4311yescharacteristic
526C22×C22⋊C4C2×D4311yescharacteristic
527#399—438no—
528#396—438no—
529#396—438no—
530#393—438no—
531#385—438no—
532#385—438no—
533#385—438no—
534#385C2×D4318yescomplemented
535#380—438no—
536#380—438no—
537#379—438no—
538C2×#95—431no—
539C2×#95—431no—
540C2×#95—431no—
541C2×#95—431no—
542C2×#95C2×D4311yescharacteristic, complemented
543C2×#95C2×D4311yescharacteristic, complemented
544C43C2×#243711yescharacteristic, complemented, Sylow
545C25—431no—
546C25—431no—
547C25—438no—
548C25—434no—
549C25—864no—
550C25—864no—
551C25—864no—
552C25—864no—
553C25—1722no—
554C25—1722no—
555C25C22×D4311yescharacteristic
556C22×Q8—434no—
557C22×Q8—864no—
558C22×Q8—864no—
559C22×Q8—1722no—
560C23×C4—24no—
561C23×C4—24no—
562C23×C4—42no—
563C23×C4—431no—
564C23×C4—431no—
565C23×C4—431no—
566C23×C4—431no—
567C23×C4—431no—
568C23×C4—431no—
569C23×C4—434no—
570C23×C4—434no—
571C23×C4—434no—
572C23×C4—864no—
573C23×C4—864no—
574C23×C4—864no—
575C23×C4—864no—
576C23×C4—864no—
577C23×C4—864no—
578C23×C4—1722no—
579C23×C4—1722no—
580C23×C4—1722no—
581C23×C4C22×D4311yescharacteristic
582C23×C4C22×D4311yescharacteristic
583C23×C4C22×D4311yescharacteristic
584C23×C4C22×D4314yes—
585C23×C4C22×D4311yescharacteristic
586C23×C4C22×D4311yescharacteristic
587C23×C4C22×D4311yescharacteristic
588C22⋊Q8—8632no—
589C22⋊Q8—8632no—
590C2×C4⋊C4—24no—
591C2×C4⋊C4—42no—
592C2×C4⋊C4—434no—
593C2×C4⋊C4—434no—
594C2×C4⋊C4—434no—
595C2×C4⋊C4—434no—
596C2×C4⋊C4—434no—
597C2×C4⋊C4—434no—
598C2×C4⋊C4—434no—
599C2×C4⋊C4—864no—
600C2×C4⋊C4—864no—
601C2×C4⋊C4—864no—
602C2×C4⋊C4—864no—
603C2×C4⋊C4—864no—
604C2×C4⋊C4—1722no—
605C2×C4⋊C4—1722no—
606C2×C4⋊C4C22×D4314yescomplemented
607C2×C4⋊C4C22×D4314yescomplemented
608C2×C22⋊C4—24no—
609C2×C22⋊C4—438no—
610C2×C22⋊C4—434no—
611C2×C22⋊C4—434no—
612C2×C22⋊C4—434no—
613C2×C22⋊C4—434no—
614C2×C22⋊C4—434no—
615C2×C22⋊C4—434no—
616C2×C22⋊C4—434no—
617C2×C22⋊C4—434no—
618C2×C22⋊C4—434no—
619C2×C22⋊C4—434no—
620C2×C22⋊C4—434no—
621C2×C22⋊C4—434no—
622C2×C22⋊C4—8632no—
623C2×C22⋊C4—864no—
624C2×C22⋊C4—864no—
625C2×C22⋊C4—864no—
626C2×C22⋊C4—864no—
627C2×C22⋊C4—864no—
628C2×C22⋊C4—864no—
629C2×C22⋊C4—864no—
630C2×C22⋊C4—864no—
631C2×C22⋊C4—864no—
632C2×C22⋊C4—8632no—
633C2×C22⋊C4—1722no—
634C2×C22⋊C4—1722no—
635C2×C22⋊C4D17218yes—
636C2×C22⋊C4C22×D4314yes—
637C2×C22⋊C4C22×D4314yes—
638#95—434no—
639#95—434no—
640#95—434no—
641#95—434no—
642#95C22×D4314yescomplemented
643#95C22×D4314yescomplemented
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—434no—
649C24—434no—
650C24—434no—
651C24—432no—
652C24—434no—
653C24—432no—
654C24—4316no—
655C24—868no—
656C24—8632no—
657C24—868no—
658C24—862no—
659C24—862no—
660C24—862no—
661C24—862no—
662C24—8632no—
663C24—862no—
664C24—868no—
665C24—862no—
666C24—862no—
667C24—868no—
668C24—862no—
669C24—862no—
670C24—862no—
671C24—1724no—
672C24—1724no—
673C24—17216no—
674C24—17216no—
675C24—17216no—
676C24—17216no—
677C24—17216no—
678C24C2×D17214yes—
679C24#1062190014yes—
680C24Q8×D4314yes—
681C24C23×D4312yes—
682C24C23×D4311yescharacteristic
683C2×Q8—868no—
684C2×Q8—868no—
685C2×Q8—1724no—
686C2×Q8—17216no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—28no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—28no—
704C22×C4—44no—
705C22×C4—416no—
706C22×C4—434no—
707C22×C4—432no—
708C22×C4—432no—
709C22×C4—432no—
710C22×C4—432no—
711C22×C4—432no—
712C22×C4—432no—
713C22×C4—868no—
714C22×C4—868no—
715C22×C4—868no—
716C22×C4—862no—
717C22×C4—862no—
718C22×C4—862no—
719C22×C4—862no—
720C22×C4—862no—
721C22×C4—862no—
722C22×C4—862no—
723C22×C4—862no—
724C22×C4—862no—
725C22×C4—862no—
726C22×C4—868no—
727C22×C4—862no—
728C22×C4—862no—
729C22×C4—862no—
730C22×C4—862no—
731C22×C4—862no—
732C22×C4—862no—
733C22×C4—862no—
734C22×C4—868no—
735C22×C4—868no—
736C22×C4—1724no—
737C22×C4—1724no—
738C22×C4—17216no—
739C22×C4—17216no—
740C22×C4—1724no—
741C22×C4—17216no—
742C22×C4C2×D17214yes—
743C22×C4C2×D17214yes—
744C22×C4D4×D4314yes—
745C22×C4C23×D4312yes—
746C22×C4C23×D4312yes—
747C22×C4C23×D4312yes—
748C22×C4C23×D4312yes—
749C22×C4C23×D4312yes—
750C22×C4C23×D4312yes—
751C4⋊C4—28no—
752C4⋊C4—44no—
753C4⋊C4—868no—
754C4⋊C4—868no—
755C4⋊C4—868no—
756C4⋊C4—868no—
757C4⋊C4—868no—
758C4⋊C4—1724no—
759C4⋊C4—1724no—
760C22⋊C4—28no—
761C22⋊C4—4316no—
762C22⋊C4—868no—
763C22⋊C4—868no—
764C22⋊C4—868no—
765C22⋊C4—868no—
766C22⋊C4—868no—
767C22⋊C4—868no—
768C22⋊C4—868no—
769C22⋊C4—868no—
770C22⋊C4—868no—
771C22⋊C4—1724no—
772C22⋊C4—1724no—
773C22⋊C4C2×D172116yes—
774C23—28no—
775C23—28no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—28no—
781C23—28no—
782C23—28no—
783C23—28no—
784C23—4316no—
785C23—434no—
786C23—434no—
787C23—434no—
788C23—434no—
789C23—8632no—
790C23—868no—
791C23—868no—
792C23—862no—
793C23—862no—
794C23—862no—
795C23—862no—
796C23—868no—
797C23—868no—
798C23—868no—
799C23—868no—
800C23—868no—
801C23—868no—
802C23—8632no—
803C23—862no—
804C23—862no—
805C23—862no—
806C23—862no—
807C23—862no—
808C23—862no—
809C23—868no—
810C23—17216no—
811C23—17216no—
812C23—17216no—
813C23—17216no—
814C23—17216no—
815C23—172128no—
816C23—1724no—
817C23—1724no—
818C23—1724no—
819C23—1724no—
820C23#13063305116yescomplemented
821C23C2×D4×D4312yes—
822C23C22×D17214yes—
823C23C22×D17212yes—
824C23C2×Q8×D4314yes—
825C23C2×Q8×D4312yes—
826C23#41×D4312yes—
827C23C2×#1062190014yes—
828C23C2×#1062190012yes—
829C23#1306337012yes—
830C23#1306337112yes—
831C23C24×D4311yescharacteristic
832Q8—17216no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—28no—
840C2×C4—28no—
841C2×C4—28no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—416no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—434no—
856C2×C4—862no—
857C2×C4—862no—
858C2×C4—868no—
859C2×C4—862no—
860C2×C4—862no—
861C2×C4—862no—
862C2×C4—862no—
863C2×C4—862no—
864C2×C4—862no—
865C2×C4—862no—
866C2×C4—862no—
867C2×C4—862no—
868C2×C4—862no—
869C2×C4—862no—
870C2×C4—862no—
871C2×C4—862no—
872C2×C4—862no—
873C2×C4—862no—
874C2×C4—17216no—
875C2×C4—17216no—
876C2×C4—17216no—
877C2×C4—1724no—
878C2×C4—1724no—
879C2×C4—1724no—
880C2×C4—1724no—
881C2×C4—1724no—
882C2×C4C2×D4×D4314yes—
883C2×C4C22×D17214yes—
884C2×C4C22×D17214yes—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—232no—
891C22—24no—
892C22—438no—
893C22—864no—
894C22—864no—
895C22—864no—
896C22—864no—
897C22—864no—
898C22—8632no—
899C22—864no—
900C22—864no—
901C22—864no—
902C22—864no—
903C22—17264no—
904C22—1722no—
905C22—1722no—
906C22—1722no—
907C22—1722no—
908C22—17216no—
909C22C22⋊Q8×D4314yes—
910C22C2×#1306330514yes—
911C22C2×#1306330518yescomplemented
912C22#1458352414yes—
913C22D4×D17214yes—
914C22#1458353614yes—
915C22#1458354414yes—
916C22#1458357214yes—
917C22C22×D4×D4311yescharacteristic
918C22C23×D17211yescharacteristic
919C22C22×Q8×D4311yescharacteristic
920C22C2×#41×D4311yescharacteristic
921C22C22×#1062190011yescharacteristic
922C22C2×#1306337011yescharacteristic
923C22C2×#1306337111yescharacteristic
924C4—24no—
925C4—24no—
926C4—24no—
927C4—42no—
928C4—42no—
929C4—42no—
930C4—864no—
931C4—1722no—
932C4—1722no—
933C4—1722no—
934C4—1722no—
935C4—1722no—
936C2—28no—
937C2—868no—
938C2—1724no—
939C2#1913825918yesdirect product factor
940C2C2×C22⋊Q8×D4311yescharacteristic
941C2C22×#1306330511yescharacteristic
942C2C2×#1458352411yescharacteristic
943C2C2×D4×D17211yescharacteristic
944C2C2×#1458353611yescharacteristic
945C2C2×#1458354411yescharacteristic
946C2C2×#1458357211yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#385C2
socleC24×C43C24
prime radicalC25×D43C22
hypercenterC2×#385D43
hypocenterC43C2×#2437
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#13063305C2semidirect
2. C22×#13063302C2semidirect
5. #19138259C2direct (N × H)
6. C2×#14582836C2semidirect
7. C2×#14582821C2semidirect
8. C2×#14582821C2semidirect
9. C2×#14582812C2semidirect
10. C2×#14582774C2semidirect
11. C2×#14582773C2semidirect
12. C2×#14582773C2semidirect
13. C2×#14582759C2semidirect
14. C2×#14582756C2semidirect
16. C2×C43×#385C2semidirect
18. C23×Dic86C22semidirect
23. C2×#13063305C22semidirect
25. C2×#13063302C22semidirect
26. C22×C4⋊Dic43C22semidirect
27. C22×C4⋊Dic43C22semidirect
28. C22×C4⋊Dic43C22semidirect
29. C22×C4⋊Dic43C22semidirect
30. C22×C4⋊Dic43C22semidirect
31. C22×Dic43⋊C4C22semidirect
32. C22×Dic43⋊C4C22semidirect
49. #14582836C22semidirect
50. #14582821C22semidirect
51. #14582821C22semidirect
52. #14582812C22semidirect
53. #14582774C22semidirect
54. #14582773C22semidirect
55. #14582773C22semidirect
56. #14582759C22semidirect
57. #14582756C22semidirect
59. C2×C43⋊#95C22semidirect
60. C2×C43⋊#95C22semidirect
61. C2×C43⋊#95C22semidirect
62. C2×C43⋊#95C22semidirect
64. C22×C4⋊C4×C43C22semidirect
65. C22×C4⋊C4×C43C22semidirect
68. C43×#385C22semidirect
69. C2×#95×C43C22semidirect
70. C2×#95×C43C22semidirect
77. C24×D43Q8semidirect
84. C22×Dic86C23semidirect
110. C2×C4⋊Dic43C23semidirect
111. C2×C4⋊Dic43C23semidirect
112. C2×C4⋊Dic43C23semidirect
113. C2×C4⋊Dic43C23semidirect
114. C2×C4⋊Dic43C23semidirect
117. C2×Dic43⋊C4C23semidirect
118. C2×Dic43⋊C4C23semidirect
145. C43⋊#95C23semidirect
146. C43⋊#95C23semidirect
147. C43⋊#95C23semidirect
148. C43⋊#95C23semidirect
162. C2×C4⋊C4×C43C23semidirect
163. C2×C4⋊C4×C43C23semidirect
168. #95×C43C23semidirect
169. #95×C43C23semidirect
205. C23×D43C2×Q8semidirect
310. C23×C43C22⋊Q8semidirect
353. C22×D43C22⋊Q8semidirect
421. C22×C43C2×C22⋊Q8semidirect
450. C2×D43C2×C22⋊Q8semidirect
475. C2×#385D43semidirect
480. C2×C43#2437semidirect
507. C22×C4⋊C4C2×D43semidirect
508. C22×C4⋊C4C2×D43semidirect
534. #385C2×D43semidirect
542. C2×#95C2×D43semidirect
543. C2×#95C2×D43semidirect
544. C43C2×#2437semidirect
606. C2×C4⋊C4C22×D43semidirect
607. C2×C4⋊C4C22×D43semidirect
642. #95C22×D43semidirect
643. #95C22×D43semidirect
820. C23#13063305semidirect
911. C22C2×#13063305semidirect
939. C2#19138259direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633052
C22×#130633022
C23×(C2×D43)⋊C42
C22×C22⋊C4×D432
#191382592
C2×#145828362
C2×#145828212
C2×#145828122
C2×#145827742
C2×#145827732
C2×#145827592
C2×#145827562
C2×#145827542
C2×C43×#3852
C2×#243743