Finite Group Databasebeta

← #25111881

Subgroups — #25111881

Order 11008.

1582 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583408C211yesmaximal, characteristic
2C2×#14582971C211yesmaximal, characteristic, complemented
3C2×#14582867C211yesmaximal, characteristic, complemented
4C2×#14582862C211yesmaximal, characteristic, complemented
5#19135392C211yesmaximal, characteristic, complemented
6#19135389C211yesmaximal, characteristic, complemented
7#19134892C211yesmaximal, characteristic, complemented
8#19134892C211yesmaximal, characteristic, complemented
9#19134890C211yesmaximal, characteristic, complemented
10#19134885C211yesmaximal, characteristic, complemented
11#19134576C211yesmaximal, characteristic, complemented
12#19134506C211yesmaximal, characteristic, complemented
13#19134504C211yesmaximal, characteristic, complemented
14#19134362C211yesmaximal, characteristic, complemented
15C2×C43×#436C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic, complemented
20#14583408—24no—
21#14583408—24no—
22C2×#13063310C411yescharacteristic
23C2×#13063307C411yescharacteristic
24C2×#13063303C411yescharacteristic
25C2×#13063302C411yescharacteristic
26C2×#13063298C411yescharacteristic
27C2×#13063297C411yescharacteristic
28C2×#13063295C411yescharacteristic
29C2×#13063293C411yescharacteristic
30C2×C4×D172C2211yescharacteristic
31C2×C4×C22⋊D43C2211yescharacteristic
32C2×C4×C22⋊D43C2211yescharacteristic
33C2×#13063282C2211yescharacteristic
34#14582971—24no—
35C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
36#14582867—24no—
37#14582862—24no—
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
40C2×(C2×D43)⋊C8C2211yescharacteristic
41C2×(C2×D43)⋊C8C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic
47C2×(C2×D43)⋊C8C2211yescharacteristic
48C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
49C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
50C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
51C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
52C2×#13063236C2211yescharacteristic, complemented
53#14582653C2211yescharacteristic, complemented
54#14582653C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56#14582653C2211yescharacteristic, complemented
57C22×M16×C43C2211yescharacteristic
58C22×M16×C43C2211yescharacteristic, complemented
59C2×C4×D4×C43C2211yescharacteristic
60C43×#436—24no—
61C2×C4⋊C8×C43C2211yescharacteristic, complemented
62C2×C22⋊C8×C43C2211yescharacteristic
63C2×C22⋊C8×C43C2211yescharacteristic, complemented
64C2×C4×C8×C43C2211yescharacteristic, complemented
65C24×D43C2×C411yescharacteristic
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—22no—
69C2×#10621898—22no—
70C2×#10621898—41no—
71C2×#10621898—41no—
72C22×Dic86C2×C411yescharacteristic
73C22×D172C2×C411yescharacteristic
74C22×D172C2×C411yescharacteristic
75C22×C22⋊D43C2×C411yescharacteristic
76C22×C22⋊D43C2×C411yescharacteristic
77C22×C22⋊D43C2×C411yescharacteristic
78C22×C22⋊D43C2×C411yescharacteristic
79C23×Dic43C2×C411yescharacteristic
80C22×C4×D43—22no—
81C22×C4×D43—22no—
82C22×C4×D43—22no—
83C22×C4×D43—22no—
84C22×C4×D43—41no—
85C22×C4×D43—41no—
86C22×C4×D43C2×C411yescharacteristic
87C22×C4×D43C2×C411yescharacteristic
88C22×C4×D43C2311yescharacteristic
89C22×C4×D43C2311yescharacteristic
90C22×C4×D43C2311yescharacteristic
91C2×#10621877—22no—
92C2×#10621877—22no—
93C2×#10621877—41no—
94C22×C43⋊C8—22no—
95C22×C43⋊C8—22no—
96C22×C43⋊C8—41no—
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99C22×C43⋊C8C2311yescharacteristic
100C22×C43⋊C8C2311yescharacteristic
101#13063310—24no—
102#13063307—24no—
103#13063303—24no—
104#13063302—24no—
105#13063298—24no—
106#13063297—24no—
107#13063295—24no—
108#13063293—24no—
109C4×D172—22no—
110C4×D172—22no—
111C4×C22⋊D43—22no—
112C4×C22⋊D43—22no—
113C4×C22⋊D43—22no—
114C4×C22⋊D43—22no—
115#13063282—22no—
116#13063282—22no—
117C2×C4⋊Dic43C2×C411yescharacteristic
118C2×Dic43⋊C4C2×C411yescharacteristic
119C2×Dic43⋊C4C2×C411yescharacteristic
120C2×Dic43⋊C4C2×C411yescharacteristic
121C2×Dic43⋊C4C2×C411yescharacteristic
122C2×C22⋊Dic43C2×C411yescharacteristic
123C2×C22⋊Dic43C2×C411yescharacteristic
124C2×(C2×D43)⋊C4C2×C411yescharacteristic
125C2×(C2×D43)⋊C4C2×C411yescharacteristic
126C2×(C2×D43)⋊C4C2×C411yescharacteristic
127C2×(C2×D43)⋊C4C2×C411yescharacteristic
128C2×(C2×D43)⋊C4C2×C411yescharacteristic
129C2×(C2×D43)⋊C4C2×C411yescharacteristic
130C2×C4×Dic43C2311yescharacteristic
131C4⋊(C43⋊C8)—22no—
132C22⋊(C43⋊C8)—22no—
133C22⋊(C43⋊C8)—22no—
134(C2×D43)⋊C8—22no—
135(C2×D43)⋊C8—22no—
136(C2×D43)⋊C8—22no—
137(C2×D43)⋊C8—22no—
138(C2×D43)⋊C8—22no—
139(C2×D43)⋊C8—22no—
140(C2×D43)⋊C8—22no—
141(C2×D43)⋊C8—41no—
142(C2×D43)⋊C8—41no—
143(C2×D43)⋊C8—41no—
144(C2×D43)⋊C8—41no—
145(C2×D43)⋊C8D414yescomplemented
146#13063236—22no—
147C22×D4×C43C2×C411yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C2×M16×C43—22no—
151C2×M16×C43—22no—
152C2×M16×C43—22no—
153C2×M16×C43—22no—
154C2×M16×C43—41no—
155C2×M16×C43—41no—
156C22×C8×C43C2311yescharacteristic
157C22×C8×C43C2311yescharacteristic
158C22×C8×C43C2311yescharacteristic
159C22×C8×C43C2311yescharacteristic
160C4×D4×C43D414yes—
161C4×D4×C43D414yes—
162C2×C4⋊C4×C43C2×C411yescharacteristic
163C2×C22⋊C4×C43C2×C411yescharacteristic
164C2×C22⋊C4×C43C2×C411yescharacteristic
165C2×C42×C43C2311yescharacteristic
166C4⋊C8×C43—22no—
167C22⋊C8×C43—22no—
168C22⋊C8×C43—22no—
169C4×C8×C43—22no—
170C24×C43C22×C411yescharacteristic
171C24×C43C22×C411yescharacteristic
172C23×D43—22no—
173C23×D43—22no—
174C23×D43—22no—
175C23×D43—41no—
176C23×D43—41no—
177C23×D43—41no—
178C23×D43—41no—
179C23×D43C22×C411yescharacteristic
180C23×D43C22×C411yescharacteristic
181C23×D43C22×C411yescharacteristic
182C2×D4×C43—41no—
183C2×D4×C43—41no—
184C2×D4×C43C22⋊C414yes—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43C22×C411yescharacteristic
194C22×C4×C43C22×C411yescharacteristic
195C22×C4×C43C22×C411yescharacteristic
196C22×C4×C43C22×C411yescharacteristic
197C22×C4×C43C2×D412yes—
198C22×C4×C43C2×D412yes—
199C22×C4×C43C2×D412yes—
200C22×C4×C43C2×D412yes—
201C22×C4×C43C2411yescharacteristic
202C2×C22⋊D43—22no—
203C2×C22⋊D43—22no—
204C2×C22⋊D43—22no—
205C2×C22⋊D43—22no—
206C2×C22⋊D43—22no—
207C2×C22⋊D43—22no—
208C2×C22⋊D43—22no—
209C2×C22⋊D43—41no—
210C2×C22⋊D43—41no—
211C2×C22⋊D43—41no—
212C2×C22⋊D43—41no—
213C2×C22⋊D43—41no—
214C22×Dic43—22no—
215C22×Dic43—22no—
216C22×Dic43—41no—
217C22×Dic43C22×C411yescharacteristic
218C22×Dic43C22×C411yescharacteristic
219C22×Dic43C22×C411yescharacteristic
220C22×Dic43C22×C411yescharacteristic
221C22×Dic43C22×C411yescharacteristic
222#10621898—44no—
223#10621898—44no—
224#10621898—44no—
225#10621898—44no—
226C2×D172—22no—
227C2×D172—22no—
228C2×D172—22no—
229C2×D172—22no—
230C2×D172—41no—
231C2×D172—41no—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43—21no—
235C2×C4×D43—21no—
236C2×C4×D43—22no—
237C2×C4×D43—22no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×C4×D43—21no—
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43—21no—
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43—21no—
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—22no—
251C2×C4×D43—22no—
252C2×C4×D43—41no—
253C2×C4×D43—41no—
254C2×C4×D43—44no—
255C2×C4×D43—44no—
256C2×C4×D43—44no—
257C2×C4×D43—44no—
258C2×C4×D43C2×D412yes—
259C2×C4×D43#4112yes—
260C2×Dic86—22no—
261C2×Dic86—22no—
262C2×Dic86—41no—
263M16×C43—44no—
264M16×C43—44no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C2×C8×C43—21no—
268C2×C8×C43—21no—
269C2×C8×C43—21no—
270C2×C8×C43—21no—
271C2×C8×C43—21no—
272C2×C8×C43—21no—
273C2×C8×C43—21no—
274C2×C8×C43—21no—
275C2×C8×C43—21no—
276C2×C8×C43C2×D412yes—
277C4⋊C4×C43C22⋊C414yes—
278C22⋊C4×C43C22⋊C414yes—
279C22⋊C4×C43C22⋊C414yes—
280C42×C43C2×D412yes—
281C42×C43C2×D412yes—
282C22⋊Dic43—22no—
283C22⋊Dic43—22no—
284(C2×D43)⋊C4—22no—
285(C2×D43)⋊C4—22no—
286(C2×D43)⋊C4—22no—
287(C2×D43)⋊C4—22no—
288(C2×D43)⋊C4—22no—
289(C2×D43)⋊C4—22no—
290C4⋊Dic43—22no—
291Dic43⋊C4—22no—
292Dic43⋊C4—22no—
293Dic43⋊C4—22no—
294Dic43⋊C4—22no—
295C4×Dic43—21no—
296C4×Dic43—21no—
297#10621877—44no—
298C2×C43⋊C8—21no—
299C2×C43⋊C8—21no—
300C2×C43⋊C8—21no—
301C2×C43⋊C8—21no—
302C2×C43⋊C8—21no—
303C2×C43⋊C8—21no—
304C2×C43⋊C8—21no—
305C2×C43⋊C8—21no—
306C2×C43⋊C8—21no—
307C2×C43⋊C8—21no—
308C2×C43⋊C8—21no—
309C2×C43⋊C8—44no—
310C2×C43⋊C8C2×D412yes—
311C23×C43—21no—
312C23×C43—21no—
313C23×C43—21no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—21no—
318C23×C43—21no—
319C23×C43—21no—
320C23×C43—21no—
321C23×C43—21no—
322C23×C43—21no—
323C23×C43C2×C22⋊C412yes—
324C23×C43C2×C22⋊C412yes—
325C23×C43C23×C411yescharacteristic
326C22×D43—21no—
327C22×D43—21no—
328C22×D43—21no—
329C22×D43—21no—
330C22×D43—21no—
331C22×D43—21no—
332C22×D43—21no—
333C22×D43—21no—
334C22×D43—21no—
335C22×D43—21no—
336C22×D43—21no—
337C22×D43—21no—
338C22×D43—21no—
339C22×D43—21no—
340C22×D43—21no—
341C22×D43—21no—
342C22×D43—21no—
343C22×D43—21no—
344C22×D43—21no—
345C22×D43—44no—
346C22×D43—44no—
347C22×D43—44no—
348C22×D43—44no—
349C22×D43—44no—
350C22×D43—44no—
351C22×D43—44no—
352C22×D43C4×D412yes—
353C22×D43#13112yes—
354D4×C43—44no—
355C2×C4×C43—21no—
356C2×C4×C43—21no—
357C2×C4×C43—21no—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—21no—
361C2×C4×C43—21no—
362C2×C4×C43—21no—
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×C43C2×C22⋊C412yes—
372C2×C4×C43C2×C22⋊C412yes—
373C2×C4×C43C2×C22⋊C412yes—
374C2×C4×C43C2×C22⋊C412yes—
375C2×C4×C43C22×D411yescharacteristic
376C2×C4×C43C22×D411yescharacteristic
377C2×C4×C43C22×D411yescharacteristic
378C2×C4×C43C2×#4111yescharacteristic
379C2×C4×C43H(5,𝔽2)11yescharacteristic
380C2×C4×C43H(5,𝔽2)11yescharacteristic
381C22⋊D43—44no—
382C22⋊D43—44no—
383C22⋊D43—44no—
384C22⋊D43—44no—
385C2×Dic43—21no—
386C2×Dic43—21no—
387C2×Dic43—21no—
388C2×Dic43—21no—
389C2×Dic43—21no—
390C2×Dic43—21no—
391C2×Dic43—21no—
392C2×Dic43—21no—
393C2×Dic43—21no—
394C2×Dic43—21no—
395C2×Dic43—21no—
396C2×Dic43—21no—
397C2×Dic43—21no—
398C2×Dic43—21no—
399C2×Dic43—44no—
400C2×Dic43C4×D412yes—
401D172—44no—
402D172—44no—
403C4×D43—22no—
404C4×D43—22no—
405C4×D43—22no—
406C4×D43—22no—
407C4×D43—44no—
408C4×D43—44no—
409C4×D43—41no—
410C4×D43—41no—
411C4×D43—41no—
412C4×D43—41no—
413C4×D43—41no—
414C4×D43—41no—
415C4×D43—41no—
416C4×D43—41no—
417Dic86—44no—
418C8×C43—22no—
419C8×C43—41no—
420C8×C43—41no—
421C8×C43—41no—
422C43⋊C8—22no—
423C43⋊C8—41no—
424C43⋊C8—41no—
425C43⋊C8—41no—
426#22400—431nomaximal, Sylow
427C22×C43—22no—
428C22×C43—22no—
429C22×C43—22no—
430C22×C43—22no—
431C22×C43—22no—
432C22×C43—22no—
433C22×C43—41no—
434C22×C43—41no—
435C22×C43—41no—
436C22×C43—41no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43—41no—
440C22×C43—41no—
441C22×C43C22×C22⋊C411yescharacteristic
442C22×C43C2×C4×D411yescharacteristic
443C22×C43#51811yescharacteristic
444C22×C43C2×#13111yescharacteristic
445C22×C43#56811yescharacteristic
446C22×C43#56811yescharacteristic
447C22×C43#56811yescharacteristic
448C2×D43—22no—
449C2×D43—22no—
450C2×D43—22no—
451C2×D43—22no—
452C2×D43—22no—
453C2×D43—22no—
454C2×D43—416no—
455C2×D43—41no—
456C2×D43—41no—
457C2×D43—41no—
458C2×D43—41no—
459C2×D43—41no—
460C2×D43—41no—
461C2×D43—41no—
462C2×D43—41no—
463C2×D43—41no—
464C2×D43—41no—
465C2×D43—41no—
466C2×D43—41no—
467C2×D43—41no—
468C2×D43—41no—
469C2×D43—41no—
470C4×C43—22no—
471C4×C43—22no—
472C4×C43—22no—
473C4×C43—22no—
474C4×C43D4211yescharacteristic
475C4×C43D4211yescharacteristic
476C4×C43#54611yescharacteristic
477C4×C43#54611yescharacteristic
478Dic43—22no—
479Dic43—41no—
480Dic43—41no—
481Dic43—41no—
482Dic43—41no—
483C2×#525—431no—
484C2×#436D4311yescharacteristic, complemented
485C2×#435—431no—
486C2×#408—431no—
487C2×#407—431no—
488#1955—431no—
489#1954—431no—
490#1870—431no—
491#1870—431no—
492#1870—431no—
493#1869—431no—
494#1798—431no—
495#1780—431no—
496#1779—431no—
497#1750—431no—
498C2×C43—42no—
499C2×C43—42no—
500C2×C43D4×C22⋊C411yescharacteristic
501C2×C43#287911yescharacteristic
502C2×C43#288011yescharacteristic
503C2×C43#293011yescharacteristic
504C2×C43#293311yescharacteristic
505C2×C43#297611yescharacteristic
506C2×C43#297811yescharacteristic
507D43—42no—
508D43—42no—
509D43—81no—
510C22×#41—431no—
511C24×C4—431no—
512C22×M16—431no—
513C22×M16C2×D4311yescharacteristic
514C22×M16C2×D4311yescharacteristic, complemented
515C23×C8—431no—
516#525—864no—
517#525—864no—
518C2×#123—431no—
519C2×#123—431no—
520C2×C22⋊Q8—431no—
521C2×C22⋊Q8—431no—
522C2×#121—431no—
523C2×#121—431no—
524C2×#120—431no—
525C2×#120—431no—
526C2×C4×D4—431no—
527C2×C4×D4—431no—
528C2×C4×D4—431no—
529C2×C4×D4C2×D4311yescharacteristic
530C2×#117—431no—
531#436—24no—
532#435—864no—
533C2×C4⋊C8—431no—
534C2×C4⋊C8C2×D4311yescharacteristic, complemented
535#408—864no—
536#407—864no—
537C2×C22⋊C8—431no—
538C2×C22⋊C8—431no—
539C2×C22⋊C8—431no—
540C2×C22⋊C8—431no—
541C2×C22⋊C8—431no—
542C2×C22⋊C8—431no—
543C2×C22⋊C8—431no—
544C2×C22⋊C8—431no—
545C2×C22⋊C8—431no—
546C2×C22⋊C8—431no—
547C2×C22⋊C8—431no—
548C2×C22⋊C8—431no—
549C2×C22⋊C8—431no—
550C2×C22⋊C8—431no—
551C2×C22⋊C8C2×D4311yescharacteristic
552C2×C22⋊C8C2×D4311yescharacteristic, complemented
553C2×#97—431no—
554C2×C4×C8C2×D4311yescharacteristic, complemented
555#336—431no—
556#336—431no—
557#336—431no—
558#336—431no—
559C43#2240011yescharacteristic, complemented, Sylow
560C25—431no—
561C2×#41—862no—
562C2×#41—862no—
563C2×#41—862no—
564C2×#41—862no—
565C2×#41—1721no—
566C2×#41—1721no—
567C22×Q8—431no—
568C22×D4—431no—
569C22×D4—431no—
570C22×D4—431no—
571C22×D4—431no—
572C22×D4—431no—
573C22×D4—431no—
574C22×D4C4×D4311yescharacteristic
575C23×C4—431no—
576C23×C4—431no—
577C23×C4—431no—
578C23×C4—431no—
579C23×C4—431no—
580C23×C4—431no—
581C23×C4—862no—
582C23×C4—862no—
583C23×C4—862no—
584C23×C4—862no—
585C23×C4—1721no—
586C23×C4—1721no—
587C23×C4C22×D4311yescharacteristic
588C23×C4C22×D4311yescharacteristic
589C2×M16—22no—
590C2×M16—22no—
591C2×M16—22no—
592C2×M16—22no—
593C2×M16—41no—
594C2×M16—41no—
595C2×M16—862no—
596C2×M16—862no—
597C2×M16—1721no—
598C22×C8—431no—
599C22×C8—431no—
600C22×C8—431no—
601C22×C8—431no—
602C22×C8—862no—
603C22×C8—862no—
604C22×C8—1721no—
605C22×C8C22×D4311yescharacteristic
606C22×C8C22×D4311yescharacteristic
607C22×C8C22×D4311yescharacteristic
608C22×C8C22×D4311yescharacteristic
609#123—864no—
610#123—864no—
611C22⋊Q8—864no—
612C22⋊Q8—864no—
613#121—864no—
614#121—864no—
615#120—864no—
616#120—864no—
617C4×D4—862no—
618C4×D4—862no—
619C4×D4—862no—
620C4×D4—862no—
621C4×D4—862no—
622C4×D4—862no—
623C4×D4D17214yes—
624C4×D4C22⋊D4314yes—
625#117—862no—
626#117—862no—
627C2×C4⋊C4—431no—
628C2×C4⋊C4—431no—
629C2×C4⋊C4—431no—
630C2×C4⋊C4—431no—
631C2×C4⋊C4—431no—
632C2×C4⋊C4C4×D4311yescharacteristic
633C2×C22⋊C4—431no—
634C2×C22⋊C4—431no—
635C2×C22⋊C4—431no—
636C2×C22⋊C4—431no—
637C2×C22⋊C4—431no—
638C2×C22⋊C4—431no—
639C2×C22⋊C4—431no—
640C2×C22⋊C4—431no—
641C2×C22⋊C4C4×D4311yescharacteristic
642C2×C22⋊C4C4×D4311yescharacteristic
643C2×C42—431no—
644C2×C42C22×D4311yescharacteristic
645C4⋊C8—22no—
646C4⋊C8—862no—
647C22⋊C8—22no—
648C22⋊C8—22no—
649C22⋊C8—434no—
650C22⋊C8—862no—
651C22⋊C8—862no—
652C22⋊C8—862no—
653C22⋊C8—862no—
654C22⋊C8—862no—
655C22⋊C8—862no—
656C22⋊C8—862no—
657C22⋊C8—862no—
658C22⋊C8—862no—
659C22⋊C8—1721no—
660C22⋊C8—1721no—
661C22⋊C8—1721no—
662C22⋊C8—1721no—
663#97—862no—
664C4×C8—22no—
665C24—431no—
666C24—431no—
667C24—431no—
668C24—862no—
669C24—862no—
670C24—862no—
671C24—1721no—
672C24—1721no—
673C24—1721no—
674C24—1721no—
675C24C2×C4×D4311yescharacteristic
676C24C2×C4×D4311yescharacteristic
677#41—1724no—
678#41—1724no—
679#41—1724no—
680#41—1724no—
681C2×Q8—862no—
682C2×Q8—862no—
683C2×Q8—1721no—
684C2×D4—41no—
685C2×D4—41no—
686C2×D4—862no—
687C2×D4—862no—
688C2×D4—862no—
689C2×D4—862no—
690C2×D4—862no—
691C2×D4—862no—
692C2×D4—862no—
693C2×D4—862no—
694C2×D4—862no—
695C2×D4—862no—
696C2×D4—862no—
697C2×D4—1721no—
698C2×D4—1721no—
699C2×D4—1721no—
700C2×D4—1721no—
701C2×D4—1721no—
702C2×D4—1721no—
703C2×D4—1721no—
704C2×D4(C2×D43)⋊C414yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—431no—
714C22×C4—432no—
715C22×C4—432no—
716C22×C4—431no—
717C22×C4—431no—
718C22×C4—431no—
719C22×C4—431no—
720C22×C4—862no—
721C22×C4—862no—
722C22×C4—862no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—861no—
727C22×C4—862no—
728C22×C4—862no—
729C22×C4—862no—
730C22×C4—861no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—861no—
734C22×C4—861no—
735C22×C4—861no—
736C22×C4—861no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—861no—
740C22×C4—861no—
741C22×C4—861no—
742C22×C4—1721no—
743C22×C4—1721no—
744C22×C4—1724no—
745C22×C4—1724no—
746C22×C4—1724no—
747C22×C4—1724no—
748C22×C4—1721no—
749C22×C4C2×C4×D4311yescharacteristic
750C22×C4C2×C4×D4311yescharacteristic
751C22×C4C2×C4×D4311yescharacteristic
752C22×C4C2×C4×D4311yescharacteristic
753C22×C4C2×D17212yes—
754C22×C4C2×D17212yes—
755C22×C4C2×C22⋊D4312yes—
756C22×C4C2×C22⋊D4312yes—
757C22×C4C23×D4311yescharacteristic
758M16—44no—
759M16—44no—
760M16—1724no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—432no—
773C2×C8—861no—
774C2×C8—861no—
775C2×C8—861no—
776C2×C8—861no—
777C2×C8—861no—
778C2×C8—861no—
779C2×C8—861no—
780C2×C8—861no—
781C2×C8—861no—
782C2×C8—861no—
783C2×C8—861no—
784C2×C8—1724no—
785C2×C8D4×D4312yes—
786C4⋊C4—862no—
787C4⋊C4—862no—
788C4⋊C4—862no—
789C4⋊C4—862no—
790C4⋊C4—862no—
791C4⋊C4(C2×D43)⋊C414yes—
792C22⋊C4—862no—
793C22⋊C4—862no—
794C22⋊C4—862no—
795C22⋊C4—862no—
796C22⋊C4—862no—
797C22⋊C4—862no—
798C22⋊C4—862no—
799C22⋊C4—862no—
800C22⋊C4(C2×D43)⋊C414yes—
801C22⋊C4(C2×D43)⋊C414yes—
802C42—861no—
803C42—861no—
804C42C2×D17212yes—
805C42C2×C22⋊D4312yes—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—432no—
819C23—432no—
820C23—861no—
821C23—861no—
822C23—861no—
823C23—861no—
824C23—861no—
825C23—861no—
826C23—861no—
827C23—861no—
828C23—861no—
829C23—861no—
830C23—861no—
831C23—861no—
832C23—861no—
833C23—861no—
834C23—861no—
835C23—861no—
836C23—861no—
837C23—861no—
838C23—861no—
839C23—1724no—
840C23—1724no—
841C23—1724no—
842C23—1724no—
843C23—1724no—
844C23—1724no—
845C23—1724no—
846C23C2×(C2×D43)⋊C412yes—
847C23C2×(C2×D43)⋊C412yes—
848C23C22×C4×D4311yescharacteristic
849Q8—1724no—
850D4—44no—
851D4—1724no—
852D4—1724no—
853D4—1724no—
854D4—1724no—
855D4—1724no—
856D4—1724no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—432no—
874C2×C4—861no—
875C2×C4—861no—
876C2×C4—862no—
877C2×C4—862no—
878C2×C4—862no—
879C2×C4—862no—
880C2×C4—861no—
881C2×C4—861no—
882C2×C4—861no—
883C2×C4—861no—
884C2×C4—861no—
885C2×C4—861no—
886C2×C4—861no—
887C2×C4—861no—
888C2×C4—861no—
889C2×C4—861no—
890C2×C4—861no—
891C2×C4—861no—
892C2×C4—1724no—
893C2×C4—1724no—
894C2×C4—1724no—
895C2×C4—1721no—
896C2×C4—1721no—
897C2×C4—1721no—
898C2×C4—1721no—
899C2×C4—1721no—
900C2×C4—1721no—
901C2×C4—1721no—
902C2×C4—1721no—
903C2×C4C2×(C2×D43)⋊C412yes—
904C2×C4C2×(C2×D43)⋊C412yes—
905C2×C4C2×(C2×D43)⋊C412yes—
906C2×C4C2×(C2×D43)⋊C412yes—
907C2×C4C2×D4×D4311yescharacteristic
908C2×C4C22×C22⋊D4311yescharacteristic
909C2×C4C22×D17211yescharacteristic
910C2×C4#41×D4311yescharacteristic
911C2×C4#1306337011yescharacteristic
912C2×C4#1306337111yescharacteristic
913C8—22no—
914C8—41no—
915C8—41no—
916C8—41no—
917C8—862no—
918C8—1721no—
919C8—1721no—
920C8—1721no—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—862no—
936C22—862no—
937C22—862no—
938C22—862no—
939C22—862no—
940C22—862no—
941C22—17216no—
942C22—1721no—
943C22—1721no—
944C22—1721no—
945C22—1721no—
946C22—1721no—
947C22—1721no—
948C22—1721no—
949C22—1721no—
950C22—1721no—
951C22—1721no—
952C22—1721no—
953C22—1721no—
954C22—1721no—
955C22—1721no—
956C22—1721no—
957C22C22×(C2×D43)⋊C411yescharacteristic
958C22C4×D4×D4311yescharacteristic
959C22#1458337111yescharacteristic
960C22#131×D4311yescharacteristic
961C22#1458366411yescharacteristic
962C22#1458366511yescharacteristic
963C22#1458366511yescharacteristic
964C4—22no—
965C4—22no—
966C4—22no—
967C4—22no—
968C4—862no—
969C4—1721no—
970C4—1721no—
971C4—1721no—
972C4—1721no—
973C4D4×C22⋊D4311yescharacteristic
974C4D4×D17211yescharacteristic
975C4#1458353711yescharacteristic
976C4#1458354411yescharacteristic
977C2—42no—
978C2—42no—
979C2—3441no—
980C2—1722no—
981C2—1722no—
982C2D4×(C2×D43)⋊C411yescharacteristic
983C2#1914303911yescharacteristic
984C2#1914304211yescharacteristic
985C2#1914329511yescharacteristic
986C2#1914332411yescharacteristic
987C2#1914363911yescharacteristic
988C2#1914365211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC2×C43×#436C2
prime radicalC2×#14583408C2
cosocleC22×C4×C43C24
hypercenterC2×#436D43
hypocenterC43#22400
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
2. C2×#14582971C2semidirect
3. C2×#14582867C2semidirect
4. C2×#14582862C2semidirect
5. #19135392C2semidirect
6. #19135389C2semidirect
7. #19134892C2semidirect
8. #19134892C2semidirect
9. #19134890C2semidirect
10. #19134885C2semidirect
11. #19134576C2semidirect
12. #19134506C2semidirect
13. #19134504C2semidirect
14. #19134362C2semidirect
15. C2×C43×#436C2semidirect
19. C23×C43⋊C8C22semidirect
35. C2×C4⋊(C43⋊C8)C22semidirect
39. C2×C22⋊(C43⋊C8)C22semidirect
48. C2×(C2×D43)⋊C8C22semidirect
49. C2×(C2×D43)⋊C8C22semidirect
50. C2×(C2×D43)⋊C8C22semidirect
51. C2×(C2×D43)⋊C8C22semidirect
52. C2×#13063236C22semidirect
53. #14582653C22semidirect
54. #14582653C22semidirect
55. #14582653C22semidirect
56. #14582653C22semidirect
58. C22×M16×C43C22semidirect
61. C2×C4⋊C8×C43C22semidirect
63. C2×C22⋊C8×C43C22semidirect
64. C2×C4×C8×C43C22semidirect
145. (C2×D43)⋊C8D4semidirect
484. C2×#436D43semidirect
514. C22×M16C2×D43semidirect
534. C2×C4⋊C8C2×D43semidirect
552. C2×C22⋊C8C2×D43semidirect
554. C2×C4×C8C2×D43semidirect
559. C43#22400semidirect

Maximal subgroups

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

subgroupindex
C2×#145834082
C2×#145829712
C2×#145828672
C2×#145828622
#191353922
#191353892
#191348922
#191348902
#191348852
#191345762
#191345062
#191345042
#191343622
C2×C43×#4362
#2240043