Finite Group Databasebeta

← #25111880

Subgroups — #25111880

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×#14583406C211yesmaximal, characteristic
2C2×#14582975C211yesmaximal, characteristic, complemented
3C2×#14582970C211yesmaximal, characteristic, complemented
4C2×#14582861C211yesmaximal, characteristic, complemented
5#19135391C211yesmaximal, characteristic, complemented
6#19135387C211yesmaximal, characteristic, complemented
7#19134892C211yesmaximal, characteristic, complemented
8#19134889C211yesmaximal, characteristic, complemented
9#19134889C211yesmaximal, characteristic, complemented
10#19134887C211yesmaximal, characteristic, complemented
11#19134577C211yesmaximal, characteristic, complemented
12#19134507C211yesmaximal, characteristic, complemented
13#19134504C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C2×C43×#408C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19#14583406—24no—
20#14583406—24no—
21C2×#13063306C411yescharacteristic
22C2×#13063306C411yescharacteristic
23C2×#13063301C411yescharacteristic
24C2×#13063301C411yescharacteristic
25C2×#13063296C411yescharacteristic
26C2×#13063296C411yescharacteristic
27C2×#13063293C411yescharacteristic
28C2×#13063293C411yescharacteristic
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×C4×C22⋊D43C2211yescharacteristic
31C2×C4×C22⋊D43C2211yescharacteristic
32C2×C4×C22⋊D43C2211yescharacteristic
33C2×#13063284C2211yescharacteristic
34#14582975—24no—
35#14582970—24no—
36C2×Dic43⋊C8C2211yescharacteristic, complemented
37C2×Dic43⋊C8C2211yescharacteristic, complemented
38#14582861—24no—
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
42C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
43C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
44C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic
47C2×(C2×D43)⋊C8C2211yescharacteristic
48C2×(C2×D43)⋊C8C2211yescharacteristic
49C2×(C2×D43)⋊C8C2211yescharacteristic
50C2×(C2×D43)⋊C8C2211yescharacteristic
51C2×#13063235C2211yescharacteristic, complemented
52C2×C8×Dic43C2211yescharacteristic, complemented
53#14582653C2211yescharacteristic, complemented
54#14582653C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56#14582653C2211yescharacteristic, complemented
57C22×#41×C43C2211yescharacteristic
58C22×M16×C43C2211yescharacteristic, complemented
59C23×C8×C43C2211yescharacteristic, complemented
60C43×#408—24no—
61C2×C22⋊C8×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C2×C22⋊C8×C43C2211yescharacteristic, complemented
64C2×C22⋊C8×C43C2211yescharacteristic, complemented
65C24×D43C2×C411yescharacteristic
66C22×C22⋊D43C2×C411yescharacteristic
67C22×C22⋊D43C2×C411yescharacteristic
68C22×C22⋊D43C2×C411yescharacteristic
69C22×C22⋊D43C2×C411yescharacteristic
70C23×Dic43C2×C411yescharacteristic
71C22×C4×D43—22no—
72C22×C4×D43—22no—
73C22×C4×D43—22no—
74C22×C4×D43—22no—
75C22×C4×D43—41no—
76C22×C4×D43—41no—
77C22×C4×D43C2×C411yescharacteristic
78C22×C4×D43C2×C411yescharacteristic
79C22×C4×D43C2311yescharacteristic
80C22×C4×D43C2311yescharacteristic
81C2×#10621872—22no—
82C2×#10621872—22no—
83C2×#10621872—22no—
84C2×#10621872—22no—
85C2×#10621872—41no—
86C2×#10621872—41no—
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89C22×C43⋊C8C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91#13063306—24no—
92#13063306—24no—
93#13063301—24no—
94#13063301—24no—
95#13063296—24no—
96#13063296—24no—
97#13063293—24no—
98#13063293—24no—
99C4×C22⋊D43—22no—
100C4×C22⋊D43—22no—
101C4×C22⋊D43—22no—
102C4×C22⋊D43—22no—
103C4×C22⋊D43—22no—
104C4×C22⋊D43—22no—
105C4×C22⋊D43D414yes—
106C4×C22⋊D43D414yes—
107#13063284—22no—
108#13063284—22no—
109C2×C4⋊Dic43C2×C411yescharacteristic
110C2×C4⋊Dic43C2×C411yescharacteristic
111C2×Dic43⋊C4C2×C411yescharacteristic
112C2×Dic43⋊C4C2×C411yescharacteristic
113C2×Dic43⋊C4C2×C411yescharacteristic
114C2×Dic43⋊C4C2×C411yescharacteristic
115C2×C22⋊Dic43C2×C411yescharacteristic
116C2×C22⋊Dic43C2×C411yescharacteristic
117C2×C22⋊Dic43C2×C411yescharacteristic
118C2×C22⋊Dic43C2×C411yescharacteristic
119C2×C22⋊Dic43C2×C411yescharacteristic
120C2×C22⋊Dic43C2×C411yescharacteristic
121C2×(C2×D43)⋊C4C2×C411yescharacteristic
122C2×(C2×D43)⋊C4C2×C411yescharacteristic
123C2×(C2×D43)⋊C4C2×C411yescharacteristic
124C2×(C2×D43)⋊C4C2×C411yescharacteristic
125C2×C4×Dic43C2311yescharacteristic
126C2×C4×Dic43C2311yescharacteristic
127Dic43⋊C8—22no—
128Dic43⋊C8—22no—
129C22⋊(C43⋊C8)—22no—
130C22⋊(C43⋊C8)—22no—
131C22⋊(C43⋊C8)—22no—
132C22⋊(C43⋊C8)—22no—
133C22⋊(C43⋊C8)—41no—
134C22⋊(C43⋊C8)—41no—
135(C2×D43)⋊C8—22no—
136(C2×D43)⋊C8—22no—
137(C2×D43)⋊C8—22no—
138(C2×D43)⋊C8—22no—
139(C2×D43)⋊C8—41no—
140(C2×D43)⋊C8—41no—
141#13063235—22no—
142C8×Dic43—22no—
143C2×#41×C43—22no—
144C2×#41×C43—22no—
145C2×#41×C43—22no—
146C2×#41×C43—22no—
147C2×#41×C43—41no—
148C2×#41×C43—41no—
149C22×Q8×C43C2×C411yescharacteristic
150C22×D4×C43C2×C411yescharacteristic
151C22×D4×C43C2×C411yescharacteristic
152C22×D4×C43C2×C411yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C23×C4×C43C2311yescharacteristic
155C23×C4×C43C2311yescharacteristic
156C2×M16×C43—22no—
157C2×M16×C43—22no—
158C2×M16×C43—41no—
159C22×C8×C43—22no—
160C22×C8×C43—22no—
161C22×C8×C43—41no—
162C22×C8×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166C22⋊C8×C43—22no—
167C22⋊C8×C43—22no—
168C22⋊C8×C43—22no—
169C22⋊C8×C43D414yescomplemented
170C24×C43C22×C411yescharacteristic
171C24×C43C22×C411yescharacteristic
172C24×C43C22×C411yescharacteristic
173C23×D43—22no—
174C23×D43—22no—
175C23×D43—22no—
176C23×D43—41no—
177C23×D43—41no—
178C23×D43—41no—
179C23×D43—41no—
180C23×D43C22×C411yescharacteristic
181C23×D43C22×C411yescharacteristic
182#41×C43—44no—
183#41×C43—44no—
184#41×C43—44no—
185#41×C43—44no—
186C2×Q8×C43—22no—
187C2×Q8×C43—22no—
188C2×Q8×C43—41no—
189C2×D4×C43—22no—
190C2×D4×C43—22no—
191C2×D4×C43—22no—
192C2×D4×C43—22no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43—41no—
196C2×D4×C43—41no—
197C2×D4×C43—41no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43C22×C411yescharacteristic
213C22×C4×C43C22×C411yescharacteristic
214C22×C4×C43C22×C411yescharacteristic
215C22×C4×C43C2×D412yes—
216C22×C4×C43C2×D412yes—
217C22×C4×C43C2×D412yes—
218C22×C4×C43#4112yes—
219C22×C4×C43C2411yescharacteristic
220C2×C22⋊D43—22no—
221C2×C22⋊D43—22no—
222C2×C22⋊D43—22no—
223C2×C22⋊D43—22no—
224C2×C22⋊D43—22no—
225C2×C22⋊D43—41no—
226C2×C22⋊D43—41no—
227C2×C22⋊D43—41no—
228C2×C22⋊D43—41no—
229C2×C22⋊D43—41no—
230C2×C22⋊D43—41no—
231C2×C22⋊D43C22⋊C414yes—
232C22×Dic43—22no—
233C22×Dic43—22no—
234C22×Dic43—41no—
235C22×Dic43C22×C411yescharacteristic
236C22×Dic43C22×C411yescharacteristic
237C22×Dic43C22×C411yescharacteristic
238C22×Dic43C22×C411yescharacteristic
239C22×Dic43C22×C411yescharacteristic
240C22×Dic43C22×C411yescharacteristic
241C2×C4×D43—21no—
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43—21no—
245C2×C4×D43—22no—
246C2×C4×D43—22no—
247C2×C4×D43—21no—
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—21no—
251C2×C4×D43—21no—
252C2×C4×D43—21no—
253C2×C4×D43—22no—
254C2×C4×D43—22no—
255C2×C4×D43—41no—
256C2×C4×D43—41no—
257C2×C4×D43—44no—
258C2×C4×D43—44no—
259C2×C4×D43—44no—
260C2×C4×D43—44no—
261C2×C4×D43C2×D412yes—
262C2×C4×D43C2×D412yes—
263M16×C43—44no—
264C2×C8×C43—21no—
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—44no—
275C2×C8×C43C2×D412yes—
276C2×C8×C43C2×D412yes—
277C22⋊Dic43—22no—
278C22⋊Dic43—22no—
279C22⋊Dic43—22no—
280C22⋊Dic43—22no—
281C22⋊Dic43—22no—
282C22⋊Dic43C22⋊C414yes—
283(C2×D43)⋊C4—22no—
284(C2×D43)⋊C4—22no—
285(C2×D43)⋊C4—22no—
286(C2×D43)⋊C4C22⋊C414yes—
287C4⋊Dic43—22no—
288C4⋊Dic43—22no—
289Dic43⋊C4—22no—
290Dic43⋊C4—22no—
291Dic43⋊C4—22no—
292Dic43⋊C4C22⋊C414yes—
293C4×Dic43—21no—
294C4×Dic43—21no—
295C4×Dic43C2×D412yes—
296C4×Dic43C2×D412yes—
297C2×C43⋊C8—21no—
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—
309#10621872—44no—
310#10621872—44no—
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×C43—21no—
324C23×C43—21no—
325C23×C43—21no—
326C23×C43—21no—
327C23×C43—21no—
328C23×C43—21no—
329C23×C43—21no—
330C23×C43C2×C22⋊C412yes—
331C23×C43C4×D412yes—
332C23×C43C23×C411yescharacteristic
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×D43C2×C22⋊C412yes—
353C22×D43#13112yes—
354Q8×C43—44no—
355D4×C43—44no—
356D4×C43—44no—
357D4×C43—44no—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—21no—
361C2×C4×C43—21no—
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—21no—
371C2×C4×C43—21no—
372C2×C4×C43—21no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43C2×C22⋊C412yes—
378C2×C4×C43C4×D412yes—
379C2×C4×C43C22×D411yescharacteristic
380C2×C4×C43C22×D411yescharacteristic
381C2×C4×C43C22×D411yescharacteristic
382C2×C4×C43C2×#4111yescharacteristic
383C2×C4×C43H(5,𝔽2)11yescharacteristic
384C2×C4×C43H(5,𝔽2)11yescharacteristic
385C22⋊D43—44no—
386C22⋊D43—44no—
387C22⋊D43—44no—
388C22⋊D43—44no—
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—21no—
400C2×Dic43—21no—
401C2×Dic43—21no—
402C2×Dic43—21no—
403C2×Dic43—21no—
404C2×Dic43—44no—
405C2×Dic43C2×C22⋊C412yes—
406C2×Dic43C2×C22⋊C412yes—
407C2×Dic43C2×C22⋊C412yes—
408C4×D43—22no—
409C4×D43—22no—
410C4×D43—22no—
411C4×D43—22no—
412C4×D43—44no—
413C4×D43—44no—
414C4×D43—41no—
415C4×D43—41no—
416C4×D43—41no—
417C4×D43—41no—
418C8×C43—22no—
419C8×C43—22no—
420C8×C43—41no—
421C8×C43—41no—
422C43⋊C8—41no—
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×C43—41no—
442C22×C43—41no—
443C22×C43—41no—
444C22×C43—41no—
445C22×C43—41no—
446C22×C43—41no—
447C22×C43—41no—
448C22×C43C22×C22⋊C411yescharacteristic
449C22×C43C2×C4×D411yescharacteristic
450C22×C43#51811yescharacteristic
451C22×C43C2×#13111yescharacteristic
452C22×C43#56811yescharacteristic
453C22×C43#56811yescharacteristic
454C22×C43#56811yescharacteristic
455C2×D43—22no—
456C2×D43—22no—
457C2×D43—22no—
458C2×D43—22no—
459C2×D43—22no—
460C2×D43—22no—
461C2×D43—416no—
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—41no—
473C4×C43D4211yescharacteristic
474C4×C43D4211yescharacteristic
475C4×C43#54611yescharacteristic
476C4×C43#54611yescharacteristic
477Dic43—22no—
478Dic43—22no—
479Dic43—22no—
480Dic43—41no—
481Dic43—41no—
482Dic43—41no—
483C2×#525—431no—
484C2×#436—431no—
485C2×#435—431no—
486C2×#408D4311yescharacteristic, complemented
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×C43—81no—
501C2×C43D4×C22⋊C411yescharacteristic
502C2×C43#287911yescharacteristic
503C2×C43#288011yescharacteristic
504C2×C43#293011yescharacteristic
505C2×C43#293311yescharacteristic
506C2×C43#297611yescharacteristic
507C2×C43#297811yescharacteristic
508D43—42no—
509D43—42no—
510C22×#41C2×D4311yescharacteristic
511C24×C4—431no—
512C22×M16—431no—
513C22×M16—431no—
514C22×M16C2×D4311yescharacteristic, complemented
515C23×C8C2×D4311yescharacteristic, complemented
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×D4—431no—
530C2×#117—431no—
531#436—864no—
532#435—864no—
533C2×C4⋊C8—431no—
534C2×C4⋊C8—431no—
535#408—24no—
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⋊C8C2×D4311yescharacteristic
550C2×C22⋊C8C2×D4311yescharacteristic
551C2×C22⋊C8C2×D4311yescharacteristic, complemented
552C2×C22⋊C8C2×D4311yescharacteristic, complemented
553C2×#97—431no—
554C2×C4×C8—431no—
555#336—431no—
556#336—431no—
557#336—431no—
558#336—431no—
559C43#2240011yescharacteristic, complemented, Sylow
560C25—431no—
561C2×#41—22no—
562C2×#41—22no—
563C2×#41—22no—
564C2×#41—22no—
565C2×#41—41no—
566C2×#41—41no—
567C22×Q8C4×D4311yescharacteristic
568C22×D4—431no—
569C22×D4—431no—
570C22×D4—431no—
571C22×D4—431no—
572C22×D4C4×D4311yescharacteristic
573C22×D4C4×D4311yescharacteristic
574C22×D4C4×D4311yescharacteristic
575C23×C4—431no—
576C23×C4—431no—
577C23×C4—431no—
578C23×C4—431no—
579C23×C4—431no—
580C23×C4—862no—
581C23×C4—862no—
582C23×C4—862no—
583C23×C4—862no—
584C23×C4—1721no—
585C23×C4—1721no—
586C23×C4C22×D4311yescharacteristic
587C23×C4C22×D4311yescharacteristic
588C23×C4C22×D4311yescharacteristic
589C2×M16—22no—
590C2×M16—22no—
591C2×M16—41no—
592C2×M16—862no—
593C2×M16—862no—
594C2×M16—862no—
595C2×M16—862no—
596C2×M16—1721no—
597C2×M16—1721no—
598C22×C8—22no—
599C22×C8—22no—
600C22×C8—41no—
601C22×C8—431no—
602C22×C8—431no—
603C22×C8—431no—
604C22×C8—431no—
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—434no—
618C4×D4—434no—
619C4×D4—862no—
620C4×D4—862no—
621C4×D4—862no—
622C4×D4—862no—
623C4×D4—862no—
624C4×D4—862no—
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⋊C4—431no—
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⋊C4—431no—
642C2×C22⋊C4—431no—
643C2×C42—431no—
644C2×C42—431no—
645C4⋊C8—862no—
646C4⋊C8—862no—
647C22⋊C8—22no—
648C22⋊C8—22no—
649C22⋊C8—22no—
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—1721no—
659C22⋊C8—1721no—
660C22⋊C8—1721no—
661C22⋊C8—1721no—
662C22⋊C8C22⋊D4314yescomplemented
663#97—862no—
664C4×C8—862no—
665C24—431no—
666C24—431no—
667C24—862no—
668C24—862no—
669C24—862no—
670C24—1721no—
671C24—1721no—
672C24—1721no—
673C24—1721no—
674C24C2×C4×D4311yescharacteristic
675C24C2×C4×D4311yescharacteristic
676C24C2×C4×D4311yescharacteristic
677#41—44no—
678#41—44no—
679#41—44no—
680#41—44no—
681C2×Q8—22no—
682C2×Q8—22no—
683C2×Q8—41no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—22no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—41no—
691C2×D4—41no—
692C2×D4—41no—
693C2×D4—434no—
694C2×D4—862no—
695C2×D4—862no—
696C2×D4—862no—
697C2×D4—862no—
698C2×D4—862no—
699C2×D4—1721no—
700C2×D4—1721no—
701C2×D4—1721no—
702C2×D4—1721no—
703C2×D4—1721no—
704C2×D4—1721no—
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—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—431no—
720C22×C4—431no—
721C22×C4—431no—
722C22×C4—432no—
723C22×C4—432no—
724C22×C4—431no—
725C22×C4—431no—
726C22×C4—431no—
727C22×C4—862no—
728C22×C4—862no—
729C22×C4—862no—
730C22×C4—861no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—861no—
734C22×C4—862no—
735C22×C4—862no—
736C22×C4—862no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—861no—
740C22×C4—861no—
741C22×C4—861no—
742C22×C4—861no—
743C22×C4—1721no—
744C22×C4—1721no—
745C22×C4—1724no—
746C22×C4—1724no—
747C22×C4—1724no—
748C22×C4—1724no—
749C22×C4—1721no—
750C22×C4C2×C4×D4311yescharacteristic
751C22×C4C2×C4×D4311yescharacteristic
752C22×C4C2×C4×D4311yescharacteristic
753C22×C4#1062189812yes—
754C22×C4D4×D4312yes—
755C22×C4D4×D4312yes—
756C22×C4C2×C22⋊D4312yes—
757C22×C4C23×D4311yescharacteristic
758M16—44no—
759M16—1724no—
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—44no—
772C2×C8—861no—
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×C8C2×C22⋊D4312yes—
785C2×C8C2×C22⋊D4312yes—
786C4⋊C4—434no—
787C4⋊C4—862no—
788C4⋊C4—862no—
789C4⋊C4—862no—
790C4⋊C4—862no—
791C4⋊C4—862no—
792C22⋊C4—434no—
793C22⋊C4—434no—
794C22⋊C4—862no—
795C22⋊C4—862no—
796C22⋊C4—862no—
797C22⋊C4—862no—
798C22⋊C4—862no—
799C22⋊C4—862no—
800C22⋊C4—862no—
801C22⋊C4—862no—
802C42—432no—
803C42—432no—
804C42—861no—
805C42—861no—
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—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—432no—
826C23—432no—
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—
846C23C22⋊C4×D4312yes—
847C23C4×C22⋊D4312yes—
848C23C22×C4×D4311yescharacteristic
849Q8—44no—
850D4—44no—
851D4—44no—
852D4—44no—
853D4—1724no—
854D4—1724no—
855D4—1724no—
856D4—1724no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—432no—
877C2×C4—432no—
878C2×C4—432no—
879C2×C4—861no—
880C2×C4—861no—
881C2×C4—861no—
882C2×C4—861no—
883C2×C4—861no—
884C2×C4—861no—
885C2×C4—862no—
886C2×C4—862no—
887C2×C4—862no—
888C2×C4—862no—
889C2×C4—861no—
890C2×C4—861no—
891C2×C4—861no—
892C2×C4—861no—
893C2×C4—861no—
894C2×C4—861no—
895C2×C4—861no—
896C2×C4—861no—
897C2×C4—861no—
898C2×C4—1724no—
899C2×C4—1724no—
900C2×C4—1724no—
901C2×C4—1721no—
902C2×C4—1721no—
903C2×C4—1721no—
904C2×C4—1721no—
905C2×C4C22⋊C4×D4312yes—
906C2×C4C4×C22⋊D4312yes—
907C2×C4C2×D4×D4311yescharacteristic
908C2×C4C2×D4×D4311yescharacteristic
909C2×C4C22×C22⋊D4311yescharacteristic
910C2×C4C2×#1062189811yescharacteristic
911C2×C4#1306337011yescharacteristic
912C2×C4#1306337011yescharacteristic
913C8—22no—
914C8—22no—
915C8—41no—
916C8—41no—
917C8—1721no—
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—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—862no—
943C22—862no—
944C22—862no—
945C22—862no—
946C22—862no—
947C22—862no—
948C22—17216no—
949C22—1721no—
950C22—1721no—
951C22—1721no—
952C22—1721no—
953C22—1721no—
954C22—1721no—
955C22—1721no—
956C22—1721no—
957C22C2×C22⋊C4×D4311yescharacteristic
958C22C2×C4×C22⋊D4311yescharacteristic
959C22#1458337211yescharacteristic
960C22#131×D4311yescharacteristic
961C22#1458366411yescharacteristic
962C22#1458366411yescharacteristic
963C22#1458366411yescharacteristic
964C4—22no—
965C4—22no—
966C4—41no—
967C4—862no—
968C4—862no—
969C4—862no—
970C4—1721no—
971C4—1721no—
972C4—1721no—
973C4D4×C22⋊D4311yescharacteristic
974C4D4×C22⋊D4311yescharacteristic
975C4#1458353911yescharacteristic
976C4#1458353911yescharacteristic
977C2—42no—
978C2—42no—
979C2—81no—
980C2—1722no—
981C2—1722no—
982C2C22⋊C4×C22⋊D4311yescharacteristic
983C2#1914303711yescharacteristic
984C2#1914304311yescharacteristic
985C2#1914329611yescharacteristic
986C2#1914331711yescharacteristic
987C2#1914363811yescharacteristic
988C2#1914365311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC2×C43×#408C2
prime radicalC2×#14583406C2
cosocleC22×C4×C43C24
hypercenterC2×#408D43
hypocenterC43#22400
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. C2×#14582975C2semidirect
3. C2×#14582970C2semidirect
4. C2×#14582861C2semidirect
5. #19135391C2semidirect
6. #19135387C2semidirect
7. #19134892C2semidirect
8. #19134889C2semidirect
9. #19134889C2semidirect
10. #19134887C2semidirect
11. #19134577C2semidirect
12. #19134507C2semidirect
13. #19134504C2semidirect
14. #19134363C2semidirect
15. C2×C43×#408C2semidirect
36. C2×Dic43⋊C8C22semidirect
37. C2×Dic43⋊C8C22semidirect
41. C2×C22⋊(C43⋊C8)C22semidirect
42. C2×C22⋊(C43⋊C8)C22semidirect
43. C2×C22⋊(C43⋊C8)C22semidirect
44. C2×C22⋊(C43⋊C8)C22semidirect
51. C2×#13063235C22semidirect
52. C2×C8×Dic43C22semidirect
53. #14582653C22semidirect
54. #14582653C22semidirect
55. #14582653C22semidirect
56. #14582653C22semidirect
58. C22×M16×C43C22semidirect
59. C23×C8×C43C22semidirect
63. C2×C22⋊C8×C43C22semidirect
64. C2×C22⋊C8×C43C22semidirect
169. C22⋊C8×C43D4semidirect
486. C2×#408D43semidirect
514. C22×M16C2×D43semidirect
515. C23×C8C2×D43semidirect
551. C2×C22⋊C8C2×D43semidirect
552. C2×C22⋊C8C2×D43semidirect
559. C43#22400semidirect
662. C22⋊C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834062
C2×#145829752
C2×#145829702
C2×#145828612
#191353912
#191353872
#191348922
#191348892
#191348872
#191345772
#191345072
#191345042
#191343632
C2×C43×#4082
#2240043